How does time function in quantum mechanics and its multiverse implications?

[PIT2]

How does time work in QM?

I remember reading something that said time doesn't really exist in QM, because there is no sequentiality, and this meant everything happened at the same time.

Can someone tell me more about this?

 

[ZapperZ]

How does time work in QM?
I remember reading something that said time doesn't really exist in QM, because there is no sequentiality, and this meant everything happened at the same time.
Can someone tell me more about this?

That doesn't make much sense. For example, just look at the time-dependent Schrödinger equation and its solution. There is clearly a time-evolution description in the very fundamental description of QM. Some people have even argued that this is a very "deterministic" part of QM.

Zz.

 

[PIT2]

This is a post i was referring to:

According to quantum theory sequence really can't exist. Superpostion suggests that people can exist in the (state of the) past at the same time as the present etc... Many people can be found stuck in the past. The question about whether the past is real or not belongs to the traditional relativist.

I'd say the equivalent of sequence in quantum studies is "regionalism". The superposition or entanglement of states "experienced" by an object do not occur in a sequence, (as in past, present, future) but it simultaneously "experiences" a region of states. It may not "experience" all states but only those states that pertain to its existence.

You have to calculate how much the past state is influencing your present, real time state. If it has no influence on your present state, then the past really isn't "real" in terms of the amount of influence it has on you, now. However, according to quantum logic, the past, present and future are all part of the region of states that support your existence. This tends to make all those states "real" in terms of being "essencial" to the existence of the present state
https://www.physicsforums.com/showthread.php?t=77232&page=4

So is this a bunch of baloney, or did I misunderstand it?

 

[ZapperZ]

You really should learn physics from a physics textbook, not from a philosophy forum.

Zz.

 

[PIT2]

I thought someone here might be able to comment on it.

 

[ZapperZ]

I just did!

I even gave you a specific example where the statement you quoted makes no sense. One only needs to look at the time evolution of the wavefunction that was derived from the Schrödinger equation to know that there IS time in QM. And we haven't even talked about the time operator in QM, and the time symmetry in CPT. If time doesn't exist, what are all these?

It is more that the writer you quoted is the one who owes an explanation in light of these obvious points in QM.

Zz.

 

[PIT2]

Alright, thank u.

 

[Juan R.]

How does time work in QM?
I remember reading something that said time doesn't really exist in QM, because there is no sequentiality, and this meant everything happened at the same time.
Can someone tell me more about this?

Well the concept of time that introduce nonrelativistic QM is approximated.

When one introduces gravity effects, the concept of time varies a lot of.

For example in canonical quantum gravity (or geometrodynamics) there is no time.

The "Schrödinger" equation -named Wheeler/deWitt equation- looks like

H|Phi> = 0

without time evolution. Precisely

The absence of time

is one of main problems of that approach to quantum gravity.

 

[member 11137]

Precisely
The absence of time
is one of main problems of that approach to quantum gravity.

Indeed.

Well the concept of time that introduce nonrelativistic QM is approximated.
When one introduces gravity effects, the concept of time varies a lot of.
For example in canonical quantum gravity (or geometrodynamics) there is no time.
The "Schrödinger" equation -named Wheeler/deWitt equation- looks like
H|Phi> = 0
without time evolution.

So far I know, quantum gravity (e. g. see S. Carlip) analyzed under the binocular of "classical general relativity" begins with an ADM approach; this is de facto introducing a time slicing. In this sense it is false to say that there is no time in this approach.
The fact that QM has no consideration for the notion of time is also false; there is precise laws describing the evolution of the different physical observables.
I think that no clear presence of time in any equation of the QM is perhaps simply indicating its instantaneous validity, for any instant or for any infinitesimaly short period of time. This equation is like a photo of the reality, it is just concerning a slice of our life. Everything looks like if the moment when the slice has been done has in fact no importance.

 

[James R]

Part of the problem with creating quantum theories of gravity, as I understand it, is that time in standard quantum mechanics is treated as a parameter rather than being on the same footing as measurable observables like position and momentum.

Can somebody tell me how string theories etc. try to solve that problem?

 

[hellfire]

So far I know, quantum gravity (e. g. see S. Carlip) analyzed under the binocular of "classical general relativity" begins with an ADM approach; this is de facto introducing a time slicing. In this sense it is false to say that there is no time in this approach.

I think that the assertion that there is no time refers to the problem that there is a freedom to choose the slicing. This is encoded into the Hamiltonian constraint. If it were possible to choose a preferred time, then there would be no Hamiltonian constraint and one could resolve the dynamics (e.g. as in the case of the relativistic free particle), but in a background independent theory of gravitation one is not allowed to choose a preferred time and therefore the degrees of freedom of the gravitational field remain so to say ‘timeless’. One can understand this also considering that a the constraint H = 0 generates a gauge transformation. Points in phase space related by a gauge transformation are equal to the dynamical trayectories (since dynamics is given by the Poisson bracket of the Hamiltonian). The distinction between points on the same trayectory depends on the selected gauge and is not physical.

 

[member 11137]

I think that the assertion that there is no time refers to the problem that there is a freedom to choose the slicing. This is encoded into the Hamiltonian constraint. If it were possible to choose a preferred time, then there would be no Hamiltonian constraint and one could resolve the dynamics (e.g. as in the case of the relativistic free particle),

Since the GR has introduced the important idea that time is a coordinate like the others, human brains of a lot of specialists are storming to understand the implications of that. I shall develop here briefly a personal and alternative representation of the time. The purpose is the discovery of a way able to better connect the relativistic and the quantum approach.
Let us imagine the following mental experiment. We are alone on a boat, lost somewhere on a see without stream in the north of Europe (e.g. between Sweden and Finland) in the middle of June. There is no wind; a misty sky is everywhere around us and because of that we have nothing to do except to look at the time. The only important object that we brought with us in this strange adventure is a clock; and old fashion one, with two moving pointers (hands) ... There is nothing else important in our boat. Because of the absence of stream and of wind, because the day in the north of Europe in the middle of June is a never ending day with a quasi constant luminosity, we would neither have sensations giving us informations about our position nor about the change of time (except may be that we would be hungry after a while) if we could not observe the motion of the pointers. What I mean with this is: for us, time on the boat is depending on the different positions of the pointers. If unfortunately the pointers of our old fashion clock are not always turning at the same speed, then time will also depends on the speed or on the variations of the speed of these pointers. At the end:
t = L[(xi), (vi)]; i = 1, 2 and 3
Adopting such a mental position is in harmony with the point of view developed in thermodynamics or in the quantum theory. But it seems to be in contradiction with the relativistic approach because it is implicitly announcing a dependence between the time and the other coordinates. In fact, it is not so easy as it apparently looks. All is depending on the definition of the speed.

but in a background independent theory of gravitation one is not allowed to choose a preferred time and therefore the degrees of freedom of the gravitational field remain so to say ‘timeless’. .

Theoretically you are rigth. But the expression "background independent theory of gravitation" appears to me to be a paradox, a non-sense ... because the (field of) gravitation always is the background. With other words, if you are dealing in a precise given field of gravitation, even changing, then you are living somewhere where the time is "flowing" in a certain given way (even if it is changing with the variations of the field).

One can understand this also considering that a the constraint H = 0 generates a gauge transformation. Points in phase space related by a gauge transformation are equal to the dynamical trayectories (since dynamics is given by the Poisson bracket of the Hamiltonian). The distinction between points on the same trajectory depends on the selected gauge and is not physical.

The gauge, so far I understand this concept, acts like an algorithm. You have the reality with a set of observables. Via the equations you get a representation of the reality (at least you hope it). Via a gauge you get another representation of the reality but you have (ex)changed the initial variables in the equations. The question is now to know if the new representation is a one to one representation, and if not, if it is a relevant one. For me, the choice of a gauge stays physical as long as the representation of the reality given by this gauge allows to do correct physical previsions ... even if its mathematical presentation is a complicated one.

 

[hellfire]

But the expression "background independent theory of gravitation" appears to me to be a paradox, a non-sense ... because the (field of) gravitation always is the background. With other words, if you are dealing in a precise given field of gravitation, even changing, then you are living somewhere where the time is "flowing" in a certain given way (even if it is changing with the variations of the field).

But it has a very precise meaning: the metric appears as a dynamical variable in the Lagrangian. It is subject of dynamics. As far as I understand, this, toghether with general covariance, is the origin of the problem.

 

[masudr]

Once you solve the equations for the metric, you then have to choose some co-ordinate representation which is locally like Minkowski space; of course there is such thing as time in GR.

 

[hellfire]

Once you solve the equations for the metric, you then have to choose some co-ordinate representation which is locally like Minkowski space; of course there is such thing as time in GR.

Yes, that situation arises with the relativistic point particle moving in a fixed spacetime background. The action is invariant under arbitrary reparametrizations. It can be shown that such systems lead to a vanishing hamiltonian. To solve the dynamics one usually selects a time coordinate within the spacetime background and eliminates the unphysical degree of freedom that was given by the reparametrization.

However, a different situation arises if we are talking about the degrees of freedom and the dynamics of the metric itself. In the hamiltonian formulation of general relativity, a vanishing hamiltonian does also appear. The question is then how to eliminate the gauge degree of freedom to get the real physical degrees of freedom. Of course you can assume that there is a nice solution to the equations which singles out a specific time coordinate (e.g. the cosmological time in spatially isotropic and homogeneous distributions of matter, or a static spherically symmetric solution), but there is no solution that preserves the complete generality given by the general hamiltonian formulation (or there is no solution which leaves the theory background independent).

I believe this lack of time evolution (or time evolution but with loss of generality) is a problem in order to define a quantum theory out of the hamiltonian formulation of general relativity. You can search in internet for references with “the problem of time”.

 

[CJames]

Once you solve the equations for the metric, you then have to choose some co-ordinate representation which is locally like Minkowski space; of course there is such thing as time in GR.

How can there be no time in GR if there is spacetime? Now I'm just lost.

 

[Juan R.]

Indeed.
So far I know, quantum gravity (e. g. see S. Carlip) analyzed under the binocular of "classical general relativity" begins with an ADM approach; this is de facto introducing a time slicing. In this sense it is false to say that there is no time in this approach.
The fact that QM has no consideration for the notion of time is also false; there is precise laws describing the evolution of the different physical observables.
I think that no clear presence of time in any equation of the QM is perhaps simply indicating its instantaneous validity, for any instant or for any infinitesimaly short period of time. This equation is like a photo of the reality, it is just concerning a slice of our life. Everything looks like if the moment when the slice has been done has in fact no importance.

So far I know, Carlip research in quantum gravity is rather approximated and focuses in only one or two aspects of this complex problem.

The "ADM approach" does not solve the time problem of (canonical) quantum gravity. In fact, is usually done is split variables into two groups and one group of variables is used like a kind of 'clock'.

1) Nobody know how select the correct clock.

2) The concept of time for the overall quantum state continues to be absent. Only it is worked a kind of 'local time' for approximated states.

3) Those 'clocks' of ADM -and related approaches- are not really clocks because are in reality quantum machines and therefore nobody know exactly how causality works therein.

As perfectly explained by Weinberg in his manual on quantum fields (volume 1) the true generator of time translations is the Hamiltonian but in quantum GR, the Hamiltonian is zero. Therefore the problem of time arises and nobody solved it still.

I think that no clear presence of time in any equation of the QM is perhaps simply indicating its instantaneous validity, for any instant or for any infinitesimaly short period of time. This equation is like a photo of the reality, it is just concerning a slice of our life. Everything looks like if the moment when the slice has been done has in fact no importance.

I'm sorry but this is 'nonsense'. Without time there is not 'instantaneus' concept. Perhaps you are confounding the problem 'of absence of time' with some kind of problem of evolution of a quantum system. There is a relationship, but the problem of absence of time is more complex that you are delineating here.

In fact, the absence of time precisely indicates that one cannot not introduce physical sense for quantum gravity wavefunctions even at a single 'instant'. One cannot even interpret the WdW equation of quantum gravity H|phi> = 0 like the quantum equation for an 'instant' of the universe.

 

[Juan R.]

Part of the problem with creating quantum theories of gravity, as I understand it, is that time in standard quantum mechanics is treated as a parameter rather than being on the same footing as measurable observables like position and momentum.

Can somebody tell me how string theories etc. try to solve that problem?

It is not solved. In string theory spacetime is treated cuasi-clasically with a well defined concept of time that coincides with time used in QFT. Then scattering amplitudes for hypotetical graviton scattering are computed using a simple generalization of usual QFT thecniques.

In rigor, this cannot be true and then one may treat the full spacetime in a quantum manner. That is called M-theory.

Nobofy know that M-theory is. M-theory has not been formulated. It is an idea...

In the other option non perturbative QG. The full spacetime is quantized (really the metric is) and then one obtain the problem of time. Time disappear from formalism doing quantum theory breaks down. For example, without defined time one cannot normalize wavefunctions.

 

[johnf]

In my opinion thermodynamics and quantum mechanics are different aspects of the same process. I would view both space and time as field-theoretical paramaters rather than as measurable dynamical observables.

I think they are both thermodynamic by-products of a deeper quantum reality which is non-local. For me therefore the question is really -how does quantum thermodynamics create our perception of space and time?

 

[QMrocks]

All obervables in QM have a complementary pair. Position with mometum, Energy with time. And because of this nature, a commutation rule exist for both pair (the uncertainty principle). Doesn't this makes time an entity of measurement too, just like its measureable complementary pair energy?

 

[johnf]

All obervables in QM have a complementary pair. Position with mometum, Energy with time. And because of this nature, a commutation rule exist for both pair (the uncertainty principle). Doesn't this makes time an entity of measurement too, just like its measureable complementary pair energy?

Yes, but I think that space and time may be 'special' in this sense. They are in my opinion parametric rather than metric or directly measurable in any real positive physical and direct way. Momentum and energy are on the other hand positively dynamic quantities. Energy-momentum is also thermodynamic. I suspect that both space and time are artifacts in our consciousness and perception generated by a cooling universe. Cosmological cooling in this sense 'defines' determines and and quantifies space and time to my thinking.

 

[Juan R.]

All obervables in QM have a complementary pair. Position with mometum, Energy with time. And because of this nature, a commutation rule exist for both pair (the uncertainty principle). Doesn't this makes time an entity of measurement too, just like its measureable complementary pair energy?

In non-relativistic QM, position and momentum ARE observables.

Energy is also an observable but time is not.

The commutation rule between energy and time does NOT exist. That exists is a 'simulation' of commutation from evolution laws that looks like commutation rule but is not

In non-relativistic QM time is not a observable like energy or momentum, it is a evolution parameter. There is not a time operator and this is the reason that time in QM is treated classically and causality is well defined.

The problem in QG is -in simple words- that one needs introduce a time operator and by mean of Hamiltonian constaints of GR, this disappear.

H |Phi> = 0.

without concept of time, there is not evolution, there is not dynamics, there is not causality, there is not correct classical limit, there is not unification with particle physics, and there is not probabilistic interpretation possible of wavefunctions.

During 50 years the problem of time continues to be unsolved.

In a basic review 2005 (http://www.livingreviews.org/lrr-2005-1), Carlip discusses the problem of time in (2+1) gravity in section 3.4.

It is easy prove that section is wrong but it is unnecesary since only focuses in (2+1) gravity. For the real case of our 4D universe Carlip writes

We cannot expect such a fortunate circumstance to carry over to full (3+1)-dimensional quantum gravity; it is an open question, currently under investigation

 

[member 11137]

Thank you for all these informations and discussions; I shall think a lot about that and come back with new ideas or propositions. I am a little bit surprised that time is not an observable allthought its effect can be observed everywhere. But this is actually more philosophy than physics and that's exactly the problem. We all suffer from the age (time) but are unable to translate this fact into equations. In this sense the remarks of johnf (post 23) are very pertinent I think. This is also certainly demonstrating that we have a lot of work to do now. Best regards

 

[member 11137]

In non-relativistic QM, position and momentum ARE observables.

Energy is also an observable but time is not.

The commutation rule between energy and time does NOT exist. That exists is a 'simulation' of commutation from evolution laws that looks like commutation rule but is not

In non-relativistic QM time is not a observable like energy or momentum, it is a evolution parameter. There is not a time operator and this is the reason that time in QM is treated classically and causality is well defined.

The problem in QG is -in simple words- that one needs introduce a time operator and by mean of Hamiltonian constaints of GR, this disappear.

H |Phi> = 0.

without concept of time, there is not evolution, there is not dynamics, there is not causality, there is not correct classical limit, there is not unification with particle physics, and there is not probabilistic interpretation possible of wavefunctions.

During 50 years the problem of time continues to be unsolved.

In a basic review 2005 (http://www.livingreviews.org/lrr-2005-1), Carlip discusses the problem of time in (2+1) gravity in section 3.4.

It is easy prove that section is wrong but it is unnecesary since only focuses in (2+1) gravity. For the real case of our 4D universe Carlip writes

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 ...

 

[johnf]

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 ...

Yes, I also favour this approach. I'm not sure that time can be fundamentally distinguished from space in any such scheme, though. relativity requires some similarity and partial equivalence in the way these two quantities are treated in physics.

I suspect the required space and time parameter functions are 'global' cosmological and thermodynamic ones. In my opinion our existence and evolution may be predicated as a 'cosmological thermodynamic counter-current' which requires us too perceive the universe as cooling and expanding. The cooling and expansion would in this sense be the 'prime mover' or free energy flux driving evolution as we perceive it.

As I stated in my earlier post (post 23)cosmic cooling creates both space and time. From a quantum mechanical - dynamical point of view, I would identify space as a product and consequence of the increased de Broglie wavelengths of the field excitations. Time on the other hand seems to require the notion of entropy for its comprehensions, and is perhaps somewhat more primitively experienced by us than space. I think we are driven in a certain direction of cosmological evolution in which entropy appears to increase, and time is a result or artifact of this.


I take a Machian view that space, time and inertia are all essentially cosmological thermodynamic functions. I regard quantum theory as more naturally a theory of the large than a theory of the small. I would consider our notions of scale to be mutually reflexive and imaging of each other.

 

[hellfire]

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?

 

[DaTario]

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.

 

[member 11137]

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.

 

[Juan R.]

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.

 

[member 11137]

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.