Special relativity and relative motion question

In summary, the conversation discusses questions related to special relativity, specifically regarding the constancy of light speed and time dilation. The first question explores how Mort would observe a laser beam moving away from him at 299,000 km/s, taking into account the principle of constancy of light speed and different frames of reference. The second question considers the possibility of a person traveling to the center of the galaxy in their lifetime, with answers discussing the limitations of traveling at or near the speed of light and the concept of time dilation.
  • #1
kirsten_2009
137
2

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!
 
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  • #2
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.
 
  • #3
Thank you! Awesome explanation!
 

1. What is special relativity?

Special relativity is a theory proposed by Albert Einstein in 1905 that describes the relationship between space and time, and how they are affected by the motion of objects. It states that the laws of physics are the same for all observers in uniform motion, and the speed of light is constant for all observers regardless of their relative motion.

2. How does special relativity differ from classical mechanics?

Classical mechanics, also known as Newtonian mechanics, is based on the laws of motion proposed by Isaac Newton and works well for objects moving at low speeds. On the other hand, special relativity takes into account the speed of light, which is a constant and can have a significant impact on the behavior of objects moving at high speeds. It also explains phenomena like time dilation and length contraction, which are not accounted for in classical mechanics.

3. What is the principle of relativity in special relativity?

The principle of relativity states that the laws of physics are the same for all observers in uniform motion. This means that there is no preferred reference frame and all physical laws should be the same regardless of an observer's relative motion. Special relativity is based on this principle and uses it to explain the effects of relative motion on space and time.

4. How does special relativity explain the twin paradox?

The twin paradox is a thought experiment that involves one twin traveling at high speeds while the other stays on Earth. When the traveling twin returns, they find that they have aged less than their twin on Earth. Special relativity explains this by the fact that time is relative and can be affected by the speed of an object. The traveling twin experiences time dilation, where time appears to move slower for them compared to the stationary twin on Earth.

5. Can special relativity be applied to everyday situations?

Yes, special relativity can be applied to everyday situations. For example, the GPS system we use to navigate relies on special relativity to account for the time differences between satellites in motion and receivers on Earth. It is also used in particle accelerators, nuclear reactors, and other modern technologies. However, the effects of special relativity are only noticeable at extremely high speeds or in extreme gravitational fields.

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