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 or “tanch” for 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!