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?


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.

Monday, February 8, 2021

Bitcoin, Speculation, and Legal Tender Laws

Note: I took Banking Law, and received one of only two As, at Georgetown University Law Center under Prof. Daniel Tarullo who, from 2009 to 2017, was a Governor of the Federal Reserve Board.

Bitcoin is currently at $43,389.

And everything you need to know about Bitcoin is contained in that one sentence.  In other words, beyond its cost, there is nothing interesting about Bitcoin (or any other electronic “currency”).

Oh, there are interesting facts about where it comes from (and the monumental waste in “producing” it), as well as the utility of block chain technology (which is actually independent of electronic currencies).  But there is nothing interesting about a Bitcoin itself, which is just a seemingly random string of bits.  This isn’t true of gold or silver or wine or emeralds or cars or real estate.  Sure, one of my rental houses might have a market value of $150,000, but there are lots of interesting facts about it other than its “exchange rate” in dollars.  For example, it provides my tenant shelter, modern plumbing, electric conveniences, a big back yard, etc.  And we can debate all day about the intrinsic value of gold, but it is a good electrical conductor and people like wearing it as jewelry.  At least it does something. 

In sharp contrast, Bitcoin doesn’t do anything.  And it’s not because it’s a string of bits.  Hell, software is just a string of bits and so is the information in your favorite movie or Netflix show.  Unlike these, 1BTC is literally a useless string of bits that is simply recognized as “one Bitcoin” by the open-source Bitcoin algorithm.  Its only value is that ascribed by those who own it and/or want it.

“OK, so what?” asks the enthusiast.  “That’s also true of fiat money like the U.S. dollar.”

My three-word answer: LEGAL TENDER LAWS.

Look, there are a thousand reasons to hate Bitcoin, so I’m not going to mention any of them except the one that no one else seems to be talking about – namely, the fact that governments extract wealth from their citizens in the form of taxation, and taxes will always be payable in the governments’ chosen currency.

There is a common fear among Bitcoin enthusiasts that the government will eventually act to shut down electronic currencies.  Sure, that’s a possibility, but that’s not the main problem with Bitcoin.  The real problem – which almost no one seems to realize – is that the government is never going to accept Bitcoin in payment for taxes.  There is no government on Earth that accepts Bitcoin as payment or as legal tender.  Why?  Because accepting payment in an alternative currency devalues their own state-sanctioned currency.  Historically, there are a few shitty rogue governments that have been so incompetent with their own monopoly over currency issuance that their economies are either effectively or legally dollarized.  Zimbabwe springs to mind with its moronic (and fascinating!) $100 trillion bills.  Within the states and territories of the United States, the U.S. dollar is legal tender, which means that all debts, particularly debts to local, state, and federal governments, are payable in this currency and nothing else. 

You cannot pay your New York property taxes in British Pounds.  You must pay it in U.S. dollars or else the state will foreclose on your property.  If you happen to have a bunch of British Pounds, luckily there are 67 million people on an island across the Atlantic who need British Pounds to pay their property taxes to their government.  The meeting of supply with demand creates an exchange rate.  You cannot pay your U.S. income taxes in Indian Rupees.  If you happen to find yourself awash in Rupees, there are 1.4 billion people who need Rupees to pay taxes to their government, and the resulting currency market will allow you to exchange your Rupees for Dollars so you can pay your income tax bill.  The government has a monopoly on the use of force, and it will ultimately use that force to collect taxes on income, sales, property, value-added, etc.

So let’s say you use 2BTC, which you bought ten years ago for a nickel (or whatever) to buy a Tesla automobile, as Tesla apparently plans to start accepting it in payment.  Under the Internal Revenue Code, that is a realization event that makes you liable for taxes on $86,778 in gains.  But you cannot pay this tax in Bitcoin, nor will you ever be able to.  (The Federal Reserve owns the planet.  OK, it sort of shares it with a few other central banks, like the Bank of England, the European Central Bank, etc.)  And since no other government forces its citizens to pay taxes in Bitcoin, there is no “exchange rate” for Bitcoin.  To pay your taxes, you have to get U.S. dollars either by earning them or selling more Bitcoin, which means that the value of Bitcoin must always be denominated in some other country’s currency.

In other words, because Bitcoin is not and never will be legal tender in any country, it will never stand on its own.  The question will always – always, always, always, always, always – be “How much is Bitcoin today?” 

And that’s a problem... an insurmountable problem for Bitcoin enthusiasts.  When you are about to make a purchase in a store in Paris, the clerk doesn’t have to ask, “How much is the Euro today?”  In fact, to most Europeans, that question wouldn’t even make sense.  After all, 1 Euro is 1 Euro!  The store clerk does not need to look up the “value” of the Euro in terms of other currencies or commodities.  She doesn’t care.  She knows she needs Euros to pay her rent, her bills, and – most importantly – her taxes.  But Bitcoin is different.  A price will NEVER be fixed in Bitcoin... every transaction involving Bitcoin will ultimately involve some person or computer asking the question, “How much is Bitcoin today?”

I don’t want Bitcoin because it has no intrinsic value or use.  Governments don’t want Bitcoin because it devalues their monopoly on currency issuance.  And here’s the thing.  Even Bitcoin owners and enthusiasts don’t want Bitcoin. 

“Andrew, shut up.  Of course they do – that’s why they bought it!” 

Wrong.  They bought it because they think others want it.  (Conversely: if they did not think others wanted it, then no one would buy it.)

I used to collect old U.S. coins because I thought they were fascinating and I loved the history.  When I would share my collection with other numismatists, occasionally one of us would say something like, “Can you believe how much this coin is worth?!”  But that wasn’t the focus of our conversation.  We talked about minting, and history, and coin material and condition, and fascinating mint errors like double-struck coins, etc.  The point is that there was substance to the conversation because we actually enjoyed and valued and appreciated the asset, with “dollar exchange rate” a secondary consideration.

Not so with Bitcoin.  After countless conversations with Bitcoin enthusiasts (who tend to show up in droves at Libertarian conventions), I have learned that conversations revolve almost entirely around these two general topics:

* “The price of Bitcoin is $_____... can you believe it?!”  (Sometimes it’s way up, sometimes it’s way down – the only apparent consistency in the Bitcoin price is its volatility.)

* “Death to the Dollar (or Pound or Yen or Transnistrian Ruble)!”

In other words, even Bitcoin owners and enthusiasts don’t value Bitcoin per se – of course they don’t!  It’s just a useless string of bits!  Rather, they value it in terms of its selling price in dollars.

Let that sink in.  Bitcoin enthusiasts hate the U.S. dollar so much that they purchase a useless string of bits whose value – as judged by their own conversations – is determined by the number of those hated U.S. dollars they can sell it for.  That is madness.

The last thing I want to mention is speculation.  If I can pick a booger and manage, through suave argumentation, to convince a handful of people that it is worth a million dollars – is it actually worth a million dollars?  Value is a very subjective thing and the phrase “market value” only has meaning in an efficient and rational market.  The fact that Bitcoin is at $43,389 is exciting to a lot of people.  There are people who will pay this amount and more for 1BTC.  There may very well be people who, under the right conditions, would pay $1 million for 1BTC.  Just keep in mind that it is pure speculation.  Unlike a tulip, which at least offers the tiny subjective value of being easy on the eyes, Bitcoin’s only “value” is its price as denominated in fiat currencies.

And as much as one might despise the U.S. dollar for its lack of intrinsic value, it at least has the ability to prevent IRS agents from confiscating one's property.  Bitcoin cannot do that.  It cannot do anything.

Bitcoin is currently at $43,389.

And that’s all there is to say.