Understanding Relativity: How a Mirror Reflects Your Image at Near-Light Speeds

[fusi0n]

If you hold a mirror at arm's length and look at your reflection, what will happen as you begin to run and a speed close to that of light (v=.99c). Will you still be able to see yourself? Will your image look any different?

 

[gurkhawarhorse]

u will see yourself run because the reflected light will come to your eyes anyway, but it will take longer every passing moment so i think u will se yourself in slowmotion.

 

[Janus]

If you hold a mirror at arm's length and look at your reflection, what will happen as you begin to run and a speed close to that of light (v=.99c). Will you still be able to see yourself? Will your image look any different?

You will notice no difference in your image at all.

 

[fusi0n]

Why will you see no difference?

 

[JesseM]

Why will you see no difference?

According to relativity, all the laws of physics should work the same way in every inertial (non-accelerating) reference frame--this includes the fact that the speed of light is the same in every inertial reference frame. Another way of saying this is that if you were in a windowless box moving at constant velocity, you would get the same results for any experiment you could do inside the box (including measuring how fast light moves from your face to a mirror) regardless of the box's velocity relative to the earth. So, even if you are moving at 0.99c in the Earth's frame, you can just as well look at this problem from the point of view of a frame where you are at rest and it is the Earth that's moving at 0.99c away from you, and since the laws of physics all work the same in this frame, you won't see anything different when you look in the mirror. Keep in mind that there's no such thing as absolute velocity in relativity, an object's velocity depends on what frame you choose, so it isn't meaningful to say someone's velocity is 0.99c unless you specify what that speed is measured in relation to (but light moves at the same speed in every frame so that's the only case where you don't have to specify--if a light beam goes by the Earth at 186,282 miles/second and then you take off in a rocket which moves at 185,000 miles/second away from the earth, you'll still find that the light beam is moving away from you at 186,282 miles/second, not 1,282 miles/second as you might expect).

 

[gurkhawarhorse]

so, am i right?

 

[JesseM]

so, am i right?

No--like I said, since the laws of physics should work the same in every reference frame, you should see exactly the same thing in a mirror that's at rest relative to you regardless of how fast you and the mirror are moving relative to the earth.

 

[εllipse]

The point that needs to be stressed is that the question really doesn't make sense. As Jesse points out, both you and the mirror are moving the same speed, so even if you're running close to the speed of light, you could just as well call yourself sitting still and the ground underneath you moving close to the speed of light. Of course, this won't explain why you get tired, but you get the idea. If you and a mirror are sitting still and the ground is moving close to the speed of light under you, why would you look different in the mirror?

 

[russ_watters]

To put it more simply, time dilation requires two reference frames - you and the mirror are in the same frame.

 

[pmb_phy]

If you hold a mirror at arm's length and look at your reflection, what will happen as you begin to run and a speed close to that of light (v=.99c). Will you still be able to see yourself? Will your image look any different?

No. Any such observation can then be used to distinguish frames of referance which are in relative motion.

Note: The Principle of Relativity states - The laws of physics are the same in all inertial frames of reference.

Pete

 

[jcsd]

Even if the mirror is not in your frame time dialtion has no effect (the image is affected by relative motion, but this is due to the fact that light takes time to go travel from you to the mirror and back again which is something that time dialtion doesn't take into account).

 

[gurkhawarhorse]

but i thought mirror is staying on the Earth and u r looking at the mirror through a telescope. foolish me.

 

[JesseM]

but i thought mirror is staying on the Earth and u r looking at the mirror through a telescope. foolish me.

In that case you were right, the image in the mirror would appear slowed-down, although as jcsd said this has nothing to do with time dilation, it's just because light is taking longer and longer to get from you to the mirror and back as you move farther away from it (so this would be true in classical physics too).

 

[gurkhawarhorse]

yay...¬!