Hi there, physics fans.
The last two episodes have been about black holes, which means I’m done with them, right?
Nope.
There’s more to learn, like what they do to time and what it’s like to fall into
one of them.
What do you say?
Sounds to me like a perfect topic for this episode of Subatomic Stories.
Black holes are locations of super strong gravity.
They bend space and affect how objects near them experience time.
This is a generally true thing, like I mentioned in episode 13.
That’s the one where I told you about atomic clocks that were so precise that they ran
at different rates when one of them was raised by a single foot on the surface of the Earth.
But near black holes, gravity is much stronger, and the effect is much bigger.
A distant observer will see clocks near an event horizon tick much more slowly than a
distant clock will do.
In addition, it takes energy for light to climb out of a black hole’s gravitational
field.
Red light is lower energy than blue light.
That means that as light leaves the vicinity of a black hole, a distant observer will see
it redder than it was when it was emitted.
And, of course, the whole thing about Einstein’s theory of general relativity, or special relativity,
for that matter, is that it tells us how different observers will experience the same thing.
So, let’s talk about how two observers will experience seeing a clock fall into a black
hole.
One observer will fall along with the clock.
The other observer will stay far from the black hole and watch it fall in.
OK, first the person falling with the clock.
General relativity says that a freely-falling clock doesn’t experience anything weird,
so it just falls in.
Plop.
That’s it.
Well, it’s a bit more complicated than that.
The simplest form of relativity describes the behavior of a tiny object – what mathematicians
call a differential volume – but that just means so small that gravity is the same everywhere
inside the object.
But real clocks have a size.
Thus, for a real person, who is in round numbers five or six feet or a meter or two in height,
they have to take into account the fact that the amount of gravity changes rapidly with
distance to a black hole.
So, if they fall feet-first, their feet will experience more gravity than their head.
The extra force on their feet will pull them apart in a process that is called spaghettification.
It’s a colorful term for what would no doubt be a grisly and painful death.
But let’s ignore that whole stretching spaghetti thing.
A person falling with a clock will just fall into a black hole.
If they look downward, they’ll see nothing come out of the black hole.
After all, that’s a black hole’s defining feature, which is that it doesn’t emit light.
But, spaghettification aside, nothing all that weird happens.
Now let’s ask what a person outside sees.
They see the person and the clock fall towards the black hole at increasing speeds.
But eventually the clock experiences strong enough gravitational fields that relativistic
effects start to kick in.
The external observer will see the clock slow down and the object will correspondingly appear
to fall slower.
In addition, the clock will look redder than it did before it started to fall.
As the observer watches, the clock will approach the event horizon, which I remind you is the
point of no return.
The event horizon is the location at which gravity becomes so strong that not even light
can escape.
But it’s also the place where time slows down.
So, as a distant observer watches the clock fall into the event horizon, time slows down.
That means that the object slows down.
And when the object gets super close to the event horizon, it effectively stops or at
least moves very slowly.
And the object gets redder and redder.
Eventually it fades to deep red, then infrared and it is invisible to the eye.
Thus, an external observer will see the clock fall, turning redder as it goes.
When the clock approaches the event horizon, it will appear to stop and dim into redness
and then invisibility.
So, that’s a pretty mind-blowing idea.
The two observers experience very different realities.
And – and this is the super-mind-blower – both of them are correct.
This example illustrates just why it is that so many non-physicists have such difficulty
with general relativity.
Heck, >>I<< wasn’t so sure I believed it until I learned about all of the experiments
that have been done to validate the theory.
It’s just kind of crazy.
I suppose that I should take a moment to talk a little about an idea that you often hear
about in science fiction, which is that two black holes can be connected and one can jump
into one of them and pop out of the other one a great distance away.
These connected black holes are called a wormhole.
In the television show Deep Space Nine, from the Star Trek franchise, a wormhole connects
two locations in the Milky Way separated by 70,000 lightyears.
A spaceship drops in and pops out far away.But, as we have seen here, this is just impossible.
First, the spaceship would get ripped apart by spaghettification.
But secondly, an outside observer would never see the spaceship enter the black hole.
And, even if it did, the black hole on the other side of the wormhole is – after all
– a black hole.
Light can’t escape from it, so a spaceship certainly can’t.
So, wormholes might exist in some theoretical and mathematical sense.
It might be true that spacetime can be connected between wormholes.
But the idea that they’ll be useful as a means of transportation is just really, incredibly,
silly.OK, so that’s a bunch to think about.
What sort of questions have we received?
It’s question time!
I love the question part.
Let’s get into it.
Many viewers asked about what appeared to be noisy dishes in the background and speculated
that some cleaning up was going on.
But if physics wizards don’t need to cut their hair, they certainly don’t deal with
such mundane things as dishes.
I’m not saying that it was a sound track to make a time lord more relatable to mortals,
but I’m not-not saying it wasn’t either.
True7himself and others admonished me for mispronouncing Karl Schwarzchild’s name.
It’s true that the correct Germanic pronunciation is Schwarzchild, but this is an English video,
so I’ve anglicized the names for an English speaking audience.
It’s not personal.
French speaking viewers tell me that I don’t get DeBroglie’s name correct either.
I’m sure they’re right.
But turnabout is fair play.
I give you all permission to pronounce my name in whatever way sounds best in your language
of choice.
Deal?
Christian Cardin and many others noticed the 1.7 second delay between the arrival of gravitational
waves and gamma rays in the collision of two neutron stars in galaxy called NGC 4993.
Some wondered if it meant that this means that gravity travels faster than light.
The answer is almost certainly no.
Remember that gravitational waves are emitted as the two stars spiral in to their doom.
The gamma rays are emitted at the moment of impact and before the two neutron stars combine
into a black hole.
Therefore, astronomers expect a slight time delay between them, with gravity arriving
first.
Good question though.
M mouse asks how gravitational waves can be emitted by black holes if nothing can escape
from them?
Hi mouse.
It was a fun cartoon from a bygone era.
Good question.
The thing to remember is that nothing can escape from the event horizon of a black hole.
Things can certainly escape from outside the event horizon.
Black holes distort space over great distances and it is the motion of space that is gravitational
waves.
It’s like a kid standing on a trampoline.
The trampoline is distorted under their feet, but the distortion isn’t >>only<< under
their feet.
No gravitational waves are emitted from inside the event horizon.
So there’s no problem.
Eric Fischer and others asked what would happen if a person was close to a pair of merging
black holes.
Hi guys!
Good question, with a surprising answer.
Let’s take the first observed black hole merger as an example.
I talked about it in the last episode.
The energy release was equivalent to three solar masses in 0.2 seconds and it occurred
about 1.3 billion lightyears away.
In round numbers, that’s about ten to the 25 power meters.
There are two quantities of interest with gravitational waves, energy and magnitude.
The energy of gravitational waves grows in a series of spheres of increasing size.
The area of a sphere is proportional to its radius squared, so the energy of a gravitational
wave decreases as the square of the distance from the source.
On the other hand, the magnitude of a gravitational wave drops off linearly with the distance,
not the square.
And the magnitude is the amount of distortion.
This is a super key point.
The first observed gravitational wave changed the length of objects by one part in ten to
the minus twenty one power.
The length of the LIGO arms are about a kilometer and the length changed by 1/1000th the size
of a proton.
One part in ten to the twenty one.
So those are the key numbers – ten to the twenty five meters and one part in ten to
the twenty one.
And, of course, the magnitude changes linearly with distance.
So suppose the merger was a billion times closer – just 1.3 light years away.
That would make the change in lengths due to gravitational waves a billion times bigger,
enough to change the height of a person by about ten to the minus twelve meters or less
than the size of an atom.
A black hole with a mass of 60-ish solar masses located just a light year away would play
havoc with the Oort cloud and fling comets toward us.
That’s without gravitational waves.
The event horizon of a black hole with 60 solar masses is about fifty miles or 80 kilometers.
So what would the effect be if we were about the same distance away from the black hole
as we are from the center of the Earth?
Call it ten thousand kilometers, give or take.
At such a distance, the spatial distortion due to gravitational waves on your height
would be about a millimeter.
So you’d probably not notice.
And, of course, at ten thousand kilometers, the simple gravity of the black hole would
be immense.
A person with a mass of 100 kilograms or about 200 pounds would effectively weigh about 800
million kilos or just shy of two billion pounds.
The bottom line is that gravitational waves are not dangerous, even if you’re close.
Gary Generous asks if gravitational waves can give us insight on the structure of the
universe beyond the visible universe.
Hi Gary.
The answer is no and we can know that quite definitively.
Since gravitational waves travel at the speed of light, by definition, we cannot see them
from beyond the visible universe.
The visible universe and gravitationally accessible universe are one and the same.
And finally Optimus Wombat love’s my youthful enthusiasm.
Hi Optimus.
Love the name.
I don’t know about youthful, but I’ll take it.
And enthusiasm is a great setup for the close.
You know the drill.
Like, subscribe, and share.
We all should be enthusiastic about such exciting physics because, well- you know- even at home,
physics is everything.