What is the role of proper time in quantum theory

In summary, the concept of proper time in quantum theory is of little use and has no meaning in the most standard case of quantum fields and multiparticle fock states. While there is a second option for a relativistic quantum theory proposed by Srednicki, it has not been fully developed and is considered more difficult than the current field theory approach.
  • #1
pellman
684
5
What role does proper time play in quantum theory? Does proper time have any meaning in QM?

By quantum theory I should perhaps say "relativistic quantum mechanics" since I don't know enought QFT to ask a proper question.

If there were a proper time [tex]\tau[/tex] parameter or dynamical variable, then a rest-mass operator [tex]i\hbar\frac{\partial}{\partial \tau}[/tex] would be its conjugate in the same way that energy is "conjugate" to time in non-relativistic QM. A specific rest mass then, such as we see assumed in the Klein-Gordon equation, would represent a eigentstate of this rest-mass operator.

But there is no degree of freedom associated with rest mass, right? We never see superpositions of states of different rest mass, right?

Of course, proper time is not completely analogous to time-as-parameter in non-relativistic QM. In non-relativistic QM, time is a global parametrization of the whole system, whereas proper time ,as usually understood, is specific to each particle.

So what is the consequence of this to our understanding of proper time within quantum theory?
 
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  • #3
pellman said:
What role does proper time play in quantum theory? Does proper time have any meaning in QM?
As I'm sure you know, proper time is a property of a curve in Minkowski space, but the motion of a particle in quantum mechanics, can't represented by such a curve. So the concept seems to be of little use. However, we can't get rid of the SR postulate that says that what a clock measures is the proper time of the curve that represents its motion. Even in QM, we have to think of the clocks we use to test the predictions of the theory as if they behave classically (and to a good enough approximation, they do).
 
  • #4
Fredrik said:
As I'm sure you know, proper time is a property of a curve in Minkowski space, but the motion of a particle in quantum mechanics, can't represented by such a curve. So the concept seems to be of little use.
You may equally say that x(t) does not have a meaning in QM. But it does, e.g. as an operator in the Heisenberg picture. In a similar sense, you can introduce x(tau) and t(tau) as a relativistic analog of the Heisenberg picture.
 
  • #5
Demystifier said:
Interesting question.
See e.g.
http://xxx.lanl.gov/abs/0811.1905 [accepted for publication in Int. J. Quantum Inf.]
and Ref. [5] in it.
For a possibility of a superposition of different masses see
http://xxx.lanl.gov/abs/0801.4471 [ Mod.Phys.Lett.A23:2645,2008]

When I read these papers I think I understand them ok. Yet I don't see how they show any better understanding of the question posed above. Can you elaborate?

Also, "unparticle" is a new concept to me. But isn't one conclusion that follows from the paper that, given the mathematical basis for QFT together with the usual interpretation, there is nothing that prevents us from considering varying mass and non-integer particles? Which is something I've noticed before. Within the theory, are specific mass and integer particles extra postulates? (Is that the same thing as saying they require a superselection rule?) If the operator [tex](a^{\dagger}(k))^{\frac{2}{3}}[/tex] makes sense mathematically (and I am not sure that it does), what rules out a state containing two-thirds of a particle?
 
  • #6
pellman said:
When I read these papers I think I understand them ok. Yet I don't see how they show any better understanding of the question posed above. Can you elaborate?
Have you been reading some of the papers in Ref. [5]? I think they are quite close to your idea.

pellman said:
Also, "unparticle" is a new concept to me. But isn't one conclusion that follows from the paper that, given the mathematical basis for QFT together with the usual interpretation, there is nothing that prevents us from considering varying mass and non-integer particles? Which is something I've noticed before. Within the theory, are specific mass and integer particles extra postulates? (Is that the same thing as saying they require a superselection rule?) If the operator [tex](a^{\dagger}(k))^{\frac{2}{3}}[/tex] makes sense mathematically (and I am not sure that it does), what rules out a state containing two-thirds of a particle?
The idea of the paper above is that only integer number of particles makes sense. In particular, [tex](a^{\dagger}(k))^{\frac{2}{3}}[/tex] does not make sense.
 
  • #7
Thanks, D.
 
  • #8
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  • #9
pellman said:
But there is no degree of freedom associated with rest mass, right? We never see superpositions of states of different rest mass, right?

Perhaps see section 4 "Probing Masses through Neutrino Mixing" of Haxton and Holstein's http://arxiv.org/abs/hep-ph/9905257
 
  • #10
The relativistic version of QM, the Dirac equation is invariant under Lorentz transformation (in contrast to the Schrödinger equation which is not). I think the use of Hamiltonian (energy-momentum picture, rather than forces, position and momentum) in an assumed fixed frame S, makes it not necessary to deal with proper time tau=gamma(u)*t.

But when it comes to derive forces, in terms of expectation values of operators, I think it would be wise to do this with proper time, .i.e., What are the eqm for the expectation values <x> you get from the relativistic version of Ehrenfest theorem? You should obtain the version with proper time!
 
  • #11
Very interesting. Especially the neutrino mixing stuff. Thank you!
 
  • #12
What role does proper time play in quantum theory? Does proper time have any meaning in QM?

I would say none. At least in the most standard case that all textbooks follow, where you have quantum fields and multiparticle fock states, no single particles with clocks.

As Atvy pointed out, Srednicki says there is a second option for a relativistic quantum theory, on which he unfortunately gives not much detail and says it is much more difficult then the field approach.
 
  • #13
pellman said:
We never see superpositions of states of different rest mass, right?

In addition to neutrino mixing, there's the mixing of [itex]K^0[/itex] mesons, which has been studied experimentally since the 1950s.
 
  • #14
Yes, no 5th dimension as time only go forward (not in my mathematics). NOT NEED 5th dimension, time NOT this - all wrong - no good. Time NOT space - no.
 
  • #15
QuantumBend said:
Yes, no 5th dimension as time only go forward (not in my mathematics). NOT NEED 5th dimension, time NOT this - all wrong - no good. Time NOT space - no.
Time no space - no good. Time is space - good. Einstein good, Newton no good. :biggrin:
 

Related to What is the role of proper time in quantum theory

What is proper time in quantum theory?

Proper time is a concept in quantum theory that refers to the time experienced by an observer who is moving along with a particle. It is the time measured by a clock that is at rest with respect to the observer and follows the same path as the particle.

Why is proper time important in quantum theory?

Proper time is important in quantum theory because it is a fundamental concept that helps us understand the behavior of particles at the quantum level. It allows us to accurately measure the time experienced by a particle, which is crucial in understanding its motion and interactions.

How is proper time related to the uncertainty principle?

The uncertainty principle states that the more precisely we know the position of a particle, the less we know about its momentum, and vice versa. Proper time is related to this principle because it is impossible to know both the position and the time of a particle with absolute precision. This is due to the fact that proper time is affected by the particle's motion, making it inherently uncertain.

Can proper time be measured directly?

No, proper time cannot be measured directly. It can only be measured indirectly by comparing it to a clock that is at rest with respect to the observer. This is because proper time is affected by the motion of the observer, making it difficult to measure directly.

How does proper time differ from coordinate time?

Proper time is different from coordinate time, which is the time measured by an observer at a fixed point in space. Proper time takes into account the motion of the observer, while coordinate time does not. This means that proper time is relative, while coordinate time is absolute.

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