Why do we move at the speed of light?

[Popper]

Sorry to bring this post back after such a long time, but I've been learning relativity (from Kleppner and Feynman) for the past month or so, and I understand this all a lot more now :).
A doubt I have though, is why Simon stated the four-velocity as $\gamma$(c,U) when (at least according to Kleppner) it should be $\gamma$(ic,U). (That's another doubt I have- why does Minkowski write it like that? Where did he derive it from?).

The purpose of the "i" is so that the magnitiude of a 4-vector uses the Eucliean metric, i.e. so that

|R| = sqrt[ (X⁰)² + (X¹)² + (X²)² + (X³)² ]

There are some textbooks who still use it. Basic Relativity by Richard A. Mould (1994) is one such example.

 

[Simon Bridge]

It's quite refreshing to see someone who understands that.

It was hard won!

There are some textbooks who still use [x0=ict].

... some lecture still use it too, as well as older papers and texts and books - so students still need to know about it.

 

[Popper]

I'm confused. What does It was shard won! mean? Perhaps my confusion is a cross cultural thing?

 

[Simon Bridge]

I'm confused. What does It was shard won! mean? Perhaps my confusion is a cross cultural thing?

I had to pry it out of my professor using a shard of glass ... the physics course requiring improvised weapons skills as a prerequisite. What you learn in combat stays with your for the rest of your life.

Or it was a typo...

 

[WannabeNewton]

I don't like the concept of a position 4-vector because you will frequently see threads asking "what happens to position vectors when we go to GR" creating quite a confusion since position vectors are meaningless in GR. It fully exploits the fact that Minkowski space-time is just the vector space $\mathbb{R}^{4}$ with a pseudo metric so the concept of a position 4-vector is far from general.

 

[HomogenousCow]

I had to pry it out of my professor using a shard of glass ... the physics course requiring improvised weapons skills as a prerequisite. What you learn in combat stays with your for the rest of your life.

Or it was a typo...

After doing some Jackson's problems I'm ready to use an improvised weapon on myself.

 

[phyti]

guitarphysics post 1:
The Minkowski spacetime graphic is an historical record of an object in motion in one spatial dimension (x), with a correlation between the x position and the (‘time’) ct position. This is sufficient info to eliminate ‘motion in time’ and motion at c.

If you decompose the constant ct light vector into a spatial component c1 (object motion) and c2 (object time), the components form a right triangle. This is the origin of ‘moving through space and time’ analogies used by Brian Greene and others .

Einstein developed the invariant interval in the form of an equality, X^2 - (ct)^2 = 0, with X the 3D spatial interval. Minkowski manipulated ct using complex variable notation to achieve a homogenous general form s^2 = ∑x^2, with ct treated as a mathematical ‘4th dimension’.