# Altering the speed of light

1. Aug 20, 2004

### plum

How might the speed of light be altered and what implications might this have for space travel?

2. Aug 20, 2004

### Simfish

IIRC, the speed of light can actually be modified in everyday circumstances. Or so as the textbook says, light is refracted when it travels between air and water because its speed is slightly different in water and in air. Similar when light travels between other media.

And the speed of light is defined to be what it is in a vacuum.

Last edited: Aug 20, 2004
3. Aug 20, 2004

Simfishy said it, light speed is altered every day. To answer your second question, it won't have any implications on space travel. The speed of light cannot be increased if that is what you were thinking.

4. Aug 20, 2004

### plum

That is what I was thinking. If nothing can travel faster than light, what if there were a device attached to a spaceship that could speed up light around the ship?

5. Aug 20, 2004

### rgoudie

It is not the light particles themselves that limit speed. It is believed that light particles move as fast as this Universe apparently allows. This maximum speed, c, and the speed that light travels have effectively become interchangeable.

That being said, there is no proof that nothing in the Universe may travel faster than c.

-Ray.

6. Aug 20, 2004

### plum

But how could the speed of light particles so coincidentally also be the divine "maximum speed that the universe allows"? Is it just because we have yet to discover things that go faster than light? Does the maximum speed that observable matter goes automatically mean that no matter can be "pushed" faster than it has ever gone before?

7. Aug 21, 2004

### check

8. Aug 21, 2004

### jtolliver

Because light is massless it must go at the speed of light(yes, this term sucks for this purpose)

If you look at the formulas for lorentz transformations you might notice they look almost like rotations. You can introduce 4-vectors(the name comes from the fact that they have 4 components), with a time component in addition to the spatial ones. The only real difficulty is that the dot product must be given by
$$\vec{u} \dot \vec{v} = u_x v_x + u_y v_y + u_z v_z - u_t v_t$$
The negative sign is because of the fact that lorentz transformations aren't quite rotations, and c doesn't appear because i just chose the units so that its 1. A vector $\vec{v}$ is called spacelike if $\vec{v} \dot \vec{v}$ is greater than 0, lightlike if it is 0, and time like if it is less than 0. The velocity classically has a magnitude and a direction. In relativity we only need the direction it is moving in spacetime, and can choose the magnitude to be whatever is most convenient(as long as this does not do something like mapping a spacelike vector into a timelike vector). The relativistic velocity is called the 4-velocity, and is usually denoted by u. The x-component of the classical velocity is given by $v_x=\frac{u_x}{u_t}$, and likewise for the other components. For a particle moving in a timelike direction the classical velocity must be less than 1(or c if you didn't set it to 1), for a particle moving in a lightlike direction it must equal 1, and for a particle with moving in a spacelike direction it must be greater than 1. The energy and momentum, instead of satisfying $E=p^2/2m$, satisfy the equation $E^2-p^2=m^2$. The energy is essentially the time component of the momentum, and its norm squared is -m^2. To see that this gives classical physics in the low velocity limit, you can expand E in a power series in terms of p. Since the square of the norm of the momentum is negative for nonzero m, and the velocity points in the same direction as the momentum, the velocity must be timelike for massive particles, and thus they obey the speed limit. Massless particles(like the photon) likewise must have a lightlike velocity, and must go at the universal speed limit. Particles whose mass squared is negative(called tachyons) must go above the universal speed limit, however they have not been observed.

Last edited: Aug 21, 2004
9. Aug 21, 2004

### pervect

Staff Emeritus
Well, all you really need to do is to get the standards committe that sets the value of the speed of light to change their minds about what this defined constant is.

Viola! You will have changed the speed of light :-)

I assume you're actually talking about 'c', BTW. The actual speed of light (EM radiation) does decrease when it travels through a dielectric.

Anyway, to try and imagine changes to physics that aren't too major that could result in a different universe with a different "speed of light" is somewhat interesting.

Speeding up space travel is a poor motivation for increasing 'c', though. We can't reach anywhere near 'c' at the moment. And one can much more easily imagine human beings living longer and having more patience for longer space trips than one can imagine actually changing the fundamental constants of the universe.

But there are a few things one can say speculatively about a different universe where the speed of light might be "different", in ways that are more interesting than a passive change in units.

Let's assume we want to keep both Maxwell's equation, and Schrodinger's equation. Then, to change the speed of light, we need to change either $$\mu_0$$ or $$\epsilon_o$$.

Of the two choices, changing $$u_0$$ has the least side effects. Basically, as the speed of light goes up, the magnetic field is going to go down. I'm really not sure what effect this would have on cosmology though - even though this is obviously an important question when designing hypothetical universes.

Changing $$\epsilon_0$$ is going to have some major side effects. The first one is that the Bohr radius, the radius of the hydrogen atom, is going to change its size. This also implies a change in its energy levels. This has the potential to upset a lot of basic chemistry, I would guess that the chemistry would be different enough that life from our universe would die. (Note: this is just a guess, it's very speculative). The further domino-like consequences of such a change are rather hard to even guess at, we can say that halving $$\epsilon_0$$ would increase the speed of light by a factor of 1.4, while halving the size of the hydrogen atom. Note this would actually "increase" the distance to the nearest star in terms of the multiple of the Bohr radius. I don't have a clue as to what would be likely to happen to cosmological issues for this sort of change.

10. Aug 21, 2004

we wouldn't need to speed up light in order to have fantastic space travel. Special Relativity has stated: As a body moves closer and closer to the speed of light, time befins to flow slower and slower for him, and distance contracts. If we wanted to get on the other side of the universe, it would take us 0.00001seconds if we were to be traveling at the speed of light. (0.00001s is still too much, it would be less, but Im just giving you an idea)
When traveling at high speeds:
$$d_o = d \sqrt{1- \frac{v^2}{c^2}}$$
$$d_o$$ is the distance experienced by the traveler, and $$d$$ is the actual distance passed.
You can play around with the equation and see what it implicates.

11. Aug 21, 2004

### plum

Yes, but speeding up light might allow relatively great speeds in which the infinite mass/ infinite energy problem could be solved (not to mention the chronology problem). What made me think of this was the conjecture, using the Varying Speed of Light theory, that there may be vast "superhighways" in deep space used by aliens for interstellar (intergalactic?) travel wherein light actually travels much faster. If the fundamental properties of these areas could be measured, could they not be replicated?

12. Aug 21, 2004

### rgoudie

Of course, this is not the case in real life. It takes light more than 1 second to travel from the Moon to the Earth, let alone across the Universe.

In fact, light particles may travel for billions of years on their journeys through the Universe.

-Ray.

Last edited: Aug 21, 2004
13. Aug 21, 2004

### Staff: Mentor

Clarification: the speed of light is constant. It does not change when light is refracted. In refraction, light is absorbed and re-emitted making for the appearance that it has slowed down.

14. Aug 21, 2004

### rgoudie

Where did you get this from?

-Ray.

15. Aug 21, 2004

### The Bob

Time Dilation. I understand this but it makes no difference to the speed of light. I read, unless it has changed, that even if we measured light from a moving vehicle or from a stationary point, the speed of light would be the same.

P.S. I then think about the Earth moving and it not being a stationary point. Frame of References are so easy to understand but difficult to get around.

Reminds me of what Hawking said about the moving train and the bouncing ball.

16. Aug 21, 2004

### Staff: Mentor

True, but irrelevant to Nenad's point. Yes, as seen by us, it takes light many years to traverse galactic distances. But if we traveled at near light speed, that distance would shrink to a mere pittance. To our clocks it would take almost no time at all.

17. Aug 21, 2004

### pervect

Staff Emeritus
The varying speed of light theory, if it's the one some guy was pushing on rec.arts.sf.science, has a fatal flaw. You expect to see one of $$\epsilon_0$$ or $$\mu_0$$ to change with $$c = 1/\sqrt{\epsilon_0 \mu_0}$$

If the speed of light is to be very great, one of the two must not only change, but change a whole lot - it must tend to zero.

This implies that a region with a high speed of light would have no magnetic field, or a significantly different value for the permittivity of free space.

Measurements of the galactic magnetic field have been made, it's non-zero (this was done by observing the Zeeman splitting in various spectral lines). Changes in the value of the permittivity would be even more obvious than changes in the Zeeman effect (the spectral lines frequencies would be wrong in a very glaring way) and aren't found either.

Note: some people *think* they may have found a change in the fine structure constant. This hasn't been widely accepted, and the magnitude of the supposed change is very small - on the order of .001 percent. Not enough to fuel any visions of "galactic superhighways" even if it is true (and it's probably just a very small measurment error of some sort).

18. Aug 21, 2004

### rgoudie

If I effect the modification above in red, then I understand what was meant. The time experienced by the entity travelling at c.

D'oh!

-Ray.

Last edited by a moderator: Aug 21, 2004
19. Aug 21, 2004

### bino

is the speed of light constent?

20. Aug 21, 2004

### pervect

Staff Emeritus
This is another good point which is rarely mentioned. *IF* we had a spaceship that could accelerate continuously at 1g, we can travel a LOT further in 20 years of ship-time (proper time) than we could if acceleration were non-relativistic.

It turns out to be pretty implausibile to have a spaceship that can continuously accelerate at 1g for such a long period, however.

A perfectly effecient photon rocket would require a mass ratio of about $$e^{20}$$ to do this iirc

http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html

gives a mass ratio of 62,000 to reach the center of the galaxy, for instance. This assumes perfect efficiency, which is highly unlikely. In fact, it's pretty unlikely that such a high-thrust high-ISP drive could exist, it would probably melt under its own waste heat considering the magnitude of the energies involved.

There are also some rather interesting problems in dealing with interstellar gas when travelling at such velocities.

It *really* is a lot simpler to just travel slower, and let the trip take longer, by going for a biological solution to allow longer lifespans and/or hibernation and/or artifical intelligence and/or downloading personalities into computer hardware, than it is to try and get velocities with significant time dilations.