Time dilation in Special Relativity needs no Lorentz transformation |

Описание: In this video we derive and explain Time dilation effect in spacial relativity. Derivation using spacetime interval with explanation is provided. The formula for time dilation is obtained using spacetime interval in a generic scenario that applies to all specific cases, for examples light clock.
We specifically show how the time-dilation works not only between a pair of inertial frames but also between an inertial and a non-inertial frame, within the framework of special relativity. Of course the one applying the time dilation formula must be an inertial observer, but he/she can use it to calculate how much dilated his/her inertial clock time is compared to the accelerated/decelerated i.e. arbitrarily moving clock.
Although the derivation of time dilation formula using the famous Lorentz transformation equation or using the example of light clock i.e., photon bouncing in a moving train is completely correct, but those treatments essentially blind-spot you to the very important fact that the time dilation works for a non-uniformly moving objects also. This can be easily shown, with a little help from calculus, if we are to derive time dilation formula using spacetime interval between two events separated by a time-like interval.

0:00 Intro
1:22 Basics: On the reference frames in Special Relativity
2:35 How to deal with non-inertial frame in Special relativity
4:30 Deriving Time dilation - World-line of a non-inertial observer
5:28. Events appearing co-located to a non-inertial observer
7:33 Using invariance of spacetime interval for non-inertial observer
8:16 Magic of calculus - Slightly different inertial frames
10:53 Why time dilation occurs?
11:49 Time dilation formula
12:47 Time dilation for large spacetime interval
13:20 Time dilation also works when Lorentz invariance does not
14:37 Time dilation between two inertial frames
15:34 Time dilation from Lorentz transformation - shortcomings

Time Dilation
What is Time dilation?
Time dilation derivation
How to derive Time dilation formula?
Proof of Time dilation effect
Derivation of time dilation formula.
Explanation of time dilation.
Timelike interval between two events.
Spacelike interval between two events.
Invariance of spacetime intervals
What is rest frame?
Spacetime diagram for timelike seperated events
Non-inertial reference frames
Accelerated observer
Accelerated frame
Non-uniformly moving observer
Non-uniformly moving frame
Why you should not use Lorentz transformation equations to derive time dilation formula?
Special Relativity
Einstein
Spacetime diagram
Spacetime coordinates
World line of an observer

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