Seeing Light-speed
Sadly, it's impossible to go to light-speed. When you do, things break.
In order to see light-speed, this story uses magic velocity units. Don't worry about how fast they are; all you need to know is that light moves at about 100mvu.
Relativity
In our universe, everything is relative. This was famously summed up by Albert Einstein in two basic postulates:
- The laws of physics treat all things in uniform motion the same.
- The speed of light is the same everywhere.
These seem obvious-- of course, the laws of physics don't play favorites! Einstein's main contribution to relativity was how he used the two postulates in a system to construct his theory of Special Relativity.
Let's start with normal, not-light-speed relativity.
Even though everyone gets different measurements, Taylor is always moving 20 mvu faster than Bob, and Allie is always moving 20 mvu faster than Taylor.
That's relativity! In space, there's no objective concept of "stationary"-- even our planet is moving around. To be accurate, you have to measure movement relatively. For example, Taylor is moving at 20 mvu according to Bob.
Even though relativity was well-known before Einstein made his theory, he wanted to re-state it for the sake of clarity. The most important idea is the second postulate:
Special Relativity
Taylor and Bob still move relatively to one another. However, the light particle always moves at 100 mvu from everyone's perspective.
If you're moving at 3 mvu (relative to me), any light that we see is moving at 100 mvu relative to both of us. This is different from if Allie was moving at 4 mvu relative to me: that would only be 1 mvu from your view.
Light's different rules make things weird.
So far, the space simulations have been ignoring a lot of the weird physics that come into effect at these speeds. Human brains aren't used to relativistic physics since we spend all our time at lower speeds.
In order to start looking at relativistic speeds realistically, let's meet the hero of our story.
Time Dilation
Maybe you've heard of this one in sci-fi movies like Interstellar books or Ender's Game. Put simply, a moving clock runs slower.
If Bob wants to get to Allie's house in 5 minutes, first he has to ask "5 minutes according to who?" If we're looking from Taylor's perspective, Bob takes gamma(0.8) seconds to cross the screen once, but Bob sees himself as taking only 1 second.
This time dilation factor follows a standard equation:
If Bob measures how long his own movement takes, that measurement is the proper time-- it's the smallest that anyone can measure for that movement (T0). Anybody else who is moving relative to Bob will measure something larger (T).
In daily life, we don't notice the differences in time measurements since they're tiny. But when you're travelling space, they're much larger! Even signals like GPS have to account for time dilation, since they use accurate clocks to triangulate your location.
Length Contraction
Velocity is distance divided by time. If c must remain the same, and time is relative, then distance must be relative too!
From an observer's perspective, the distance being compressed shows as the moving "squishing" in the direction of motion.
From Bob's perspective, his "squish" (or "contraction") will always be 100%-- he'll stay the same as normal. Because time can never run backwards, length can never be increased-- only decreased. From Taylor's perspective, Bob is around 1/gamma(0.8)*100% as long as he would be at rest.
Bob's own conception of his length is called the rest length; it has the symbol L0. Anybody else's measurement will be called the contracted length, and given the symbol L.
Just like time dilation, length contraction follows a standard formula:
Mass Expansion
The law of conservation of momentum is a fundamental part of physics. In any system, momentum must be preserved.
Because momentum is mass times velocity, and because velocity is relative to the speed of light, for momentum to stay the same, mass must change.
This visualisation shows mass as an overlay.
Because time only dilates (goes up) and never contracts (goes down), mass will always expand when an object goes faster.
Bob will still measure his mass as the same value (the rest mass, or M0), but a moving observer will see that he's more massive. This measurement is called the expanded mass, or M.
In this equation, if Bob sees himself as being 60kg, Taylor will see him as gamma(0.8)*60kg!
This expansion follows a similar equation:
In Conclusion,
Once Bob gets through physics demonstration space and gets to Allie, everyone gets in their spaceships. Feel free to play around with this simulation! It's mostly physically accurate (gravity isn't counted).
(In case you were curious, the reference frame of the sliders is separate from any of the spaceships)