Special Relativity: Relative speeds of particles

In summary, the problem is to show the relative speed of one particle with respect to the other when fired at the same time from a point in orthogonal directions with equal speed u. The given solution involves using the Lorentz Transformation Equations. The student attempts to solve the problem by choosing a frame where one particle is at rest and transforming the velocity of the other particle with respect to this one. However, they run into confusion with the two-dimensional nature of the problem and lack of understanding of velocity sums. The solution may involve simply plugging into a formula for relative velocity calculation.
  • #1
comwiz72
17
0

Homework Statement



OK, we have started all this special relativity stuff, and I must admit I am confused, all this Inertial Reference Frame stuff :S

Here's the problem:
Two particles are fired at the same time from a point, with equal speed u, in orthogonal directions.

Show that the relative speed of one particle with respect to the other is:

u[tex]_{R}[/tex] = u(2 - [tex]\frac{u^{2}}{c^{2}}[/tex])[tex]^{\frac{1}{2}}[/tex]

Homework Equations



Lorentz Transformation Equations
The given solution

The Attempt at a Solution



OK, well what I have gathered is that I must pick for the observer a frame where one of the particles is at rest, right? And then I tried to transform the velocity of the other particle with respect to this one.
So I tried, using normal non-relativistic ideas, to obtain via Pythagoras the relative speed, which was [tex]\sqrt{2u^{2}}[/tex]. Then I tried to operate using gamma on this velocity. However, it did not seem to get me anywhere :S
I'm bad at explaining this :S but I thought that maybe my problem was that I chose a frame which is at rest, but one particle is still moving inside the frame (?) if that makes any sense. The fact that the particles are in two dimensions is the confusion, I could calculate the relative velocity if they were in one axis just fine, my problem is this second direction.

Any guidance? I don't want the answer, that won't help me understand this tricky subject, just a little hint on all this I.R.F. stuff and what I've done wrong.
 
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  • #2
Have you derived the rules for addition or subtraction of velocities? If you have, you need to make sure you understand them. If not, you are probably expected to simply plug into the formula for relative velocity calculation. No doubt, the formula itself will be found in your text.
 
  • #3
Hmm, we didn't go over velocity sums in class, and i don't see any formula for it :S
 

1. What is the theory of special relativity?

The theory of special relativity is a fundamental concept in physics that describes the relationship between space and time. It was first introduced by Albert Einstein in 1905 and has since been widely accepted as a key theory in understanding the behavior of particles and the laws of physics.

2. How does special relativity explain the relative speeds of particles?

Special relativity explains the relative speeds of particles by stating that the laws of physics are the same for all observers in uniform motion. This means that the speed of light is constant for all observers, regardless of their relative motion. Therefore, the relative speeds of particles can be calculated using the principles of special relativity.

3. What is the difference between special relativity and general relativity?

Special relativity deals with the relationship between space and time for observers in uniform motion, while general relativity includes the effects of gravity and acceleration. In other words, special relativity is a special case of general relativity when there is no acceleration or gravity present.

4. Can special relativity be tested and proven?

Yes, special relativity has been extensively tested and has been proven to be accurate in its predictions of the behavior of particles. One of the most famous experiments that tested special relativity is the Michelson-Morley experiment, which confirmed the constancy of the speed of light.

5. How does special relativity impact our understanding of the universe?

Special relativity has had a profound impact on our understanding of the universe. It has provided a framework for understanding the behavior of particles and has led to the development of other important theories such as quantum mechanics. It has also challenged our traditional ideas about space and time and has opened the door for further exploration and discoveries in the field of physics.

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