Hey Everyone. We have some fun new merch at the merch store,
we’ll let you know more at the end of the episode.
Warp drives may or may not be possible, but if they are then could a distant alien
civilization’s warp fields produce gravitational waves that we could
see here on Earth? Well according to a recent study that may be the case.
We are entering a golden era of gravitational wave astronomy. Over the past nine years LIGO -
the laser interferometer gravitational wave observatory
has found around 90 mergers between black holes or neutron stars, with sensitivity
increasing with each new observing run. Using everything we’ve learned from LIGO, we’re now
planning the next generation of detectors, like Cosmic Explorer, the Einstein telescope,
and the newly approved Laser Interferometer Space Antenna LISA. We have a good idea of some of
what these detectors will see—from spinning white dwarfs to merging supermassive black
holes. But what will they find that we aren’t expecting? Whenever we open a new window to
the universe we find unexpected phenomena. Maybe in one of these windows there be aliens.
Specifically, if there are advanced alien civilizations out there,
and if these civilizations travel the universe with warp technology, could we
detect signatures of the massive distortion in spacetime caused by those warp bubbles? Well,
we wouldn’t be doing this episode if the answer wasn’t at least a remote maybe. Specifically,
a new study finds that the collapse of a warp bubble of moderate size within
our galactic neighbourhood should be visible as gravitational waves for future detectors.
Let’s pick this apart to see if and when we’ll discover our first alien warp bubble.
First a recap. Warp drives have long been a useful tool in science fiction to evade the
pesky speed limit of the universe: lightspeed. And then, back in 1994, Mexican physicist Miguel
Alcubierre found a solution for the superluminal warp field within the classical framework of
general relativity. Obviously we covered this in a previous video.The loophole that
Alcubierre used is that, while it’s impossible to travel through space faster than light,
there’s no limit to the speed with which a patch of space can move relative to another patch. We
know for sure that this superluminal relative motion of patches of space occurs. For example,
two sufficiently distant regions of the universe are moving away from each other faster than light
due to the expansion of the universe. And we can think of the space beneath the event horizon of
a black hole as moving at superluminal speeds relative to the distant exterior.
The Alcubierre warp field works by expanding space behind a patch of
space and contracting it in front, which ends up pushing this bubble of space forward. And
because general relativity allows it, there’s no fundamental limit to the speed that bubble
can reach. Now just put a spaceship in the bubble and you have a warp ship.
So why don’t we have our own warp drives yet? Well, because they may be impossible,
and even if they’re possible they have some pretty insane requirements.
The Alcubierre warp field is a valid solution to the Einstein equations. Those equations
relate the geometry of space with the mass and energy that space contains. The geometry
is captured by the metric on the left side of the Einstein equations. Almost any imaginable
spacetime geometry can be described by the metric, including the Alcubierre warp field.
The equations of general relativity then tell you what distribution of mass and energy space needs
to have in order to be warped into your chosen metric—that’s the stress-energy tensor on the
right. But not every imaginable metric corresponds to a physically possible mass-energy distribution.
The Alcubierre metric looks to be one such impossible configuration. For one thing,
it violates something called the null energy condition. Put simply,
to curve space as the warp metric demands, the corresponding stress-energy tensor
demands a space containing an enormous amount of negative mass. Unfortunately,
this so-called exotic matter is almost certainly not possible. Workarounds have been discussed,
like using the Casimir effect. Erik Lentz even came up with a warp solution that may not require
negative mass. Although, even this suffers the other big problem with the Alcubierre field—the
amount of energy required to move even a small vessel capable of carrying people
is estimated to be the mass-energy equivalent of anything between a large moon to an entire star.
We have videos on these recent alternative proposals, but the new paper by Katy Clough,
Tim Dietrich and Sebastian Khan goes back to the OG Alcubierre field. They make no claims about the
physical or practical possibility of constructing this field in the first place. Instead, they ask
what really happens to a warp bubble after the fact, assuming it somehow gets made. And,
of utmost importance, does a warp bubble produce gravitational waves that we could detect?
So the Alcubierre metric describes a bubble of space that can travel faster
than light. When in motion at a constant velocity,
the warp bubble should not produce any gravitational waves. It should
produce them when accelerating or slowing down or perhaps when forming or switching off. In short,
when the warp field is undergoing some evolution over time beyond constant motion. Unfortunately,
the Alcubierre solution doesn’t say anything about how the metric should evolve over time.
And this is what the researchers explore in detail in their paper—the natural evolution
of an Alcubierre bubble according to general relativity. This is no easy calculation.
Understanding the time evolution of a metric and its corresponding mass-energy distribution
requires something called an equation of state. In the paper, the authors point out
that there is no known equation of state that would sustain the required metric over time.
That means it’s not enough to just have exotic matter, you also need a yet-unknown behavior of
that matter to lead to the also-yet-unknown equation of state to sustain the bubble.
But let’s assume some advanced civilization figures out how to make exotic matter and
contain it so that it holds together for the journey across the galaxy.
Again, at constant velocity spacetime would be perfectly flat far away, meaning there wouldn’t
be any observable gravitational waves. But we also know that the warp bubble does not
hold its shape if the delicately engineered drive stops constraining exotic matter with the required
equation of state. So what happens when the drive is switched off? Or what happens if it fails?
In the latter case it’s probably very bad for the aliens, but may be very good for us because
it could produce observable gravitational waves. So how do we calculate what happens
when you burst a warp bubble? It’s not easy. While Einstein’s equations are very elegant,
calculations can quickly become horrendously messy. After all, we’re trying to evolve complex
distributions of matter through 4-D spacetime. For this reason the researchers used numerical
relativity simulations—which means calculating each time step based on the previous time step.
To do this they needed to split 4-D spacetime into slices of 3-D space—or
hypersurfaces—at consecutive times. The aim is a sort of flip-book in which each
page is a 3-D spatial volume, and flicking through the pages gets us to the evolution
of that space and so reconstructs a 4-D spacetime containing an evolving metric.
So they rewrite the Alcubierre metric in terms of a three dimensional metric that lives on the
hypersurface and introduce a few functions that tell us how to translate between different ways
of slicing—different hypersurfaces—and how they embed into the overarching 4D
spacetime. The starting metric on the first page of the flipbook has a corresponding
initial configuration of matter, and that matter should evolve as the metric evolves.
So far so good. Up until now, this has all been pretty standard practice for simulating general
relativity. This is the same framework we’d use to tackle more realistic, dare I say mundane
problems, like the merger of black holes. But simulating warp drives is not such smooth sailing.
Remember that we need this equation-of-state thing in order to evolve the Alcubierre metric and the
corresponding mass-energy distribution over time. And remember also that we don’t know of
an equation of state that allows this metric to be stable. But that’s OK, because we’re trying to see
what happens when the warp bubble fails. This means its possible to come up with a workable
equation of state for a failing warp bubble with, admittedly, a few speculative assumptions about
things like the pressure, timescales of the decay, and the resulting matter after the collapse.
Even if these assumptions about the equation of state of non-existent
matter are about as accurate as assuming a spherical Klingon in a frictionless vacuum,
the point is that even with sensibly imperfect assumptions we can still learn something about
the physics. As well as progress with the calculation, which is always nice.
So, we’ve set up the first page of our flipbook—one of our hypersurfaces with
a matter configuration, which in turn gives us our desired Alcubierre metric. We’ve specified
the equation of state, and so we’re ready to simulate. By specifying these initial data,
Einstein’s equations and the equation of state take over and the computer can
evolve the geometry of spacetime and the distribution of matter from one
hypersurface to the next. Once we reach the final hypersurface flipbook page
we can stitch together spacetime again and watch as it evolves through the simulation.
So, how exactly does it evolve?
Let’s say an advanced alien species takes a trip to see their cosmic neighbours. On this
occasion they allow the new recruit to pilot the warp drive. Everything’s going great until
they miss a warning light coming from the matter containment field and… the warp bubble bursts,
destroying the ship and crew in the process. We’ve all been there. Or,
depending on exactly how this stuff works, maybe this was a controlled dispersion
of the warp bubble once they reached the destination. But the catastrophic
version is likely to make bigger waves, and also better represents the simulation in this paper.
The first thing that happens is that the warp bubble collapses inwards, presumably
obliterating the ship, and then expands outwards, all at the speed of light. That
outward expansion is accompanied by a series of gravitational waves—ripples
that follow the massive fluctuations in spacetime curvature of the ruptured bubble.
So what would these waves look like to us? The signal shape would be very
different to the black hole or neutron star mergers we’ve seen. In fact,
the researchers likened the signal to the head-on collision between black holes,
but without the characteristic ringdown at the tail end as the merged black hole settles down.
That means, if we could detect an event, it would stand out as not being from a natural source.
But could we detect these gravitational waves in the first place? The study calculates that
the collapse of a 1km radius warp bubble traveling at 10% light speed would produce a signal at the
Earth with a strain of 10^-21 if it happened one megaparsec away - that’s around 3 million light
years - or a bit further away that the Andromeda galaxy. A strain of 10^-21 means lengths here
would be shifted back and forth by a factor of one over a billion trillion. Sounds tiny,
but that’s exactly the strain limit that LIGO can detect. So can LIGO detect bursting warp
bubbles in Andromeda? Not quite. The frequency of this 10%-lightspeed kilometer-radius warp
bubble’s gravitational waves are 300kHz, which is way higher than LIGO’s sensitivity range.
While high frequency detectors operating in the Mega to Giga hertz range are being considered,
focus for now is on much lower frequency sources—the larger
slower natural phenomena that are much more likely to be real. So, for the time being,
don’t expect headlines saying we’ve detected the gravitational wave signature
of a stalled hyper-advanced extraterrestrial warp drive.
But it’s pretty exciting that the detector capable of seeing such a thing is within our technological
grasp. And although any signal is well outside LIGO’s frequency, it’s possible that the
gravitational waves from a burst warp bubble will appear even stronger than the 10^-21 strain. For
example, if it’s from within our own galaxy then it’s much closer than 1 megaparsec and so will be
“louder”. If the warp bubble is traveling faster than 0.1c then it emits more intense gravitational
waves on bursting. But 10% lightspeed requires a mass-energy equivalence of 1% the mass of the sun,
so let’s not get greedy. I should also add that, while superluminal speeds are technically possible
for warp bubbles, in the words of the authors would likely lead to pathologies—aka physics
breaking—and anyway require computational resources beyond this study to investigate.
There’s some other good news: if we do detect the gravitational wave signal of a bursting warp
bubble, we may see more than just those waves. After the bubble collapses, the exotic matter
escapes—waves of positive and negative energy, which might lead to an electromagnetic counterpart
to the gravitational wave signal. We call such signals multimessenger events, and we routinely
search for the other messengers—typically photons and neutrinos—for every gravitational wave we
detect. We routinely do see the electromagnetic counterpart of neutron star mergers for example.
Even if we never detect an alien warp signal—perhaps because they don’t exist—this
type of research is still interesting. Warp drives may have their issues, but they are motivated by
the extremely well-tested theory of general relativity. It’s instructive to poke at the
edges of such theories to test the limits of their validity and to come to a better
understanding of what’s actually possible, and what’s not. We can add new intuition and
techniques to our toolbox for understanding the possible universe. Or—far less likely,
but who knows—we build a high-frequency gravitational wave detector and immediately
witness a gravitational pop, pop, pop—the unmistakable bursting of bubbles warped spacetime.
Hey Everyone. We have a few new items for sale at the merch store. First up is a new limited
edition wormhole enamel pin. If you'd like to show the world that you'd rather instantly be
at some other patch of space time then you should snap up this is a 1.5 inch enamel pin on 2x3 inch
holo foil backing card. Next up is our Quantum Mechanics Officially Observer design, which will
let everyone know that you are in fact an official observer of quantum mechanics. The design will
be featured on a t-shirt, a hoodie as well as our first ever 2.75 inch embroidered patch with velcro
backing. The t-shirt and hoodie will remain on the merch store, but the wormhole pin and embroidered
patch will be a limited edition pre-sale that will ship in the first week of September.