Geeks abound!

Listening to:
Reading: Stephen King's "1804"

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Ok, so I've been watching some geeky movies lately and it's made me miss the physics I was doing a few months ago and will soon be doing again. Thinking of Primer I got to wondering about time dilation and how much of an effect it has with things that travel at everyday speeds.

Starting off with human beings and using Lorentz's Time Dilation Equation I thought of Paula Radcliffe:

Paula ran the London Marathon (42.195 kilometers, or 42,195 meters) in the record time of 2:15:25 (or 8125 seconds), moving, on average, at 5.193236769ms^-1.

If we suppose that "t'" in this instance can be considered the observed time (as far as I can tell) this means that we have to multiply it by the square root of 1 minus the velocity of the body squared over the speed of light squared. The value of t' multiplied by this is equal to t. This is about 8124.999999999999878093402159375. This means that, on overage, during the course of the London Marathon, we experienced 1.2190659784062500274364533910957x10^-13s more time than Paula. It's not a staggering amount, but the fact that we experienced any more time (even though the amount is getting on for very close to 0) is quite mind boggling.

What if we now think about particles in a particle accelerator? It reputed that the guys over at CERN can accelerate a particle to about 0.99c (that being 99% of the speed of light, which is pretty fast). Lets say that they send it wizzing around their brand new synchrotron, the Large Hadron Collider, for 5 seconds. I have no idea how accurate that time is because I haven't studied this kind of stuff in detail, but at the speeds we're talking about it should have some intriguing effects.

Travelling at 0.99c (296,794,533ms^-1) for 5s (where this value is t'), the value of t produced for this is only 4.949999993s. This doesn't sound a lot, but imagine it had been in there for 5 hours (or 18,000s), this value would be 1781.99997s. That's just under 20 seconds of time we experienced at a totally different rate to that particle. Now, imagine it'd been doing that for, say, 100 years (3155760000s). The difference is 31557604.42s, which is 365.250051 days. That's just over a year.

That's mind blowing, in case you hadn't noticed.