Monday, February 20, 2012

Explaining Relativity part.2

I'm gonna be writing something that is outside of my usual expertise and I will admit in advance, I may be getting this wrong somewhere. If you happen to be a physics expert and spot any mistake, please let me know.
Meanwhile, I will explain what I understand and what I have done.

Theory of Relativity is kinda like the theory that says "if you are moving very fast, like close to speed of light fast, time goes slow and length gets shorter".
In physics term or as relativity treats them, space and time are closely related. The ratio that length and time changes relative to the velocity is simply inverse of each other with Lorentz Factor.
That is useful, because that means I can represent the time with length. It's basically the same ratio, so calculating the length is also about calculating the time. Time is intangible but length is, so it is nice to finally be able to give a form to time!

Bellow is a strip of paper that I brought in to the class to explain how time changes with different velocity.

Taking that further, I worked out different changes of length contraction with different velocity; from 1% of speed of light up until 100% of speed of light. I corresponded that with the width of A4 paper (210mm):
Let's take 16% of speed of light as an example. When an object is moving at 16% of speed of light, it looks 0.012% shorter from the frame of reference. So if A4 paper was flying at 16% of speed of light, in theory width will look like 207mm and not 210mm.
(The length would stay the same, and A4 paper is experiencing the time 1.013% slower.)
I used 99 sheets of paper, page numbered each, where each paper corresponds to each % of speed of light. i.e. page 16 corresponds to 16% of speed of light. There is no page 100 because at 100, the equation becomes 0. I don't really know what that suppose to mean, I'll figure it out sometime soon.

Yes, the front view is rather boring:

But it does look nice from the back (oh and it feels really good too!):

This version, that goes all the way up till 100% (or 99 pages) is the best representation of the concept of visualizing the Theory of Relativity, and the volume and all makes it quite poetic. But it doesn't have to go all the way up to 100% as the length get too small for a practical usage. It can be a 30 pages notebook for physicists/students, or a book that contains information about relativity, and it doesn't sacrifice all its practicality.
Ultimately it's just a book with different page sizes. And now that I've worked out the sizes for each page, I can reproduce it for whatever purpose.

A4 size is the standard paper size for graphic designers and normal usage of paper in general, so it makes sense to have it shrink and thus we can appreciate the change in sizes.
It's treats book as a medium with a relationship between a page and a sequence of pages.

In terms of binding, I was expecting it to be quite difficult but it turned out not too bad. I had to divide them into three different sections and it took a bit of time but the process was not complex and the end product looks nice. Thanks to bookbinding pro Douglas!

やりながら、「本=1ページの幅(サイズ)もしくは面積と、その蓄積(連続するページ)の関係性を持ったもの」、と考えれば、折線グラフって、本として表現出来るということに気づいた。応用し放題だなあ。でも、これ(相対性理論)は時間と長さについてだから、適切だと思う。
つまり、1つのページの幅か面積かが、折線グラフの点に当たり、その蓄積のボリュームが変化を表すという。本というメディアは時間軸を持っているという当たり前のことを改めて実感。でも、完成すると、ちょっと地形みたいでもある。
ひとつのものを、別のものに置き換えて、メタフォー探しの遊びをしてるみたい。