Astronomers are the worst at naming things. I mean seriously. Dark energy AND dark matter? Who can remember which is which. But perhaps one astronomer has just fixed
it, with a theory that says perhaps actually they are they same stuff. Dr. Jamie Farnes, astrophysicist at Oxford just
published a paper suggesting that both dark energy and dark matter may result from the
same phenomenon. And it’s pretty wild: negative mass particles
continuously popping into existence between the galaxies. This rather extravagant claim resulted in
a hysterical response from the media. Our viewers’ perfect blend of bright-eyed
curiosity and cynical skepticism led to many MANY requests for us to do an episode on this
new result. You got it. Today on Space Time Journal Club, let’s
pick apart J.S. Farnes 2018, “A unifying theory of dark
energy and dark matter: Negative masses and matter creation within a modified Lambda-CDM
framework”. As with any new theory combining dark matter
and dark energy, probably it helps to know what they are first. This will be a true too-long-didn’t-watch,
because we’ve been over both a bunch. So, dark matter: the galaxies are spinning
too fast. Based on the gravity from visible matter alone
they shouldn’t be able to hold themselves together. They should scatter their stars into the void. So we conclude that galaxies, and for that
matter the universe, has 5-10 times as much matter as we can actually see. We call it dark matter, and try as we might
we can’t find the presumably-exotic particle that constitutes it. Dark energy is completely different – or
so the standard story goes. Observations of distant supernovae tell us
that the expansion of the universe is accelerating. That acceleration matches the effect you would
get if empty space itself had a tiny bit of energy. As more space comes into existence because
of that expansion thing the more“dark energy” you get, which causes more acceleration. Actually, we gotta think a bit harder about
why dark energy causes accelerated expansion, it’s important for the new paper. The standard picture of dark energy is that
it’s an actual greater-than-zero energy of the vacuum of space. According to Einstein’s general theory of
relativity, any such positive energy produces an inward-pulling gravity. That’s true of dark energy. So why does it result in an outward-pushing,
accelerating expansion? That’s a super-subtle point that took us
like 5 episodes to explain. The big reveal was in this one, where we pick
apart the second Friedmann equation. That’s the solution to the Einstein equations
that tells you the rate of acceleration of the expansion of the universe. But here’s the punchline: if empty space
has a constant, positive energy density then it also has a negative pressure. For obscure reasons that we delve into those
episodes, negative pressure produces an anti-gravitational effect. So dark energy has competing effects – its
positive energy density gives it a positive gravitational effect but its negative pressure is anti-gravitational. In the case of dark energy the latter wins,
and so the expansion of the universe accelerates. An important part of this is that the energy
density of dark energy is constant, so it doesn’t dilute as the universe expands. In Einstein’s equations and the Friedmann
equations, that constant energy density is represented by the cosmological constant,
or Lambda. And a positive Lambda means accelerating expansion. OK, enough with the review. Let’s look at the paper. Jamie Farnes was looking for a way to get
an anti-gravitational effect that explained both dark energy AND dark matter. He tried to do this in very different way:
with negative mass. In physics, we usually assume that mass is
always positive. Forgetting that pressure stuff for a moment,
positive masses and energies always have a positive gravitational effect. They attract other things. So what about negative masses? The answer is complicated - it’s not always
obvious how weird stuff like negative masses translates from general relativity to Newton’s
laws. But for now let’s follow the paper’s argument,
which is based on Newtonian physics. In Newtonian gravity, you multiply the two
masses together along with some other stuff to get the strength of their mutual gravitational
attraction. Two positive masses always give an attractive
force by definition. Two negative masses should cancel each other’s
signs so also give you an attractive force. But with one negative and one positive mass,
the final force of gravity has the opposite sign - that makes it repulsive. Dr. Farnes takes the Newtonian argument a step
further. Mass determines the strength and direction
of the gravitational field – that’s gravitational mass. It also determines the way objects respond
to forces via Newton’s 2nd Law. In this equation, mass is inertial mass. It should be the same as gravitational mass
for the equivalence principle to hold. For a positive inertial mass, direction of
acceleration is the same as direction as the applied force. For a negative mass, this equation suggests
that acceleration is in the opposite direction to the applied force. Push a negative mass away from you it’ll
move towards you, pull it and it’ll move away. According to this Newtonian interpretation. So Farnes argues that the “attractive”
gravitational force between two negative masses should actually drive them apart. This is supposed to give the outward push
to replace dark energy. At the same time, the repulsive force between
a negative and positive mass should repel the positive and attract the negative mass. That’s a bizarre situation, but as I’ll
explain in a moment it’ll give us our dark matter replacement. In fact let’s start with dark matter because
that’s a bit more straightforward. The author uses these ideas about the interactions
of negative and positive mass particles to create an N-body simulation. Basically, he programs a virtual universe
into his computer with both positive and negative mass particles, along with his interpretations
of Newton’s laws. Those simulations showed that galaxies do
indeed spin more quickly when surrounded by negative mass particles. This is because the positive mass in the galaxy
attracts a halo of negative mass, but at the same time that positive mass is repelled inwards
by the surrounding halo. This confines the galaxy from the outside
so it can spin faster than if it were held together by its gravity alone. This is a pretty cool result. To make the same negative mass stuff also
emulate dark energy requires an extra gigantic assumption. The problem is that our negative masses will
dilute away as the universe expands. To fix this, Farnes proposes that these negative
masses are constantly created as the universe expands. That keeps the density of negative masses
constant, even as the density of positive masses falls. The result is a very diffuse negative mass
fluid that fills the universe and constantly replenishes itself. There’s no real justification for this,
besides a shoutout to Fred Hoyle and Hermann Bondi who proposed similar things in their
severely debunked steady state universe idea. But that’s cool – the physical justification
behind dark energy is pretty tenuous too. So, you remember I said that a constant POSITIVE
energy density can be expressed as a cosmological constant? And that a positive Lambda results in an antigravitational
negative pressure? Well a constant NEGATIVE energy density – like
the one proposed by Farnes, gives a negative cosmological constant. That gives a positive pressure, and in general
relativity positive pressure adds an attractive gravitational force, no matter what causes
it. If we look at the second Friedmann equation,
which is really the analog of Newton’s law of gravity for the whole cosmos, this negative
mass fluid – as a negative cosmological constant – has the same competing effects
as regular dark energy, but in the opposite direction. The direct effect is repulsive – antigravitational
– which I guess was the original motivation for using negative matter. But that effect is overwhelmed by the effect
of the pressure, which in this case is attractive – it works to recollapse the universe. Now Farnes acknowledges that his proposal
gives a negative cosmological constant that ultimately decelerates, but there’s some
contradiction because he also suggests that it’s a good dark energy replacement because
it acts like a cosmological constant. And yet a negative cosmological constant gives
you an extremely different universe. Dr. Farnes does a couple of calculations that
are consistent with a negative lambda. He uses the first Friedmann equation – that’s
this thing - to correctly conclude that a universe with a negative cosmological constant
should have a sinusoidal scale factor. He interprets that to mean the universe should
oscillate endlessly in size. But that’s a bit mixed up. In fact that sinusoidal solution is only valid
for the bit of the sine wave where the universe is expanding from zero time – the big bang
- slowing down towards the first peak and then collapsing again. The negative cosmological constant is the
source of that slow-down and for the subsequent accelerating collapse. But there’s no real oscillation. The end of this universe is here, where it
gets back to zero size. Plugging negative masses into general relativity
allows you to break causality. You can build traversable wormholes, Alcubierre
warp fields, time-machines, anti-unicorns. This is a strong indication that negative
mass can’t exist. OK, so these are my complaints on theoretical
grounds. But what about the data? Does a universe with a constant negative energy
density fit the observations? There are two main things to check. First, does it predict an expansion history
that fits the supernova observations that originally discovered dark energy? Those supernova results suggest a universe
that started expanding rapidly and then slowed down due to the gravity of matter – mostly
dark matter. But then that deceleration turned around as
dark energy kicked in, resulting in the current accelerating expansion. With a negative cosmological constant and
this sinusoidal expansion, any slowdown happens near the turnaround point presumably tens of billions of years in the future. That’s hard to fit to the supernova data. Farnes calculates an age for his universe
of 13.8 billion years assuming a very low negative energy density, but that really just
corresponds to the very first straight part in the rise in the sine curve, which is almost a
constant expansion rate. We already know that a constant expansion
rate happens to give a similar age to the standard dark energy age. But a constant or near-constant expansion
rate definitely does not fit the supernova data. The second thing to check is the cosmic microwave
background. I’m not going to go into this in detail
– again, we’ve done it before. Just quickly, the density fluctuations seen
in the afterglow of the Big Bang reveal a universe that is spatially flat. Dark energy, with its positive energy density,
when added to the energy of both regular and dark matter, are needed to explain this spatially
flat universe. If you replace both dark energy and dark matter
with negative-energy stuff, then the universe becomes negatively curved. What we call anti-deSitter space. Which is good for string theorists, as Farnes
notes, but not for observers because that’s not consistent with what we see. So I guess I’m saying that the paper had
some really interesting ideas, but ultimately doesn’t hold together. I think what really bugged me wasn’t the
paper, but rather the media response. It felt like there was no effort at all to
check with other sources about whether this was news-worthy. Super lazy journalism. Except for WIRED – they really nailed it. And what about Dr. Jamie Farnes? He’s a talented astrophysicist. Those galaxy rotation simulations are fascinating. I think it’s courageous to look at fringe
ideas like this, but maybe don’t do press releases without getting triple-checked by
cosmologists. I’m also happy to be corrected on anything
I said, and I’ll address that in the comment responses next time. After all, it’s easy to get confused by
the compounding negatives in what is probably not a negative mass, anti-gravitational, positive
pressure, anti-deSitter space time.
