Lightspeed.

[Enmos]

Yes that post makes sense to me. I have been trying to work this out with my son. I believe the light would meet you at 2/3 of the way there yes.

Ok

So if the light is traveling at 1.5c relative to the mirror, the light is traveling three times as fast as the ship.
So in the same time that the ship travels half the distance to the mirror the light travels three times as far. That's to the mirror and half-way back, which is where the ship is.

[TBodillia]

Well, first, how is t faster than 0.75t? If it takes one year to hit the mirror and return, 0.75t is 9 months...that's faster.

Second, c, speed of light, is the speed limit of the universe. The beam of light will not move at 0.5c+c it will always be just c.

[Enmos]

Well, first, how is t faster than 0.75t? If it takes one year to hit the mirror and return, 0.75t is 9 months...that's faster.

Yes, that's what I said. You gave the answer 0.75t, which is faster than t.
Wait.. 9 months ? You are confusing the OP with post 9.

Second, c, speed of light, is the speed limit of the universe. The beam of light will not move at 0.5c+c it will always be just c.

Well, that is the problem at hand (see post 9).

[parmalee]

What bit ? Or did you delete the post ?

Sorry, I was conceding that I agree as regards the first post.

Replace the mirror, in example two, with an observer. If you turn on the light, while stationary, the observer will see the light one year hence. If you are traveling at .5c and you turn on the light, does the observer see the light in 2/3 year? I think the light should still reach the observer in 1 year, as the speed of light is the speed of light and the speed of the source of light is inconsequential, right?

[parmalee]

Ok

So if the light is traveling at 1.5c relative to the mirror, the light is traveling three times as fast as the ship.
So in the same time that the ship travels half the distance to the mirror the light travels three times as far. That's to the mirror and half-way back, which is where the ship is.

But the light cannot travel at 1.5--it's a constant or the limit, right?

Edit: Right. The light MUST travel at c relative to the observer, so it would seem that the light must travel at 1.5 with respect (or towards) the mirror. But, supposing that mirror is an observer--how does that work?

[Waiting]

The light is not traveling at 1.5 c to the mirror observer. Light always travels at c.

[Enmos]

But the light cannot travel at 1.5--it's a constant or the limit, right?

The light is not traveling at 1.5 c to the mirror observer. Light always travels at c.

How is it traveling at 1c relative to the observer and at 1c relative to the mirror out in space, while traveling at 0.5c ??

I know c is the limit, but..

[Enmos]

I'm off to bed (3:27AM). I'll check back here tomorrow.
Thanks for the replies so far !

[parmalee]

Sadly, I feel that I probably could have answered this back when I was 15, but now all I know are decidedly non-rigorous subjects like philosophy, anthropology, literature, and music. (Well, not non-rigorous, but rigorous in a different way)

[Waiting]

That is the key to relativity Enmos. All is relative. No matter what speed you are moving at the speed of light is c. Also with relativity simultaneity goes out the window. This is of course very confusing which is why relativity boggles almost everyone.

[Enmos]

That is the key to relativity Enmos. All is relative. No matter what speed you are moving at the speed of light is c. Also with relativity simultaneity goes out the window. This is of course very confusing which is why relativity boggles almost everyone.

So you are just ignoring the contradiction ?
If Object 1 is on course for a stationary object and moving at speed v₁ relative to the stationary object and Object 2 is projected from it at speed v₂ relative to Object 1 and in the same direction as Object 1, then the speed of Object 2 relative to the stationary object is v₁+v₂.
I don't care if it's light or a ball. There is a discrepancy that hasn't been explained other than by saying that it just is so.

[parmalee]

Time dilation? Perhaps the reflected light reaches the observer after she has traveled 2/3 of the way, rather than only half the way. But for the observer only half a year has passed?

[Enmos]

Time dilation? Perhaps the reflected light reaches the observer after she has traveled 2/3 of the way, rather than only half the way. But for the observer only half a year has passed?

How could half a year have passed if they are traveling at 0.5c and have traveled a distance of half a light year ?

[parmalee]

How could half a year have passed if they are traveling at 0.5c and have traveled a distance of half a light year ?

No, I'm suggesting that for the observer half a year has passed--but the observer has actually traveled 2/3 of the way rather than 1/2 the way. Doesn't a moving clock progress more slowly than a stationary clock?

[Enmos]

No, I'm suggesting that for the observer half a year has passed--but the observer has actually traveled 2/3 of the way rather than 1/2 the way. Doesn't a moving clock progress more slowly than a stationary clock?

Yes, I know you meant that.
If the observer travels 2/3 of a light year at 0.5c then the time that has passed (as it appears to the observer) is (2/3)*2*0.5=2/3 of a year, assuming that the clock runs twice as slow as it would when stationary of course.
To a outside stationary observer it took them (2/3)*2=4/3 of a year.

[parmalee]

Yes, I know you meant that.
If the observer travels 2/3 of a light year at 0.5c then the time that has passed (as it appears to the observer) is (2/3)*2*0.5=2/3 of a year, assuming that the clock runs twice as slow as it would when stationary of course.
To a outside stationary observer it took them (2/3)*2=4/3 of a year.

Do you think that this is what is to account for the apparent discrepancy?

[Enmos]

Do you think that this is what is to account for the apparent discrepancy?

No, because in either 'possibility' the observer is traveling at 0.5c.
If the light would move towards the stationary mirror at 1c the light and the observer will meet up again at 2/3 of the way.
If the light would move towards the stationary mirror at 1.5c the light and the observer will meet up again at 1/2 of the way.
Both are 'possibilities' of the same situation.

[parmalee]

No, because in either 'possibility' the observer is traveling at 0.5c.
If the light would move towards the stationary mirror at 1c the light and the observer will meet up again at 2/3 of the way.
If the light would move towards the stationary mirror at 1.5c the light and the observer will meet up again at 1/2 of the way.
Both are 'possibilities' of the same situation.

But I think that the reflected light must reach the observe at the 2/3 way point, because the speed of light is a constant; and, of course, the speed of light must appear to be the same for the observer independent of motion. However, if the time has slowed from the perspective of the observer, the light still seems to appear as though it is traveling at the speed of light.

If your watch is running at normal speed and you travel 10 k over the course of an hour, it seems to you--the observer-- that you have traveled 10 k/hour; however, if your watch is slowed--running at half-speed--then, from your perspective, you have actually traveled at 20 k/hour.

So if you are traveling at .5c, the light still does travel at c from your perspective because your "watch" (or time) has slowed. But if I am observing this phenomenon from the stationary starting point, the light appears to travel at c and you appear to travel at .5c--so from my perspective, the light is only traveling .5c faster than you but it still appears to travel at c from my stationary perspective. The reason that the light does not appear to be traveling only at .5c away from you is because your watch/time has slowed.