I The Arrow of Time and the Reversibility of Decay Processes in Physics

[bhobba]

(there is NO position or time observable at the relativistic level)

Hmmmm.

Not so sure of that one:
http://arnold-neumaier.at/physfaq/topics/positionQFT

There are a couple of others as well but let's start with that one.

It was written by Dr Neumaier so questions are best directed at him.

Thanks
Bill

 

[rkastner]

Thanks, I am aware of this attempt to define a position operator by N-W. You only get a localized state in a particular frame, so it's not a covariant operator description as is required for a relativistic theory. Again, spatiotemporal parameters (x,t) are symmetry parameters, not conserved physical quantities. This is why quantum field theory is done by 'demoting' position to the same status as time, and replacing spacetime coordinate operators with field operators. Another intuitive way to understand the situation is in terms of particle creation: smaller spatiotemporal localizations involve higher momenta and energies, which create particles, so we can't be sure we have a single particle at a singular position. The most natural way to go is to admit that spatiotemporal quantities are not fundamental the way energy and momenta are. The form of the propagator (simpler in E,p representation) supports this as well. I'll add here a paper that valiantly tries to preserve position eigenstates but confesses that they would involve infinite and even imaginary masses: http://asg.sc.edu/sites/asg.sc.edu/files/attachments/Position%20Operators%201969.pdf (p. 181, below eq 40) They try to wave that fact off by saying 'one never achieves exact localization in nature'--which essentially confesses that there is no system possessing a property of well-defined position, which is my point.

 

[bhobba]

'one never achieves exact localization in nature'

Agreed - but I don't see the problem with that. I don't see the decoherence program claiming that. Sure our models have exact positions but everyone knows that's just a good approximation - everyone knows exact positions are not possible.

Thanks
Bill

 

[rkastner]

The significance of noting that energy/momentum is a real observable, while spacetime coordinates are not, is that it solves at least one aspect of the 'factorization problem'. I.e., many researchers who are trying to explain the appearance of the macroscopic realm from the microscopic realm assume that all observables are on the same footing. But at the relativistic level, which is the real level at which Nature operates, energy/momentum is more fundamental--more physically real--than the spacetime coordinate description. So an explanation for emergence of the macroscopic world of appearance needs to take that into account. That is what PTI (now called RTI for relativistic TI) does. In contrast, standard 'decoherence & unitary-only' approaches just help themselves to primal distinguishability in order 'derive' distinguishability. They think you have to do this because they have no way to solve the 'factorization' problem given the supposed equivalence of all the usual observables.

 

[bhobba]

I am having trouble following some of your concerns.

First - no question the factorization issue is a genuine problem - we need theorems that it doesn't matter how you factorize a system it makes no difference - you get the same result. I believe they will eventually be forthcoming but until they are its an issue.

However some points don't make sense to me.

1. It is well known from a number of texts that standard QM is the 'dilute' limit of QFT eg:
https://www.amazon.com/dp/9812381767/?tag=pfamazon01-20

2. Standard QM has, in its domain of applicability, proven correct without exception. Only phenomena such as spontaneous emission, which since it deals with electrons coupled to the quantum EM field is really part of QFT are an issue.

BTW I have no time for those dismissive of TI - its legit and those that deny it are simply letting their prejudices getting in the way of the truth. That's not science.

Thanks
Bill

 

[rkastner]

My concern is laid out in the paper I've linked: the unitary-only approach to explaining 'apparent collapse', i.e. the emergence of the macroscopic world, doesn't work, because it assumes what it is trying to prove. One can see this also on p. 14 of Wallace's big book on the Everett Interpretation, as I note here:(from https://arxiv.org/abs/1603.04845):
"The insistence on 2 [the universe has initially separable, localizable degrees of freedom such as distinguishable atoms] appears, for example, in Wallace’s invocation of “additional structure on the Hilbert Space” as ostensibly part of the basic formalism (Wallace 2012, p. 14-15). Such additional structure–preferred sets of basis vectors and/or a particular decomposition of the Hilbert space–is imposed when quantum theory is applied to specific situations in the laboratory. However, what we observe in the laboratory is the already-emergent classical world, in which classical physics describes our macroscopic measuring instruments and quantum physics is applied only to prepared quantum systems that are not already entangled with other (environmental) degrees of freedom.
If the task is to explain how we got to this empirical situation from an initially quantum-only universe, then clearly we cannot assume what we are trying to explain; i.e., that the universe began with quasi-localized quantum systems distinguishable from each other and their environment, as it appears to us today. Yet Wallace includes this auxiliary condition imposing structural separability under a section entitled “The Bare Formalism” (by which he means Unitary-Only), despite noting that we assign the relevant Hilbert space structures “in practice” to empirical laboratory situations. The inclusion of this sort of auxiliary condition in the “bare formalism” cannot be legitimate, since such imposed structures are part of the application of the theory to a particular empirical situation. They thus constitute contingent information, and are therefore not aspects of the “bare formalism,” any more than, for example, field boundary conditions are part of the bare theory of electromagnetism. These separability conditions are auxiliary hypotheses to which we cannot help ourselves, especially since the most general state of an early quantum universe is not one that comes with ...distinguishable degrees of freedom. Thus, the addition of this condition amounts to ...circular reasoning, or (at worst) outright affirming of the consequent, illicitly propping up the claim that quasi-classical world “branches” naturally appear in an Everettian (unitary- only) picture. "

So the problem is that, in unitary-only evolution, the universal state must be considered to have distinguishable features from the very beginning in order to 'derive' the distinguishability attributed to 'einselection'. The latter does the heavy lifting in the purported 'explanation' of the emergence of the macroscopic world. But in order to get that, there must be a 'system of interest', distinguishable from its 'environment'--which presupposes someone who can identify ('be interested in') at least a semi-localized system. But if, for example, the initial universal state consisted only of systems in eigenstates of momentum, nobody would ever have a localizable 'system of interest'. So right away there is an hoc tooling of the universal state such that it will yield us what we want. This sort of hand-tooling of the initial state is required in a unitary-only model in order to get even apparent collapse (but not in a collapse model like TI). As noted above, Wallace smuggles this hand-tooling in as ostensibly part of the 'bare formalism', when clearly it is not--it is application of the formalism along with specific auxiliary conditions obtaining empirically. If the whole point is to account for determinate empirical experience, then unitary-only theorists cannot assume that from the outset! When challenged on this, they basically assert that it's necessary because that's the only possible explanation--another logical fallacy (see the above paper for details on this point).
The reason I brought up the existence of a genuinely preferred observable is that this is a common objection to the TI solution. It also arises as a concern among unitary-only researchers as well. So I'm pointing out that energy/momentum are the preferred observables.
And yes of course you can find nonrelativistic QM as a limit of the relativistic theory. But Nature operates relativistically--she doesn't stop particle creation just because we're not paying attention that domain at the moment. This is why position/time are not ontologically fundamental properties of quantum systems, yet energy/momentum are. Similarly, the orbit of Mercury doesn't stop precessing just because we're not paying attention that.
Thanks for your questions and for your open-mindedness regarding TI. (My latest submission to the arxiv on TI, discussing how it explains the microscopic origin of irreversibility and thus the 2nd law of thermodynamics, has been placed on hold. The paper is an invited submission to Entropy. It can be viewed here: http://philsci-archive.pitt.edu/id/eprint/12718 )

 

[rkastner]

Follow-up: the paper I referred to above ( http://philsci-archive.pitt.edu/id/eprint/12718 ) has now been apparently accepted as a submission to the arxiv.

 

[secur]

@rkastner, thanks for this paper "A Physical Basis for the Second Law of Thermodynamics: Quantum Nonunitarity". The explanation of 2nd law is convincing. It depends on completion of the measurement process in two steps:

First, the transition from density operator to density matrix by completion of all OW/CW transactions. Whether one "believes in" RTI or not, this is a valid and simple way to look at it.

Second, the collapse:

The second step in the measurement transition is non-unitary collapse to one of the outcomes |! !| from the set of possible outcomes {i} represented by the weighted projection operators | ! |!|! !| in the density matrix above. This can be understood as a generalized form of spontaneous symmetry breaking, a weighted symmetry breaking: i.e., actualization of one of a set of possible states where in general the latter may not be equally probable.

Note that this process is not unique to, or explained by, RTI. It's just the standard collapse postulate. Right?

From these the derivation of 2nd law follows correctly, AFAIK.

I have reservations about this, ...

In addition, the relativistic level of TI (referred to as RTI) provides a basis for the directionality of the irreversibility inherent in the measurement transition, thereby establishing an arrow of time consistent with the Second Law. In this respect, the arrow of time is not explained by entropy increase; rather, it is a crucial component of the explanation for the increase in entropy toward the future.

... the discussion seemed to involve circular reasoning. However presumably it's a standard TI argument, so if you can provide a ref that has more details, probably it would answer my objection. Anyway, it doesn't affect the main explanation of the 2nd law, if we just assume the arrow of time (i.e., the direction of "future").

BTW these two footnotes from page 5 accidentally appear on page 2 also:

2 As their names indicate, both of these objects are wavelike entities — specifically, they are deBroglie waves.
3 However, TI is best understood in the Heisenberg picture, in which the observables carry the time dependence and the offer wave is static; this is to be discussed in a separate work.

 

[dlgoff]

Subscript typo on page 3?

Should be?

 

[rkastner]

Thanks very much to both of you for catching these typos, and Secur for the questions.
Re the collapse postulate, as I note in the paper, the status of that is very unclear in the standard approach. It seems to me that it needs to be real ontological collapse to provide a physical justification for Boltzmann's 'molecular chaos' assumption, which is not on firm ground at the moment.
In TI we get real physical collapse, not just updating of our information about a system (or something that 'looks like collapse' as in the Everettian/decoherence approach). You need the response of absorbers to break the linearity of the Schrodinger evolution in order to define where in the process real physical collapse occurs--so that gas molecules really are correctly, physically described by the master equations. So that's why TI provides something here that we don't get in other approaches. Basically it changes the 'collapse postulate' from an unexplained, ad hoc postulate to a theoretical model of how and why collapse occurs, and why the outcomes have the probabilistic weights that Max Born came up with on a hunch (in a footnote in 1931).
I"m not quite sure what your second concern is. The idea is just that emission has to precede absorption, and that's why absorption is always in the future direction relative to the emission, which establishes an arrow of time independently of entropy considerations. So there's a distinction between the two issues. This is in contrast to those who claim that the arrow of time is explained solely by entropy increase. I give a reference in the last footnote, that explains why either choice of boundary conditions for the direct-action theory (as discussed in Davies 1972) results in the same apparently future-directed phenomena--basically both the Feynman and Dyson propagators yield the same effect. (People in a Dyson-universe would just label their time parameter oppositely from people in a Feynman-universe. ) So I don't see anything circular here.
Edit update: sorry, I see you were asking specifically about the 2nd step of the measurement transition and I'm not sure I addressed that to your satisfaction above. But once we have the basic non-unitary step, the probabilities can be interpreted epistemically, and therefore it's reasonable to suppose that the system has a determinate value at that point, and we just don't know which one.

 

[secur]

I"m not quite sure what your second concern is. The idea is just that emission has to precede absorption, and that's why absorption is always in the future direction relative to the emission, which establishes an arrow of time independently of entropy considerations..

Well, I'm not sure about this. But how do we know which is emission, and which absorption? Isn't it because the first one comes first? The two are symmetrical processes under time-reversal aren't they? After all a photon can't tell the difference, they both happen at the same time (to the photon) and the only distinction is which end of the path they're on. So - if that's true - we know which is emission only because it comes first, and then you're saying we know which comes first, because it's emission.

BTW it seems to me the collapse itself provides time direction, there's a definite asymmetry of the wavefunction before and after.

Edit update: sorry, I see you were asking specifically about the 2nd step of the measurement transition and I'm not sure I addressed that to your satisfaction above. But once we have the basic non-unitary step, the probabilities can be interpreted epistemically, and therefore it's reasonable to suppose that the system has a determinate value at that point, and we just don't know which one.

Right, the first step is well-explained by TI (or RTI, same explanation relativistically). But the 2nd step needs an extra assumption. Indeed it's "reasonable to suppose" it, once TI has ensured the creation of density matrix, and I have no problem with doing so. But it's not explained, specifically, under R/TI.

 

[rkastner]

Well, I'm not sure about this. But how do we know which is emission, and which absorption? Isn't it because the first one comes first? The two are symmetrical processes under time-reversal aren't they? After all a photon can't tell the difference, they both happen at the same time (to the photon) and the only distinction is which end of the path they're on. So - if that's true - we know which is emission only because it comes first, and then you're saying we know which comes first, because it's emission..

Well no, the emission event is identified as such by the emitter, which drops down to a lower energy state as a result of the emission. I.e., the emitter loses energy, while the absorber gains it, and that's what distinguishes emission from absorption. The emitter and absorber change in opposite ways.
Keep in mind that the direct action theory explains loss of energy by a radiating charge--it's the response of absorbers that account for that. Without that response, there is no loss of energy by a would-be emitting atom and no gain of energy by a would-be absorbing atom--nothing happens in a completely time-symmetric field situation which is the basic propagation in the direct-action theory. The absorber response is what introduces the asymmetry. For the Feynman propagation boundary condition, absorber response cancels out the advanced field to the past of the emitter, reinforces the 1/2 strength field between emitter and absorber to full strength, and cancels out the retarded field to the future of the absorber. This is a time-asymmetric process; the past and future cancellations occur for different components of the field. So in a sense the direct-action theory carries with it a form of temporal symmetry-breaking. This is necessary for any real (on-shell) photons to be propagating anywhere at all. But it's an elegant picture, because it makes the real photon a connection between two participants (the emitter and absorber) that are thereby changed and time-ordered as a result of the interaction. In contrast, in the standard theory, the necessary real photon propagation is put in 'by hand' via a sourceless field. (Sounds like magic to me.) As Wheeler himself noted in 2003, the direct-action theory has a much more physically grounded explanation for the radiation process.

Right, the first step is well-explained by TI (or RTI, same explanation relativistically). But the 2nd step needs an extra assumption. Indeed it's "reasonable to suppose" it, once TI has ensured the creation of density matrix, and I have no problem with doing so. But it's not explained, specifically, under R/TI.

OK I get your concern. As you've noticed, TI's big contribution is the basic nonunitary transition from a pure to a well-defined mixed state. Once you have a mixed state that can be interpreted epistemically, it's legitimate to say that the system has a determinate but unknown property. In contrast, you can't legitimately say that in the standard "decoherence" approach, because at best you only get improper mixed states, and those cannot be interpreted epistemically. (See, e.g., http://www.siue.edu/~evailat/pdf/qm11.pdf) So once you have an epistemic mixture, as in TI, the measurement problem is solved. Now, of course there is no causal, deterministic story for how the system ends up in one state as opposed to the others; but that shouldn't be a surprise to us by now. It's a reflection of genuine ontological indeterminacy-- which means: something truly unpredictable happens. Nature apparently does not obey the 'principle of sufficient reason'. Or maybe, as I've explored a little in my latest book, perhaps this is Nature's way of leaving room for volition...? Remember Dyson's remark that: "I think our consciousness is not just a passive epiphenomenon carried along by the chemical events in our brains, but is an active agent forcing the molecular complexes to make choices between one quantum state and another. In other words, mind is already inherent in every electron, and the processes of human consciousness differ only in degree but not in kind from the processes of choice between quantum states which we call "chance" when they are made by electrons.” (Disturbing the Universe)

 

[secur]

Ok, you're right, there's energy asymmetry of emitter / absorber. The thought was, as indicated, just off the top of my head.

Re. Dyson, never bothered to read him, but figured that out (and much more) 3 years before he wrote that book (1978). Last century I pushed the consc-QM idea in the field of Consciousness Studies, finally gave up in 2001. I predicted, back then, that people will finally be ready for it around 2030 - 2040. Still think that's about right.

As I remember, on your website you explicitly deny that consc has anything to do with it. Certainly you may be right. I don't know that it does. But, obviously, it might. Do you know a discussion board where such issues are allowed?

 

[rkastner]

Thanks--I should clarify that actually I don't deny that consciousness has anything to do with collapse. What I do deny is the standard appeal to an ill-defined 'external conscious observer'. Absorber response triggers the measurement transition, as described in my 2nd law paper. Now, whether absorbers have consciousness is a separate -- and very intriguing -- issue, as I've noted above. But the absorber is always part of the process, and it's well-defined within the direct-action theory. So it's not an ad hoc 'external conscious observer'. The latter came about because people could not explain the measurement transition from within the theory itself. The TI model does this. A recent blog post hopefully will clarify this issue, and of course I welcome discussion of these issues on my website: https://transactionalinterpretation...t-measurement-is-not-necessarily-observation/

 

[secur]

Thanks, I'll intend to contribute comments to your blog. Looks like you already understand many of my "radical" ideas, unlike PF. However PF is more fun because for the most part no one here agrees with me about anything, and I love to argue :-)

Talking about arguing ... on second thought I still have a problem with deriving arrow of time from emission / absorber.

... the emission event is identified as such by the emitter, which drops down to a lower energy state as a result of the emission. I.e., the emitter loses energy, while the absorber gains it, and that's what distinguishes emission from absorption. The emitter and absorber change in opposite ways.

Before the event emitter has more energy, less after; and vice versa for absorber. But now imagine we reverse time, and approach the event from the future, towards the past. In that case "before" (which, with regular time direction, is "after") the event the absorber has more energy, less after; and vice versa for the emitter! So the process is, in fact, time-symmetric.

And here's another point. The energy gain/losses, and in fact the whole process of photon transfer from emitter to absorber, is well understood in mainstream science and doesn't depend on TI. So if it truly defined the arrow of time, everyone (such as Sean Carroll) would already know it. But they don't.

I see you have a couple blog posts on "arrow of time" so I'll check those out, and no doubt become better able to discuss the issue.

 

[rkastner]

As far as 'well understood', the standard theory uses an ad hoc free field to 'explain' loss of energy by a radiating charge. I'm not sure that counts as 'well understood,' even if has become somewhat of a dogma. TI does better, as Wheeler himself noted in 2003.
Also, most physicists subscribe to a 'block world' in which there is no time directedness whatsoever, so they certainly cannot account for an arrow of time in that ontology. In contrast, in PTI, the future is genuinely open and it has an intrinsic temporal direction. I discuss this in my books.

Regarding what is 'reversible': here we have to be careful. The only 'reversibility' obtaining in what you describe above is replacing a world having Feynman-type propagation (positive energy toward increasing time index, negative energy toward decreasing time index) with a world having Dyson-type propagation (negative energy toward increasing time index, positive energy toward decreasing time index). Either way, you get a directedness with respect to time, i.e, decay processes (described by Gamow vectors) occur with respect to one particular temporal direction and not the other. This is the time-asymmetry I'm talking about, and why I was hoping you would take look at the reference in my paper (last footnote). In either case, excited states emit toward one particular temporal directions--not both. That is all I'm saying here. We call the temporal direction in which decays occur the 'future' and associate it with increasing time index. In the 'reversed' case, the same phenomena occur and the time index would just have the opposite sign from ours. In both cases, processes have a 'handedness' with respect to time, aligned with the Gamow vector.
Edit addendum: also, if you take into account that the emitted state is the pure state and the absorbed state is a mixed state, with a genuine indeterminacy about which absorber gains the energy, that is not reversible. I.e., you can't 'reverse the film' and see something that looks like a normal process. The starting point in the reversed case would be a mixed state and that's not how emission works.