physics - speed of light

[dr froyd]

i just had a thought regarding the question "why can't you travel faster than the speed of light", and im gonna share it

i've seen all kinds of convoluted and non-intuitive explanations for this. If you google it the first answer is "because it requires infinite energy", that seems the most popular answer. Then there's stuff related to the algebra of the time-dilation formula, "locality", etc etc. None of these touch on the actual core of the question. Yes, it might require infinite energy, but that's a practical problem which has little to do with the postulates of special relativity.

at the end of the day the answer is very simple (i believe): it's a logical impossibility due to a single assumption: constant speed of light in all reference frames. The concepts of energy etc are not even needed.

for example:
say we have a space ship that can travel 10x speed of light. We conduct a race between the ship and a photon (to nowhere in particular - we just launch them in the same direction simultaneously).

now we immediately created a contradiction, because
- for an external observer, the ship will be ahead of the photon (and pull away at 10x the photon's speed)
- from the ship's perspective, the ship will lag behind the photon (as it must see the photon pull away at 1x speed of light)

and that's it - 2 different outcomes depending on perspective. In contrast, as long as ship's speed is less than speed of light, we can make it consistent via time dilation and length contraction.

so one can put it simply as: in a system with constant speed of light in all reference frames, nothing can travel faster than that speed. It's purely logical/geometrical thing

obviously feel free to correct me if this is wrong

 

[dr froyd]

here is an example of some guy - supposedly an authority on the subject - talking about energy required to accelerate to speed above c.


he even says that relativity is fine with speeds > c as long you didn't accelerate to that speed.

but.. you can derive the impossibility of going above c merely from the Lorentz transformations.
[math]t'= \gamma (t - vx / c^2) \\ x' = \gamma (x - vt) \\ y' = y \\ z' = z \\ \text{where}\;\;\; \gamma = (1 - v^2 / c^2)^{-1}[/math]which is simply coordinate transformations under constant speed of light.

where's the "energy" in these equations? where's acceleration? Nowhere to be found...

 

[fluffy]

Does this mean that space is or is not expanding via the big bang?

If it is a matter of just you relative momenti where you are next to a photon, then space is not curved, you just think it is by you relation to other objects. Thus the space expansion is not really warped space as a substance. Gravity has to be something other than a warping of a fabric.

 

[fluffy]

Photons travel in spirals.

If you stretch them then they alter time.

That's to say matter compacts as the photon remains constant.

 

[dr froyd]

just a quick addition after reading Einstein's original special relativity paper:

early on in the paper when discussing the physical meaning of the Lorentz transformations - i.e. long before he goes into bodies with mass, energy etc, he writes:

"the greater the value of v, the greater the shortening. For v = c all moving objects—viewed from the “stationary” system—shrivel up into plane figures. For velocities greater than that of light our deliberations become meaningless"

much later on, when deriving the relativistic energy of bodies with mass he comments:

"... Thus, when v = c, W becomes infinite. Velocities greater than that of light have — as in our previous results—no possibility of existence."

in other words, by the time he gets to relativistic energy, he already knows speeds > c are not possible, and the energy/acceleration stuff is just to show that it's consistent with the Lorentz stuff.

 

[dr froyd]

Does this mean that space is or is not expanding via the big bang?

If it is a matter of just you relative momenti where you are next to a photon, then space is not curved, you just think it is by you relation to other objects. Thus the space expansion is not really warped space as a substance. Gravity has to be something other than a warping of a fabric.

that would be general relativity. Gravity, curved space etc etc. This is much more basic

 

[dr froyd]

alright alright i think i got to the bottom of it

saying that going faster than light is impossible because it requires infinite energy is literally the equivalent of saying it's impossible because it's impossible.

i.e. it's a tautology or circular reasoning.

because: why do you need infinite energy? Well as Einstein derives the relativistic kinetic energy he puts
[math]W = \int^v_0 \gamma^3v dv = mc^2 \left \{ \frac{1}{\sqrt{1 - v^2 / c^2}} - 1\right \}[/math]
and based on that, since you must have v < c, he says otherwise W is infinite. But what makes it infinite? Well it's Lorentz factor [math]\gamma[/math]. I.e. the infinite-energy result is derived from the fact that in a system with constant speed of light in all reference frames you must have v < c.

 

[fractalwalrus]

alright alright i think i got to the bottom of it

saying that going faster than light is impossible because it requires infinite energy is literally the equivalent of saying it's impossible because it's impossible.

i.e. it's a tautology or circular reasoning.

because: why do you need infinite energy? Well as Einstein derives the relativistic kinetic energy he puts
[math]W = \int^v_0 \gamma^3v dv = mc^2 \left \{ \frac{1}{\sqrt{1 - v^2 / c^2}} - 1\right \}[/math]
and based on that, since you must have v < c, he says otherwise W is infinite. But what makes it infinite? Well it's Lorentz factor [math]\gamma[/math]. I.e. the infinite-energy result is derived from the fact that in a system with constant speed of light in all reference frames you must have v < c.

Ah looks like the limits of language again (which math qualifies as). Also, one can appear to travel faster than light by warping space time or using wormholes. It probably is not what you were looking for, but here's an explanation of the Albubierre drive if you have not hear of it:

 

[EndogenousRebel]

Looks messy.

Sounds like a easy enough test to have the right answer. in a vacuum or whatever. So it, sounds right up quantum physics alley.