Cherenkov Radiation -- How does this not break causality?

[peanutaxis]

TL;DR

How do particles travelling faster than light can through a medium be possible?

Hi,

I want to try to solve this puzzle in my head.

They say that faster than c travel would break causality. And yet particles can travel through a medium faster than light can in that medium. But surely if that can happen then a particle can arrive at a place faster than information about the particle can, and this seems identical to faster than c travel. In both situations something is arriving before information about that something can.

??
:)
p

 

[PeterDonis]

particles can travel through a medium faster than light can in that medium.

Yes.

But surely if that can happen then a particle can arrive at a place faster than information about the particle can

No. The speed of information is limited by the speed of light in vacuum, not the speed of light in a medium.

 

[Ibix]

In both situations something is arriving before information about that something can.

The existence of an invariant speed that it is impossible to exceed is a consequence of the geometry of spacetime. Light in a vacuum just happens to travel at that speed (it's not actually a coincidence, but we don't need to care about why here). The limit at which causal influences can propagate is determined by the structure of spacetime, not the speed at which light happens to be travelling.

To put it another way, it's worth mentally separating the constant $c$ from the speed of light. Light only sometimes travels at $c$, but $c$ is always the same.

 

[Dale]

TL;DR Summary: How do particles travelling faster than light can through a medium be possible?

a particle can arrive at a place faster than information about the particle can

A particle arriving faster than information about it leaving does not break causality. What breaks causality is information about a particle leaving coming back to where it left but before it left.

 

[DrGreg]

It's also worth noting that in the literature the symbol $c$ usually means the speed of light in vacuum, and you'd usually use a different symbol (e.g. $c_\text{water}$) to denote the speed of light through a medium.

 

[FactChecker]

If a particle arrives somewhere, that IS information.

 

[Vanadium 50]

Uh, why do you think this is quantum? How does that impact the answer you are looking for?

 

[peanutaxis]

Uh, why do you think this is quantum? How does that impact the answer you are looking for?

If a particle arrives somewhere, that IS information.

....The limit at which causal influences can propagate is determined by the structure of spacetime, not the speed at which light happens to be travelling....

No. The speed of information is limited by the speed of light in vacuum, not the speed of light in a medium.

My undesrtanding - which may well be wrong - was that the reason why the speed of causality is the speed of light is because the method by which interactions take place was via virtual and real photons. When in a medium, then, the speed of causality would also be slowed.

 

[Ibix]

My understanding - which may well be wrong - was that the reason why the speed of causality is the speed of light is because the method by which interactions take place was via virtual and real photons. When in a medium, then, the speed of causality would also be slowed.

That is wrong, yes. There are plenty of interactions that aren't electromagnetic, and causality really has nothing to do with the speed of light. You can build theories where light never travels at $c$ (corresponding to a photon with mass) and it doesn't change the causal structure of the universe.

 

[A.T.]

...the speed of causality is the speed of light ...

The "speed of causality" is the speed that is invariant under Lorentz Transformations (speed of light in vacuum).

When in a medium, then, the speed of causality would also be slowed.

No, because the Lorentz Transformation doesn't care if there is a medium or not.

 

[FactChecker]

In the geometry of the Lorentz transformation, there is no such thing as a relative speed greater than some finite constant, $c$. That is not a consequence of any property of light, it is the other way around. Light, and anything else that goes at a relative speed of $c$ will be constant. That includes any electromagnetic wave in a vacuum. The fact that the speed of light in a vacuum was experimentally measured to be constant was simply used as proof, not a cause, that $c$ was finite. Because $c$ is the upper limit of relative speed in this geometry, a cause-effect relationship over a distance can not be faster than $c$. How light behaves in other circumstances does not change anything.

 

[Dale]

My undesrtanding - which may well be wrong - was that the reason why the speed of causality is the speed of light is because the method by which interactions take place was via virtual and real photons. When in a medium, then, the speed of causality would also be slowed.

Did you not read my post #4? Even if your idea of the speed of causality were correct, how would it cause a causality violation?

 

[FactChecker]

A particle arriving faster than information about it leaving does not break causality. What breaks causality is information about a particle leaving coming back to where it left but before it left.

That would certainly do it. But to say that it is necessary seems very similar to the inability to measure the one-direction speed of light. Are the two related?

 

[Ibix]

Are the two related?

Distantly. You can't measure the one way speed of light because time ordering isn't uniquely defined for spacelike separated events. Allowing faster than $c$ travel and abusing that lack of ordering is one way to get grandfather paradox-style causality violations - the tachyonic anti telephone is an example.

 

[vanhees71]

The "speed of causality" is the speed that is invariant under Lorentz Transformations (speed of light in vacuum).


No, because the Lorentz Transformation doesn't care if there is a medium or not.

I'd rather ask what "speed of causality" means. I've no clue!

 

[Ibix]

I'd rather ask what "speed of causality" means. I've no clue!

The speed of an object on a null worldline, the set of which that pass through an event define the boundary between the causal future of an event and "elsewhere", is how I've been interpreting it.

 

[vanhees71]

But "speed of causality" doesn't make sense. What you mean is that a measurable signal propagates with the speed of light if the corresponding field is massless. Of course there are plenty of signals which propagator which lesser speeds (like sound waves).

 

[jbriggs444]

But "speed of causality" doesn't make sense. What you mean is that a measurable signal propagates with the speed of light if the corresponding field is massless. Of course there are plenty of signals which propagator which lesser speeds (like sound waves).

So you would be happier with a phrase such as "speed limit for causality"?

 

[vanhees71]

I don't know, how "causality" can have a speed limit. Relativistic causality demands that only time-like separated events can be causally connected, i.e., it means that signals can only propagator with a speed equal or less than $c$.

 

[PeterDonis]

Relativistic causality demands that only time-like separated events can be causally connected

Timelike or null.

 

[Ibix]

I don't know, how "causality" can have a speed limit. Relativistic causality demands that only time-like separated events can be causally connected, i.e., it means that signals can only propagator with a speed equal or less than $c$.

Speed of causality isn't necessarily the best terminology and certainly doesn't extend well to GR, but I don't see the problem with it as a laymans rendering of "causal influences cannot propagate along spacelike lines".

 

[peanutaxis]

That is wrong, yes. There are plenty of interactions that aren't electromagnetic, and causality really has nothing to do with the speed of light. You can build theories where light never travels at $c$ (corresponding to a photon with mass) and it doesn't change the causal structure of the universe.

Ah, okay. This is at the core of my misunderstanding here I think.