Is quantum physics "retro-deterministic"?

[Gerinski]

The question relates to the deterministic views of people like Descartes or Pierre de Laplace, the infamous "an omniscient intelligence who could know precisely the position and momentum of every single particle in the universe would be able to predict the future with total accuracy, past, present and future would be all the same before her eyes".

It's clear that quantum physics denies "future-oriented" determinism, knowing with arbitrary precision the matter-energy configuration at any given spacetime coordinates does not allow us to predict the future configuration at a later spacetime coordinate, only probabilistic predictions can be made. So far so good.
My question is about the "past prediction possibility" (I don't know if the word "retrodiction" could be used here).
I have sometimes read, I don't know if true or not, that the Heisenberg Uncertainty Principle does not apply to the past. That for particles in the past we can know with arbitrary precision what their position and momentum was along their worldline, at least until we hit the previous interaction with other particles. That the HUP applies only when trying to predict the future position and momentum, but not the past.

Obviously we believe that studying the huge amount of information contained in the present universe we can quite confidently reconstruct the past. This is the base of cosmology. Knowing the present state of the universe and the laws of physics we seem pretty confident that we can "retrodict" what the past must have been like, the formation of the present galaxies, the preceding proto-galaxies, the dark ages, the CMB, and even to the point of believing that we can know how it all started down to when the universe was a few minutes old (or at least say, when it was very hot).

My question is, so according to quantum physics a precise matter-energy configuration (let's call it "A") at spacetime coordinates X does not allow us to predict the future configuration(s). "A" can lead to different outcomes, of which we can only make probabilistic statements.

But if we consider "A" towards the past, is the same true? Could "A" be the result of different previous states so knowing A does not allow us to deduce the previous history? In other words may "A" be consistent with different previous states? Or is "A" consistent only with one specific previous configuration given the laws of physics, so that knowing "A" allows us to know the previous state(s) precisely?

Because if "A" (say, the present state of our universe) could be the result from several different preceding states, how can we be so confident about cosmology? Only because by "probabilistic retrodiction" our favored cosmological story seems the most likely of the (possibly many) several possible pasts?

Thanks !

 

[PeterDonis]

I have sometimes read, I don't know if true or not, that the Heisenberg Uncertainty Principle does not apply to the past.

Can you give a specific reference? (And not a pop science book, but an actual textbook or peer-reviewed paper.)

Generally speaking, the Heisenberg uncertainty principle is not a general statement that "we can only make probabilistic predictions in QM". It is a much more specific statement about not being able to simultaneously measure non-commuting observables.

Obviously we believe that studying the huge amount of information contained in the present universe we can quite confidently reconstruct the past. This is the base of cosmology.

And of the rest of science. If we run an experiment, we believe that we can obtain definite results and record them for future reference.

The short answer to your question is that nothing in quantum mechanics prevents us from doing this. The probabilistic nature of quantum mechanics applies to predictions of future measurement results. It does not mean that, once you've made a measurement, you can only probabilistically know what the result of it was.

 

[Khashishi]

Ultimately, this rests on whether a wavefunction collapse is something that really happens, or just something that appears to happen. Standard quantum mechanics tells us that the wavefunction for a system undergoes deterministic evolution when no measurement occurs, but then the wavefunction suddenly collapses when a measurement occurs. Whenever a collapse occurs, some information about the past is lost. So it's not possible to reconstruct the past from the present.

In some interpretations of quantum mechanics, wavefunction collapse doesn't actually occur, and in some others, wavefunctions aren't real things. So, we can't really say.

 

[Derek P]

The question relates to the deterministic views of people like Descartes or Pierre de Laplace, the infamous "an omniscient intelligence who could know precisely the position and momentum of every single particle in the universe would be able to predict the future with total accuracy, past, present and future would be all the same before her eyes".

It's clear that quantum physics denies "future-oriented" determinism, knowing with arbitrary precision the matter-energy configuration at any given spacetime coordinates does not allow us to predict the future configuration at a later spacetime coordinate, only probabilistic predictions can be made. So far so good.

Not necessarily "so far so good", I'm afraid. Probabilities for observations are part and parcel of QM, but whether nature itself behaves probabilistically is moot. In the Many Worlds Interpretation (MWI), for instance, there is only smooth continuous (unitary) evolution of the wavefunction: the probabilities that we see emerge due to the quantum behaviour of our instruments and senses. Of course, normal people instantly reject the idea of "all those other worlds" but they (the worlds, not the normal people) play no active role in MWI, they are just the disconcerting by-products of some work which started life as an explanation of why we see probabilities in an otherwise deterministic theory.

My question is about the "past prediction possibility" (I don't know if the word "retrodiction" could be used here).
I have sometimes read, I don't know if true or not, that the Heisenberg Uncertainty Principle does not apply to the past. That for particles in the past we can know with arbitrary precision what their position and momentum was along their worldline, at least until we hit the previous interaction with other particles. That the HUP applies only when trying to predict the future position and momentum, but not the past.

No that isn't true. The HUP applies to any wavefunction. For instance with a double slit experiment, you measure the sideways momentum by the angle of deflection at the slits. You also resolve the position at the screen. But to measure both at the same time you would have to have measured the position at the slits, i.e. determined the "which slit" information. The position on the screen does not allow you to reconstruct a unique path through just one slit. Perhaps it will help you if I tell you that the HUP is not about primarily about predicting (or retrodicting) values for physical variables. It is about how tightly the variables are defined by a given wavefunction.

Another example: you measure the position and that kind of fixes it - you get the same position (unless the particle is moving) if you measure it again, the undertainty is removed. You can then measure the momentum. This renders the position uncertain. Interpret it how you may, there is no time when you have or had precise measurements of both. Mathematically the moment you apply collapse, you lose the precision of one measurement to get the other one.

Obviously we believe that studying the huge amount of information contained in the present universe we can quite confidently reconstruct the past. This is the base of cosmology. Knowing the present state of the universe and the laws of physics we seem pretty confident that we can "retrodict" what the past must have been like, the formation of the present galaxies, the preceding proto-galaxies, the dark ages, the CMB, and even to the point of believing that we can know how it all started down to when the universe was a few minutes old (or at least say, when it was very hot).

My question is, so according to quantum physics a precise matter-energy configuration (let's call it "A") at spacetime coordinates X does not allow us to predict the future configuration(s). "A" can lead to different outcomes, of which we can only make probabilistic statements.

Under QM, the question is meaningless. There is no precise configuration "A". You can have any number of precise observations, any one of which alters "A" a bit. From say u(A), v(A'), w(A'') we can construct an approximate (classical) configuration which is good enough in many practical situations.

But if we consider "A" towards the past, is the same true? Could "A" be the result of different previous states so knowing A does not allow us to deduce the previous history? In other words may "A" be consistent with different previous states? Or is "A" consistent only with one specific previous configuration given the laws of physics, so that knowing "A" allows us to know the previous state(s) precisely?

Given the above, what we can know about a state by measurements leaves room for many pasts just as it does many futures. If we turn from what we can know to the underlying state and if we assume that collapse is an artifact then there is just quantum state "A" which evolved from "A in the past" and will evolve into "A in the future".

Because if "A" (say, the present state of our universe) could be the result from several different preceding states, how can we be so confident about cosmology? Only because by "probabilistic retrodiction" our favored cosmological story seems the most likely of the (possibly many) several possible pasts?
Thanks !

Oh that's easy! The total uncertainty of any system is h-bar. Cosmological observations are on a vast scale compared to h-bar. Until you start dealing with field equations the models are very coarse-grained. Nobody would know or care whether particle number 92929658923...739276947348293 was where we think it was - i.e. somewhere in the fireball or somewhere in the fireball plus a few Planck lengths to the left. The field equations give us the general rules for how the stuff behaves so the question of discovering the exact state doesn't arise. If we could know the precise wavefunction of the universe then it would (barring collapse) allow us to reconstruct the past state precisely. But we don't know it and it's impossible to measure it. But all is not lost. We can think of what we do know about the universe as defining a large bundle of possible states, each of which maps to a slightly different Big Bang. A few may even map to something completely different but the overwhelming majority map to early states that are (macroscopically anyway) very similar. so it's overwhelmingly likely that our reconstructions are right.

edit:
Laplace was in fact correct (assuming no wavefunction collapse, because his statement assumes determinism), though he put the point in terms of knowing the position and momentum of every particle. It just needs to be updated.

An intellect which at a certain moment would know the entire quantum state of the universe, if this intellect were also vast enough to submit the data to analysis, it would embrace in a single formula the wavefunctions of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes.

 

[Gerinski]

Can you give a specific reference? (And not a pop science book, but an actual textbook or peer-reviewed paper.)

Thanks to all. As I tried to make clear in the thread level, I'm Basic, most of what I know comes from popular science books even if I try to choose them from scientists which I believe have some solid reputation. I have also read quite a few actual papers and although I often miss the math I like reading the texts. But in this particular point I can not tell some specific sources right away, I should search again in some of my books to tell you exactly on which one(s) have I read this kind of statements, but I know it's been more than once. If I find some I'l surely post it but indeed it will most likely be some popular science book(s).

But if I may ask more generally for my understanding, hoping that you all kindly forgive my ignorance, if we measure a particle's position at time X (not caring about its momentum) and we measure it again at a later time Y and we find it at some other position (again not caring about its momentum), do those 2 position measurements not enable us to infer what its position and momentum must have been between time X to Y? Common sense suggests it should, shouldn't it?

To Derek P, thanks a lot also to you for the reply. If I understand you well, the present can indeed be consistent with different past histories, but the overwhelming majority of them are macroscopically almost identical, so we can rely on that for our "retrodiction of the past". Yet I understand that the uncertainty towards the future is much more open. A present configuration can evolve towards many different states, pretty different from each other.

So does that not mean that the uncertainty is not symmetrical towards the future as it is towards the past? Towards the past we can infer that the present configuration must have come from a narrow diversity of pasts, while towards the future the range of potential future configurations is very wide open?

Thanks again.

 

[StevieTNZ]

Thanks to all. As I tried to make clear in the thread level, I'm Basic, most of what I know comes from popular science books even if I try to choose them from scientists which I believe have some solid reputation.

Which books have you read so far?

 

[PeterDonis]

if we measure a particle's position at time X (not caring about its momentum) and we measure it again at a later time Y and we find it at some other position (again not caring about its momentum), do those 2 position measurements not enable us to infer what its position and momentum must have been between time X to Y?

No, because quantum particles do not have classical trajectories.

Common sense suggests it should, shouldn't it?

But common sense is based on classical physics, not quantum physics. And every time we've been able to do experiments where common sense says one thing should happen but quantum physics says a different thing should happen, quantum physics has turned out to be right. As Feynman once said, "quantum mechanics was not wished upon us by theorists". Physicists were forced to develop QM because they were finding experimental results that classical physics simply could not explain.

If I understand you well, the present can indeed be consistent with different past histories, but the overwhelming majority of them are macroscopically almost identical, so we can rely on that for our "retrodiction of the past".

That's generally true in a field like cosmology, yes; but what you are leaving out is that our knowledge of the present is not knowledge of a single quantum state; it's knowledge of a macroscopic state, which is compatible with many different microscopic quantum states. And our "retrodiction" of the past is based on using classical laws that are good approximations when applied to macroscopic states. And in a field like cosmology, for example, we use the same classical laws to predict the future at a macroscopic level, so our predictions are of single future macroscopic states, which are compatible with many different microscopic quantum states. So there is no asymmetry at the macroscopic level.

Where quantum uncertainty comes into play is when we are making a measurement of a single microscopic quantum system. When we make such a measurement, our prediction of the results, in general, can only be probabilistic, so in that sense our predictions are uncertain. But once a result is recorded, it is recorded; there is no corresponding uncertainty about results that have already been recorded.

 

[Derek P]

do those 2 position measurements not enable us to infer what its position and momentum must have been between time X to Y?

The momentum measurement is completed at the second positional measurement. Which renders the momentum uncertain. So there is no overlap where you can say both measurements apply at once.

So does that not mean that the uncertainty is not symmetrical towards the future as it is towards the past? Towards the past we can infer that the present configuration must have come from a narrow diversity of pasts, while towards the future the range of potential future configurations is very wide open?

No, the uncertainty is always >= h-bar, there is no asymmetry. The divergence of macroscopic states is simply the second law of thermodynamics at work. edit - But that would take us way beyond a B level thread and no doubt result in requests for peer-reviewed sources...

 

[Gerinski]

Which books have you read so far?

Well my bookshelves must hold perhaps 60 to 80 popular science books of different kinds, not only physics or cosmology, I'm 51 and I got introduced to science as a kid with 1972's Asimov's Guide to Science and since then I have read quite a few, from people like Feynman, Penrose, Paul Davies, Hawking, John D. Barrow, David Deutsch, Ian Stewart, Brian Clegg, John Gribbin, Murray Gell-Mann, George Smoot, Sean Carroll, Charles Seife, Brian Green, Kaku, Brian Cox, Max Tegmark...

our "retrodiction" of the past is based on using classical laws that are good approximations when applied to macroscopic states. And in a field like cosmology, for example, we use the same classical laws to predict the future at a macroscopic level, so our predictions are of single future macroscopic states, which are compatible with many different microscopic quantum states. So there is no asymmetry at the macroscopic level.

But it looks that the possible consistent states towards the past are rather narrow, while the possible consistent states towards the future are quite wide, even speaking macroscopically. The many possible future macrostates may be qualitatively very similar to each other in macroscopic terms, but they seem anyway more diverse than the diversity of consistent past states which seem to be much more narrowly defined. I still feel some asymmetry, but I guess it comes only from the 2nd Law?

 

[A. Neumaier]

Retrodiction is as uncertain as prediction. Remember how little we know about the past - and all of it has to be reconstructed from a finite collection of observations connected by a thread of theory and educated conjectures.

The fundamental laws of quantum mechanics are reversible in time. If we learn a new fact about the past (e.g., by systematically going through tentative records) we have measured the past in the same way as we measure the future once it arrives.

Dissipative quantum mechanics (i.e., allowing for the loss of degrees of freedom to the environment) is even worse - there we can predict the future better than the past. A stirred cup of tea left alone will reach equilibrium with certainty, while from the final state it is impossible to infer anything about its past.

if we measure a particle's position at time X (not caring about its momentum) and we measure it again at a later time Y and we find it at some other position (again not caring about its momentum), do those 2 position measurements not enable us to infer what its position and momentum must have been between time X to Y?

Yes, this is indeed more or less the way momentum is inferred from particle tracks. But the measured positions are uncertain, which implies a much bigger uncertainty in the resulting momentum. There is no way to escape the Heisenberg uncertainty relation.

 

[Gerinski]

Ok thanks!

 

[Derek P]

But the measured positions are uncertain, which implies a much bigger uncertainty in the resulting momentum.

Yes, but...

It depends on the experimental arrangement but it is not difficult to use a shutter to fix the position and time with arbitrary precision at both measurements. And with a slightly more sophisticated contraption you can sort the incoming beam into time bins, though in this case we do not detect the particle but let it propagate however it sees fit down a particular path. A second measurement then gives the time of flight for each particle and thus its momentum. So even if there's a statistical spread between cases, the individual values can be as precise as you like.

Certainly the quantum model denies that the momentum was ever precise and I think the OP understands more than enough to see that there is an apparent anomaly. The question has to be not whether we can make measurements of, ahem, complementary properties, with arbitrary precision but whether we can make them at the same time. In other words, was there ever a moment in the reconstructed history when we can say the particle had such-and-such a definite position and such-and-such a definite momentum? It would, of course destroy QM if this were possible, even retrospectively. But it isn't. The nearest to this situation is at the moment of measurement, where the particle has a definite momentum before measurement and a definite position afterwards. These days one would look to the dynamics of the measurement interaction and see a smooth transition (as long as the number of particles does not change, which makes it more complicated). However, earlier interpretations just asserted the Born Rule ad hoc. So we would have to adopt a heuristic that if you assert collapse of the wavefunction, the measured values are not valid for that single moment of measurement. Then there is no anomaly.

 

[A. Neumaier]

it is not difficult to use a shutter to fix the position and time with arbitrary precision at both measurements.

No.

You cannot construct a shutter with sharp enough borders to guarantee this - at some point the molecular structure of the shutter gets in the way.

Moreover, even elementary particles are extended (e.g., the electron has a positive charge radius) so specifying a particle position to too many decimals accuracy is as meaningless as specifying the position of New York on the globe to mm accuracy.

 

[Gerinski]

So we "retrodict" the past history of the universe based on the information present in the current universe plus the laws we know of. And the laws are time-symmetrical.
Would it be correct to say then, that the present contains as much information about the past as it does about the future?

 

[A. Neumaier]

Would it be correct to say then, that the present contains as much information about the past is it does about the future?

Only with a very formal (and hence nonintuitive) notion of ''information''.

Since when predicting we make use of the second law (i.e., ignore unmeasured loss of information to the environment) , the actual predictions are not time-symmetric. It depends on the system whether prediction or retrodiction is more informative in the naive sense.

For a pendulum, we can predict the complete future - as long as the only forces acting are gravitation and friction (someone stopping the pendulum is much less predictable unless you carefully observe the someone's motives). On the other hand we can predict the past only up to the time the pendulum was set in motion - and we cannot tell when this was unless we observed it.

On the other hand, if something made of glass is smashed on the floor we cannot predict the pieces and where they go.

Similar examples can be found on the quantum level.