# Special relativity (A.P. French 7.5)

In summary, the problem asks to express the recoil and scattering angles in terms of the corresponding angles in the zero-momentum system, and show that they reduce to the non-relativistic equivalents when v<<c. This is done by considering the collision in the center-of-mass frame and then transforming to the lab frame.

## Homework Statement

A particle of rest mass m and velocity v collides elastically with a stationary particle of rest mass M. Express the recoil and scattering angels in terms of the corresponding angles in the zero-momentum system. Show that your answers reduce to the non-relativistic ones if v<<c

## Homework Equations

I think I have to show that (mc^2)/(1-(v/c)^2)^1/2 reduces to .5mv^2 by using the binomial theorem when v<<c. since momentum is related to kinetic energy.

## The Attempt at a Solution

That's not what the question is asking you to do. In the center-of-mass system, say the particle with mass m scatters at an angle of ##\theta'##. What happens to the other particle? Now what does this collision look like as seen in the lab frame? What angle ##\theta## in the lab frame corresponds to the angle ##\theta'## in the COM frame?

Once you figure that out, you're supposed to show it reduces to the non-relativistic equivalents when v<<c.

## What is special relativity?

Special relativity is a theory proposed by Albert Einstein in 1905 to explain the relationship between space and time. It is based on two main principles: the constancy of the speed of light and the relativity of motion. It is a fundamental theory in physics that has been extensively tested and verified.

## How does special relativity differ from classical mechanics?

Special relativity differs from classical mechanics in that it is based on the concept of spacetime, where space and time are interconnected. It also introduces the idea that the laws of physics are the same for all observers in uniform motion, regardless of their relative velocity. In contrast, classical mechanics assumes that time and space are absolute and that the laws of physics are the same for all observers.

## What is the role of the speed of light in special relativity?

The speed of light, denoted by c, is a fundamental constant in special relativity. It is the maximum speed at which all matter, energy, and information in the universe can travel. This speed is the same for all observers, regardless of their relative motion. Special relativity uses the speed of light to define the relationship between space and time.

## What is time dilation in special relativity?

Time dilation is a phenomenon predicted by special relativity where time appears to run slower for objects that are moving at high speeds. This means that a clock on a fast-moving object will tick slower than a clock at rest. This effect is only noticeable at speeds close to the speed of light and has been confirmed by numerous experiments.

## Can special relativity be applied to everyday situations?

Yes, special relativity is applicable to everyday situations. While its effects may not be noticeable in our daily lives, they are taken into account in many technologies, such as GPS systems, which rely on precise time measurements. Special relativity is also crucial in understanding the behavior of particles at high speeds, such as those in particle accelerators.

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