Naked Science Forum

Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Dimensional on 20/01/2022 20:03:45

Title: Is this a correct spacetime diagram with world lines?
Post by: Dimensional on 20/01/2022 20:03:45
The diagram has 3 objects in it with 3 world lines in yellow.  There is a rock traveling really fast through the origin in the primed frame.  There are 2 more rocks at rest in the unprimed frame.  I also put the rocks on the x' axis just to remind me what is happening in the frame of reference of the rock that is traveling.  Is all of this roughly correct?
Title: Re: Is this a correct spacetime diagram with world lines?
Post by: Halc on 20/01/2022 23:17:09
The one rock (diagonal yellow line) seems to be moving dang fast in both frames, not just the primed frame. Faster in the unprimed frame.

About the angles:
You've not shown a 'light speed' line originating from the origin, but it would go at a 45 angle and the x' and ct' lines would be symmetric about that (equidistant), and they're not. The ct' line as you've drawn it is too close to the light line.

As for the two rocks, they're shown at one set of locations in the unprimed frame (intersections of their worldline with the grey x' line), and another location (dots) in the primed frame. These are objective events and the rocks cannot be in two locations at the same time in the primed frame as shown. So the red dots belong at the intersections, not where you've drawn them. Their worldlines will tilt to non-vertical if you do the Lorentz transform where the primed frame has perpendicular axes.
Title: Re: Is this a correct spacetime diagram with world lines?
Post by: Eternal Student on 21/01/2022 00:47:29
Hi.

   Here's an annotated diagram with some of the points that Halc raised (see attachment).

I also put the rocks on the x' axis just to remind me what is happening in the frame of reference of the rock that is traveling.
   That's a little bit worrying.  I'm not sure I've understood but I'm a little concerned that you might be thinking that the primed frame is one where the rock passing through the origin is actually at rest.   
   All of the 3 rocks are moving in the primed frame.

Best Wishes.
Title: Re: Is this a correct spacetime diagram with world lines?
Post by: Dimensional on 21/01/2022 05:32:44
Hi.

   Here's an annotated diagram with some of the points that Halc raised (see attachment).

I also put the rocks on the x' axis just to remind me what is happening in the frame of reference of the rock that is traveling.
   That's a little bit worrying.  I'm not sure I've understood but I'm a little concerned that you might be thinking that the primed frame is one where the rock passing through the origin is actually at rest.   
   All of the 3 rocks are moving in the primed frame.

Best Wishes.
Thanks, I did not know that all 3 rocks are moving in the primed frame.  Then what is the point of reference of the primed frame?

And I did not know that the two rocks are on the world lines from the unprimed frame.
Title: Re: Is this a correct spacetime diagram with world lines?
Post by: Halc on 21/01/2022 13:42:01
Thanks, I did not know that all 3 rocks are moving in the primed frame.  Then what is the point of reference of the primed frame?
The worldline of a statioary object in the primed frame would be parallel to ct' axis, just like the worldlines of the two rocks stationary in the unprimed frame are parallel to ct.

Why this specific choice of primed frame was chosen for the picture is something only the author of the picture can answer.

Quote
And I did not know that the two rocks are on the world lines from the unprimed frame.
The worldline of any object is a set of objective events, and events are not frame specific. You can transform the line to a different frame (say one in which the rocks are not stationary), but all the events are still the same events. Only in the one frame in which they are stationary do they map to the same location in space, so only in that one frame are they parallel to the time axis.

This is related to my original comment about the angles of some of the lines, ct' in particular.
These are not necessarily wrong since the scales of the two axes are not labeled.
They're both in distance (meters say), but maybe the long x axis goes from 0 on the left to 10 meters on the right, and the shorter ct axis goes from 0 at the bottom to 20 meters at the top, in which case the axes, while both in meters, are simply not to the same scale. So the drawing is not necessarily wrong in that way unless the scales are similar.
If they are scaled similarly, then your diagonal yellow 'high speed rock' is moving at considerably faster than c since it goes to the right faster than it goes up.