Faster than c?

Why can nothing be faster than light? Surely, the more energy you have, the faster you are. And there is no maximum amount of energy you can have, right?
I tried to look online, but to say I do not understand a word would not be accurate at all.

@absicht_MAUERzuBAUEN said in #1:

Why can nothing be faster than light?

That isn't true.

@pkill said in #3:

light can also be slowed down and distorted, but i assume you are talking about light without obstructions.
Yeah c by definition is the velocity of light in vacuum.

Think of it as the fastest that information can be transferred.
Photons are massless. A particle with mass needs infinite energy to move at C.
There is a theoretical particle (Tachyon) that can only travel faster than C, but that's a whole nuther story.
Photons are the information-carriers because they are the only massless particle (so far identified) that is found as a solo.
Quantum Entanglement implies instantaneous information transfer, but discussing that will make your head hurt.

@absicht_MAUERzuBAUEN
You are wrong. It's not proven that speed of light is 'entity figure'.
There are many things faster than speed of light, haven't you read about objects/planets in space which move much faster than speed of light.

@Akbar2thegreat said in #6:

You are wrong. It's not proven that speed of light is 'entity figure'.
There are many things faster than speed of light, haven't you read about objects/planets in space which move much faster than speed of light.

What do you mean by "entity figure"?
Also, in science there are no proofs. Only falsified and not yet falsified hypotheses. The latter of which can combine to form a scientific theory.

There are to my knowledge no massive (mass greater than zero) objects which have been found to travel through space at speeds exceeding (or merely equalling) c. Could you point me towards a source so that I know what you're talking about? Thanks!

There are distant galaxies with recession velocities greater than c. But that's not because they are actually moving through space near c (galaxies are relatively stationary in space, they usually have slow peculiar velocities through space), it's because of space itself expanding between us and the distant galaxy. Making the galaxy appear to move away from us. The speed of light doesn't impose a limit on the rate of the metric expansion of space itself, so this doesn't violate Einstein's special relativity. SR only states that no massive object can travel through space at or faster than c. And this prediction has so far held up to scrutiny.

There are also light echos: https://en.wikipedia.org/wiki/Light_echo
And apparent superluminal motion in the jets of some quasars: https://en.wikipedia.org/wiki/Superluminal_motion

Both are actually an artefact of the finite nature of the speed of light. No massive object is actually moving through space at c or at a speed exceeding it in either case. Only the apparent motion (from our perspective on earth) seems to exceed c. The actual motion happens near, but never at or above the speed of light.

@absicht_MAUERzuBAUEN said in #1:

Why can nothing be faster than light? Surely, the more energy you have, the faster you are. And there is no maximum amount of energy you can have, right?

I'll be your algebra autopilot here:
The energy E of an object with mass m (greater than zero) moving at velocity v ≥ 0 according to special relativity is:
E=γmc^2,
where γ is the so called Lorentz factor γ = 1/(√(1 - (v/c)^2)) ≥ 1 and c is the speed of light c = 299,792,458 m/s.

If the object is at rest (velocity v=0) this reduces to Einstein's famous equation for rest energy E_0:
E_0=m*c^2

This is because γ(v=0) = 1/(√(1 - (0/c)^2)) = 1/(√1) = 1
We can also express the Lorentz factor in terms of the total energy E and the rest energy E_0 = m*c^2 as follows:

γ = E/(m*c^2)
or
γ = E/(E_0)

Now let's look back at the original expression for the Lorentz factor and begin rearranging for v:

γ = 1/(√(1 - (v/c)^2))
Take the reciprocal of both sides:
1/γ = √(1 - (v/c)^2)
Square both sides to get rid of the square root:
(1/γ)^2 = 1 - (v/c)^2
Subtract one from both sides and multiply by minus one afterwards:
(v/c)^2 = 1 - (1/γ)^2
Take the square root of both sides (let's ignore the negative solution, it represents movement in the opposite direction):
v/c = ±√(1 - (1/γ)^2)
Multiply both sides by c:
v = c*√(1 - (1/γ)^2)

Substitute γ = E/(E_0) into the equation:
v = c*√(1 - ((E_0)/E)^2)
We have obtained an equation for velocity v in terms of total energy E, our v(E).

You said:

Surely, the more energy you have, the faster you are. And there is no maximum amount of energy you can have, right?

Both are correct. However this does not preclude the possibility for a maximum speed.
The minimal value for E is E_min = E_0. Therefore:

v(E_min) = c√(1-((E_0)/(E_0))^2) = c√(1-1) = c√(0) = 0
So we again see that when the total energy E equals the rest energy E_0, the velocity of the object must be v(E_0) = 0.
As E increases, so does v:
v(E=2E_0) = c√(1-((E_0)/2(E_0))^2) = c√(1-(1/2)^2) = c√(1-1/4) = c√(3/4) = ((√3)/2)c ≈ 0.866c
v(E=3E_0) = c√(1-((E_0)/3(E_0))^2) = c√(1-(1/3)^2) = c√(1-1/9) = c√(8/9) = ((√8)/3)c ≈ 0.943c
v(E=4E_0) = c√(1-((E_0)/4(E_0))^2) = c√(1-(1/4)^2) = c√(1-1/16) = c√(15/16) = ((√15)/4)c ≈ 0.968c
v(E=5E_0) = c√(1-((E_0)/5(E_0))^2) = c√(1-(1/5)^2) = c√(1-1/25) = c*√(24/25) = ((√24)/5)c ≈ 0.980c
etc.

So indeed "the more energy you have, the faster you are". But for each additional copy of rest energy you add, the increase in velocity becomes smaller and smaller. It's monotonically increasing, but bounded by c. In principle there's no upper bound on the total energy E of the object, but no matter how large E gets, v will always be smaller than c. Said in terms of limits:

lim_(E to ∞) v(E) = lim_(E to ∞) c*√(1 - (E_0/E)^2) = c

You can play around with the graph of v(E) on desmos and see that it always asymptotically approaches c (no matter what the rest energy is): https://www.desmos.com/calculator/rrfifig2km

That's not a physical explanation though, you can find something like that here: https://en.wikipedia.org/wiki/Speed_of_light#Upper_limit_on_speeds
In short, speeds exceeding the speed of light would break causality and lead to all sorts of paradoxes!

But I thought that doing the math of special relativity would be fun and helpful.

@Thalassokrator said in #8:

I'll be your algebra autopilot here:
The energy E of an object with mass m (greater than zero) moving at velocity v ≥ 0 according to special relativity is:
E=γmc^2,
where γ is the so called Lorentz factor γ = 1/(√(1 - (v/c)^2)) ≥ 1 and c is the speed of light c = 299,792,458 m/s.

If the object is at rest (velocity v=0) this reduces to Einstein's famous equation for rest energy E_0:
E_0=m*c^2

This is because γ(v=0) = 1/(√(1 - (0/c)^2)) = 1/(√1) = 1
We can also express the Lorentz factor in terms of the total energy E and the rest energy E_0 = m*c^2 as follows:

γ = E/(m*c^2)
or
γ = E/(E_0)

Now let's look back at the original expression for the Lorentz factor and begin rearranging for v:

γ = 1/(√(1 - (v/c)^2))
Take the reciprocal of both sides:
1/γ = √(1 - (v/c)^2)
Square both sides to get rid of the square root:
(1/γ)^2 = 1 - (v/c)^2
Subtract one from both sides and multiply by minus one afterwards:
(v/c)^2 = 1 - (1/γ)^2
Take the square root of both sides (let's ignore the negative solution, it represents movement in the opposite direction):
v/c = ±√(1 - (1/γ)^2)
Multiply both sides by c:
v = c*√(1 - (1/γ)^2)

Substitute γ = E/(E_0) into the equation:
v = c*√(1 - ((E_0)/E)^2)
We have obtained an equation for velocity v in terms of total energy E, our v(E).

You said:

Both are correct. However this does not preclude the possibility for a maximum speed.
The minimal value for E is E_min = E_0. Therefore:

v(E_min) = c√(1-((E_0)/(E_0))^2) = c√(1-1) = c√(0) = 0
So we again see that when the total energy E equals the rest energy E_0, the velocity of the object must be v(E_0) = 0.
As E increases, so does v:
v(E=2E_0) = c√(1-((E_0)/2(E_0))^2) = c√(1-(1/2)^2) = c√(1-1/4) = c√(3/4) = ((√3)/2)c ≈ 0.866c
v(E=3E_0) = c√(1-((E_0)/3(E_0))^2) = c√(1-(1/3)^2) = c√(1-1/9) = c√(8/9) = ((√8)/3)c ≈ 0.943c
v(E=4E_0) = c√(1-((E_0)/4(E_0))^2) = c√(1-(1/4)^2) = c√(1-1/16) = c√(15/16) = ((√15)/4)c ≈ 0.968c
v(E=5E_0) = c√(1-((E_0)/5(E_0))^2) = c√(1-(1/5)^2) = c√(1-1/25) = c*√(24/25) = ((√24)/5)c ≈ 0.980c
etc.

So indeed "the more energy you have, the faster you are". But for each additional copy of rest energy you add, the increase in velocity becomes smaller and smaller. It's monotonically increasing, but bounded by c. In principle there's no upper bound on the total energy E of the object, but no matter how large E gets, v will always be smaller than c. Said in terms of limits:

lim_(E to ∞) v(E) = lim_(E to ∞) c*√(1 - (E_0/E)^2) = c

You can play around with the graph of v(E) on desmos and see that it always asymptotically approaches c (no matter what the rest energy is): www.desmos.com/calculator/rrfifig2km

That's not a physical explanation though, you can find something like that here: en.wikipedia.org/wiki/Speed_of_light#Upper_limit_on_speeds
In short, speeds exceeding the speed of light would break causality and lead to all sorts of paradoxes!

But I thought that doing the math of special relativity would be fun and helpful.

Any possibility that Einstein was your great grandfather and he explained all that to u?

@obladie said in #5:

Quantum Entanglement implies instantaneous information transfer, but discussing that will make your head hurt.
Well not really. You can't use Quantum entanglement to actually transmit information (this is the root of the so-called EPR paradox I think).