Spacetime intervals

[geordief]

Suppose we take two points on a Minkowski spacetime  diagram   and "connect" them with different pairs of physical events.

 

So one if the points is the origin and the other  is any arbitrary point

 

The first pair of physical events is  a massless object fired,* from the origin through a vacuum  and leaving a physical mark ** at the site of the second point on the Minkowski  map.

The second pair of physical  events is a spaceship travelling at c/2 and arriving at the site of the mark made by the  massless object.(at a different time and spatial distance)

The third pair of events is just a bullet following a similar trajectory. 

So there are three related spacetime intervals.

I think.I may be right to say that the first  spacetime interval is zero?

 

Of the other two  intervals  the bullet strikes me as being the longer.

 

Have I understood  and presented the scenarios correctly?

 

If we line up all the potential pairs of physical  events does the spacetime interval  associated with each increase on inverse proportion to  the speed of the trajectory involved?

*The first event of the pair

**The second event of the pair 

 

 

[Genady]

2 minutes ago, geordief said:

(at a different time and spatial distance)

The points in Minkowski spacetime ARE events. The same point cannot be at a different time or spatial distance, in a given reference frame. 

[geordief]

1 minute ago, Genady said:

The points in Minkowski spacetime ARE events. The same point cannot be at a different time or spatial distance, in a given reference frame. 

OK(I feared as much) but  are my scenarios real scenarios even if wrongly described  and are there 3 different ,but related spacetime intervals attached to them?

[Genady]

4 minutes ago, geordief said:

OK(I feared as much) but  are my scenarios real scenarios even if wrongly described  and are there 3 different ,but related spacetime intervals attached to them?

Here is the diagram. Spatial coordinate is horizontal, temporal is vertical.

The light, the ship, and the bullet leave the origin, i.e., the same point in space at the same time. The orange line is the light trajectory, the blue is the ship, and the red is the bullet. (No gravity.)

[geordief]

1 minute ago, Genady said:

Here is the diagram. Spatial coordinate is horizontal, temporal is vertical.

The light, the ship, and the bullet leave the origin, i.e., the same point in space at the same time. The orange line is the light trajectory, the blue is the ship, and the red is the bullet. (No gravity.)

Suppose we shine a light on the Moon (from the Eath) and  also (imagine there is no gravity) aim a bullet to reach the same point  on the Moon much later

 

 

Can that be depicted on a Minkowski  diagram.(an  extra vertical line at the top of the orange line  that the red line meets ,perhaps?)

[Genady]

3 minutes ago, geordief said:

Suppose we shine a light on the Moon (from the Eath) and  also (imagine there is no gravity) aim a bullet to reach the same point  on the Moon much later

 

 

Can that be depicted on a Minkowski  diagram.(an  extra vertical line at the top of the orange line  that the red line meets ,perhaps?)

Yes, here:

Event 1: the light hits a point on the Moon. Event 2: the bullet hits the same point on the Moon.

[geordief]

1 hour ago, Genady said:

Yes, here:

Event 1: the light hits a point on the Moon. Event 2: the bullet hits the same point on the Moon.

Thanks.Well ,from the origin the spacetime interval to the point 1 is zero,I think .

Do the corresponding intervals increase as the angle  of the trajectory wrt the spatial axis  increases?

When the speed is least (say the speed of a Trump  conviction) ,is the spacetime interval greatest?

[Genady]

11 minutes ago, geordief said:

Thanks.Well ,from the origin the spacetime interval to the point 1 is zero,I think .

Do the corresponding intervals increase as the angle  of the trajectory wrt the spatial axis  increases?

When the speed is least (say the speed of a Trump  conviction) ,is the spacetime interval greatest?

Yes, you're right.

ds² = dt² - dx².

(c=1)

[md65536]

3 hours ago, geordief said:

The first pair of physical events is  a massless object fired,* from the origin through a vacuum  and leaving a physical mark ** at the site of the second point on the Minkowski  map.

The second pair of physical  events is a spaceship travelling at c/2 and arriving at the site of the mark made by the  massless object.(at a different time and spatial distance)

You wrote "I feared as much" but I think you got it close enough to not fear.

Here, Genady has drawn the world lines of the different particles, onto the same Minkowski diagram. The diagram, and the coordinates on their grid, represent the measurements for one particular inertial observer (aka. inertial reference frame). You can draw the same worldlines on a Minkowski diagram for a different observer, and the subluminal "time like" world lines will be at different angles.

If you make a physical mark at some fixed location in a this particular Minkowski diagram, and extend it through time, you get a vertical line like the Moon's. So this diagram represents the rest frame of the moon. If your mark is at rest, all events at that mark have the same spatial component (but they have different time component), and the spatial distance of the pairs of events you described will be the same in this particular frame's Minkowski coordinates.

Edited June 17, 2023 by md65536