# Time in quantum physics

1. Sep 30, 2007

### ivan

hi
I have this question about time in quantum physics: how does quantum physics consider time? Is it absolute or relative? Or otherwise, when one makes calculations in quantum physics do they use same time or relativity-based time?

2. Sep 30, 2007

### meopemuk

The issue of time in relativity (special and general) and in quantum theory is very controversial. The "problem of time" is, in my opinion, the most fundamental unresolved problem in modern theoretical physics, whose solution is the key for consistent quantum description of relativistic and gravitational phenomena. There are lots of debates around this issue. Still there is no consensus, and I can tell you only my personal point of view.

Modern relativistic quantum theory exists in the form of the quantum theory of fields (QFT). The main physical (i.e., comparable to experiment) quantity calculated by QFT is the S-matrix, i.e., amplitudes of scattering processes. These amplitudes are independent on time. So, QFT is not interested in finding out the detailed time evolution of states and observables. At least, I haven't seen any QFT calculations of time-dependent processes that were compared with experimental data. Yes, QFT formulas involve a parameter t, which is usually intepreted as "time". However, in the final expression for the S-matrix this parameter is integrated from $-\infty$ to $\infty$, so, any relationship to the time evolution is lost.

Eugene.

3. Sep 30, 2007

Time must be a force or a by product of energy no?

Light must get really bored if time slows down at its cursing speed :)

if time is not real why have we spend so many thousands of years measuring it and obsessing over it and its used in lots of maths.

I think the problem is the inability to bottle it, cut and paste or slow it down makes its doubt if its real or not but here it is all around me, I think.

Last edited: Sep 30, 2007
4. Oct 2, 2007

### ivan

Let me ask you this, please. Time is still a variable or physical entity used to calculate certain other variables in GR and SR or in QM(if such a thing is used in it), am I right? If so, then How is time measured in these physics? By a device, say like a watch or by something else?

If we do not know what is the time(I just accepted your statement about time controversy as such), is it possible to talk about things like velocity or acceleration that are time dependent variables?

Thank you very much again.

5. Oct 2, 2007

### masudr

In QM, as in standard classical mechanics, you choose a frame in which to do physics, and that settles your time.

In GR, we postulate that physics should be the same, no matter what frame we choose. Even absurd ones that zwiggle around in ridiculous ways (although I guess these should be smooth paths). Even those frames, which intuition has taught you, cannot possibly have the same physics as more sensible frames (such as "fixed to the earth" etc.) GR does a remarkable job of showing that physics can be equivalent in any frame.

QM, however, as it currently stands, does not yet have a formulation (as far as i know) where the physics looks identical in any frame.

6. Oct 2, 2007

### meopemuk

I think I have have pretty good understanding of what time is. I just wanted to warn you that this understanding is not a part of consensus. In my opinion, time is a classical parameter that is measured in each reference frame by its own clock. There is no difficulty in defining time-dependent observables, time derivatives, etc.

It is important to note that there is a fundamental difference between time and position. Position is an "observable" because its measurements depend on the state of the system for which the position is measured. Thus position is represented by a Hermitian operator in quantum mechanics. Time is not an observable, because its value does not depend on the state of the observed system. We can "measure" time (by looking at the clock) even if there is no physical system to observe. So, time should be regarded as an attribute of the reference frame rather than an "observable", which, by definition, is an attribute of the observed physical system.

In spite of this fundamental difference, Einstein's special relativity regards both time and position as equivalent coordinates on the Minkowski space-time. This is in a deep contradiction with different roles played by time and position in quantum mechanics. For this reason, I think it is impossible to combine special relativity and quantum mechanics in one comprehensive approach. QFT cannot be counted as such an approach, because, as I described in the previous post, the time dependence of states and observables is disregarded in QFT.

Eugene.

7. Oct 2, 2007

### ivan

does this mean that if you choose 2 frames, say the earth and a rocket which starts accelerating movement with regard to the earth, quantum events might be going on differently?

8. Oct 2, 2007

### ivan

Sorry, I did not mean to insult you. What I meant was there's no objective description of time since there's no unitary idea of time in physics, or different parts of physics.

I want to clarify this for me. If I'm mistaken please correct me. When we say position is an 'observable' we probably mean that a particle's (or macroscopic object's) position can be observed. Observation can be performed through a 'naked' eye or some type of measuring device like florescent screen that can light up when particle hits it.

You've mentioned Hermitian operator. I do not know that much math. So, when I talk about observing a position of a something I mean I could sea what you (as a physicist) could see physically in a given experiment. You describe observation in a certain abstract way to make physics meaningful, though finally it all comes to observing things through vision or hearing (whether seeing a flash or hearing a click).

This is not quite clear to me. By 'no phycial system' I guess you mean no physical system other than the clock. Since I think the clock also presents the physical system which we observe. This might include the observation of the positions of the clock's arms.

I want to ask time dilation questions but I don't think I can understand answers until I know I talk the same language as you do.

Thanks again to everybody who take time and quench my curiosity.

9. Oct 3, 2007

### masudr

What I mean is in relativity, the formulation is such that the transformation rules between results obtained in different frames is standard (i.e. tensor transormation rules). In QM, the transformations of the observables required to take you from one reference frame to another will not, in general, be the same.

10. Oct 3, 2007

### meopemuk

You are absolutely right that different definitions of time in different parts of physics (e.g., in quantum mechanics and in special relativity) cannot be tolerated. There should be a unique definition of time across all physics. I suggest that quantum-mechanical definition (time as a classical parameter of reference frames) should be used.

Yes, you are basically correct.

It is important to understand that theoretical physics is not supposed to give us a comprehensive picture of the world. Its role is more modest: it must describe and predict results of measurements performed in well-controlled experimental setups. When you perform an experiment you usually have a pretty good idea about what is the observed physical system (atom, molecule, crystal, rock, planet, etc.), what is the measuring apparatus (bubble chamber, Geiger counter, ruler, telescope, etc.), and what constitutes the "measurement" (flash, click, blackening of the photographic plate). If a theory can predict exactly (the probabilities of) these flashes and clicks, then the role of theory is fulfilled.

Each observer (or reference frame) should have one specific device called "clock". When observer performs a measurement he also looks at the clock reading and assigns a label "time" to the measurement. This label does not depend on what physical system was observed and what physical property of the system was probed. In this respect "time" is very different from other "observables", such as position, momentum, spin, energy, etc. which are intimately related to the observed physical system and its state.

This depends on you experimental setup. Yes, you may decide to treat the clock as your physical system and treat the position of the clock's arm as the observable. Then the clock is no longer a measuring device (i.e., not a part of the reference frame), but the observed physical system. In this case you should use some other device as a clock (i.e., for generating time labels of measurements) in your reference frame. The bottomline is that in experiment you must always have a clock which is not a part of your observed system, but a part of your measuring setup.

Eugene.

11. Oct 3, 2007

### ivan

Before I ask you next question with your permission, I want to digress from the main point for a second. You have expressed this idea before and I completely agree with you. Namely, in physical theories we have many abstract descriptions. You have mentioned one of this somewhere in quantum physics' topic: this was Hilbert space. I do not know what type of mathematical space is that, but I now that We can't see or feel that space in any way and it is an abstract space. Though it does not exist(or at least we can't directly observe such a thing) you use it to 'calculate' the nature. Then you see that such calculations perfectly feet the world. So, regardless of what is the reality, by such a mathematical construct you predict things the way you are going to hear it or see it. In other words that concept does it's job.

Now as you said in QFT time parameter is used for calculations. Though time is not considered as observable entity. I also assume that QFT at least predicts what it's supposed to predict. So here time parameter is used to calculate observable events. In a sense time here is as abstract as Hilbert space and for that matter any abstract concepts. I want to make some comparison here to show you if I correctly understand that. I've read in one of the math books how a middle century mathematician(I think it was Cardano, I may be wrong though) introduced the concept of complex numbers (it was called imaginary numbers for this reason) to find real solutions to cubic equations of certain types. So this number was kind of bypass product which helped to find real number solutions.

Now my questions: Is time in GR and SR as abstract as it is in QFT, in other words is it used just to calculate other observable quantities? Or is it something as real as a position of a particle or heavenly body?

Thanks again.

12. Oct 4, 2007

### meopemuk

I think this is very accurate description of the role of abstract concepts, such as Hilbert space, in theoretical physics.

I think we both agree that time is a real observable thing that can be measured by clocks. So, any complete and successful physical theory must have a prominent place reserved for time. More specifically, the theory should be able to describe the time evolution of physical systems and this description should match the time evolution observed in experiments.

Relativistic QFT is definitely a successful theory. It predicts with astonishing precision certain properties, such as the Lamb's shifts of atomic levels or the electron's magnetic moment. However, is it a complete theory? I think that the answer is "no", because all successful predictions of QED are related to "static" phenomena in which the time dependence doesn't play a role. The best example is scattering cross-sections. Although these quantities are used to describe time-dependent processes (collisions of particles), they tell us very little about the time evolution of these particles. The cross-sections are similar to asymptotic values of a function (at plus and minus infinities), which don't tell much about the shape of the function at finite arguments.

If what I am saying is true, then how come that nobody has noticed this inadequacy of QFT for the description of fundamental particles? The answer is simple. Particle physics normally deals with high-energy processes in which (almost) everything occurs so quickly that no experimental device can measure the time dependence. All we can do is to see the uneventful time evolution of free reactants before the collision and free products after the collision. For description of such limited experimental data QFT scattering cross-sections are more than sufficient.

I think that the main reason why QFT cannot properly incorporate the notions of time and time dependence is that QFT is based on Einstein's special relativity in which it is assumed that time and space form a unified 4-dimensional Minkowski space-time continuum. (Note that this is an assumption, rather than a fact proven from some undeniable postulates.) As I wrote elsewhere, the idea of space-time unification is completely foreign to quantum mechanics in which time is a numerical attribute of the reference frame and position is an observable of the physical system. This incompatibility of the roles played by space and time in special relativity and in quantum mechanics is the main reason why by forcing QM and SR to coexist within QFT we get an incomplete theory.

Eugene.

13. Oct 4, 2007

### Anonym

Sorry for intervention. I have no intention to spoil your discussion. Only side remark. First of all, thank you. I desperately tried to remember who introduced the complex numbers. Now you remind me (it seems I read that in Novoselov book).

Now, consider a cubic equation with the real coefficients. Sometimes you have three real solutions and “understand” everything. Then you introduce another reference frame, shifted with respect to the original, and according to your attitude you face something incomprehensible and abstract. If your cubic function describes the potential energy, then the solutions of the corresponding cubic equation describe the classical turning (stationary) points which have the crucial importance in understanding of QM as explained by the “fathers”.

I think you would express yourself better by writing: I do not know what type of mathematical space is that, but I know that I can't see or feel that space in any way and it is an abstract space. The difference is that now you blame yourself only and not a nature that you (we) are stupid. Therefore, now we have a chance.

In addition to Eugene POV, I suggest reading J. Hilgevoord, “Time in quantum mechanics: a story of confusion”, Studies in History and Philosophy of Modern Physics, 36, 29 (2005)) as the introduction to the topic.

Regards, Dany.

14. Oct 4, 2007

### meopemuk

Hi Dany,

Thanks for the reference. I found Hilgevoord's article on the web (Microsoft Word document)

http://www.phys.uu.nl/igg/publications/time.doc [Broken]

A very interesting piece with some fresh ideas, although I disagree with almost everything written there.

Eugene.

Last edited by a moderator: May 3, 2017
15. Oct 4, 2007

### Anonym

Hi Eugene,

Thanks for the reference. I will study it. I find even acknowledgements very interesting. However, I referred to another paper where Dirac, Heisenberg, Bohr, Schrödinger, von Neumann and Pauli POV’s are discussed.

Regards, Dany.

16. Oct 5, 2007

### ivan

Thanks for nice words.

17. Oct 5, 2007

### Anonym

And read A.Vosnesensky “Plach po dvum nerogdennim poemam”. It works. Gelau uspecha!

Regards, Dany.

18. Oct 6, 2007

### frieza

obvsly relative.. in the view of quantum physics the time factor is being regarded as relative as time can not be considered as a constant one in space

19. Oct 8, 2007

### ivan

I apologize for this question asked in this thread, but I tried to avoid opening new thread. My question relates to simultaneity in relativity. Say we have a moving frame A with regard to a rest frame B. A moves with velocity v in the B's frame. If two events in A (from the A's observer's point of view) happen at the same time then how this two simultaneous events will be separated in time for B observe? What's the formula to calculate this time difference?

Thanks again.

20. Oct 8, 2007

### meopemuk

The connection between time and position of the same event viewed from two different inertial frames is given by Lorentz transformations. See http://en.wikipedia.org/wiki/Lorentz_transformations

Eugene.