[MUSIC PLAYING] 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? [MUSIC PLAYING] 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. Thank you to CuriosityStream for
supporting PBS Digital Studios. CuriosityStream is a
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curiositystream.com/spacetime. And use the code SPACETIME
during the sign-up process. 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."
The first question I had when I heard the news was to wonder how it impacted string theory. I'm glad that this clarifies that it has nothing to do with compactified dimensions, so String Theory is still in play. (I was pretty sure that data that invalidated String Theory would be much bigger news.)
I came here searching for discussions on this videos, but no comments... so here I go:
What are the effecs of these calculations to the scientific status quo? Anyone versed in physics could give us a review about this paper, on how trustworthy it is and how well accepted is this being?
Also, a friend of mine who follows spiritism got really worried cause they use multiple dimensions to fit their idea of spiritual world, and this discovery could un-say what they say about the universe.
Sounds like Matt remembers me :) great video.
That clarifies everything!