In perturbation theory and path integral formalisms of relativistic QM, such as quantum electrodynamics, one specifies initial and final states, as per the form of the Dirac equation which is power 2 in space and time (momentum and energy). This is what is meant by a path or trajectory.

If we do this with final position states for all positions on the back screen, we reconstruct the wavefunction defined over all of those points. The wavefunction and the Green's function are highly related. — Kenosha Kid

The so-called states you talk about here, are not actual states, they are probabilistic. This is the difference I've been telling you about, between a description and a statement of probabilities. And a reconstruction of the wavefunction over all the points produces a map of probabilities, not a description of an actual trajectory.

Furthermore, the precepts of special relativity, which as you say puts time and space on an equal footing, make it difficult (if not impossible) in some instances, to distinguish temporal aspects from spatial aspects. The problem being that there is a real difference between a spatial separation and a temporal separation, because by the nature of time, a temporal separation is not invertible, while a spatial separation is. The separation between time1 and time2 cannot be treated in the same way as the separation between spatial point A and point B, because the empirical evidence demonstrates that things only move from time 1 to time 2, and the opposite is impossible. If you put time and space on equal footing, and allow for reversal of time in your theory, you have allowed a principle which is inconsistent with empirical evidence.

There is a way around this temporal reality which might help you with the transactional interpretation. In metaphysics and theology there are principles which allow that a power, or active force, (normally represented as final cause), might act prior to the passing of time. This is how a free willing being can change the way that material existence will be, from one moment to the next.

So for example, if the passing of time is determined by us through reference to physical change, then there also must be a cause of physical change itself, which is necessarily prior to the passing of time. As each moment of time passes the material world will exist, or be, in a particular way at that moment. The power, or force, which causes the material world to be as it is, at each moment as time passes at the present, must be prior to the passing of time at the present, and therefore a cause which is in the future.

These descriptions aren't incompatible. Any wavefunction can be written as a superposition of Eigenstates of any measurement operator. If my electron collapses to an exact position state, for instance, and an electron in the screen is a wave-packet spread around that position, either the latter has to be scattered away from that position or the former is blocked from being found there. — Kenosha Kid

When one of them excludes the possibility of the other, this means that the two are incompatible. We can represent two of them as mathematically equivalent if we want, like ice is the solid state of liquid water, and the two might be mathematically equivalent, but that it is in the form of ice excludes the possibility that it is liquid water, because the two are incompatible, meaning that it would be contradictory if it is both liquid and ice at the same time.

The very idea of an electron with a definite ‘position’ or ‘momentum’ is meaningless prior to an experiment that measures it.

'Position' is a state. All of the possible positions constitute a complete basis set. Any wavefunction can be written as a superposition of these positional basis functions (the Eigenstates of the position operator). After measurement of position, the wavefunction somehow collapses to a single position. This is an example of the measurement problem.

Likewise 'momentum' is a state. All of the possible moments constitute a complete basis set. Any wavefunction can be written as a superposition of these momentum basis functions (the Eigenstates of the momentum operator), including an Eigenstate of the position operator (which is a plane wave in momentum space). After measurement of momentum, the wavefunction somehow collapses to a single momentum. This is another example of the measurement problem.

It is not that the electron doesn't exist when it's a wave: the wave conserves charge, mass, etc. It's that the wave spontaneously changes from a superposition to a single Eigenstate upon measurement.

Here's a random image I found of an electron wavefunction in some wave-packet state collapsing to a position Eigenstate on measurement of position:

And a reconstruction of the wavefunction over all the points produces a map of probabilities, not a description of an actual trajectory. — Metaphysician Undercover

Please read what I wrote again and make an effort to absorb it.

The problem being that there is a real difference between a spatial separation and a temporal separation, because by the nature of time, a temporal separation is not invertible, while a spatial separation is. — Metaphysician Undercover

This is your repeated claim but it's not shown. Neither in relativity nor relativistic quantum mechanics is there a preferred direction of time. Histories of particle motions constitute worldlines in 4D, with no intrinsic arrow.

The separation between time1 and time2 cannot be treated in the same way as the separation between spatial point A and point B, because the empirical evidence demonstrates that things only move from time 1 to time 2, and the opposite is impossible. — Metaphysician Undercover

Actually the empirical evidence proves that time and space are interchangeable, i.e. those dimensions in one frame of reference get mixed together in another frame of reference. Look up the Lorentz transformations.

The power, or force, which causes the material world to be as it is, at each moment as time passes at the present, must be prior to the passing of time at the present, and therefore a cause which is in the future. — Metaphysician Undercover

Interesting. It sounds a bit similar to the OP, in so far as the physical requirements of the existence of the material world in the future dictate the possible causes in the past. Coherence is very much a wavefunction feature.

When one of them excludes the possibility of the other, this means that the two are incompatible. — Metaphysician Undercover

See my above response to Wayfarer. A wavefunction can *always* be written as a linear combination of states from any basis set. This is the expansion postulate of QM.

Neither in relativity nor relativistic quantum mechanics is there a preferred direction of time. Histories of particle motions constitute worldlines in 4D, with no intrinsic arrow. — Kenosha Kid

That's exactly why these theories are deficient, they are not consistent with empirical observation. Empirical observation provides us with a unidirectional time. Those theories do not give us a principle to account for the reason why time is unidirectional, thus allowing you to work with a reversible time. Therefore the theories are deficient with respect to empirical observation, in that sense.

We can say that the second law of thermodynamics provides a principle to account for the direction of time, and this is what makes ideals such as Aristotle's eternal circular motion, and perpetual motion machines impossible, in reality. And as you said, the Copenhagen interpretation allows for a loss of information, making it consistent with that law. I believe that Bohm proposes that the entire universe be considered as one whole, to deal with this problem. But special and general relativity do not provide adequate principles to deal with the entire universe as one whole, as is evident from concepts like dark matter and dark energy, so the need for hidden variables appears.

You propose a simple ideal, the notion that time is reversible, and create from this ideal, the notion of an equality between emission and absorption, which is dependent on the notion that a future moment is invertible with a past moment. Of course this ideal has no bearing on the reality which we know, within which there is a substantial difference between past and future. The whole idea reminds me of people with less than high school education, proposing ideas for perpetual motion machines, without any respect for conservation of energy and the second law of thermodynamics. The fact that this idea is coming from someone who claims to have a PhD in this field just baffles me. Shame on you! I want to repeat what Timmy said to me ,"what school taught you that?"

Actually the empirical evidence proves that time and space are interchangeable, i.e. those dimensions in one frame of reference get mixed together in another frame of reference. Look up the Lorentz transformations. — Kenosha Kid

The Lorentz transformations provide mathematical principles for reconciling different frames of reference. They provide no empirical evidence that time and space are interchangeable. They might be applied under the assumption that time and space are interchangeable, but such application leads to the problems I mentioned above, which is evidence that this assumption is wrong.

Interesting. It sounds a bit similar to the OP, in so far as the physical requirements of the existence of the material world in the future dictate the possible causes in the past. Coherence is very much a wavefunction feature. — Kenosha Kid

Not quite. "Causes in the past" are epistemic determinations. This is the way that we as intelligent beings represent a line of temporal continuity. We say that Q happened at an earlier time, and cause R at a later time. But this is not a true representation of reality, being simply a representation of our apprehension of temporal continuity. In reality, whatever comes to be at t1, as Q, is caused by something in the future of t1, and whatever comes to be at t2, as R is caused by something in the future of t2. The only true causes are always in the future. and being in the future, they have not material, or physical existence. We know them as the immaterial cause of material existence (immaterial Forms, God).

See my above response to Wayfarer. A wavefunction can *always* be written as a linear combination of states from any basis set. This is the expansion postulate of QM. — Kenosha Kid

Sure, just like a quantity of H2O can be expressed as a combination of ice and liquid, but that's an admission that you cannot distinguish the boundary which you claim to be able to determine with those principles. When the precise boundary between H2O as liquid, and H2O as solid cannot be exactly established and appears to be vague, we can express the states along that vague boundary as a combination of both, some of the water is frozen, some is liquid. But such an expression just indicates that the boundary cannot be determined, and the method of expression is an acceptance of this. When we cannot apply the law of excluded middle we say that somehow it is a combination of both.

Therefore the theories are deficient with respect to empirical observation, in that sense. — Metaphysician Undercover

And yet no one has devised an experiment to show that photon emission/absorption is unidirectional, or motion is unidirectional, or matter/antimatter pair creation/annihilation is unidirectional, and these constitute almost all of the elementary phenomena studied by the most empirically-tested theory ever: quantum electrodynamics.

Going beyond QED, we do see arrows of time emerging: weak nuclear decay, the Higgs mechanism, cosmology, thermodynamics. I have drafted a follow-up thread to this one touching on the last two which are interesting because fundamentally they are reversible. Thermodynamics, for instance, is just the motions, creation and destruction of particles. General relativity retains the bidirectionality of special relativity. The cosmological and thermodynamic arrows of time appear circumstantial rather than fundamental.

The actual arena of CPT-violating phenomena is very small, but might be vital, e.g. in explaining the absence of antimatter in the universe. However for most experiments, such as the double slit experiment, they are not relevant at all.

Copenhagen and common sense are at odds with this, which might explain why the pioneers of quantum mechanics had the issues they did. Bohr and Heisenberg worked mainly in the non-relativistic approximation where time is unidirectional, and, funnily enough, their preferred interpretation of QM is unidirectional. Meanwhile Dirac was doing it right and seeing reversibility in more accurate equations.

The Lorentz transformations provide mathematical principles for reconciling different frames of reference. They provide no empirical evidence that time and space are interchangeable. — Metaphysician Undercover

Not interchangeable, just mixed. There is no privileged reference frame in which you can say 'this time axis is time, these spatial ones are space', and you can find an infinite other frames in which part of time becomes spatial and part of space becomes temporal. It is the four-vector that is physical, not its space-time components.

In reality, whatever comes to be at t1, as Q, is caused by something in the future of t1, and whatever comes to be at t2, as R is caused by something in the future of t2. The only true causes are always in the future. and being in the future, they have not material, or physical existence. We know them as the immaterial cause of material existence (immaterial Forms, God). — Metaphysician Undercover

Ah. Not so interesting.

Sure, just like a quantity of H2O can be expressed as a combination of ice and liquid, — Metaphysician Undercover

No. No, not at all like that.

Is making a measurement in QM and getting a specific result time reversible? How much of "time reversibility" might be artifacts of the mathematics that describe phenomena?

:chin:

And yet no one has devised an experiment to show that photon emission/absorption is unidirectional, or motion is unidirectional, or matter/antimatter pair creation/annihilation is unidirectional, and these constitute almost all of the elementary phenomena studied by the most empirically-tested theory ever: quantum electrodynamics. — Kenosha Kid

These are all temporal processes. Time is empirically proven as unidirectional. By simple deduction therefore, these processes are unidirectional. There is no experiment required, that's the beauty of deduction. What more do you want, an experiment which tries to run time backward, and finds out that this is impossible? Good luck with that.

Copenhagen and common sense are at odds with this, which might explain why the pioneers of quantum mechanics had the issues they did. — Kenosha Kid

It's a little more than just common sense. That time is unidirectional is the most fundamental and important empirical principle which we have. Knowledge of the truth of this principle influences everything we do, every day of our lives. The future is different from the past. The former consists of possibilities, which we can influence the outcome of, toward things we want, and away from things we don't want, while the latter consists of facts which cannot be changed. When something bad happens to you, you cannot change that, it has happened, but if you apprehend something bad that could happen in the future, you can take steps to avoid it.

Sure, one can argue determinism by arguing that there is no difference between future and past, that both consist of fixed facts, like the past, but that's a childish argument. And even children learn very quickly the difference between future and past. If your argument for determinism is simply a denial of the obvious difference between future and past, then this thread is ridiculously pointless.

Meanwhile Dirac was doing it right and seeing reversibility in more accurate equations. — Kenosha Kid

OK, you really seem to believe the proposition that time is reversible, and applying this proposition in physics is "doing it right". I sincerely hope that you do not really have a PhD in physics if this is an indication of what is being taught in physics these days.

'Position' is a state. All of the possible positions constitute a complete basis set. — Kenosha Kid

Sorry - hadn’t noticed this response till just now because I wasn’t tagged in it.

You’re still glossing over the basic conceptual problem implicit in your phrase ‘any given electron’. This implies that there is an electron ‘there’ - which is then qualified by saying ‘oh well, it depends on what you mean by “there” ‘. The diagram you provided does nothing to dispel this.

The question of whether sub-atomic particles really exist or not is central to all of this. I’m suggesting that they exist in a metaphorical sense, as constructs within a theoretical framework. Put another way, the answer to the question ‘does an electron exist’ is neither yes nor no.

Heisenberg again:

the inherent difficulties of the materialist theory of the atom, which had become apparent even in the ancient discussions about smallest particles, have also appeared very clearly in the development of physics during the present [i.e. 20th] century.

This difficulty relates to the question whether the smallest units are ordinary physical objects, whether they exist in the same way as stones or flowers. Here, the development of quantum theory some forty years ago has created a complete change in the situation. The mathematically formulated laws of quantum theory show clearly that our ordinary intuitive concepts [e.g. of ‘existence’] cannot be unambiguously applied to the smallest particles. All the words or concepts we use to describe ordinary physical objects, such as position, velocity, color, size, and so on, become indefinite and problematic if we try to use then of elementary particles. I cannot enter here into the details of this problem, which has been discussed so frequently in recent years. But it is important to realize that, while the behavior of the smallest particles cannot be unambiguously described in ordinary language, the language of mathematics is still adequate for a clear-cut account of what is going on.

During the coming years, the high-energy accelerators will bring to light many further interesting details about the behavior of elementary particles. But I am inclined to think that the answer just considered to the old philosophical problems will turn out to be final. If this is so, does this answer confirm the views of Democritus or Plato?

I think that on this point modern physics has definitely decided for Plato. For the smallest units of matter are, in fact, not physical objects in the ordinary sense of the word; they are forms, structures or—in Plato's sense—Ideas, which can be unambiguously spoken of only in the language of mathematics.

The Debate between Plato and Democritus, a keynote speech at a physics conference in the 1950’s (bolds added).

I think the philosophical issue here is that we’re so wedded to a realist paradigm that we can’t see it any other way. It’s natural to believe that subatomic particles are truly existent. I think this is why Einstein asked, exasperatedly, ‘does the moon continue to exist when nobody’s looking at it?’ His implication was, of course it does, and this is why quantum theory must be incomplete or incorrect in some way. Heisenberg describes this as ‘dogmatic realism’. But this is one of the reasons the discovery of the uncertainty principle is said to have such profound philosophical implications.

One more anecdote - there’s a well-known saying by Bohr that ‘those who haven’t been shocked by quantum physics haven’t understood it’. This too was related by Heisenberg, and was in respect of a lecture that Bohr had given to the Vienna Circle. They all nodded sagely and applauded warmly at the end of Bohr’s lecture. And that’s when he made that remark, again, somewhat exasperratedly. Not, one imagines, that it made any difference. :-)

Meanwhile Dirac was doing it right and seeing reversibility in more accurate equations. — Kenosha Kid


OK, you really seem to believe the proposition that time is reversible, and applying this proposition in physics is "doing it right". I sincerely hope that you do not really have a PhD in physics if this is an indication of what is being taught in physics these days. — Metaphysician Undercover

Yes, to think that the collective professor-hood of world physics didn't think to come and check what you personally find intuitively plausible before constructing their curricula. What an oversight!

I hope you guys invent time travel soon, cause I really liked the 80's.

These are all temporal processes. Time is empirically proven as unidirectional. By simple deduction therefore, these processes are unidirectional. There is no experiment required — Metaphysician Undercover

Then don't describe it as empirical. What it is is a strongly held belief.

That time is unidirectional is the most fundamental and important empirical principle which we have. — Metaphysician Undercover

And yet you just said we don't need empirical evidence because a claim is sufficient.

If your argument for determinism is simply a denial of the obvious difference between future and past, then this thread is ridiculously pointless. — Metaphysician Undercover

Fine. If all you have is an insistence to the contrary, your response is ridiculously pointless.

But it is important to realize that, while the behavior of the smallest particles cannot be unambiguously described in ordinary language, the language of mathematics is still adequate for a clear-cut account of what is going on.

And this is sufficient. If the mathematical entity -- the wavefunction -- is doing its job in yielding accurate predictions of statistical outcomes, it corresponds to something real. It doesn't need to be the case that the epistemic object we deal with be identical to the ontic thing it represents. That's true generally in mathematical physics.

Heisenberg's Platonism is his own affair... It is not a statement about QM but about his personal philosophy of reality. He is welcome to it, of course, but no one else is obliged to adhere to it.

it corresponds to something real. — Kenosha Kid

Well, one is quite entitled to take that with a large grain of salt. Or at least recognise that it is a methodological postulate, more than a statement about ‘what is’. And as Heisenberg was one of the figures who devised this entire field of science, I find his philosophy of it quite persuasive.

If the mathematical entity -- the wavefunction -- is doing its job in yielding accurate predictions of statistical outcomes, it corresponds to something real. — Kenosha Kid

Only in the very limited scope of the quantum, not in making predictions in the macro world. The wavefunction is useless in predicting what trajectory to take when aiming a rocket at the Moon or predicting the identity of who committed a crime. What role could the wavfunction play in a "theory of everything"? Why is classical physics still useful in yielding accurate predictions? Does that not mean that classical physics is doing its job? Then why are they incompatible?

Then don't describe it as empirical. What it is is a strongly held belief — Kenosha Kid

And the output of the detectors only becomes known when it is consciously observed by a person. The hypothesis of a measurement before this conscious observation lacks compelling theoretical or empirical grounding.
After all, QM offers no reason why the whole system—electrons, slits and detectors combined—wouldn’t be in an entangled superposition before someone looks at the detectors’ output.

Yes, to think that the collective professor-hood of world physics didn't think to come and check what you personally find intuitively plausible before constructing their curricula. What an oversight! — Isaac

It's not a matter of intuitive plausibility, it's a matter of empirical evidence.

Then don't describe it as empirical. What it is is a strongly held belief. — Kenosha Kid

Obviously, it's a strongly held belief because it is empirical. Empirical means based in observation and experience rather than theory. Clearly, the strength in the belief that time is unidirectional is provided for by experience and observation, and therefore it is empirical. The idea that time is reversible is provided for by theory (such as the special theory of relativity) and is therefore non-empirical.

And yet you just said we don't need empirical evidence because a claim is sufficient. — Kenosha Kid

That's not what I said. I said deductive logic is sufficient. And, the premises of the deductive argument are validated by empirical evidence. The idea that time is unidirectional is not simply a claim, it is a proposition strongly supported by empirical evidence.

Fine. If all you have is an insistence to the contrary, your response is ridiculously pointless. — Kenosha Kid

What is pointless, is for someone like you, to come into a philosophy forum, and argue determinism based on premises derived from science fiction, produced from the fringes of relativity theory, enabled by the deficiencies of the faulty boundaries of that theory. We can argue whatever we want, if we take our premises from science fiction.

As I tried to tell you days ago, your efforts would be much more productively spent if you sought the medium within which the waves exist, so that you can establish a relationship between that medium and material (massive) existence. The Michelson-Morley experiments demonstrate that this relationship is completely unknown to us. Rather than pretending that there is no such medium, and going off into the opportunities for science fiction created by that misunderstanding, we need to put effort toward understanding the nature of that medium.

And this is sufficient. If the mathematical entity -- the wavefunction -- is doing its job in yielding accurate predictions of statistical outcomes, it corresponds to something real. It doesn't need to be the case that the epistemic object we deal with be identical to the ontic thing it represents. That's true generally in mathematical physics. — Kenosha Kid

This might be true, but it provides no directional guidance for interpretation. Statistical evidence and mathematics provide for prediction, Theory provides a description of what occurs. Now, there is a gap between these two which is bridged with interpretation. So, as an example, I can map the position of sunrise day after day for years, and develop predictive capacity, (like Thales predicted the solar eclipse), then I can relate this predictive capacity to my theory (which may be science fiction) that a giant dragon carries the sun in its mouth from sunset to release it again on the eastern horizon at sunrise, at the predicted spot. The deficiencies of my interpretation are exposed as 'how does the dragon act so mechanistically to find the exact point of release every day?'. Your science fiction interpretation demonstrates the inverse problem. You assign mechanistic reliability to something which is understood as stochastic.

Obviously, it's a strongly held belief because it is empirical. Empirical means based in observation and experience rather than theory. Clearly, the strength in the belief that time is unidirectional is provided for by experience and observation, and therefore it is empirical. — Metaphysician Undercover

Yeah, that's really not how empiricism works. You can't look at a red car and state that your strongly held belief that all cars are red is empirical. If you want to know whether the elementary process of QED are reversible or not, you can't look at thermodynamics and say, "Well, that's irreversible, therefore everything is!" That's just backward thinking.

I said deductive logic is sufficient. — Metaphysician Undercover

It's not deductive, it's inductive.

What is pointless, is for someone like you, to come into a philosophy forum, and argue determinism based on premises derived from science fiction, produced from the fringes of relativity theory, enabled by the deficiencies of the faulty boundaries of that theory. — Metaphysician Undercover

Fine, ignore the thread. I will certainly be ignoring your contributions to it.

Yeah, that's really not how empiricism works. You can't look at a red car and state that your strongly held belief that all cars are red is empirical. If you want to know whether the elementary process of QED are reversible or not, you can't look at thermodynamics and say, "Well, that's irreversible, therefore everything is!" That's just backward thinking. — Kenosha Kid

We are not talking about whether this or that specific process is reversible, we are talking about whether time is reversible. It is an empirical fact that time is not reversible, this is made evident by the second law of thermodynamics. It never has reversed, and there is absolutely no reason to believe that it ever will, this would violate that law. Though it makes good science fiction to talk about a reversal of time, it is literally backward thinking.

Now, all elementary processes of QED known to human beings, are temporal processes. And, time is not reversible. Therefore no elementary process of QED known to human beings is reversible. If there are some processes which are non temporal then they are unknown to human beings, and to portray them as a plain reversal of a temporal process is simple naivety. It doesn't even make sense to talk about non temporal things as processes.

If you want to look at some aspects of QED as being not describable as temporal processes, then you need to get beyond this simple idea that a non temporal thing is a straight reversal of a temporal process. Once you remove the constraints of "temporal process", which means to follow the direction of time, then you open a whole new realm of possibility in thinking, and there is really no reason to restrict your thinking to a simple reversal. In fact, it makes no sense to think that something outside the constraints of time would mimic a process constrained by time, but do it in reverse. That would be like assuming that if something was not constrained by gravity, it would act in a way opposite to gravity. What reason is there to think in this way?

t's not deductive, it's inductive. — Kenosha Kid

Look again, the argument is deductive. P1.Time is not reversible. P2. All the known processes of QED are processes in time. Therefore no processes of QED are reversible. P1 is inductive, that's why I say it is an empirical principle, it's based in experience, observation. But the argument that no process of QED is reversible is deductive. Do you see the logic? All processes are temporal, they are features of the passing of time, that's the nature of what a "process" is. Time is not reversible, and this is evident from the second law of thermodynamics, therefore all these things which we call processes, which are features of the passing of time, are not reversible.

Certain mathematical formulae or processes in physics show a symmetry in the time variable. How this relates to "going back in time" is a reasonable question.

"Going back in time" is incoherent unless the entire universe is going in reverse. Any particular process undergoes changes at a frequency relative to other processes. What is the observable difference between a process oscillating between two states and a process going forwards and backwards in time?

Walking forwards and then backwards is changing my state, but I'm still moving forward in time because the change in state is relative to the change going on in the rest of the universe. I didn't move backwards in time relative to you, I just changed my spatial state relative to you. Only if the entire universe reversed its process would it make sense to say that "time" is reversed.

When I study elementary dynamical systems in C, I sometimes employ functions that "reverse iterate", and those systems show the time symmetry. Time dependent vector fields - like force fields that fluctuate - show symmetry occasionally. Here is an elementary and casual discussion of the subject.

Incidentally, what does QM have in common with a savings account? :cool:

Certain mathematical formulae or processes in physics show a symmetry in the time variable. How this relates to "going back in time" is a reasonable question. — jgill

Most fundamental processes do. Mass, charge, position, acceleration, energy, density, electric field, potential and polarization are the same under time-reversal. Pretty much everything else transforms into another physical process or property, such as velocity, momentum, angular momentum, current, magnetic field, and of course time coordinate. That is, for any processes describing these, the time-reversal is itself a physical process.

There's really only two things that have an intrinsic arrow of time, i.e. where the time-reversal of a process is not another physical process: weak dynamics (such as in radioactive decay) at low temperatures, and statistically improbable initial conditions, e.g. initialising a system into an ordered state, which gives us the second law of thermodynamics. Thermodynamics itself is reducible to QED, i.e. consists entirely of reversible phenomena. The Einstein equations also do not privilege a direction of time, with the cosmological arrow likewise an artefact of boundary conditions not elementary processes.

It's worth clarifying that we're not generally speaking of things changing direction in time. The advanced wavefunctions of the OP are always moving in reverse to our psychological arrow of time. Changing direction in time requires an imaginary component to the Lorentz boost, so can only be considered for *virtual* processes, such as virtual electron-positron pair creation/annihilation.

Incidentally, what does QM have in common with a savings account? :cool: — jgill

One likes to believe it's got every possibility of being positively valued until one measures it?

Is making a measurement in QM and getting a specific result time reversible? How much of "time reversibility" might be artifacts of the mathematics that describe phenomena? — jgill

As you may know, unitary quantum mechanics conserves information. So given an arbitrary state for a system, any earlier state can be determined. In this sense, a system is reversible (i.e., inverse transformations can be applied to the system to restore the earlier state).

Where things get more complicated is when a measurement is taken. At that point, information is generally lost to the environment due to wavefunction collapse. However even then, the pre-measurement state can be determined by someone else isolated from that system and observer.

For example, consider a quantum coin that begins in a "heads" state and is transformed to a superposition of "heads" and "tails". Suppose an observer measures "tails". They cannot determine from that state what the original state was. But an isolated observer can (in principle).

This recent paper by Zurek (one of the pioneers of decoherence theory) provides the details:

I compare the role of the information in classical and quantum dynamics by examining the relation between information flows in measurements and the ability of observers to reverse evolutions. I show that in the Newtonian dynamics reversibility is unaffected by the observer’s retention of the information about the measurement outcome. By contrast—even though quantum dynamics is unitary, hence, reversible—reversing quantum evolution that led to a measurement becomes, in principle, impossible for an observer who keeps the record of its outcome. Thus, quantum irreversibility can result from the information gain rather than just its loss—rather than just an increase of the (von Neumann) entropy. Recording of the outcome of the measurement resets, in effect, initial conditions within the observer’s (branch of) the Universe. Nevertheless, I also show that the observer’s friend—an agent who knows what measurement was successfully carried out and can confirm that the observer knows the outcome but resists his curiosity and does not find out the result—can, in principle, undo the measurement. This relativity of quantum reversibility sheds new light on the origin of the arrow of time and elucidates the role of information in classical and quantum physics. Quantum discord appears as a natural measure of the extent to which dissemination of information about the outcome affects the ability to reverse the measurement. — Quantum reversibility is relative, or does a quantum measurement reset initial conditions? - Zurek

Time is an illusion. Change is real.

An object/process doesnt move forwards or backwards through time. It simply changes and how it changes is a property of the process, not of time.

Again, what is the observable difference between time being reversed and some process undergoing change? How can you tell if the process is really time reversed or simply undergoing natural changes between two or more process-defining states?

If your bank account had money deposited and then withdrawn, your bank account didn't move backwards in time. Depositing and withdrawing are natural states of bank accounts changing, not a state of time moving forwards or backwards.

Time dependent vector fields - like force fields that fluctuate - show symmetry occasionally. Here is an elementary and casual discussion of the subject. — jgill

That's an interesting article John. It shows how one might predict the movement of an object through a force field using a vector field. I think what Kenosha Kid is arguing is that a particle predicts its own end point by receiving information backwards in time from that end. The existence of the particle between emission and absorption can then be represented as a determinable symmetry between the need to be emitted and the need to be absorbed. But this requires a direct relation (ideal reversibility) between emission and absorption.

Certain mathematical formulae or processes in physics show a symmetry in the time variable. How this relates to "going back in time" is a reasonable question. — jgill

There is a problem with the use of equations in modern mathematics which you know I've discussed in other thread. Mathematicians tend to treat the two sides of the equation as signifying the very same thing, some ideal (eternal Platonist) mathematical object. However, if you look at an equation such as 2+2=4 (the example in the other thread), you'll see that the + represents an operation which is absent from the other side of the equation. An operation is a time dependent process. Therefore, to properly interpret the meaning of that equation we need to recognize that we have established equality between a time dependent operation on the left, and a time independent quantity on the right. This indicates that the effects of time have been dismissed from the expression of equivalence (the equation) as irrelevant, inessential, or accidental.

The mathematical equation according to modern axioms, is constructed without regard for the effects of time. What is represented is mathematical objects (eternal Platonist), and the difference between different operations (temporal processes) is dispensed as a difference which makes no difference. So when mathematics is applied in physics, it is inevitable that there will be symmetry in the time variable. The evidence is abundant, as Kenosha Kid attests, above. The very axioms which mathematicians employ, the premises for the mathematical proceedings, have already dismissed the effects of time as irrelevant. Consequently, the conclusions drawn will show that the effects of time are irrelevant, therefore temporal processes are represented as reversible.

A good example of the problem involved with ignoring the temporality of mathematical operations is the difference between the conventions employed in the two operations (processes) called multiplication and division. In multiplication we start with a definite quantity, and increase that quantity. This produces a well defined fundamental unit and the product cannot be outside the boundaries of that defined unit. There is no remainder as there may be in division. In division however, we allow the unit to be divided indefinitely, producing repeating decimals and irrational numbers. Therefore the conventions of division annihilate the fundamental unit, there cannot be a fundamental unit according to those conventions. Now we can make two opposing principles or axioms, one for multiplication, that we must start with a fundamental unit, and one for division, that there is no fundamental unit, as the unit is infinitely divisible.

The difference between multiplication and division, that they cannot be inversions of each other under current conventions, becomes very evident in wave theory, such as that employed in music. The octave serves as the fundamental unit, and we can create harmonies through either multiplication or division. But there is a problem in division which creates inconsistency, dissonance, in the tones created by division, with the tones created by multiplication. So there are two conventional ways of dividing the octave, just temperament, and equal temperament, each based in different principles designed to mitigated the difference between division and multiplication. The principal issue is that the initial choice for the fundamental unit, the octave, is arbitrary. Having an arbitrary unit as the fundamental unit, manifests in the reality of division being not a direct inversion of multiplication. This problem is foundational to the Fourier uncertainty, and it will not be resolved until we determine a fundamental unit which is not arbitrary, and adhere to the principle that the unit cannot be divided. Only then could we have a true ideal which would allow multiplication and division to be inversions of each other.

At that point, information is generally lost to the environment due to wavefunction collapse. — Andrew M

Just a clarification, it is not lost to the environment in the Copenhagen interpretation: it is simply deleted. Decoherence is the process of information loss to the environment, in which superpositions cannot be sustained by macroscopic objects because of the large number of degrees of freedom. When an electron is found at y, the contribution at y' is dissipated. Last time I checked, consensus was this is real but insufficient to account for apparent wavefunction collapse, although Penrose advocated this view at some point.

https://plato.stanford.edu/entries/qm-decoherence/#ConApp

They cannot determine from that state what the original state was. But an isolated observer can (in principle). — Andrew M

This is specifically the Von Neumann-Wigner interpretation. In Copenhagen, the wavefunction collapses objectively.

I didn't cover Von Neumann-Wigner in the OP because it's kind of a magic version of MWI: in both cases, the first observer is in a state of having made a measurement (entangled), but for the second observer everything is still in superposition (unentangled). What I like about Von Neumann-Wigner is the relativism, but I dislike the magic. However, various findings in the last few years have provided experimental evidence for that relativism. It seems to me consistent with an MWI with stricter branching criteria, which is less magic. These experiments generally rely on something called *non-destructive measurements* whose status is questioned.

https://advances.sciencemag.org/content/5/9/eaaw9832.full

Anyway, point being that these various interpretations are not interchangeable. The docoherence picture of wavefunction collapse is at odds with Copenhagen, MWI, transactional QM, and Wigner's friend. Likewise Wigner's friend is at odds with Copenhagen, decoherence and transactional.

I get the impression I have not well conveyed what is meant by a reversible process or how it relates to independence of time direction or real physical processes. Below is two sets of four Feynman diagrams to illustrate the point.



Time is the vertical axis, a given dimension in space the horizontal. The solid lines denote massive particles, in this case an electron/positron; the squiggly lines represent photons. The solid lines have arrows because the particle in question is not its own antiparticle, e.g. the antiparticle of an electron is a positron, not an electron. The squiqqly lines have no arrow because the photon is its own antiparticle.

The first diagram A1 depicts a known physical process called pair annihilation, in this case the annihilation of an electron with a positron or anti-electron. The two particles move together, resonate, and decay into a pair of photons.

The frame invariance of relativity suggests that the temporal and spatial aspects of this process should be interchangeable, i.e. if we rotate the diagram 90 degrees such that time becomes space and space becomes time, the diagram should still represent a physical process, and indeed it does. A2 represents a scattering event, in this case one which a positron absorbs a photon and later re-emits it. A further rotation by 90 degrees leads to A3: a complete time- and space-reversal of the first diagram, and this too is a physical process called pair creation, the reverse of pair annihilation. A final rotation gives us the fourth diagram wherein we see that absorption followed by emission time-reversed is still absorption followed by emission.

The next set B1-B4 show the same processes but with the absorption and emission events reversed. As we see, we still have the pair creation and annihilation rotations, merely with photon momenta exchanged. One can complete this set by incorporating spin.

This is a broader depiction of what is meant by reversibility in the OP: that rotating a physical process about space and time yields another physical process. The vast majority of physical processes are included in QED which has the above characteristics, i.e. is independent of whether a dimension is temporal or spatial, directed one way or the other. Within this majority of elementary processes covered by QED, nature does not have a preferred reference frame, including directionality.

Incidentally, what does QM have in common with a savings account? :cool: — jgill

This is not meant as a pun. Under stipulations that will make the Kid's eyes roll, there is a fundamental form or principle underlying the math of both. Start with a very simple version of Schrödinger's equation:

$ih\frac{\partial \psi }{\partial t}=H\psi ,\text{ }\psi =\psi (x,t)$. Then get rid of that annoying Hamiltonian by stipulating $\frac{{{\partial }^{2}}}{\partial {{x}^{2}}}\psi ={{C}_{0}}\psi$. Now, writing this as a normal derivative, since x is held constant in the partial, $\frac{d\psi }{dt}={{C}_{1}}\psi$.

Now, turn to a savings account with a yearly interest rate r (like r=.03) compounded n times per year. At the end of a year one has an amount under continuous compounding,
$A={{\left( 1+\frac{r}{n} \right)}^{n}}{{A}_{0}}\to {{e}^{r}}{{A}_{0}},n\to \infty$. Which is the solution to the differential equation, $\frac{dA}{dt}=rA$.

Underlying both DEs is the fundamental relationship: The instantaneous rate of change of something is proportional to the amount at that time. The first DE has the imaginary i in its "constant", and ${{e}^{i\theta }}=\cos (\theta )+i\sin (\theta )$ works its magic.

(I know, I've made a mess of the physics!) :gasp:

The frame invariance of relativity suggests that the temporal and spatial aspects of this process should be interchangeable... — Kenosha Kid

This is the problem I explained to you earlier. Proceeding from spatial location A to location B is reversible, and the reverse may be represented as proceeding from B to A. Going from time 1 to time 2 is not reversible. Therefore it is inaccurate to represent the temporal and spatial aspects of a process as interchangeable. I believe that's why there is a distinction between space-like and time-like in the conventional application of relativity theory. You seem to disregard this convention with your science fiction.

If the mathematical entity -- the wavefunction -- is doing its job in yielding accurate predictions of statistical outcomes, it corresponds to something real. It doesn't need to be the case that the epistemic object we deal with be identical to the ontic thing it represents. That's true generally in mathematical physics. — Kenosha Kid

Thanks, that's pretty well the only point I was getting at.

Just a clarification, it is not lost to the environment in the Copenhagen interpretation: it is simply deleted. — Kenosha Kid

Yes, good point.

Decoherence is the process of information loss to the environment, in which superpositions cannot be sustained by macroscopic objects because of the large number of degrees of freedom. When an electron is found at y, the contribution at y' is dissipated. Last time I checked, consensus was this is real but insufficient to account for apparent wavefunction collapse, although Penrose advocated this view at some point.

https://plato.stanford.edu/entries/qm-decoherence/#ConApp — Kenosha Kid

I'm not sure I follow your last sentence (and I read the SEP section). If, on measurement, the superposition state information is lost to the environment (apart from the measured value) then what else could be required for apparent collapse to have occurred?

They cannot determine from that state what the original state was. But an isolated observer can (in principle).
— Andrew M

This is specifically the Von Neumann-Wigner interpretation. — Kenosha Kid

Not specifically. This is just unitary QM. For example, MWI and RQM both agree with this prediction and are both referenced in the paper you linked:

The friend can even tell Wigner that she recorded a definite outcome (without revealing the result), yet Wigner and his friend’s respective descriptions remain unchanged (6). [Deutsch]
...
Another option is to give up observer independence completely by considering facts only relative to observers (24) [Rovelli] — Experimental test of local observer independence

Also the Zurek paper I linked specifically addresses the von Neumann-Wigner interpretation and states that retention of information suffices for collapse. (Which the paper treats as relative.)

The familiar ‘paradox’ of Wigner’s friend offers an interesting setting for this discussion. Wigner speculated [9] (following to some extent von Neumann [1]) that ‘collapse of the wavepacket’ may be ultimately precipitated by consciousness. The obvious question is, of course, ‘How conscious should the observer be?’

The answer suggested by our discussion is that—if the evidence of collapse is the irreversibility of the evolution that caused it—retention of the information suffices. Thus, there is no need for ‘consciousness’ (whatever that means): The record of the outcome is enough. On the other hand, the observer conscious of the outcome certainly retains its record, hence being conscious of the result suffices to preclude the reversal—to make the ‘collapse’ irreversible. Quantum Darwinism [11,25–34] traces the emergence of the objective classical reality to the proliferation of information throughout the environment. — Quantum reversibility is relative, or does a quantum measurement reset initial conditions? - Zurek

Anyway, point being that these various interpretations are not interchangeable. The docoherence picture of wavefunction collapse is at odds with Copenhagen, MWI, transactional QM, and Wigner's friend. Likewise Wigner's friend is at odds with Copenhagen, decoherence and transactional. — Kenosha Kid

Zurek is a decoherence guy and he agrees with the Wigner's friend predictions. You seem to be treating decoherence as objective.

Also I'm curious why you say Wigner's friend is at odds with transactional QM. Is it an objective collapse interpretation, like GRW?