Lorentz Transformations Acceleration: A simple problem

In summary: If the answer is yes then you can move on to the next step. If not then you need to find a way to convert the coordinate accelerations into proper accelerations before you can solve for the light path.
  • #1
Albertgauss
Gold Member
290
37
Hi all,

I came up with the following problem myself and am trying to solve myself. I haven't seen it in any txtbook, grad or undergrad.

Suppose you have the ground frame (Earth).
Earth sees ship1 start at t=0, v=vo1, at x=xo1.
Earth sees ship2 start at t=0, v=vo2, at x=xo2

All velocities are near c. All objects travel along the x-axis only. Let ship2 start ahead of ship1, that is xo2 > xo1.

Earth sees ship2 begin to accelerate at a constant acceleration A at t=0.

If ship1 sends a radio signal (light speed) to ship2, at what position and time will all frames----- Earth, ship1, and ship 2--- say the signal arrives at ship2?

I can easily get x,t v,a for ship 2 as the Earth measures them. That's pretty common, but I can't find any lorentz-transformations for the same set of variables in the frame of ship1 or ship2. I'm willing to do the hard work, but can someone guide me to a resource or some help with how to get X,t for the different frames for such a situation?
 
Physics news on Phys.org
  • #2
Ah yes, The great Albert Guass, one of the greatest mathematicians and physicits of the 1900s :)

I think MTW treats accelerated frames in special relativity. You might find some answers there.
 
  • #3
Since you are asking for an approach I would first calculate everything in coordinate time, which would be simplest if you take the ground frame.

So you first need to convert the proper accelerations from the rockets into coordinate accelerations which are not constant but decreasing with coordinate time. Then you need to setup the equations for the two spaceships in terms of location and coordinate time. Then pick a point where you want a light signal to leave, with that you can setup the equation for the light path and use this to solve where this light meets the other rocket.

Once you got that you need to convert the coordinate times into proper times.

So the fist thing I would ask you is do you know how to express an equation for a rocket with constant proper acceleration in terms of the ground frame?
 
Last edited:

1. What are Lorentz Transformations?

Lorentz Transformations are equations used in special relativity to describe how the measurements of space and time of an event change for different observers in relative motion.

2. How do Lorentz Transformations account for acceleration?

Lorentz Transformations take into account the acceleration of an object by incorporating the concept of proper time, which is the time measured by a clock co-moving with the object.

3. What is a simple problem that involves Lorentz Transformations and acceleration?

A simple problem involving Lorentz Transformations and acceleration is calculating the change in an object's mass and length as it accelerates to near the speed of light.

4. How do Lorentz Transformations affect our understanding of time and space?

Lorentz Transformations demonstrate that time and space are relative and can appear differently to observers in different frames of reference. This challenges our traditional understanding of time and space as absolute concepts.

5. Are Lorentz Transformations only applicable to objects traveling at near the speed of light?

No, Lorentz Transformations can be used for any situation involving relative motion, regardless of the speed. However, their effects become more pronounced at higher speeds, such as those approaching the speed of light.

Similar threads

  • Special and General Relativity
3
Replies
101
Views
2K
  • Special and General Relativity
2
Replies
54
Views
1K
  • Special and General Relativity
Replies
10
Views
548
  • Special and General Relativity
Replies
6
Views
1K
  • Special and General Relativity
Replies
5
Views
948
  • Special and General Relativity
Replies
22
Views
1K
  • Special and General Relativity
Replies
33
Views
2K
  • Special and General Relativity
Replies
3
Views
948
  • Special and General Relativity
Replies
24
Views
2K
  • Special and General Relativity
Replies
20
Views
1K
Back
Top