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Time in QM

  1. Oct 22, 2005 #1
    How does time work in QM?

    I remember reading something that said time doesnt 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?
     
  2. jcsd
  3. Oct 22, 2005 #2

    ZapperZ

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    That doesn't make much sense. For example, just look at the time-dependent Schrodinger 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.
     
  4. Oct 22, 2005 #3
    This is a post i was refering to:

    So is this a bunch of baloney, or did I misunderstand it?
     
  5. Oct 22, 2005 #4

    ZapperZ

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

    Zz.
     
  6. Oct 22, 2005 #5
    I thought someone here might be able to comment on it.
     
  7. Oct 22, 2005 #6

    ZapperZ

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    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 Schrodinger 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.
     
    Last edited: Oct 22, 2005
  8. Oct 22, 2005 #7
    Alright, thank u.
     
  9. Oct 23, 2005 #8
    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.
     
  10. Oct 23, 2005 #9
    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.
     
  11. Oct 23, 2005 #10

    James R

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    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?
     
  12. Oct 24, 2005 #11

    hellfire

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    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.
     
  13. Oct 25, 2005 #12
    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.
    Theoretically you are rigth. But the expression "background independant 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).
    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.
     
  14. Oct 25, 2005 #13

    hellfire

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    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.
     
  15. Oct 25, 2005 #14
    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.
     
  16. Oct 25, 2005 #15

    hellfire

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    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 belive 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”.
     
    Last edited: Oct 25, 2005
  17. Oct 25, 2005 #16
    How can there be no time in GR if there is spacetime? Now I'm just lost.
     
  18. Oct 29, 2005 #17
    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'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.
     
    Last edited: Oct 29, 2005
  19. Oct 29, 2005 #18
    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.
     
  20. Oct 30, 2005 #19
    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?
     
  21. Oct 30, 2005 #20
    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?
     
  22. Oct 30, 2005 #21
    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.
     
  23. Oct 30, 2005 #22
    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 dissappear.

    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

     
    Last edited: Oct 30, 2005
  24. Oct 30, 2005 #23
    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
     
  25. Oct 30, 2005 #24
    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 ...
     
  26. Oct 30, 2005 #25

    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.
     
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