# Simple (?) special relativity question

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1. Jul 1, 2014

### Involute

If someone stands up through the sunroof of a car travelling down the freeway at 60 mph and measures the speed of a beam of light they shine from a flashlight in the direction the car's going, they'll record it as c. This is intuitive (no need for relativity). Someone on the roadside, however, will also record it as c, since the speed of light is constant for all reference frames. Does this mean that the light actually slows down (with respect to the car) by 60 mph (this slowing down would not be detected by the person in the car since their ruler will shorten and clock will slow down)? If so, why? What causes the light to slow down? If not, what's going on? Thanks.

2. Jul 1, 2014

### ghwellsjr

Can you please describe how you think someone can make this measurement?

3. Jul 1, 2014

### Staff: Mentor

It doesn't slow down. Its speed is c at all times in all frames.

The separation speed between the car and the light is different in different frames, but that is because different frames disagree on the speed of the car, not the light.

4. Jul 1, 2014

### Involute

ghwellsjr:

> Can you please describe how you think someone can make this measurement?

There's a reflector some distance in front of the car and precisely calibrated distance measurements to the reflector on the side of the road. Time the rountrip of the beam, adjust roundtrip distance for distance traveled by the car ... voila?

5. Jul 1, 2014

### Involute

DaleSpam:

What's the "separation speed between the car and the light?"

6. Jul 1, 2014

### Staff: Mentor

The separation speed is the rate at which the distance between two objects increases.

7. Jul 1, 2014

### ghwellsjr

That's not going to work. Of course at such low speeds, it will be just about impossible to show why it won't work so I'm going to show you what happens with the car going at 60% of the speed of light instead of 60 mph.

Here's a spacetime diagram showing the car in green, two markers in blue and black and the reflector in red:

The timing device on the car is Time Dilated. The green dots mark off 1 microsecond increments of time so it takes 8 microseconds for the car to get from the blue marker which is 8000 feet from the reflector to the black marker which is 2000 feet from the reflector. The passenger concludes that the light traveled a total of 10000 feet in 8 microseconds or 1250 feet per microsecond which is wrong. The correct answer is 1000 feet per microsecond.

Do you want to try again?

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8. Jul 2, 2014

### pervect

Staff Emeritus
You are ignoring some important relativistic effects, for instance the length contraction of the rulers (your precisely calibrated distance measurements) on the side of the road. When you ignore unfamiliar relativistic effects, you wont get the right answers to your questions (which in this case appears to be the relativistic velocity addition law).

Do you have a textbook to guide you in learning relativity, or are you trying to reinvent it by yourself?

9. Jul 2, 2014

### nikkkom

https://en.wikipedia.org/wiki/Special_relativity

?

"Comparison between flat Euclidean space and Minkowski space" section in particular.

It has a picture ("Orthogonality and rotation of coordinate systems compared...") which explains why exactly speed of light does not change when you have a boost (change of observer velocity) in Minkovski space.

10. Jul 2, 2014

### pervect

Staff Emeritus
The wiki article seemed a overly complex to me. A simpler approach is this:

If the speed of light is constant then x=ct or x=-ct, which can be rewritten as (x-ct)=0 or (x+ct)=0.

We can combine these two equations into one: (x+ct)(x-ct)=0, as multiplication of two quantites is zero if and only if one or both of them is zero. We can rewrite x+ct)(x-ct) as x^2 - (ct)^2 just by multiplying it out.

Then we only need to ask: if x^2 - (ct)^2 is zero in one frame, is it zero in all frames?

A bit of algebra shows that this is not true with the Galilean transformation, but that it is true with the Lorentz transformation.

If the terms "Galilean transformation" and "Lorentz transformation" aren't familiar to the OP (and I suspect they may not be, but of course it's hard to guess a poster's background) I'll recommend getting a textbook on SR and reading about them, this is at the heart of the question of what special relativity is about.

11. Jul 2, 2014

### nikkkom

I was referring to the wiki picture which shows how during Lorentz transformation t axis "tilts" by some angle, and *x axis tilts by the same angle* in the opposite direction. In the picture it is very obvious that this syncronized change in two axes leaves their median line, x=t, unchanged. That's the worldline of light. Since it doesn't change, speed of light is constant during the transformation.

Last edited: Jul 3, 2014