Special relativity and relative motion question

[kirsten_2009]

Homework Statement

Hello all,

I have a couple of questions that I am a little unsure of. Could you please let me know if my answers are correct? But more importantly could you let me know if my reasoning is correct? Thanks in advance!

1. Mort stands on Earth. Velma moves away from him in a rocket, at 299,000 km/s (1000 km/s slower than lightspeed). Mort sends a laser beam toward Velma. As the tip of the beam passes her rocket, Mort observes:

A.) the beam moving away at 300,000 km/s.
B.) the beam moving just 1000 km/s faster than Velma.
C.) Both of the above.
D.) the beam moving 300,000 km/s faster than Velma.
E.) All of the above.

2. The center of our galaxy is 30,000 light years away. Could a person possibly travel there in her own lifetime?
A.) No, because a person cannot travel at lightspeed. B.) No, because the trip would take longer than 30,000 years, and nobody lives this long.
C.) No, because time dilation applies only to clocks and not to biological phenomena such as a person's lifetime.
D.)Yes, by traveling faster than lightspeed, because of time dilation or the "relativity of time."
E.) Yes, by traveling at nearly lightspeed, because of time dilation or the "relativity of time."

Homework Equations

The Attempt at a Solution

1. (C) -Because Mort would observe the light beam moving away from his at the speed of light because of the principle of constancy of light speed but would also see it move 1000 km/s faster than Velma because of the different frames of reference? ...I don't know...special relativity is so bizarre... :S

2. (E) -It can't be (D) because I don't think anything can move faster than the speed of light correct? However, at just below the speed of light it would be possible for the person traveling to complete this trip according to their frame of reference...but not possible for those "observing" from Earth...?

Thank you very much!

 

[phinds]

Your answers and logic are solid. Velma would see the beam moving at c relative to her but velocity addition in SR is, as you seem to realize, not "additive" in the standard way but has to use Lorentz transforms, so Mort does see it as only 1000 faster than Velma. This is, of course, a bit misleading because Mort can't SEE the beam at all once it passes his eyes, he can only calculate it relative to the himself/Velma system and would would also know that SHE will see it moving at c. He could also calculate that if the beam were to hit a mirror on the spaceship and she turned on her own laser at the same time, he would get both beams arriving at c (but so heavily red-shifted that he might have to be a lizard to see them

The confusion comes about because of the difference between recession/closing velocities (which DO add without Lorentz transforms and can be larger than c) than relative velocities.

 

[kirsten_2009]

Thank you! Awesome explanation!