Relativity as an effect of quantum theory

[Edgard Neuman]

Hi,

I have this idea of mine about relativity and quantum theory, and I'd like to know if it is absurd or if there some idea in it. I have my own understanding of those theories, I hope you won't disqualify me too fast for this. (please excuse my english, it's not my main language)

So. First we have quantum theory, which can describe matter using Feynman diagrams : a lot of "classical" scenarios made of trajectories and interactions (particule paths), that are combined to get the actual sum of probabilities. This, I know, is a well verified interpretation.

We suppose that, for any scenario, the particules are "unmodified" between interactions.

The conservations principles define what happen at each interaction (for instance, a photon would deviate an electron)

If you put this in relativity theory, you have the same scenario, which can be describe in any frames, after applying any Lorentz transformations.

These transformations, as you know it, change speeds and also distances between events.

At that point, it seems to me that given a scenario, or a group of scenarios for a given system, some specific frame can be defined as those who minimize distances. For a given system, it seems to me that this specific frame can be described as the inertial frame of reference.

Think now about the probabilities you have, for instance, to see a particule from a given system, regarding to the interactions that are possible in all the scenarios.

Let's suppose, that, at a very low level of description, a conservation principle implies that the evolution for a system is not happening "by itself" but only in reaction to interactions with the rest of the universe.

Can we imagine that the probability of interaction, for a given system with its own reference frame, can define the quantity of information transmited and received by the system to an other. And so, for a group a particule moving in the universe, could it define "the inner quantity" of events, as if the clock of the system was simply more or less ticking, according to the probabilities of interactions with the univers ?

We could consider then that time is not define by the system itself, but more the result of external events reaching to it (simply variating with the speed) ?

And so, we could say that relativity is the result interaction probabilities in quantum theory ?

Edited August 21, 2013 by Edgard Neuman

[ajb]

And so, we could say that relativity is the result interaction probabilities in quantum theory ?

 

In the standard approach to quantum field theory on Minkowski space-time you use the Poincare symmetry to single out the vacuum. Now, things are much more complicated on a general curves space-time, unless the space-time is particularly nice. Here the metric is also used explicitly.

 

We do have quantum topological field theories and these do not care about the metric you use, they only care about the topology. That is they are "background independent".

 

Quantum gravity should be a theory like this. So, it should be possible to see the classical structure of general and special relativity as some kind of limit or derived notion. But without a working theory of quantum gravity we cannot say for sure.

[Edgard Neuman]

I only consider the special relativity.

The poincare symmerty, I don't understand how it singles out vacuum. Can you explain ?

For instance, let's say we take the velocity distribution of particules in a specific reference frame. For this distribution to be invariant under the Lorentz transformation, it has to have a specific form where more particule are close to the speed c (something like cosh?).

(i found this book http://adsabs.harvard.edu/abs/1973PhLA...44..537B , but not the function itself)

But that doesn't answer to my point, which ask if the fact that relative time speed (dt) for an object according to an other, could be (or not) explained by some variations in the probability of quantum interactions between each other.

Like if each mass spread a "clock field" (some way explained by quantum physics), and moving into it would slow clocks relative to it.. (obvioulsy, it's not the simple effect of speed, which would make the clock faster).

My first idea was that the speed of particule could change the probabily of basic interactions. So instead of simple "ball like" interaction, speed would effect the probability.. (but it would have been already surely detected).. my other idea is that speed could globaly modify fine structure constants of a system, which would directly change it's clock (it would be undetectable by the system itself, like relativity).

To proove it, we would have to find, in quantum theory, a mechanism, that give you the formula : dt²=1-(v/c)²

[ajb]

The poincare symmerty, I don't understand how it singles out vacuum. Can you explain ?

For a relativistic quantum field theory, the vacuum state should be invariant under the Poincare group and unique. This is one of the Wrightman axioms for quantum field theories.

 

To proove it, we would have to find, in quantum theory, a mechanism, that give you the formula : dt²=1-(v/c)²

The thing is that quantum theory is usually assumed to already posses the symmetries of special relativity. I assume then you want to create another theory, with another group of symmetries (Gallilian maybe) and then show how special relativity emerges?

 

I have no idea if that is possible.

[Edgard Neuman]

The fact that the quantum theory is invariant under Lorentz transformation, mean that given the states of particles we consider, after the speeds positions(etc) are transformed, the whole thing is still in accordance with the theory.

I don't think that necessarily imply that the vacuum itself is invariant (the vacuum could be described for instance by the velocities distribution of virtual particles, and not any distribution is invariant when frame reference change : it should slide and sum near the egdes ( = c)). I don't know what the quantum theory says about distributions of virtual particles caracteristics.

Edited August 23, 2013 by Edgard Neuman

[ajb]

I don't think that necessarily imply that the vacuum itself is invariant...

The vacuum state is invariant under the Poincare transformations. As I said, this is important in relativistic quantum field theory.

[PureGenius]

I think that quantum field equations should include black hole interactions at the atomic level it explains the hidden mass science has not come up with a reasonable theory to explain .Also the probability of anyone discovering a way to formulate a quantum theory incorporating classic style linear equations into a new systemwhat An interesting idea.

[Edgard Neuman]

The fact that a theory is invariant by a transformation doesn't imply that its states are equivalent before and after the transformation for an observer.

Let's say (on a single axis) that the probability to find a given particle with the speed X (between -c and c) is a constant.

The lorentz transformation by a frame whose speed is Y would change the speed from X to (X+Y)/(1+(X*Y)²/c²) (https://en.wikipedia.org/wiki/Special_relativity#Composition_of_velocities).

The speed distribution would certainly not be constant anymore (the vaccum would be rather different), even if the behavior of the new particles would be conform with Quantum theory.

Of course, I understand that the fact that vaccum is the same by any lorentz transformation : so the speed distribution (of virtual particles) must be very specific, for it not to change by X -> (X+Y)/(1+(X*Y)²/c²) transformation. That I don't know.

Edited August 23, 2013 by Edgard Neuman

[ajb]

Without the Poincare invariance of the vacuum state, and the invariance of the theory, different observers will not agree on the number of particles in a given state. Thus the Poincare invarience of the vacuum is usually a requirement. Or in other words, the Poincare invariance fixes a natural vacuum for you.

 

However, if one includes external time or space dependent sources then one does have the situation that different observers will disagree on the number of particles in a given state. This is of some importance in quantum field theory on curved space-times and is the root of Hawking radiation, for example.

[Edgard Neuman]

Without the Poincare invariance of the vacuum state, and the invariance of the theory, different observers will not agree on the number of particles in a given state. Thus the Poincare invarience of the vacuum is usually a requirement. Or in other words, the Poincare invariance fixes a natural vacuum for you.

 

Yes I understand that. The answer (the specific invariant distribution) must be in the book I referenced..(I can't find it on the web)

What is weird for me now, is that the form of this function should be like the letter "U" within ]-c;c[ limits (because when you apply the transformation of a frame close to "c" , more particles should be seen with a velocity close to c.).

Let's say we have a lot of virtual electrons and positrons (in average equals according to the vacuum null momentum and charges) at random speed according to this distribution which is invariant : there should be much more electron close to the "c" velocity than close to 0 (the "U" shape of the function). This is what bothers me.

This fact make me think that some quantum effect should explain why those very fast (and so energetic) particles are not as effective as the slow ones (or are they ?). This effect would be a consequence of the quantum theory.

And then we could use this mecanism to explain why a given system, with high speed, seem to have a slown down time : High velocity system, would be, somehow, relativily disconnected to the observer, and it would so explain both : that vaccum can contain high velocity virtual particles, and that time is slown for each one from the other.

That could maybe explain relativity by this effect.

 

I have an other way to say that : let's say that for a particle, probability of interacting with photon depends of the speed of the particle : because it's a wave, photon would be stretched along particle trajectory (it would be relative of course).

So for a system seen in a high speed frame, photon should be much less interacting with electrons and positrons (the fine structure constant). Could this explain why "time" appears slown ? Photon interactions could logicaly be the ticks defining the clock of the atoms.

[ajb]

The problem is you need to describe your ideas mathematically. The photon has special relativity all ready written into its formulation.