# Relativity question

1. Apr 9, 2013

### rajeshmarndi

The speed of light is relative. Wouldn't two observer in different frame of inertial reference will have different result , that is triggered by the light.

Say, There is an ground observer and an observer in a moving car, the car headlight will get ON, when it hit a horizontal metal, placed at a certain point on the road. There is an time recorder instrument placed at a specific point on the road, which get activated when the metal is hit by the car or when the car head light get ON. This time instrument would stop when the light from the car headlight reaches the instrument.

Both observer will not agree on the distance the light would travel on the road in a given time. That is the car observer will say after a given time the light would reach certain point B on the road, where as ground observer would say the light would reach certain point A on the road in that time. Point B is further than point A.

Lets say the time instrument is placed at point A on the road.

The time instrument according to car observer would record less time, since the light according to him in that given time would have crossed point A and reached point B. Where as for the ground observer, the light would reach point A in that time.

Therefore they will not agree on the time recorded on the instrument. What would be the actual time get recorded in the instrument?

Thanks.

2. Apr 9, 2013

### Simon Bridge

No it isn't. Quite the opposite: the speed of light in a vacuum is always the same.

3. Apr 9, 2013

### ghwellsjr

Let me see if I've got this straight. There is a metal plate in the road that is connected by a wire to a timer that is further down the road. When the car runs over the metal plate, it automatically turns on its headlight and sends a signal down the wire to start the timer. At the timer is a light detector which turns off the timer when the light from the headlight hits it. Correct?
I'm not sure I have the description correct but if I do, then the signal will travel down the wire at the speed of light, the same as the beam from the headlight is traveling through space toward the timer and the light detector. Therefore, the signal to start the timer will cooincide with the light detector being tripped and so the timer will record zero time. It doesn't matter what frame you analyze this in as the speed of light in the air is the same as the speed of and electrical signal in the wire.

If I don't have the description correct, please explain where I went wrong.

4. Apr 9, 2013

### Simon Bridge

When you set up these thought experiments you have to be very careful about what you mean...

Lets see if I've got this right (you should sketch the situation):
The cars headlamps switch on when it reaches position x=0 on the road at t=0.
Synchronize rulers and clocks in each reference frame to this event.

An another position x=L, there is a light detector.
The detector also has a clock - synchronized with the one by x=0 - and it records the time that the light from the headlamps strikes it.

In the road-frame the time between headlights going on and detection of the light is Δt=L/c

In the car-frame, the distance to the detector is L' = L/γ so Δt'=L'/c < Δt ... but that is the time measured by a clock that is moving in the cars reference frame.

i.e. Δt=γΔt' in accordance with time dilation.
Remember - moving clocks run slow - according to the observer in the car, the clocks on the road are the ones that are moving.

That what you are talking about?

The phrase "actual time" has no meaning. You can only talk about the time recorded by some observer in some reference frame. Observers will disagree about what time stuff happens.

i.e. How does the car observer know about what is recorded on the detector on the road?

Last edited: Apr 9, 2013
5. Apr 9, 2013

### rajeshmarndi

Sorry for not mentioning this.
I mean the signal from the metal to activate the timer should be instaneous. That is it is totally mechanical. Let say there is a horizontal metal bar placed at a height so that when the car passed that point, it will hit the horizontal bar. This horizontal bar is again mechanically directly connected to a long rod, the other end being the timer. Just like a single rod, when one end goes down, the other end goes up. So no signal has to travel any distance. This way the timer get activated simultaneously when the horizontal bar is hit.

6. Apr 9, 2013

### Staff: Mentor

Sorry, but that won't work. You may want to read this FAQ entry: Can I send a signal faster than light by pushing a rigid rod?

7. Apr 9, 2013

### Simon Bridge

@rajeshmarndi: it is more common to use two synchronized clocks to get the kind of effect you want.
When the car reaches the position of the first clock, it records the time t1, and the headlights go on. The second clock, a distance L down the road, records the time t2 that the headlamp-light reaches it. Δt=t2-t1.

You should realize though, that, although the two clocks are synchronized in the road-frame, they will not be synchronized in the car-frame, causing disagreements.

8. Apr 9, 2013

### WannabeNewton

See here after you've read the FAQ article: http://einstein.stanford.edu/content/relativity/q1973.html. Also check out Landau and Lifgarbagez "Classical Theory of Fields", pages 46-47 if you can.

9. Apr 9, 2013

### ghwellsjr

As others have pointed out, you cannot communicate instantly over a distance mechanically. Do you understand and accept this? If so, do you want to modify your scenario into something that is realizable or do you want to abandon the whole idea?

10. Apr 9, 2013

### Simon Bridge

... after all, there is no need for a timer ;)