Tuesday, 13 March 2012

Relativity and Problem Solving Time Loops

Science and math geeks have two reasons to celebrate today.

Firstly, today is Pi Day!! In some countries todays date is written as 3/14 which are the first three digits of the Mathematical constant $\pi$ . So people around the world get together to celebrate the world's most famous mathematical constant.

Today is also the Birthday of THE Albert Einstein who has become something of a mascot for physics and science in general. The strange thing was, although Einstein became famous among the general public during the early 1900s for his theories, nobody really understood his theories. They just liked the crazy consequences.

I was really expecting a Google Doodle for the occasion on the Google homepage but they decided to honour  Akira Yoshizawa instead. (Google, you have disappointed me.)

Speaking of Einstein, my A-Levels are now over. So I'm getting plenty of time to delve deep into those obscure bits of physics which were too time consuming for an A-Level student. I've been reading up a lot on Einstein's Theory of Relativity in the last two months. I can finally say that I understand the basics of tensors without feeling dishonest.

A few posts ago, when I was testing out $\LaTeX$ I put down this equation in with many others.

$R_{{\mu}{\nu}} - \frac{1}{2} g_{{\mu}{\nu}} R + g_{{\mu}{\nu}} \Lambda = \frac{8{\pi}G }{c^{4}} T_{{\mu}{\nu}}$

This summarizes everything about the theory of relativity in one elegant equation and this equation is what I hope to eventually understand. Right now, the only part of the equation I know anything about is the $g_{{\mu}{\nu}}$ or the metric tensor.

Learning about relativity inevitably leads to thinking about the mind boggling consequences of time travel. I came across this really interesting application of theoretical time travel while reading on the internet. This trick works even if it is only possible to send information back to the past.

Imagine I have a machine using which can send a Word file "Something.doc" back to the past. If I am trying to crack a simple 3 digit number lock, I can use the time machine to my advantage.

I wait for my future self to send me a file labelled "Combination.doc". If the file contains a combination I try out the combination. If the combination works, I create a file named "Combination.doc" , write down the correct combination and send it back to my past self.

If the combination does not work, I add one to the 3 digit number, write it down in the newly created "Combination.doc" and send it back to my past self.

If if commit to doing this, the only situation which does not lead to a paradox is when I send back to the past the correct combination and so the very first time I open the file, it must contain the correct combination! It's kind of like a "do ... while" programming loop in real life.

The amazing thing is that this technique allows a person to solve any problem which involves combination without any effort at all! This could work even on email accounts which lock you out if you enter the wrong password. Since the information is going back in time, even if the the loop tests the  passwords a billion times, the actual password entry happens only once outside the time loop. Or you could get a hundred percent on any multiple choice test without reading a single question (Of course, if you're smart enough to invent this machine, you probably don't need to answer the questions in the first place.)!

I wonder if this would actually work if we had a real information time machine.

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