It’s fair to say that black holes are the scariest objects in the universe.
Happily for us, the nearest is probably many light years away.
Unless of course Planck relics are a thing - in which case they might be literally everywhere.
Black holes are scary because they’re so… final..
They’re surrounded by this surface we call the event horizon, whose defining property
is that nothing that falls beneath it can ever emerge.
And if nothing can emerge from a black hole, then black holes must be A) black - they can’t
emit light, and B)
eternal - they can only grow in size, never shrink.
At least, that’s the black hole as it appears in the mathematics of Einstein’s general
theory of relativity.
But general relativity is NOT the whole picture.
Back in 1974, a young genius named Stephen Hawking showed that if you bring quantum mechanics
into the equation, quite literally, then the black hole is neither black nor eternal.
He showed that black holes must radiate, and so slowly leak away their mass in what we
now call Hawking radiation.
In a way quantum mechanics saves us from the eternal black hole … except perhaps that it doesn’t.
If you calculate the evaporation of the black hole all the way to the very last instant
- quantum mechanics may well play a second trick and save that final speck of the black
hole with the smallest conceivable size.
These remnant black holes, or Planck relics, may be everywhere.
To understand Planck relics we need a quick review of Hawking radiation.
This is something we covered in gory detail previously, so for now just the parts that
we need for today.
Hawking’s discovery of his black hole radiation was really ingenious.
It came from thinking about how black holes interact with the quantum fields from which
all elementary particles arise.
Now to do this properly, you really need a theory of quantum gravity, which we don’t
even have now and certainly didn’t in 1974.
But Hawking used a sort of a hack - a brilliant workaround - to prove that if an event horizon
forms in a vacuum, then the vacuum states of the quantum fields have to be disrupted.
To a distant observer it would look like the black hole is radiating particles.
Hawking even figured out what that radiation should look like: it should be thermal.
The distribution of particle energies should follow a blackbody spectrum, as though the
black hole has a real temperature.
In the common pop-sci description of Hawking radiation you often hear about particle-antiparticle
pairs appearing at the event horizon.
One gets trapped, allowing the other to escape.
This is misleading; for one thing, the radiation doesn’t appear right above the event horizon.
Instead the wavelength of the emitted particles are about the size of the whole event horizon,
so they sort of emerge from the entire region surrounding the black hole.
For the black hole left behind when a massive star dies, the event horizon is several kilometers
in radius.
For such black holes the Hawking radiation is just photons - electromagnetic waves with
kilometers-long wavelengths, so really, really low energy radio waves.
Such a black hole would appear very cold, and would leak away its energy very slowly.
But as the black hole shrinks in mass and in size, its Hawking radiation also decreases
in wavelength - but it increases in energy.
That means the black hole appears to heat up, and the evaporation rate increases.
This leads to a runaway process, and so the final stage of the evaporation should be positively
explosive.
That gives us this nice picture of a far, far distant future in which the stars have
gone out and we only have black holes, which one by one vanish in bright pops of Hawking
radiation.
These days most physicists agree that Hawking radiation is a thing.
Researchers have come up with different hacks for combining general relativity and quantum
mechanics and they reached the same conclusion.
But these are still hacks - approximations that involve different assumptions, or only
work in certain ideal circumstances.
One big assumption is that the space near the event horizon isn’t TOO strongly curved
compared to the smallest quantum scale.
When Hawking made that assumption, it enabled him to mathematically connect the high-gravity
region near the black hole with a very distant zero-gravity region where the Hawking radiation
is observed.
That’s reasonable for most sizes of black hole, but Hawking’s entire calculation falls
apart when the black hole has shrunk down to the tiniest quantum scales.
At that point you need a proper theory of quantum gravity to describe the process.
Without that theory, we have no way to describe the final stage of black hole evaporation
- so it’s reasonable to ask - does that final pop really happen?
Think about it this way.
A red hot poker glows because it has an enormous number of iron atoms, vibrating with every
possible energy.
In that motion they produce thermal radiation that includes every possible wavelength of
light.
But if you zoom in on a single iron atom - it can’t emit every wavelength of light.
It jiggles in its little crystal lattice cage with very specific vibrational modes, producing
photons of specific energies.
So a large black hole is like our entire poker - there are many ways that the quantum fields
can fluctuate around it.
The black hole loses energy one photon at a time, but the process seems smooth and continuous.
But as the black hole gets very small, the allowed vibrational modes start to get restricted.
You no longer have a smooth, statistical spectrum to your thermal radiation - the black hole
will leak its remaining mass in sudden, discrete steps.
And at some point, there may be no allowed transitions that can take away the last of
the black hole’s mass.
In which case the Hawking radiation ceases, and the black hole becomes stable.
So when does this happen?
If it happens at all, it’ll be when the average energy of the Hawking radiation is
close to the entire rest-mass energy of the remaining black hole.
In other words, when you get to the point where a single photon would take away the
rest of the black hole’s mass.
If that’s not an allowed transition, then the remnant will become stable.
This would be when the black hole’s mass is around 20 micrograms - what we call the
Planck mass.
It doesn’t sound like much but that’s around 2 billion Joules of energy.
Such a black hole would have an event horizon of around 10^-35 meters - the Planck length.
This is the size-scale where general relativity and quantum mechanics come into hopeless conflict,
and is sometimes thought of as the smallest possible chunk of space.
So might Planck-sized black hole relics, or Planck relics, actually exist?
Well, let me start by saying that we know for sure that general relativity doesn’t
work on Planck scales, so even if Planck relics do exist they probably don’t look just like
mini versions of big black holes.
But assuming that they a[re allowed in the theory, are they also allowed in the real
universe?
The only way to make black holes in the modern universe is in the deaths of massive
stars.
The smallest such black holes will take something like 10^66 years to Hawking-radiate their
entire mass away.
That’s much longer than the current age of the universe, none of these black holes
will have become Planck relics.
For Planck relics to exist now we need a way to make black holes that are much smaller than a star.
A black hole with a mass of a billion tons or lower could have decayed to a relic by
now - and fortunately there’s a way to make those.
It’s something we discussed before - primordial black holes.
In the extreme energies and densities near the Big Bang, there are a few different ways
to produce enormous numbers of black holes, potentially of a wide range of masses.
There are some scenarios that allow extremely large numbers of very tiny black holes.
As we talked about recently, the most important consequence of having Plank relics from primordial
black holes is that these could potentially explain dark matter.
Plank relics are really perfect candidates - they’d be completely invisible no matter
how many of them were..
And you’d need a lot to say the least because dark matter makes up 80% of the mass of the
universe.
It may have been possible to create this insane abundance of black holes if they formed during
the epoch of cosmic inflation.
This is the hypothetical time just when the universe was expanding exponentially quickly,
and can be thought of as the bang in the big bang.
Back then, the density fluctuations may have been strong enough to generate crazy numbers
of tiny black holes.
Besides explaining Dark Matter, another reason to want Planck relics to be a thing is that
they may solve a vexing difficulty that was introduced with Hawking radiation - the black
hole information paradox.
We did a video on this also, but long story short: if black holes radiate a perfect thermal
spectrum then, by definition, that radiation has maximum entropy and contains no information
about whatever fell into the black hole.
So you completely evaporate a black hole and then all the quantum information that went into it
is deleted from the universe.
That breaks one of the most sacred rules of quantum mechanics - the conservation of quantum
information.
But what if black holes never fully evaporate?
What if all the information they eat is trapped forever in the tiny Planck relic?
OK, that’s some quality data compression.
It also breaks another rule about how much information a given region of space can contain
- the Bekenstein bound.
A way around this has been proposed - what if space inside black holes actually expands
to a region larger than the event horizon?
I mentioned this inflation thing earlier - what if at the singularity of a black hole a new
inflation is triggered?
Then all that information would have plenty of room to exist, no matter the size of its
package.
This conjures images of insane numbers of minuscule black holes swarming through the
universe, and in each one a new inflation - a new universe?
OK, we’re getting a bit too far out there - which is saying something given that we’re
talking about the most out-there objects in the universe.
Let’s get a bit more down to earth before we wrap up.
If Planck relics account for all of dark matter, are they around us right now?
I did a quick calculation and got that in an average city there might be … one.
Just one Planck relic per 30km cube, and that’s enough to make up most of the mass in the
universe.
Because that’s how empty most of space is.
Now feel free to do the math yourself and tell me I’m wrong.
Or just ponder on the coolness that somewhere nearby there may be an actual black hole,
a tiny hole punctured in your neighborhood’s fabric of spacetime.
Today we’re covering comments from the last two episodes: the one about how it’s not
aliens yet, and then the one on how to mess with the limits of the uncertainty principle
in detecting gravitational waves.
You guys had a lot to say about the value of pursuing the “it’s aliens” hypothesis.
verus our partially facetious mantra that it's never aliens. I want to clarify my position on this.
I want it to be aliens.
I really do.
And that’s what makes me most wary about the aliens hypothesis.
In almost every scientific investigation there’s going to be some hypothesis that you favor,
even if you’re unaware of it.
The effect of such a bias is that you can tend to interpret all evidence in the light
of that particular hypothesis.
It’s called confirmation bias, and its effect is insidious.
In the case of the aliens hypothesis - this one is particularly dangerous because literally
any unexplained phenomenon can be fit into some version of the extreme high-tech aliens
story.
It’s as unuseful as invoking the supernatural to fill in the cracks of our understanding.
It’s the extraterrestrial of the gap.
That said, as Simone Spinozi wittily queries: Aren't aliens also a natural phenomena?
Well, if they exist then they are, and that’s why we absolutely should keep an open mind
about the hypothesis while at the same time being extremely cautious about the pitfalls
of confirmation bias.
So saying “it’s never aliens” isn’t about “not having the courage” to pursue
a fringe idea - it’s about absolute scientific rigor so that when it really is aliens you’ll
know you did your due diligence and can have any faith whatever your conclusion actually is.
In that episode I mentioned the Sherlock Holmes quote; which taken literally is a sure path
to hopeless confirmation bias.
It goes: Once you eliminate the impossible, whatever is left, however improbable, must
be the truth.
But this assumes that you have the omniscience to imagine all possible hypotheses.
HeckNo offers a poetic modification: Once you eliminate the impossible, you are left
with all the things you didn't think about.
Many of you also commented on the release of supposed UFO footage by the navy.
Don’t worry - I’m not ignoring that - it was released just after the episode was published.
I’m scratching my head over it and will say more on it if I decide it’s warranted.
OK, onto the episode where we looked at how the Heisenberg uncertainty principle can be
gamed to improve measurements - in particular in gravitational wave detectors.
JG 46 wants to know how to build a divide to split photons to make them entangled.
This is done through a process called spontaneous parametric down-conversion, and is a behavior
of certain crystals.
You might know that regular laser light is produced when an incoming photon causes an
electron in a crystal to drop in energy to produce an identical photon matched in phase
and direction of the first.
In certain materials known as non-linear crystals, the incoming photon is absorbed and the energy
is instantly emitted as two photons.
Those photons are entangled with each other because various properties are correlated
- in particular phase, polarization, and momentum.
These are incredibly useful devices - as well as being used to create squeezed states of
light, they’re used in all sorts of other quantum optics applications like the various
quantum eraser experiments.
So LIGO themselves actually commented on this one.
Well, not officially LIGO, but LIGO scientist Maggie Tse reached out to us to point out
an error.
We said that LIGO is planning to begin using squeezed light in a future run.
That’s wrong.
In fact it was used for the first time in the most recent observing run.
Dr. Tse is part of the squeezed light team, and led their paper on the subject where they
report up to 50% higher detection rates, exactly as predicted.
Thanks for reaching out, Dr. Tse - and sorry we were a little behind on the news.
Many of you criticized our title from last week - we called it “Breaking the Uncertainty
Principle”, but you rightly - if pedantically - pointed out that it should have been bending
or correctly using the uncertainty principle.
We stand corrected and make a note of which words are appropriate descriptors to use for
squeezed light in regards to Heisenberg, to wit: bending - good, breaking, bad.
Fake liner compliments my side-stepping skills - it’s as though I know exactly when text
or pictures will appear before effortlessly gliding aside like a river-dancer.
Thanks - by these are just standard tricks used in film … by us space aliens.