Showing posts with label quantum mechanics. Show all posts
Showing posts with label quantum mechanics. Show all posts

Monday, May 17, 2021

The (Quantum Computing) House of Cards

In the physics community, there is a house of cards built upon a nearly fanatical belief in the universality of quantum mechanics – i.e., that quantum wave states always evolve in a linear or unitary fashion.  Let’s call this fanaticism the Cult of U.

When I began this process a couple years ago, I didn’t realize that questioning U was such a sin, that I could literally be ostracized from an “intellectual” community by merely doubting U.  Having said that, there are a few doubters, not all of whom have been ostracized.  For instance, Roger Penrose, one of the people I most admire in this world, recently won the Nobel Prize in Physics, despite his blatant rejection of U.  However, he rejected U in the only way deemed acceptable by the physics community: he described in mathematical detail the exact means by which unitarity may be broken, and conditioned the rejection of U on the empirical confirmation of his theory.  As I describe in this post, Penrose proposes gravitational collapse of the wave function, a potentially empirically testable hypothesis that is being explored at the Penrose Institute.  In other words, he implicitly accepts that: a) U should be assumed true; and b) it is his burden to falsify U with a physical experiment.

I disagree.  In the past year, I’ve attempted (and, I believe, succeeded) to logically falsify U – i.e., by showing that it is logically inconsistent and therefore cannot be true – in this paper and this paper.  I also showed in this paper why U is an invalid inference and should never have been assumed true.  Setting aside that they have been ignored or quickly (and condescendingly) dismissed by nearly every physicist who glanced at them, all three were rejected by arvix.org.  This is both weird and significant.

The arXiv is a preprint server, specializing in physics (although it has expanded to other sciences), supported by Cornell University, that is not peer reviewed.  The idea is simply to allow researchers to quickly and publicly post their work as they begin the process of formal publication, which can often take years.  Although not peer-reviewed, arXiv does have a team of moderators who reject “unrefereeable” work: papers that are so obviously incorrect (or just generally shitty) that no reputable publisher would even consider it or send it for peer review by referees.  Think perpetual motion machines and proofs that we can travel faster than light.

What’s even weirder is that I submitted the above papers under the “history and philosophy of physics” category.  Even if a moderator thought the papers did not contain enough equations for classification in, say, quantum physics, on what basis could anyone say that they weren’t worthy of being refereed by a reputable journal that specializes in the philosophy of physics?  For the record, a minor variation of the second paper was in fact refereed by Foundations of Physics, and the third paper was not only refereed, but was well regarded and nearly offered publication by Philosophy of Science.  Both papers are now under review by other journals.  No, they haven’t been accepted for publication anywhere yet, but arXiv’s standard is supposed to be whether the paper is at least refereeable, not whether a moderator agrees with the paper’s arguments or conclusions! 

It was arXiv’s rejection of my third paper (“The Invalid Inference of Universality in Quantum Mechanics”) that made it obvious to me that the papers were flagged because of their rejection of U.  This paper offers an argument about the nature of logical inferences in science and whether the assumption of U is a valid inference, an argument that was praised by two reviewers at a highly rated journal that specializes in the philosophy of physics.  No reasonable moderator could have concluded that the paper was unrefereeable. As a practical matter, it makes no difference, as there are other preprint servers where I can and do host my papers.  (I also have several papers on the arXiv, such as this – not surprisingly, none of them questions U.)

But the question is: if my papers (and potentially others’ papers) were flagged for their rejection of U… why?!

You might think this is a purely academic question.  Who cares whether or not quantum wave states always evolve linearly?  For example, the possibilities of Schrodinger’s Cat and Wigner’s Friend follow from the assumption of U.  But no one actually thinks that we’ll ever produce a real Schrodinger’s Cat in a superposition state |dead> + |alive>, right?  This is just a thought experiment that college freshmen like to talk about while getting high in their dorms, right? 

Is it possible that there is a vested interest… perhaps a financial interest… in U?

Think about some of the problems and implications that follow from the assumption of U.  Schrodinger’s Cat and Wigner’s Friend, of course, but there’s also the Measurement Problem, the Many Worlds Interpretation of quantum mechanics, the black hole information paradox, physical reversibility, and – oh yeah – scalable quantum computing. 

Since 1994, with the publication of Shor’s famous algorithm, untold billions of dollars have flowed into the field of quantum computing.  Google, Microsoft, IBM, and dozens of other companies, as well as the governments of many countries, have poured ridiculous quantities of money into the promise of quantum computing. 

And what is that promise?  Well, I have an answer, which I’ll detail in a future post.  But here’s the summary: if there is any promise at all, it depends entirely on the truth of U.  If U is in fact false, then a logical or empirical demonstration that convincingly falsifies U (or brings it seriously into question) would almost certainly be catastrophic to the entire QC industry. 

I’m not suggesting a conspiracy theory.  I’m simply pointing out that if there are two sides to a seemingly esoteric academic debate, but one side has thousands of researchers whose salaries and grants and reputations and stock options depend on their being right (or, at least, not being proven wrong), then it wouldn’t be surprising to find their view dominating the literature and the media.  The prophets of scalable quantum computing have a hell of a lot more to lose than the skeptics.

That would help to explain why the very few publications that openly question U usually do so in a non-threatening way: accepting that U is true until empirically falsified.  For example, it will be many, many years before anyone will be able to experimentally test Penrose’s proposal for gravitational collapse.  Thus it would be all the more surprising to find articles in well-ranked, peer-reviewed journals that question U on logical or a priori grounds, as I have attempted to do.

Quoting from this post:

As more evidence that my independent crackpot musings are both correct and at the cutting edge of foundational physics, Foundations of Physics published this article at the end of October that argues that “both unitary and state-purity ontologies are not falsifiable.”  The author correctly concludes then that the so-called “black hole information paradox” and SC disappear as logical paradoxes and that the interpretations of QM that assume U (including MWI) cannot be falsified and “should not be taken too seriously.”  I’ll be blunt: I’m absolutely amazed that this article was published, and I’m also delighted. 

Today, I’m even more amazed and delighted.  In the past couple of posts, I have referenced an article (“Physics and Metaphysics of Wigner’s Friends: Even Performed Premeasurements Have No Results”), which was published in perhaps the most prestigious and widely read physics journal, Physical Review Letters, but only in the past few days have I really understood its significance.  (The authors also give a good explanation in this video.)

What the authors concluded about a WF experiment is that either there is “an absolutely irreversible quantum measurement [caused by an objective decoherence process] or … a reversible premeasurement to which one cannot ascribe any notion of outcome in logically consistent way.”

What this implies is that if WF is indeed reversible, then he does not make a measurement, which is very, very close to the logical contradiction I pointed out here and in Section F of this post.  While the authors don’t explicitly state it, their article implies that U is not scientific because it cannot (as a purely logical matter) be empirically tested at the size/complexity scale of WF.  This is among the first articles published in the last couple decades in prestigious physics journals that make a logical argument against U.

What’s even more amazing about the article is that it explicitly suggests that decoherence might result in objective collapse, which is essentially what I realized in my original explanation of why SC/WF are impossible in principle, even though lots of physicists have told me I’m wrong.  Further, the article openly suggests a relationship between (conscious) awareness, the Heisenberg cut between the microscopic and macroscopic worlds, and the objectivity of wave function collapse below that cut.  All in an article published in Physical Review Letters!

Now, back to QC.  After over two decades of hype that the Threshold Theorem would allow for scalable quantum computing (by providing for fault-tolerant quantum error correction (“FTQEC”)), John Preskill, one of the most vocal proponents of QC and original architects of FTQEC, finally admitted in this 2018 paper that “the era of fault-tolerant quantum computing may still be rather distant.”  As a consolation prize, he offered up NISQ, an acronym for Noisy Intermediate-Scale Quantum, which I would describe as: “We’ll just have to try our best to make something useful out of the 50-100 shitty, noisy, non-error-corrected qubits that we’ve got.”

Despite what should have been perceived as a huge red flag, more and more money keeps flowing into the QC industry, leading Scott Aaronson to openly muse just two months ago about the ethics of unjustified hype: “It’s genuinely gotten harder to draw the line between defensible optimism and exaggerations verging on fraud.”

Fraud??!!

The quantum computing community and the academic members of the Cult of U are joined at the hip, standing at the top of an unstable house of cards.  When one falls, they all do.  Here are some signs that their foundation is eroding:

·       Publication in reputable journals of articles that question or reject U on logical bases (without providing any mathematical description of collapse or means for empirically confirming it).

·       Hints and warnings among leaders in the QC industry that promises of scalable quantum computing (which inherently depends on U) are highly exaggerated.

I am looking forward to the day when the house of cards collapses and the Cult of U is finally called out for what it is.

Friday, May 14, 2021

Another Comment on “Physical Reversibility is a Contradiction”

Scott Aaronson, whose argument on reversibility of quantum systems I mentioned in this post, responded to it (and vehemently disagreed with it).  Here is his reply:

Your argument is set out with sufficient clarity that I can unequivocally say that I disagree.

Reversibility is just a formal property of unitary evolution.  As such, it has the same status as countless other symmetries of the equations of physics that seem to be broken by phenomena (charge,
parity, even just Galilean invariance).  I.e., once you know that the equations have some symmetry, you then reframe your whole problem as how it comes about that observed phenomena break the symmetry anyway.

And in the case of reversibility, I find the usual answer -- that it all comes down to the Second Law, or equivalently, the "specialness" of the universe's past state -- to be really compelling.  I don't see anything wrong with that answer.  I don't think there's something obvious here that the physics community has overlooked.

And yes, you can confirm by experiments that dynamics are reversible. To do so, you (for example) apply a unitary transformation U to an initial state |Ψ>.  You then CHOOSE whether to
(1) apply U-1, the inverse transformation, and check that the state returned to |Ψ>, or

(2) measure immediately (in various bases that you can choose on the fly), in order to check if the system is in the state U|Ψ>.

Provided we agree that Nature had no way to know in advance whether you were going to apply (1) or (2), the only way to explain all the results -- assuming they're the usual ones predicted by QM -- is that |Ψ> really did get mapped to U|Ψ>, and that that map was indeed reversible.  In your post, you briefly entertain this obvious answer (when you talk about lots of identically prepared systems), but reject it on the grounds that making identical systems is physically impossible.

And yet, things equivalent to what I said above -- by my lights, a "direct demonstration of reversibility" -- are now ROUTINELY done, with quantum states of thousands of atoms or even billions of
electrons (as with superconducting qubits).  Of course, maybe something changes between the scale of a superconducting qubit and the scale of a cat (besides the massive increase in technological difficulty), but I'd say the burden is firmly on the person proposing that to explain where the change happens, how, and why.


I sincerely appreciated his response... and of course disagree with it!  I’m going to break this down to several points:

You then CHOOSE whether to
(1) apply U-1, the inverse transformation, and check that the state returned to |Ψ>,

First, I think he is treating U-1 as a sort of deus ex machina.  If you don’t know whether a system is reversible, or how it can be reversed, just reduce it all down to a mathematical symbol corresponding to an operator (such as H, for Hamiltonian) and its inverse, despite the fact that this single operator might correspond to complicated and correlated interactions between trillions of trillions of degrees of freedom.  Relying on oversimplified symbol manipulation makes it harder to pinpoint potentially erroneous assumptions about the physical world.

Second, and more importantly, if you apply U-1, you cannot check that the state returned to |Ψ>.  Maybe (MAYBE!) you can check to see that the state is |Ψ>, but you cannot check to see that it “returned” to that state.  And while you may think I’m splitting hairs here, this point is fundamental to my argument, and his choice of this language indicates that he really doesn’t understand the argument, despite his compliment that I had set it out “with sufficient clarity.”

The reason you cannot check to see if the state “returned” to |Ψ> is because that requires knowing that the state was in U|Ψ> at some point.  But you can’t know that, nor can any evidence exist anywhere in the universe that such an evolution occurred, because then the state would no longer be reversible.  (You also can’t say that the state was in U|Ψ> by asserting that, “If I had measured it, prior to applying U-1, then I would have found it in state U|Ψ>,” because measurements that are not performed have no results.  This is the “counterfactuals” problem in QM that confuses a lot of physicists as I pointed out in this paper on the Afshar experiment.)  So if you actually apply U and then U-1 to an isolated system, this is scientifically indistinguishable from having done nothing at all to the system. 

or
(2) measure immediately (in various bases that you can choose on the fly), in order to check if the system is in the state U|Ψ>.  …In your post, you briefly entertain this obvious
answer (when you talk about lots of identically prepared systems), but reject it on the grounds that making identical systems is physically impossible.  And yet, things equivalent to what I said above -- by my lights, a "direct demonstration of reversibility" -- are now ROUTINELY done, with quantum states of thousands of atoms or even billions of electrons (as with superconducting qubits). 

In this blog post, I pointed out that identity is about distinguishability.  I didn’t say that it’s impossible to make physically identical systems.  It’s easy to make two electrons indistinguishable.  By cooling them to near absolute zero, you can even make lots of electrons indistinguishable.  But the only way to create Schrodinger’s Cat is to create two cats that even the universe can’t distinguish – i.e., not a single bit of information in the entire universe can distinguish them.  In other words, for Aaronson's argument (about superpositions of billions of electrons in superconducting qubits) to have any relevance to the question of SC, we would have to be able to create a cat out of fermions that even the universe can’t distinguish. 

Tell me how!  Don't just tell me that this is a technological problem that the engineers need to figure out.  And do it without resorting to mathematical symbol manipulation.  I'll make it "easy."  Let's just start with a single hair on the cat's tail.  Simply explain to me how the wave function of that single hair could spread sufficiently (say, 1mm) to distinguish a dead cat from a live cat.  Or, equivalently, explain to me how the wave functions of two otherwise identical hairs, separated by 1mm, could overlap.  Tell me how to do this in the actual universe in which even the most remote part of space is still constantly bombarded with CMB, neutrinos, etc.  So far, no one has ever explained how to do anything like this.

Of course, maybe something changes between the scale of a superconducting qubit and the scale of a cat (besides the massive increase in technological difficulty), but I'd say the burden is firmly on the person proposing that to explain where the change happens, how, and why.

I strongly disagree!  As I point out in “The Invalid Inference of Universality in Quantum Mechanics,” the assumption that QM always evolves in a unitary/reversible manner is an unjustified and irrational belief.  Anyway, my fundamental argument about reversibility, which apparently wasn’t clear, is perhaps better summarized as follows:

1)     You cannot confirm the reversibility of a QM system by actually reversing it, as it will yield no scientifically relevant information.

2)     The only way to learn whether a system has evolved to U|Ψ> is to infer that conclusion by doing a statistically significant number of measurements on physically identical systems.  That’s fine for doing interference experiments on photons and Buckyballs, but not cats. 


Friday, April 23, 2021

Physical Reversibility is a Contradiction

I’m working on a project/presentation on whether scalable quantum computers are possible.  A quantum circuit can be simplified as application of a unitary matrix to an initial state of qubits.  Unitary matrices represent reversible basis shifts, which means that the computation must be shielded from irreversible decoherence events (or subject to quantum error correction to the extent possible) until the purposeful measurement of qubits at the end of the computation.

The word “reversibility” has come up a lot in my reading.  Essentially, the idea is that physical laws seem, for the most part, to be the same whether time is run forward or backward.  For example, if you were shown a video of a planet orbiting some distant star, you would not be able to tell whether the video was being played forward or in reverse.  Yet we experience time to move in a particular direction (namely, the future).  This has led to a centuries-long debate about the “arrow of time”: whether physical laws are reversible or whether there is actually some direction built into the fabric of the physical world.

It’s time to nip it in the bud: the physical world is not time-reversible.

As an example of a typical argument for classical reversibility, imagine dropping a porcelain teapot on a wooden floor.  Of course, it will irreparably break into probably hundreds of pieces.  “In principle,” they say, “if you know the positions and trajectories of all those pieces, you can then apply forces that will completely reverse the process, causing the pieces to recombine to the original teapot.” 

But that’s crap.  We already know, thanks to the Heisenberg Uncertainty Principle (“HUP”), that the pieces don’t have positions and momenta to infinite precision.  That alone is enough to guarantee that any attempt to apply time-reversed forces to the pieces will, thanks to chaos, fail to result in a perfect recombination of the pieces.  (One of my favorite papers discusses how even “gargantuan” black holes become chaotic over time, thanks to HUP.)  This problem is only compounded by the fact that any measurement of the positions and/or momenta of the pieces will inevitably change their trajectories very slightly also. 

So quantum mechanics guarantees that the classical world is not and cannot be time-reversible.  But I’ve recently realized that the notion of time-reversibility in quantum mechanics is not only false… it’s actually a contradiction.  In Section F of this post, I had already realized and pointed out that there is something logically contradictory about the notion of Schrodinger’s Cat (“SC”) or Wigner’s Friend (“WF”).  (I copied the most relevant section of that post below.)

The idea is simple.  To actually create SC, which is a macroscopic superposition state, the cat (and its health) has to correlate to a vial of poison (and whether it is broken), which has to correlate to some quantum event.  These correlations are colloquially called “measurements.”  But to prove (or experimentally show) that the cat is in a macroscopic superposition state, you have to do an interference experiment that undoes the correlations.  In other words, to show that the measurements are reversible (as assumed by the universality of QM), you have to reverse the measurements to the extent that there is no evidence anywhere in the universe (including the cat’s own clock) that the measurements happened. 

Remember, scientific inquiry depends on evidence.  We start by assuming that SC is created in some experiment.  But then the only way to show that SC is created is… to show that it was not created.  The very evidence we scientifically rely upon to assert that SC exists must not exist.  Proving SC exists requires proving that it does not exist.  This is gibberish.  (David Deutsch tried to explain away this problem in this paper but failed.  Igor Salom correctly pointed out in this paper that any attempt to correlate the happening of a measurement inside the otherwise “isolated” SC container will inevitably correlate to the result of that measurement, in which case the measurement event will be irreversible.)

Whether discussing WF, SC, quantum computers, etc., if the evolution of a quantum mechanical system from time t1 to t2 is actually reversible at t2, then that must mean there is no evidence at t2 of its evolution.  And if you actually reverse the system to how it was at t1, then there can be no evidence of (and thus no scientific fact or meaning about) its having evolved or done anything from t1 to t2.  There can be no evidence anywhere, including as “experienced” by the system itself, because even by its own internal clock, there was no evolution to t2.  For a reversible system that is actually reversed, there just is no scientific fact about its having had any evolution.  And for a reversible system that is actually measured, so that information exists in the universe about its state (correlations, etc.), then that system is no longer reversible.

Finally, I want to mention that even for a quantum mechanically reversible system, in order to reverse it, you must have already set up the system to be reversible.  For example, if you want an exploding bomb to be reversible, you can’t let the explosion happen and then go hunting for all the fragments to measure their trajectories, etc.  Setting aside the classical problems I mentioned earlier (e.g., by measuring the particles you change their positions/momenta), the problem quantum mechanically is that once the happening of the event correlates to some particle that you don’t already have full control over, it’s too late… evidence now exists.  If a quantum superposition did exist at an earlier time, it no longer does because it has now, thanks to the decoherence event, irreversibly reduced to a definite state.

This is an error that Scott Aaronson seems to make.  Aaronson, one of the most brilliant people ever to discuss the relationship between physics and consciousness (such as in this paper), makes a compelling argument here (also here) that consciousness might be related to irreversible decoherence.  However, he seems to think of quantum mechanical reversibility as something that depends on a future event, like whether we take the time to search for all the records of an event and then reverse them.  For example, he posits that the irreversible decoherence related to one’s consciousness means that “the records of what you did are now heading toward our de Sitter horizon at the speed of light, and for that reason alone – even if for no others – you can’t put Humpty Dumpty back together again.”

But that’s wrong.  The reason you can’t put Humpty Dumpty back together again is not because evidence-carrying photons are streaming away… it’s because the fall of Humpty Dumpty was not set up before his fall to be reversible.  So a system described by wave function Ψ(t) can only be reversible at t2 if it is set up at earlier time t1 to be reversible (which means, at least in part, isolating it from decoherence sources).  But if you actually do succeed in reversing it at time t2 to its earlier state Ψ(t1), then there can never be scientific evidence that it was ever in state Ψ(t2).  Therefore, as a scientific matter, reversibility is a contradiction because the only way to show that a system is reversible is to show that it did not do something that it did.

Of course, assuming you could prepare lots of systems in identical states Ψ(t1), you could presumably let them evolve to state Ψ(t2), and then measure all of them except one, which you would then reverse to state Ψ(t1).  If the measured systems yield statistics that are consistent with the Born rule applied to state Ψ(t2), then you might logically infer that the system you reversed actually “was” in state Ψ(t2) at some point.  However, there’s a real problem, especially with macroscopic objects, with producing “identical” states, as I discuss here.  It is simply not physically possible, “in principle” or not, to make an identical copy of a cat.  Therefore, any attempt to scientifically show that SC exists requires showing that it does not exist. 

Physical reversibility is a contradiction.

_________________________________________________

From Section F of this post:

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 [the "universality" assumption that quantum states always evolve linearly and reversibly], 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;

2)         U is true;

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

4)         Therefore, U cannot be shown true.

Thursday, February 25, 2021

“Interaction-Free Measurements” in Quantum Mechanics are Not Surprising

Let’s say I write a paper logically showing why the fragments of a detonating nuclear bomb cannot exceed the speed of light.  Would that be interesting?  Perhaps the nuclear bomb aspect might make the paper a little sexier, but clearly the paper wouldn’t add anything new to our understanding of special relativity (SR).  Nobody who understood SR would be surprised by the paper.  In the unlikely event that I managed to get the paper published, nobody would cite it, right?  And anyone who did cite it as a “surprising” result clearly doesn’t understand SR.  Right?  Having said that...

Quantum mechanics is all about one thing: negative probabilities.  Everything about it, particularly why it’s weird, can be summarized in the following very simple point about double-slit interference experiments.  It was found, empirically, that when we send a certain kind of stuff (“particles,” such as photons or electrons) through a very narrow slit in a plate, and we detect them on a screen that is parallel to and far away from the plate (called the far-field approximation), we find that individual particles are detected, and if we detect enough of them, their distribution forms what is called the Fraunhofer diffraction approximation:

(Please ignore the axis units.)  In the above example, the probability of detecting a particle at, for example, location A is relatively high.  It was also found, empirically, that if we redo the experiment using two closely-spaced narrow slits (say, a left slit and a right slit), we find that the detected particles form what is called an interference pattern:

Notice that the interference pattern seems like it could fit inside the diffraction pattern shown earlier; we call this the diffraction envelope.  In the above example, the distance between the slits is about four times the slit width, and the greater this ratio, the narrower the distance between peaks inside the diffraction envelope.  Notice also that the likelihood of detecting a particle at location A is now zero. 

That’s right.  If only one slit had been open, the probability of detecting a particle at this point would have been nonzero.  So how is it that by adding another slit – by adding another possible path through which a particle could reach location A – we decrease its likelihood to reach location A?  The answer, mathematically, is that by adding probability amplitudes of waves prior to taking their magnitude, terms that are out of phase can cancel each other, resulting in a negative probability.  The answer, conceptually, is that the “particle” isn’t really a particle until it is actually detected.  It is only by assuming that there is a particle that traversed either the left slit or the right slit that we run into trouble.

And that’s it.  That’s the very essence of quantum mechanics. 

Now, let’s say that you’re about to do a double-slit interference experiment on electrons.  Just before you start, you have to use the bathroom so you put your lab partner in charge.  When you return, your lab partner says, “I was messing around with the double-slit plate and a foreign object – maybe a speck of dust – might have gotten stuck in the right slit.  But the left slit is fine.”  You go ahead with the experiment and send a single electron through, which you happen to detect at location A.  What does this tell you?

It tells you that an object must be in the right slit, because if they were both fully open, then interference would have prevented the detection of the electron at location A on the screen.  It also tells you that because the electron was in fact detected on the screen, it was not absorbed (or scattered) by the object in the right slit.  In that sense, you have managed to figure out that an object is in the right slit without actually hitting the object with an electron. 

There is absolutely nothing interesting or surprising about the above point.  In other words, once you’ve accepted that quantum mechanics allows negative probabilities, then of course you can set up a quantum mechanical interference experiment in which the detection of a particle in a particular place (or by a particular detector) renders information about the presence or absence of another object that obviously did not absorb or scatter that particle.

In 1993, a famous paper was published in which the above example was characterized as an “interaction-free measurement.”  (The Wikipedia entry on it is terribly written but at least gives the general idea.)  It described what came to be known as the Elitzur-Vaidman bomb tester, in which a bomb would go off if its sensor absorbs a single photon, but defective sensors (of defective bombs) would allow photons to pass through unaffected.  The general idea is nothing more than what I described above – you can set up the experiment so that detection of a photon in a particular place (such as location A) tells you that the sensor/bomb is operational even though the sensor did not absorb the photon. 

The whole “bomb detection” notion was just a way to make the paper a little bit sexier but didn’t add anything to our understanding of quantum mechanics.  To be fair, the paper wasn’t completely useless... it did explain how to increase the efficiency of detection to 50%.  (A paper published in 1995 showed how to push the efficiency much higher.)  In my example above, the likelihood of detecting an electron at location A is of course very low, yielding a very low efficiency, but the fact that it is nonzero is what clearly demonstrates that an object can be “measured” in the right slit without it absorbing or scattering the electron. 

And there is nothing interesting or surprising about that fact over and above the fact that quantum mechanics allows negative probabilities. 

So why did I write this post about a 1993 paper whose conclusion should have been obvious to anyone who understood quantum mechanics?  Because it has been cited over 800 times by publications, many of which continue to characterize “interaction-free measurement” as some kind of inexplicable paradox within quantum mechanics.  What might that tell us about the credibility of those papers or their authors as experts on quantum mechanics?

Part of the confusion is the incorrect notion that an “interaction” only occurs if the object being detected (bomb sensor, speck of dust, etc.) actually absorbs or scatters a particle.  Quantum mechanical waves are constantly interacting with other objects.  In the double-slit interference experiment above, the waves emanating from only the left slit (when the right slit is clogged with a dust speck) are different from waves that would emanate from both the left and right slits, which is why the screen detection distributions differ.  Therefore, the electron wave did interact with the speck of dust in the right slit even if the entirety of the electron wave ultimately collapses onto the screen and not the speck of dust.  In other words, to say that the electron didn’t interact with the right slit presupposes that the electron is a particle, but it does not assume a particle form until it is detected!  The entire misnomer of “interaction-free measurement” assumes that only “particles” can interact, but photons and electrons do not take on particle-like qualities until they are measured!  (Specifically, the particle- and wave-like characteristics of an object are complementary.)

Some of this confusion is clarified by Vaidman himself (such as here) and by other papers (such as this).  I am not criticizing the discussion.  I am simply pointing out that “interaction-free measurements” should never have been surprising in the first place.

Monday, February 22, 2021

Does Consciousness Cause Collapse of the Quantum Mechanical Wave Function?

No.

First, at this point I am reasonably confident that collapse actually happens.  Either it does or it doesn’t, and non-collapse interpretations of QM are those that have unfounded faith that quantum wave states always evolve unitarily.  As I argued in this paper, that assumption is a logically invalid inference.  So given that we don’t observe quantum superpositions in the macroscopic world, I’d wager very heavily on the conclusion that collapse actually happens.

But what causes it?  Since we can’t consciously observe a (collapsed) quantum mechanical outcome without being conscious – duh! – many have argued that conscious observation actually causes collapse.  (Others have argued that consciousness and collapse are related in different ways, such as collapse causing consciousness.)  In this blog post, I discussed the consciousness-causes-collapse hypothesis (“CCCH”) in quantum mechanics.  I pointed out that even though I didn’t think CCCH was correct, it had not yet been falsified, despite an awful paper that claimed to have falsified it (which I refuted in this paper).

Two things have happened since then.  First, I showed in this paper that the relativity of quantum superpositions is inconsistent with the preparation of macroscopic quantum superpositions, which itself implies that CCCH is false. 

Second, this paper was published a few days ago.  Essentially, it’s a Wigner’s-Friend-esque thought experiment in which a poison-containing breaks or does not break at 12pm, per a QM outcome, but the person in the room will be unconscious until 1pm.  That’s it.  If CCCH is correct, then collapse of the wave function will not occur until the person is conscious at 1pm... but if he is conscious at 1pm, how could the wave state possibly collapse to an outcome in which the person dies at noon?  It’s a very simple logical argument (even though it is not explained well in the paper) that is probably valid, given some basic assumptions about CCCH.

So when does collapse actually occur?  I’ve been arguing that it happens as soon as an event or new fact (i.e., new information) eliminates possibilities, and the essentially universal entanglement of stuff in the universe (due to transitivity of correlation) makes it so that macroscopically distinct possibilities are eliminated very, very quickly.  For example, you might have a large molecule in a superposition of two macroscopically distinct position eigenstates, but almost immediately one of those possible states gets eliminated by some decoherence event, in which new information is produced in the universe that actualizes the molecule’s location in one of those position eigenstates.  That is the actual collapse, and it happens long before any quantum superposition could get amplified to a macroscopic superposition.

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.