Universal Speeding: The Lorentz Group

 There are two important, well-known rules about interstellar travel:

1.  Nothing can travel faster than light.
2.  If you want to get anywhere interesting in a reasonable amount of time then you need to go faster than light.

This leads to three options:

1.  You just can't go anywhere. 
2.  You can go someplace nearby, but you have to stay on your ship for a very long time. 
3.  You must break rule one.

Option 1 can be rejected as boring.  Option 2 I've already looked at in the form of generation ships.  Let's talk about Option 3: If the speed of light is the universal speed limit then let's start speeding.  Before we can exceed the speed limit we need to know what the speed limit is, and why it's the limit.  So why can't anyone go faster than the speed of light?  Let's have a look.

Let's begin with some very basic concepts in Special Relativity, because we'll need them later.  Typically this is introduced in introductory classes at the university and high school level by arbitrarily introducing something called the Lorentz Factor, γ.  A better introduction might show how γ can be derived from Galilean Relativity and Lorentz Invariance as we did in the previous post.

While this approach is useful and instructive for discussing ideas like time dilation and length contraction, and while it does demonstrate why we shouldn't be able to exceed the speed of light, it doesn't help us understand the source of these issues much less suggest a way to solve them.  

To do that, we'll need to introduce the formal language of four-vectors to discuss in detail how time and space are connected.

Universal Speeding: Using The Four-Force

 There are two important, well-known rules about interstellar travel:

1.  Nothing can travel faster than light.
2.  If you want to get anywhere interesting in a reasonable amount of time then you need to go faster than light.

This leads to three options:

1.  You just can't go anywhere. 
2.  You can go someplace nearby, but you have to stay on your ship for a very long time. 
3.  You must break rule one.

Option 1 is boring, so we'll ignore it.  Option 2 is something we're already looking at.  For now, let's talk about Option 3: If the speed of light is the universal speed limit then let's start speeding. 

Before we can exceed the speed limit we need to know what the speed limit is, and why it's the limit.  So why can't anyone go faster than the speed of light?  Let's begin with some very basic concepts in Special Relativity, because we'll need them later.  We've already shown how the Lorentz Factor γ can be derived from Galilean Relativity and Lorentz Invariance.  While this approach is useful and instructive for discussing ideas like time dilation and length contraction, it only tells us that going faster than light should be strange, not why we simply can't get there.

Universal Speeding: An Introduction to Relativity

There are two important, well-known rules about interstellar travel:

1.  Nothing can travel faster than light.
2.  If you want to get anywhere interesting in a reasonable amount of time then you need to go faster than light.

This leads to three options:

1.  You just can't go anywhere. 
2.  You can go someplace nearby, but you have to stay on your ship for a very, very long time. 
3.  You must break rule one.

Option 1 is boring, so we'll ignore it.  I've already spoken at some length about Option 2 and generation ships, and probably will speak about it again.  For now, though, let's talk about Option 3: If the speed of light is the universal speed limit then let's start speeding. 

Before we can exceed the speed limit we need to know what the speed limit is, and why it's the limit.  So why can't anyone go faster than the speed of light?  Well, why not have a look?

Let's begin with some very basic concepts in Special Relativity, because we'll need them later.  Typically this is introduced in introductory classes at the university and high school level by arbitrarily introducing something called the Lorentz Factor, γ.  Let's start by trying to understand where this magical factor comes from and why it stops us from going faster than light.

  Einstein's theory of Special Relativity is required by two postulates: Galilean Relativity and Lorentz Invariance.