Would someone like to peer review my relativity?

Nov 2013
552
30
New Zealand
I made a geogebra thingy to try and illustrate time dilation. Hopefully this link will work:

https://www.geogebra.org/m/xXE5SheR

This has a slider v but you need to scroll about half way down to see it. It was supposed to represent velocity but because I got confused about the time axis pointing upwards it ended up representing the reciprocal of velocity. Anyway changing the velocity changes the hyperbola axis intercepts which I am imagining is showing time dilation.

To calculate the hyperbola axis intersections I used the following calculations:

https://gist.github.com/kiwiheretic/51918eebf21be3278eb072379454967c

I am a little confused as to why I got \(\displaystyle \frac{v}{\sqrt{v^2-1}}\) as that part doesn't look right but it does produce the expected outcome of the tangent lines of the hyperbola intersecting the axiswhich is the way that Peter Collier seem to do it (see attachment) except that I scaled the hyperbola so that their tangent lines intersected the axis at integral positions of 1,2,3, ... . (I was trying to figure out how a moving observers co-ordinate grid maps to a stationary observers co-ordinate grid at the time.)

Or am I doing something wrong?
 

Attachments

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Pmb

PHF Hall of Fame
Apr 2009
1,576
331
Boston's North Shore
I haven't had much luck concentrating lately. That's why I was unable to help in the other thread. However I hate not being able to help. I printed out your attempt at a derivation in the other thread. If a time comes this week when I'm better able to concentrate I'll do my best to take at look at this.
 
Nov 2013
552
30
New Zealand
Don't stress over that. I'm not working to a timeline. Just doing it for my own edification.

Consider this post a fresh attempt. The other thread I have effectually abandoned it as I realize now my approach was wrong.
,
your health is your top priority. Just when you get opportunity is fine.
 
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Jun 2016
1,198
565
England
Lets be Honest.

I would love to help except for one crucial problem;
I am a lazy ##### (insert word or phrase to taste).

If I get the urge later, I will have a look.
I will give up quickly if it is too difficult.
 
Nov 2013
552
30
New Zealand
Did it look unclear or confusing? Don't let the words "peer review" put you off. Its essentially just a time dilation derivation.
 
Jun 2016
1,198
565
England
I've had a quick look and get the basic idea of what you are trying to do,
but I can't properly follow the maths.
I'm not familiar with GeoGebra and the time it would take to figure out the details of your graph is outside my attention span.

I am personally never entirely convinced that the mapping of the time cones and the lines of simultaneity of relatively moving observers on to a 2D surface really illuminates the idea, or just compounds the confusion.
However, if you can get your illustration tidied up, then the way the curves all change as the relative velocity changes could perhaps help to clarify the way the mapping operates.
It might help to have the relative velocity expressed as a percentage or fraction of c.
 
Nov 2013
552
30
New Zealand
I am personally never entirely convinced that the mapping of the time cones and the lines of simultaneity of relatively moving observers on to a 2D surface really illuminates the idea, or just compounds the confusion.
However, if you can get your illustration tidied up, then the way the curves all change as the relative velocity changes could perhaps help to clarify the way the mapping operates.
It might help to have the relative velocity expressed as a percentage or fraction of c.
I thought I was using velocity as a fraction of light, when v=1 the line is 45 degrees to both axis. Don't need to know about GeoGebra in view only mode, just need to know how to move a slider