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  • This episode was made possible by generous supporters on Patreon.

  • Hey Crazies.

  • Let me tell you, light is crazy fast.

  • It travels at 671 million miles per hour.

  • That's 186,000 miles per second

  • or 300,000 kilometers per second

  • or 30 centimeters nanosecond!

  • Whatever units you choose, that's crazy fast.

  • Fast Fast!

  • So fast, it might leave you wondering:

  • How fast is that exactly?

  • Let's do some comparisons!

  • The fastest humans in history were the Apollo 10 astronauts at 0.006% the SOL.

  • The fastest human-made object was the Juno space probe at 0.025% the SOL.

  • Andromeda is hurtling toward the Milky Way Galaxy at 0.04% the SOL.

  • All of these are tiny fractions of that 671 million mph.

  • Physicists have only really gotten close to the speed of light with subatomic particles.

  • The record for a proton in the Large Hadron Collider is 99.999 999% the SOL.

  • Now that's fast!

  • Fast Fast!

  • I'm a mad scientist though.

  • We can do better!

  • I have a specially designed rocket just for this purpose.

  • This seems dangerous.

  • I probably shouldn't do this myself.

  • We'll use Rocket Clone.

  • Oh, right.

  • We lost him during the Twins Paradox video.

  • Guess I'll have to make another one.

  • [Machine Noises]

  • Alright, now we have a Rocket Clone. Let's do this.

  • Say he gradually accelerates away from my space station.

  • Faster and faster and faster.

  • How long will it take him to reach light speed?

  • Well, he won't.

  • See, accelerating a rest mass like a person or a rocket requires energy.

  • For example, a rocket transforms energy from its fuel into kinetic energy.

  • It will continue to accelerate as long as it burns fuel.

  • Even if he somehow managed to turn all of the energy in the observable universe

  • into kinetic energy for himself, he'd still only be going 99.999...

  • That's 100 nines after the decimal place, which is still not 100%.

  • It would literally take an infinite amount of energy over an infinite amount of time

  • to accelerate up to exactly the speed of light.

  • It's impossible.

  • That being said, there are things in the universe that go at exactly light speed.

  • Namely, light.

  • And that's any light from the spectrum, not just visible light.

  • But also gravitational waves and anything else without rest mass.

  • Gluons.

  • Anyway, that speed does exist, but the fact that it's impossible for massive

  • objects to reach it has a weird side effect.

  • No matter how fast you go, light will always be faster.

  • 671 million mph faster.

  • Light is so fast that it breaks our understanding of how speed works.

  • How can it always be going the same speed faster than you?

  • Because space-time.

  • We're going to need a space-time diagram.

  • If you're not familiar with those, you should go check out this video first.

  • Alright, let's bring back Rocket Clone for another experiment.

  • If, instead of accelerating, he travels at steady speed his space-time path will look

  • like this.

  • Let's consider the part between my space station and, oh I don't know, Wolf 359.

  • They're about 8 light years apart and the trip takes about 14.5 years.

  • We know speed is space divided by time, so 8 light years divided by 14.5 years is

  • 0.55 light, or 55% the speed of light.

  • We can draw those measurements as a triangle, which makes the speed the tangent of an angle,

  • but not the tangent you know and love.

  • Most people don't love trigonometry.

  • Really?

  • Yes, really.

  • Weird.

  • Anyway, this isn't a regular tangent.

  • It's a hyperbolic tangent ortanchfor short.

  • Switching from my point of view to Rocket Clone's is a hyperbolic rotation.

  • Don't ever forget Relativity Rule #3.

  • Huh?

  • Let me just show you.

  • These are my coordinates.

  • These are Rocket Clone's.

  • Me.

  • Rocket Clone.

  • Me.

  • Rocket Clone.

  • The space and time axes rotate in opposite directions

  • to line up with the observer taking the measurements.

  • That's called a hyperbolic rotation because the coordinates on each axis

  • move along hyperbolas.

  • The more his path is tipped from mine the faster he's moving according to me.

  • So let's look at a bunch of different speeds and see what happens.

  • This is stationary.

  • This is 10% the SOL.

  • Here's 25%

  • 50%

  • 75%

  • 90

  • 99

  • 99.9999

  • Seeing a pattern here?

  • They're approaching this diagonal path.

  • Even the accelerated rocket from earlier approaches it.

  • That diagonal is the path that light would take in space-time.

  • At least, if it was traveling the same direction.

  • Both this rocket and this light are traveling to the right.

  • If we sent another set to the left, it would look like this.

  • The angles in here are weird though.

  • These two angles give us 55% the speed of light,

  • but this angle only gives us 84.5%, not 110%.

  • These two angles give us exactly the speed of light

  • and this angle also gives us exactly the speed of light.

  • Any angle measured from those diagonal paths will give you exactly the speed of light.

  • Every single one of these angles gives us exactly the speed of light.

  • That is some crazy distortion!!

  • The point is that a hyperbolic rotation keeps the speed of light constant.

  • The speed of light is measured to be exactly the same by everyone, no matter what.

  • So here's what we've learned:

  • The speed of light is the upper limit for speed in any direction.

  • It's 671 million mph, which is unimaginably fast.

  • So fast, that no matter how fast you go, light will always be faster.

  • 671 million mph faster!!

  • Just in case this hasn't completely sunk into your brains yet.

  • Even if you're going 670 million mph, light is still going 671 million mph faster than you.

  • That's crazy!!

  • So, how crazy do you think light is?

  • Let us know in the comments.

  • Thanks for liking and sharing this video.

  • Don't forget to subscribe if you'd like to keep up with us.

  • A special thanks goes out to Patreon patrons like Ilya Yashin and Drake Dragon

  • for helping make this show possible.

  • And until next time, remember, it's OK to be a little crazy.

  • For those of you saying: You think the acceleration still matters for

  • the Twins Paradox.

  • Well, yeah, sure, it matters, just not in the way people usually says that it does.

  • The acceleration doesn't suddenly explain time differences between observers.

  • It just makes it possible for them to compare notes.

  • Anyway, thanks for watching!

This episode was made possible by generous supporters on Patreon.

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光の速さは? (How Fast Is Light?)

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    大文 に公開 2021 年 01 月 14 日
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