I've always known a little bit about special relativity, but at one point started getting pretty interested in it,
learning more about how certain things affect time and space. Not just gravity, but speed as well. Then how exactly
it affects time and space. How going quickly causes Time Dilation and length Contraction, both fascinating concepts,
where simply moving at a really fast speed will change and warp both time and space.
Keep in mind this is simply my understanding of how it works, I may be wrong or innacurate.
Time Dilation, at least in terms of speed, is basically how time is affected when moving at very high speeds. Time Dilation
can be found by using Lorentz's equation, being
y = 1 / SQRT ( 1 - ( v^2 / c^2 ) )
V^2 / c^2 can also just be replaced with the percentage of the speed of light you are travelling squared. So for 90%, you just put
0.9^2.
This will then result in a factor, for example, if you plug in 0.87, or are travelling 87% the speed of light, it will result in
a Lorentz Factor of 2. Which basically means that for every two seconds on the 'ship' only one second passes on earth.
This factor may seem small, but beings to exponentially increase the closer you get to the speed of light, get up to 99.99% the speed of
light, and you get a Lorentz factor of 70.7. 99.999% the speed of light however, gets up to 223.6
I'll try to explain why Time Dilation occurs, the easiest explanation I found, was by using a Photon clock. This is basically two mirrors
facing each other, with a Photon bouncing between them. Assume every time the Photon hits the buttom mirror, thats a tick, or a 'second.'
Now (Relative to earth) The Photon will just travel up, then down, between the mirrors. However, if you put the Photon Clock on something
moving very fast, it also has a horizontal motion as well. Inside the ship, it looks normal, but relative to earth, you would be able to see
the Photon moving in a diagonal path. This increases the distance the Photon has to travel.
So basically, the faster you move the longer the Photon takes, if you were moving 87% the speed of light, every two ticks on earth, would only
be one tick in the ship.
This affects everything though, as information has to travel, even though it moves very quick, the increase velocity causes it to travel a longer
distance. This means everything moving at that velocity takes long to 'compute.' Which causes time to slow down for everything moving at that speed.
Gravity and Spactime. This has been soemthing I've been more familiar with for a while, how Gravity affects both space and time. For instance, Travelling near a black hole, with such intense gravity, will greatly slow down time for you. Take the movie Interstellar as a good example. One representation of Gravity, although a little bit innacruate, is like a trampoline. The Greater the gravity, the more it pushes down on the trampoline, or 'space.' This is kind of a visual representation to show how nearby things will be drawn to it.
| Time Dilation: | Calculator |
| Length Contraction: | Calculator |
| Aweseome Channel: | Mahesh Shenoy |
Length Contraction is something I know less about, but basically, when moving at very high speeds, that will warp how you see space. The main cause
of this affect, is that no matter the reference point, Light will appear to be treaveling at the speed of light. Even if you are travelling at nearly
the speed of light, then light will still appear to be travelling at the speed of light. As I said I don't know much about how exactly it works, but
but that will cause space to become a bit warped and strange from the view of the ship.
UPDATE: I have learned more about length contraction, and it is genuinly very fascinating. As much as time dilation is even.
Turns out length contraction works in a very similar way. The basis, the faster you travel, the less distance you have to cover. It is
nearly negligible at small speeds, but once you get up to the speed of light, it changes things remarkably. The forumla for it is simple.
L = L0 * SQRT( 1 - (v^2 / c^2) )
Basically the length (relative to the traveller) is equal to the proper length. (length relative to a staitionary observer.) times
by the rest of that formula. So the square root of 1 - speed squared divided by the speed of light squared.
This is super interesing, the faster you travel, the less distance you have to travel in total. So not only do you get their faster becouse
you are travelling faster, but you also have less distance to cover overall.
I even coded a simple calculator to calculate this for you, I found out that when running a hundred meters, so at an average speed of
about 3 m/s. You are actually travelling about 5 Femtometers less then 100 meters. This is negligible, but still really
fascinating.
As I said above, the reason this happens, is becouse no matter the reference point or frame taken. Light will always appear
to be travelling at the speed of light. Becouse of this, space and time have to change to make it all work together.