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Speed of light is not really just speed of light, but universal speed limit of causality. Light (electromagnetic waves just happens to be one of the few things capable of hitting that limit. Even the effect of gravity is limited to speed of light. PBS Space time has a good video on this - https://www.youtube.com/watch?v=msVuCEs8Ydo&t=5s.

So to answer your question, no it is not possible for anything to affect us any faster than the universal speed limit of causality (that light happens to be able to hit).


There is at least one known exception: neutrinos from a supernova. (Don't get too excited, this doesn't contradict Einstein, as we'll see.) In the hot, dense core of a supernova, photons will scatter around for a while before escaping. Neutrinos, which interact much less often than photons, and travel also more or less at the speed of light, get out basically right away. The difference can be as much as a few hours! Of course it's the high-energy photons that are more dangerous, so the neutrinos are really more like an early-warning system.

See e.g.: https://en.wikipedia.org/wiki/SN_1987A

This is very misleading. In fact, neutrinos are not going faster than speed of light (c), they are going faster than photons that are emitted from the supernova.

Not just that, but lights when it passes through a medium slows down depending on it's refractive index (speed of light in water is about 225 000km/h while in vacuum it's 300 000km/h). This is important distinction as recently we had an uproar when it looked like neutrinos are slightly faster than c (in the end, it was a measurement error).

You can observe effects of particles going faster than speed of light in a medium if you look at photographs of Cherenkov radiation.

The correct way to say it is that the speed of light is the speed of causality only in vacuum. In any medium the speed of light is slower but the causality or other fields (for example gravity field) that are not impeded by matter can and will propagate faster than the speed of light.

Where does there exist a vacuum?

How does a particle or its environment measure the particle's traversal of a truly empty space?

That comment never wrote that neutrinos were faster than the speed of light?

No, but he did write "There is at least one known exception", the misleading part.

> in vacuum it's 300 000km/h

300 000 km per second

Are you sure it's km/s? :D

As https://en.wikipedia.org/wiki/Speed_of_light puts it:

"Its exact value is 299,792,458 metres per second (approximately 300,000 km/s"

Yes, it is.

I'm sure it's a typo, but for others: speed of light is 300'000 m/s in vacuum, not km/h.

It's not a typo - it's 299,792,458 m/s - approx 300,000,000 m/s or 300,000 km/s

That's still not an exception though. Neutrinos escape first by virtue of the fact that they don't interact with matter and don't bounce around, while light does. They aren't travelling faster than light, just travelling a shorter distance.

The question wasn't about how fast neutrinos can travel but whether we can detect something before we see it.

So x event happened 550,000 years ago and the radiation from it might kill us. You say that we may get a warning from neutrinos before the harmful stuff kills us?

But we detect things with particles other than just light.

Its possible to exceed the local speed of light in many classes of material.


> can the reverse happen with space events where light reaches you then something else?

I read that as: Can something come along and snuff us out after we've observed the light wave component of the event, such as a shock wave of some sort?

>I read that as: Can something come along and snuff us out after we've observed the light wave component of the event, such as a shock wave of some sort?

That is the only way it can happen.

My (limited) understanding is that the limit is only applicable to movement through space. The expansion of the universe is not bound by the limit, as it is expansion of space itself. Thus it seems incorrect to talk about a “universal speed limit of causality”. Am I missing an essential concept?

> Thus it seems incorrect to talk about a “universal speed limit of causality”. Am I missing an essential concept?

Probably. Why would points becoming more distant due to expansion of space be a counterexample to the speed of light being a limit on the speed of causal propagation? Spatial expansion doesn't move anything, so it can't propagate information.

It doesn't move anything, but it does mean that things that are now far away used to be closer, and therefore had the ability to affect us, but now don't.

Not that it matters, because the speed of light is still the limit: if they could influence us when they were closer, that would have happened by now.

> Spatial expansion doesn't move anything, so it can't propagate information.

It certainly moves matter-energy in different regions of space with respect to one another.

TIL. Very interesting.

The speed of shadow can be faster than light though.


I think those answers are actually wrong. When the object casting the shadow moves, the shadow remains in the same place for an observer in it until the light from the source reaches the observer inside the shadow.

I know that's a weird explanation, so consider:

  t0: S~~~>O     U (shadow exists)

  t1: S~~~~~~>   U (shadow exists)
  t2: S~~~~~~~~~>U (shadow !exist)
Where "S" is a light source, "O" is an opaque object, "~" are photons traveling to the right, "U" is the observer, and "t0", "t1", and "t2" are times (increasing).

At time "t0", "U" thinks he's in the shadow.

At time "t1", "U" thinks he's in the shadow.

At time "t0", "U" thinks he isn't in the shadow, since the photons are now hitting him.

A similar calculation/thought-experiment can be done for shadows with "angular momentum", in case you think the tangential velocity of the shadow will exceed the speed of light.

Thanks for that nice diagram! What happens when the light source moves and the shadow is far bigger than the object casting it ? Wouldn't the speed of the shadow on the surface be faster than the speed of light ?

For example, when a light source is super close to an object and the shadow gets super big really far away, and the light source moves?

  t0: SO          U1 (U1 in shadow)
  t1: S~~~~~~~~~~>U1 (shadow leaves top first)
       O~~~~~~>   .
         ~>      .

Dotted line is the path of a fixed point on the shadow during the time S moves.

I didn't do the precise math, but I'm pretty sure the tangential velocity of the shadow along the dotted line won't be greater than the speed of light. The curvature of the "wave front" formed by the tips of the arrows ">" above will be lesser than the dotted line curvature, so the photons near the top of the diagram hit the dotted edge before the ones towards the bottom. This is because the source, S, takes time to move away from O.

Note that the wavefront formed by the photons moves radially outward from S, but ascii art is limiting.

No information can be conveyed by the wavefront and so nothing is actually moving than the speed of light. What you diagrammed is called the Lighthouse Paradox:

* https://en.wikipedia.org/wiki/Lighthouse_paradox

There are similar things that appear to exceed the speed of light:

* https://en.wikipedia.org/wiki/Faster-than-light

See "group" and "phase" velocities for similar things to the lighthouse.

A shadow isn’t actually a thing. It’s an image, like a mouse pointer. If I had a sufficiently large screen, and I made the mouse pointer jump (by setting its position) to the other end of the screen, I could calculate its speed and make that number higher than the speed of light. But has anything actually moved? No it hasn’t, because a mouse pointer, like a shadow, is only an illusionary image of a thing, not an actual thing.

An absence of something can only be defined relative to that something and never taken just by itself. So a shadow only exists as a function of light (no light) or a consequence of the absence of light. So it would not travel faster than light in a way that can carry additional information.

Quantum entanglement works faster than light but cannot carry any information. As such the speed of causality (and implicitly of light) is still the real limit.

Thanks for this clarification. I have been wondering about this for awhile and your explanation helped a lot.

from the point of view of someone in the shadow, and subsequently not in the shadow, the speed of light is still the limit. If the light source is 1LY away, it will take 1LY for me to notice that I am no longer in shadow, regardless of how fast the shadow moves. There's no way of measuring the shadow movement that isn't limited by the speed of light.

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