Observing objects moving close to light speed

  • #1
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Would someone be kind enough to tell me if I'm getting this correct.

Prob_4.gif


Problem A
A spherical light source is 1 light year away from Point A at point B.
It moves at near light speed in a circumference around Point A to Point C for a distance of 1 light year.
When the light reaches it's destination it turns off.
What does a person at Point A observe?

Answer: Nothing for 1 year and then a light moving in a straight line at a constant speed for about a year before disappearing.

Problem_4.gif


Problem B
A spherical light source is at Point B, 1 light year away from Point A.
It moves to Point C at constant near light speed.
When the light reaches it's destination it turns off.
What does a person at Point A observe?

Answer: Nothing for 1 year and then a light moving in a straight line appearing to decelerate for about a 1.41 years before disappearing.

Problem C
A spherical light source is at Point A.
It moves to point B at constant near light speed.
When the light reaches it's destination it turns off.
What does a person at Point A observe?

Answer: A light moving away from them in a straight line appearing to decelerate for 2 years before switching off.

Problem D
A spherical light source is at Point A along with an observer. They both have atomic stop watches.
As both stop watches start the light moves at a constant near light speed to Point B, then Point C, then Point D, then Point A without resting.
What will the person at Point A observer on each clock at 1, 2, 3 and 4 years (assuming he has a decent telescope)?

Answer:
1 year: Observer clock=1 year, light's clock observed as ~0.5 years
2 year: Observer clock=2 years, light's clock observed as ~1 year
3 year: Observer clock=3 years, light's clock observed as ~1.75 years (???)
4 year: Observer clock=4 years, light's clock observed as ~4 years

I think I'm likely wrong, and if so, please could you explain why?
 

Answers and Replies

  • #2
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Everything seems fine except the last experiment where you fail to consider time dilation. You're only considering the lag effect caused by the finite speed of light.
 
  • #3
PeterDonis
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Problem A
A spherical light source is 1 light year away from Point A at point B.
It moves at near light speed in a circumference around Point A to Point C for a distance of 1 light year.
When the light reaches it's destination it turns off.
What does a person at Point A observe?

Answer: Nothing for 1 year and then a light moving in a straight line at a constant speed for about a year before disappearing.
This doesn't make sense; you said the light moves in a circular arc with a radius of 1 light-year around Point A. That means the person at A will see the light moving in a circular arc, not a straight line. The arc will have an arc length of 1 light-year, but that just means the angle through which A sees the light move is 1 radian. It doesn't mean the light is moving in a straight line relative to A.

Problem B
A spherical light source is at Point B, 1 light year away from Point A.
It moves to Point C at constant near light speed.
When the light reaches it's destination it turns off.
What does a person at Point A observe?

Answer: Nothing for 1 year and then a light moving in a straight line appearing to decelerate for about a 1.41 years before disappearing
This looks OK.

Problem C
A spherical light source is at Point A.
It moves to point B at constant near light speed.
When the light reaches it's destination it turns off.
What does a person at Point A observe?

Answer: A light moving away from them in a straight line appearing to decelerate for 2 years before switching off.
This looks OK too.

Problem D
A spherical light source is at Point A along with an observer. They both have atomic stop watches.
As both stop watches start the light moves at a constant near light speed to Point B, then Point C, then Point D, then Point A without resting.
What will the person at Point A observer on each clock at 1, 2, 3 and 4 years (assuming he has a decent telescope)?

Answer:
1 year: Observer clock=1 year, light's clock observed as ~0.5 years
2 year: Observer clock=2 years, light's clock observed as ~1 year
3 year: Observer clock=3 years, light's clock observed as ~1.75 years (???)
4 year: Observer clock=4 years, light's clock observed as ~4 years

I think I'm likely wrong, and if so, please could you explain why?
I'm not sure how you're getting these answers, since at least the first two are just repeats of problems C and B above. Call the time of launch t = 0 by the person at A's clock. From Problem C, he will see the light moving away from him, apparently decelerating, for 2 years by his clock, until t = 2. Then, by Problem B, he will see the light moving at an angle away from him (from B to C) for about 1.41 years, until about t = 3.41. By symmetry, the geometry of the last two legs is just like the first two in reverse; but now the light source is moving towards A instead of away, so the 3rd leg (C to D) will appear to take 1 year minus about 0.41 years, as seen by the observer at A, or about 0.59 years, until about t = 4. And since the light source is traveling close to the speed of light, the final leg (from D back to A) will appear to take almost no time at all as seen by the observer at A; the light source itself will arrive back at A almost as soon as the light it emits when it is at D. So the observer at A will read t = 4 when the light source arrives back at A.

The only thing left to address is what a clock that is moving along with the light source will read; but since you've stipulated that the light source moves at nearly c, the time elapsed on a clock moving with the light source will be nearly zero. The closer the light source's speed gets to c, the closer to zero the elapsed time will be. As dauto noted, you failed to address this issue in your estimates of the time elapsed on the light's clock. There will also be some effect on the clock readings seen at A due to the time delay of light traveling from the light source to the observer at A; but if the light source is traveling at close to c, this effect will be small since the elapsed time on the clock moving with the light source is small anyway.
 
  • #4
PeterDonis
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Everything seems fine except the last experiment
No, the answer given to the first experiment is wrong too. See my previous post.
 
  • #5
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No, the answer given to the first experiment is wrong too. See my previous post.
No, it isn't. An arc seen from the center looks like a straight line.
 
  • #6
PeterDonis
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No, it isn't. An arc seen from the center looks like a straight line.
No, it doesn't, if you properly take into account the variation in distance from the "center" for a straight line.

In the arc case (case A), the distance of the light source from the observer remains constant. That means there is no apparent deceleration/acceleration; the apparent speed of the light source remains constant.

In the straight line case (case B), the distance of the light source from the observer changes. That means there is apparent deceleration/acceleration; the apparent speed of the light source does *not* remain constant (because the light-speed travel time changes).

If by "moving in a straight line" the OP actually mean "apparently moving in a transverse straight line, with no apparent deceleration/acceleration", then it would be a correct description for case A; but since he used the same language, "moving in a straight line", for the other cases, it did not seem as though he was aware of the difference if the apparent "straight line" is actually a circular arc. That's why I stressed that difference.
 

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