# Speed of the light and time dilation

1. Apr 19, 2012

### sejyne

Lorenz-factor has remarkable influence at speeds near to light, but formula itself has no limits. So, time dilation occurs also with slow speeds.

From my point of view (an observer), Venus and Mars have different speeds which means different time dilation and this means different speed of light.

So, both planets are sending a ray of light towards me with different speeds. - Which is not possible.

If time dilation would be an imaginary phenomenon, there wouldn't be any problems. But when two worlds with different time dilation meets each others, there is a problem.

What explains this?

2. Apr 19, 2012

### mathman

The Lorentz transformation applies to objects moving at less than the speed of light. Light itself has the same speed in all inertial frames.

3. Apr 20, 2012

### bahamagreen

"But when two worlds with different time dilation meets each others, there is a problem."

That would be a problem except that light is literally, measurably, and physically always a local phenomenon. There is no observation of distant light. Measured, captured, seen light is always local light. In this respect, light as we know it (always local) is consistently well behaved.

4. Apr 20, 2012

### HallsofIvy

Staff Emeritus
Yes.

No. A fundamental point of relativity is that the speed of light is the same in all coordinate systems. Time dilation will affect the frequency of the light, not its speed.

5. Apr 20, 2012

### sejyne

Thank you, I got some idea - and perhaps understanding comes later.

Same matter but different example:

A spaceship is flying with a speed of 30% of the light and if I calculated right, Lorenz factor is 1,05. Does it mean that the time in spaceship goes 5% slower and "twin paradox" is on the way? He's hands and heart and everything moves 5% slower except the light?

Pilot puts the light on and the ray of light goes from lamp to the window. If he checks, how much time this takes, does he's watch give the value in seconds as on the earth?

6. Apr 20, 2012

### HallsofIvy

Staff Emeritus
The whole point of the name "relativity" is that it makes no sense to say "speed 30% of the speed of light" without say what this is measured relative to. I assume you are postulating some observer so that the space ship is flying at 30% of the speed of light relative to that observer.

Relative to the outside observer, yes. As far as a person in the space ship is concerned, there is no change.

The pilot is motionless relative to the spaceship so he sees the light moving at c. The outside observer sees the light moving at speed
$$\frac{u+ c}{1+ \frac{uc}{c^2}}= \frac{u+ c}{1+ \frac{u}{c}}$$
Multiplying both numerator and denominator by c,
$$\frac{(u+ c)c}{c+ u}= c$$

That is, both pilot and the outside observer see light moving at speed c. That is exactly what "the speed of light is the same in any coordinate system" means.

Last edited: Apr 20, 2012
7. Apr 22, 2012

### sejyne

I think I've got rid of one problem.

In my example the space ship moves with a speed of 30% from 299.792.458m/s. Inside the ship, after the pilot's opinion, the light is moving 5% faster, 314.267.888m/s. When the ship goes 99% of light, the pilot's speed indicator shows 2.125.172.389m/s.

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The "speed indicator" of the Earth has also some variation. In what month the light goes as fastest?

8. Apr 22, 2012

### Staff: Mentor

OK, so your ship is moving at 0.3c with respect to something (the earth, for example).
No, with respect to the ship, the light is seen to move at speed c, as usual.

9. Apr 22, 2012

### sejyne

I never believed this would be easy...

Base is the earth and an observer is there. The space ship moves with a speed of 30% from 299.792.458m/s and time inside the ship goes 5% slower than on the earth.

What is the speed of the light inside the space ship
a) after observer?
b) after pilot?

10. Apr 22, 2012

### DrGreg

a) 299 792 458 m/s
b) 299 792 458 m/s
Relativity doesn't just cause time dilation, it also causes length contraction and the relativity of simultaneity.

11. May 2, 2012

right!