c is technically the speed of causality. The speed at which perturbations in the fields that make up the universe propagate.
The speed of light is a consequence of this, not the cause. Calling c the "speed of light" is putting the cart before the horse.
Photons (being massless) have 100% of their velocity in the spatial dimensions and no velocity in the time dimension. They move at the maximum speed that any change in the electrostrongweak force can propagate in our universe because they are not free to do anything else.
From a photon's POV a trip across the entire universe happens instantaneously - taking no time whatsoever.
Einstein causality, i.e that no physical effect propagates faster than light. In QFT it it is modeled by the rule that space-like separated measurements commute.
That merely equates the term "causality" to propagating waves. It doesn't introduce any new concept. Ontologically, there are only quantum fields in space-time. The physical laws governing them imply from their mathematics that they cannot contain any propagations faster than c. But attaching the term "causality" to it doesn't really add anything here.
This does not equate causality with propagating waves. I also did not claim it is a new concept. Instead I said physics has a precise and fundamental concept of causality.
How is it fundamental? You can do all the physics without reference to it. It is a consequence of the equations, not a premise.
Edit: It is not actually a complete consequence, because cause and effect imply a directonality that the equations do not have, being time-symmetric. At the same time, this directionality or asymmetry has no derivable consequences for the practical physics, meaning having the asymmetry doesn't add anything. This is one of the conceptual troubles that introducing "causality" here brings.
It is used in theories that discuss particles with imaginary mass, such as tachyons, that travel backwards in time.
Theories that violate causality are considered unphysical, whereas theories in which measuring such time traveling particle, cannot be distinguished from creating a particle that moves forward in time are not.
Physicists put this into the theories as an assumption at a fundamental level, e.g. they put it as an axiom into axiomatic QFT. This is why it is fundamental. Also arrow of time is something else than Einstein causality.
"Photons (being massless) have 100% of their velocity in the spatial dimensions and no velocity in the time dimension"
I kinda see what you're trying to say, but these words aren't a particularly good match for the math in special relativity. To an observer, any photon's velocity 4-vector looks like V = (c,c,0,0). That's a "c" in the spatial direction the photon's moving, and a "c" in the time direction. So, plenty of velocity in the time direction.
What is zero is the _proper time_ along a photon's trajectory through space & time. An observer who's co-moving with the photon (call me if you ever meet one, we can write a paper together) would see a) the photon holding still and b) no time passing.
special relativity is undefined at v = c. so no from a photons point of view the trip doesn’t happen in an instant nor does the length of the universe shrink to zero. there is no definition for a photons point of view. time dilation and length contraction only apply when comparing a moving frame of reference to one that is at rest and photons have no rest frame.
And when you think about c as the speed of causality, it becomes a lot more obvious why FTL travel/communicate is (almost certainty) impossible without breaking causality....
You are going faster than causality, of course it breaks.
The other option is to break relativity, which is what most science fiction media does, often accidentally.
If you think it is implied that c stands for the first letter of the word causality, then reading the article should be enough to convince you otherwise.
Einstein published his seminal works in German, and we'd be more likely to have E=mk².
Huh. I'm admittedly no astrophysicist, but I don't recall encountering this "photons have no velocity in the time dimension" before.
Maybe I'm one of today's lucky 10,000[1].
It's not true. It's a mashup of a few ideas that don't belong together.
1. an object at rest has a world line which points (has tangent vectors) in the time dimension
2. light has proper time (dtau) = 0, so clocks moving at the speed of light dont tick
3. the magnitude^2 of an objects 4-velocity is c^2 (objects move through spacetime at c)
4. light has no 4-velocity (because dtau=0, you cant divide by zero)
You can't say (3) means objects have 4-velocity c in spacetime and light has 3-velocity c in space and so that means the time component of 4-velocity for light is zero.
But, it is sort of common to observe the somewhat trippy fact that, unlike matter, photons don’t experience time passing, right? (Although, I will be honest, I could not ever really grok relativity like a physicist. However, I can enjoy the Lorentz factor going to infinity as v goes to c).
From my understanding, it's more correct to say that time is undefined for massless objects.
Through special relativity, our understanding of mass, gravity, and spacetime are linked. If something has no mass, then special relativity can't describe how gravity affects it's spacetime reference.
Remember, however, that this explanation is based on the mathematics that explain the observations we've made or theorized. Just as the map is not the territory, the math is not the universe.
It is, in my opinion, not extremely obvious from the usual descriptions of relativity, but basically when you move faster and faster, you trade your velocity through time for velocity through space. Rather then a funny result, that is the theory.
If you're at rest, you have maximum time velocity (1 you-second per frame-second). If you're at the speed of light, it's zero you-seconds per frame-second.
This is described by the Minkowski space, which is a metric that puts two events the same distance apart in spacetime regardless of reference frame.
Greg Egan's series "Orthogonal" looks into what the universe would look like if time didn't have the opposite sign (so that time is another dimension just like x, y, z). The effects of that one sign change are very wierd.
Thanks for the answer. I had forgotten about the No-communication theorem.
This led me into another rabbit hole :-) of why c is 299,792,458 m/s and for example not 499,792,458 m/s or some other value, and the fundamental constants that bring this value. [1]
Is there a current theory that tries to justify those constants that bring the current value of c ? Are those values the ones that must be, for the current Universe to be feasible?
Veritasium has a few recent videos on Action. In one of them I believe he shows speed of light expressed as one unit of action, which implies that it’s the highest “resolution” any propagation can resolve at based on the fundamentally smallest path integral anything can traverse, or something.
I'm not sure if there is a good theory on why it ends up being this speed, but if any of the constants were even slightly different we wouldn't be in this universe to talk about it.
The speed of light is 1c and is a fundamental constant.
Humans choose to express it in metres and seconds.
A meter is huge if you compare it to the Planck length. Humans are pretty big creatures compared to fundamental particles, so we have a big basic unit of length. But seconds are gargantuan, because humans are absolutely glacial if you compare them to the time it takes light to travel a Planck length.
It's like a continental plate asking why humans zip around so fast.
> The speed of light is 1c and is a fundamental constant.
Yes, but why is the value that it is and not higher or lower? From my (basic) research it seems, it could be plus or minus 20% a different value, and the current Universe would still be feasible.
No, the point is that if it was 20% bigger we would not be here to ask those questions :-) Stars fusion or weak atomic interactions would not work. Maybe Hari Seldon decided....
That touches on a long-running very complicated debate around quantum mechanics, hidden variables, spooky action at a distance, no-communication, etc.
For various quantum effects that seem to be paradoxes by classical physics what is happening "under the covers"? Does the delayed choice experiment really send information backwards in time? Even if it appears to do so if we can't at least send information back in time with that mechanism isn't it just sophist philosophy at that point?
For my part I'm not smart enough to claim to have answers to anything but my intuition is there are no quantum paradoxes. Delayed choice does not send anything back in time. We don't experience quantum phenomena at the macro scale so our intuition and reasoning are ill-suited to thinking about it. That easily leads us to incorrect conclusions.
The speed of light is a consequence of this, not the cause. Calling c the "speed of light" is putting the cart before the horse.
Photons (being massless) have 100% of their velocity in the spatial dimensions and no velocity in the time dimension. They move at the maximum speed that any change in the electrostrongweak force can propagate in our universe because they are not free to do anything else.
From a photon's POV a trip across the entire universe happens instantaneously - taking no time whatsoever.