# How can time slow down and speed up for a particle simaltaneously?

Suppose there's a kangaroo baby in its mother's pouch and there's a light bulb 300,000 km from them. If someone turns on the bulb, both kangaroos will agree that the light bulb takes 1 s to turn on because they are at the same location in space. Even if the baby starts moving toward the bulb the instant it is turned on, the first photon from the bulb will reach both in one second (relative to their respective frames of reference) because the relative velocity of light is the same for all observers irrespective of their speeds. The baby won't receive the photon earlier because velocities don't add in special relativity.

Now, if someone is midway between two light sources and starts moving toward one, they will receive the two photons emitted by the two sources at the same time. So time should slow down for them to receive the photon from the light source they are getting closer in the speed of light and faster with the other light source.

• draw a diagram and all will be revealed Oct 19, 2021 at 14:19
• Putting aside the specifics in the body of the question and just responding to the title: Every time you accelerate, your clocks simultaneously speed up in some frames and slow down in others. Oct 19, 2021 at 15:24

There are two mistakes in your reasoning.

Firstly, you are wrong to suppose the baby moving towards the source will not see the light before the mother does. The light from the source will have to travel further to reach the mother after it has passed the baby, so the mother will see the light after the baby has seen it.

Secondly, the observer moving between two stationary light sources will not see light from each of them at the same time if they flashed at the same time in their frame of reference when the observer was midway between them. The observer will first see light from the source they are travelling towards and then see the light from the source they are travelling away from.

The moving observer would only see the light from the two sources arriving simultaneously if they flashed simultaneously in the observers frame of reference while they were equidistant from the observer.

So time should slow down for them to receive the photon from the light source they are getting closer in the speed of light and faster with the other light source.

This is not correct. Time dilation does not depend on direction, only the speed.

Now, if someone is midway between two light sources and starts moving toward one, they will receive the two photons emitted by the two sources at the same time.

I believe that your mistake is here. You may be missing the relativity of simultaneity. There are two frames of interest, the frame where the “someone” is moving and the frame where they are at rest. In order for “someone” to receive the light flashes at the same time they must be emitted simultaneously in the frame where they are at rest. In the frame where they are moving the emissions will not be simultaneous. Instead the front flash will occur later than the rear flash. So both frames will agree that “someone” receives the light at the same time, but will disagree about the timing of the flashes.