I was on the taxi this morning, pondering things as usual when an old idea popped in my mind. Well, it’s more like a semi congealed mush rather than an idea, but I though someone more knowledgeable in the field of physics could help shape it up.

Would it be accurate, or at least conceptually correct in describing c (the speed of light in a vacuum) as the “Time Barrier”, just as Mach 1 is the sound barrier, the speed at which sound waves propagate through a given medium?
In a way, that nothing can happen sooner than c, rather than the usual visualization of nothing being able to move faster than c.

If that is the case I wonder how that would relate to the increase of mass/energy of an object at relativistic speeds.

It is a *velocity *barrier beyond which light (or anything else) cannot go. The speed of light does not define the universal speed limit, rather the universal speed limit sets the speed that light can go.

The speed of sound in air is not a barrier in the same sense - it was a hump over which humans had a problem getting for a few years, that’s really all. It has no implications beyond how fast sound waves happen to move in our atmosphere.

I don’t think I quite understand what you’re getting at with your term “time barrier”. The effect of any cause cannot propagate faster than c, that’s true. But if you take two entangled particles, separate them a long way, and observe one so its spin resolves (to, say, ‘up’), the other will instantly collapse to ‘down’ regardless of their distance apart. That appears to humans as an effect moving faster that c, but thanks to quantum weirdness it isn’t.

This may not help at all, but let’s have a go. Everything travels through spacetime at c. If you do manage to get yourself up to the speed of light (which is tricky, apparently) time - for you - will stop. Photons don’t experience time, which might be fun for them, or maybe really boring.

By Time Barrier compared to the Sound Barrier I mean the maximum velocity at which time would propagate, just as the Sound Barrier is the maximum speed at which sound waves propagate through a medium. I suppose speed of time would be more appropriate, just as in speed of sound.

So rephrasing, how conceptually correct would be to consider c, as the universal speed limit, being defined by the “speed of time”? That is, massive objects can’t move faster than c because to do so they’d have to push ahead of it’s own time reference, so to speak break this time barrier, thus messing causality six ways to Friday.

Let me clarify were I’m coming from with the question.
The normal explanation for why massive objects can’t reach (or exceed) c is because as the speed increases the mass of the object does too, and so does the energy necessary to further accelerate the object, at c both the mass and energy could be infinite, therefore it’s impossible to get there.
Now, light of course moves at c in a vacuum, and usually it’s explained by photos being massless therefore not having the same problem. But, if the limiting factor would be mass growing to infinity as speed increases then if would follow that a photon, having no mass would just as well waltz past c without a care. Therefore, the limiting factor, in my reasoning, would not be mass and/or energy at all, that’s why I ended up thinking if the limit is set by how fast can time propagate (if it actually does propagate)

Well, I have heard something broadly like the OP is saying on a physics programme (presented by Brian Cox IIRC).

But bear in mind that the last physics thread I was in I dropped the ball (so to speak), so pinch of salt at the ready…

It was explained that we all have a vector through 4D spacetime, and when we accelerate, all we’re doing is rotating that vector so it points more along the spatial dimensions and less along the time direction. At the limit, this vector points entirely down the spatial dimensions and has a zero time component (at c any journey is instantaneous from the perspective of the entity travelling).

Conversely, when we are not accelerating at all, the vector basically points in the time dimension. So in this sense we can say that time is moving forwards at the speed of light.

As a prominent leading practitioner of comic book physics I can undeniably state that the way the Flash and Superman traveled through time was simply by exceeding the speed of light (the Flash on a treadmill). In this reality, I couldn’t say.

I’m not at all surprised that Prof. Pepperwinkle remembers his history so well. The only point I would add is that not only did they travel to the past in exactly that manner, but they did refer to it as “breaking the time barrier”.

As I understand it (which isn’t all that well to be honest), c, is a property of space. Space is not “nothing”. It has properties, it can twist and bend, expand and contract. There are even particles that constantly, and suddenly erupt out into existence, and then vanish.

It is space-time that, for some reason, sets the maximum speed at c. As you near c, space-time contracts along your vector nearing 0 as you approach the speed of light. So in a way, space-time contorts itself in such a way so as to prevent you from going faster than c.

No, Superman didn’t need a treadmill; he’d circle the Earth to build up speed. IIRC he traveled clockwise to go into the future and counter-clockwise to go into the past.
Yes, they did call it breaking the time barrier. Often.

But I wasn’t really trying to jerk the thread, here. If I’ve made any contribution it’s to point out that some people were equating the speed of light with the time barrier 50 years ago.

I think a better way to think of it* is that sitting still** you are already travelling through time at c. As you move faster though space you move slower through time. Until you get to c, at that point you are moving purely through space.

this is basically what Mijin said but using shorter words.

You have had some good answers saying that c represents a speed barrier and that you can regard everything as travelling though spacetime at a ‘speed’ of c; all you can do is change how much you travel through space rather than through time.

In that context asking why you cannot go faster than c is like asking why you cannot point upwards more that vertical. It is a function of the geometry in which we live.

Another reason you cant violate c is that it would create cherenkov radiation of infinite power as soon as you moved through space (the bluish glow you get from water covered reactors as electrons locally exceed c in the water)

OK, I think I get it now.
Since it’s difficult to wrap my head around four dimensional coordinate systems I think I could simplify it into two dimensions, space and time, X and Y in a graph or rather as a vector of fixed length.
So at rest the vector points vertically, in the direction of Y and time ticks along at the regular pace, on the other hand the horizontal component (moving through the three space coordinates condensed into one for sanity’s sake) would be zero, AKA, standing still.
Now to get moving the vector would tilt down towards X, therefore the Y component (time) would decrease until the point were the vector is parallel to X and the time component is zero, since speed is Time * Distance speed would be zero too, therefore no matter could possibly move at c. Except for those meddling photons and their timeless quirkiness of course.

Yes. Fundamentally, then, c is a conversion factor: Multiply something with the units distance/time (a velocity) by time and you get a distance back out; therefore, c converts lengths of time into lengths of distance.

This allows us to elegantly describe what happens in the absence of a significant gravitational field using four-vectors (that is, vectors with four dimensions) in what’s called the ‘Minkowski space’, which describes distance using something called a ‘Minkowski metric’ which isn’t really a metric at all, in the strict mathematical sense. Why not? Because, sometimes, it can give a ‘distance’ that’s a negative number; in this case, it gives negative distances between things that are ‘back in time’ or ‘forwards in time’ from each other, or, equivalently, things that, in some reference frames, can be observed to occur at the same place but can never be observed to occur at the same time. This is a nicely graphics-heavy description of this.

That’s all special relativity (SR), which applies equally well all the way down to quantum physics. A quantum theory that takes special relativity into account is called a quantum field theory (QFT); the specific QFT that talks about photons and electrons and describes radiation (including light), electricity, and all matter you’ll ever experience directly is called quantum electrodynamics (QED).

Notice how I said ‘in the absence of a significant gravitational field’ above: Once you add in any substantial amount of gravity, you have to expand SR into general relativity (GR); if you’re trying to do that at the quantum level, you’re a theoretical physicist and are probably about to correct me on some point. In any event, we still haven’t found a theory that gives us all of the predictive power of our QFTs and all of the predictive power of GR in a unified whole. This is why we say we don’t know what happens at the center of black holes: As a black hole’s singularity is a strong gravitational field packed into a size we need quantum theories to reason about, both QFTs, which can’t handle strong gravity, and GR, which isn’t quantum, kinda break down, and we don’t have anything else.

This is pretty much it, though it’s also important to be aware that spacetime is hyperbolic in nature, which means that there are no smooth transformations that take an objects velocity from <c to c or >c

The equation is actually Speed = Distance / Time, and doesn’t really apply here as it is based on classical physics, and applies only to situations where relativistic effects are negligible.

It isn’t the reason particles with mass cannot travel at c. That is because the mass of an object tends towards infinity as it approaches c. So it takes ever more energy to accelerate as you approach c.
Light has zero rest mass and only a small mass while in motion (no, I don’t understand this either).