B Near Light Speed Runner: Will We See the Light?

[lovicodo]

hello,
i am a near light runner
at 3000000 km from us there is a mirror
to start the run , my friend turns on a very powerful lamp and i start running toward the mirror
me and my friend will see both the light coming back after 20 seconds?

 

[PeroK]

hello,
i am a near light runner
at 3000000 km from us there is a mirror
to start the run , my friend turns on a very powerful lamp and i start running toward the mirror
me and my friend will see both the light coming back after 20 seconds?

Are you able to do any of the calculations yourself?

 

[Matterwave]

Your friend would measure 20 seconds with his clock, you would measure a shorter time on your clock. See the twin paradox for more explanation.

More realistically, you would die due to acceleration when you were trying to change directions near instantaneously when you reach the mirror.

 

[PeroK]

Your friend would measure 20 seconds with his clock, you would measure a shorter time on your clock. See the twin paradox for more explanation.

More realistically, you would die due to acceleration when you were trying to change directions near instantaneously when you reach the mirror.

I think the runner is only running at normal speed.

 

[Matterwave]

I think the runner is only running at normal speed.

Oh, I interpreted the "i am a near light runner" and the title of "near light speed runner" to mean the OP is running at nearly light speed. o.o

 

[Nugatory]

hello,
i am a near light runner
at 3000000 km from us there is a mirror
to start the run , my friend turns on a very powerful lamp and i start running toward the mirror
me and my friend will see both the light coming back after 20 seconds?

You start off standing next to the light source, and start running when it is turned on? I'm assuming yes.

Assuming that we're using a clock that is not moving relative to your friend, the light source, and the mirror... the light will get back to the friend in 20 seconds. You, however, will be very close to the mirror when the light reaches it and is reflected, so the light will pass you on its return well before it reaches your friend. Thus, that clock will read less than 20 seconds when the light passes you.

Or we could use your wristwatch or some other clock that is at rest relative to you, and analyze the problem as if you are not moving but your friend, the light source and the mirror are (the mirror is in front of you and moving closer, the light source and your friend started where you were but are now behind you and moving away). The distance traveled by the light on the round trip to the mirror and back to you is just twice the distance between you and the moving mirror at the moment when the light reaches it - but that distance has to be calculated using the frame in which you are at rest so the starting distance is not 300000 km.

You should definitely take the hint from @PeroK and try the calculations yourself. You'll want to use the Lorentz transformations, and you simplify things a bit by using light-seconds instead of kilometers as the unit of distance (so $c=1.0$) and take the running speed to be 4/5 (that is, .8c) as that simplifies the arithmetic considerably.

 

[Nugatory]

Oh, I interpreted the "i am a near light runner" and the title of "near light speed runner" to mean the OP is running at nearly light speed. o.o

I'm interpreting that way as well. Perhaps the original poster can clarify?

In any case, there's no twin paradox if the runner is running towards the mirror and not turning around themselves. There are, however, other relativity of simultaneity considerations.

 

[Matterwave]

I'm interpreting that way as well. Perhaps the original poster can clarify?

In any case, there's no twin paradox if the runner is running towards the mirror and not turning around themselves. There are, however, other relativity of simultaneity considerations.

Ah yeah, I think there some errors in my interpretation as well. I thought OP was asking like OP is racing the light so OP would have to return to the starting point as well.