Exploring the Standard Model's Role in Prohibiting FTL

[Jarwulf]

I was reading Baez's FAQ at http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/FTL.html#17" and I came across this nugget

Except for gravity, all physical phenomena are observed to comply with the "Standard Model" of particle physics. The Standard Model is a relativistic quantum field theory which incorporates the nuclear and electromagnetic forces as well as all the observed particles. In this theory, any pair of operators corresponding to physical observables at space-time events separated by a spacelike interval "commute" (i.e. their order can be reversed). In principle, this implies that effects cannot propagate faster than light in the standard model, and it can be regarded as the quantum field theory equivalent of the infinite energy argument.

Alright I understand that 3+2 = 2+3 but I don't get how that translates into an infinite energy prohibition on FTL.

 

[PeterDonis]

I'm not sure that "quantum field theory version of the infinite energy argument" should be taken literally, as though infinite energy were somehow involved in the QFT version; I think it's just an observation that the QFT argument he gives is "one way in which things cannot be made to go faster than light, rather than a proof that there is no way to do so".

The QFT argument itself is simply that, since the ordering of spacelike-separated events is frame-dependent, the field operators at spacelike-separated events must commute in order for the QFT's predictions to be frame-invariant (i.e., the predictions can't depend on the order of the operators, since that's not frame-invariant at spacelike separations). But if the operators commute, then there's no way for any quantum effect to "propagate" between two spacelike-separated events; i.e., no quantum effect can travel "faster than light". Like you, I don't see any "infinite energy" in there, but it is a "way in which things cannot be made to go faster than light".

 

[Bill_K]

It's important to remember this property of quantum field theory (causality) the next time you hear people say things like "positrons are electrons traveling backwards in time." That makes it sound like a future event can send an influence into the past in the form of an antiparticle, which of course is not the case. Causality is exactly the reason why antiparticles are necessary at all. A theory that contained just electrons would violate causality by permitting propagation of signals outside the light cone. Adding the antiparticles fixes the problem.

 

[Jarwulf]

I'm not sure that "quantum field theory version of the infinite energy argument" should be taken literally, as though infinite energy were somehow involved in the QFT version; I think it's just an observation that the QFT argument he gives is "one way in which things cannot be made to go faster than light, rather than a proof that there is no way to do so".

Alright I'm a little dense so you'll have to bang things in me a little harder.

The QFT argument itself is simply that, since the ordering of spacelike-separated events is frame-dependent, the field operators at spacelike-separated events must commute in order for the QFT's predictions to be frame-invariant (i.e., the predictions can't depend on the order of the operators, since that's not frame-invariant at spacelike separations). But if the operators commute, then there's no way for any quantum effect to "propagate" between two spacelike-separated events;

What I'm getting from this is basically a scaled down version of the time travel prohibition in SR. Causality between spacelike separated events will allow event B to occur before event A in some FrameofRef leading to causality violations thus FTL is impossible. Except replace 'causality violations' with 'breakdown of QFT invariance' right?

an operator can be considered like a property of an event. So Property of Event A and Property of Event B have differing orders of occurrence based on the FrameofRef. Thus since QFT predictions are true for every frame they can't depend on the order of the properties of event A and B. Therefore since no order can be given to A or B there is supposedly no cause between them.

 

[PeterDonis]

What I'm getting from this is basically a scaled down version of the time travel prohibition in SR. Causality between spacelike separated events will allow event B to occur before event A in some FrameofRef leading to causality violations thus FTL is impossible. Except replace 'causality violations' with 'breakdown of QFT invariance' right?

I'm not sure what you mean by "QFT invariance" other than just another way of saying "causality violations". The quantum version basically *is* a prohibition of causality violations, same as the "classical" SR version. See next comment.

an operator can be considered like a property of an event. So Property of Event A and Property of Event B have differing orders of occurrence based on the FrameofRef. Thus since QFT predictions are true for every frame they can't depend on the order of the properties of event A and B. Therefore since no order can be given to A or B there is supposedly no cause between them.

Pretty much correct. The only change I would make is that an operator is more like a measurement made at a given event. So if Event A and Event B are spacelike separated, the operators have to commute because the results of measurements at those two events can't depend on the order in which the measurements are made (since that order is frame-dependent but the measurement results have to be frame-independent).

The reason this ties into causality is that if there is a causal link between Event A and Event B, then the results of a measurement made at one event should affect the results of a measurement made at the other event, which means that the ordering of the events should affect the outcomes of the measurements. (For example, if I throw a baseball at time t, it might possibly break a window at time t + 2 seconds; but it can't possibly break a window at time t - 2 seconds.) But the above shows that that can't happen if the events are spacelike separated. So two events that are spacelike separated can't be causally linked.

Note, too, that the above reasoning applies equally well to "classical" SR, with no quantum effects included. So the "classical" and the quantum versions are really saying the same thing.