# Special relativity problems — More details below

• billllib
In summary: Galilean physics.In summary, the conversation discussed a problem involving special relativity and the calculation of speed. The formula for speed in special relativity was provided, as well as a link to a book for more information. The problem was then explained and it was mentioned that it could also be solved using Galilean physics. The formula for speed in Galilean physics was given, and the correct interpretation of the problem in Galilean terms was provided. The conversation then moved on to discussing resources for understanding Galilean physics and the specific calculation involved.
billllib
[Note from mentor: this was originally posted in a non-homework forum, so it lacks the homework template.]

Summary:: Special relativity problems. More details below

The formula for speed for special relativity is

V = (u-v) / (1-u*v) / (c^2)
Here the book http://www.people.fas.harvard.edu/~djmorin/Relativity Chap 1.pdf

pg 40
B)

I need to figure out the speed of D?

I don't even know how to do this in Galilean physics if D is not given.

The only thing I know about relative velocity is from this video.

Could someone start off explaining the problem in Galilean physics?
page 41

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So, the problem is:

A train (A) of (proper) length ##L## is overtaking another train (B) of (proper) length ##L##. The speeds of these trains are ##v_A, v_B##, say.

A person (D) walks along train B, starting when the front of train A reaches the rear of train B, and getting to the front of train B just at the rear of train A passes. I.e. D walks along train B in the time it takes A to overtake B. How fast does D have to walk?

1) We want to solve this problem in classical physics.

2) We want to upgrade the solution for SR.

3) We want to calculate the time of the overtaking from the perspective of A, B and D.

I created an image. Scene 2 I know is wrong but I don't know why the vectors are wrong?
I think to get D reference frame in gallian physics I go A = 4c/5. B = 3c/5.

The formula for galilian physics is V = u - v. Since the arrows are A----> <----V.

D = (A ) - (- B) --> A + B. Is this correct for classical physics? I think I solve the rest if this correct.End of summary of private message.

To solve the problem I go V = u+v / 1- uv / c^2.
Plugging in the variables I would go D = A+B / 1- AB / c^2.
Is this correct? In the private message I sent a picture describing vectors . I didn't get the velocity vectors correct. Could you explain what I got wrong in scene 2 of the pictures I sent ?

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Assuming you want ##D## to move along the length of ##B## in the time it takes ##A## to overtake ##B##, then in Galilean terms the velocity of ##D## is the average of ##A## and ##B##:

##v_D = \frac{v+u}{2}##

And, in ##D##'s reference frame, ##A## and ##B## move with equal and opposite velocities of magnitude ##\frac{v-u}{2}##.

You can check this by using the Galilean velocity addition. Using primes for velocities in ##D##'s frame we have:

##v'_A = v_A - v_D = v - \frac{v+u}{2} = \frac{v-u}{2}##

and

##v'_B = v_B - v_D = u - \frac{v+u}{2} = \frac{u-v}{2} = -v'_A##

The relativistic calculations are much harder, but are clearly explained by Morin.

Quick question, do you have a link or an online resource that explains the question in Galilean physics? What is the name of this specific calculation in Galilean physics?

## 1. What is special relativity and why is it important in science?

Special relativity is a theory proposed by Albert Einstein in 1905 that explains the relationship between space and time. It states that the laws of physics are the same for all observers in uniform motion and the speed of light is constant in all inertial reference frames. It is important in science because it has led to a deeper understanding of the fundamental principles of the universe and has been confirmed by numerous experiments.

## 2. How does special relativity affect our perception of time and space?

Special relativity states that time and space are relative concepts and are dependent on the observer's frame of reference. This means that time can appear to pass at different rates for different observers and the perceived length of an object can also vary based on the observer's motion. It also introduces the concept of time dilation, where time appears to move slower for objects moving at high speeds.

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

Special relativity deals with the relationship between space and time in inertial reference frames, while general relativity extends this concept to include acceleration and gravity. General relativity also includes the curvature of spacetime due to the presence of massive objects, while special relativity assumes a flat, uncurved spacetime.

## 4. What are some real-world applications of special relativity?

Special relativity has been essential in the development of modern technologies such as GPS systems, which rely on the precise synchronization of clocks in satellites and on the ground. It is also used in particle accelerators, nuclear reactors, and spacecraft navigation. Additionally, special relativity has helped scientists understand the behavior of objects moving at high speeds, such as in nuclear reactions and the formation of black holes.

## 5. Are there any controversies or limitations of special relativity?

While special relativity has been extensively tested and confirmed, there are some areas of physics where it does not fully account for the observed phenomena. For example, it does not incorporate the effects of quantum mechanics or gravity. There are also ongoing debates about the compatibility of special relativity with other theories, such as string theory. However, overall, special relativity remains a crucial and widely accepted theory in modern physics.

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