# Qm and SR

1. Jul 23, 2010

### robheus

Acc. to QM no two particles can be in the same state at the same position at the same time, but how does that reconcile with SR where two observers do not agree on simultaneity?
Do some observers see baryonic stuff violate this postulate?

2. Jul 23, 2010

### jfy4

That is the discrepancy between QM and Rel. In QM there are things like Time ordering operations, and space-time points. But in Rel. the idea of events being ordered in time is relative, and there are space-time points. This is the problem in physics many people are trying to solve right now, how to unite these two remarkably successful theories even though they are both so philosophically different.

3. Jul 23, 2010

### robheus

Is it possible to design an experiment that could show wether a phenomena which acc. to QM theory alone would be impossible (Pauli exclusion), but acc. to SR (based on different perspective on simultaneity because of different inertial frames of reference) is possible?

4. Jul 23, 2010

### dulrich

Two observers will agree on whether the particles are at the same position at the same time. The relativity of simultaneity has to do with whether events separated in space are simultaneous or not.

5. Jul 23, 2010

### humanino

In early discussions of SR, we often refer to two observers disagreeing on the simultaneity of events at different points in space. But an event in space-time remains defined as the intersection of two light rays, and that is manifestly Lorentz invariant. Qccording to QM no two particles can be in the same position at the same time, that is consistent with SR already.

edit

6. Jul 23, 2010

### torquil

These two theories were united long ago in what is called relativistic quantum field theory. It seems you are talking about a quantum theory of gravitation, which is something different.

7. Jul 23, 2010

### Glen Bartusch

Admit it, guys: there's this continuing war between QM and SR. And let's face it: those who side in the QM camp just don't understand Special Relativity. :)

8. Jul 23, 2010

### Glen Bartusch

Lol, and what's the difference between gravitational mass and inertial mass? According to Einstein, not a thing. Whether the motion be translational or linear, the two forms are one and the same. This equivalence is what makes it impossible to unite 'gravity' with the Standard Model, and likewise illustrates the band-aid approach to some solutions in the problem of particle interaction.
If 'relativity' is true, and if 'quantum field' theory is true, then why the title, "relativistic quantum field theory"? Why not just "field theory"?

9. Jul 23, 2010

### Glen Bartusch

Assume the particles to which you refer are photons. Then indeed, one observer must necessarily observe a younger or older photon relative to the observation of the other observer.

10. Jul 23, 2010

### Ben Niehoff

Because we need to distinguish it from classical field theories (such as electromagnetism and GR), and non-relativistic quantum field theories (such as many condensed matter theories).

"Relativistic" means that the theory obeys Lorentz symmetry. "Quantum" means the theory implements some version of the Heisenberg algebra. "Field theory" means it is a theory of functions on spacetime, which are called "fields".

11. Jul 23, 2010

### jostpuur

Being in the same state is not same thing as being in the same position. Eigenstates of Hamiltonians are never perfectly point like.

Could it be that exclusion principle could be used to construct some paradoxes, just like entanglement can be used? Apparent instantaneous action, and that stuff?

12. Jul 23, 2010

### jfy4

Relativistic Quantum Field Theory is the covariant form of quantum field theory, not a union between relativity and QM. Relativistic Quantum Field Theory is not a union, it is an expression of QFT in new terms. Relativity is the whole comprehensive relative motion of bodies, what we call gravity now, and has yet to be united successfully with QM.

13. Jul 23, 2010

### ismaili

I guess there is some misunderstanding between some jargons.
Jfy4 is talking about the union of "general relativity" with quantum mechanics.
However, Ben is talking about the union of "special relativity" with quantum mechanics.

And I think special relativity has been married to quantum mechanics well already.
Quantum Field Theory actually is the union.
And the possible candidates to describe "quantum gravity", which is the union of general relativity with quantum mechanics, include string theory.
Weinberg even pointed out several heuristic argument why the meet of special relativity and quantum mechanics produces "Quantum Field Theory" in his book.

14. Jul 23, 2010

### haael

In QM time is also uncertain. In SR you can have one observer that thinks the time was $$t_0$$ and the other observer that has time $$t_1$$. But QM says that both these numbers are just random, in reality you have (simplifying) $$t_0 +- \Delta t$$ and $$t_1 +- \Delta t$$. If these ranges overlap, the time is the same.

15. Jul 24, 2010

### alxm

The Pauli Principle is not at odds with Special Relativity in any way.

It's a consequence of Special Relativity!

16. Jul 24, 2010

### tom.stoer

Relativistic quantum field theory (rel. QFT) is perfectly well defined ; in this context there is no problem or clash of QM and SR.

The problem is that SR (and QFT) require a fixed spacetime background to set up the quantization procedure. Once this fixed stage goes away and you want to quantize on arbitrary dynamical spacetimes (as in GR!) it becomes difficult.

In addition time is not random in QM or QFT. It is a coordinate, not a dynamical observable (in QM and QFT observables are uncertain, coordinates and parameters are not).

17. Jul 25, 2010

### RUTA

While the spacetime structure of QM is blockworld, it is not Minkowskian. See

G. Kaiser, J. Math. Phys. 22, 705-714 (1981) and
A. Bohr & O. Ulfbeck, Rev. Mod. Phys. 67, 1-35 (1995).

Specifically, as pointed out in Bohr & Ulfbeck (Eq. 76), the time coordinate transformation involves a translation (giving blockworld) but no factor of gamma (no dilation).

18. Jul 25, 2010

### robheus

How?

19. Jul 25, 2010

### alxm

http://en.wikipedia.org/wiki/Spin-statistics_theorem" [Broken]

And if my grandmother was a bus, she'd have wheels.

Last edited by a moderator: May 4, 2017
20. Jul 25, 2010

### BruceG

Quantum field theory textbooks are traditionally very bad at explaining this point. I found the introductory chapter in Quantum Field Theory [Srednicki] very illuminating. Regarding attempts at relativistic quantum mechanics:

"..We can solve our problem, but we must put space and time on an equal footing at the outset. There are two ways we can do this. One is to demote position from its status as an operator, and render it as an extra label, like time [this is the quantum field theory approach]. The other is to promote time to an operator..relativistic quantum mechanics can indeed be developed along these lines, but it is surprisingly complicated to do so."

The second approach though is used as standard in string theory, where space and time are operators parametrised by world sheet coordinates of the string.

21. Jul 25, 2010

### RUTA

Not necessarily. She could've been an electrical conductor. No wheels there.

22. Jul 25, 2010

### tom.stoer

You certainly don't want to propose string theory here (as it procudes more problems than it solves.)

I think the first stept is to understand space and time in non-rel. qm., then in rel. qm, and after that to understand rel. QFT.

23. Jul 26, 2010

### BruceG

I wasn't proposing string theory here as a solution to combining quantum mechanics and general relativity.

Sticking to special relativity, there are two ways to formulate a quantum theory consistent with Lorentz invaiance.

1. First Quantization approach: space-time is an operator.

2. Second Quantized approach: space-time parametises a quantum field.

Both ways are equally valid. Second Quantization is best for point particle theories because it keeps track of the possibly infinite number of particles. With String theory you can do more at the First Quantized level because the infinite particles are coded into the string vibrations. Of course there is no empirical justification for moving from points to strings.

24. Jul 26, 2010

### ismaili

I think you proposed a good point.
But I don't quite understand the relation of this point with the first, and second quantisation.
Allow me to clarify what you were talking about.
Maybe I should ask the question: what is the definition of first and second quantisation?

My previous understanding is that, 2nd quantisation means we postulate equal-time canonical (anti-)commutation relations among fields; 1st quantisation means we are doing relativistic quantum mechanics only, i.e. we treat fields NOT as operators but as wavefuntions.
So, in this definition, first quantized theory should also treat space-time coordinates as parameters?

In string theory, we are actually doing relativistic quantum mechanical string.
Because we don't have fields of target space-time coordinates.
Instead, we have a 2D conformal field theory on the world-sheet.
But this doesn't mean that we have a quantum field theory of strings.
(I didn't study string field theory at all, so I don't know what's the quantum field theory of strings actually.)

So, in the first quantisation of strings, i.e. string theory, the target space-time coordinates become operators, which is unusual in first quantisation theories. Is this fact due to the connection of two faces of string theory:target/worldsheet space?
I mean, since we have to CFT on the worldsheet side, so all $$X^\mu(\tau,\sigma)$$ become the quantized fields on the worldsheet, so $$X^\mu$$ are operators.
Then, from the viewpoint of target space, we are doing first quantisation of strings, however, all space-time coordinates become operators.

Is my understanding correct?

Last edited: Jul 26, 2010
25. Jul 26, 2010

### fundamentally

The reason why relativity exists can only be understood in quaternionic Hilbert space. Relativity is caused by the way spacetime is defined. But the real cause is the quaternion waltz (c=ab/a) which equals b for complex numbers, but does not do so for quaternions. The waltz occurs when a unitary transform affects an observation. Thus, nearly always! With complex QM, you will never notice that it exists. The introduction of spacetime goes together with the introduction of proper time and coordinate time. If you describe dynamics by using coordinate time then you experience a Minkowski metric (or a Lorentzian metric in curved space). In that case exists a maximum speed c of information transfer. If you stay with proper time, then there is no maximum speed. The representation of an item in Hilbert space can move without being observed. In that case there is no speech of coordinate time. In that case only proper time makes sense.
More details can be found at http://www.scitech.nl/English/Science/Exampleproposition.pdf [Broken].

Last edited by a moderator: May 4, 2017