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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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