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MATT O'DOWD: Thanks to CuriosityStream for supporting
PBS Digital Studios.
The hunt for extra dimensions sounds like science fiction.
Fortunately, with the discovery of gravitational waves,
we're now living in a science fiction future.
So how many dimensions are there?
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We may have mentioned once or twice
that the new era of gravitational wave
astronomy is going to open new windows to the universe
and unlock many mysteries.
When does all of that start to happen?
Oh, it has.
We're already making definitive statements
about hypotheses that were previously untestable.
Today, on "Space Time Journal Club,"
I want to tell you about one in particular described
in a new paper, "Limits on the Number of Spacetime Dimensions
from GW170817," by Pardoa, Fishbachb, Holzb, and Spergela.
The key to this breakthrough was the gravitational wave event
observed in August of 2017, GW170817.
A pair of neutron stars spiralled together and merged.
These superdense remnants of dead stars
churned the fabric of space and time in their death spiral.
And the LIGO and Virgo gravitational wave
observatories detected the resulting ripples.
Unlike merging black holes, which are invisible,
merging neutron stars explode spectacularly.
The resulting kilonova is first observed in gravitational waves
and then as a gamma ray burst.
In GW170817, the flash of gamma radiation
arrived 1.7 seconds after the gravitational waves.
This was followed by a glow across the electromagnetic
spectrum and, ultimately, with the discovery
of the distant galaxy in which the explosion happened.
Among other things, this optical identification
gave a completely independent measurement
of the distance traveled by the gravitational waves.
This allowed us to make some really important conclusions
about how gravity travels through space.
In the case of today's paper, it allows
us to measure how many dimensions that space actually
has.
Yeah, that's actually a serious question.
We think of space as three-dimensional.
Add one dimension of time to give us 4D space-time,
which we'll also refer to as 3-plus-1-dimensional
space-time.
But adding the extra spatial dimensions
beyond the usual three could actually explain a lot,
from the difference between gravity
and the other forces of nature to the nature of dark energy.
But before we get all hyper-dimensional,
let's think a bit more about 3 plus 1D space-time
and how gravity, light, and matter behave there.
Imagine a pulse of light traveling
from some distant source.
We can think of light rays spreading up evenly
over an expanding spherical shell.
If we see that pulse, it means our eye or our telescope
intercepts some of those light rays.
The brightness of the pulse is determined
by how many rays we intercept.
So as this shell expands, the light rays
become more spread out.
Intensity drops proportional to the surface area of the shell,
which is proportional to the square
of its radius, the square of the distance to the source.
This is the famous inverse square law.
But what if we, instead, lived in 2D space?
Then the same pulse would spread out over an expanding circle,
not a sphere.
It would diminish in intensity proportional
to the circumference of that circle,
and also proportional to the radius--
so the distance to the source, not the distance squared.
The way pulses fade in brightness
depends on the number of dimensions, typically
proportional to 1 over the distance
to the power of the number of dimensions minus 1.
So in 4-plus-1-dimensional space-time,
brightness should drop off more quickly than in 3D space.
This relationship also applies to the force
felt in a gravitational field.
In our universe, gravity appears to diminish according
to the inverse square law, as reflected in Newton's law
of universal gravitation.
We do see slight deviations in very strong
gravitational fields, like close to the sun.
But even there, Einstein's general relativity
describes gravity perfectly with three spatial dimensions.
In general, general relativity in 3 plus 1 space-time
does a great job at describing gravity
in the large-scale universe.
But there are some things about this version of gravity
that seem peculiar--
for example, its pathetic strength.
While the electromagnetic strong and weak forces are all
in the same ballpark in terms of strength,
gravity is vastly weaker, 10 to the power of 32 times weaker,
than even the weak nuclear force.
The only reason we see so much gravity
is that its range is infinite-- and unlike the nuclear forces.
And it doesn't cancel out, like the electromagnetic force.
This mismatch in strength might be
because gravity is really fundamentally
different to the other forces.
But that idea makes some physicists sad.
Many would like to find a "theory of everything"
which merges the forces of nature into the same über
force.
That means gravity has to look just
like the other forces at very high energies.
It needs to be intrinsically strong,
but then become weakened in the low-energy, large-scale regime
of the familiar universe.
One fun way to do that is to throw
in an extra spatial dimension.
If you recall, intensity drops off more quickly
the more dimensions you have.
So you drain gravity into an extra dimension.
But you restrict all the other stuff in the universe--
matter, radiation, astronomers-- to only three
spatial dimensions.
All of that stuff will behave relatively normally,
while gravity is weakened.
Let's get a little bit more technical.
There are these theoretical objects called branes.
We can think of them as geometrical structures
of potentially any number of dimensions
on which the quantum field and their corresponding particles
can live.
They're used in string theory, where they typically have
a large number of dimensions.
11 is popular.
But in string theory, all but three spatial dimensions
of the brane are inaccessible.
They're finite and coiled up on themselves,
compactified, allowing us to cram them
into three spatial dimensions.
But you can also flip this idea around.
You can imagine a three-dimensional brane,
a 3-brane, embedded in a space-time
with four spatial dimensions, where
the extra dimension of space is extended rather than compact.
Most of the stuff in such a universe,
including all of the fundamental forces besides gravity,
would be restricted to the 3-brane.
Tune your theory just right, and you get normal physics
for matter and radiation in three spatial dimensions--
for example, the usual inverse square law for light.
On some spatial scales, you even get the inverse square law
for gravity.
But on other spatial scales, gravity
can behave very differently.
If gravity spreads out in four dimensions rather than three,
then it should become much weaker.
This can be used to explain the general weakness
of the gravitational force on all but the tiniest scales.
It can also be used to explain another mysterious phenomenon,
dark energy.
This is something we've gone into in great depth.
But in short, the expansion of the universe
seems to be accelerating.
This is usually thought of as coming
from the action of the energy of the vacuum.
But there's another way to get this type of acceleration.
In our hypothetical universe with four spatial dimensions,
gravity is already weak on the scale of the solar system
and the galaxy.
But it can become even weaker on larger scales.
Depending on how you tweak the theory,
gravity can obey an inverse square law
on galactic scales, where it's sort of coupled
to the three spatial dimensions of the 3-brane.
But it starts to obey the inverse cubed law
on much larger scales.
In fact, the 3-brane itself, which
defines the three-dimensional structure
on which our observable universe exists,
can actually expand into the extra fourth spatial dimension.
To us, that would look like an accelerating expansion
of the universe.
It would look like dark energy.
So how do you even test a wild idea like this?
Well, here's where we finally get back
to our gravitational waves.
If the gravitational field can extend
into this hypothetical extra spatial dimension,
then gravitational waves should lose energy
to that extra dimension as they travel through space.
Here's where I have to complicate
things a tiny bit more.
But I promise, we're nearly there.
Wild light and the force of gravity
appear to obey the inverse square law.
In regular 3D space, gravitational waves
drop in intensity proportional to just distance,
not distance squared.
But it's the same general trend.
If space has four or more dimensions,
then gravitational waves should drop off in intensity
faster than you'd expect in three dimensions.
So that gives us a simple test.
Just observe a gravitational wave
and figure out how much its intensity dropped off
over the distance traveled.
Does that match what you expect in a universe with three
spatial dimensions?
If the dropping intensity was too much,
then you have evidence for extra dimensions--
basic stuff, right?
All you need is a billion-dollar network of gravitational wave
detectors and a way to independently measure
the distance the wave traveled.
Fortunately, we have both.
We have LIGO and Virgo.
And now we also have GW170817.
The electromagnetic signal from these
merging exploding neutron stars allowed
us to measure its distance completely independently
to the gravitational wave signal, something
that's impossible with black hole mergers.
One other important factor here--
in order to determine how much intensity
was lost by the gravitational wave,
we need to know how intense it was
when it started its journey.
A super convenient property of gravitational waves
is that you can figure this out by looking at other properties
of the merger event--
namely, the masses of the merging objects
and the frequency of the wave combined
with our independent distance measurement.
OK.
So what's our conclusion?
How many extra dimensions did we discover?
Uh, zero, precisely zero.
The gravitational wave lost the right amount of intensity
for a 3-plus-1-dimensional space-time.
There was no observable leakage of gravity
into extra spatial dimensions, pretty much ruling this out
as an explanation for dark energy.
There still might be compactified extra dimensions.
So string theorists are OK for now.
By the way, comparison of the electromagnetic and
gravitational wave arrival times also
allowed us to verify that gravity really
does travel pretty much exactly at the speed of light.
This ruled out or constrained various alternative theories
to general relativity.
This sort of null result might sound like the less interesting
outcome.
I mean, how cool would it have been
to discover extra dimensions?
But don't be disappointed.
It's completely mind-blowing that we can even
test these crazy ideas.
Ruling them out narrows the vast scope
of possible theoretical models for our universe,
bringing us closer and closer to the truth.
And apparently, that truth doesn't include a 3-brane
embedded in an extended 4-plus-1-dimensional
space-time.
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Last week, we talked about the hardest problem in physics,
exploring the conflicts between general relativity and quantum
theory towards the development of a theory of quantum gravity.
You guys had the best questions.
Devin Faux asks whether gravity is maybe
the exception to the rule that the forces arise
from quantizing [INAUDIBLE] fields.
Well, totally, it might be.
Theories of quantum gravity go in both directions.
So-called theories of everything try
to quantize gravity by placing it
within the same framework as the other forces
to show that it arises from the same underlying mechanism.
These are grand unified theories.
And string theories are an example.
Other theories treat gravity very differently
to the other forces.
But they still end up with a space-time fabric
that is fragmented on its smaller scales.
An example is loop quantum gravity.
One thing that it's hard to do is
to keep space-time continuous on the smaller scales.
If space-time is indefinitely divisible,
then you get hopeless conflicts with quantum theory.
Something about its structure has to change on those scales.
But it may not be the same sort of changes
you get when you quantize, say, the electromagnetic field.
Hecatonicosachoron doesn't understand
why renormalization works, conceptually speaking,
and when it is that it doesn't work.
OK.
So when you use perturbation theory to calculate
an interaction in field theories,
feedback effects give infinite loops of interactions.
More crudely, when you try to calculate something
with a long series of approximate corrections,
those corrections can create infinities.
Renormalization resets the scale to something finite
by measuring one or more actual physical properties
of the system.
This only works if the number of measurements you need to make
is finite.
For the simplest attempts at quantum gravity,
you need infinite measurements.
So it's non-renormalizable.
Iago Silva and Rubbergnome jumped in
to give better answers and then got
into an extended and quite high-level argument
about the right approach to understanding renormalization.
Eventually, they took it offline to continue.
They "got a room," so to speak.
We can only assume that they are figuring it out to this day.
Guys, when you're done, please let us know how it went.
Some quickfire answers--
John Gibbs-- yes, if general relativity and quantum
mechanics are both right, then we
should have Planck-length virtual black holes popping
into and out of existence.
That would be bad.
And we'd notice-- hence, the conflict.
adamdecoder1, the difference between deleting quantum
information and just removing it from the universe, e.g.,
by dropping it into a black hole,
is an interesting philosophical point.
Probably, they're very different.
But do some reading on complementarity for more info.
Michael Jordan asks, but why male models?
Are you serious?
I just told you that a moment ago.
Feynstein 100 is sad about not being featured
on comments as often as before.
Oh, boo, hoo, hoo.
You want back, Feynstein?
Show me what you got.
Show me that old brilliance and wit.
[INAUDIBLE] Vacuum Diagrams, Gareth [INAUDIBLE]
complaining-- they just keep at it.
Whining won't get you anywhere, except this time.
This time, it really worked the tree.
Brilliance, wit, and/or whining--
that's what it takes to make it on "Space Time."