💭 Einstein's 2 postulates:

<aside> <img src="https://s3-us-west-2.amazonaws.com/secure.notion-static.com/e0a74fa7-aa8d-441d-8450-6db299ce4a75/Postulate_1.png" alt="https://s3-us-west-2.amazonaws.com/secure.notion-static.com/e0a74fa7-aa8d-441d-8450-6db299ce4a75/Postulate_1.png" width="40px" /> Postulate 1: all inertial frames are equivalent. The results of experiments do not depend on which inertial frame they are carried in

</aside>

<aside> <img src="https://s3-us-west-2.amazonaws.com/secure.notion-static.com/126da0a7-0719-48e8-a9d4-03d1cceb00ae/Postulate_2.png" alt="https://s3-us-west-2.amazonaws.com/secure.notion-static.com/126da0a7-0719-48e8-a9d4-03d1cceb00ae/Postulate_2.png" width="40px" /> Postulate 2: Speed of light in empty space is the same in all inertial frames

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from this we can conclude all the following phenomenon's:

https://www.youtube.com/watch?v=uTyAI1LbdgA&t=548s&ab_channel=ScienceClicEnglish

⌛ Time Dilation:

$$ \boxed{\Delta t=\gamma \Delta t_0} \qquad\qquad \gamma=\frac{1}{\sqrt{1-\left(\frac{v}{c}\right)^2}}

$$

An interactive demonstration of time dilation, change the sliders and see what happens!

An interactive demonstration of time dilation, change the sliders and see what happens!

Example:

A star exploded into a supernova and emits 2 wave of gas 5 seconds apart, you are travelling in a spaceship at $V=\frac{\sqrt{3}}{2}c$ away from the explosion. You measure the time it takes for the supernova to emit the second wave, what value do you get

Time Dilation 1.png

🍎 In classical physics we would expect it to the same amount of time $\Delta t=\Delta t'=5\text s$

🔭 In classical physics if we assume information is transmitted at the speed of light we would have to consider that during the first and second wave the ship had moved so in the second it would have to travel a larger distance: $d=V\times \Delta t$ and during that extra distance light would need to catch up with the ship so it would go through that distance at speed $v=c-V$ which means: $\Delta t'=\Delta t+\frac{d}{v}=\Delta t+\frac{V\times\Delta t}{c-V}=\frac{c\times \Delta t}{c-V}=37.3\text s$

✨ In relativist physics we have:

$$ \Delta t'=\gamma\Delta t=\frac{\Delta t}{\sqrt{1-\frac{v^2}{c^2}}}=\frac{5}{\sqrt{1-\left(\frac{\sqrt{3}}{2}\right)^2}}=\boxed{10\text s} $$

📏 Length contraction:

$$ \boxed{L=\frac{L_0}{\gamma}} \qquad\qquad \gamma=\frac{1}{\sqrt{1-\left(\frac{v}{c}\right)^2}} $$

https://www.desmos.com/calculator/ucnzonhsoj

Example: