# Deriving Special Relativity Formulae Steps

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• Clever Penguin
In summary, the conversation discusses how the special relativity formulae are derived, specifically focusing on the equation for time (t) in relation to distance (d), speed (v), and the angle (θ) of a light clock. It is explained that in order to find t, the Pythagorean theorem should be used instead of an equation with two unknowns. The resulting formula is t0 = t(1- (v2/c2))-1/2.
Clever Penguin
I was bored, so I decided to derive the special relativity formulae.
I drew the following diagram of a light clock:

In order to find t, I did sinθ=d/ct
Which gives tsinθ=d/c
Which gives t=d/csinθ

If v = 0, vt = 0, and θ = 90
sin90 = 1
t = d/csinθ = d/c
We call this t0If v is greater than 0, vt is greater than zero, and θ is less than 90
sin90 is less than1
t = d/csinθ is greater than d/c

We use Pythagoras to get t0=t(1- (v2/c2))-1/2

What are the steps involved in getting to this answer?

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Clever Penguin said:
In order to find t, I did sinθ=d/ct
Usually both t and θ are considered unknowns. So writing one equation in two unknowns doesn't help. You should use the Pythagorean theorem instead to get one equation in one unknown.

Clever Penguin
Dale said:
Usually both t and θ are considered unknowns. So writing one equation in two unknowns doesn't help. You should use the Pythagorean theorem instead to get one equation in one unknown.

Valid point

so (ct)2 = d2 + (vt)2

Last edited:
Clever Penguin said:
Valid point

so (ct)2 = d2 + (vt)2
Yes. Then rearranging and using ##d/c=t_0## gives you the desired formula

Dale said:
Yes. Then rearranging and using ##d/c=t_0## gives you the desired formula

thanks

## 1. What is Special Relativity?

Special Relativity is a theory developed by Albert Einstein in the early 20th century that describes how space and time are affected by the motion of objects in the universe. It is based on the idea that the laws of physics are the same for all observers in uniform motion, regardless of their relative velocities.

## 2. What is the purpose of deriving Special Relativity formulae?

The purpose of deriving Special Relativity formulae is to understand the mathematical relationships between space, time, and velocity in the special case where objects are moving at constant speeds. This allows us to make precise predictions and calculations about how objects will behave in different reference frames.

## 3. What are the steps involved in deriving Special Relativity formulae?

The steps involved in deriving Special Relativity formulae include defining a reference frame, considering the relative motion of objects in that frame, using the principles of Special Relativity to derive equations for time dilation and length contraction, and then using these equations to derive the famous equation E=mc^2.

## 4. Why is it important to understand Special Relativity formulae?

Understanding Special Relativity formulae is important because it is a fundamental theory of modern physics that has been proven to be accurate through numerous experiments and observations. It also has many practical applications, such as in the development of GPS technology and nuclear energy.

## 5. Are there any limitations to Special Relativity formulae?

Yes, there are limitations to Special Relativity formulae. They only apply to objects moving at constant speeds in a straight line, and they do not take into account the effects of gravity. Additionally, they are based on the assumptions of a flat, non-accelerating universe, which may not accurately describe the entire universe.

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