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The Philosophical Implications of Quantum Information Theory
I was asked to write up a pithy summary of the upshot of this paper. This is the best I could manage.
One of the most remarkable features of the world we live in is that we can make measurements that are consistent across space and time. By "consistent across space" I mean that you and I can look at the outcome of a measurement and agree on what that outcome was. By "consistent across time" I mean that you can make a measurement of a system at one time and then make the same measurement of that system at some later time and the results will agree.
It is tempting to think that the reason we can do these things is that there exists an objective reality that is "actually out there" in some metaphysical sense, and that our measurements are faithful reflections of that objective reality. This hypothesis works well (indeed, seems self-evidently true!) until we get to very small systems, where it seems to break down. We can still make measurements that are consistent across space and time, but as soon as we stop making measurements, then things start to behave very differently than they did before. The classical example of this is the two-slit experiment: whenever we look at a particle we only ever find it in one particular place. When we look continuously, we see the particle trace out an unambiguous and continuous trajectory. But when we don't look, the particle behaves as if it is in more than one place at once, a behavior that manifests itself as interference.
The problem of how to reconcile the seemingly incompatible behavior of physical systems depending on whether or not they are under observation has come to be called the measurement problem. The most common explanation of the measurement problem is the Copenhagen interpretation of quantum mechanics which postulates that the act of measurement changes a system via a process called wave function collapse. In the contemporary popular press you will often read about wave function collapse in conjunction with the phenomenon of quantum entanglement, which is usually referred to as "spooky action at a distance", a phrase coined by Einstein, and intended to be pejorative. For example, here's the headline and first sentence of the above piece:
More evidence to support quantum theory’s ‘spooky action at a distance’
It’s one of the strangest concepts in the already strange field of quantum physics: Measuring the condition or state of a quantum particle like an electron can instantly change the state of another electron—even if it’s light-years away." (emphasis added)
This sort of language is endemic in the popular press as well as many physics textbooks, but it is demonstrably wrong. The truth is that measurement and entanglement are actually the same physical phenomenon. What we call "measurement" is really just entanglement on a large scale. If you want to see the demonstration of the truth of this statement, read the paper or watch the video or read the original paper on which my paper and video are based. Or go back and read about Von Neumann measurements or quantum decoherence or Everett's relative state theory (often mis-labeled "many-worlds") or relational quantum mechanics or the Ithaca interpretation of quantum mechanics, all of which turn out to be saying exactly the same thing.
Which is: the reason that measurements are consistent across space and time is not because these measurements are a faithful reflection of an underlying objective reality. The reason that measurements are consistent across space and time is because this is what quantum mechanics predicts when you consider only parts of the wave function and ignore other parts.
Specifically, it is possible to write down a mathematical description of a particle and two observers as a quantum mechanical system. If you ignore the particle (this is a formal mathematical operation called a partial trace of an operator matrix ) what you are left with is a description of the observers. And if you then apply information theoretical operations to that, what pops out is that the two observers are in classically correlated states. The exact same thing happens for observations made of the same particle at two different times.
The upshot is that nothing special happens during a measurement. Measurements are not instantaneous (though they are very fast ) and they are in principle reversible, though not in practice.
The final consequence of this, the one that grates most heavily on the intuition, is that your existence as a classical entity is an illusion. Because measurements are not a faithful reflection of an underlying objective reality, your own self-perception (which is a kind of measurement) is not a faithful reflection of an underlying objective reality either. You are not, in point of metaphysical fact, made of atoms. Atoms are a very (very!) good approximation to the truth, but they are not the truth. At the deepest level, you are a slice of the quantum wave function that behaves, to a very high degree of approximation, as if it were a classical system but is not in fact a classical system. You are in a very real sense living in the Matrix, except that the Matrix you are living in is running on a quantum computer, and so you -- the very close approximation to a classical entity that is reading these words -- can never "escape" the way Neo did.
As a corollary to this, time travel is impossible, because in point of metaphysical fact there is no time. Your perception of time is caused by the accumulation of entanglements in your slice of the wave function, resulting in the creation of information that you (and the rest of your classically-correlated slice of the wave function) "remember". It is those memories that define the past, you could even say create the past. Going "back to the past" is not merely impossible it is logically incoherent, no different from trying to construct a four-sided triangle. (And if you don't buy that argument, here's a more prosaic one: having a physical entity suddenly vanish from one time and reappear at a different time would violate conservation of energy.)
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Comments (55)
Thanks, this helped me fill in some gaps. In Ron Garret's piece that you linked above, a comment has a link to a very nice article by Aharonov et al titled Can a Future Choice Affect a Past Measurement's Outcome?. (Hint: yes.)
Just FYI, I am Ron Garret. Also just FYI, the Aharonov study does not show that future choices can affect a past measurement's outcome. If this were possible, you could use it to send yourself information about the future of (say) the stock market and become the richest person on earth.
I don't understand Aharonov's experiment enough to say what it does or doesn't show. But your argument surely does not disprove his claim, since he is talking about particular circumstances, not making a general claim that there is some method that will tell you general truths about the future such as what the stock market is going to do. In fact, he does not appear to be saying that you can send yourself information at all, in a form which will be intelligible to you before the future events.
So I read the paper, and it is kind of a cool experiment, but it does not show that "future choices can affect a past measurement's outcome." Explaining why would require a separate article (maybe time to re-open main!) But the TL;DR version is this: if you want to argue that A affects B then you have to show a causal relationship that runs from A to B. If you can do that, then you can always come up with some encoding that will allow you to transmit information from A to B. That's what "causal relationship" means. But that is (unsurprisingly) not what Aharonov et al. have done. They have merely shown correlations between A and B, and then argue on purely intuitive grounds that there must have been some causal relationship between A and B because "Bell's theorem forbids spin values to exist prior to the choice of the orientation measured." While this is true, it's misleading because it implies that spin values do exist after a strong measurement. But that is not true. There is no fundamental difference between a strong and a weak measurement. There is a smooth continuum between weak and strong measurements, and at no point during the transition from weak to strong does the spin value begin to "actually exist" (a.k.a. wavefunction collapse).
I disagree. Following Pearl, I define "A causes B" to mean something like: (DO:A) raises the probability of B.
Bob's choice in the evening to make strong measurements along the beta-axis, raises the probability of Alice's noon measurements along the beta-axis measurements having been the ones that showed the best correlation. It doesn't raise the probability of any individual measurement being up or down, but that's OK. Even on a many worlds interpretation, where perhaps every digital up/down pattern happens at some "world" and the overall multi-world distribution is invariant, "probability" refers to what happens in our "world", so again that's OK.
Correlation can only be observed after the fact, in the evening, not at noon. So isn't this just a case of Bob affecting Bob+Alice's immediate future, where they go over the results? Why do I say Bob's choice affected Alice's results? Because correlation is a two-way street, and in this case there isn't much traffic in the forward direction. Alice's measurements only weakly affect Bob's results.
Yes, but there's still some terminological sleight-of-hand going on here. It is only fair to say that a future A affected a past B if P(B) is well defined without reference to A. In this case it's not. Because B is defined in terms of correlations between measurements made at T1 (noon) and measurements made at T2 (evening) then B cannot be said to have actually happened until T2.
No, it's an n-squared-minus-one-way street. It appears to be a two-way street in one (very common) special case (two macroscopic systems mutually entangled with each other), but weak measurements are interesting precisely because they do not conform to the conditions of that special case. When you go beyond the conditions of the common special case you can't keep using the rhetoric and intuitions that apply only to the special case and hope to come up with the right answer.
You're right. Good point.
Don't you mean n-factorial? Anyway, ... hmm, I need to think about this more.
Yeah, probably. It's actually probably N!-1 because you have to trace over one degree of freedom to obtain a classical universe. But the details don't really matter. What matters is that it's >>N.
I disagree: if you interpret EPR experiments as wavefunction collapse rather than many worlds, then you can conclude that either one measurement affects the other, or both affect each other. But you cannot come up with any encoding that will allow you to transmit information.
Yes, of course that's true. But collapse is only an approximation to the truth. It is a very good approximation in many common cases. But the Aharonov experiment is interesting precisely because it is a case where collapse is no longer a good approximation to the truth, and so of course if you view it through the lens of collapse things are going to look weird. To see why collapse is not always a good approximation to the truth, see the references in the OP.
To be honest, I never saw how it would be "self evident" that not only there is some "objective reality" out there but that we also have an accurate representation of it. How would we know our representation is accurate? We don't have access to an objective observer, we don't even have access to a non-human observer. Immanuel Kant said, back in the 18th century, that in truth, the "laws of nature" are "laws of human perception [of nature]".
I recently wondered if the idea that our perception of reality is an accurate representation of the underlying objective reality was actually a commonly held idea around here. In Eliezer's short story "Three Worlds Collide", he has the characters say as much, because they assume that the periodic table and mathematics would be the same for every other species. But there is no reason to assume that is true.
I like your article, but have some naive questions: Where starts the original research part? That is how differs your article from existing interpretations of QM?
Will your interpretation of QM present any new testable predictions? Will it allow any new useful things?
What is the nature of observer in it?
None of this is original research on my part. My only contribution is pedagogical. QIT doesn't make any predictions that QM doesn't make because it's an interpretation, just another way of looking at the math. But the reason it's a better way of looking at the math is that it solves the measurement problem. It explains measurement in terms of entanglement. It reduces two mysteries to one. IMHO that's progress.
How far does it go in solving the measurement problem? Can you derive the Born rule? Can you settle the single/many world dichotomy?
Yes.
That depends on what you mean by "settle". The only thing that you can definitively say is that the transition between the quantum and the classical is gradual, not abrupt. Because of this, any statement about a classical world is necessarily an approximation of some sort, and all approximations break down if you lean on them in the right way. Copenhagen breaks down most easily because it only applies under some very particular circumstances. Those circumstances happen to be very common, which is why Copenhagen is not completely useless, but nowadays it is common to do experiments under which the Copenhagen approximation conditions do not apply. Multiple-worlds is mathematically tenable, but it has some very serious problems as an explanatory theory and it makes predictions that even its adherents seem unwilling to accept.
Personally, I find the rhetoric of QIT/relational-QM/Ithaca to be far less taxing on my intuition than multiple-worlds. These interpretations acknowledge that classical reality is a slice of the wave function, that there are many different ways to slice up the wave function to obtain a classical reality, and therefore there are many potential classical realities. But there is one classical reality that is privileged to me because it happens to be the one that I'm living in, which is to say, it's the reality that is mutually entangled (and therefore classically correlated) with the massively-mutually-entangled system that is me. In an absolute sense I am no more or less real than all the other potential mes that you get by slicing up the wave function in different ways, but I don't care about that except in the abstract. Day-to-day, what matters to me -- this me, the one that is writing these words -- is what is correlated with (this) me.
The cool thing about this is that if you are reading these words -- the ones written by this me -- then you are entangled with me and therefore classically correlated with me and therefore we are both emerging from the same slice of the wave function, and so the exact same argument applies to you: both of us can proceed on the assumption that our classical reality is the One True Classical Reality even though we can both understand in the abstract that this isn't really true, and that by doing the right kinds of quantum experiments we can actually demonstrate to ourselves that it isn't really true. For me personally, that makes QIT the best approximation to use because it's the one that applies in the greatest variety of circumstances and has the fewest conceptual problems. But it's ultimately a matter of personal preference.
Doesn't the QIT you describe make the exact same predictions, also the Russian roulette you mentioned?
But there's no single privileged future you, right?
Nope.
There is no single privileged future me now, but when my future becomes my present there will be. (Also, see note below.)
You can actually do this experiment: listen to a geiger counter, or tune an old-school TV to an inactive channel and watch the snow on the screen. The math says that during this process there are an inconceivably vast number of you's being split off every time the geiger counter clicks (or fails to click) or every time you perceive a light or dark pixel on the screen. But you will only ever experience being one of those you's. Yes, all those other you's do exist, but the you that you perceive yourself to be can never interact with any of them, so they may as well not exist for the one you that you perceive yourself to be. And so the one you that you perceive yourself to be may as well live your life as if all those other you's didn't exist even though they really do.
(NOTE: there is really no such thing as "now", and you don't even have to go quantum to see that. Simultaneity gets tossed out the window with special relativity. There is my "now" and there is your "now" and they will not, in general, be the same.)
Hi lisper,
I found your paper easy to follow and maybe insightful (I'll have to read it more carefully the second time) but like qmotus, I don't understand your reasoning in this thread. I'm assuming MWI is just an interpretation of unitary QM, so makes all the same mathematical predictions as other non-collapse theories. And the roulette story is just one way of looking at it, from the perspective of what I consider my (classical) self and what I call the future.
Since you are not claiming that QIT makes different mathematical predictions than MWI, how can you claim they make different predictions at all?
QIT and MWI don't make any different predictions that are testable in a single classical universe (obviously, because QIT and MWI are just different interpretation of QM, so they both make the same predictions for all observables, namely, the predictions made by QM).
QIT and MWI are simply differences in perspective -- the God's eye view (MWI) versus the mortal's-eye-view (QIT). Neither view is "correct", but since I (the thing engaged in this conversation) am a mortal, I choose the mortal's-eye-view as more relevant for day-to-day decision making. But as I keep saying, it's ultimately a matter of personal preference.
The problem with quantum roulette is that it takes a prediction made from a God's-eye-view and tries to apply it in a mortal's-eye-view context. Yes, God will be able to see that there is a you that survived the process and went on to live the life of Riley. But whether or not you will be able to see that is a very open question. (God will also be able to see a lot of branches of the multiverse containing your friends and loved ones mourning your untimely death.)
Note that playing quantum roulette successfully depends crucially on the speed with which you can kill yourself. Trying to play by slitting your wrists, for example, doesn't work because once you see that your wrists are slit you can't roll that back. So the success of the enterprise depends entirely on killing yourself fast enough that you don't become aware of your imminent and (in the relevant branches of the multiverse) unavoidable death. How fast is fast enough? Well, that is (literally!) the sixty-four-million-dollar question. Unless you have an answer that you are very confident is the correct one, it seems to me like an imprudent risk to take.
(This comment is a reply to another branch of this discussion as well.)
I disagree. To keep things simple, let's suppose that the bullet, if it hits, really will kill the participant with practically 100% certainty and will do so practically immediately (I'll come to this a bit later). In that case the only outcome the participant can expect to experience, and that they will experience with certainty, is that the gun didn't fire. This is exactly what happens if you take the mortal's-eye-view; God, as you mentioned, will notice that elsewhere in the multiverse, the participant did get hit. Now, whether the participant cares about their loved ones or the copies that die in the attempt is a matter of preferences, but if we're simply talking about which outcome to experience, this is how it goes, I think.
With this I agree, which is why I think the quantum Russian roulette or quantum suicide scenarios are mostly interesting as a thought experiment, as they're intended to be. But there are practical situations that are somewhat analogous: think, for example, about a terminally ill patient who faces an almost certain death within several days. Should they expect to survive or continue to experience things, and if so, in what way? My understanding is that according to quantum mechanics, there are all kinds of weird scenarios with non-zero probability that make "survival" possible, such as simply surviving one more day indefinitely despite all odds, being miraculously cured, or maybe being resurrected by a hyper-advanced future civilization in a simulation. Note that, in principle, this probably applies to any possible life-and-death situation.
I used the word "experience" a number of times there, which brings me to a point you made in another comment:
I don't think this can of worms is that bad. We have a pretty good grasp of what it means to be conscious, even if we can't define it exactly; and also we're (at least I am) pretty confident that it's a purely physical phenomenon with nothing supernatural and thus subject to the laws of QM. I think that's enough. Where it does get a bit problematic is when we're talking about scenarios like the one with the terminally ill patient; presumably there's also a possibility that the patient's consciousness degrades until it no longer makes sense to call them conscious, since there's probably no clear line anywhere separating conscious and non-conscious in this way. (This might also imply that if we should expect to die, we should expect to do so by very slow decay, like patients with Alzheimer's, which doesn't sound too good to me.)
I agree with most of what you say. Consciousness is not supernatural. But it is still problematic because:
"Only outcome you can experience" is not quite the same thing as "Will experience with certainty." Let's go back to the case where you survive in both branches. The outcome you do experience is the only outcome that you can experience. The trick is that this is really two statements disguised as one. After the event there are two you's, you1 and you2. The outcome that you1 do experience is the only outcome you1 can experience, and the outcome you2 do experience is the only outcome you2 can experience. This remains true (I believe) even if one of those experiences is the null experience of having your consciousness enter the cosmic void.
Reasonable people could disagree, I suppose. We can never know what the null experience "feels like" because by definition it doesn't feel like anything. Personally, I find even the possibility that this argument could be correct to be sufficient reason for me to avoid playing quantum roulette. But everyone needs to choose their own risk posture.
Yes, that's the point. Every future version of you will of course call themselves "you".
Although I don't want to advocate performing the roulette experiment, I do disagree. If it's a quantum certainty that all future branches of you die off, perhaps due to a conservation law, then only those versions of you which didn't go down that branch will be conscious.
Even if it isn't certain, because it seems like we are more likely to experience the branches that match our classical explanations in the following scenario after a few minutes I would expect to be version 3. Version 1 is of course impossible and only with a very short-sighted definition of self do I need to consider version 2.
Well, I'd rather say that I will perceive being every one of them; it's just that no future me will perceive being more than one of the future mes. The terminology gets quite confusing here, but I think the Quantum Russian Roulette you mentioned (and quantum suicide and immortality, by extension, for example) is one situation where this aspect of quantum theory becomes somewhat apparent, which is why I think it would be interesting if you elaborated a bit more on how you think the predictions QTI and MWI make differ from each other.
It depends on what you mean by "I". This is the crux of the matter. MWI takes a God's-eye perspective and looks at the whole wave function. On that view, there are many you's (i.e. many slices of the wave function that contain macroscopic systems of mutually entangled particles that perceive themselves to be you).
QIT takes the perspective of the-you-that-you-currently-perceive-yourself-to-be. You will only ever perceive one of that kind of you.
For the purposes of making decisions it makes more sense to take the latter perspective because it's the-latter-kind-of-you that is making the decisions and has to live with the consequences.
I would say that a major difference between MWI and various collapse interpretations is that there are situations where according to collapse interpretations there most likely will be no future you; but according to MWI there surely will, although their amplitude is low (the aforementioned Russian roulette is one such situation, for instance). I find it somewhat difficult to think about those from the perspective you advocate.
No. Not "will". IS. If you're going to take the God's eye view then you have to let go of your intuitions about time along with your intuitions about classical reality. The wave function is a static four-dimensional thing. Time emerges from the wave function in exactly the same way that classical reality does. You have to be careful not to apply terminology from the mortal's-eye-view to the God's-eye-view. That's how you get yourself into trouble.
UPDATE: Here is a popular article about how time emerges from entanglement.
Only commenting on one point here.
The argument that something is "logically incoherent" has been used to justify many a false conclusion about the observed universe, don't do that.
Your other argument against time travel is better, but not airtight: it violates not the conservation of energy but the dominant energy condition in general relativity, Basically, for something to disappear, all of its mass has to vanish somewhere and no faster than with the speed of light. So maybe you get turned into a neutrino stream and or something. A better reason for why time travel (but not timeline forking) is incompatible with General Relativity is the uniqueness of the metric. But this is becoming a discussion of a real science, not philosophy.
If you were to ban every mode of argument that has ever been used to justify a false conclusion then it would be impossible to argue for anything.
Heaven forfend! ;-)
I don't buy your first argument against time-travel. Even under the model of the universe as a static mathematical object connected by wave-function consistency constraints, there is still a consistent interpretation of the intuitive notion of "time travel":
The "passage" of time is the continuous measurement of the environment by a subsystem (which incidentally believes itself to be an 'observer') and the resulting entanglement with farther away parts of the system as "time goes on" (i.e. further towards positive time). Then time-travel is a measurement of a "past" state or described differently (but the same thing) an entanglement between a subsystem (the location in the past the traveler visited) and its surroundings, which does not respect the common constraint that entanglement propagates at speed of light (because the traveler came from some future location (and its past light-cone) which is -- "surprisingly" -- entangled with the past). While violating common understanding of space-time, it is not logically impossible in this understanding of the universe.
This time-travel allows interaction with the past (which are not different from observations anyway).
Do I overlook something here?
No, what you say is correct, but you don't even need to bring entanglement into it at all: moving faster than light is the same thing as moving into the past (in some reference frame). This is why information can't propagate faster than light.
The kind of time travel that I'm talking about here is not merely sending information into the past but sending yourself into the past, that is, sending your body into the past. But that's not possible because your body is on the most fundamental level made of entanglements, and entanglements define the arrow of time.
... um, no. We can't reliably do either of those things. You need to add some qualifiers.
The rest, I didn't understand. That's to be expected, though.
Well, I didn't say we could do it reliably. :-) But we can do it. You can look at something and say, "It's green" and I can look at the same thing and agree, "Yes, it is green." And then we can look at the same thing a minute later and say, "It's still green." The remarkable fact is not that we can do this 100% of the time, but that we can do it at all.