So, I just learned some basic formula's about special relativity, I was wondering something about one certain formula:

t = t0 / sqrt( 1 - v^2 / c^2 )

Let's say I was on a frickin' fast rocket that travels at c, and I would be watching at a process that (when I wouldn't be traveling at c, but I would travel just as fast as the process) took 1 second.

This means the time the process took to get 1 second ahead in time would take how many seconds?

t = t0 / sqrt(0) = t0 / 0

What would be going on in this situation? Could somebody with a fysiks background explain this to me?

N.B. Rinse and repeat for length contraction (object length would be 0?) and mass increase (mass would be m0 / 0?)

What is this, some process on your amazing rocket that you are watching? It's also going at c, so from your perspective it would take 1 second.

Disclaimer: I suck at physics

I think it would be as you said -- mass goes to infinity at c and length goes to zero. Also the reason why nothing can actually reach c.

From YOUR PERSPECTIVE, everything will be exactly the same. Mass will be the same. Length will be the same.

From the perspective of anyone not in your frame of reference, you will have no length and infinite mass.

That's exactly the question Einstein asked himself when he was a teenager, when he first started thinking about relativity. What would I see if I were travelling at the speed of light?

The answer that he eventually came to, and you've come to as well, is that you cannot travel at or beyond the speed of light (unless you're massless, like a photon). You see from your time dilation equation, if v exceeds c you get a square root of a negative number, and you get an imaginary value for time. This has no physical meaning, all observables are real.

A massive object cannot travel at the speed of light. What would you see if you were travelling near the speed of light? That's a much more interesting question. For an idea of the visual aberrations,


But there'd be all sorts of relativistic doppler effects too, so all the colours would shift probably out of the visible spectrum.

Stuff like this is why I have so much respect for physicists.

Sorry for not being very clear. I meant a process taking place out of this amazing rocket I have, at a speed of c relative to me.

So, what if a photon actually traveled at the speed of light:
This explains why a photon's mass is 0, because otherwise, it would have quite the impact if it would hit something.
From the perspective of the photon, every process taking place around it with a relative speed of c would take an infinite ammount of time? Is this what they mean with distortion of the space-time fabric? Does only the tiny space-time area around the photon gets affected by its speed?

The way I understand it now (and I don't think I understand much...), from the photon's point of view, it is traveling at a normal speed, but time around it is standing still.
What is happening from our point of view when an object is traveling at c? Does it just mean it is traveling at c?

What would a "normal speed" be?

well, the photon would be traveling (when in a vacuum yada yada yada, it's theoretical physics annyway) at c, right? then everything around the photon would take an infinite ammount of time to complete. This means time around the photon would practically be standing still, right?

Theoretical physics does not mean 'any crazy idea will do!!!', there's a vast amount of mathematical justification required before anything is considered a theory.

In SR, the faster you travel through space the slower you travel through time. Instead of talking about 'velocity' in the classical sense, in SR we use the 'velocity 4-vector' which describe the components of time and space. The length of this 4-vector is always c.
The photon is travelling at maximum speed through space, so it is not moving at all through time. From the photon's perspective, there is no time.

The bending of spacetime is only a feature of General Relativity, which also describes gravity. Matter tells spacetime how to bend, spacetime tells matter how to move. You'll need to learn how to use tensors before you can learn GR though.

then shouldn't a particle traveling at c be everywhere at the same time, when a spectator is looking at it? This is truly mind-boggling.

Well considering according to relativity you CAN'T go faster than the speed of light, it's not surprising that the formula would not allow you to go faster than the speed of light.

Assuming c is the constant for the speed of light. It's been a while since I've done this stuff.

And yes, I read a fascinating book once that explained relativity, something travelling at the speed of light will always appear to anyone at any velocity to be travelling at the speed of light relative to them.

From its perspective, it is everywhere at the same 'time' (as there essentially is no time) and we can't transform our reference frame into the reference frame of the photon.

Every object (in Minkowski spacetime) has a 4-vector with magnitude c (in many textbooks we set c=1, called natural units). A photon doesn't have a velocity 4-vector normalised to c, as that normalisation isn't Lorentz invariant, it has a 4-momentum that is lightlike and in any reference frame the spacelike and timelike parts have equal absolute magnitudes. Lorentz transformations preserve the normalisation, no transformation can boost a timelike vector into a lightlike vector.



In a hand-wavy way, you could say that mass of a system determines how much of the 4-velocity is spent in spatial dimensions, and as the photon has no mass it is forced to spend all of its time in the temporal dimension and this means we can't transform an observer with a Lorentz transformation to the photon's rest frame.

However, it's not really possible to talk about the reference frame of a photon at all in a particularly meaningful way..

A photon still travels along a worldline, and if A and B are distinct events on that worldline then either A is in the casaul past of B (so that A can influence B) or vice versa, so in this case it does not make sense to say that 'time stops' for a photon or that all events occur simultaneously as there is a definite causal sequence of the photon's events.

The question of the 'reference frame of a photon' is sort of meaningless, but meaningless in a highly non-trivial way.