Time in QM

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  • #26
hellfire
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When one selects a preferred time-slicing to define a quantum theory based on it (as Carlip seams to suggest), other quantum theories based on different time-slicings must not be unitarily equivalent to the first one and to each other, because the Stone-von Neumann theorem does only apply to systems with finite degrees of freedom. How is this problem considered in the framework of quantization of general relativity?
 
  • #27
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Suppose you take an experiment with a physical system (ex. pendulum) in which certain physical observable is known to decay exponentially (ex. amplitude of oscillation). So, if you agree with some time unity and agree with the decay law, then I think you should also agree that measuring this physical observable means to measure indirectly the time elapsed from the initial condition.

My point is : time seems to be a quantity which can be measured. And its measurement addresses always an specific physical (and material) system, providing the conditions to the existence of a system of reference as in Eisntein's discussions on Relativity.
 
  • #28
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DaTario said:
Suppose you take an experiment with a physical system (ex. pendulum) in which certain physical observable is known to decay exponentially (ex. amplitude of oscillation). So, if you agree with some time unity and agree with the decay law, then I think you should also agree that measuring this physical observable means to measure indirectly the time elapsed from the initial condition.
My point is : time seems to be a quantity which can be measured. And its measurement addresses always an specific physical (and material) system, providing the conditions to the existence of a system of reference as in Eisntein's discussions on Relativity.
Although we are not discussing of my proposition but about how time works in QM, your point of view is a good point for me (thanks). The first self critic I would send to my self is that a "time" depending on the states of the system makes the time very similar to the concept of temperature... A little bit strange isn't it? On the other side if you try to apply my idea to the propagation of the light, ... it works not so bad.
 
  • #29
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Blackforest said:
Even if the Carlip's approach "only" concern the 2+1 universe, it gives some tools and ideas to go further; he is not the only one exploring this terra incognita. Every idea is wellcome I think. Every unsuccessful path is a path that others are no more obliged to follow and that's time saved !!! Coming back to my description post 12 and the ideas of johnf (post 23), I would propose to consider the time in fact as a function of position and momentum, that is a function depending on the states of the system ...
That is, you omit the part when Carlip agree that "his" idea do not hold in 3+1.

Moreover, on your own proposal, you simply ignore that position is not an observable in relativistic quantum mechanics (or field theory) and also ignore that GR is a constrained dynamics.
 
  • #30
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Juan R. said:
That is, you omit the part when Carlip agree that "his" idea do not hold in 3+1.
Moreover, on your own proposal, you simply ignore that position is not an observable in relativistic quantum mechanics (or field theory) and also ignore that GR is a constrained dynamics.
So far I understand QM (only; = not Q Gravity), we have:
1°) Physically observable phenomenon; e.g.: a particle.
2°) Parameters and variables that help us to describe the physical situation or state in which the phenomenon is; e.g.: its position, its momentum, …
3°) In fact a certain probability to really measure a given value for a given variable. In QM this is obtained with the introduction of the wave function [I note that it depends on the position and on the time Y(r, t)];
4°) This proceeding leads to the notion of operator associated with an observable variable; e.g. for the position and (h/2pi). Ñ for the momentum
5°) this concept can be (and is) generalized and an operator can be (and is) represented by a matrix
When you say that position is not an observable within the field theory (I believe you) this means that a position has no correlated operator in this theory. I suppose you refer effectively to one of the difficulties that Carlip is enouncing in his book 2 + 1 Quantum Gravity page 2: “Ordinary Quantum field Theory is local but the fundamental observables in quantum gravity are necessarily non local.”…
As amateur and as "Mister naïve" on this forum I would do following remarks:
1°) At quantum scale, what can we really observe? It is strongly depending on the precision of our instruments (electronic microscopy, NMR, …). So; and so far some pictures that I could see in scientific reviews, we are able to “see” some atomic structures. It is true that even at this small scale, we are far away from the quantum scale. In this sense we are actually not equipped to directly observe a position at quantum scale. In Carlip’s book it is written (page 2 point 6; difficulties) that “perturbative quantum field theory depends on the existence of a smooth, … but there is no reason to believe that the short distance limit of quantum gravity even resembles a smooth manifold”… To sum up we know nothing. We are condemned to do some intellectual conjectures concerning the “how could this look out?” This also means that we are obliged to work “by extrapolation”. Starting with concepts that are working good at greater scales (e.g. atomic scale).
Personal remark: this is an invitation to consider that the most interesting thing at quantum scale is the local metric; it could be “a priori” anyone and contain discontinuities, holes, … I defend the idea that perturbations of the metric are physical phenomenon that can sometimes be interpreted as particles… If the way I am developing this idea is the good one and if I do it with the good tools is another point; but as said by myself unsuccessful paths are time saved for the others. And since I am just an amateur it doest really matter if I success or not: I only do it for fun. In this sense I was also not defending Carlip that I don’t personally know.
Concerning the fact that GR is a constrained dynamics; of course I don’t ignore it. I repeat I am not a professional and my time is limited to explore and calculate. I did not finish to learn and to incorporate the actual knowledges into my approach. This is certainly leading to an incomplete or incorrect one. I would be happy if some one could give me his impression concerning my essay to demonstrate the Lorentz –Einstein Law (see my homepage). This essay is actually under consideration by the administrators of this Internet site at independent Research and I am waiting for the judgment.
Personal remark: to surround this difficulty concerning the “time-slicing” of the A.D.M. approach, I do any slicing, precisely 4D slicing, to preserve the fact introduced by the GR that no preference should appear between the different coordinates (spatial and temporal). This explain the necessity to cut “along” a any given local metric. The critic arising from this way of doing is that it introduces a 4D vector field correlated with the state of the background and for which I have actually no clear interpretation.
Best regards.
 
  • #31
hellfire
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Blackforest said:
When you say that position is not an observable within the field theory (I believe you) this means that a position has no correlated operator in this theory. I suppose you refer effectively to one of the difficulties that Carlip is enouncing in his book 2 + 1 Quantum Gravity page 2: “Ordinary Quantum field Theory is local but the fundamental observables in quantum gravity are necessarily non local.”…
Position is only a label in quantum field theory, same as time. The question about the position of a particle at a given time seams not to be really meaningful in a strict sense. Instead, one asks about the value of the field at a given label (position and time) and makes use of the notion of propagators as correlation functions of the values of the field for different labels.

In my opinion Carlip's claim that you are quoting here seams not to be related to this. I would guess that the fact that observables in quantum gravity are postulated to be non-local might be related to the holographic principle (the real degrees of freedom and the physics take place at the boundaries of volumes), but this is far beyond my knowledge.
 
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  • #32
CarlB
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PIT2 said:
How does time work in QM?
Here's my(speculative) version of how time works in QM. The official version is satisfactory for producing predictions but somewhat lacking in ontological interpretation.

Both QM and QFT can be put into a wave / particle duality. The connection between the wave and the particle is probabilities is defined by the squared magnitude of probability wave. For the relativistic theory, the wave function is defined in space-time.

To an experimenter, it is clear whether to use the particle model (i.e. probabilities of various outcomes) and wave model for an experiment. If the experiment has already been performed, then its results must be thought of in terms of probabilities of various particle results. If the experiment has not yet been performed, then probabilities will not do because of the possibility of quantum interference. For experiments still in the future, the wave description of the situation must be used.

If by "passage of time" we mean the stuff we experience as we grow older, that must be modeled in physics by wave function collapse. If, instead, by "passage of time" we mean the method we use to extend a solution to Schroedinger's equation at time t to time to a solution at time t+dt, then we must mean the unitary operator of quantum mechanics.

These two definitions of "passage of time" imply that we really need two temporal dimensions to fully describe a point in an experiment. One of the time dimensions, say t_1, gives a measure of time in the second sense given above. It refers to the number of seconds since the big bang. The other time dimension, t_2, gives the number of seconds between "now" and the big bang. If t_1 > t_2 then we must use a particle method of describing the event because it is in the past as compared to now. If t_1 < t_2, then we must use the wave method because the event is still in the somewhat indefinite future.

This sort of thinking implies that there must be a continuous deformation of a wave function description of an experiment to a particle description. This can be done if one rearranges quantum mechanics a bit.

Carl
 
  • #33
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Blackforest said:
So far I understand QM (only; = not Q Gravity), we have:
1°) Physically observable phenomenon; e.g.: a particle.
Wery well!

Blackforest said:
2°) Parameters and variables that help us to describe the physical situation or state in which the phenomenon is; e.g.: its position, its momentum, …
ONLY on nonrelativistic quantum mechanics. Only observable on R-QFT is the S-matrix and properties directly derived from them, for example energy.

Blackforest said:
3°) In fact a certain probability to really measure a given value for a given variable. In QM this is obtained with the introduction of the wave function [I note that it depends on the position and on the time Y(r, t)];
In relativistic QM (R-QFT), there is not wave-functions. The quantum state is represented by a funtional Y (phy_1, phy_2, phy_3... ) of field configurations phy_j at spacetimes points. Position is not a dynamical variable. Time enter as a parameter. I am talking of special relativity + QM (R-QFT). In quantum gravity, time dissapears.

Blackforest said:
4°) This proceeding leads to the notion of operator associated with an observable variable; e.g. for the position and (h/2pi). Ñ for the momentum
5°) this concept can be (and is) generalized and an operator can be (and is) represented by a matrix
When you say that position is not an observable within the field theory (I believe you) this means that a position has no correlated operator in this theory. I suppose you refer effectively to one of the difficulties that Carlip is enouncing in his book 2 + 1 Quantum Gravity page 2: “Ordinary Quantum field Theory is local but the fundamental observables in quantum gravity are necessarily non local.”…
Even ignoring some basic thecnical details you are simply ignoring (take a course in the topic) when 'I' say that position is not an observable is because in R-QFT position is not a dynamical variable. I am not talking about quantum gravity just about standard R-QFT. The nondynamical character of position follows from uncertainty relations in the relativistic regime. This is the reason that only scattering amplitudes are defined in R-QFT and particle physics.

Carlip's appeal to 'locality' is irrelevant for this discussion.

Blackforest said:
In Carlip’s book it is written (page 2 point 6; difficulties) that “perturbative quantum field theory depends on the existence of a smooth, … but there is no reason to believe that the short distance limit of quantum gravity even resembles a smooth manifold”…
Just speculation.

Blackforest said:
I would be happy if some one could give me his impression concerning my essay to demonstrate the Lorentz –Einstein Law (see my homepage). This essay is actually under consideration by the administrators of this Internet site at independent Research and I am waiting for the judgment.
Good luck!
 
  • #34
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Juan R. said:
Wery well!
ONLY on nonrelativistic quantum mechanics. Only observable on R-QFT is the S-matrix and properties directly derived from them, for example energy.
In relativistic QM (R-QFT), there is not wave-functions. The quantum state is represented by a funtional Y (phy_1, phy_2, phy_3... ) of field configurations phy_j at spacetimes points. Position is not a dynamical variable. Time enter as a parameter. I am talking of special relativity + QM (R-QFT). In quantum gravity, time dissapears.
Even ignoring some basic thecnical details you are simply ignoring (take a course in the topic) when 'I' say that position is not an observable is because in R-QFT position is not a dynamical variable. I am not talking about quantum gravity just about standard R-QFT. The nondynamical character of position follows from uncertainty relations in the relativistic regime. This is the reason that only scattering amplitudes are defined in R-QFT and particle physics.
Carlip's appeal to 'locality' is irrelevant for this discussion.
Just speculation.
Good luck!
Thank you for the extensive answer. I understand now better the difference between my approach and the conformal approaches QM, R-QFT, ... In fact trying to think about what an impermanent geometric background could be (this is the -perhaps false- representation that I develop concerning the context for a quantum gravity theory), I inconsciently incorporate the idea that the backgrounds moves and with this kind of though, position becomes evidently a dynamical variable... That's my error; ok. Best regards.
 
  • #35
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the best beginning of a description of Time I have seen- [and am currently trying to grok the best that I can]- which stems from Everett MWT- conjectured by Page and Wooters in 83 and currently being supported by David Deutsch/et al at the Centre for Quantum Computation- is the idea that the 'past' and the 'future' are special cases of different universes in the Multiverse where the laws of physics-principally Entropy- establish a causal relationship with an observer and their world that restricts the possible states that could causally result in the current observer's state to very specific cases which emerge/appear as the 'fossil record/memory' of an observer's 'fixed past'- and that because of the randomness of entropy the 'future' does not have such a specific set of possible states- so an infinitude of different universes will diverge out from what were once nearly identical states and the 'future' that the observer sees is simply the state that that single instance of the observer happened to find themselves in- but ALL the possibilities [according to many worlds interpretations] occurred and each of these universes has a divergent copy of the observer with a different 'future' outcome that all share the same 'past' due to the causal constraints of entropy-

this system of specific universes with a causal construction defined by Entropy emerges subjectively to each instance of an observer as a fixed past/present with an open non-deterministic future [well actually each and every future is rigorously deterministic- but there is no way to predict which of the transfinite outcomes a single instance of the observer will subjectively find themselves in] and a subjective sensation of forward moving change as a result of the observer [and other clock-like systems] continuously comparing their current state with previously remembered states-

the thinking goes that if we can construct a workable theory of Quantum Gravity- that the details of the apparent flow of time and the relationship of universes connected by causality and entropy in this way will be much better understood
 
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