Saturday, January 30, 2021

Fucking COVID

First, let me say that there are many, many, many, many people in the world who are suffering far worse than I am.  But invalidating my own feelings just makes my suffering worse.  Here are some ways I am suffering and feeling frustrated, irritated, and disconnected as a direct result of this virus.

I am sick of decisionmakers only considering the fatality rate of the actual virus when making strong pronouncements, rules, and/or edicts.  I made this point back in April in my only Facebook post on this topic.  There are lots of other factors that should be considered in the analysis, such as:

·         People who are dying of starvation because the slowdown in the world economy, thanks in part to shutdown orders, is literally depriving the millions of people in the world who already can barely feed themselves.  Even among those who aren’t literally dying of starvation, there are untold millions who are dying from otherwise preventable or treatable diseases and problems because of their falling real incomes.

·         People who are dying of suicide, alcoholism, drug overdoses, and complications of depression and poor physical and mental health brought on or exacerbated by this crisis.

·         The overall decrease in happiness (“utility”) in the world, linked to economic slowdowns, physical and emotional isolation, etc., etc.

I hate that it has only recently become somewhat socially acceptable to mention these other factors.  Yes, public policy must consider lives potentially lost to COVID, but it should not ignore lives and livelihoods that may be lost as a direct result of these policies. 

I am sick of being told what to do by authoritarians acting unilaterally.  Yes, governors and mayors (as heads of their respective executive departments) have short-term emergency powers, but this situation is no longer short-term.  Long-term legal solutions should be effected by legislatures and tempered by courts.  There is absolutely no good reason or explanation for why, a year after the virus first hit U.S. soil, decisions about which New York City restaurants can open and at what capacity are still being decided at the arbitrary whim of a single person.

I am sick of the fatigue and the ever-changing goal post.  In March of last year, we were told that shutdowns and closures were temporary so that we can “flatten the curve” so as to not overwhelm the healthcare industry.  We did that.  And then the curve started dropping.  But then the goal changed to something like, “We need to stay locked down until we reduce the positivity rate below X%.”  Where did that come from?  More importantly, such a number is absolutely meaningless unless there is consistency in the rate at which people are tested.  If New York’s positivity rate is 3%, for example, and South Dakota’s is 30%, does that imply that South Dakota is far worse off than New York?  Of course not.  If New York freely tests anyone and everyone (and if people’s jobs there depend, as they often do, on regular testing), then a 3% positivity rate might actually mean that, say, 1% of the population has the virus... while if South Dakota only tests people who are hospitalized and who have COVID symptoms, then their 30% positivity rate might actually correspond to, say, 0.1% of the population having the virus.  (On a recent trip to Florida, I discovered just how complicated, expensive, and inconvenient it was to get a COVID test, while in NYC I can easily get a free test any day of the week just a couple blocks from my apartment.)  The fact that I have to explain this very simple example to show how statistics can deceive – and which no one seems to be talking about, including the condescending intellectual elite who have weaponized the word “science” – is irritating and mind-boggling.  (As a side note, the weaponization of the word “science” is especially infuriating when scientists whom we should trust, like Dr. Fauci, simply make up numbers to manipulate public perception.  I think his intention was good, but that’s irrelevant – it makes him lose credibility as a scientist.)

I am sick of masks.  I hate wearing them.  They are not just uncomfortable, but I hate that they impede communication.  They muffle voices and hide facial expressions and moving lips, all of which are used in human communication.  I hate having to speak more loudly to people because of the muffling of my mask, and I hate that my facial expressions are similarly muffled.  It just makes me less likely to interact and communicate with people at all.  It makes me not want to go anywhere or do anything, which is fine because there is nowhere to go and nothing to do anyway.

I am sick of never knowing what is required, legally or socially, and I am sick of feeling pressured to act in ways that I know are baseless or even irrational.  Are we supposed to wear a mask AND “socially distance”?  What is the protocol for inside versus outside?  No one suggests (I don’t think!) that spouses should wear masks around each other, but what if my wife works closely with a small group of people who eat together out of necessity?  Does that mean she can invite them and their spouses over to our house for a mask-free game night... or must we play an awkward game of cards in which we’re all separated by six feet and breathing through N95 masks?  Literally the social fear of not knowing all the rules (because there is no consistent set of rules) is enough to want to avoid gatherings at all, no matter how desperately we might need them for our emotional survival.  I can’t even imagine being a single college student today and being told to wear a mask and not kiss while having sex.  No normal human would do this, right?  It sometimes makes me wonder if those in charge are playing a massive prank to see just how far they can push the rules.  (“Do you think we could get restaurants to agree to a 6% maximum occupancy and serve only pureed entrées that are sucked through a straw attached to their mask?”  “Yeah!  And all male patrons should be required to wear N95 condoms!”)

Moreover... Do these rules arise from a responsibility to others or to myself?  For example, the virus is spread by saliva and mucus, so if I don’t talk or even open my mouth... if I cover my face when I sneeze... then how can I spread it to anyone, particularly if I’m already standing six feet away?  This issue has come up a few times when I was wearing a mask over my mouth but not my nose.  (Apparently I have a big nose, which makes a mask even more uncomfortable.)  If I have to sneeze, I pull my mask up – which is disgusting, of course, but I guess that’s what others have to deal with.  Beyond sneezing, there is essentially no risk of me spreading a virus to others from my nose, yet I’ve been ordered by various people out in public to cover my nose.  I usually do, to avoid a confrontation, but why should I?  One might reply, “Because you can get the virus with your nose exposed, and you have a responsibility not to get the virus that you can then spread to others.”  But that doesn’t make sense.  If I’m already careful about not spreading germs to others, then what right does anyone have to tell me that I can’t assume a risk to myself?  Do I have the right to acquire the virus if I want?  If I decided that I just wanted to get the virus for, say, the antibodies it would provide, and I knew someone infected who was happy to provide the requisite saliva, is it my right to choose?  I think the answer in a genuinely free country is obviously yes, but I can hear the protests already!  Anyway, my point is that there is room for actual debate about the pros and cons of each rule and how they depend on situation, but what actually happens – at least in my case – is that the social complications and awkwardness of trying to balance my own comfort with my aversion to offending people with my attempt to read social cues with my unwillingness to let bullies dictate rules for everyone else with my efforts to prevent spreading COVID to my older relatives and friends with my desire to actually have fun while other people have fun... ugh... all this just makes me say “Fuck it” and stay at home.

I am sick of the phrase “socially distance.”  Whoever coined it was either a complete idiot who doesn’t know what the word “social” means, because the requirement is actually to physically distance, or was brilliant, because they knew that the constant physical distancing would, over time, emotionally wear people down and cause them to socially isolate from others.

I am sick of the polarized extremes that force people to pick a “team” and prevent them from thinking for themselves.  Do I really have to choose being either a condescending elitist mask nazi or a confederate-flag-toting anarchist?  Can’t I just say that this forced economic shutdown and physical isolation must end soon without being accused of wanting people to die of the virus?

Personally, here is how I am suffering from COVID... and I am suffering:

My primary hobby is travel.  I’ve been to 96 countries.  I canceled three trips last year, including a six-week round-the-world trip with my wife who had just finished a grueling four-year physician residency during which I barely spent any time with her.  Not only have I not traveled anywhere in the past year, but there appears to be no end in sight to this “pandemic” (another word I am sick of), with prospects of returning to any semblance of normalcy diminishing by the day.  I can’t plan anything.  The rules keep changing.  Do I need to wait until after I’m vaccinated?  At this rate, it might not be until summer, and by then, will there be a hundred new vaccine-resistant variants/mutations?  Will I be traveling in some country that was “open” when their government suddenly closes their borders?  Will I be walking around some foreign city but all its museums and restaurants are closed and I’m staying in an otherwise deserted hotel?  This all just makes me feel very hopeless and depressed.

This “virtual” learning is a disaster.  I don’t learn well this way and I suspect that few others do.  I have absolutely no idea how kids are dealing with this.  Oh, that’s right – they’re not.  I started a graduate physics program at NYU specifically for the opportunity to make friends, collaborate with colleagues, have interesting discussions, and learn with others.  The in-person time with professors and fellow students has always helped me to learn and to feel connected, but there is NONE of that now.  Death to Zoom.  Yes, some classes are offered “in-person” (or “hybrid,” which is almost worse than just plain “virtual”) and I took General Relativity last semester in part because it was in-person.  To do so, I satisfied all the requirements but what was the reward?  On average, there was only one other student in class, and even if there were more, there were no rooms or areas in which we could actually collaborate, so what was the point?  I am taking one class this semester, in part to keep my affiliation with NYU, but if normal in-person learning does not resume by Fall (and by “normal” I mean being able to go through one fucking day without thinking about masks, socially distancing, vaccines, nasal swabs, reduced capacity, etc., etc.), then I don’t see the point of continuing in the program. 

I am not connecting with people.  As an INTJ, I can certainly enjoy plenty of alone time, but I need connection, as do all humans.  It is depressingly ironic that I am calling and emailing people less now that I am connecting with them less in person.  That’s due to several factors:

·         We need in-person connection, in part because of body language and other nonverbal communication; spontaneous ideas and adventures happen when people are physically together that can’t happen when we’re staring at each other over Zoom; and we experience new things together that are actually worth talking about later!

·         In-person connection inspires deeper connection and a desire for follow-up phone calls and emails.

·         Right now, we aren’t, as a society, doing much, so there’s not much to talk about.  I have little interest in talking to a friend over the phone about COVID, my lack of connection in physics, my lack of traveling... my lack of anything!

Setting aside my dearth of social connection, I am experiencing the additional detriment of lack of connection in physics.  A little over two years ago, I started working essentially full-time in the field of the foundations of physics and the physics of consciousness, etc.  I have made significant and rewarding progress, both in learning as well as innovating and contributing.  Not only do I now have a relatively deep understanding of the foundations of quantum mechanics that has allowed me to make several contributions, I’ve also come to a deeper understanding of the relationship between physics and consciousness, free will, and other deep philosophical issues.  So that’s good.  However, it’s hard to do anything alone for a long time.  Even Henry David Thoreau eventually had to leave Walden Pond and rejoin society.

And in large part I’ve been working on physics entirely alone.  I’ve tried really, really, really hard to connect with people.  I started two different physics masters programs (ECU and NYU); I prepared to attend two conferences (one canceled and the other almost uselessly virtual); I’ve reached out directly to hundreds of professors, paper authors, graduate students, etc.; I’ve written and posted my own papers and YouTube videos; yada yada yada.  Despite these efforts, I feel almost completely disconnected and alone in this field.  Almost no one understands me, what I’m working on, or what I’ve figured out.  Among my friends and family, this work is far beyond the understanding and interest of anyone I know, although my wife and a couple other people certainly try!  Among people in the actual field – people with whom I’ve been trying to connect for several years now – maybe 1% of these contacts have actually resulted in any meaningful connection.  I am profoundly thankful for and humbled by these few contacts, and several of them have been both intellectually and emotionally supportive.  Ironically, among the tiny handful who have both understood and validated my work, a few of them happen to be the top of the top.  For instance, as I mention in this post, this paper was rejected by referees until the journal’s chief editor, Carlo Rovelli himself, took the extremely unusual step of publishing it despite the reviews because it raises “an interesting and well-argued point.”  I won’t give further details in this post, but as it turns out the reviewer I described in this post – who was one of the only people to actually understand and validate the argument I made in this paper – is one of the most intelligent, original, and influential thinkers in the field.  So I certainly am thankful for the few genuinely positive connections I’ve made, although it’s just not enough (at least right now) to emotionally and intellectually sustain me.  I need to go to conferences and attend classes and have in-person connections to keep me feeling stimulated, inspired, and connected.  Right now – and in the foreseeable future – that is simply impossible. 

So my suffering comes down to this: I am just not looking forward to anything.  I feel like my life is perpetually on hold with every day undetectably bleeding into the next.  I am sick of constantly waiting for normalcy.  I am sick of not knowing when, or even if, I will be able to travel, to efficiently learn about the physics of consciousness, to emotionally connect with friends, to intellectually connect with colleagues.  I am sick of not knowing when I will again feel engaged, inspired, in flow.

Pain is usually a sign that something’s wrong.  If I feel my hand burning, it might be because of some miswired neurons or something wrong with my skin, in which case medication might be appropriate.  But it might also be because my hand is in a fire, in which case the best solution is to pull it out!  Poor mental health – depression, anxiety, etc. – presumably evolved in humans to help us identify and fix problems and to ultimately thrive.  Sometimes, poor mental health is due to chemical imbalances that can be addressed with medication.  Sometimes it’s due to emotional trauma that can be addressed with counseling.  Sometimes it’s due to poor physical health that can be addressed with diet and exercise.  To the extent that poor mental health is the body reacting inappropriately to the world, then by all means let’s address the symptoms.  No sense in feeling the pain of anxiety when there’s nothing to feel anxious about... take a pill for crying out loud!

But sometimes, poor mental health is a direct result of circumstance and it’s the body’s appropriate response to dangerous or unhealthy surroundings.  Dulling that pain with a pill might only serve to increase one’s tolerance to what is, or should be, an intolerable situation.  I can’t speak for anyone else, but it is clear to me that the world I live in is currently intolerable.  Not that I can’t tolerate it, but that I shouldn’t. 

I don’t know what the solution is.  Like many others, fatigue is setting in.  If I knew for certain that normalcy would return by, say, July, then I could wait it out.  But if I am honest with myself, I am having growing doubts that normalcy will return at all, much less by summer.  Maybe it’s time to accept that the world I grew up in is gone forever: one in which everyone had more-or-less the same source of news and people didn’t choose their news media based on the “facts” they want to believe; one in which people could go to parties, dance clubs, restaurants, and theaters without constantly worrying about viruses; one in which human connection was almost exclusively in-person; one in which I might have 20 close friends who know my good and bad sides and with whom I can be vulnerable, instead of 2000 Facebook “friends” or 200,000 Instagram “followers” who envy my beautiful and successful life but know nothing about my doubts or sadness or despair because I only post the enviable stuff.

Maybe it’s time to mourn the loss of that world and move on.  (I suppose with such low expectations, I can only be pleasantly surprised if normalcy actually does return later this year...)  I don’t know what to do, but I know I have to do something differently.  Maybe it’s time to abandon physics for awhile and take a road trip with my dog to some national parks.  Maybe I need to build something – maybe not quite the scale of the Agora Grand, but nevertheless interesting and useful and creative.  Who knows?  Suggestions welcome! 

Thank God for my wonderful wife and my friends and family, even if I don’t connect with them as often as I should.  Thank God that I am well fed and live in a nice apartment with amenities that Cleopatra could only dream about.   Thank God I can still think with clarity.

 

God – please give me the grace and peace to accept the things I cannot change, the courage and strength to change the things I should, and the clarity and wisdom to know the difference.

Wednesday, January 27, 2021

Is Scalable Quantum Computing Possible? And Why Does It Matter?

Tomorrow I begin a class on quantum computing at NYU, taught by Javad Shabani.  In preparation, I am reading Scott Aaronson’s fascinating Quantum Computing Since Democritus.

The notion of quantum computing is simple.  Computers rely on bits – transistors that serve as little on-off switches.  By starting with an initial string of bits and then manipulating them in a particular way according to software (e.g., turning “on” or 1 switches to “off” or 0, etc.), a computer can essentially perform any calculation.  Computers don’t need to be made of transistors, of course, but that tends to be much more efficient than using, say, Tinker Toys.  A quantum computer is simply a computer whose bits are replaced with “qubits” (quantum bits).  Unlike a classical bit that can only take the state 0 or 1, a qubit can be in a superposition of 0 and 1 (or, more precisely, state α|0> + β|1>, where α and β are complex amplitudes and |α|2 is the likelihood of finding the qubit in state |0> and |β|2 is the likelihood of finding the qubit in state |1> if measured in the {|0>,|1>} basis). 

The reason this matters is that because there are “infinitely many” (well, not really, but certainly lots of) possible states for a single qubit, because α and β can vary widely, while there are only two states (0 or 1) for a classical bit.  In some sense, then, the “information content” of a qubit (and ultimately a quantum computer) is vastly greater than the information content of a classical bit (and corresponding classical computer).  If you think your iPhone is fast now, imagine one with a quantum computer processor!

At least... that’s the advertisement for quantum computing.  In reality, there are several problems with actual quantum computing.  I won’t dig too deeply into them, as they’re well described by articles such as this, but here are a few:

·         Nobody knows what to do with them.  There are a couple of particular kinds of software, such as Shor’s algorithm for factoring large composite numbers, that would have useful implications for cryptography and information security.  Beyond that, there don't seem to be many real-world applications of quantum computers that would be significantly faster than classical computers.

·         Qubits must remain isolated from the rest of the world (except for their entanglements with other qubits) during the computation, but this is a massively difficult problem because of decoherence.  You can have a microSD card with literally billions of classical bits... you can stick it in your pocket, use it to pick a piece of chicken out of your teeth, drop it in the toilet, probably zap it in the microwave for a few seconds... and it will probably still work fine.  (Full disclosure: I’ve never actually tried.)  But qubits are so ridiculously sensitive to influences from the world that it takes a huge multi-million-dollar system just to adequately cool and isolate even a dozen qubits.

·         Even if there were a way to adequately isolate lots of qubits, as well as entangle and manipulate them in a way necessary to execute a useful algorithm, and even if you could do this for a reasonable price on a reasonably sized device, error correction seems to be a major problem.  Errors are caused (at least in part) by decoherence, and quantum error-correction means are supposedly possible in principle, but these means (e.g., requiring 1000 additional error-correcting qubits for each existing qubit) may prove seriously problematic for the future of quantum computing.

At the end of the day, the real question is not whether a “quantum computer” consisting of a handful of entangled qubits is possible – of course it is, and such computers have already been built.  Rather, it is whether the problems of isolation, decoherence, and error-correction will prevent the possibility of "scaling up" a quantum computer to some useful size.  Aaronson famously offered $100,000 for “a demonstration, convincing to me, that scalable quantum computing is impossible in the physical world.”  I want to know the answer to this question not just because it’s such a massively important question pervading modern science and technology, but also because of its relationship to my own work on consciousness, with implications going both ways.  Specifically, what might the physical nature of consciousness tell us about the possibility of scalable quantum computing, and what might the possibility of scalable quantum computing tell us about the physical nature of consciousness?

Here’s an example.  I have been arguing for some time (e.g., in this paper and this post) that macroscopic quantum superpositions, like Schrodinger’s Cat (“SC”) and Wigner’s Friend (“WF”), can never be demonstrated, even in principle, because any “macroscopic” object (e.g., a dust particle, a cat, a planet, etc.) is already so well correlated to other objects through a history of interactions (including “indirect” interactions because of transitivity of correlation) that it can never exist in a superposition of macroscopically distinct position eigenstates relative to those other objects.  Of course, the majority opinion – practically the default position – among physicists and philosophers of physics is that WF is possible.  Nevertheless, even those who claim that WF is possible will admit that it’s really difficult (and perhaps impossible) in practice and will often resort to the plausibility of conscious AI (i.e., “Strong AI”) to save their arguments.  David Deutsch in this article, for example, spends dozens of pages with lots of quantum mechanics equations “proving” that WF is possible, but then spends a half page saying, essentially, that OK, this probably isn’t possible for an actual flesh-and-blood human but we might be able to do it on a computer and since it’s obvious that consciousness can be created on a computer... blah blah...

The problem, of course, is that not only is it not obvious, but I showed in these papers (here and here) that consciousness actually cannot be created on a computer because it is not algorithmic.  So if the possibility of WF depends on AI being conscious, and if computer consciousness is in fact physically impossible, then there must be some explanation for why WF is also physically impossible – and that explanation may equally apply to the impossibility of large quantum computers.  Further, many proponents of the possibility of computer consciousness, such as Aaronson, suspect that we’ll need a quantum computer to do the job, in which case the possibility of WF and conscious AI may hinge on the possibility of scalable quantum computing.   

Anyway, this is all to say that much of what I have discovered, innovated, and now believe about consciousness, quantum mechanics, information, Wigner’s Friend, etc., is closely related to the question of whether scalable quantum computing is possible.  Before actually beginning the class on quantum computing, here is my prediction: I think that scalable quantum computing is, in fact, impossible in the physical world.  Here’s why.

First, the possibility of scalable quantum computing, like the possibility of macroscopic quantum superpositions, follows from the assumption of “U” (i.e., the “universality” or “unitary-only” assumption that a quantum wave state always evolves linearly).  But U is an invalid logical inference as I argue in this paper; I actually think it is irrational to believe U.  In other words, it seems that the primary argument in support of scalable quantum computing is actually a logically invalid inference.  Further, I think that most of those who believe U (which is probably the vast majority of physicists) don’t even know why they believe U.  As a bettor, I would say that the smart money goes on those who actually understand (and, better yet, can justify) the assumptions they make.  The fact that so many of those who believe in scalable quantum computing also assume U leads me to doubt their claims.

Second, the possibility of scalable quantum computing depends on foundational questions about quantum mechanics, and very few scientists (including those who assert that scalable quantum computing is possible) actually understand quantum mechanics.  I know this may sound arrogant... how can I possibly claim to understand QM well enough to conclude that so few people do?  Well, that isn’t what I said – although, incidentally, I do believe I now understand QM at a level far more deeply than most.  You don’t have to understand a topic to be able to identify logical contradictions.  Unlike my brilliant physician wife, I know next to nothing about medicine or the human body, but if I heard a doctor say, “The brain does X” and then later say “The brain does not do X,” then I will know that the doctor does not understand the brain.  So it is with QM.  Here are a couple of papers in which I’ve addressed contradictions by physicists discussing QM (here, here, and here), and it drives me absolutely bonkers at the cognitive dissonance required for a physicist to say something like “Schrodinger’s Cat is both dead and alive.”

Third, and most importantly, I think that scalable quantum computing will run into the same problem as macroscopic quantum superpositions, which (as discussed above and in the cited papers) I think are impossible to create and empirically demonstrate.  I’m not sure it’s exactly the same problem, but it’s really similar.  For example, I argued here that when a tiny object measures the position of a measuring device, it inherently measures the position of other objects in the rest of the universe, whose positions are already well correlated to that of the measuring device.  Will that argument apply to, say, a million qubits that are entangled with each other but isolated and uncorrelated to other objects in the universe?  I don’t know, but it certainly suggests a similar problem. 

On a related note, I have argued that a superposition state of a single particle can grow via quantum dispersion, but as the object grows in size, a potential superposition suffers two problems: reduction in the rate of dispersion (thanks to the Uncertainty Principle) and increase in the rate of decoherence.  We can do double-slit interference experiments on objects as large as maybe a thousand atoms, although anything much beyond that seems to be impossible for all practical purposes.  I suspect the same problem, or something comparable, will arise with groups of entangled qubits.  In other words, I am reasonably confident that there is a set of quantum superpositions that are physically impossible to empirically demonstrate, even in principle – and I would bet that whatever physical mechanism prevents such superpositions would also prevent scalable quantum computing.   

But I don’t know for certain.  For example, I don’t know how an individual qubit is placed in an initial (superposition) state, nor do I know how groups of qubits are entangled and manipulated in the way necessary to perform the desired algorithm.  It may turn out that the only real limitation is decoherence, and perhaps error correction may indeed be adequate to overcome decoherence limitations.  I sincerely doubt it, but these are the sorts of questions I am looking forward to answering this semester!

Friday, January 22, 2021

Do Conscious States Depend on History?

I’ve had a few additional thoughts further to my recent post on counting conscious states, particularly on the extent to which a given conscious state is history-dependent (i.e., depends on its history of prior conscious states) and whether a particular conscious state can be created de novo (i.e., from scratch, without the person experiencing that state having actually experienced previous conscious states).

Imagine that a person has actually experienced a particular series of conscious states (which of course depend, at least in part, on the stimuli sensed).  For the sake of simplicity, I’ll just assume that there’s a conscious state for each stimulus “frame,” and for ≈10 distinct frames/second, there are about 300 million stimulus frames per year.  I’m 43 now, and not sure whether we should start counting conscious frames from birth or sometime later, but let’s say that I’m just about to experience my ten billionth conscious state.  In my last post, I gave a (very, very) rough estimate for the minimum number of information bits necessary to specify such a state.  That number may be large – say, on the order of a trillion bits – but it’s not ridiculous and is less information capacity than many people have on their mobile phones.  Whatever that number happens to be – that is, the minimum number (B) of bits necessary to specify a particular conscious state – the point is this: By assumption, the instantiation of those B bits in the configuration necessary to create conscious state C1 will indeed create that state C1.  (For the following argument, it doesn’t matter whether the mere existence/instantiation of that particular configuration of bits is adequate, or whether that configuration must be executed on some general-purpose computer/machine.)

In other words, by assumption, some conscious state C1 is sufficiently encoded by some series of B bits that may look like: 0011010100110111110... (trillions of bits later)... 10001001111100011010.  There may be a lot of bits, but the idea is that if physicalism is true and the information content of any given volume is finite, then any particular conscious state must be encoded by some string of bits.  If this seems odd to you, it’s definitely the majority opinion among physicists and computer scientists who actually think about this kind of stuff.  For example, Scott Aaronson characterizes the situation this way:

“Look—I don’t know if any of you are like me, and have ever gotten depressed by reflecting that all of your life experiences, all your joys and sorrows and loves and losses, every itch and flick of your finger, could in principle be encoded by a huge but finite string of bits, and therefore by a single positive integer. (Really? No one else gets depressed about that?)”

For the record, I don’t get depressed about that because I don’t believe it’s true, although I’m still trying to formulate my reasoning for why.  OK, so let’s assume that I have in fact experienced ten billion conscious states.  The state I am currently experiencing is C10,000,000,000 (let’s call it CT), and a tenth of a second ago I experienced conscious state C9,999,999,999 (let’s call it CT-1), and a tenth of a second before that I experienced C9,999,999,998 (let’s call it CT-2), and so on back.  Again, by assumption, each of these states is encoded by a particular string of bits.  So here’s my question: is it possible to just recreate state CT  de novo without, in the process, also producing state CT-1?

Here’s another way of phrasing the question.  Is the person who is experiencing conscious state CT someone who actually experienced CT-1 (and CT-2 and so on back), or someone who just thinks/believes that he experienced CT-1?  Is there a way to produce someone in state CT without first producing someone in state CT-1?  I don’t think so; I think that state CT is history dependent and literally cannot be experienced unless and until preceding state CT-1 is experienced.  After all, if conscious states are indeed history independent, then the experience of CT is precisely the same no matter what precedes it, and that could lead to some odd situations.  Imagine this series of conscious experiences:

Series #1

C1000: sees alligator in the distance

C1008: gets chomped by alligator

C1045: puts tourniquet on chomped arm

C2000: eats own birthday cake

C3000: rides on small plane to experience skydiving

C3090: jumps out of airplane to experience thrilling freefall

C3114: pulls rip cord of parachute

C3205: lands safely on ground

 

If conscious states are history independent, then the person’s experience at C3205 is precisely the same even if the physical evolution of the world actually caused the following ordering of conscious states:

Series #2

C1045: puts tourniquet on chomped arm

C3000: rides on small plane to experience skydiving

C1008: gets chomped by alligator

C3090: jumps out of airplane to experience thrilling freefall

C2000: eats own birthday cake

C3114: pulls rip cord of parachute

C1000: sees alligator in the distance

C3205: lands safely on ground

 

I can’t see how the above series would make any sense, but more importantly I can’t see how, even if it did make sense, the experience of conscious state C3205 could possibly be the same in both cases.  If I’m right, it’s because conscious states are history dependent and state C3205 actually cannot be experienced immediately after C1000.

I’m not sure where I’m going with this.  If conscious states are history dependent (which is what I’ve suspected all along, as in this paper) then lots of interesting implications follow, such as that conscious states cannot be copied, consciousness is not algorithmic, etc.  (I believe I've already independently shown these implications in this paper.)  The above analysis certainly suggests history dependence but is not a proof.  Maybe the way to prove it is by first assuming that conscious states are independent of history – in which case conscious state C3205, for example, can be created de novo without first creating conscious state C3204 (which can be created de novo with first creating conscious state C3203, etc.) – and then see whether that assumption conflicts with observations and facts about the world.

Remember that, by assumption, state C3205 is just instantiated by a (very long but finite) string of bits, say 0011010100110111110...  So imagine if we start with a long series of on-off switches all initially switched off.  We turn some of them on until eventually we have instantiated the correct series (0011010100110111110...), which encodes state C3205.  But it does not (and cannot) matter the order in which we flip those switches.  I have to think more about the mathematics, but I suspect that in guaranteeing that C3205 is independent of history, so that it and every preceding conscious state can be instantiated independently of its own history, we will end up needing far, far more bits than my original estimate of N^T.  I suspect that even the most conservative estimate will show that if conscious states are history independent, then consciousness will require far more information storage than is currently believed to reside in the brain. 

Then again, I really don’t know.  This is still just the initial seed of a thought. 

Sunday, January 17, 2021

Counting Conscious States

Information is physical, which means there is a limit to the amount of information that can fit in a given volume.  If you try to cram more information into that volume, the physical mass of that information will literally collapse into a black hole.  That limit is called the Bekenstein bound and is truly a massive limit.  For instance, the total informational bound that could be contained in a volume the size of the human brain is around 10^42 bits, which means that the total number of possible brain states is around 2^(10^42).  The total informational capacity of the entire visible universe is on the order of 2^(10^120) states.

Why does this matter?  Physicalism (as contrasted with dualism) says that conscious states are produced by physical states; if a first conscious state is distinct from a second conscious state, then they must be produced by different physical states.  All of my papers (and most or all of my blog posts) so far have assumed physicalism is true, in part because anyone who doubts physicalism is usually condescendingly dismissed, ignored, or scoffed at by the scientific community, and in part because I don’t see why the Creator of the already ridiculously complicated universe would have omitted a physical explanation/mechanism for consciousness.  In other words, unless there is a reason to believe that consciousness does not entirely depend on underlying physical state, I see no need, for now, to reject physicalism.  Nevertheless, physicalism would be falsified if one could show that the number of distinct conscious states exceeded the number of physical states, because that would require that a single physical state could produce more than one distinct conscious state.

One avenue for evaluating physicalism, then, is to literally count distinct conscious states.  For example, if one could show that the total number of possible distinct conscious states by a particular person exceeded 2^(10^42), then that would prove that consciousness cannot depend (entirely) on the brain; if one could show that the number of possible distinct conscious states exceeded 2^(10^120), then that would literally falsify physicalism. 

A few years ago, Doug Porpora wrote a fascinating paper that attempted to prove that the total number of distinct conscious states is actually infinite.  One of his arguments, for instance, is that if we assume that there are some natural numbers that we cannot think about, then there must be a maximum number (call it Max) that we can think about and a minimum number (call it Min) that we cannot think about.  But if we can think about Max, certainly we can think about Max+1 or Max^2, which means that Max is not the maximum number we can think about and the original assumption (that there are some natural numbers that we cannot think about) is false.  A related argument is that by identifying the minimum number that we cannot think about (and even naming it Min), we are thinking about Min, which means that Min is not in the set of numbers that we cannot think about!  Again, the original assumption is false.  There is more to the argument than this but it gives you the general flavor of its proof-by-contradiction strategy.  One commenter has attempted to refute Porpora’s argument in this paper, and Porpora may be working on a reply. 

This got me thinking again about the importance of counting distinct conscious states, which very few people seem to have attempted.  Of course, if Porpora’s logical argument is correct, then physicalism is false because even though 2^(10^120) is a ridiculously and incomprehensively large number, it is still trumped by ∞.  But we should also realize that both of the quantities we are considering are extremes.  Infinity is extreme, of course, but so is the Bekenstein bound.

Let’s take a more realistic approach.  There are something like 100 billion neurons in the human brain.  If each neuron acts like a digital bit, then the total number of distinct brain states is 2^(100 billion).  Neurons are actually complex cells with very complicated connections to each other.  I don’t think any neuroscientist seriously regards neurons as acting in any way like digital bits.  However, I do think it is interesting to ask the question of whether or not the number of distinct conscious states exceeds 2^(100 billion).  If there were a way to answer that question – by somehow counting conscious states – then it would do a couple things:

·         Assuming physicalism is true, discovering that the number of distinct conscious states exceeds 2^(100 billion) would confirm that the brain is not a digital computer with neurons acting as digital bits.

·         It would provide a methodology for counting conscious states that may provide further insights about the physical nature of consciousness.

On that note, let me suggest such a method.  First, let me start with the notion of one stimulus “frame,” which is the particular collection of physical stimuli that one might detect through the five senses at any given moment.  Let’s assume that there are N consciously distinct (frames of) stimuli.  What I mean by that is that there are N different combinations of stimuli from the person’s senses that the person would be able to distinguish.  Consider these different sets of stimuli:

·         Watching a sunset while hearing crashing waves while tasting white wine while smelling the salty ocean while feeling sand under one’s feet;

·         Watching a sunset while hearing crashing waves while tasting red wine while smelling the salty ocean while feeling sand under one’s feet;

·         Watching a sunset while hearing seagulls while tasting white wine while smelling the salty ocean while feeling sand under one’s feet.

If we actually took the time to list them, we could certainly produce a very, very long list of consciously distinct stimuli.  Some of them might differ very subtly, such as two stimuli that are identical except for the temperature of the sand differing by one degree, or a slight difference in sound frequency distribution from the seagulls, or a slight but perceptible difference in the cloud distribution above the sunset.

What matters, in enumerating consciously distinct stimuli, is whether a person could distinguish them, not whether he actually does.  If he could distinguish two stimuli, either by consciously noticing the difference or simply having a (slightly) different conscious experience based on the difference, then that difference must be reflected in the underlying physical state.

So how many such distinct stimuli are there?  Lots.  One could certainly distinguish millions of different visual stimuli, many thousands of different sounds and tactile sensations, and at least hundreds of different tastes and smells.  This is a ridiculously conservative claim, of course; there are professional chefs, for example, who can probably differentiate millions of different tastes and smells.  On this very conservative basis, there are probably far, far more than 10^18 (around 2^60) distinct stimuli for any given person.  If there were only 10^18 distinct conscious states or experiences, then in principle it would only require about 60 bits to specify them. 

However, history matters.  Conscious experience does not depend just on one’s stimuli in the moment, but also on prior stimuli (as well as prior conscious experience).  To specify a person’s conscious experience, it is not enough to specify his current stimuli, as his experience will also depend on past stimuli.  For example, imagine the different conscious experiences at time t1:

Case A – No significant change from t0 to t1:

t0: Watching a sunset while hearing crashing waves while tasting red wine while smelling the salty ocean while feeling sand under one’s feet.

t1: Watching a sunset while hearing crashing waves while tasting red wine while smelling the salty ocean while feeling sand under one’s feet.

Case B – Significant change from t0 to t1:

t0: Watching a sunset while hearing crashing waves while tasting white wine while smelling the salty ocean while feeling sand under one’s feet.

t1: Watching a sunset while hearing crashing waves while tasting red wine while smelling the salty ocean while feeling sand under one’s feet.

The stimulus at t1 is the same in both cases, but the conscious experience would clearly be different.  In Case A, the person may simply be enjoying the surroundings, while in Case B, he may be confused/surprised that his wine has suddenly changed flavor and color.

What that means is even if the information necessary to specify the particular stimulus at time t1 is 60 bits, that information is not sufficient to specify the person’s conscious experience at that time.  In other words, history matters, and instead of just counting the number of possible distinct stimuli, we need to consider their order in time. 

So, for N consciously distinct stimuli, let’s assume that one’s conscious experience/state at a given time is sensitive to (i.e., depends on) the time-ordering of M of these stimuli.  The total number of possible states, then, is just the permutation N!/(N-M)!, but assuming that N>>M, this total number of states ≈ N^M.  

So in the above example, the number of possible physical states necessary to allow the person to consciously distinguish Case A from Case B is not N, but N^2.  If N requires, say, 60 bits of information, then at least 120 bits are required to specify his conscious state at time t1.  But of course the situation is far worse.  We can imagine a series of ten consecutive stimuli, ending at time t9, which the person would consciously experience in a manner that depended on all ten stimuli and their order.  It makes no difference whether the person actually remembers the particular stimuli or their order of progression.  As long as he has a conscious experience at t9 that is in some (even miniscule) manner dependent on the particular stimuli and their order, then that conscious state is one of at least N^10 states, requiring at least 600 bits to specify.

Now note that his experience at t9 is a unique one of at least N^10 states, just as his experience at later time t19 is a unique one of at least N^10 states, and so forth until time t99.  But if his conscious experience at time t99 is sensitive to the ordering of his conscious experiences at t9, t19, t29, etc., then the conscious state at t99 is one of at least N^100 states, requiring at least 6000 bits to specify.  Once again, this analysis has nothing to do with whether the person remembers any specifics about his prior stimuli or experiences; all that matters is that his conscious experience at t99 depends to some degree on the ordering of experiences at t9, t19, etc., and that his experience at t9 depends to some degree on the ordering of stimuli at t0, t1, etc.

It’s easy to show, then, that the total number of possible conscious states is N^T, where T is the total number of individual “frames” of stimulus that one experiences over his life.  How many is that?  Well, 100 years is about 3 billion seconds, and we certainly experience more than one “frame” of stimulus per second.  (Otherwise, TVs would not need a refresh rate of around 30 frames/second.)  So, for 10 frames/second, we might estimate the total number of possible conscious states at about N^(30 billion).  If N is 2^60, then the total number of conscious states is 2^(1.8 trillion), requiring at least 1.8 trillion bits to specify.

I find it fascinating how close this is to the number of neurons (100 billion) in the human brain.  For extremely rough back-of-the-envelope calculations like this, an order or two of magnitude is certainly “close.”  The storage capacity of the human brain has been estimated somewhere in the tens to thousands of terabytes, and once again the above rough estimate is within a couple of orders of magnitude of this amount.

What this tells me is that this method of counting distinct conscious states is viable and potentially useful and valuable.  By getting better estimates for the number of stimuli that a person can distinguish, for example, we might find that the rough estimate above (≈ trillion bits) is far too high or far too low, which could then provide insights on our understanding of the brain as: a computer; a digital computer; a digital computer with neurons acting as bits; and the independent source of consciousness.  Of course, such an analysis will never get us anywhere near the Bekenstein bound or infinity, as addressed by Porpora’s paper, but I still think we can learn interesting and important things about the physical nature of consciousness by counting distinct conscious states.

Finally, I think the above analysis hints at something fundamental: that consciousness is history-dependent.  This is something I discuss at length in my paper on the Unique History Theorem, but the above arguments suggest a similar conclusion by a very different analysis.  If one’s conscious experience at time t99 depends to some degree on his experience at t98, which in turn depends on his experience at t97, and so on back, then it may not be possible to produce a person de novo in a particular conscious state C1 who has not already experienced the particular sequence of conscious states on which state C1 depends.

In any event, I think it makes sense to seriously consider and estimate the number of potentially distinct conscious states, taking into account a human’s sensitivity to different stimuli and the extent to which ordering of stimuli affect conscious states.  I think this approach could yield potentially fascinating knowledge and implications about the brain and the physical nature of consciousness.

Thursday, December 17, 2020

Linear/Unitary Quantum Mechanics Cannot Apply Universally

In my last post, I provided several arguments why the inference of U is logically invalid.  As a quick rehash, many (perhaps most) of the big problems in foundational physics arise from an assumption (“U”) that the quantum mechanical wave function always evolves linearly or unitarily, so that when a small object in quantum superposition interacts with a large system, the large system “inherits” the superposition.  Because U asserts that this is always true, no matter how big the system, then cats (like Schrodinger’s Cat) and people (like Wigner’s Friend) can exist in weird macroscopic superposition states.  This is a problem because, well, we never observe cats or anything else in superposition in our ordinary lives!  There are lots more problems and weird implications that follow from U, so it’s amazing just how few people have (at least in the academic literature) questioned U. 

Today’s post is my attempt to actually disprove U.  I use a variety of novel logical arguments to show that U is actually false -- or, at least, empirically unverifiable, which would place it outside the realm of science.  Together, these posts will be put together and submitted as a journal article even if that minimal effort is unrewarded. 

III.       A NEW LOGICAL ARGUMENT AGAINST U

In Section II, I attempted to show that U is not scientifically justified as a valid inference because relevant empirical evidence supports only ¬U.  In this section, I will present a new logical argument attempting to show an example in which U cannot be experimentally verified even in principle.  In other words, not only does U lack experimental verification, I will argue that U cannot be experimentally verified.  I will first discuss the nature of a quantum superposition from a logical standpoint, then address the extent to which quantum superpositions must be relative.  Finally, I will present three variations on the argument.

A brief caveat: this argument is more likely to benefit the skeptics of U than of its devoted adherents.  Consider this statement: “A scalable fault-tolerant quantum computer can be built.”  Let’s assume for the moment that it is in fact false, and could logically be shown to be false because of some inconsistency with other facts about the universe, but happens to be empirically unfalsifiable.  Those who are already convinced that the statement is true will be unlikely to be persuaded by a priori logical argumentation.  If they are in the field of quantum computing, they may be responsible for directing private and public funding toward achievement of a fundamentally unfulfillable goal.  Waiting either for success or empirical falsification, they continue to throw good money after bad, depriving more viable scientific goals of funding.

Such is the case with the assumption of U.  If U is in fact false, but turns out to be empirically unfalsifiable, then any logical argument against U will probably not be compelling to anyone who is already convinced of U.  Instead, the following arguments are probably most accessible and relevant to those scientists who are already skeptical of U.  Throughout the following analyses, I will simply assume U true and show how that assumption leads to logical problems.

A.        What is a Quantum Superposition?

Let’s return to the double-slit interference experiment in which a particle passes through a plate having slits A and B and assume that the experiment is set up so that the wave state emerging from the plate is (unnormalized) state |A> + |B>.  What does that mean?  |A> represents the state the particle would be in if it were localized in slit A, while |B> represents the state the particle would be in if it were localized in slit B.  If the particle had been in state |A>, for example, then a future detection of that particle would be consistent with its having been localized in slit A.[1] 

However, superposition state |A> + |B> is not the same as state |A>.  In other words, state |A> + |B> is not the state of the particle localized in slit A, nor is it the state of the particle localized in slit B.  However, it is also not the state of the particle not localized in slit A (because if it were not in A, it would be in B), nor is it the state of the particle not localized in slit B.  Therefore, for a particle in state |A> + |B>, none of the following statements is true:

·         The particle is in slit A;

·         The particle is not in slit A;

·         The particle is in slit B;

·         The particle is not in slit B.

While these statements may seem contradictory, the problem is in assuming that there is some fact about the particle’s location in slit A or B.  Imagine two unrelated descriptions, like redness (versus blueness) and hardness (versus softness).  “Red is hard” and “red is soft” might seem like mutually incompatible statements, one of which must be true and the other false, but of course they are nonsensical because there just is no fact about the hardness of red, or the redness of soft, etc.  Analogously, for a particle in state |A> + |B>, there just is no fact about its being localized in slit A or B.  The problem is in assuming that “The particle is in slit A” is a factual statement – that there exists a fact about whether or not the particle is in slit A.  Unfortunately, the assertion that there exists such a fact is itself incompatible with the particle being in state |A> + |B>.

Note also that state |A> + |B> is not a representation of lack of knowledge; it does not mean that the state is actually |A> or |B> but we don’t know which, nor does it have anything to do with later discovering, via measurement, which of state |A> or |B> was correct.  If an object is in fact in a superposition state now, a future measurement does not retroactively change that fact.  (See, e.g., Knight (2020).) 

If an object is in state |A> + |B>, then there just is no fact about its being in state |A> or |B> – not that we don’t know, not that it is unknowable, but that such a fact simply does not exist in the universe.  This counterintuitive notion inevitably leads many to confusion.  After all, if a cat could exist in state |alive> + |dead>, and if that state is properly interpreted as there being no fact about its being alive or dead, what does that say about the cat?  Wouldn’t the cat disagree?  And what quantum state would the cat assign to you?   Of course, if SC turns out to be impossible to create, even in principle, then these worries disappear. 

B.        Relativity of Quantum Superpositions

In the above example, |A> represented the state the particle would be in if it were localized in slit A.  To be more technical, |A> is an eigenstate of the position operator corresponding to a semiclassical localization at position A.  But where exactly is “position A”?  If there is one thing that Galileo and Einstein collectively taught us, it’s that positions (among other measurables) are relative.  That recognitional already instructs us that state |A> + |B> is meaningless without considering that the locations of positions A and B are relative to other objects in the universe.  In other words, quantum superpositions are inherently relative.  There are two types of relativity of quantum superpositions I’ll discuss:

·         Weak Relativity of quantum superpositions: Measurement outcomes (eigenstates of an observable) are relative to other measurement outcomes. 

·         Strong Relativity of quantum superpositions: Essentially an extension of Galilean and Einsteinian Equivalence Principles, Strong Relativity requires that if a first system (such as a molecule) is in a superposition from the perspective of a second system (such as a laboratory), then the second system is in a corresponding superposition from the perspective of the first system.  For instance, if a microscopic object is in a superposition of ten distinct momentum eigenstates relative to a measuring device, then the measuring device is conversely in a superposition of ten distinct momentum eigenstates relative to the microscopic object. 

While the notion of “quantum reference frames” is not new (Aharanov and Kaufherr (1984) and Rovelli (1996)), the above notion of Strong Relativity has only recently been discussed in the academic literature (Giacomini et al. (2019), Loveridge et al. (2017), and Zych et al. (2018)).  If it is true, then it’s relatively easy to show, as I did in this paper, that SC is a myth and that macroscopic quantum superpositions cannot be demonstrated in principle.  In a sense, the truth of Strong Relativity excludes the possibility of SC nearly as tautology, since if a lab from whose perspective a cat is in state |alive> + |dead> can equivalently be viewed from the perspective of the cat, then which cat?  And what quantum state would describe the lab from the cat’s perspective?  From the perspective of the live cat, perhaps the cat would view the lab in the superposition state:

|lab that would measure me (the cat) as live> + |lab that would measure me (the cat) as dead>

And if we think that cat states |alive> and |dead> are interestingly distinct, can you imagine how incredibly and weirdly distinct those eigenstates would seem from the perspective of the live cat?  Rewriting the above state with a little more description, the lab would appear from the live cat’s perspective as state:

|lab that would measure me (the cat) as live, which isn’t surprising, because I am alive> +

|lab that is so distorted, whose measuring devices are so defective, whose scientists are so incompetent, that it would measure me (the cat) as dead>

The second eigenstate is actually far worse than described.  Every single measurement made by that lab would have to correspond, from its perspective, to a dead cat; the scientists in it, when looking at the cat, when receiving and processing trillions of photons bouncing off the cat, would have to see a dead cat!  And it’s worse than that.  Even when the scientists leave the lab, the universe requires that the story stays consistent; no future fact about the lab, its measuring devices, or its scientists – or anything they interact with in the future – can conflict with their observation of a dead cat, even though that second eigenstate is from the perspective of a live cat![2]

I derived the notion of Strong Relativity independently and therefore regard it as nearly obviously true.  Nevertheless, because it is by no means universally accepted (or even known) by physicists or philosophers, I won’t depend on it in this paper.  Instead, I’ll use Weak Relativity, which is obviously and necessarily true.  For instance, a particle is only vaguely specified by state |A> + |B>.  For a scientist S in a laboratory L who plans to use measuring device M to detect the particle whose state |A> + |B> references positions A and B, we should be asking whether positions A and B are localized relative to the measuring device M, the lab L, the scientist S, etc.  In other words, is the particle in state |A>M + |B>M, |A>L + |B>L, or |A>S + |B>S?

Why does this matter?  Surely position A is the same position relative to the measuring device, lab, and scientist.  And for essentially all practical purposes, that’s true, which is probably why the following analysis is absent from the academic literature.  After all, how could the measuring device, scientist, etc., disagree about the location of position A? 

As discussed in Section II, quantum uncertainty disperses a wave packet, so over time a well-localized object tends to get “fuzzy” or less well localized.  Why don’t we notice this effect in our ordinary world?  What keeps the scientist from becoming delocalized relative to the lab and measuring device?  First, the effect is inversely related to mass.  We barely notice the effect on individual molecules, so we certainly won’t notice it with anything we encounter on a daily basis.  Second, events, such as impacts with photons, air molecules, etc., are constantly correlating objects to each other and thus decohering relative superpositions.  For example, the air molecules bouncing between the scientist and measuring device are constantly “measuring” them relative to each other, preventing their wave packets from dispersing relative to each other.     

So while the scientist might in principle be delocalized from the measuring device by some miniscule amount, that amount is much, much, much smaller than could ever be measured, and is therefore irrelevant to whether position A is located relative to the scientist S, the measuring device M, or the lab L.  Therefore, it’s usually fine to write state |A> + |B> instead of |A>M + |B>M, etc., because |A>M + |B>M ≈ |A>L + |B>L ≈ |A>S + |B>S.[3]

However, if U is true, then producing SC or WF (and correspondingly enormous relative delocalizations[4]) are actual physical possibilities, if perhaps very difficult or impossible to achieve in practice.  If we’re going to talk about cat state |alive> + |dead>, or a superposition of a massive object in position eigenstates so separated that they would produce distinct gravitational fields (Penrose (1996)), or macroscopic quantum superpositions in general, then we can no longer be sloppy about how (i.e., in relation to what) we specify a superposition of eigenstates.  That said, I’ll now argue how keeping track of these relations between systems implies that there are at least some macroscopic quantum superpositions (such as SC) that cannot be measured or empirically verified, even in principle.

C.        The Argument in Words

A scientist S (initially in state |S>) wants to measure the position of a tiny object O.  The object O is in a superposition[5] of position eigenstates corresponding to locations A and B, separated by some distance d, relative to the scientist S.  Neglecting normalization constants, |O> = |A>S + |B>S.  To measure it, he uses a measuring device M (initially in state |M>) configured so that a measurement of the position of object O will correlate device M and object O so that device M will then evolve over (some brief but certainly nonzero) time to a corresponding macroscopic pointer state, denoted |MA> or |MB>.  Device M in state |MA>, for example, indicates “A” such as with an arrow-shaped indicator pointing at the letter “A.”  In other words, device M is designed/configured so that if M measures object O at location A, then M will, through a causal chain that amplifies the measurement, evolve to some state that is very obviously different to the scientist S than the state to which it would evolve had it measured object O at location B.  The problem, reflecting Weak Relativity, is that device M measures the location of object O relative to it.  Relative to device M, the object O is in state |A>M + |B>M, which means that a correlating event between O and M will cause M to evolve into a state in which macroscopically indicating “A” correlates to its measurement of the object at position A relative to M, and vice versa for position B.

Of course, this doesn’t typically matter in the real world.  The scientist S is already well localized relative to device M; there is essentially no quantum fuzziness between them.  Because |A>M + |B>M ≈ |A>S + |B>S, measurement of the object O at A relative to M is effectively the same as its measurement relative to S, so the device’s macroscopic pointer state will properly correlate to the object’s location at position A or B relative to S, which was exactly what the scientist wanted to measure.  However, under what circumstances would it matter whether |A>M + |B>M ≠ |A>S + |B>S, and how could this situation come to pass?

Let’s say that the experiment is set up at time t0; then at time t1 the device M “measures” the object O via some initial correlation event, after which M then evolves in some nonzero time Δt to a correlated macroscopic pointer state; and then at t2 the scientist S reads the device’s pointer.

Under these normal circumstances, at time t0, object O is in a superposition relative to both M and S.  (Said another way, relative to M and S, there is no fact at t0 about the location of O at A or B.)  Its being in a superposition is what makes possible an interference experiment on O to demonstrate its superposition state.  Skipping ahead to time t2, the scientist S is correlated to M and O – i.e., the object’s position at B, for example, is correlated with the device’s pointer indicating “B” and the scientist’s observation of the device indicating “B.”  At time t2, object O is no longer in a superposition relative to either M or S.  (Said another way, relative to M and S, there is a fact at t2 about the location of O at position A or B.)  Consequently, at t2 it is not possible, even in principle, for the scientist S to do an interference experiment on object O or device M to demonstrate a superposition, because they aren’t.  It is not a question of difficulty; I am simply noting the (hopefully uncontroversial) claim that by time t2, the position of object O is already correlated to that of the scientist S, so he now cannot physically demonstrate, via an interference experiment, that there is no fact about O’s location at A or B relative to him.

Let me summarize.  At t0, object O is in a superposition relative to S, so scientist S could in principle demonstrate that with a properly designed interference experiment.  Device M, however, is well localized relative to S, so scientist S would be incapable at t0 of showing M to be in a superposition.  At t2, neither O nor M is in a superposition relative to S, so S obviously cannot perform an interference experiment to prove otherwise.  The only question remaining is: what is the state of affairs at time t1 (or t1+Δt)?[6]  The standard narrative in quantum mechanics, which follows directly from the assumption of U, is the following von Neumann chain:

Equation 1:

t0:                     |O> |M> |S>

                        = (|A> + |B>) |M> |S>

t1 (or t1+Δt):    (|A> |MA> + |B> |MB>) |S>

t2:                    |A> |MA> |SA> + |B> |MB> |SB>

According to Eq. 1, at time t1 object O and device M are correlated to each other but scientist S is uncorrelated to O and M.  Said another way, O and M are well localized relative to each other (i.e., there is a fact about O’s location relative to M) but S is not well localized to O or M (i.e., there is not a fact about the location of O or M relative to S).  If that is true, then scientist S would be able, at least in principle, in an appropriate interference experiment, to demonstrate that object O and device M are in a superposition relative to him.  No one claims that such an experiment would be easy, but as long as there is some nonzero time period (in this case, t2 - t1) in which such an experiment could be done, then maybe it’s just a question of technology.  The problem, as I will explain below, is that there is no such time period.  The appearance of a nonzero time period (t2 – t1) in Eq. 1 is an illusion caused by failure to keep track of what the letters “A” and “B” actually refer to in each of the terms.

Let’s assume Eq. 1 is correct: that at time t1, the location of O is correlated to M but is not correlated to S.  That means that the location at which M measured O, which is what determines the macroscopic pointer state to which M will evolve, is not correlated to the location of O relative to S.  Consequently, the macroscopic pointer state to which M will evolve will correlate to the location of O relative to M at t1, but because that location of O (relative to M) is not correlated to its location relative to S, the macroscopic pointer state of M will itself be uncorrelated to O’s location relative to S.  Then, at t2, S’s observation of M’s pointer will therefore be uncorrelated to O’s location relative to him. 

Let me reiterate.  Object O is in a superposition of position eigenstates |A>S and |B>S relative to scientist S.  He asks a simple question: “Will I find it in position A or B?”  To answer the question, he uses a measuring device M that is designed to measure the object’s position and indicate either output “A” or “B.”  But if Eq. 1 is correct, then when he looks at the device’s output, a reading of “A” does not tell him where the object was measured relative to him, which is what he was trying to determine!  Rather, the device’s output tells him where the object was measured relative to the device, to which, at time t1, he was uncorrelated.

If Eq. 1 is correct at t1 that M is in a superposition relative to S (by virtue of its entanglement with object O), then the device’s measurement and subsequent evolution are uncorrelated to the location of object O relative to scientist S.  In other words, if Eq. 1 is correct, then as far as scientist S is concerned, measuring device M didn’t measure anything at all.  Instead, the macroscopic output of the device M would only correlate to the object’s location relative to S if M was well correlated to S at time t1, in which case Eq. 1 is wrong.

I should stress that the current narrative in physics is not just that Eq. 1 is possible, but that a comparable von Neumann chain occurs in every quantum mechanical measurement, big or small.  At t1, device M, but not scientist S, is correlated to the position of object O.  But what I’ve just shown is that if that’s true, then the position of O to which M is correlated is a different position of O than the scientist S intended to measure, such that the device’s output will necessarily be uncorrelated – and thus irrelevant – to the scientist’s inquiry.  If Eq. 1 is correct – if macroscopic device M, which is correlated to object O, can be in a superposition relative to scientist S – then measuring devices aren’t necessarily measuring devices and the very foundations of science are threatened.

Conundrum as this may be, it’s not even the whole problem with Eq. 1.  We have to ask how it could be that the measuring device failed.  Remember that what the scientist wants to measure is the object in state |A>S or |B>S, but the device M is only capable of measuring the object in state |A>M or |B>M.  When he starts the experiment at t0, he and device M are already well correlated, the presumption being that a measurement by the device of |A>M, when observed by the scientist, will correlate to |A>S.  But if Eq. 1 is correct, then the correlation event at t1 is one that guarantees that this can’t happen, which means that at t1, |A>M ≠ |A>S.  So even though |A>M ≈ |A>S at t0, Eq. 1 implies that |A>M ≠ |A>S at t1 (and by a significant distance).  That is, the quantum fuzziness between device M and scientist S (both macroscopic systems) would have to grow from essentially zero to a dimension comparable to the distance d separating locations A and B.  The analysis in Section II, particularly regarding relative coherence lengths and wave packet dispersion, shows that such a growth over any time period, and certainly the short period from t0 to t1, is impossible in principle.

Let me paraphrase.  At t1, device M has measured object O relative to it, so there is a fact about O’s location relative to M.  But if we stipulate as in Eq. 1 that there is not a fact about O’s location relative to S (by claiming that it’s still in a superposition relative to S), then what M has measured as position A (|A>M) might very well correspond to what S would measure as position B (|B>S) – or more generally, M’s indicator pointer will not correlate to O’s location relative to S.  That just means that, at t1, M did not measure the location of O relative to S.  The only way this could have happened is if |A>M and |A>S, which were well correlated at time t0, had already become adequately uncorrelated via quantum dispersion by time t1.  This is physically impossible.  Therefore Eq. 1 is incorrect: at no point can scientist S measure device M in a superposition.

D.        The Argument in Drawings

In this section, I’ll provide a comparable logical argument with reference to drawings.  In Fig. 1a, object O is shown at time t0 in a superposition of position eigenstates corresponding to locations at AS and BS relative to scientist S, where the object O is shown crosshatched to represent its superposition, relative to S, over two locations.  Measuring device M has slots (a) and (b) and is configured so that detection of object O in slot (a) will, due to a semi-deterministic causal amplification chain, cause device M to evolve over nonzero time Δt to a macroscopic pointer state in which a large arrow indicator points to the letter “A,” and vice versa for detection of object O in slot (b).  Because the device’s detection of object O in slot (a) actually corresponds to measurement of the object O at location AM relative to M (and vice versa for slot (b)), the device M is placed at time t0 so that AM ≈ AS and BM ≈ BS for the obvious reason that the scientist S intends to measure the object’s location relative to him and therefore wants the device’s indicator to correlate to that measurement.  Finally, the experiment is designed so that the initial correlation event between object O and device M occurs at time t1, device M evolves to its macroscopic pointer state by time t1+Δt, and scientist S reads the device’s pointer at t2.

Fig. 1a

Figs. 1b and 1c show how the scientist might expect (and would certainly want) the system to evolve.  In Fig. 1b, the locations of O relative to M and S are still well correlated (i.e., AM ≈ AS and BM ≈ BS), so the device’s detection of object O in slot (a) correlates to the object’s location at AS.[7]  Then, in Fig. 1c, device M has evolved so that the indicator now points to letter “A,” correlated to the device’s detection of object O in slot (a).  Then, when scientist S looks at the indicator at time t2, he will observe the indicator pointing at “A” if the object O was localized at AS and “B” if it was localized at BS, which was exactly his intention in using device M to measure the object’s position.

         

Fig. 1b                                                             Fig. 1c

Notice, however, that at time t1 the object O is not in a superposition relative to S, nor is device M (which is correlated to object O).  At t1, object O is indeed localized relative to device M, and since AM ≈ AS and BM ≈ BS, it is localized relative to scientist S.  We don’t know, of course, whether object O was detected in slot (a) or (b), and Fig. 1b only shows the first possibility, but it is in slot (a) or (b) (with probabilities that we can calculate using the Born rule), with slot (a) correlated to AS (which is localized relative to S) and slot (b) correlated to BS (which is also localized relative to S).  If that weren’t the case, then object O’s position would still be uncorrelated to device M, which negates the correlation event at t1.  In other words, at time t1 in Fig. 1b, object O is localized at AS or BS – i.e., there is a fact about its location relative to S – whether or not S knows this.[8]  Because object O is localized relative to S at t1, S cannot do an interference experiment to show O in superposition, nor can S show device M, which is correlated to O, in superposition.

Now, suppose we demand, consistent with Eq. 1, that at time t1, scientist S can, in principle, with an appropriately designed interference experiment, demonstrate that object O and device M are in a superposition (relative to S).  That requirement implies that the object’s location, as measured by M via the correlation event at t1, does not correlate to the object’s location relative to S.  The device’s detection at t1 of the object O in, for example, slot (a), which corresponds to its measurement of the object at AM, cannot correlate to the location of the object at AS – otherwise S would be incapable of demonstrating O (or M, to which O is correlated) in superposition.  Thus, to ensure that object O remains unlocalized relative to S when the correlation event at t1 localizes object O relative to M, that location which M measures as AM by detection of object O in slot (a) cannot correlate to location AS. 

Fig. 2a

This situation is shown in Fig. 2a in which both object O and device M are shown in a superposition of position eigenstates relative to S.  The object’s crosshatching, as in Fig. 1a, represents its superposition, relative to S, over locations AS and BS.  Analogously (but without crosshatching), device M localized at MA is shown superimposed on device M localized at MB.  Importantly, MA is the position of device M that would measure the position of object O at AM (by detecting it in slot (a)) as AS, while MB is the position of device M that would measure the position of object O at AM (by detecting it in slot (a)) as BS.  Because O remains uncorrelated to S at t1 (as demanded by Eq. 1), the measuring device M that detects O in slot (a) must also be uncorrelated to S at t1.  Again, the same is true for device M that detects O in slot (b), which is not shown in Fig. 2a.  What is demonstrated in Fig. 2a is that the correlation event at t1 between device M and object O that localizes O relative to M requires that M is not correlated to S, thus allowing S to demonstrate M in a superposition, as required by Eq. 1.  Then, in Fig. 2b, at time t1+Δt, device M has evolved so that the indicator now points to letter “A,” correlated to the device’s detection of object O in slot (a). 

Fig. 2b

 

However, now we have a problem.  In Fig. 2b, the pointer indicating “A,” which is correlated to the device’s localization of object O at AM, is not correlated to the object’s localization at AS.  When the scientist S reads the device’s indicator at time t2, it is not that the output is guaranteed to be wrong, but rather that the output is guaranteed to be uncorrelated to the measurement he intended to make.  Worse, it’s not just that the output is unreliable – sometimes being right and sometimes being wrong – it’s that the desired measurement simply did not occur.  The correlation event at time t1 did not correlate the scientist to the object’s location relative to him.

Therefore, to guarantee that object O (and device M, to which it is correlated) is in superposition relative to scientist S at t1, as required by Eq. 1, the location AM as measured by device M cannot correlate to location AS relative to scientist S; thus there is no fact at t1 about whether the measurement at AM (which will ultimately cause device M to indicate “A”) will ultimately correlate to either of locations AS or BS relative to S.  (Similarly, there is no fact at t1 about whether location BM will correlate to either AS or BS.)  That is only possible if that location which device M would measure at t1 as AM could be measured by scientist S as either AS or BS, which is only possible if AM ≠ AS.

To recap: At t0 the scientist S sets up the experiment so that AM ≈ AS and BM ≈ BS, which is what S requires so that measuring device M actually measures what it is designed to measure.  If Eq. 1 is correct, it implies that at time t1, AM ≠ AS and BM ≠ BS.

This has two consequences.  First, we need to explain how (and whether) device M could become adequately delocalized relative to scientist S so that AM ≠ AS and BM ≠ BS in the time period from t0 to t1.  Remember, we are not talking about relative motion or shifts – we are talking about AM and AS becoming decorrelated from each other so as to be in a location superposition relative to each other.  In other words, how do AM and AS, which were well localized relative to each other at time t0, become so “fuzzy” relative to each other via quantum wave packet dispersion that AM ≠ AS at time t1?  They don’t.  As long as the relative coherence length between two objects is small relative to the distance d separating distinct location eigenstates, then the situation in which AM ≠ AS cannot happen over any time period. 

Second, the quantum amplification in a von Neumann chain depends on the ability of measuring devices to measure what they are intended to measure.  A state |A>S + |B>S can only be amplified through entanglement with intermediary devices if those terms actually become correlated to states |A>S and |B>S, respectively.  But if, as required by Eq. 1, there is some nonzero time period (t2 - t1) in which scientist S could in principle measure M and O in a superposition, then the device’s measurement of the object’s location relative to it cannot correlate to the object’s location relative to S, in which case future states of S cannot be correlated to either |A>S or |B>S.  Eq. 1 is internally inconsistent and is therefore false.  There is no time period in which scientist S can measure M and O in a superposition.

E.        The Argument in Equations

A quick warning: as discussed in Section II(b), the QM mathematical formulism is the cause of the measurement problem and inherently cannot be part of the solution.  The problem with Eq. 1, which follows directly from U and has been shown to be problematic in the previous sections, will not be apparent by using the traditional tools and equations available in QM.  In the following analysis I will explain and adopt a new nomenclature that I hope will be helpful in relaying the arguments of the prior sections. 

Another quick warning.  The assumption that SC and WF, for example, are experimentally possible in principle depends on the ability of an external observer to subject them to a “properly designed interference experiment,” which is one in which the chosen measurement basis is adequate to reveal interference effects between the separate terms of the superposition.  No one denies that the required measurement basis for revealing a cat in superposition over |dead> and |alive> states would be ridiculously complicated and extremely technologically challenging.[9]  However, there are some, such as Goldstein (1987), who claim that every measurement is ultimately a position measurement.  If so, then no experiment could ever demonstrate a complicated macroscopic quantum superposition like SC.  Further, as I’ll discuss in more detail in Section F, the measurement basis required to demonstrate SC is also one that guarantees that SC does not exist, leading to a contradiction that, I will argue, renders moot any seeming logical paradox.

Regarding nomenclature: by state |A>S, I mean the state of an object O that is located at position A relative to the scientist S, by which I mean a state in which there is a fact about its location relative to S, whether or not S knows it.  And what does that mean?  It means that if O is in state |A>S at time t0, then S will not, after t0, make any measurements, have any experiences, etc., that are inconsistent with that fact or even, more importantly, any of its consequences.  And that certainly includes interference experiments.  Because |A>S is a state of object O located at position A relative to scientist S, it implies a state of the scientist S that is correlated to the location of O at position A relative to him.  The scientist S in that state, which I’ll write |SOA>, may or may not ever measure the location of object O, but if he does, he will with certainty find object O at position A (or somewhere that is logically consistent with the object having been located at position A when the object was in state |A>S).[10]  Said differently, |A>S is a state of object O in which scientist S would be incapable of measuring O in orthogonal state |B>S, state |A>S + |B>S, or any future state logically inconsistent with |A>S.

For instance, imagine if whether it rains today hinges on some quantum event that is heavily amplified, such as by chaotic interactions.  (Indeed, Albrecht and Phillips (2014) brilliantly argue that all probabilistic effects, certainly including weather, are fundamentally quantum.)  Specifically, imagine that a tiny object, located in Asia and in spin superposition |up> + |down>, was “measured” by the environment in the {|up>,|down>} basis by an initial correlating interaction or event, followed by an amplification whose definite mutually exclusive outcomes, correlated to the object’s measurement as “up” or “down,” are that it either will or will not, respectively, rain today in Europe.  If that object were in fact in state |up>, in which case it will rain today in Europe, then no observer would make any measurements or have any observations that are inconsistent with that fact.  Of course, the observer in Europe would not immediately observe that fact or its consequences, but once the fact begins to manifest itself in the world, that observer will eventually observe its effects – notably rain.  That observer – the one correlated to observing rain – now lives in a universe in which he will not and cannot make a contradictory observation (i.e., one logically inconsistent with the fact of |up> or its consequences).

Of course, a superposition is fundamentally different.  For an object in state |A>S + |B>S, there is no fact about the object’s location at position A or B relative to scientist S.  While |A>S is a state in which O is in fact located at A relative to S, which implies that S is in state |SOA> that is correlated to the location of O at position A relative to him, it is a mistake to assume that |SOA> exists without |A>S – i.e., it is a mistake to assume that they are already correlated prior to a correlating or entangling event.  After all, prior to a correlation event, the state of S can mathematically be written in lots of different bases, most of which would be useless or irrelevant.  Even though it may be correct that an object O is in state |A>S + |B>S, that same superposition can be written in different measurement bases, and the state in which O will be found upon measurement will depend on the relevant measurement basis.  So just as O can be written in state |A>S + |B>S (among others) and S can be written in state |SOA> + |SOB> (among others), neither |A>S nor |SOA> come into being until, in this case, a position measurement correlates them.  Before the correlation event, there is no object O in state |A>S just as there is no scientist S in state |SOA>, while after the correlation event there is.

Let me elaborate.  If object O is in state |A>S + |B>S, then it is in fact not in either state |A>S or |B>S, which also means that the scientist S is not in state |SOA> or |SOB>.  Remember that the scientist in state |SOA>, if he measures object O, will with certainty find it at position A.  But if object O is in fact in state |A>S + |B>S, there is no such scientist.  That the state of O can be written as |A>S + |B>S implies that the state of S can be written as |SOA> + |SOB>.  Just as object O is in neither state |A>S nor |B>S (or, stated differently, there is no object O in state |A>S or |B>S) and there is therefore no fact about its location at A or B relative to S, we can also say that scientist S is in neither state |SOA> nor |SOB> and there is no fact about whether he would with certainty find O at position A or B.  Until a measurement event occurs between O and S that correlates their relative positions, there is no scientist S that would with certainty find object O at A (or B), just as there is no object in state |A>S or |B>S.  It’s not an issue of knowing which state the scientist is in, for if S were actually in |SOA> or |SOB> but did not know which, then he was mistaken about being in state |SOA> + |SOB>.  That is, before the correlation event, there is no scientist in state |SOA> or |SOB>.  Rather, what brings states |SOA> and |SOB> (as well as |A>S and |B>S) into existence[11] is the event that correlates the relative positions of S and O:

Equation 2:

t0:         |O> |S> = (|A>S + |B>S) |S> = (|A>S + |B>S) (|SOA> + |SOB>)

            = |A>S |SOA> + |B>S |SOA> + |A>S |SOB> + |B>S |SOB>

t2 (event correlating their positions): |A>S |SOA>  + |B>S |SOB>

Note that at time t0, the scientist in state |S> is still separable (i.e., unentangled) with |O> and can, in principle, demonstrate O in a superposition relative to him.  However, the correlation event at t2 entangles S with O so that no scientist (whether in state |SOA> or |SOB>) can measure O in a superposition.  Mathematically, the correlation event eliminates incompatible terms, leaving only state |SOA> correlated to |A>S and state |SOB> correlated to |B>S.  States |B>S and |SOA>, for example, are only incompatible from the perspective of position measurement.  If the correlation event is one that measures O in a different basis, then each of |B>S and |SOA> can be written in that basis and the correlation event caused by the measurement will not necessarily eliminate all terms.[12]  This point further underscores that writing the state of S as |SOA> + |SOB>, and its expansion in Eq. 2, are purely mathematical constructs until the event at t2 that correlates the positions of O and S brings |SOA> and |SOB> into existence and allows us to eliminate incompatible terms.

Let’s return to the original example in which scientist S utilizes intermediary device M at time t1 to measure the position of object O relative to him, which is initially in state |A>S + |B>S.  Of course, Weak Relativity requires that device M is only capable of measuring positions relative to it, but scientist S has set up the experiment so that at time t0, |A>M ≈ |A>S and |B>M ≈ |B>S.  In the following nomenclature, |MOA>, for example, is a state of device M correlated to localization of object O at position AM (relative to M).  M in state |MOA> can certainly try to measure O in a basis other than position, but the existence of M in state |MOA> implies that O has already been localized at AM so that the outcome of a subsequent measurement will not be inconsistent with its initial localization at AM.  It is important to note that |MOA> is not itself a macroscopic pointer state; rather, assuming device M is designed correctly[13], |MOA> is a state that cannot evolve to a macroscopic pointer state correlated to object O located at BM.  In other words, a macroscopic pointer state of M indicating “A” will be correlated to |MOA> and not |MOB>.  Therefore, I’ll write that pointer state, which evolves from state |MOA> over nonzero time Δt, as |MAOA>.  Using this nomenclature, we can expect, according to the assumption of U, the following von Neumann-style measurement process:

Equation 3:

t0:         (|A>S + |B>S) |M> |S> ≈ (|A>M + |B>M) |M> |S>

= (|A>M + |B>M) (|MOA> + |MOB>) (|SOA> + |SOB>)

t1 (event correlating positions of O and M):   (|A>M |MOA> + |B>M |MOB>) (|SOA> + |SOB>)

t1+Δt:   (|A>M |MAOA>  + |B>M |MBOB>) (|SOA> + |SOB>)

t2:        |A>S |MAOA> |SAOA> + |B>S |MBOB> |SBOB>

At t1, the event between O and M correlates their positions, thus eliminating incompatible terms and ultimately entangling O with M so that they are no longer separable.  At t1, there is no M that can show O in a superposition (of position eigenstates relative to M). 

Eq. 3 assumes that the event correlating the scientist to the rest of the system does not occur until time t2.  It assumes that at t1, |S> is separable from (i.e., unentangled/uncorrelated with) states of device M and object O and remains separable until an entangling event at time t2.  If that’s true, then while |S> can be written as |SOA> + |SOB> (as above), it can also be written in lots of incompatible ways whose mathematical relevance depends on the nature of the measurement event that correlates S to M and O.  However, for |S> to be separable at t1, there cannot have already been an event that correlates S to M and O.  Is that true?  I will argue below that because M and S are already very well correlated in position (i.e., |A>M ≈ |A>S and  |B>M ≈ |B>S), the event at t1 correlating the positions of O and M is one in which M measures the position of O relative to S, which ultimately correlates the positions of O and S, preventing S from being able to measure O or M in a relative superposition.

Prior to the correlation event at t1, object O can be written as |A>M + |B>M (i.e., the position basis relative to M), |P1>M + |P2>M + |P3>M + ... (i.e., the momentum basis relative to M), and various other ways depending on the measurement basis.  It is the correlation event that determines which basis and thus brings into existence one set of possibilities versus another.  So it is the correlation event between M and O, which measures O in the position basis relative to M, that brings into actual existence states |A>M and |B>M.  That is to say, after t1, states |A>M and |MOB> are no longer compatible because O in fact was measured in the position basis by M and state |A>M is what was measured by |MOA> (just as state |B>M is what was measured by |MOB>).  Relative to M at t1, O is no longer in superposition; it is in fact located at either AM or BM.  One might object with the clarification that “it is in fact located at either AM or BM relative to M,” but that’s redundant as positions AM or BM already reflect reference to device M.  The correlation event at t1, as a matter of fact, localizes the object O at either AM or BM.  The only question is what meaning these positions have, if any, for scientist S. 

In other words, in an important sense, the event at t1 does correlate the scientist to the object: she now lives in a universe in which O is located at AM or one in which O is located at BM, because that is exactly what it means for her to say that device M measured the position of O at t1.  Said another way, she in fact lives in a universe in which device M has measured object O at AM or one in which M has measured O at BM, even though she does not yet know which, and whether or not |A>M and |B>M are semiclassical position eigenstates from her perspective.  This is necessarily true, for that is exactly what it means to assert that a measurement event at t1 correlates M and O. 

This point is so important and fundamental that it is worth repeating.  The statement, “M measured the position of O,” where O was initially in state |A>M + |B>M, means that either O was localized at AM or else at BM; if it did not measure O at one of those locations, then “M measured O” has no meaning.  So when M measures O at t1, object O is no longer in superposition |A>M + |B>M; scientist S now lives in a world in which device M has measured the position of object O, and that position is either AM or BM, not a superposition.  Proponents of U and/or MWI are certainly free to say that M measured O at both AM and BM in different worlds.  Perhaps the universe “fissions” so that one device, in state |MOA>, is correlated to the object located at AM while another, in state |MOB>, is correlated to the object located at BM.  In that case, scientist S also fissions so that one scientist – let’s call her state |SOAm> – is correlated to |A>M |MOA> and another, in state |SOBm>, is correlated to |B>M |MOB>.

Thus the object O at time t1 is not in superposition |A>M + |B>M from the scientist’s (or anyone’s) perspective, but that does not tell us anything about whether the object O is in a superposition relative to scientist S or whether a position measurement by S on O would have some guaranteed (if unknown) outcome.  Specifically, consider the scientist in state |SOAm> who is correlated to the object in state |A>M.  If, for example, |A>M = |A>S + |B>S (in other words, if the location of O at AM is itself a superposition over locations AS and BS) then O remains in a superposition relative to S.  Scientist S would remain uncorrelated to the object’s position until after she measures it.  The problem with this scenario is twofold, as broached in previous sections.  First, if |A>M is indeed uncorrelated to |A>S, then the device’s macroscopic pointer state, as observed by the scientist at t2, will necessarily be uncorrelated to the measurement that the scientist intended to make – specifically, the location of O at AS or BS.  But even if one is willing to reject the phrase “quantum measurement” as an oxymoron, the bigger problem is that there is no physical means, even in principle, by which states |A>M and |A>S, which were well correlated at t0, could become adequately uncorrelated by some arbitrary time t1.

So, given that |A>M ≈ |A>S and |B>M ≈ |B>S at t0 through to time t1, then just as the object O is no longer in superposition |A>M + |B>M at t1, it is also not in superposition |A>S + |B>S.  In this case, the scientist (in state |SOAm>) who is correlated to the object in state |A>M is also correlated to the object in state |A>S, which implies that the scientist is also in state |SOA> – i.e., she now lives in a universe in which object O was localized at AS at t1 and she will not measure or observe anything in conflict with that fact.  Thus, if preexisting correlations between M and S are such that |A>M ≈ |A>S and |B>M ≈ |B>S, then S is not separable from M and O at t1 because the event that correlates the positions of M and O will simultaneously correlate the positions of S and O.  Therefore, once the positions of M and O have been correlated, there is no time period – not just a small time, but zero time – in which S is separable and can measure M or O in a superposition.

An alternative explanation is this.  The correlation event at t1 brings into existence |A>M alongside |MOA> (as well as |B>M alongside |MOB>).  But because |A>M ≈ |A>S and |B>M ≈ |B>S , both |A>S and |B>S are also inevitably brought into existence.  But |A>S is a state of object O that is located at AS relative to S; if it exists, then there must be a corresponding scientist state |SOA> that would measure O at AS.

Prior to the correlating event at t1, the states of object O and device M could have been written, mathematically, in uncountably different ways depending on the chosen basis, but that freedom disappears upon the basis-determining correlation event.  The basis of measurement is what calls into existence the various possible states of O and M.  The only question is whether that correlating event can affect the existence of possible states of other objects to which M is already correlated.  I think the answer is clearly yes: if a correlating event can call into existence state |A>M, which implies the existence of correlated state |MOA>, and if |A>M ≈ |A>S, does this not also imply the existence of correlated state |SOA>?  In light of the above analysis, Eq. 3 is corrected as follows:

Corrected Equation 3:

t0:         (|A>S + |B>S) |M> |S> ≈ (|A>M + |B>M) |M> |S>

= (|A>M + |B>M) (|MOA> + |MOB>) (|SOAm> + |SOBm>)

t1 (event correlating positions of O and M):   (|A>M |MOA>  + |B>M |MOB>) (|SOAm> + |SOBm>)

= |A>M |MOA> |SOAm> + |B>M |MOB> |SOBm>

≈ |A>S |MOA> |SOA> + |B>S |MOB> |SOB>

t1+Δt:   |A>S |MAOA> |SOA> + |B>S |MBOB> |SOB>

t2:         |A>S |MAOA> |SAOA> + |B>S |MBOB> |SBOB>

So what’s wrong with Eqs. 1 and 3?  It’s simple.  They fail to consider the effect of preexisting correlations between systems.  By assuming that O does not correlate with S at t1 (allowing O and M to exist in superpositions relative to S until t2), it follows that M cannot correlate to S, which is possible only if |A>M ≠ |A>S at t1. But not only is this a physically impossible evolution if |A>M ≈ |A>S at t0, it implies that the measuring device M didn’t (and therefore cannot) succeed.  Said differently: If device M measures O relative to S, then Eq. 1 is wrong at t1 (because the correlation with S would be simultaneous and therefore S can’t show superposition), but if device M does not measure O relative to S, then Eq. 1 is wrong at t2 because S does not get correlated to O’s location relative to him (and the device M is useless). 

The problem with Eqs. 1 and 3 is that they assume that S’s observation of M’s macroscopic pointer state at t2 is the event that correlates S with O.  That assumption is indeed the very justification for SC, because it allows a nonzero time period (t2 – t1) in which a cat, whose fate is correlated to some quantum event, exists (and can in principle be measured) in a superposition state relative to an external observer.  If the observer remains uncorrelated to the outcome of the quantum event until after observing the cat is its “macroscopic pointer state” of |dead> or |alive>, then the observer can (in principle) show SC in a superposition over these two states prior to his observation.  But as we can see in the above Corrected Eq. 3, the event correlating the positions of O and S – which is the same one correlating the positions of O and M – is independent of M’s future macroscopic pointer state and whether or not S observes it.

F.         Contradictions Abound

I have argued above that the statement, “M measured the position of O at t1,” only has meaning if it also correlates the scientist (and any other observer) to a world in which the object is measured at position AM (or one in which the object is measured at BM).  And because positions relative to M are so well correlated to positions relative to S (and every other large object), the statement “The positions of M and O are correlated at t1” necessarily implies “The positions of S and O are correlated at t1.”  There is no time period after t1 in which O or M are (or can be demonstrated) in a superposition relative to her.  In Corrected Eq. 3, I have argued that the correlation event between M and O also correlates S to O by creating states |SOAm> and |SOBm> so as to produce entangled state |A>M |MOA> |SOAm> + |B>M |MOB> |SOBm>, and that in this state |S> appears to be inseparable. 

Despite my analysis in the previous sections, devout adherents of the assumption of U (and the in-principle possibility of creating SC, for example) are unlikely to be swayed and will insist that |S> is separable at t1.  So let me accommodate them.  What would be required to maintain |S> as separable at t1 to ensure that S can measure O and M in a superposition?  Easy!  Just set up the experiment so that |A>M = |B>M.  That would yield a combined state in which |S> is certainly separable, but it is also one in which device M didn’t actually measure anything.  So, starting from a situation in which “M measured the position of O at t1,” in which case scientist S becomes simultaneously entangled to O by nature of that measurement, all we must do to ensure the separability of S is to change the world so that it is not the case that “M measured the position of O at t1.”  In a very real sense, the only way to separate |S> from the entangled state caused by the correlation event between M and O is to retroactively undo that correlation event.  In other words, the statement “M measured O at t1” implies a correlation with S that renders it inseparable, unless we are able to “undo” (or make false) the statement.

And lest I be accused of arguing tongue-in-cheek, let me point out an intriguing fact about U, nearly absent from the academic literature. Ultimately, for S to measure the correlated system M/O in a superposition relative to her, she must measure it in an appropriate basis that would reveal interference effects.  Crucially, the measurement process in that basis is one that would by necessity reverse the process that correlated M and O and would thus “undo” the correlation.  For instance, when someone asserts that SC can be created and measured in an appropriately designed interference experiment, such an experiment is necessarily one that would “turn back the clock” and undo every correlation event.[14]

Let’s forget for a moment how ridiculously technologically difficult it would be to perfectly time-reverse all the correlating events inside the SC box.  Here is a much bigger problem.  If we open the box and look – that is, measure the cat in basis {|dead>,|alive>} – we will never obtain evidence that the cat (or the system including the cat) was ever in a superposition.  But if we somehow succeed in measuring the system in a basis that would reveal interference effects, then it will retroactively undo every correlation and un-fact-ify every fact that could potentially evidence the existence of a cat in state |dead> + |alive>.  So in neither case is there, or can there be, any scientific data to assert that SC is an actual possibility (which follows from the inference of U).  SC cannot be empirically confirmed because any measurement that could demonstrate the necessary interference effects is one that retroactively destroys any evidence of SC.[15]  On this basis alone, the assertion that SC is a physically real possibility, which follows from the assumption of U, is simply not scientific.  Let me elaborate.  Consider this statement:

Statement Cat: “The measurement at time t1 of a radioactive sample correlates to the integrity of a glass vial of poison gas, and the vial’s integrity correlates at time t2 to the survival of the cat.” 

Let’s assume this statement is true; it is a fact; it has meaning.  A collapse theory of QM has no problem with it – at time t1, the radioactive sample either does or does not decay, ultimately causing the cat to either live or die.  According to U, however, this evolution leads to a superposition in which cat state |dead> is correlated to one term and |alive> is correlated to another.  Such an interpretation is philosophically baffling, leading countless students and scholars wondering how it might feel to be the cat or, more appropriately, Wigner’s Friend.  Yet no matter how baffling it seems, proponents of U simply assert that a SC superposition state is possible because, while technologically difficult, it can be demonstrated with an appropriate interference experiment.  However, as I pointed out above, such an experiment will, via the choice of an appropriate measurement basis that can demonstrate interference effects, necessarily reverse the evolution of correlations in the system so that there is no fact at t1 (to the cat, the external observer, or anyone else) about the first correlation event nor a fact at t2 about the second correlation event.  In other words, to show that U is true (or, rather, that the QM wave state evolves linearly in systems at least as large as a cat), all that needs to be done is to make the original statement false:

1)         Statement Cat is true;[16]

2)         U is true;

3)         To show U true, Statement Cat must be shown false.

4)         Therefore, U cannot be shown true.

This is nonsense.  To summarize: U is not directly supported by empirical evidence but is rather an inference from data obtained from microscopic systems.  The inference of U conflicts with empirical observations of macroscopic systems, giving rise to the measurement problem and subjecting the inference of U to a higher standard of proof, the burden of which lies with its proponents and remains unmet.  However, the nature of the physical world seems to enforce a kind of asymptotic size limit above which interference experiments, and verification of U in the realm in which it causes the measurement problem, seem FAPP impossible.  I argued in Section II(d) that this observation serves as evidence against an inference of U, providing a further hurdle to the proponent’s currently unmet burden of proof.

I then provided several novel logical arguments in Section III showing why preexisting entanglements between a scientist and measuring device guarantee that a measurement correlating the positions of the device and an object in superposition simultaneously correlate the positions of the scientist and the object.  As a result, there is no time at which the device is or can be measured in a superposition relative to the scientist, in which case U is false because there are at least some macroscopic superpositions, such as SC and WF, that cannot be verifiably produced, even in principle.  Further, I showed that even if such an interference experiment could be done, such an experiment would, counterintuitively, not show U to be true.  That is because if U is true then it applies to a statement about a series of events (measurements, correlations, etc.), but showing that U applies to that statement requires showing that statement to be false.  This contradiction confirms that U cannot, even in principle, be verified.

The final point I’d like to bring up is this.  Undoing a correlation between two atoms that are not themselves well correlated to other objects in the universe may not be technologically difficult.  The statement, “Two atoms impacted at time t1” only has meaning to the extent there is lasting evidence of that impact.  An experiment or process that time-reverses the impact can certainly undo the correlation, but then there is just no fact (from anyone’s perspective) about the original statement.  Quantum eraser experiments (e.g., Scully and Drühl (1982) and Kim et al. (2000)) are intriguing examples of this.

However, everything changes for macroscopic objects; cats, stars, and dust particles are already so well correlated due to past interactions that trying to decorrelate any two or more such objects is hopeless.  Perhaps the analysis of Section III can be boiled down to something like, “Preexisting correlations between M and S, which are large objects with insignificant relative coherence lengths, prevent M from ever existing or being measured in superposition relative to S.  When M correlates to O, it does not inherit the superposition of O independently of S (as suggested by linear dynamics); rather, S correlates to O simultaneously and transitively with M.”

Due to this transitivity of correlation, universal entanglement pervades the universe.  Everything is correlated with everything else and any experiment that aims to demonstrate a cat in quantum superposition by measuring it in a basis that decorrelates it from other objects is doomed to fail, not merely as a practical matter but in principle.  Even if there were a way to undo the correlations between the cat, the vial of poison, and the radioisotope, this could only be done by someone who was not already well correlated to the cat and who could manage to remain uncorrelated to it during the experiment.  This, in light of the prior analysis, is so ridiculously untenable that it warrants no further discussion.

REFERENCES

Aaronson, S., Atia, Y. and Susskind, L., 2020. On the Hardness of Detecting Macroscopic Superpositions. arXiv preprint arXiv:2009.07450.

Aharonov, Y. and Kaufherr, T., 1984. Quantum frames of reference. Physical Review D30(2), p.368.

Albrecht, A. and Phillips, D., 2014. Origin of probabilities and their application to the multiverse. Physical Review D90(12), p.123514.

Deutsch, D., 1985. Quantum theory as a universal physical theory. International Journal of Theoretical Physics24(1), pp.1-41.

Giacomini, F., Castro-Ruiz, E. and Brukner, Č., 2019. Quantum mechanics and the covariance of physical laws in quantum reference frames. Nature communications10(1), pp.1-13.

Goldstein, S., 1987. Stochastic mechanics and quantum theory. Journal of Statistical Physics47(5-6), pp.645-667.

Kim, Y.H., Yu, R., Kulik, S.P., Shih, Y. and Scully, M.O., 2000. Delayed “choice” quantum eraser. Physical Review Letters84(1), p.1.

Loveridge, L., Busch, P. and Miyadera, T., 2017. Relativity of quantum states and observables. EPL (Europhysics Letters)117(4), p.40004.

Rovelli, C., 1996. Relational quantum mechanics. International Journal of Theoretical Physics35(8), pp.1637-1678.

Scully, M.O. and Drühl, K., 1982. Quantum eraser: A proposed photon correlation experiment concerning observation and" delayed choice" in quantum mechanics. Physical Review A25(4), p.2208.

Zych, M., Costa, F. and Ralph, T.C., 2018. Relativity of quantum superpositions. arXiv preprint arXiv:1809.04999.


[1] Having said that, if the particle had actually been in state |A> + |B>, then a future detection would also be consistent with its having been localized in slit A; only after many such experiments will the appearance (or lack) of an interference pattern indicate whether the original state had been |A> or |A> + |B>.

[2] We view the world as eigenstates of observables, so if Strong Relativity is correct, then so must the cat.  There is nothing special in this example about choosing the live cat’s perspective.  From the perspective of the dead cat, the lab is in the following equally ridiculous superposition: |lab that would measure a dead cat, which isn’t surprising, because it is dead> + |lab that is so distorted, whose measuring devices are so defective, whose scientists are so incompetent, that it would measure a dead cat as alive>.  The point of this example is to show that the impossibility of SC follows almost tautologically from the Strong Relativity of quantum superpositions.

[3] |A>M ≈ |A>S, for instance, does not say that location A is the same distance from M as from S.  Rather, it says that location A relative to M is well correlated to location A relative to S; there is zero (or inconsequential) quantum fuzziness between the locations; M and S see point A as essentially the same location.

[4] A SC state |alive> + |dead> corresponds to many macroscopic delocalizations, whether or not the centers of mass of |alive> and |dead> roughly correspond.  For instance, a particular brain cell in a cat in state |alive> would be located a significant distance from the corresponding brain cell in a cat in state |dead>.

[5] Unless otherwise stated, the word “superposition” in this analysis generally refers to a superposition of distinct semiclassical position eigenstates.

[6] The standard narrative does not really distinguish between the state at t1 and t1+Δt so I’ll treat them as the same time in the following equation.

[7] No collapse or reduction of the wave function is assumed in this example or anywhere else in this paper.  Fig. 1b simply shows the correlation between detection in slot (a) and location AS; there would also be a correlation (not shown) between detection in slot (b) and location BS.

[8] Actually, he can’t know this.  Whether or not S is “isolated” from M, the speed of light limits the rate at which S might learn about O’s localization.

[9] Although not all commentators are particularly forthright about this; Deutsch (1985) hides the complexity and difficulty of such a basis by representing them mathematically with a few symbols. 

[10] To clarify: if the object’s state is |A>S at t0, then physical evolution of the object over time limits where the object might be found in the future, such that scientist S in state |SOA> will never find object O at a location that is logically inconsistent with its state |A>S at t0.

[11] Again, throughout this analysis I assume that U is true.  For clarity, a collapse theory of QM would assert that after the correlation event at t1, the scientist assumes either state |SOA> or |SOB> – that is, after the measurement, he will observe that the state of object O has collapsed into either state |A>S or |B>S.  On the other hand, MWI would assert that after the event, both scientists exist in different worlds, one correlated to localization of object O at A and the other at B.  But until the correlation event, no theory or interpretation of QM claims that there are any scientists in states |SOA> or |SOB>.

[12] For instance, if measurement event correlates the momenta of O and M instead of position, then the term |B>S |SOA> will not, as a mathematical matter, disappear, but only because it can be written as a series of terms that includes, among others: |object has momentum P> |scientist will not measure object’s momentum other than P>, where P is some semiclassical momentum eigenstate.

[13] Actually, this is not a required assumption.  Whether or not device M is designed properly, M in state |MOA> cannot evolve to any state, macroscopic or not, that is correlated to object O having been located at orthogonal position BM.  In other words, if M in state |MOA> evolves to a macroscopic pointer state pointing to “B,” then we can conclude that M failed as a measuring device.

[14] Aaronson et al. (2020) correctly point out that being able to confirm a cat in a superposition requires “having the ability to perform a unitary that revives a dead cat.” 

[15] This assertion is true for all observers, including the cat.  If such an interference experiment could actually be performed, then no time elapsed from the perspective of the cat (and everything inside the box).  From the cat’s perspective, it never entered a SC superposition and thus there is nothing that it’s like to experience a SC (or WF) superposition.  Even if an external observer would measure time elapsed throughout the interference experiment – which I think is doubtful for many reasons that exceed the scope of this paper – the experiment is necessarily one such that there is no fact about the happening of any correlation events inside the SC box.

[16] Of course, I can certainly show, empirically, that Statement Cat is true, simply by setting up the experiment and watching it progress.