Special Relativity – Reflection at Speed of Light: Analyzing Concepts and Implications

reflectionspecial-relativityspeed-of-light

I have looked online to no avail. There is two competing answers and I am curious to know which one is right.

Someone asked me this question. If you are traveling at the speed of light can you see your reflection in a mirror in front of you?

My answer to the question is no, I would figure that in order for that to happen the light reflecting off you that would appear in the mirror must travel faster than the speed of light to actually reach the mirror (which we all know is impossible).

He says the answer is yes, that it is all relative to the current frame of reference.

Can anyone validate the correct answer with possible references?

Best Answer

This question cannot really be answered because you cannot travel at the speed of light. See Accelerating particles to speeds infinitesimally close to the speed of light?

If you were massless, you would always travel at the speed of light. However, in that case you would not perceive the passing of time. In relativity, the time that passes for an observer depends on the proper time. The proper time for a light-like trajectory is always zero, so photons themselves do not experience the passage of time.

If you travel very near to the speed of light - perhaps 99.9% light speed relative to Earth, you would still be able to view yourself normally in a mirror you carried with you. That is ensured by the principle of relativity, which states that all physical processes work the same way at any constant speed.

Related Solutions

Special Relativity – What Is the Speed of Tachyons?

If a tachyon starts from where you are and goes away at faster than the speed of light, you will see the photons it emits earlier than it actually departs. So you will see all these photons coming as if the tachyon were coming toward you at a speed slower than light, and then bang, the tachyon leaves. In fact, the faster it is going away, the slower it appears to be arriving.

EDIT: You can just tell this from a space-time diagram:

T  s   C
| /   /
|/   /    f
| s /    /
|/ /  f /
| /  / /
|/__/_/___X
|  / /
| / /
|/ /
| /
|/

Here, the time T axis is vertical and the space X axis is horizontal. Line C represents the speed of light. Photons move parallel to that line.

If something is moving away from you slower than light, it is a diagonal line falling in the slow (s) region. When it emits photons, they travel parallel to C, so each one arrives back at you at a later time. That's the normal behavior that you're used to.

If something is moving away from you faster than light, it is a diagonal line in the fast (f) region. When it emits photons, they travel parallel to C, and thus arrive back to you at a negative time, relative to when the object left you. In fact the faster it's moving (closer to horizontal) the earlier its photons will arrive (negative T). The slower it's moving (closer to C) the more its photons will appear to come all at once, just before it "departs".

Special Relativity – Interaction of Special Relativity with Mirror Reflections

The mirror is equivalent physically to a legitimate person mimmicking you behind an open gap... so apply the same logic as two trains coming towards each other at relativistic speeds.

Best Answer

Related Solutions

Special Relativity – What Is the Speed of Tachyons?

Special Relativity – Interaction of Special Relativity with Mirror Reflections

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