B Math-Based Time Dilation Paper: Seeking Suggestions

[Philip Norheim]

I'm writing a mathematical paper on time dilation. Does anyone have any suggestions on how to incorporate math into the topic? I'm considering applying a Loedel diagram. The emphasis needs to be on the math, and not the physical aspects, though they can be introduced through the use of math. The paper is due tomorrow, so any help would be GREATLY appreciated.

 

[jedishrfu]

I hate to tell you this but its a little late to ask for help here or anywhere. Hopefully you've been working on it up until now.

If this paper is on time dilation then you should be including the relativistic equations that define it.

https://en.wikipedia.org/wiki/Minkowski_diagram

and possibly Google / Khan Academy can help too:

https://www.google.com/search?newwi...0i22i10i30j33i10i160j33i10j33i160.VjYVZFPLx_o

Good Luck!

Tim Urbans talk on the Master Procrastinator might be helpful too:

https://www.ted.com/talks/tim_urban_inside_the_mind_of_a_master_procrastinator?language=en

Closing thread.

 

[Philip Norheim]

Thank you! I did some work on the following "proof" (I'm not even sure if it qualifies as proof within math.) It's based on a video I watched, from what looked like Khan academy.

 

[Matterwave]

At what level are you doing this project? Some of the mathematical aspects to time-dilation can be seen from the general Lorentz transformations which form the Lorentz Group. Maybe you could talk about the Lorentz group and its group structure and algebra. If you want to get more broad, you can go over the Poincare group and its group structure and algebra. Time dilation is just one effect of a Lorentz transformation.

 

[Philip Norheim]

I'm in high school, in the IB diploma programme.

 

[Matterwave]

Ah, in that case, going into group structure and algebras is probably beyond the level at which you want to present...

 

[Philip Norheim]

My current plan for structuring the essay will be to start by explaining special relativity and time dilation in simplified terms, to give and idea as to what it is. Further on, I'll use the proof, and then I'm considering using Minkowski diagram or a Loedel diagram. I might also look into the Lorentz group, if I have time for it. I'm thinking about using data from GPS satellites, as a way to show practical proof of time dilation.

 

[jedishrfu]

There’s also muon decay that illustrates it too and the jet plane experiment traveling in opposite directions.

 

[Philip Norheim]

Found this: https://www.thinkib.net/physics/page/18370/space-time-diagram-geogebra
Not sure what parts to use though.

 

[jedishrfu]

You could take screenshots of the interactive graph showing how space and time change based on the velocity.

Also have you looked at the twin paradox? That can be shown via minkowski diagrams with light signal worldliness.

 

[Nugatory]

explaining special relativity and time dilation i

Be sure to explain how it is that time dilation is symmetrical: If A and B are moving relative to one another, A (considering themselves to be at rest while B is moving) finds B's clock to be running slow while B (considering themselves to be at rest while A is moving) finds A's clock to be slow. If you can't explain this then not only are you not explaining anything, you are propagating misinformation.
(You will need the relativity of simultaneity to explain how A's clock can be slow relative to B's clock and also B's clock can be slow relative to A with no paradox or contradiction).

 

[Philip Norheim]

How should I introduce Minkowski diagrams in a way such that it emphasizes the mathematical aspects of it?

 

[Sorcerer]

How should I introduce Minkowski diagrams in a way such that it emphasizes the mathematical aspects of it?

Minkowski diagrams are pretty much all math as far as I’m concerned. Just don’t draw little rocket ships on the diagram. But if it’s not too late you could also add some fluff to your paper by coming at it from a linear algebra perspective, because the fundamental concept investigated with time dilation is transformations and mappings, which while very much used in physics are a huge part of math. You see all kinds of transforms/transformations/mappings in math, like Laplace transforms in differential equations (an integral transform where you are mapping from one domain to another), or transforming from Cartesian to polar or spherical coordinates, etc.

In particular with time dilation obviously it’s the Lorentz transformation that is important. But the point I’m making is that you can fill an entire page simply discussing transformations, mentioning various ways that mathematicians utilize transformig from one coordinate system to another, one domain to another, etc. It wouldn’t even have to be too technical. You could fill a paragraph talking about Laplace transforms without really even knowing what they are. Yes, this is shady, but I’m assuming you’re trying to get a good grade ;).