# Derivation of relativity equation

• musicmar
In summary, the conversation is about combining equations 4.4 and 4.5 to derive equation 4.22. The attempt at a solution involves solving for E^2 and (pc)^2 and then subtracting them to get the desired result.
musicmar

## Homework Statement

Combine Eqs. 4.4 and 4.5 to derive Eq. 4.22

## Homework Equations

4.4: p= m u/ (sqrt(1-(u2/c2)))
4.5: E= m c2/ (sqrt(1-(u2/c2)))
4.22: E2-(pc)2= (mc2)2

## The Attempt at a Solution

(sqrt(1-(u2/c2))) = mu/p

(sqrt(1-(u2/c2))) = mc2/E

1 - u2/c2 = m2u2/p2

1 - u2/c2 = m2c4/E2

u2/c2=1-m2u2/p2

u2/c2=1-m2c4/E2

Now combining:

1 - m2u2/p2 =
1 -m2c4/E2

m2u2E2=m2c4p4

Clearly, this is not Eq. 4.22 above. So, I either made a small mistake somewhere or missed a larger concept.

Thank you.

Just a small mistake. You're not trying to solve these equations, so equating them isn't quite the right direction.

You're trying to show that $$E^2 - (pc)^2 = (mc^2)^2$$
Use your two other equations to solve for E^2, and (pc)^2; then subtract them. The right answer will pop out.

## 1. What is the derivation of the relativity equation?

The derivation of the relativity equation involves using mathematical principles to explain the relationship between space and time in the theory of relativity. It was first derived by Albert Einstein in his famous paper "On the Electrodynamics of Moving Bodies" in 1905.

## 2. Why is the relativity equation important?

The relativity equation, also known as the Lorentz transformation, is important because it provides a mathematical framework for understanding the effects of relative motion on space and time. It is a fundamental principle of modern physics and has been used to make accurate predictions in various fields, such as astronomy and particle physics.

## 3. How is the relativity equation derived?

The relativity equation is derived using the principles of special relativity, which state that the laws of physics should be the same for all observers, regardless of their relative motion. It involves manipulating and solving equations based on the speed of light and the concept of time dilation and length contraction.

## 4. Can the relativity equation be simplified?

The relativity equation can be simplified in certain situations, such as when the relative velocities between two objects are much smaller than the speed of light. In this case, the equations of motion can be simplified using the principles of classical mechanics. However, in cases where the relative velocities are close to the speed of light, the full relativity equation must be used.

## 5. Are there any real-world applications of the relativity equation?

Yes, there are many real-world applications of the relativity equation. For example, it is used in GPS systems to account for the time dilation effects of satellites orbiting the Earth. It is also important in particle accelerators where particles reach speeds close to the speed of light. Additionally, the relativity equation has been confirmed by numerous experiments and is a crucial component of our understanding of the universe.

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