Quantum mechanics without spacetime

[math_04]

Hi,

I am wondering what everyone here thinks about some of the work that has gone into researching quantum mechanics without spacetime. I am only a third year physics student at college (having done classical mechanics, electromagnetism and quantum mechanics upto perturbation theory, special relativity...so it is probably way over what I know) but it does seem an interesting avenue.

I only began thinking of this when my friend and I, began talking about the Big Bang and how popular documentaries say that the concept of space-time breaks down? I guess space and time, when applied to quantum theory, can be strangely different to what we think of in a classical world like entanglement or even the uncertainty principle. Is the concept of quantum mechanics without spacetime similar to loop quantum gravity? I tried googling some info but I quickly ran into papers that I could barely understand like the one below.

http://arxiv.org/abs/gr-qc/0406054

 

[meopemuk]

Here is another take on the relationship between quantum mechanics and spacetime:

E.V. Stefanovich, Is Minkowski Space-Time Compatible with Quantum Mechanics? Foundations of Physics 32 (2002), 673-703.

Eugene.

 

[math_04]

Thanks for the article meopemuk! It was an interesting read although I have a couple of questions.

1. In the section on special relativity, you write that the Lorentz transformations are derived for 'photonic events only'. I only thought that people used photonic events to talk about time measurement in relativity because it was simple and easy to understand and that you could use massive particles but it is very complicated?

2. The gist of your paper according to me, correct me if I am wrong, is that special relativity, depends on the conception of space-time (things like trajectories, how you measure time) but that quantum mechanics is a whole different ball game where traditional concepts of space-time do not mean anything? Therefore, what you seem to be saying is that superluminal speeds in a quantum world are possible?

 

[meopemuk]

1. In the section on special relativity, you write that the Lorentz transformations are derived for 'photonic events only'. I only thought that people used photonic events to talk about time measurement in relativity because it was simple and easy to understand and that you could use massive particles but it is very complicated?

Yes, in special relativity one often uses photon-related events (like emission and absorption of light pulses) for establishing Lorentz transformations, because photons are basically non-interacting particles always moving with the speed of light. So, calculations of their trajectories and events (like intersections of trajectories) are very simple. After establishing Lorentz transformations for such photonic events one must answer an important question: are the same transformations still applicable to events involving other particles, in particular, massive particles that interact with each other, such as electrons, protons, etc?

One possible answer is "yes": Lorentz transformations are universally applicable to all events in Nature (we are not talking about gravity here). Then, one can introduce the notion of the 4-dimensional Minkowski space-time unification and try to formulate interacting theories that obey these universal Lorentz transformation formulas. The Currie-Jordan-Sudarshan no-go theorem shows that it is very difficult (impossible?) to formulate such theories.

Another possible approach is to say that Lorentz transformations may be OK for photons and non-interacting particles. But for interacting systems boost transformations of their properties may depend on interactions between constituent particles. Everybody knows that time translation transformations (time evolution) do depend on interactions acting in the system. Also, most people know that time translations and boosts are related to each other via Poincare group properties. From these two basic facts one can conclude that boosts may be interaction-dependent too. So, Lorentz transformation formulas may require corrections that depend on interactions between particles.

2. The gist of your paper according to me, correct me if I am wrong, is that special relativity, depends on the conception of space-time (things like trajectories, how you measure time) but that quantum mechanics is a whole different ball game where traditional concepts of space-time do not mean anything? Therefore, what you seem to be saying is that superluminal speeds in a quantum world are possible?

Not exactly. The reference to quantum mechanics is not necessary. The argument was based on this reference simply because in quantum mechanics it is easier to construct an interacting theory of particles that satisfies the principle of relativity. This construction is done by means of an unitary representation of the Poincare group in the Hilbert space. Then, in the so-called instant form of dynamics one finds that both the Hamiltonian (the generator of time translations) and the boost operator are interaction-dependent. This means that both time evolution and boost transformations are affected by the presence of interactions. This also means that universal linear Lorentz transformations of special relativity cannot be applied to interacting systems. This is true for both quantum and classical systems of particles.

These ideas were applied to a numerical example of a 2-particle system in

B. T. Shields, M. C. Morris, M. R. Ware, Q. Su, E. V. Stefanovich, R. Grobe, Time dilation in relativistic two-particle interactions, Physical Review A 82 (2010) 052116.

Eugene.

 

[strangerep]

B. T. Shields, M. C. Morris, M. R. Ware, Q. Su, E. V. Stefanovich, R. Grobe, Time dilation in relativistic two-particle interactions, Physical Review A 82 (2010) 052116.

Is there a reason why you and your coauthors didn't put a preprint of that paper on the arXiv ?

 

[meopemuk]

Is there a reason why you and your coauthors didn't put a preprint of that paper on the arXiv ?

Hi strangerep,

No good explanation. Maybe they don't do arXiv over there in Illinois as much as we do it over here in California. I've sent you the final draft of this paper by e-mail.

Cheers.
Eugene.

 

[meopemuk]

B. T. Shields, M. C. Morris, M. R. Ware, Q. Su, E. V. Stefanovich, R. Grobe, Time dilation in relativistic two-particle interactions, Physical Review A 82 (2010) 052116.

Is there a reason why you and your coauthors didn't put a preprint of that paper on the arXiv ?

Here it is: http://arxiv.org/abs/1303.2555

Eugene.