The search for a single number,
 the Hubble constant,...
...the rate of expansion of our universe,...
...has consumed astronomers for generations.
Finally, two powerful
 and independent methods...
...have refined its measurement
 to unprecedented precision.
The only problem...
 is that they don't agree,...
...and it's causing to question...
...some of the most basic assumptions
 about the universe.
In 1929, Edwin Hubble...
 discovered the universe.
He gave us
 our first incontrovertible proof...
...that there are galaxies
 outside the Milky Way,...
...by measuring the distances
 to the spiral nebulae
They were many millions
 of light years from us,...
...far outside the Milky Way, 
and so must be galaxies in their own right.
Combined with the Doppler shift
 velocity measurements of Vesto Slipher,...
...Hubble revealed that the galaxies
 are not only receding from us,...
...but they are receding at a rate
 proportional to their distance.
An impossibly vast universe
 had been discovered beyond the Milky Way,...
...and at the same time
 that universe was revealed to be expanding.
The galaxies appear to be racing away from us,
 because the intervening space is expanding.
We encapsulate the expansion of the universe
 with a single number, called the Hubble constant.
H-naught  (H0)
It tells us how fast the galaxies appear to be
 retreating from us, dependent on their distance apart
But, more fundamentally, H0 tells us
 the rate of expansion of the universe...
...in the modern era.
Ever since Hubble's great discovery,...
...the search for H0
 has been the all-consuming obsession...
...of thousands of astronomers
across the generations.
And, understandably,...
...the rate of expansion of the universe,
 combined with the gravitational effect...
...of the matter and energy it contains,...
...can be used to determine
 its entire expansion history,...
...from the Big Bang to its final fate.
And it's fundamental for interpreting
 our observations of the distant universe,...
...whose light has traveled billions of years
 through this expanding cosmos.
You can imagine the alarm
 when the two most powerful methods...
...used to measure this fundamental parameter,
 the Hubble constant,...
...gave different results!
But before we get to that, let's talk about
 the great quest to measure the Hubble constant.
Until the new millennium, the best we could do
 was to estimate H0 within a factor of 2,...
... somewhere between 50 and 100
kilometers per second per megaparsec.
These strange units
 warrant some explanation.
Km/s, that's for
 the recession speed of a given galaxy.
Megaparsecs is for its distance,...
...with 1 megaparsec being
 around 3.3 million light-years.
If the Hubble constant were, say,
 75 km per second per megaparsec,...
...then for every 1 mega parsec distance,...
...we'd expect the galaxy to be retreating from us
 at an additional 75 kilometers per second.
Historically,
 measurement of the Hubble constant...
...meant measuring the recession velocity and distance
 for as many galaxies as possible.
The velocity part is relatively easy.
Just do as Vesto Slipher did,
 and measure redshift.
This is the lengthening of the wavelength 
of light from that galaxy,...
...which was stretched as it travels to us
 through an expanding universe.
The distance...
 that's tricky.
Hubble used Cepheid variables,...
...giant stars, 
 during the last phases of their lives.
They pulsate with a period...
...that's related to their true brightness,
 as discovered by Henrietta Leavitt.
Measuring Cepheid periods in other galaxies
 gave Hubble their true brightnesses,...
...as though undimmed by distance.
Cepheids became what we call "standard candles",
 objects of known luminosity,...
...whose observed brightness, therefore,
 tells us their distance.
But this calculation
 involves assumptions and uncertainties.
For one thing, the Cepheid
 period-luminosity relationship...
...first had to be calibrated,...
...based on nearby Cepheids,...
...whose distances can be figured
 using stellar parallax
Tracking their tiny motions on the sky,
 as Earth orbits the Sun.
This stepwise determination of astronomical distances
 is called the cosmic distance ladder.
With each step on the ladder,
uncertainties compound.
Add this to our uncertainties in the behavior and observation of Cepheids themselves,...
...and the precise measurement
 of the Hubble constant...
...has been a slow laborious process.
As larger telescopes
 and more expansive surveys were completed,...
...we gradually whittled down
 the errors in H0.
An important advance was 
the development of new standard candles.
Cepheids are good, but can only be seen
 out to a certain distance.
Supernovae can be seen much further,...
...and type 1a supernovae are the key.
These result when white dwarfs,
 ancient remnants of dead stars,...
...absorb too much material
 from a binary partner
Runaway fusion
 causes them to detonate.
The resulting explosion
 has highly predictable brightness,...
...making them
 excellent standard candles.
In the 1990s,...
...astronomers were using these supernovae
 to better nail down the Hubble constant.
They inadvertently discovered...
...that the expansion of the universe
 is actually accelerating,...
...revealing the existence of dark energy.
One of the Nobel Prize winning researchers
  behind this discovery is Adam Riess.
Riess has continued the quest...
...to refine our measurement of H0
 to ever greater precision.
A big part of his work is to improve the calibration
 of type 1a supernovae as standard candles.
Riess's Supernovae H0 for the Equation of State
 project, - SHOES -,...
...uses the Hubble Space Telescope
 to match old supernovae observations...
...with new, more reliable Cepheid variables.
By improving this run
 on the cosmic distance ladder,...
...all past supernovae distances
 also improve.
Recent teams have now narrowed down the Hubble constant to 73.5 ± 1,7...
...kilometers per second per megaparsec
That 2%-ish uncertainty...
...is a hell of a lot better
 than the old factor of 2 uncertainty.
So, where's the crisis?
Well, in order to fully believe
 a measurement like this,...
...we prefer it to be made
 through independent methods.
The SHOES project measures the recession of galaxies
 up to around 2 billion light years away.
So it's a more or less direct measurement
 of the CURRENT expansion rate.
But there's another way to go.
What if we could measure the expansion rate
 of the universe at the very beginning?
Then, we could figure out what its current expansion rate should be, given our best understanding...
...of all the gravitational influences
 that affected that expansion since the Big Bang.
So, we'd better hope
 that it does give the same result,...
...or there is a big problem,
 with either our supernova measurements...
...or with our understanding
 of how the universe evolved.
Spoiler: ...
 there IS a problem.
There's another reason to try to calculate H0 from observation of the early universe
It's that that observation I'm referring to
 is far more reliable than Cepheids and supernovae.
I'm talking about the
 Cosmic Microwave Background radiation, the CMB.
This is a topic we've been over,
 so, for now, just the TLDR.
The Cosmic Microwave Background is the remnant
 heat glow of the universe's initial hot dense state.
Released around 400,000 years
 after the Big Bang,...
...when the universe had finally cooled down enough
 to become transparent to light.
We still see it today,...
...now stretched by a factor of 1,100
 by its near 14 billion year journey...
...through an expanding universe.
This is the map of the CMB across the entire sky,...
...created by the Planck satellite.
The speckles are
 tiny differences in temperature,...
...corresponding to tiny
 differences in density.
The blue regions are a factor of 100,000
 cooler than the red regions,...
...and also slightly more dense
These over-densities...
...would go on to collapse into the vast
 clusters of galaxies of the modern universe.
So,...  how can the CMB
 tell us the Hubble constant?
The key is
 the sizes of those speckles.
In the era just before the release of the CMB,
 matter and light were trapped together.
Matter wanted to collapse
 under its own gravity,...
...while light generated a powerful pressure
 to resist that collapse.
These counteractive forces
 produced oscillations,...
...really vast sound waves
 that rippled across the universe.
These are
 the baryon acoustic oscillations,...
...and they occurred
 on all different sized scales,...
...sloshing between high and low density,
 over those 400,000 years.
Then,...
...the release of the CMB meant that light and matter
 were no longer coupled together.
And so those oscillations stopped.
The state of the oscillations
 at the moment of that release...
...is imprinted on the CMB,
 in those speckles.
We usually show
 the distribution of speckle sizes...
...with what we call a power spectrum,...
...which basically shows the abundance
 of speckles of different sizes.
The location of these peaks...
...tells us which oscillation modes...
...just happened to be at their peaks...
...at the moment the CMB was released.
This, in turn, depends
 on the density of matter and radiation,...
...as well as the expansion rate
 of the universe in that early epoch.
So, how do you get the Hubble constant,
 i.e., the current expansion rate, from all of this?
Well, first you figure out
 what starting cosmological parameters...
...could give the power spectrum
 observed by Planck.
Those parameters include the starting combination
 of both dark and light  matter, and radiation,...
...as well as the initial expansion rate.
And then,...
...you figure out how the universe
described by these parameters...
...should evolve to the present day.
This sounds involved,...
...but the Planck power spectrum is so rich
 with information, that the Planck team...
...claim to have calculated H0
 with even better precision than SHOES.
The problem is,
 the results don't agree.
The Planck H0 is 66.9 ± 0.6
 kilometers per second per megaparsec,...
...compared to the supernova result
 of 73.5 ± 1.7.
Now, they're actually
 remarkably close,...
...given we figured them out
 from data at the opposite ends of time.
But they also seem
 irreconcilably different,...
...3,7 sigma different in fact.
Which means a 1/7000 chance...
...that that level of difference
 could have happened through random errors.
This is the crisis in cosmology.
This discrepancy first emerged in 2016, when
Riess's new calibration of the supernova-derived H0...
...revealed it to be in real conflict
 with the Planck result from a couple of years earlier.
Since then, calibrations have been improved,
 results have been rechecked,...
...and independent methods have been used
 to calibrate the supernovae as standard candles.
The difference is real,...
...and, in fact, 
the error bars are only getting smaller.
Okay, before we declare
 all cosmology broken,...
...let's think about the two main possible sources
 of this discrepancy.
First: there are unknown
 systematic sources of uncertainty...
...in either the supernova
 or Planck measurements.
Biases, that are driving one or the other
 to be too high or too low.
Perhaps we don't understand
 Cepheid variables like we thought,...
...or perhaps gravitational lensing alters the 
Planck speckles differently to how we thought.
Ongoing efforts are ruling out
 systematic errors one by one,...
...but it's possible there's still something
 we haven't thought of yet
Second:  there's some unknown physics...
...that needs to be taken into account
 for the CMB calculation.
This is the most exciting possibility
There are a few options.
So let's start a new list.
One:  A new type
 of very fast-moving particle.
Insufficient numbers could skew the energy balance
 of the early universe, and mess up the calculation.
That particle could be
 the sterile neutrino,...
...a hypothetical, non-interacting neutrino,
 that isn't part of the standard model.
Two:  Dark matter particles
 behave differently to how we thought.
Perhaps dark matter interacts more strongly
 with matter and radiation,...
...which would shift the sizes
 of those CMB speckles.
Three:  Dark energy isn't constant.
The current calculations assume that dark energy
 is described by the cosmological constant,...
...which, by definition,
 doesn't change.
But if dark energy increases,...
...that could explain why we observe
 a higher H0 in the modern universe...
...than is predicted by extrapolating
 from the early universe.
The answer will depend on whether the more
 correct measurement of the Hubble constant...
...comes from Planck or SHOES.
New observations and new telescopes
 will refine these numbers even further.
Independent methods, like using
 gravitational lensing, or gravitational waves,...
...will weigh in on one side or the other.
Perhaps the uncertainties will be refined,
 and the two results will converge.
That'd be cool.
The near centennial quest to measure
 the expansion rate of the universe will be concluded.
Or perhaps the discrepancy will persist.
That would be even cooler
We'll have a new tool...
...to investigate the mysterious physics
 of dark energy, dark matter,...
...or of unknown particles
 beyond the standard model.
For now, we continue
 our obsessive quest for H0...
...and for what it'll tell us
 of the origin and fate of our expanding space-time.
In today's comment responses,
 we need to catch up on 2 episodes.
First, it's our journal club
 on Dr. Jamie Farnes' paper...
...about negative mass dark fluid...
...as a unifying explanation
 of both dark matter and dark energy.
Then we'll get to comments
 on our CPT symmetry episode.
So, a friend of a friend
 of Dr. Farnes' chimed in.
Leo Staley's friend says that Dr. Farnes
 doesn't necessarily believe the claims of his paper,...
...but rather its purpose
 was to spark interesting ideas among physicists.
Well, okay.   I totally respect that motivation
 to publish even quite fringe ideas,...
...and he certainly
 sparked a conversation.
I mean, look,
 I'm still talking about it.
Andrew Paulfreyman points out that...
...the gravitational lensing measurements
 of dark matter...
...will give the exact opposite results
 if dark matter is due to this negative mass fluid...
...than if it's actual,
 positive mass matter.
And my intuition tells me
 that this is right.
Gravitational lensing
 is the bending of light by a gravitational field.
We see it in the warping
 of images of distant objects,...
...due to the gravitational fields
 of more nearby galaxies.
We can use that warping
 to measure masses.
And yeah, those measures tell us
 that dark matter has positive mass
I'd need to do the simulations,
 but I have a feeling...
...that we wouldn't even see
 this sort of strong gravitational lensing...
...if the effect of dark matter
 was due to this dark fluid.
Marik Zilberman's
 distaste for negative masses...
...is that they produce perpetual motion machines
 and paradoxes left and right.
Exactly what I thought.
When a theory leads to these - sort of - 
pathological predictions, it's a big red flag.
And we're actually going to do
 a challenge question episode,...
...to explore these paradoxes.
Stay tuned.
Okay, let's move on to our episode
 on the ultimate symmetry of nature,...
...the simultaneous reversal
 of charge, parity, and time.
First up:  a few of you asked questions
 about time reversal, so I want to clarify.
The T in CPT symmetry
 isn't a literal rewinding of the clock.
It's best thought of
 as a reversal of all motion,...
...both linear and angular momentum.
Everything reverses direction.
If the universe has
 this sort of T symmetry,...
...then, if you reverse all motion,...
...the universe will evolve exactly backwards,
 to its initial state.
Turns out that's not the case,...
...as demonstrated by the different forward/backward reaction rates in certain quantum interactions.
But the universe IS symmetric
 under full CPT inversion.
Now, a CPT inverted universe
 is not the same as this universe,...
...but the laws of Physics are the same.
The point is that you can't tell
 which of the two you're in.
TinyFox Tom asks whether mass
 would be inverted under CPT symmetry.
And I guess you're referring to the idea
 that time-reversed energy has its sign flipped.
So, the simple answer is no,
 because the T in CPT isn't a true time reversal.
But in the case of a true time reversal,
 the answer is, essentially, yes.
And a negative mass particle,
 moving backwards in time,...
...is mathematically the same as a positive mass particle moving forward in time
That notion makes sense in the math,...
...and is used in, for example, Feynman's
 path integral formulation of quantum mechanics.
But it's not so obvious whether this idea
 corresponds to anything physical.
Rishit Vora asks how a T inversion
 would affect a black hole?
Well, a true time reversal
 that included the interior of a black hole...
...should transform it into a white hole.
Everything that ever fell in
 would come rushing out,...
...and presumably reassemble itself into
 the stars, spaceships, monkeys,...  that originally fell in.
As to the motion reversal symmetry
 of the T in CPT,...
...frankly, I'm not sure, because we don't know
 the state of matter in the black hole.
But, at any rate, remember
 that T symmetry is broken.
Both the T of CPT
 and true time reversal symmetry.
So a rewound black hole shouldn't revert exactly
 to whatever it formed from.
That doesn't mean
 information is lost.
Just that it ends up
 in a different form.
And back to dark fluid for a sec.
Mr. Nation [?] has his own unified theory
 of the Dark Sector.
He reveals to us
 that dark energy equals dark matter,...
...times the speed of dark...
...squared.
[  DE  =  dm•(cd^2)  ]
Genius on so many levels.
Not only scientific levels,
 but still, levels.
