# Could the speed of causality be (significantly) faster than $c$?

The other day my son (13) asked me whether it was possible that light went very slightly slower than our best measured $$c$$, and at the same time had a very tiny mass, but we aren't able to measure these because they are so small. Although I told him that I didn't think that that was possible or made sense, it got me to thinking along a related trajectory:

We think of $$c$$ as the speed of light but really it's the speed of universal causality/information (I'll just say "causality", but you can read both). In fact, $$c$$ isn't just for light; it's the speed of any massless wave, right? So what if the actual limit of causality isn't $$c$$, but that's just the fastest speed that we know of things happening causally in the known universe. Maybe the actual speed limit of causality is significantly faster than $$c$$, and we just don't know of anything that goes faster than $$c$$ (maybe disentanglement?)

• Then what would be the meaning of "our best measured c"? The speed of what? All measurements were done for light, weren't them?
– nasu
Commented May 11, 2022 at 18:03
• It's more helpful to take $c$ as the speed of causality, and then ask how we can constrain the mass and sub-$c$ speed of photons. This is actually a suitable question for physics.se, because relativity isn't really about light per se. The best theoretical argument I can offer against photons having mass, as opposed to an empirical argument that if they have a mass it's very small (with the resulting speed very close to $c$ as I've defined it) is that the Higgs field shouldn't give mass to all four electroweak gauge bosons.
– J.G.
Commented May 11, 2022 at 18:05
• Photons and light are two different things, the way bricks and buildings are different. See this for light newscientist.com/article/dn4474-light-frozen-in-its-tracks . Photons always travel with velocity c. It aint simple, it needs mathematics. Commented May 11, 2022 at 18:40
• I strongly disagree with this question being closed. Requiring the OP to define "the speed of causality" is a ridiculously narrow grounds and if the speed of light (or causality or massless particles) does not concern physics I am damned if I know what does concern physics. Commented May 11, 2022 at 22:23
• @StephenG-HelpUkraine The problem with notions of a "speed of causality" is that everyone thinks they know what it is, but when you try to write down a definition that you can actually use in a physical formalism, it becomes surprisingly hard or people start writing down different things. Commented May 12, 2022 at 10:58

The $$c$$ that appears in the equations of relativity (including the famous $$E = m c^2$$ is the speed of causality. This is the special, unique speed that is the same for all observers regardless of their relative motions. Because it is the same for all observers, it acts as a scale factor linking space and time.

Only one such unique speed can exist, and there have been many measurements of it. It is certainly possible that this is not the speed of light; as your son suggested, it's conceivable that light has a tiny mass and hence moves slightly slower than $$c$$. But the relativistic $$c$$ (speed of causality/maximum speed) can't be significantly different from the speed of light or we would have noticed it, e.g. in particle accelerators (where things are moving very close to the maximum possible speed). And as other commentators have pointed out, there are very good theoretical reasons to suppose that light is massless and hence the speed of light is the speed of causality.

• I get that there has to be one unique speed of causality (one scaling factor for space/time), but does it have to be the one we have got in hand at the moment? Maybe the one we have is just the maximum speed that we can accelerate things to at the moment, and we landed on that one because is is the speed that massless "particle/waves" move, but some quantum phenomena seem to violate this, and we haven't figured out how to get these together yet. If the causality limit was faster than the maximum speed that masses particles move would unification be easier?. Commented May 15, 2022 at 21:07
• There are plenty of experiments that show that $c$ (conventionally called "the speed of light") is the same for all observers -- that's what makes it the unique scaling factor for space and time. So no, there can't be another one. The speed of light could, perhaps, be slightly lower than $c$, but so far both theory and experiment says it isn't. Commented May 16, 2022 at 10:50

There is no such thing as an unambiguous "speed of causality", because causality itself is a very vague notion when you actually try to nail it down.

What is true is that the speed that we call the speed of light - but is, as you say, actually meant to be the speed of all massless particles - limits information transfer in the following sense:

For any event $$x$$ (i.e a time and a place) in spacetime, there is a set of events (the past lightcone and the events inside it) which can "causally" influence what happens at the event. The light cone is precisely the set of events from which something travelling at the speed of light can reach $$x$$ - from any event outside of it you would need to travel faster-than-light.

Since nothing - massless or massive - can travel faster than the speed of light, you might be tempted to say that therefore, of course, the speed of light is "the speed of causality"; how could anything influence something else without travelling? But the problem is, again, that our intuitive notion of what it means to be "cause and effect" - or to have "causality" - doesn't really map neatly to the physical ideas of something travelling, nor does the light-cone picture of causality alone really produce a world of "cause and effect" that we would like.

On the one hand, without travelling faster-than-light, it is possible to imagine spacetimes with so-called closed timelike curves, and something travelling along such a curve is in its own past lightcone. Cause without effect, or rather an effect that is its own cause. Is this "causality"? What is the "speed of causality" in this case? (The common answer is that such spacetimes are bad because they "violate causality".)

On the other hand, quantum theory makes everything even more complicated (as usual) - Bell's theorem tells us that either there are "effects" that propagate superluminally, or the world is not realist (for more discussion of this, see this answer of mine and this answer of mine). Crucially, which of these two to choose is a realm of metaphysics called quantum interpretations, but the predictions of quantum mechanics do not (or only in extremely contrived cases, depending on who you listen to) depend on the interpretation chosen. And so, the "speed of causality" - indeed, perhaps causality itself - is exposed as the incoherent idea that it is: In some interpretations of quantum mechanics, this speed is infinite - measurements on "one part" of a wavefunction instantaneously affect every part of this wavefunction, throughout the whole universe - and in others it is still finite, and a measurement doesn't actually have to propagate any changes at all, and there's probably all sorts of hybrid interpretations, and yet it doesn't make one bit of difference to their predictions of the world we observe.

For further ruminations on the incoherence of the idea of causation, I recommend Norton's (in)famous paper "Causation as Folk Science".

Firstly note that the speed of light is now defined as an exact value. Light will travel at this speed in a vacuum simply because we defined it that way. We used to define a meter and measure the speed, but years ago "they" (the people who define standards of measurement) decided it was more accurate to define the speed and the meter is derived from that.

So there's no way for light to travel at any other speed now.

Now there have been particles we once thought were massless, and massless particles in relativity always travel at the speed of light (photons are justy one example of massless particles). Those particles were neutrinos, but eventually small differences in their velocity from that of light led us to understand that they had mass and travel slower than light (but still very close to light speed because their mass is so small that it takes very little kinetic energy to move them very fast).

We also have been able to compare the speed of gravity (the speed changes in gravitational fields propogate at) to the speed of light thanks to the wonderful LIGO experiments. There's an experimental error, but at this point we have no reason to think that gravity does not propogate at the speed of light as well. It pretty much works that way with everything we can test - if we expect it to travel at the speed of light it will within the error range we can manage with our experiment.

So what if the actual limit of causality isn't c, but that's just the fastest speed that we know of things happening causally in the known universe

All our theories would be broken, but broken in a way that would be very hard to fix because they'd still be almost right. This would be a kind of doomsday scenario for most physicists.

Maybe the actual speed limit of causality is significantly faster than c, and we just don't know of anything that goes faster than c

Well if we don't know of it, it's not smething physics can talk about at all. It's just wild speculation, not physics.

It's hard to imagine a way to disconnect the speed of light from the speed of causality without pretty major reworking of physics. Again this would be rather like being told that you've to fix some major problem in your jet aircraft while at the same time not changing anything it does now apart from the new problem. I am sure people are working on theories with variable speeds of light and all mod cons, but getting those to agree with everything we already know is the problem. You can design any theory you like (they're published all the time), but making them work as well as existing theories is the problem. Remember we like existing theories because they can be used to predict how stuff behaves very accurately.

It is only fair to point out that there are many alternative theories to general relativity which are either discarded, still debated or still being developed which may provide a theoretical basis for things liek a variable speed of light. These are very advanced research topics which I do not claim to fully understand myself. Mainstream physics basically sticks with what they know works well, which is general relativity while (always) looking for something better. But testing a better theory often has to wait for the technical aility to make measurements to catch up. So we await developments.

• The statement, "So there's no way for light to travel at any other speed now," is not really correct. The definition that sets the speed of light to a fixed, constant value assumes certain facts—in particular, that the speed of light in vacuum is isotropic, spacetime independent, and frequency independent. So far as we know, all those things are true, and they have been confirmed to high accuracy, but in terms of the definition, they are experimentally-motivated assumptions that are necessary for the definition to make sense.
– Buzz
Commented May 11, 2022 at 20:31
• @Buzz All very well and good, but the details of the standard are not really what we're discussing here. It is the standard and that's all there is to it until the committee decides to change that (which none of us are expecting I'd presume). It would take some mighty impressive experimental results (and theory backing it) to justify that. So we're stuck with the definition, although I admit it does feel unituitive somehow that we define a speed and derive a lenght, rather than the other way around. Commented May 11, 2022 at 20:56
• In the context of this question, however, the validity of those assumptions cannot be taken for granted.
– Buzz
Commented May 11, 2022 at 20:58

The speed of light is routinely slowed in dielectric material and also in high gravitational fields. This is changing the dielectric constants of space increasing the capacitance per distance, which implies space is not empty but a field of very small frictionless balls. In some way, its like we are in a vast ocean of space.

This implies that gravity increases the density of medium light travels through.

We know that the density of the early universe was higher and things were closer, so I would expect light from distant objects to take longer to reach us.

If we look at false vacuum models, it may be possible to reduce vacuum density so in that the speed of light would be faster.

There is another effect in that we are in center of large mass of observable universe, which distorts our view. While we feel no gravity, we are in fact in middle of an large object.