Is Unitarity Limited by Real Clocks in Quantum Gravity?

[marcus]

Bei Lok Hu at the University of Maryland has a review article on the "fundamental decoherence" research topic, which devotes detailed attention to the treatment by Gambini and Pullin.

I think it's an interesting topic for several reasons, so I'll give some links. Here's the paper by B.L. Hu et al.:
http://inspirehep.net/record/781938 (Intrinsic and Fundamental Decoherence: Issues and Problems)
http://inspirehep.net/author/profile/B.L.Hu.1 (profile of Bei Lok Hu)

Here are G&P's papers on this topic:

http://inspirehep.net/record/645205 47 cites (A Relational solution to the problem of time in quantum mechanics and quantum gravity induces a fundamental mechanism for quantum decoherence)
http://inspirehep.net/record/653376 38 cites (Realistic clocks, universal decoherence and the black hole information paradox)
http://inspirehep.net/record/674573 12 cites (Fundamental decoherence in quantum gravity)
http://inspirehep.net/record/712912 38 cites (Fundamental decoherence from quantum gravity: A Pedagogical review)
http://inspirehep.net/record/735013 25 cites (Relational physics with real rods and clocks and the measurement problem of quantum mechanics)

I think the gist of it is that in GR natural processes occur at different rates all over the place. There is no official/ideal time, so the best one can do is correlate the other observables to some choice of *real clock*. The definition of unitary evolution is only as good as the clock.

It seems that Eugene Wigner came up with a theoretical limit on the precision-lifespan of a real clock (how accurate for how long a time a clock could be made without it foiling you by turning into a black hole). And Gambini Pullin adapted Wigner's limit on real clocks to find a theoretical limit on the lifespan of unitarity.

You will have to refer to their "Realistic Clocks" paper, http://arxiv.org/abs/hep-th/0406260, because I can't reproduce their argument in detail, but the upshot seems to be that if one focuses on black hole evaporation the unitarity of evaporation dies out on a timescale comparable to the lifespan of the black hole itself.

 

[marcus]

==quote from conclusions of G&P http://arxiv.org/pdf/hep-th/0406260.pdf ==
Summarizing, we have shown that unitarity in quantum mechanics only holds when describing the theory in terms of a perfect idealized clocks. If one uses realistic clocks loss of unitarity is introduced. We have estimated a minimum level of loss of unitarity based on constructing the most accurate clocks possible. The loss of unitarity is universal, affecting all physical phenomena. We have shown that although the effect is very small, it may be important enough to avoid the black hole information puzzle.
==endquote==

A moment's reflection reveals the importance of their result. The only operationally meaningful unitarity is unitarity based on a realistic clock. There is a limit to the precision and stability of a realistic clock and therefore unitarity has limits *in principle*. There are limits *in principle* to the timescales over which unitarity is applicable and can be expected.

Gambini and Pullin find, in the interesting case of black hole evaporation, that the term limit for unitarity is comparable to the estimated evaporation time of the black hole.

 

[marcus]

Assuming unitarity in the BH evaporation process leads to various bizarre conclusions.
For a taste of the current brew skip to shortly after minute 60 of Smerlak's 29 May PIRSA talk.
http://pirsa.org/14050027/
Last gasp ‎of a black hole: why unitary evaporation must be non-monotonic
Speaker(s): Matteo Smerlak
Abstract: I will describe the relationship between radiated energy and entanglement entropy of massless fields at future null infinity (the "Page curve") in two-dimensional models of black hole evaporation. ‎I will use this connection to derive a general feature of any unitary-preserving evaporation scenario: the Bondi mass of the hole must be non-monotonic. Time permitting, I will comment on time scales in such scenarios.
Date: 29/05/2014

the talk is based on two recent papers with Eugenio Bianchi:
http://arxiv.org/abs/1405.5235
http://arxiv.org/abs/1404.0602

I think what we are seeing is more like the "last gasp of unitarity" (where misapplied over time scales comparable to the age of the universe.)

Between minute 60 and 66 he is simply disposing of the the Hawking (semiclassical) evaporation scenario by showing that it leads to singularities/inconsistency (so "one should stop believing in it")
Then around minute 67 he introduces other scenarios (which still assume unitarity).
The first of these is the "Hayward proposal". At minute 73:50 he says that the Hayward scenario is "ruled out" because purification of the final state occurs in a burst, violating energy conservation. The authors have a theorem that purification must be slow. Unfortunately after about minute 70 he was running out of time, and there were a lot of questions from the audience--he didn't have time to prove or even discuss the theorem that purification must be slow (which was included in the initial plan of the talk).

 

[marcus]

Some quotes:
"When one introduces realistic clocks, quantum mechanics ceases to be unitary and a fundamental mechanism of decoherence of quantum states arises. We estimate the rate of universal loss of unitarity using optimal realistic clocks. In particular we observe that the rate is rapid enough to eliminate the black hole information puzzle: all information is lost through the fundamental decoherence before the black hole can evaporate."
(http://arxiv.org/abs/hep-th/0406260)

"...general relativity is a generally covariant theory where one needs to describe the evolution in a relational way. One ends up describing how certain objects change when other objects, taken as clocks, change. At the quantum level this relational description will compare the outcomes of measurements of quantum objects."
(http://arxiv.org/abs/gr-qc/0603090)

"...as ordinarily formulated, quantum mechanics involves an idealization. That is, the use of a perfect classical clock to measure times. Such a device clearly does not exist in nature, since all measuring devices are subject to some level of quantum fluctuations. The equations of quantum mechanics, when cast in terms of the variable that is really measured by a clock in the laboratory, differ from the traditional Schroedinger description. Although this is an idea that arises naturally in ordinary quantum mechanics, it is of paramount importance when one is discussing quantum gravity. This is due to the fact that general relativity is a generally covariant theory where one needs to describe the evolution in a relational way..."
(http://arxiv.org/abs/quant-ph/0608243)

To paraphrase, in the real world duration and distance are defined operationally by physical measurements which is to say by events. In reality there is no such thing as abstract idealized "time". There are various natural processes, whose rates, when compared, depend on their relative motion and their position in the gravitational terrain. Defining an observer's proper time ultimately depends on the choice of some physical process to be the observer's clock.
Unitarity is only as good as the physical clock, and cannot be taken as absolute. It is potentially misleading to assume unitarity on timescales comparable to the present age of expansion.

 

[Paulibus]

...It is potentially misleading to assume unitarity on timescales comparable to the present age of expansion.

I understand 'unitarity' to be a fashionable way of expressing the long-held assumption that mass/energy is conserved, absolutely and always. For example, when a fundamental particle -- say an isolated electron -- is described by a quantum wave function whose absolute square value, integrated over all space, sums to unity, one is expressing a belief that the electron always exists somewhere. By extension, an ordinary carbon atom should also persist permanently, validating the advertisement 'A Diamond is Forever'. Is this now being revealed as just a romantic commercial snare?

 

[marcus]

nice example,
for convenience I'll put some PF links about distinction between pure states (unit vectors in the H-space, can be superpositions) and mixed states. Unitarity preserves pureness.
https://www.physicsforums.com/showthread.php?t=595708
https://www.physicsforums.com/showthread.php?t=242158
https://www.physicsforums.com/showthread.php?t=535917

A unitary transf. is one that takes pure states to pure states. Unit vectors to unit vectors (hence the name). So the pure/mixed distinction is important here. If system is in a pure state and you know the state, then you know all there is to know (e.g. regarding the spin or polarization) about the system. This does not mean you can predict the outcome of every possible measurement. You just know all the rules of nature allow you to know. E.g. if it has been determined that the spin is "up" in a certain orientation, along a certain axis, and you know that, then you still can't predict what it will be along ANOTHER axis. But you know everything about the spin that nature allows you to know.
In a mixed state there is missing information---something you could in principle know but don't. Like in a two-slit setup where it actually bumped something while passing thru one of the slits, but you didn't notice which. So for you it is in a state 1/2 R plus 1/2 L.

There's also this very strenuous technical treatment of the pure/mixed business. I list but don't recommend.
http://pages.uoregon.edu/svanenk/solutions/Mixed_states.pdf

Mixed states can have probabilities summing to one, but they aren't unit vectors in the Hilbert space. A unitary transformation takes unit vectors to unit vectors. Conceptually, it preserves completeness of the info. You don't lose info about the system when a unitary is applied, the way you would if it evolved into a mixed state. (a mixture of pure states where you didn't know which one.)

Loss of unitarity means loss of predictability. I think. Have to go, back later today.

 

[marcus]

I should have said "then you know all you can know about the system" (rather than "all there is to know").
I want to re-iterate part of the previous post:
"You just know [as much as] the rules of nature allow you to know. E.g. if it has been determined that the spin is "up" in a certain orientation, along a certain axis, and you know that, then you still can't predict what it will be along ANOTHER axis. But you know everything about the spin that nature allows you to know."

I think unitarity amounts to more than "a fashionable way of expressing the long-held assumption that mass/energy is conserved,…"

It seems to be more about information (predictability of future, reconstructibility of past) than about conservation of energy etc. I'll get back to this in the morning when hopefully I can be more coherent :^D

 

[Paulibus]

Thanks for those links, Marcus. I now see that unitarity is more than just simplistically conserving
mass/energy, as I had assumed. Instead the conserved feature associated with unitarity seems to
be probability, as explained in Merzbacher’s discussion of The Optical Theorem (his Quantum
Mechanics, 2nd ed., p.505). Since quantum mechanics is all about the probablistic evolution of
‘systems’ that have attributes like names, mass/energy, charge and angular
momentum. I suppose that it is the continuity of these attributes, including the continued existence and
identity of the system itself, say during a scattering event, that demands conservation of an
appropriate probability, a.k.a. unitarity?

 

[marcus]

Hi, Paulibus! I got distracted by other things yesterday and forgot to get back to this thread. Thanks for replying and continuing the conversation despite my negligence. Looking back, I think what I said in #6 and #7 is basically OK. Likewise what you say in #8, although there are two ways of looking at it.

I think you can look at unitarity as preserving information or as preserving probability. BTW if it is not too off-topic you know the Heisenberg vs Schrödinger difference in perspective on QM? With Schrö there is a wave function (say for a single particle) that evolves in time. With Heisen it is the OPERATORS that evolve in time! Think of the STATE as just a fixed vector and the operators are matrices which can evolve, and to get NUMBERS you apply a matrix to the fixed state vector and take inner product. <ψ, Aψ>

So in Heisen the "observables" evolve and the the "state"is just a fixed vector in the Hilbertspace that serves as a device to get actual numbers from the evolving operators that represent "observables".

And then there is an algebraic trick where you represent the evolution of observable matrix A by bracketing it with a unitary matrix U
A_new = U* A_old U

And that AMOUNTS TO THE SAME THING as applying the unitary transformation U to the STATE ψ
TO GET A NEW STATE. But basically the Heisen approach ignores "wave functions" and focuses on matrix mechanics----with states being unit vectors in an abstract inner product vector space. It is "relational" in the sense that it focuses on observations---the matrices correspond to possible measurements or interactions or detections...
===================
For the moment just forget I said that about the Heisenberg perspective. Let's focus on the Schrö picture with just one particle. The wave function is defined on space and is an amplitude to find the particle at that spot and it is square integrable and it is a UNIT VECTOR in an obvious inner product vector space (of functions) and amplitude times its conjugate can be seen as a probability which integrates to ONE. And a unitary transformation on the vector space of wave functions takes unit vectors to unit vectors so by definition it preserves this property of adding up to one.
So one can say "unitary means it preserves probability". It's nice and intuitive.
===================
But maybe it is the wrong way to look at QM. The wave function is only defined on space or space time when you have a SINGLE particle, and with many particles it is defined on a multidimensional phase space. And as soon as there are interactions the number of particles might change and the dimension of the phase space keeps changing! So mathematically it's an unworkable mess
and what they actually do is use the HEISENBERG approach to establish a quantum FIELD THEORY in which you have MATRIX-VALUED FUNCTIONS DEFINED ON spacetime.

With the Schrö approach you have to give up defining functions on ordinary 4D Minkowski spacetime, because your functions are too simple valued, they are just complex amplitude valued. It doesn't work except in the very simple case. But with the Heisen approach you get to keep 4D Minkowski spacetime and all the operator-valued fields are defined on the same spacetime.

So then the question comes back: what does "unitary" mean, in this field theory context, where we no longer have a "wave function" telling simply the amplitude of a particle to be at some particular place at some moment.

I think now unitary means more something like preserving information, or preserving coherence, predictability. It is not as clear what the intuitive meaning is. I'll try to suggest it by the most elementary possible (in fact embarrassingly simple) example

Suppose |R> and |L> are two unit vectors in a complex inner product vector space. And suppose their inner product is zero (they are orthogonal). I'll abbreviate sqrt 0.5 by .707
Then .707|R> +.707|L> is a unit vector, it has norm = 1
but .5|R> +.5|L> is not a unit vector, it has norm = 1/2
That second one corresponds to where the thing bumped something as it was going thru a slit so it went thru one or the other but you did not notice which. So with probability 1/2 it went thru R and with prob 1/2 it went thru L. But you don't know which! You lost some information. The thing decohered. I'll try to present a better example later, maybe involving spin up and spin down, or an "EPR" type Alice and Bobber. The PF threads I linked to earlier provide some helpful discussion.

 

[marcus]

Paulibus, I want to recall the essential passages from Gambini Porto Pullin papers I quoted earlier and emphasize their relevance to the Planck star model black hole and to the LQG bounce. If the information engulfed by a black hole has finite shelf life then, in the Planck star context that tells us something about the LQG bounce. And in particular it tells us that it produces a blank slate structure-wise, so that we should not be surprised by the low geometric entropy at the start of cosmological expansion.

Some quotes:
"When one introduces realistic clocks, quantum mechanics ceases to be unitary and a fundamental mechanism of decoherence of quantum states arises. We estimate the rate of universal loss of unitarity using optimal realistic clocks. In particular we observe that the rate is rapid enough to eliminate the black hole information puzzle: all information is lost through the fundamental decoherence before the black hole can evaporate."
(http://arxiv.org/abs/hep-th/0406260)

"...general relativity is a generally covariant theory where one needs to describe the evolution in a relational way. One ends up describing how certain objects change when other objects, taken as clocks, change. At the quantum level this relational description will compare the outcomes of measurements of quantum objects."
(http://arxiv.org/abs/gr-qc/0603090)

"...as ordinarily formulated, quantum mechanics involves an idealization. That is, the use of a perfect classical clock to measure times. Such a device clearly does not exist in nature, since all measuring devices are subject to some level of quantum fluctuations. The equations of quantum mechanics, when cast in terms of the variable that is really measured by a clock in the laboratory, differ from the traditional Schroedinger description. Although this is an idea that arises naturally in ordinary quantum mechanics, it is of paramount importance when one is discussing quantum gravity. This is due to the fact that general relativity is a generally covariant theory where one needs to describe the evolution in a relational way..."
(http://arxiv.org/abs/quant-ph/0608243)

To paraphrase, in the real world duration and distance are defined operationally by physical measurements which is to say by events. In reality there is no such thing as abstract idealized "time". There are various natural processes, whose rates, when compared, depend on their relative motion and their position in the gravitational terrain. Defining an observer's proper time ultimately depends on the choice of some physical process to be the observer's clock.
Unitarity is only as good as the physical clock, and cannot be taken as absolute. It is potentially misleading to assume unitarity on timescales comparable to the present age of expansion.

The logic is based on comparing two different time-scales. A distant outside observer (à la Gambini et al) sees information-bearing structure fall into the black hole and then after a very long time that info has expired and does not come out during evaporation. Translating that to the Planck star model, the gamma ray burst (GRB) at the end of the bounce is a total blank. (From the outsider's viewpoint the bounce has been time-dilated so that it takes a long time).

But consider how it looks from the viewpoint of an observer rides in with the collapse and witnesses the bounce and the ensuing GRB. For him it all happens very quickly. And yet all the structure in what fell in is wiped out.
Something special was going on. It probably has to do with the fact that during LQG bounce quantum effects make gravity repel instead of attract.

That understanding of what occurs during black hole bounce carries over to the case of the cosmological bounce. It should not surprise us that the geometry which appears there is even and blank---no pockmarks and wrinkles---doesnt have a lot of structure written into it from the prior contracting phase.

 

[Paulibus]

Thanks for your thought-provoking posts 9 and 10. From the point of view of someone trying to
understand where fundamental physics is going I found them stimulating. Some comments:

...I think now unitary means more something like preserving information, or
preserving coherence, predictability. It is not as clear what the intuitive meaning is.

I agree and think that the simplest interpretation of 'unitarity' is that it's a preserver of information
collected under the umbrella of 'identity'; whether the system or object under consideration is
described mathematically by a wave function or a by an S(scattering)-matrix, it's identity remains
in focus as it evolves with time.

 

[marcus]

Fundamental decay of unitarity (and the "blank rebound problem")

Paulibus, I'm trying to delineate what I've heard called the "blank rebound problem" or words to that effect, which seems to come up in Loop gravity and cosmology if you make the "Gambinian" assumption that precise timing decays over time. Assuming such, unitarity itself decays over long spans of time. We are talking spans of time that are over a million-fold the present age of the universe. The only meaning unitarity can have is operational (e.g. clocks and rods) and it the concept can be indistinguishable from perfection over measurable spans of time or even conceivable spansm and yet be found wanting on inconceivably long scales like the lifespan of an astrophysical black hole. So I just refer back to those Gambini et al quotes and say "lets assume they're right".

Then talking about astrophysical objects, the final gamma burst of a Planck star is blank, all info about what fell into form it has expired. This is from the outsider's viewpoint. But what about an hypothetical observer who falls in and participates in the bounce.

For him the bounce happens quickly. He has to see everything turn blank in the blink of an eye. His own memory of the past has to be wiped!

Because when the observer comes flying out in the star's final gamma burst he hast to agree with the outsider that the burst is nondescript virgin energy with no microstate memories. So there must be something special about the Loop black hole bounce. It does a blank rebound.

How can that happen? That, I guess, is the "blank rebound problem".

 

[marcus]

For him the bounce happens quickly. He has to see everything turn blank in the blink of an eye...

Wait. Maybe "in the blink of an eye" is meaningless. Maybe all clocks malfunction above a certain density.
Gambini et al, when calculating the theoretical limit on the endurance of unitarity, found that the best clock was a black hole (for long-lasting stability and precision). the observer would cause it to "ring" and keep time with its frequency. But above a certain frequency Loop quantum corrections make gravity repel---so a black hole clock would burp itself out of existence. What clock could function competently at Loop bounce density?

Can one even say how long the bounce takes, from the participant's viewpoint?

Unitarity needs the passage of time, measured by some clock, in order to be defined. what if clocks cease to function at some point in the bounce? when the density exceeds a certain threshold?

I likely must discard the idea of a participant observer and stick with Gambini Porto Pullin's idea of an outside observer---one outside the black hole who can witness the collapse that forms it and then measure how long it takes to evaporate using a separate timepiece.

I keep having to go back to the quotes (e.g. in post #10) from the Gambini et al papers.

What I want to do is learn something about the Loop black hole bounce, which will then carry over to the cosmological bounce and explain why one should expect expansion to begin with a "blank slate" low entropy state.

Can one even say how long the Loop cosmological bounce takes, from the participant's viewpoint?

And what other viewpoint could there be, since the cosmos is all-inclusive?

For someone in the past, looking forward, how long does the actual bounce take, since he can never see expansion start. How long does it take for someone in the expanding phase, looking back, since there an hiatus blocks his view of the contracting phase? Maybe time-evolution around that point is ill-defined, essentially because of a shortage of clocks. :-)

 

[marcus]

This looks like it might be relevant. I noticed it does not cite the earlier papers of Gambini et al.
http://arxiv.org/abs/1403.6457
Purity is not eternal at the Planck scale
Michele Arzano
(Submitted on 25 Mar 2014)
Theories with Planck-scale deformed symmetries exhibit quantum time evolution in which purity of the density matrix is not preserved. In particular we show that the non-trivial structure of momentum space of these models is reflected in a deformed action of translation generators on operators. Such action in the case of time translation generators leads to a Lindblad-like evolution equation for density matrices when expanded at leading order in the Planckian deformation parameter. This evolution equation is covariant under the deformed realization of Lorentz symmetries characterizing these models.
6 pages.

 

[Islam Hassan]

Having read all your posts, I as a layman gather that this research is somewhat of a breakthrough. Again from the point of view of a layman, how ground-breaking is this?

Is unitarity effectively threatened as a fundamental premise of physics or is this a limited, specific quirk of QM that has little/no implication for the wider scope of physics as a whole.

For example, I understand that the conservation of energy in GR is problematic on cosmological scales but that doesn't infirm the theory in itself. Is this the same kind of observation that we now have with unitarity?IH

 

[marcus]

Having read all your posts, I as a layman gather that this research is somewhat of a breakthrough. Again from the point of view of a layman, how ground-breaking is this?

Is unitarity effectively threatened as a fundamental premise of physics or is this a limited, specific quirk of QM that has little/no implication for the wider scope of physics as a whole.

For example, I understand that the conservation of energy in GR is problematic on cosmological scales but that doesn't infirm the theory in itself. Is this the same kind of observation that we now have with unitarity?


IH

I think that is an intelligent comparison (with conservation of energy in GR) and I'll try thinking of it that way.

It's good to maintain a sense of proportion, and I think that is primarily what you are looking for. I appreciate having another interested person to talk with about these issues even though I cannot say they represent breakthrough or groundbreaking physics.

We can't say for sure that the 2004-2006 Gambini Pullin result is right (though it well could be),
moreover it is only one of several proposed solutions to the BH evaporation paradox
(all of which so far seem to lead to further paradoxical or bizarre consequences!)
and even if it is right there would only be a very mild effect on the general principle of unitarity
(because they conclude that unitarity spoils very slowly, over billions of years, at the rate the best clocks get out of synch).

G&P are respected influential physicists and so far as I know no one has pointed out any flaw in their argument. So it makes sense, I think, to take seriously the possibility that they could be right (unitarity expires over very long durations, as time itself loses definition) and see where that might lead us.

For all practical purposes, unitarity is perfect and permanent (on a human and particle-physics timescale) but nevertheless I would like to share with you why I find it interesting to follow out the consequences of Gambini Pullin reasoning.

The interesting paradox, for me, comes when I combine the LQG black hole bounce picture with Gambini Pullin.
E.g. google "Planck star" and you get the paper of Rovelli Vidotto which points out that "a black hole is a shortcut to the distant future". At very high density, according to its LQG quantization, gravity repels and causes a bounce. But natural processes are slowed, deep down in a gravity well. so the bounce (and eventual gamma ray burst ,GRB, explosion) takes a long time to happen, seen from outside.

if it makes sense to think of a conventional observer, with a clock, riding in on the collapse and participating in the bounce and riding out in the GRB explosion then what that observer sees should obey unitarity

He takes a shortcut to the distant future and for him (unless time measurement for him is somehow interrupted) the whole process from collapse to final explosion takes a short time---so the process should be indistinguishable from ideal unitary.

but for the outside observer at some distance from the black hole collapse, who waits for the final explosion, the process takes many billions of years and should be recognizably non-unitary.

That is unless something novel happens right at the point of the LQG bounce which resolves the contradiction. I have been wondering what that could be, and asking if it could have anything to do with what ARZANO wrote about earlier this year. He seems to be suggesting that when information is compressed to very small scale then these very small scale processes can suffer a degradation of unitarity. I just came across his paper yesterday, and need to spend a little time looking at it, or get someone else more expert to explain it to me. (I am NOT expert, more the interested bystander who happens to be fascinated with QG and cosmology.)

 

[marcus]

I found a 2010 video talk by Arzano which can serve as an introduction to some of what is discussed in the March 2014 paper:

...
http://arxiv.org/abs/1403.6457
Purity is not eternal at the Planck scale
Michele Arzano
(Submitted on 25 Mar 2014)
Theories with Planck-scale deformed symmetries exhibit quantum time evolution in which purity of the density matrix is not preserved. In particular we show that the non-trivial structure of momentum space of these models is reflected in a deformed action of translation generators on operators. Such action in the case of time translation generators leads to a Lindblad-like evolution equation for density matrices when expanded at leading order in the Planckian deformation parameter. This evolution equation is covariant under the deformed realization of Lorentz symmetries characterizing these models.
6 pages.

Here is the 2010 online video:
http://pirsa.org/10050017/
Fun from none: deformed Fock space and hidden entanglement
Michele Arzano
Attempts to go beyond the framework of local quantum field theory include scenarios in which the action of external symmetries on the quantum fields Hilbert space is deformed. A common feature of these models is that the quantum group symmetry of their Hilbert spaces induces additional structure in the multiparticle states which in turns reflects a non-trivial momentum-dependent statistics. In certain particular models which might be relevant for quantum gravity the richer structure of the deformed Fock space allows for the possibility of entanglement between the field modes and certain ''planckian'' degrees of freedom invisible to an observer that cannot probe the Planck scale.
19/05/2010

 

[stevendaryl]

I have a bunch of questions about non-unitarity, although I may not be qualified to understand the answers.

First, the statement about the lack of ideal clocks implying a breakdown of unitarity seems strange to me. Science always has to deal with non-ideal measurements, but we don't usually feel the need to rewrite the laws of physics to take into account our flawed measurement devices. Perhaps the distinction is that in other branches of physics, we can understand our measuring devices as giving an approximation to some ideal, while in quantum gravity, there is no way to even define what the ideal would be?

Second, in ordinary single-particle quantum mechanics, unitarity is connected with the laws of probability; we want the integrated probability density to equal 1, and unitarity insures that if this is true at one time, it will always be true. If we allow non-unitary evolution, then I'm not sure what that means for the probabilistic interpretation of quantum mechanics.

 

[marcus]

Perhaps the distinction is that in other branches of physics, we can understand our measuring devices as giving an approximation to some ideal, while in quantum gravity, there is no way to even define what the ideal would be?
...

Hi Steven, thanks for the comment! I think that's a clear way to put it and goes to the heart of the matter. It's actually true for 1915 GR as well. You've probably heard about the "problem of time" in GR. There is no way to define the "ideal time" in GR until you have solved the equation and fixed on a specific solution--and then you get different proper times for different observers.

There is a nice brief discussion of this for non-specialist near the beginning of Carlo Rovelli's 2006 essay "unfinished revolution" that served as the first chapter of a book on the various approaches to quantum gravity. If you are curious I think googling "rovelli revolution" would get it.

So you already have this no-ideal time in the general rel theory and, as the essay explains, the problem is even more serious when you go towards quantum GR, because in quantum theory continuous trajectories do not exist, reality is stripped down to intermittent interactions. Sporadic events. Discrete "observables".

... If we allow non-unitary evolution, then I'm not sure what that means for the probabilistic interpretation of quantum mechanics

Well, I have trouble with the single particle Schrödinger "wave function" picture of quantum mechanics. because for one thing when you have many particles you no longer have a wave function defined on space time and if particles are interacting and being created/annihilated the wave function picture gets a bit confusing. So the picture of QM I have is operators defined on a Hilbertspace, that is basically a complex vector space with inner product. I lean towards the Heisenberg version of QM.

You know what UNIT VECTORS are---the analog of the unit circle in the complex plane---vectors with norm one. For me a unitary operator is one that maps unit vectors to unit vectors.

Since unit vectors in QM are called "pure states" a unitary operator is one that preserves purity.

A probabilistic combination of pure states, like for instance 1/2 |R> + 1/2 |L>, would not necessarily have norm one. If |R> and |L> are orthogonal, it would have norm 1/2, instead of norm 1. You can check by multiplying out the inner product (but this could all be familiar to you).
So this kind of probabilistic combination is a called a MIXED STATE.

So as I see it you can have transformations which DO preserve probability but which are NOT unitary because they take a pure state ( norm 1) to a mixed state (e.g. norm 1/2).

You may already know all this stuff but I want to be as clear and basic as I can, about it, because other people might be reading the thread.

My excuse for taking this point of view is that the prevailing quantum theory, that is the basis of the Standard Model of matter, is quantum field theory (QFT) which is very much a Heisenberg-type formalism. It consists of OPERATORS distributed over the 4D spacetime of special rel.
"Operator-valued distributions" At any point of spacetime you have a bunch of operators .

I can think of them as observables corresponding at least in part to measurements or particle detections which I might or might not make around that point.

And all these operators are transformations on the one Hilbertspace, of "states". A state represents comprehensive information about the system as a whole (all its particles etc), and the chosen state is what allows us to make each and every observable-type operator give us a real number, if we think of making an observation with that operator. There is just ONE STATE for all that huge welter of operators distributed all over the spacetime. You can think of operators evolving over time, while the state remains the same (barring new info input). That's the essential feature of the Heisenberg picture as opposed to the Schrödinger one.

Basically just explaining a point of view (which I subscribe to) about what unitary means:
it means "preserves pure states" and gradual loss of unitarity means that a pure state can devolve down into a probabilistic mixture. I hope you can see how it looks from my viewpoint.

 

[marcus]

Steven, the "unfinished" character of quantum theory comes from, more than anything else, the fact that QFT is SPECIAL relativistic rather than GENERAL. It is defined on the 4d ("Minkowski") spacetime of special relativity, with its Lorentz or Poincaré group symmetry. And it does not know anything about GR.

The gradual expiration of unitarity is a GENERAL relativity effect. I don't see how you can even describe it within the mathematical framework of (special) relativistic QFT. Maybe other people can, but I can't. I suspect that what Gambini and Pullin found in their 2004-2006 papers about this could very well be right and yet
1. on ordinary particle and human timescales it doesn't matter because expiration is so slow as to be undetectable
2. people won't be able to mathematically EXPRESS the gradual loss of unitarity until they actually have arrived at a general relativistic quantum field theory.

Since we have turned a page I had better bring forward the quotes from those papers by Gambini Porto Pullin.

 

[kith]

You will have to refer to their "Realistic Clocks" paper, http://arxiv.org/abs/hep-th/0406260, because I can't reproduce their argument in detail, but the upshot seems to be that if one focuses on black hole evaporation the unitarity of evaporation dies out on a timescale comparable to the lifespan of the black hole itself.

Thanks for linking this paper. Having a QM background with little knowledge of QFT and even less of GR, I see for the first time how the notion of "fundamental" non-unitarity could make sense.

 

[Paulibus]

... on ordinary particle and human timescales it doesn't matter because expiration is so slow as to be undetectable

Nicely put. Here "it" is unitarity, which is an abstract synonym for the familiar human term 'ímmortality'. That's what stable fundamental particles are born to be, and we are not. An idle thought: the bounce will turn out to be a result of this enviable attribute!

 

[TrickyDicky]

The measurement problem in quantum theory has been expressed as something caused by the linearity of the unitary evolution process. In GR non-linearity is introduced. Has someone explored a fundamental non-linear unitarity rather than a fundamental non-unitarity in quantum gravity?

 

[marcus]

Hi TD and Paulibus! TD I don't have an answer to your question. I don't know of any way that the aberration of a real timepiece can be mathematically modeled. The decay of unitarity that Gambini et al discuss is based on there being no other definition of time than correlation with a realistic clock--a designated quantum observable. Such a thing is necessarily slightly erratic, and unpredictably so.
Since we turned a page I'll bring forward some basic quotes from Gambini et al papers. This is the PREMISE. It could be that Gambini et al are wrong! What we want to do here is assume they are right and see what follows from that assumption.

http://inspirehep.net/record/645205 47 cites
(A Relational solution to the problem of time in quantum mechanics and quantum gravity induces a fundamental mechanism for quantum decoherence)

http://inspirehep.net/record/653376 38 cites
http://arxiv.org/abs/hep-th/0406260
(Realistic clocks, universal decoherence and the black hole information paradox)

http://inspirehep.net/record/674573 12 cites
http://arxiv.org/abs/gr-qc/0501027
(Fundamental decoherence in quantum gravity)

http://inspirehep.net/record/712912 38 cites
http://arxiv.org/abs/gr-qc/0603090
(Fundamental decoherence from quantum gravity: A Pedagogical review)

http://inspirehep.net/record/735013 25 cites
http://arxiv.org/abs/quant-ph/0608243
(Relational physics with real rods and clocks and the measurement problem of quantum mechanics)

"Summarizing, we have shown that unitarity in quantum mechanics only holds when describing the theory in terms of a perfect idealized clocks. If one uses realistic clocks loss of unitarity is introduced. We have estimated a minimum level of loss of unitarity based on constructing the most accurate clocks possible. The loss of unitarity is universal, affecting all physical phenomena. We have shown that although the effect is very small, it may be important enough to avoid the black hole information puzzle."
--Realistic clocks paper http://arxiv.org/pdf/hep-th/0406260.pdf

"When one introduces realistic clocks, quantum mechanics ceases to be unitary and a fundamental mechanism of decoherence of quantum states arises. We estimate the rate of universal loss of unitarity using optimal realistic clocks. In particular we observe that the rate is rapid enough to eliminate the black hole information puzzle: all information is lost through the fundamental decoherence before the black hole can evaporate."
--Realistic clocks paper

"...general relativity is a generally covariant theory where one needs to describe the evolution in a relational way. One ends up describing how certain objects change when other objects, taken as clocks, change. At the quantum level this relational description will compare the outcomes of measurements of quantum objects."
--Fundamental decoherence: pedagogical review paper

"...as ordinarily formulated, quantum mechanics involves an idealization. That is, the use of a perfect classical clock to measure times. Such a device clearly does not exist in nature, since all measuring devices are subject to some level of quantum fluctuations. The equations of quantum mechanics, when cast in terms of the variable that is really measured by a clock in the laboratory, differ from the traditional Schroedinger description. Although this is an idea that arises naturally in ordinary quantum mechanics, it is of paramount importance when one is discussing quantum gravity. This is due to the fact that general relativity is a generally covariant theory where one needs to describe the evolution in a relational way..."
--Relational physics with real rods and clocks

To paraphrase, in the real world duration and distance are defined operationally by physical measurements, which is to say by events. There is no such thing as abstract idealized "time". Instead there are various natural processes, whose rates, when compared, depend on relative motion and position in the gravitational terrain. Defining an observer's worldline depends on already having a solution of the GR equation. Defining an observer's proper time also depends on the choice of some physical process to be the observer's clock.
Unitarity is only as good as the physical clock, and cannot be taken as absolute. It is potentially misleading to assume unitarity on timescales comparable to the present age of expansion.

 

[TrickyDicky]

TD I don't have an answer to your question.

Thanks anyway Marcus. Your comments are always clarifying nevertheless.

"Summarizing, we have shown that unitarity in quantum mechanics only holds when describing the theory in terms of a perfect idealized clocks...
"...as ordinarily formulated, quantum mechanics involves an idealization. That is, the use of a perfect classical clock to measure times. Such a device clearly does not exist in nature, since all measuring devices are subject to some level of quantum fluctuations There is no such thing as abstract idealized "time".
Unitarity is only as good as the physical clock, and cannot be taken as absolute.

These seem quite reasonable premises and I have no problem assuming they are right. I just was under the impression that the clock idealization in QM was not exactly to blame on the unitary evolution process itself but more specifically on its linearity enforced also by the QM postulates.

 

[marcus]

TD, I want to continue discussing the Gambini et al idea about extremely slow though inevitable decline of unitarity. But as a brief digression I'm also curious to know if you have any reaction to this recent radical proposal from Steven Weinberg. I'm not sure what to make of it but it might have some indirect bearing on the "purity is not eternal" issue.

http://arxiv.org/abs/1405.3483
Quantum Mechanics Without State Vectors
Steven Weinberg
(Submitted on 14 May 2014)
It is proposed to give up the description of physical states in terms of ensembles of state vectors with various probabilities, relying instead solely on the density matrix as the description of reality. With this definition of a physical state, even in entangled states nothing that is done in one isolated system can instantaneously effect the physical state of a distant isolated system. This change in the description of physical states opens up a large variety of new ways that the density matrix may transform under various symmetries, different from the unitary transformations of ordinary quantum mechanics. Such new transformation properties have been explored before, but so far only for the symmetry of time translations into the future, treated as a semi-group. Here new transformation properties are studied for general symmetry transformations forming groups, rather than semi-groups. Arguments are given that such symmetries should act on the density matrix as in ordinary quantum mechanics, but loopholes are found for all of these arguments.
28 pages

 

[TrickyDicky]

Weinberg always has interesting things to say, I think the shift in emphasis he proposes from pure states to density matrices is in the good direction, but not radical enough. Then again radicality lies in the eye of the beholder.

 

[xristy]

motl on weinberg

Motl has some rather lengthy comments on the Weinberg paper.

 

[marcus]

Weinberg always has interesting things to say, I think the shift in emphasis he proposes from pure states to density matrices is in the good direction, ...

If I catch your drift, I think I agree! Weinberg's proposal seems to be suggesting a shift towards a mildly "instrumentalist" view of QM
(observations interactions and predictions are what matter, don't think of state unit vectors as real physical objects. Think of the Hilbertspace and the operator algebra as INSTRUMENTS the observer uses to represent his info, his measurements etc., not something in nature.)

But he doesn't go all the way. There are extreme instrumentalists who would go so far as FORBID ever speaking of anything as existing that is not observable. Only talk about relations between measurements, otherwise "it's not physics."

Maybe there is a continuum of views on QM between strict instrumentalism on the one hand and, on the other, the kind of semi-realist or "relational" stance mentioned by Gambini et al. There one acknowledges that physics is largely about observations, interaction events, predictions, perceptions… but one can still HOPE that the successful models approximate an underlying reality.
According to this moderate relational view one can still consider oneself a realist, and one is permitted to talk as if the models approximately describe reality. And one can hope that improving the model, making it more broadly and successfully predictive, will make it a truer approximation of the world. Relationalists (like e.g. Rovelli) always emphasize that although different observers perceive what has happened differently they can RECONCILE their stories by getting together and finding a common account.

Anyone interested can google "Relational EPR" and get a paper (with references to earlier RQM sources) or google "rovelli cosmology relational" and get a video of a talk given at Oxford last year presenting relational view of quantum foundations and cosmology.

That said, the point relevant to this topic is anyone who is even moderately instrumentalist is playing to Gambini et al strong suit:
if only observations are physically meaningful then there is no TIME apart from seeing how readings of realistic clocks correlate with other observables.

 

[marcus]

So if there is no ideal time---no time apart from observing correlations with the physical processes we designate as clocks---then there is no perfect eternal unitary evolution. Unitarity is only as good as the clocks are. This gets me back to the problem that has been bothering me:

Gambini et al adapt and extend Wigner's ideas to reckon the slowest possible decay rate of unitarity. They find the info that fell into hole fades out on the timescale of hole evaporation. Let's assume Gambini et al are right about the rate of decay.

Typical hole evaporation times seen by outside observer are enormous, billions of times the present age of cosmic expansion.

How do you define the evaporation time as "measured" (if that is possible) by an "inside" observer (if one could exist) who falls into the hole and participates in the rebound?

 

[stevendaryl]

So if there is no ideal time---no time apart from observing correlations with the physical processes we designate as clocks---then there is no perfect eternal unitary evolution. Unitarity is only as good as the clocks are.

I'm not sure if this along the same lines, or not, but Julian Barbour has a program of removing time from physics and replacing it by relationships. His book "The End of Time" describes it.

 

[marcus]

I'm not sure if this along the same lines, or not, but Julian Barbour has a program of removing time from physics and replacing it by relationships. His book "The End of Time" describes it.

Hi Steven! I remember reading a beautiful essay of his where he uses classical mechanics and in effect turns a system like the solar system into a big clock. He extracts time from classical dynamics. The essay won first prize in a FQXi contest. You may have read it. He gives more attention to specific detail than Gambini Porto and Pullin do. But it is along similar lines in the sense that they too consider natural systems as clocks.

They use theoretical reasoning to get BOUNDS on how stable and precise physical clocks can be.
One thing they consider as a longterm frequency standard is a vibration mode of a black hole. (Harder to imagine how one would excite and observe said vibration, compared with Barbour's observation of a planetary system )

I neglected to say just now: if anyone hasn't read the two "Planck star" papers, just google
"planck star" and
"planck star phenomenology"

That is the basis of the problem that this thread is about. According to Loop QG, black holes bounce. This leads to the "Planck star" model of black hole. Extreme gravitational time dilation means that the rebound, which happens quickly from an inside perspective, takes billions of years seen from outside. The rebound results in a long-delayed energetic gamma ray burst at the end of the star's life.

Gambini et al would expect the outside observer to see no information writ in the final GRB (nothing that would allow one to reconstruct knowledge of what initially fell in.)
How does that square with the apparently quick (possibly unitary) evolution which occurs inside?
Is there something in the bounce itself which "resets" any possible clocks. Are any clocks that survive the bounce possible at all?

 

[erkokite]

I would like to submit for your inspection a paper which strikes me as relevant:
http://iopscience.iop.org/1367-2630/16/5/053041/article

 

[marcus]

Thanks! To me it seems like a fascinating idea for an experiment. Can the two systems remain entangled (in the usual sense) if time for the two is progressing at very different rates? It seems that their relative placement in the gravitational potential should have some effect. I'll get the arxiv.org and the inspire.org links in case anyone wants to look up author profiles or see if other researchers have cited this. I am glad you called attention to this:

http://arxiv.org/abs/1306.1933
Testing the effects of gravity and motion on quantum entanglement in space-based experiments
David Edward Bruschi, Carlos Sabín, Angela White, Valentina Baccetti, Daniel K. L. Oi, Ivette Fuentes
(Submitted on 8 Jun 2013)
We propose an experiment to test the effects of gravity and acceleration on quantum entanglement in space-based setups. We show that the entanglement between excitations of two Bose-Einstein condensates is degraded after one of them undergoes a change in the gravitational field strength. This prediction can be tested if the condensates are initially entangled in two separate satellites while being in the same orbit and then one of them moves to a different orbit. We show that the effect is observable in a typical orbital manoeuvre of nanosatellites like CanX4 and CanX5.
8 pages, 2 figures. I. Fuentes previously published as I. Fuentes-Guridi and I. Fuentes-Schuller.

http://inspirehep.net/record/1237905?ln=en
sample author profile:
http://inspirehep.net/author/profile/I.Fuentes.2

 

[marcus]

People seem to be accumulating a number of reasons to be suspicious of the standard Hawking BH evaporation story.
There is a sizable literature to the effect that assuming unitary evaporation leads to bizarre conclusions---lately the "firewall" and also I should mention Bianchi Smerlak finding that unitary evaporation implies a kind of "hiccup" where the BH temporarily gains mass.

There are competing scenarios where the BH bounces, turning into a gamma ray burst, or else a "white hole" the time reversal of collapse.

Bojowald recently posted a paper affirming his notion that the bounce (at least in cosmological case) involves a temporary change of signature.

And Erkokite just called attention to an experimental hypothesis that entanglement might decay between two systems experiencing different rates of time evolution due to different position in gravitational potential. (Is there a connection here with Gambin Pullin's reasoning about decay of unitarity during BH evaporation, as seen by outside observer/)

I think I'll have to leave this for the night and hope to see the situation more clearly in the morning.