Hi there, physics fans.
Twelve episodes and we’re just getting started.
Explanations and questions seem to be a good
mix, after all, questions lead to more explanations.
And so, the cycle continues.
Which reminds me, I wrote an IOU to a viewer
by the name of Oisnowy who was wondering what
we know about the masses of neutrinos.
I hate to owe a debt, so that means I know
what I’m going to talk about in this episode
of subatomic stories.
Measuring the mass of neutrinos is really
hard.
First, they don’t interact very much.
Second, they’re super light.
Third, it’s hard to imagine getting them
to slow down enough to stick on a scale.
From a practical point of view, it’s very
tricky.
In episode ten, I told you about how neutrinos
with a specific flavor don’t have a fixed
mass and how neutrinos with a specific mass
don’t have a specific flavor.
The specific flavor neutrinos are the electron,
muon and tau ones, and the specific mass neutrinos
are the one, two, and three ones.
If you haven’t seen episode ten, it’s
probably worth watching that first.
These nuances make it much more complicated
about what we can and can’t say about neutrino
masses.
But let me give it a try.
To begin with, we have a reasonable handle
on the differences between the masses of the
one, two, three guys.
It’s the differences in those masses that
govern how fast neutrinos oscillate.
By combining lots of measurements, from beams
of muon neutrinos shot to distant detectors,
to the metaphorical glow of electron neutrinos
emanating from nuclear reactors, we’ve worked
these numbers out.
There is yet another complication.
We don’t know the differences of between
nu-one, nu-two, and nu-three.
That would be too easy.
Instead what we know is the difference between
the square of the masses, for instance mass
one squared minus mass two squared.
If we do that, we know that mass one squared
minus mass two squared is about seven point
five times ten to the minus five electron
volts squared.
The third neutrino has a very different mass.
Mass two squared minus mass three squared
is about two point four times ten to the minus
three electron volts squared.
The value of Mass one squared minus mass three
squared is about the same.
What we don’t know is whether m three is
big and m one and m two is small, or the other
way around.
We’re still trying to figure that one out.
So that’s what we know from measurements
of the masses of the three numbered neutrinos.
What about the three different flavors?
Well, one way to do that is to use energy
conservation.
For instance, when a neutron decays, it decays
into a proton, and electron, and an electron
neutrino- well, antimatter neutrino, actually.
We know that both energy and momentum are
conserved.
We can measure the energy and momentum of
the proton and electron, and we can work out
the energy and momentum of the neutrino.
From that, we can work out the neutrino’s
mass.
That’s in principle.
However, the mass is so small that there are
better ways to do the measurement.
And this is to measure the energy of the electron
coming out of the collision.
The energy of the decay is shared between
the electron and neutrino.
This means that the energy of the electron
will follow a spectrum and the electron energy
will be a maximum when the neutrino carries
the minimum energy.
You can calculate the maximum energy the electron
can have if the neutrino is massless and then
just look for deviations from that prediction.
It’s easy to say and very hard to do.
Thus far, nobody has been successful.
However, the KATRIN experiment uses tritium
decays to set a limit.
What they have found is that the mass of an
electron neutrino is between 0.02 electron
volts and 1 electron volt.
One electron volt is about 1/500,000th of
the mass of an electron.
Using similar techniques, researchers can
put limits on the mass of the muon and tau
neutrinos with much worse precision.
The current world limits are that the muon
neutrino must have a lower mass than 190 thousand
electron volts and the tau neutrino must have
a mass of less than 18.2 million electron
volts.
So, we see that the numbers for the tau and
muon neutrino are less precise.
This doesn’t mean that they’re heavier.
Those limits are more about the precision
of the respective experiments.
There is one more measurement that limits
the mass of neutrinos and it comes not from
the particle physics experiments, but rather
from ones that look at space and back to the
Big Bang.
During the Big Bang, neutrinos were formed,
and they interacted with all of the energy
and matter of the universe.
These interactions affected the matter distribution
of the early universe.
By looking at a number of cosmic parameters,
including small variations in the cosmic microwave
background radiation, which is the fossil
remnant energy of the Big Bang, as well as
other parameters of the universe, astronomers
can put a limit on the sum of the masses of
the three known neutrinos and they find that
the sum of the three neutrinos must have a
mass of under 0.15 electron volts.
So those are the known limits.
If we take the numbers I’ve mentioned and
combine them in the simplest way, we would
say that the mass of electron neutrinos is
above 0.02 electron volts and the sum of all
of the three must be less than 0.15 electron
volts.
Of course, you can’t combine things so simply.
But it gives you a sense of what the mass
of neutrinos must be like.
I think it’s safe to say that it will be
quite a while before we work this all out.
Okay, so that’s what we know about the mass
of neutrinos.
I hope that pays my debt in full to Oisnowy.
Okay- who’s up for some questions?
Questions and comments are my favorite part
of the episode, especially when I encounter
kindred spirits.
In a previous episode I told you that I was
admonished by a viewer for an improper pronunciation
of the Greek letter “ni.”
A lot of viewers minds went exactly where
mine did.
I love you guys.
That was a fun movie.
I have decided that am no longer a physicist
who says “ni.”
I am now a physicist who says
“Ekki-Ekki-Ekki-Ekki-PTANG.
Zoom-Boing.
Z' nourrwringmm”
Several viewers questioned my description
of where the energy went when the early matter
and antimatter annihilated a few seconds after
the Big Bang.
I said that it went into the cosmic microwave
background radiation.
They correctly pointed out that the CMB came
from a time about 380,000 years after the
Big Bang.
What gives?
Well, both things are right, but the full
explanation is more intricate than my simple
answer.
That’s an unavoidable consequence of answering
complex questions in under a minute.
In the first second of creation, matter and
antimatter annihilated, releasing gamma rays.
Those gamma rays heated the remaining matter.
Because the universe was what is called thermal
equilibrium, that means that matter absorbed
and emitted energy at equal rates.
A consequence of that is that, on average,
the number of photons didn’t change as long
as the universe was in thermal equilibrium.
The universe expanded and cooled, with the
wavelength of the photons gradually lengthening
as the universe expanded.
Then, about 380,000 years ago, the temperature
dropped to about 3,000 degrees Kelvin or about
5,000 degrees Fahrenheit.
At that temperature, the electrons and protons
at the time could combine, making neutral
hydrogen.
The photons that existed at the time then
could travel across space to be detected today.
The numbers of photons were similar to those
that existed when the matter and antimatter
annihilated, and we can model any differences.
That’s how the photons from the matter/antimatter
annihilation epoch directly ties to the CMB.
Sergey Simon remembers a thing from Star Trek,
the Next Generation called a Heisenberg Compensator,
which corrected for the effects of the Heisenberg
Uncertainty Principle and asks how it could
be built.
Hi Sergey!
The short answer is that it can’t.
However, there is an interesting anecdote
about that.
Michael Okuda, technical consultant for the
show was asked how the Heisenberg Compensator
worked.
He replied, “It works very well, thank you.”
Imre Fabian asks about how a neutrino can
convert a proton into a neutron, when he thought
it required an electron.
Hi Imre.
Actually, both can work.
An electron converts a proton into a neutron
by emitting a negative W boson and turning
into a neutrino.
The W boson then hits an up quark in the proton,
converting it into a down quark and therefore
the proton into a neutron.
The situation is similar with a neutrino,
well actually an antimatter neutrino, but
I didn’t distinguish between them in the
previous episode.
An antimatter neutrino also emits a negative
W boson and converts into a positron.
The W boson does the same thing to the proton.
So, antineutrinos can convert protons into
neutrons, although neutrinos can’t.
But that’s a deeper level of truth than
I usually cover in the answers to these questions.
Ice lh compliments me on my explaining skills
and asks what makes someone good at it.
Hi Ice.
First, thank you for your kind words.
I don’t know how other people do it, but
I can tell you how I do it.
To do cutting edge physics requires a mastery
of complex mathematics.
I understand math very well and I can solve
the equations step by step to get an answer,
but that process doesn’t give me any sort
of intuition.
So, in order for me to understand what’s
going on, I have to translate the process
into simple visual analogies.
They have to be very simple and very visual
to get into my thick head.
Once I’ve done that, the meaning of the
mathematics snaps into focus and tells me
a powerful and compelling story.
Then, I just share those analogies and they
seem to help others.
So that’s my process.
It boils down to my need to give context to
the math.
Tomas Malina tells a painfully bad physics
dad joke.
Hi Tomas!
By now, it should be very clear that I’m
very fond of physics dad jokes.
So, let me challenge my viewers.
Put your favorite bad dad science joke in
the comments and I’ll call out my favorites
in the next episode.
Keep it clean and family friendly.
If you don’t, I’ll call your mom and the
two of us will give you a sad look and tell
you how disappointed we are.
Nobody wants that.
Okay, so that’s all the time we have for
questions.
Let us know what you’re thinking in the
comments, and please subscribe and share on
social media.
Hopefully you’re enjoying videos and learning
some physics along the way.
That would be great because, even at home,
physics- and bad dad science jokes, of course-
is everything.
