Lorentz transformation, special relativity problem

In summary, the problem involves two frames, S and S', moving with respect to each other in the x-axis with some velocity. An event occurs in S' at x'_1 = 1.0 c*year at t'_1 = 1.0 year, and another event occurs at x'_2 = 2.0 c*year at t'_2 = 0.5 year. The two events are simultaneous in S. The origins of S and S' are coincident at time t' = t = 0. Using the equations t' = \gamma \left(t - \frac{vx}{c^2}\right) and x' = \gamma \left(x - vt \right),
  • #1
mhen333
16
0

Homework Statement


Frame S and S' are moving with respect to each other in the x-axis with some velocity. An event happens in S' at x'_1 = 1.0 c*year at t'_1 = 1.0 year. Another event happens at t'_2 = 2.0 c*year at t'_2 = 0.5 year. The two events are simultaneous at some point in S. The origins of S and S' are coincident at time t' = t = 0. Find the relative velocity of the frames, and the time in S when the events are noticed.


Homework Equations



[tex] t ' = \gamma \left(t - \frac{vx}{c^2}\right)[/tex]
[tex] x ' = \gamma \left(x - vt \right)[/tex]

The Attempt at a Solution



I really didn't even know where to start. I know that t_1 and t_2 as seen from S are equal, because the events were simultaneous. I tried listing out the equations, but I don't have enough equations for the amount of variables that I need to solve for. The assignment has already been turned in, and I know the answer of V (it was given in the back of the book), but I'd really like to know how to do the problem.
 
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  • #2
You have

[tex]\begin{align*}
t'_1 &= \gamma\left(t_1 - \frac{vx_1}{c^2}\right) \\
t'_2 &= \gamma\left(t_2 - \frac{vx_2}{c^2}\right)
\end{align*}[/tex]

Subtract the first equation from the second. What do you get?
 
  • #3
I get the right answer, thanks a ton!

I just need to do a lot more problems until I get comfortable with it, I think.

Thanks again!
 

1. What is the Lorentz transformation in special relativity?

The Lorentz transformation is a mathematical equation developed by Dutch physicist Hendrik Lorentz, which describes how the measurements of time and space change from one inertial reference frame to another. It is a fundamental principle of Einstein's theory of special relativity.

2. Why is the Lorentz transformation important in special relativity?

The Lorentz transformation is important because it explains how the laws of physics remain the same for all inertial observers, regardless of their relative motion. It also plays a crucial role in predicting phenomena such as length contraction, time dilation, and the relativity of simultaneity.

3. How does the Lorentz transformation differ from Galilean transformations?

The Lorentz transformation differs from Galilean transformations in that it takes into account the speed of light as a constant, rather than assuming that it is infinite. This leads to the concept of space and time being relative to the observer's frame of reference, rather than absolute.

4. Can the Lorentz transformation be applied to any kind of motion?

The Lorentz transformation can only be applied to motion that is inertial, meaning that the velocity of the object is constant. It cannot be used for objects that are accelerating, as this would require the use of the more complex equations of general relativity.

5. Are there any real-life applications of the Lorentz transformation?

Yes, the Lorentz transformation has many real-life applications, particularly in the fields of particle physics and high-speed technology. For example, it is used in the design and operation of particle accelerators, GPS systems, and spacecraft navigation. It also plays a crucial role in understanding the effects of near-light-speed travel on astronauts and their equipment.

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