Lorentz velocity transformations - relativity

In summary, the question asks for the speed of two spaceships, A and B, approaching each other with the same speed as measured by an observer on Earth. The "relative speed" refers to the speed of one spaceship measured by an onboard observer in the other spaceship's frame, and the "speed" of each spaceship refers to its speed relative to an observer at rest on Earth. Using the Lorentz transformation equation, u' = u-v / (1-uv/c^2), where u is the relative speed of the spaceships (0.70c), and v is the speed of one spaceship measured in the frame of the other, the speed of each spaceship can be calculated.
  • #1
tatiana_eggs
70
0

Homework Statement



Two spaceships approach each other, each moving with
the same speed as measured by an observer on the
Earth. If their relative speed is 0.70c, what is the speed of
each spaceship?

My current understanding of the problem.
S= wrt observer on Earth
S'=wrt one of the spaceships
u= ??
u'=speed of spaceship B if S' is wrt spaceship A.
v = speed of S' wrt S (how does v fit into this problem?)

Homework Equations



I'm great with the equations and algebra of Lorentz transformations, I'm just having trouble understanding/visualizing what the question is asking and assigning variables to knowns and unknowns.

u' = u-v / (1-uv/c2)

The Attempt at a Solution



I'd appreciate it if someone could reword the problem or answer me:

What does "their relative speed" mean? Is that their speed in S (wrt Earth) or relative to each other? Also, when "what is the speed of each spaceship" is asked, do they mean the speed of each spaceship relative to Earth or relative to each other? Lastly, are "with respect to" and "relative to" interchangeable terms?

Thanks a bunch
 
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  • #2
The relative speed usually means the speed of an object in the coordinate system bound to the other object. The task would be too simple oterwise.

So we already know the speed of each spaceship relative to the other (it's 0.70c) and you should derive their speed in S.
 
Last edited:
  • #3
tatiana_eggs said:

Homework Statement



Two spaceships approach each other, each moving with
the same speed as measured by an observer on the
Earth. If their relative speed is 0.70c, what is the speed of
each spaceship?

My current understanding of the problem.
S= wrt observer on Earth
S'=wrt one of the spaceships
u= ??
u'=speed of spaceship B if S' is wrt spaceship A.
v = speed of S' wrt S (how does v fit into this problem?)

Homework Equations



I'm great with the equations and algebra of Lorentz transformations, I'm just having trouble understanding/visualizing what the question is asking and assigning variables to knowns and unknowns.

u' = u-v / (1-uv/c2)

The Attempt at a Solution



I'd appreciate it if someone could reword the problem or answer me:

What does "their relative speed" mean? Is that their speed in S (wrt Earth) or relative to each other? Also, when "what is the speed of each spaceship" is asked, do they mean the speed of each spaceship relative to Earth or relative to each other? Lastly, are "with respect to" and "relative to" interchangeable terms?

Thanks a bunch

1- Let A and B be our spaceships. The "relative speed" here is the speed of spaceship B measured by an onboard observer in A's frame and vice versa.

2- The relative speed is meant to be the one belonging to B, for example, that an onboard observer on A measures in the frame of his own.

3- Here the "speed" of each spaceship refers to the speed measured with respect to an observer being at rest on the Earth.

4- In the textbooks around the topic of GR or SR, authors mostly prefer to use 'relative to' in place of with 'respect to'. But if you saw the latter somewhere, you wouldn't be panicking yourself as it is the same as 'relative to'.

But about the main question: Just make use of Maxim's idea.

AB
 
  • #4
Thanks so much, guys, that really helped me. I got the answer now.
 

Related to Lorentz velocity transformations - relativity

1. What is the concept of Lorentz velocity transformations in relativity?

Lorentz velocity transformations are a set of equations that describe how velocities appear to change when observed from different inertial reference frames in Einstein's theory of special relativity. They take into account the fact that the speed of light is constant for all observers, regardless of their relative motion.

2. How do Lorentz velocity transformations differ from Galilean transformations?

Lorentz velocity transformations differ from Galilean transformations in that they take into account the effects of time dilation and length contraction, which are predicted by special relativity. These effects become significant when objects are moving at speeds close to the speed of light, whereas in Galilean transformations, the laws of physics appear the same regardless of the observer's relative motion.

3. Can Lorentz velocity transformations be applied to any type of velocity, or only to velocities close to the speed of light?

Lorentz velocity transformations can be applied to any type of velocity, including velocities that are much smaller than the speed of light. However, their effects become more significant as the velocity approaches the speed of light.

4. How do Lorentz velocity transformations affect the concept of simultaneity?

In Lorentz velocity transformations, the concept of simultaneity is relative, meaning that events that appear to be simultaneous to one observer may not appear simultaneous to another observer in a different reference frame. This is a consequence of time dilation and length contraction, which cause time and space to appear differently for different observers.

5. What are some real-life applications of Lorentz velocity transformations?

Lorentz velocity transformations are used in various fields, such as astrophysics, where objects are moving at high speeds and special relativity must be taken into account. They are also used in the design of particle accelerators, as well as in the GPS system, which relies on precise timing measurements that are affected by time dilation.

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