This is a map of the multiverse.
Or in physics-ese, it’s the maximally extended Penrose diagram of a Kerr spacetime.
And in english: when you solve Einstein’s equations of general relativity for a rotating
black hole, the universe does not come to an abrupt halt at the bottom of the gravitational pit
Instead, a path can be traced out again but you do not end up in the universe that you
started in.
Like I said, it’s a map of the multiverse.
In order to learn some multiverse cartography, and to decide whether the strange new regions
on this map are real, we’re going to need to continue a journey that we began a little
while ago when we explored the region just above a rotating black hole.
Back then we stopped short of dropping below the event horizon - the boundary of no return.
Today we’re going to take that plunge.
A black hole results when enough mass is concentrated in a small enough space that the gravitational
field becomes too strong for even light to escape.
The inescapable surface surrounding a black hole is called the event horizon.
If that mass is NOT rotating and does not have any electric charge, the result is a
Schwarzschild black hole, which is about as simple as these bizarre objects can get.
Add a little spin or charge and things get even weirder.
Now, we’re going to focus on rotating black holes here, but a lot of this also applies to charged
black holes, as we’ll see.
A rotating black hole is described mathematically by the Kerr metric.
It describes the way spacetime warps and flows in the vicinity of a spinning mass.
We sometimes call a rotating black hole with no electric charge a Kerr black hole.
Let’s think about what that rotation does in familiar terms.
Think of the worst spinny amusement park rides, or an astronaut high-g training machine - you'd
feel yourself flung outwards by centrifugal force.
Well, in a Kerr black hole that rotation results in an outward pressure that partially counteracts
the inward flow due to gravity.
This leads to weird effects.
Above the event horizon is the ergosphere - a place where the fabric of space itself
is whipped into a vortex so fast that not even light can resist its motion.
The event horizon itself is distorted - wider at the equator than the poles, just like the
rotating earth.
We saw all that in a previous episode.
Now let’s peek below the event horizon to see how weird things really get.
Before we do that, let’s remember how to read our multiverse map - our Penrose, or
Carter-Penrose diagram - maybe it’ll help us find our way out again.
A couple of things to remember about this map.
Time flows up - for the most part - and one dimension of space is left or right.
Light always travels a 45 degree path, and normal objects can only travel paths steeper
than that.
Your so-called “future light cone” encompasses the parts of the multiverse you could possibly
get to at less than light speed.
Your past light cone shows you the parts of the multiverse that you can see, because light
has had time to reach your position from those parts.
As we take this journey we’re also going to plot our path on the Penrose diagram.
When we first enter the Kerr black hole, we find it’s just like every non-rotating Schwarzschild
black hole we’ve ever visited.
Down becomes the future, because falling space drags us there faster than the speed of light.
Space and time switch places.
In a regular black hole we’d be crushed by the central singularity pretty quickly.
But now as we fall the outward pressure due to the black hole’s rotation starts to win
against that inward flow.
In fact the flow eventually slows to less than the speed of light.
This leads to a second event horizon called the inner horizon.
Now, some pretty terrible things happen here, and you don’t survive the crossing.
But we’re going to pretend that you’re Deadpool or something you get across intact-ish
- what do you see?
On the other side, space and time switch back to their proper order.
You’re now free to not fall, so you can jet around and explore the interior.
Below you is the black hole singularity - but it looks odd.
The singular, central point has been spun out into a ring of infinite density.
It’s surrounded by a second ergosphere, where again the rotational flow of space exceeds
light speed.
So what next?
First probably take a ride in the ergosphere, because why not?
When you’re dizzy enough you can try to turn around and go back the way you came through
the inner horizon, or you can plunge through the singularity ring.
In either case, you’re in for a weird time.
To understand what happens here, we have to think like a general relativist.
In order to create these maps of spacetime, physicists use the equations of general relativity
to trace what we call geodesics - these are the paths that objects take when not experiencing
any force.
For example, the path a ball takes if I drop or throw it - after it leaves my hand.
A nice way to map the gravitational field is according to the geodesics of objects in
freefall that start motionless relative to the gravitational body.
For example, if you drop a trillion balls from space they’ll trace the downward cascade
of space - and that flow would be pretty spherically symmetric.
Same with the interior of a Schwarzschild black hole - every ball, every geodesic reaches
the same point and, very importantly, ends there.
But within a Kerr black hole, the singularity is a ring, and the trillion balls would fall
towards the disk bounded by that ring.
Only the ones exactly on the equator hit the ring and, those geodesics do end - same infinite
squish as in a Schwarzschild black hole.
But those that approach the disk experience an overwhelming anti-gravitational force from
the spinning singularity.
Our balls, and the geodesics they follow, rebound and travel back out.
Before we take that outward ride, let’s push a little harder and try to get through
the ring.
With a lot of speed - and I mean a LOT - it’s possible to overcome the anti-gravitational
field in the middle of the ring and punch through.
But you don’t find yourself on the other side of the same region.
The ring is like a portal to a new, very different region of spacetime - and that’s because
the geodesics passing through one side do not map to those passing through the other.
Through the portal things get very weird.
For one thing, the ring singularity becomes entirely repulsive - as though it had negative
mass.
Also, there are no horizons above you - there’s a straight path to the outside universe - but
it is certainly not our universe.
For one thing, the lack of event horizons above you means the ring is a naked singularity,
as well as being repulsive.
Surrounding the ring on this side is a toroidal region in which it’s possible to accelerate
to infinite speed.
And as some of you probably remember - faster than light travel means the possibility of time travel.
There are trajectories in this torus that lead you back to your starting location - in both
space AND time.
So-called closed-timelike curves.
This is the Carter time machine, after the aussie physicist Brandon Carter who did much
of the early exploration of the Kerr spacetime.
This time travel and naked singularity stuff is good reason to think this part of the mathematical
structure of the Kerr black hole is NOT real.
We’ll come back to how it can be avoided in the math - for now, let’s whip once around
back to our own past and hop back through the ring.
At this point we can follow an outgoing geodesic across the inner horizon.
However you’re in for a surprise.
That outgoing flow continues above the inner horizon, and will eventually eject you past
the outer horizon.
That’s a little confusing because black holes are supposed to be inescapable.
So what’s with this conveyor belt of space taking you out of the black hole?
Don’t you have the same conveyor belt pulling you in over that same region?
Well you sort of cross the same space, but not through the same time.
The black hole is in your past.
You’d need to travel back in time-slash-faster than light to get back there.
Extending the Kerr metric from ring singularity into the future leads to something else.
It leads to what looks like a white hole.
Now we saw that in the Schwarzschild solution, a white hole exists in the past of a purely
hypothetical eternal non-rotating black hole.
The Kerr black hole also has a white hole in the past, but it has one in the future
too.
And that’s where the outgoing geodesics go, carrying you with them.
But not only is the black hole in your past - the entire universe that you came from is
in your past.
You caught a glimpse of the entire history of that universe the moment you crossed into
the white hole.
That white hole will eject you as forcibly as the black hole pulled you down.
But eject you where?
Well this has to be a new universe, because it’s definitely not the one you came from.
It’s not the bizarro negative time traveling universe either - here, the laws of physics are the same as
where you started - at least as far as general relativity is concerned.
If you try to head back to the white hole, you won’t find it - you’ll only find a
new black hole that lies in its future.
If you enter that you’ll be able to take the entire fair ground ride once again,
skipping ahead to yet another universe, and so on ad infinitum.
This may all sound fun, but unfortunately there’s the inconvenient fact of your utter
obliteration before you ever cross the inner event horizon in the first place.
The complete Penrose diagram for the Kerr spacetime has not one, but two inner event
horizons leading to two parallel wormholes.
You reach one if you embrace your fall and head down, the other if you try to resist
and exit the black hole.
These correspond to the region below the event horizon but they’re causally disconnected,
the difference being that time flows forward if you go in one direction and backwards
if the other.
So you have this messed up situation where the direction of the flow of time actually
clashes at the inner horizon.
This would be okay-ish if the black hole was empty, but it’s not okay if there’s even
the tiniest bit of matter or radiation.
If there’s any stuff at all in the black hole then the forward flow of time carries
a current of positive energy, while the backwards carries negative energy.
When they meet they don’t cancel out - instead they stream past each other producing enormous pressure.
That pressure produces its own gravitational effect on par with the black hole itself,
accelerating the streams further.
The result is an exponential runaway effect.
So if you do get to the inner horizon you are in a bath of energy on par with the Big Bang.
Good luck with that.
Besides, this so-called mass inflation means the inner structure of the Kerr black
hole is catastrophically unstable, and the whole thing collapses, shutting off any potential
magical portals to time machines or new universes - probably before they ever exist.
This whole counter-streaming instability thing was figured out by Roger Penrose in the context
of charged, non-rotating black holes.
But it almost certainly applies to Kerr black holes also because the two are very similar.
In electrically charged, or Reissner-Nordström black holes the electromagnetic field within
causes massive tension, or negative pressure that produces an antigravitational effect.
That resists the inward flow just like rotation does in a Kerr black hole.
You have the same inner horizon and chain of wormhole-connected universes.
They just don’t have the ring singularity leading to the bizarro-verse, so Kerr is more
fun than Reissner-Nordström.
So there you have it.
Now you know everything you need in order to travel the multiverse and travel through
time.
Just a little wishful thinking, a rotating black hole, and don’t forget to slip your
map in your back pocket.
Never travel the multiverse without a Carter-Penrose diagram of the maximally extended Kerr spacetime.
Last time we talked about the greatest failed experiment in the history of physics - the
Michelson-Morley experiment, and how it did away with the idea of the luminiferous aether,
and so doing paved the way for the acceptance of Einstein's relativity.
Your comments were relatively fantastic.
Elliot Heath wonders if we are now in a similar position to the end of the 19th century now
- in that we might be on the cusp of massive change.
Well, unlike 120 years ago, I wouldn't say physicists today are under any illusions that
physics is "complete".
They're very aware that there are big gaps in their understanding.
And I'd say most HOPE for massive change, because that's probably whats needed to find a way
forward.
Will that next step be as surprising as relativity and the quantum revolution?
I personally think it will be - whatever points beyond the current mess may need to be revolutionary
and come from an unexpected direction - otherwise surely we'd have seen it before.
Zatar123 asks whether the Michelson Morley experiment has been performed at much higher
velocities to get a better reading - say 10% the speed of light.
Well the answer is essentially no.
the solar system is moving at 368 km/s relative to the rest-frame of the cosmic microwave
background radiation - and that's as close as you can define to an absolute definition of "stillness".
So to do better you'd need a device traveling faster than that - essentially impossible
even for a spacecraft, at least currently.
But the experiment has been performed with much higher precision using other methods
- lasers, vacuum chambers, strange quantum mechanical states of light - you name it.
No indication has ever been found that the speed of light depends on the speed of the
device or of the observer.
Many of you took issue at my bad math.
I said infinity times zero is zero.
Indeed that isn't generally true.
I was being a bit lazy - what I wanted to get across was the following: As you rewind
the universe towards zero age, distant points in space end up closer and closer - and there
is no point that is so distant that it won't be arbitrarily close to you at some point in the
rewind BEFORE time gets to zero.
So in an infinite universe, every definable galaxy or definable location ends up right here on
top of us at some point in the rewind.
The universe approaches infinite density in the limit as time approaches zero.
But you were right to be annoyed at my lazy math language.
Paolo Sena tells us that Quintessence is literally “quinta essentia” or fifth element in
Latin.
Paulo, I did not know that.
Thank you- that's some erudite nerdery right there.
And we had plenty of the other types of nerdery also - I mentioned the math nerds already,
but I was especially excited to see plenty of roleplaying game nerds talking about Sons
of Ether and accusing me of being part of the magic technocracy.
Well I always thought of myself as more order of hermese, or maybe hufflepuff, but I defer
to the wisdom of the sorting hat that is the youtube comment section.
Nerds.