Motion of Null, Timelike & Spacelike Particles

[Nusc]

For a null particle, ds^2 = 0,
Timelike, ds^2 >0,
spacelike, ds^2 < 0,

how would you characterize the motion of each particle?

 

[Ibix]

For a null particle, ds^2 = 0,
Timelike, ds^2 >0,
spacelike, ds^2 < 0,

how would you characterize the motion of each particle?

How have you attempted to answer this question? What are the relevant formulae?

 

[Nusc]

How have you attempted to answer this question? What are the relevant formulae?

Null Particles move at speed c, time-like particles move at speed slower than c, space-like move faster than c (tachyons)

The equation is the metric. ds^2 = g_ab dx^a dx^b

I only mentioned the speed, but not the trajectory. What are null trajectories?

 

[Ibix]

Null Particles move at speed c, time-like particles move at speed slower than c, space-like move faster than c (tachyons)

Yes. Note that tachyons are purely hypothetical.

I only mentioned the speed, but not the trajectory. What are null trajectories?

They are the trajectories of something. What do you think?

 

[Nusc]

In 2D Minkowski Space you can calculate the metric.

Ok nevermind I got it.

How would you do this in 4 D though?

 

[Ibix]

How would you do this in 4 D though?

How would you do what?

 

[Mister T]

Null Particles move at speed c, time-like particles move at speed slower than c, space-like move faster than c (tachyons)

I'm familiar with the adjectives timelike, spacelike, and lightlike. They are used to described intervals between events. If, for example, two events have a timelike separation, then it's possible for a massive (as opposed to massless) particle to be present at both events. A massless particle is present at two events with a lightlike separation. There is no particle that can be present at two events with a spacelike separation because the particle would have to travel faster than light to accomplish the task.