Thread by @KidRebellion

In the theory of #specialRelativity, time (t) and the well-known spatial coordinates (x, y, z) are all treated equally. Just as particles can have physical quantities in space such as position, velocity, momentum, acceleration, etc.

Particles can also have a component of these quantities along the time axis. Indeed everything we see is moving all the time, even the stationary bodies. Stationary bodies are stationary in space (with respect to us only), but they move all the time along the time axis.

Since time can't be separated from our measurement of the universe, how can we visualize that new axis? We live in a 3D space and our minds aren't capable of realizing extra dimensions, hence there's no way to depict the 4 dimensions all at once.

We have to omit at least one spatial axis so we can have a grasp on how time and space are related to each other. Therefore, we use #spacetime diagrams.
This figure shows a spacetime diagram with 2 spatial axes lying on the yellow plane and a time axis perpendicular to that plane

This spacetime diagram is obtained by omitting 2 spatial axes. So we only have 1 spatial axis (x) and 1 temporal axis (ct), where (c) is the speed of light in vacuum. The time (t) is multiplied by (c) to maintain homogeneity of physical units.

Now the question is, how to interpret those diagrams?
The first thing that can be noticed is the light cone. The upper half (called nappe) represents positive values (future), whereas the lower nappe represents negative values (past). And the present is at the apex (t = 0).

The apex is where the tips of the two cones meet (the blue point). Also, there's the generatrixes (the red lines that makes up the cone) which is the path that light always takes in spacetime. That's why it's named as "light cone".

The last thing is, how interpret the motion of a particle in that diagram?
The trajectory of a particle in the spacetime diagram is called a "world line". There're 4 cases for world lines that can give a good understanding of those diagrams.

Case A: a particle with a world line along the time axis means it's only moving in time but stationary in space. This applies to any particle which isn't moving with respect to us (v = 0).

Case B: a world line inside the light cone implies a motion in both time and space. Such particles are called "timelike" particles. This includes any particle moves with velocity less than the speed of light (v < c).

Case D: a world line along the light cone generatrix. Only massless particles (such as light -photons-) can take this world line! Such particles are called "lightlike" for obvious reasons. Lightlike particles travel in spacetime at the speed of light (c).

Case C: a world line ouside the light cone. These are non-physical particles, they can NEVER exist according to the theory of special relativity. These non-physical particles are called "spacelike". They travel with velocity greater than the speed of light (v > c).

Done ✔
Fig 1, 2 from google photos.
Fig 3 from:
"Covariant Physics: From Classical Mechanics to General Relativity and Beyond" by Moataz H. Emam, professor of physics at SUNY
Which I recommend if you want to learn about relativity from scratch.

#Physics #Einstein #Science

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