# Light at speeds faster than the speed of light?

#### Quds Akbar

I am no big expert on Relativity, though I know that objec cannot exceed the speed of light due to the restriction put by energy-mass equivalence.
And since light and many waves have no intrinsic mass, they are able to move at such a speed, but why is the speed strictly the speed of light and no more, why can't light, having little to no mass, move faster than its speed?

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#### russ_watters

Mentor
Isn't that just a tautology, that light travels at the speed of light? Or are you asking why the speed of light is what it is?

#### Quds Akbar

Isn't that just a tautology, that light travels at the speed of light? Or are you asking why the speed of light is what it is?
Why the speed of light is what it is, and thanks in advance.

#### HallsofIvy

Homework Helper
One way to look at it is to use "Maxwell's equations" for electric and magnetic vector fields, E and B, where $E_x$ and $B_x$ are the components of the electric and magnetic fields, respectively, in the x direction, $E_y$ and $B_y$ in the y- direction, and $E_z$ and $B_z$ in the z-diredtion:

$$\nabla\cdot E= \frac{\rho}{\epsilon_0}$$
$$\nabla\cdot B= 0$$
$$\nabla\times E= -\frac{\partial B}{\partial t}$$
$$\nabla\times B= \mu_0\left(J+ \epsilon_0\frac{\partial E}{\partial t}\right)$$

where $\rho$ is the charge density, $\epsilon_0$ is the "permittivity of free space", $\mu_0$ is the "permeability of free space", and J is the electric current density.

One can eliminate B from those equations getting a second order differential equation in E only: $$\nabla^2 E= \frac{1}{c^2}\frac{\partial^2 E}{\partial t^2}$$ or, equivalently, eliminate E to get $$\nabla^2 B= \frac{1}{c^2}\frac{\partial^2 B}{\partial t^2}$$ where $c= \frac{1}{\sqrt{\mu_0\epsilon_0}}$. Those are "wave equations". The solution of such a solution can be shown to be a wave with constant speed, c.

#### Nugatory

Mentor
Why the speed of light is what it is, and thanks in advance.
As HallsOfIvy explains above, you can calculate the speed of light from Maxwell's equations of electricity and magnetism - and indeed, Maxwell did that in 1861 when he first came up with his equations. Of course, Maxwell came at it from the other direction. He found that his equations predicted electromagnetic waves travelling at a particular speed, noticed that that speed was the same as the measured but not yet explained speed of light, so proposed the hypothesis that light was the electromagnetic radiation predicted by his equations.

#### theodoros.mihos

The speed of light inside a material is less than the speed of light as a global constant. There is a possibility for a movement inside a material with speed grater than the speed of light in this material because there is no such limit by relativity.

#### fast_squirrel

Thanks for the answer using the Maxwell equations. But still, the next question is :
Why can't any object move at a fatser speed than the speed of light in the vacuum ?

#### jerromyjon

If nothing moves faster than light in vacuum, no force could reach it to accelerate it further.

#### Nugatory

Mentor
Thanks for the answer using the Maxwell equations. But still, the next question is :
Why can't any object move at a fatser speed than the speed of light in the vacuum ?
I send a flash of light in a given direction, and at the same time you take off in a spaceship traveling the same direction. From your point of view, you are at rest while the light flash is moving away from you at c in one direction (same speed of light for all observers!) and I and the earth are moving away from you in the opposite direction. Thus, you are always between the earth and the flash of light; you never pass it.

Back on earth, I am looking at the same situation - you are between me and the light signal, never passing it. However, from my earthbound point of view I am at rest while you and the light signal are moving away from me. The speed of the light signal relative to me is c, the light signal is moving away from me at that speed, and you're moving in the same direction but never pass it; therefore your speed relative to me is less than c.

• Stephanus

#### Quds Akbar

Thanks for the answer using the Maxwell equations. But still, the next question is :
Why can't any object move at a fatser speed than the speed of light in the vacuum ?
Because of its increasing mass due to energy mass equivalence, and since light has no mass, I was asking why light itself cannot move faster than the speed of light.
But I am only in middle school so I did not quite understand the mathematical equations, but I still want to thank you guys for the answers.

#### Nugatory

Mentor
Because of its increasing mass due to energy mass equivalence, and since light has no mass, I was asking why light itself cannot move faster than the speed of light.
Mass-energy equivalence is a conclusion that comes from the speed of light being constant - you'll get to mass-energy equivalence, in a somewhat roundabout way, by analyzing all the consequences of assuming a constant speed of light. Thus, the constant speed of light is built into the mass-energy relationship - objects with mass increase their energy and momentum by moving faster, and light increases its energy and momentum by increasing its frequency while still moving at the same speed.[/QUOTE]

#### andresB

I'm I recalling correctly, there is also the argument that if something travel faster than light you could violate causality.

#### fast_squirrel

I send a flash of light in a given direction, and at the same time you take off in a spaceship traveling the same direction. From your point of view, you are at rest while the light flash is moving away from you at c in one direction (same speed of light for all observers!) and I and the earth are moving away from you in the opposite direction. Thus, you are always between the earth and the flash of light; you never pass it.

Back on earth, I am looking at the same situation - you are between me and the light signal, never passing it. However, from my earthbound point of view I am at rest while you and the light signal are moving away from me. The speed of the light signal relative to me is c, the light signal is moving away from me at that speed, and you're moving in the same direction but never pass it; therefore your speed relative to me is less than c.
Ok, but this does not imply the impossibility of a particle coming from the cosmos and going faster than c

#### fast_squirrel

I'm I recalling correctly, there is also the argument that if something travel faster than light you could violate causality.
I like this answer, but do you , or any one, knows how to demonstrate it ?

I like this answer, but do you , or any one, knows how to demonstrate it ?
If you look at the speed of light for what it is -- the speed of fluctuations in the electromagnetic field, and notice that most things we encounter are due to electromagnetic forces, such as touching, then it is pretty obvious:

If I could move faster then the speed of light, then I could quickly move my hand through your head and then outrun the ramifications -- the forces my hand should have experienced. Another way you could look at it is that you have already rammed my hand with your head but I simply outrun the consequences.

No expert here but I think it makes sense.

#### Ibix

I like this answer, but do you , or any one, knows how to demonstrate it ?
It's a straightforward consequence of the Lorentz transforms. If two things happen far enough apart that not even light can get from one to the other then their order is not fixed. In some frames, event A happens first; in others event B happens first.

Edit: The above is poorly phrased. A slightly more careful way to write it is:

It's a straightforward consequence of the Lorentz transforms.If two things happen far enough apart in space and close enough together in time that not even light can cross the distance between them in the time between them, it turns out that their order is not fixed. In some frames one of the things (call this event A) happens before the other (call this event B) and in some frames it is the other way round

Now if event A is the emission of a tachyon and event B is its absorption, then in some frames it was absorbed before it was emitted. One can fairly easily set up paradoxical scenarios where one sends a message telling your past self not to send the message. That's a causality violation.

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• 1977ub

#### DrGreg

Gold Member
I'm I recalling correctly, there is also the argument that if something travel faster than light you could violate causality.
I like this answer, but do you , or any one, knows how to demonstrate it ?
It's a straightforward consequence of the Lorentz transforms. If two things happen far enough apart that not even light can get from one to the other then their order is not fixed. In some frames, event A happens first; in others event B happens first.

Now if event A is the emission of a tachyon and event B is its absorption, then in some frames it was absorbed before it was emitted. One can fairly easily set up paradoxical scenarios where one sends a message telling your past self not to send the message. That's a causality violation.
For details, look up Tachyonic antitelephone.

#### Nugatory

Mentor
Ok, but this does not imply the impossibility of a particle coming from the cosmos and going faster than c
(Going faster than c relative to what?)

It does.
I position myself in its path and wait until the particle passes me. I fire my light signal in the direction it's travelling at the moment that it passes me, and we have the same situation that I described before - the light signal has to remain in front of the particle if it's travelling at c relative to the particle.

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#### engineer13

Let me set up a hypothetical situation. Say we have a photon traveling through space at c. There is also a singular point behind this photon emitting a magnetic field that the photon is traveling through. Whilst in this field the photon splits into an e+ and e- for an infinitesimally small span of time. During this time the magnetic field is able to interact with the components of the photon. Due to the fact that the magnetic field is pushing away would it cause the photon to go faster than the speed of light in that short span of time or would the magnetic field pull on the other component and slow the photon just as much as it speeds it up?

[mentor's note: personal theory unrelated to the question has been removed]

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#### Nugatory

Mentor
Let me set up a hypothetical situation. Say we have a photon traveling through space at c. There is also a singular point behind this photon emitting a magnetic field that the photon is traveling through. Whilst in this field the photon splits into an e+ and e- for an infinitesimally small span of time. During this time the magnetic field is able to interact with the components of the photon. Due to the fact that the magnetic field is pushing away would it cause the photon to go faster than the speed of light in that short span of time or would the magnetic field pull on the other component and slow the photon just as much as it speeds it up?
There are two things going on here. First, a single photon cannot split into an electron/positron pair unless there is a heavy nucleus nearby to allow for conservation of momentum (google for "pair production" for more details) so you really cannot think of the two particles as "components" of the photon. If the photon does decay into an electron/positron pair, we end up with two massive particles both travelling at less than the speed of light relative to any and all observers. Should these meet and annihilate, that reaction will produce two new photons both travelling at the speed of light relative to any and all observers.

Second, you seem to be trying to ask a variant of a very common (and sensible) question: suppose something is travelling at very close to the speed of light and we give it an extra kick? For example, I have a gun that fires bullets with a muzzle velocity of .2c; I mount my gun on the nose of a spaceship flying past you at .9c; why wouldn't the bullets be moving at (.9+.2)c which is 1.1c and faster than the speed of light relative to you? The answer, as I mentioned above, is relativistic velocity addition (google for that too).

#### engineer13

Thank you, I had forgotten that the electrons would have mass and thus be unable to move at the speed of light. Also I do understand relativistic velocity addition (something like (v1+v2)/c or something), but thank you for explaining it (I like that this forum is friendly to people who aren't that experienced with relativity).

#### Nugatory

Mentor
Thank you, I had forgotten that the electrons would have mass and thus be unable to move at the speed of light. Also I do understand relativistic velocity addition (something like (v1+v2)/c or something), but thank you for explaining it (I like that this forum is friendly to people who aren't that experienced with relativity).
It's $w=(u+v)/(1+uv)$ if we measure distance in light-seconds and time in seconds so that c comes out equal to one and we don't have to worry about multiplying or dividing by it, u is the speed of the spaceship relative to the ground, v is the speed of the bullet relative to the spaceship, and w is the speed of the bullet relative to the ground. It's a good exercise to try setting v equal to one, the speed of light (that's one light second per second) to see how fast a flash of light from the spaceship will be moving relative to the ground.

#### Wes Tausend

Gold Member
...

Here is some peculiar food for thought:

From a philosophical point of view (and experiment), we calculate that particles, or bodies, traveling at the speed of light would have to foreshorten to zero forward dimension, forward being the direction of travel. Since all movement is relative, we may deduct that the space that the movement must travel through must also foreshorten to zero dimension to an imaginary observer on the particle, or body. Any faster than c and the shortened length of the entire passing universe would cease to exist at all with the direction of travel becoming an unhandy negative spacial dimension and the arrow of time going backwards.

Consider, we can only speak of light-years of length according to an observer at rest. Light itself travels with apparent internal time slowed to zero (stopped) which gives it somewhat of an internal instantaneous speed from one end of the universe to the other regardless of how "long" the universe may be. An imaginary traveler at full lightspeed would not age no matter how far he or she traveled. And light through a perfect vacuum theoretically also arrives fresh as a daisy.

Of course passing space cannot logically have a negative dimension by anything traveling faster than c, including light (And of course even travel at c is also verboten for matter/mass/people). Nor can the traveler get younger, although many of us hold out hope.

Essentially, to logically conclude, there is apparently no room for light to travel any faster than it does.

Wes
...

#### Nugatory

Mentor
From a philosophical point of view (and experiment we calculate that
I'm not sure what you mean by "a philosophical point of view", but there are neither experiments nor calculations that support the conclusion that
particles, or bodies, traveling at the speed of light would have to foreshorten to zero forward dimension, forward being the direction of travel.
There are no experiments supporting this conclusion because there are no bodies moving at the speed of light, so nothing to experiment with.

It's easy to find incorrect calculations that appear to support this conclusion, but not correct ones. Usually the error is to apply a formula that is only justified under assumptions that are equivalent to no travel at the speed of light to something travelling at the speed of light. The "impossible" zero length that results isn't telling us that we can't travel at the speed of light because we'd be foreshortened to zero length, it's telling us that we've misapplied the math.

#### Wes Tausend

Gold Member
I'm not sure what you mean by "a philosophical point of view", but there are neither experiments nor calculations that support the conclusion that

There are no experiments supporting this conclusion because there are no bodies moving at the speed of light, so nothing to experiment with.

It's easy to find incorrect calculations that appear to support this conclusion, but not correct ones. Usually the error is to apply a formula that is only justified under assumptions that are equivalent to no travel at the speed of light to something travelling at the speed of light. The "impossible" zero length that results isn't telling us that we can't travel at the speed of light because we'd be foreshortened to zero length, it's telling us that we've misapplied the math.
Nugatory,

Sorry. Thank you for replying and trying to gently guide me.

I'm not sure I understand. By "philosophical point of view" I meant the invention of the Lorentz-FitzGerald contraction ratio. By experiment, I mean the Michelson-Morley measurements which seem to confirm that dimension must reduce to zero at lightspeed. I thought I could surely draw my assumptions from these concepts to apply an alternate perspective that would add to the discussion. Where did I go wrong here?

I know my views are dated. Perhaps that is my problem. Or lacking adequate classroom experience, I may simply draw incorrect conclusions from what I read. I haven't had the calculus which is a serious impediment in this branch of science, so I rely on pictoral, or geometric comparisons I think similar to the thought process of Feynman or Faraday. I know Feynman was an accomplished mathematician, but he seemed to think in visualizations. Geometry and diagrams first, math proofs later.