# Why c in a vacuum?

1. Feb 15, 2007

### Ragnar

Why is the c in the the time dilation formula have the be the speed of light in a vacuum and not the one in the medium through which an observer sees it move?

Say for example we do that thought experiment used to derive the formula, in a much denser medium(in which the speed of light is still the same to all observers but slower like a diamond). In that case shouldn't c be the speed of light within that medium?

2. Feb 15, 2007

### rbj

because it is the c in a vaccum that must be observed to be the same c by all observers moving at constant velocities.

3. Feb 15, 2007

### Staff: Mentor

The speed of light in a medium does depend on the velocity of the medium relative to the observer. Fizeau measured this effect for light in water, as far back as the 1850s.

4. Feb 15, 2007

### Ragnar

THen wouldn't that mean that time dilation and therefore all relativistic effects only apply in vacuum? i mean since the speed of light is not the same to all observers in non vacuum.

Last edited: Feb 15, 2007
5. Feb 15, 2007

### Staff: Mentor

No, relativistic effects apply everywhere, not just in a vacuum. All relativity requires (or assumes) is that the speed of light in a vacuum is the same for all observers. (Think of that specific speed as being a kind of universal speed limit.) Lower speeds (including that of light itself in some medium) are not the same for all observers. But relativistic effects still apply.

6. Feb 15, 2007

### Ragnar

but why do they still apply? is it because of the postulate that says that all the laws of physics are the same in all inertial frames?

7. Feb 15, 2007

### Staff: Mentor

No, you use the familiar value of $c$ when calculating relativistic effects, regardless of whether you're in a vacuum or in a medium. In the context of relativistic equations, you shouldn't think of $c$ narrowly as being "the speed of light", but rather as something like "the universal limiting speed." Light happens to travel at that speed when it's in a vacuum, but not when it's in a medium.

8. Feb 15, 2007

### Ragnar

Oh ok i get it now. darn i'm stupid.

9. Feb 15, 2007

### anantchowdhary

SOrry i dont understand why Ragnar is wrong.Can u please explain again thoroughly.

Suppose we perform an experiment with light in vacuum and the same experiment for time dilation in air.Wouldn't they give different results?

FOr ex lets take the time dilation experiment in wich a person on a railway platform measures the time taken for light inside a train to traverse some distance.

The event's time is also measured by the person in the train.

The people in vacuum would agree to time dilation.
But in air(say) the equation for time dilation wouldnt apply as both would not observe the speed of light to be constant as it wudve not reached the universal speed limit at which all speeds are non-relative

10. Feb 15, 2007

### tim_lou

if you perform the thought experiments in relativity in a medium, then the symmetry is broken. Because, if you are moving in a train underwater, you know you are moving because you can feel the water passing you. (if you are in vacuum that would be impossible) If you know physics well enough, you can take the moving water into account and the take the moving water into account and work out the math, you should get the same result.

11. Feb 16, 2007

### anantchowdhary

how so?the condition for time dilation that the speed of light is the same to each observer will be violated.Wont it?

12. Feb 16, 2007

### anantchowdhary

13. Feb 16, 2007

### Schrodinger's Dog

OK think of the value d now this value is the maximum speed of anything in the universe.

Now using the equation e=md^2

Does that make it easier?

Divorce yourself from speed here, light propagates at c in a vacuum, but c just happens to be a limiting factor also, you could just as easily call it d the speed limit of matter/energy in the universe.

We're not relating e=md^2 to light exactly more to the universal speed limit.

$$t' = \gamma \left(t - \frac{v x}{d^{2}} \right)$$

$$\Delta t' = \gamma \left(\Delta t - \frac{v \Delta x}{d^{2}} \right)$$

Last edited: Feb 16, 2007
14. Feb 16, 2007

### MeJennifer

No that is incorrect Tim Lou.
The water is just as much moving as the train is. No symmetry is broken. The only symmetry breaking is when an observer (or an object) accelerates.

15. Feb 16, 2007

### anantchowdhary

@Schrodinger's Dog

I understand that c is a limit,beyond which relativity ceases to exist.But still if we derive the time dilation equation in water,we wont get the same result

16. Feb 16, 2007

### Hootenanny

Staff Emeritus
No we won't. As Schrodinger's Dog and others (Doc Al, jtbell) have explained in this thread, the fundemental 'speed limit' of the universe has some value. This value happens to be the same speed at which light propagates in a vacuum. The ultimate speed limit of the universe has the same value irrespective of the medium through which we are travelling. For example it is possible for particles to travel through some medium (other than a vacuum) at a speed greater than the speed at which light propagates through the medium and therefore the speed of light in some medium (other than vacuum) cannot be the ultimate speed limit. For more information search for The Cherenkov Effect and see this FAQ

17. Feb 16, 2007

### Staff: Mentor

The speed of light in a vacuum, c, is the "speed limit" that defines the connection between space and time between moving frames. That connection is contained in the Lorentz transformations and other equations describing relativistic effects, such as "time dilation".

I think I understand what you are talking about. For example, using pulses of light in a vacuum one can construct a "light clock" and derive the time dilation formula. This derivation is easy, since the speed of light in a vacuum is the same for all observers.

But if you build a light clock in water, the pulses would travel at less than c. You could still derive the formula for time dilation, but you cannot use the simplifying assumption that the light pulses have the same speed for all observers. Instead, you'd have to use the relativistic addition of velocity relations to compute the speed of the light pulses in water for different observers. This makes the derivation much harder! Nonetheless, you will end up with the same time dilation formula.

18. Feb 16, 2007

### Staff: Mentor

That isn't what the postulate says! As already said above, the postulate says the speed of light in a vacuum is the same for all observers.

All you do by adding a medium to the mix is add another unrelated effect that has to be subracted-out to find the real answer (edit - as Doc said two posts above...). Think about it this way: if a clock measures time by the oscillation of cesium atoms, how does the fact that there is air around the cesium atoms affect how fast they oscillate? It doesn't - it just adds a signal delay for someone watching them oscillate.

19. Feb 16, 2007

### neophysique

In a denser medium, the speed of light would be c "to all observers"
inside the medium with c having a smaller value than the c in vacuum.
The relativistic equations for the new medium would only apply to
inertial frames that have the same density as the new medium.

On the other hand, SR is a result of confusion over performing an experiment
inside a stationary frame and watching the result from a moving frame so
that is a different and probably much bigger problem than the one you are looking at.

Last edited: Feb 16, 2007
20. Feb 16, 2007

### anantchowdhary

Sorry.I think ur wrong.THe speed of light in a denser medium WILL be relative as it has not reached the non-relative speed barrier which is the speed of light in vacuum