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.