# Could somebody help me check the solution please. (special relativity)

• phalanx123
In summary, the light pulse takes l0/c to travel from the nose of the rocket to the tail, and it takes 2*l0/c to get back to the nose.

#### phalanx123

A rocket of length l0 measured in its rest frame S0 is traveling away from an observer in a frame S with a velocity u = 2/3 c. A light pulse is emitted from the nose of the rocket (x' = l0) at t0 = 0 and travels to the tail (x' = 0) where it is reflected back to the nose.

In S0, when does the light pulse reach the tail and when does it get back to the nose?

How long does the light pulse take to travel from nose to tail and back again
as determined by the observer in S?

Here is my solution

the time the pulse takes to travel from nose to tail is l0/c.
The time when it get back to the nose is t=2*l0/c.

For the second part, the total time it takes is gamma*2*l0/c where gamma=1/(1-v^2/c^2)^1/2 and v=2/3c

I think my solution is too simple, have I misunderstood the question ? Could somebody help me check it please. Thanks

phalanx123 said:
the time the pulse takes to travel from nose to tail is l0/c.
The time when it get back to the nose is t=2*l0/c.
Correct.

For the second part, the total time it takes is gamma*2*l0/c where gamma=1/(1-v^2/c^2)^1/2 and v=2/3c
Also correct, but do you understand what allows you to apply the simple time dilation formula? Since, in the rocket frame, a single clock is used to measure the round-trip time of the light pulse, you are justified in using the time dilation formula (which describes the behavior of a single moving clock).

What if they asked for the time the pulse takes to get from nose to tail according to observers in S?

Doc Al said:
What if they asked for the time the pulse takes to get from nose to tail according to observers in S?

Would that not be gamma*l0/c where gamma is the same as defined above?

phalanx123 said:
Would that not be gamma*l0/c where gamma is the same as defined above?

No, it wouldn't. That case is actually a bit more complicated to answer since two clocks are involved in the rocket frame, one at the nose and another at the tail. So you can't just apply the time dilation formula to that time interval, since no single clock directly measures it.

You can figure that one out by considering what distance the light must travel according to the S frame observers. (You'll need to take into account both length contraction and the motion of the rocket during the light's journey from nose to tail.)

Oh I see. so if the signal returned to the nose, only one clock is involved, so the time dilation can be used. but when measure the time interval between the emmission and reflection at the back, the events takes place at diffenrent places, so two clocks were involved, in that case the Lorentz transformation has to be used. Is my explanation/logic right?

Exactly right. (You could figure it out just using the known behavior of light, clocks, and measuring sticks... but that's equivalent to using the LT.)

Ok thank you very much. That cleared the SR up a little for me ^_^

## 1. What is special relativity?

Special relativity is a theory developed by Albert Einstein in 1905 that explains how objects in motion behave, particularly at high speeds. It is based on the idea that the laws of physics are the same for all observers, regardless of their relative motion.

## 2. How does special relativity differ from general relativity?

Special relativity deals with objects moving at constant velocities in a straight line, while general relativity takes into account the effects of gravity and the curvature of space-time. General relativity is a more comprehensive theory that builds upon special relativity.

## 3. What is the principle of relativity?

The principle of relativity states that the laws of physics should be the same for all observers, regardless of their relative motion. This means that there is no preferred frame of reference, and the laws of physics should be invariant under transformations between frames of reference.

## 4. What are some key concepts in special relativity?

Key concepts in special relativity include the constancy of the speed of light, time dilation, length contraction, and the equivalence of mass and energy (as described by Einstein's famous equation, E=mc^2). These concepts help explain the strange behaviors of objects moving at high speeds.

## 5. How has special relativity been tested and confirmed?

Special relativity has been tested and confirmed through numerous experiments and observations, including the famous Michelson-Morley experiment, which showed that the speed of light is constant regardless of the observer's frame of reference. Other evidence includes the behavior of particles in particle accelerators and the observations of cosmic rays.