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  • so the symbol on to talk about is gamma little gamma, which gets used for lots of different things.

  • But in this particular context, I'm gonna talk about it to use in special relativity.

  • Relativity is something that everyone is actually familiar with.

  • It's the fact that the laws of physics are kind of the same in whatever reference frame you in.

  • So, for example, when you're sitting on an airplane, unless you look out the window, you're really not aware of the fact that you're traveling with 500 miles an hour that if you were to, you know, sitting at your table to throw something up in the air ball up in the air, it would just fall back down again.

  • And so on.

  • The laws of physics are basically the same, even though you're moving relative to view the high speed.

  • And what special relativity says is that a laws of physics are basically the same in any reference frame that's moving a constant speed.

  • And when you work through the mass of all that and what I actually implies, one of the quantities that sort of comes out all over the place is tthe same mathematical expression comes out all over the place, which is one over the square root, or one minus V squared over C squared, where V is the speed at which the reference frame is moving and sees the speed of light.

  • And this comes up so often that it actually given its own symbol.

  • It's called gamma.

  • It is it's, ah, symbol that occurs all over the place in special relativity, for example, one of the places it occurs most blatantly is a thing called time dilation, which is that if you're in a reference frame, which moving along, it's bean the It turns out that your clocks move more slowly than things that a stationary relative to you.

  • So, in fact, if you were to just watch the speed at which time was ticking away on a clock in something that's moving like a rocket moving at some velocity V, it actually moves more slowly.

  • Then the clock set of stationary on the factor by which it moves more slowly in one over gamma.

  • And so, for example, if you put the numbers in for something traveling at 90% of the speed of light when you plug them into that formula for Gamma Gamma comes out about to be over, too.

  • So that means that something moving 90% of the speed of light, the clocks there will be traveling at about a factor of two slower than those of the state.

  • This sounds very bizarre, right?

  • Because people are used to the idea that clock so just clocks.

  • It was like that as long as they're behaving themselves, they should all ticket one second per second on this idea that the rate at which time progresses depends on what reference frame you really is pretty bizarre, but this very strong experimental evidence that he actually really works.

  • One of the simplest experiments is it turns out that there are particles crashing into the earth's atmosphere, crashing into the top of the earth's atmosphere, sort of 40 or 50 kilometers up when they crash into the earth's atmosphere.

  • These cosmic rays smashing in the atmosphere, turn into new ones you create Mulan's turns out nuances.

  • A particle have very short lifetimes elementary particle, that case very quickly, and so they don't actually in the time between them being created, they actually will decay before they get to the ground.

  • even traveling at close to the speed of light, they don't have time to get to ground level.

  • And so, in the absence of special relativity, you would predict that you should never detect any of these mules if you have a mule on detective on the ground because although they're being created up there, they don't actually have time to travel all the way to the ground.

  • But because they're traveling at close to the speed of light, that means that their internal clocks are going slower.

  • And when your crocs are going slower, everything goes slower, including this process of radioactive decay that these particles actually decay more slowly than they would do if they were just sitting station within the lab.

  • Which means they actually do have time to get away from where they're created, tens of kilometres up down to ground level.

  • So if you have a muon detector in the lab, you can actually detect these cosmic mules, even though in the absence of special relativity, none of them should ever made it all the way from the way have ignition sequence.

  • So there's probably the most famous story of this associating with this effective time dilation is this thing called the Twins paradox, which is that if you were, you start with a pair of identical twins and you send one of them off on a rocket ship to Alpha Centauri on go off some fraction of heart of high fraction of the speed of light.

  • So they traveling sufficiently close to the speed of light.

  • You have to worry about these things.

  • The one who travels away, goes off to our Centauri and then comes back again because they're moving.

  • The person who stays at home would see this person's clock traveling more slowly.

  • And so, therefore, by the time the twin who's gone to Alfa Centauri and then come back again gets back again, they'll actually be younger than the twin who stayed at home Now.

  • The reason why this is a paradox is because everything is relative.

  • Which means now, let's look at it from the twins point of view, who was on the Rocket from the twins?

  • Point of views on the rocket.

  • He just stayed in the rocket the entire time.

  • From his perspective, viewers shot off in the opposite direction for a while, and then when he turned round your shot back again.

  • So from his perspective, he just stayed stationary on the other twin, the one who stayed on earth, diddle the moving move backwards and came back again.

  • And so, by exactly the same argument between who's actually gone all the way to represent Ori and back again, would argue.

  • Actually, I've seen white twin doing traveling at high speed so I would see my twins clocks troubling more slowly and therefore my twin should be younger than me, so that you end up with this paradox that each of them, by this argument of special relativity, will claim that they should then be younger than the twins on the resolution to this paradox is because the reason actually a symmetry in this situation, which is because the twin who actually did the journey at some point had to turn around and come back.

  • And that means that the twin who did the journey didn't stay in the same reference frame the whole time.

  • He was initially in one reference frame, traveling one way, and then later on was in another reference frame, traveling the other way, which means at some point he must have accelerated decelerated to a stop in an accelerated back the other way on as soon as you introduce acceleration into the mix of things and special relativity doesn't work anymore.

  • And if you really want to resolve this twin paradox properly, you have to consider general relativity, which is the version of relativity.

  • You have to use a student.

  • You have accelerations.

  • So the one who would end up being younger is actually the one who went to Alfa Centauri.

  • The ultimate resolution.

so the symbol on to talk about is gamma little gamma, which gets used for lots of different things.

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タイムディレイ - 60のシンボル (Time Dilation - Sixty Symbols)

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    林宜悉 に公開 2021 年 01 月 14 日
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