Hi there, physics fans!
We’ve spent a lot of time talking about
black holes, because black holes are undeniably
interesting.
However, it’s time to return to our roots
and talk about tiny things.
It’s been said that the Planck length is
the smallest possible length, but that’s
not the entire tale, as I will tell you in
this week’s episode of sub, sub, Subatomic
Stories.
In episode 15, Divyansh Vishwakarma asked
about the Planck length and whether it was
proof that loop quantum gravity was real.
I promised to answer, and I didn’t forget.
It is often said by non-cautious people that
the Planck length is the smallest length,
the Planck time is the shortest time, and
the Planck energy is the highest energy.
But that’s not really true.
So, just what are these Planck constants?
Our story begins in 1899 with Max Planck,
a German theoretical physicist, and one of
the legends of quantum mechanics – in fact,
he was one of the original architects of the
first quantum revolution.
Here are two pictures of him, one before and
one after he made his contributions to quantum
mechanics.
That’s proof if I ever saw it that quantum
mechanics blows your mind.
One of the things Planck did was to try to
come up with what are called natural units
or units on which everyone can agree.
This remains a problem even today, as you
can see in some of my videos, where people
occasionally make snippy comments about whether
I use imperial or metric units.
Planck reasoned that any scientifically sophisticated
society could measure a few quantities in
whatever units they used.
They are the speed of light, which has units
of length per time; the gravitational constant,
which has units of length cubed, per mass,
per time squared; the reduced Planck constant,
which has units of length squared times mass
per time; the Boltzmann constant, which has
units of length squared times mass per time
squared per temperature; and the Coulomb constant
of electricity, which has units of length
cubed times mass per time squared per charge
squared.
Planck then took these scientifically measured
quantities and made various ratios of them
to get a desired unit.
For instance, to get a unit of time, he took
the reduced Planck constant times the Gravitational
constant, divided by the speed of light to
the fifth power, and then took the square
root of all of that.
The result is the Planck time, which has a
numerical value of 5.4 times ten to the minus
44 seconds.
But some other culture, with different units,
could do the same thing and come up with a
Planck time of 12 zortblats or something.
But since these are the same thing, we now
have a way to convert zortblats to seconds
and back again.
Planck went on and defined the Planck length,
mass, temperature, charge, etc.
I’ve put some of them here on the screen.
Planck was rightfully proud of his accomplishment
and wrote in his paper, which was in German,
of course, but translated here it said “... it
is possible to set up units for length, mass,
time and temperature, which…retain their
meaning for all times and for all civilizations,
including extraterrestrial and non-human ones,
which can be called ‘natural units of measure’.”
Pretty cool.
If we’re ever visited by ET, we’ll at
least be able to agree on unit conversions.
So, this part of the story is clear.
However, in the intervening century and more,
the lore has morphed from Planck units being
natural units, to being the smallest possible
things.
How did that happen and is it true?
That story stars in 1959 with Alden Mead,
who was a chemist at the University of Minnesota.
He had an idea connecting gravity and the
smallest length.
His idea wasn’t popular, and it took him
five years of arguing with journal referees,
when in 1964 he published his paper entitled
“Possible Connection Between Gravitation
and Fundamental Length.”
I admit I didn’t read it when it came out.
I was kinda young.
What Mead did was consider the effect of gravity
on how light is diffracted when you send it
through a very small aperture.
Everybody ignores this effect, because it’s
so small.
But, at small enough scales, the effect of
the Heisenberg Uncertainty principle becomes
relevant here.
The Heisenberg Uncertainty principle says
that it is impossible to simultaneously measure
an objects position and motion.
Mead showed that it is impossible to measure
the position of an object to a precision smaller
than the Planck length and, from that, we
can say similar things about the Planck time.
I put a link to his paper in the description.
So, what does Mead’s work really mean?
It doesn’t say that the Planck length is
the smallest possible length.
What it says is that at the Planck length,
the effect due to gravity is large enough
that it can no longer be ignored.
What he says is that, at the Planck length,
the laws of physics as we know them totally
fail and have to be replaced by something
better.
Perhaps that something will allow for shorter
distances.
We don’t know.
We need a theory of quantum gravity for that,
which I talked a bit about in episode 13.
I spoke to Mead back in 2013.
He was retired by then.
He contacted me because he stumbled upon an
article I wrote about Planck units, which
gave him credit.
He filled me in on the decade long conversation
about how the scientific community morphed
from thinking he was crazy, to accepting he
had a point, to saying the Planck scale was
the shortest.
He even pointed me to a public conversation
he had in 2001 with Nobel Prize winning physicist
Frank Wilczek.
I put a link to the conversation in the description.
If you’re interested, it’s worth your
time.
The bottom line is that the Planck length
is >>NOT<< necessarily the shortest length,
but it is a length at which existing physics
>>HAS<< to fail and needs to be replaced with
something better.
So, it’s an important size, but it may not
be the smallest size.
OK, hopefully I taught you something you didn’t
know and given you something to ponder.
Let’s see what questions we have this week.
Questions…questions are always fun.
Let’s jump right into it.
Duggydo notes that if the expansion of the
universe is increasing the wavelength of light,
that means that the light’s energy is decreasing.
Given that physicists say that energy is conserved,
where does the energy go?”
Hi Duggydo.
So, the answer might surprise you.
Conservation of energy isn’t always real.
Now, me saying that conservation of energy
isn’t really true is pretty staggering and
requires some explanation.
Bear with me, because this is somewhat technical.
The story begins with a theorem created by
Emmy Noether, called Noether’s Theorem.
This theorem connects conservation laws with
mathematical properties of the theories that
describe them.
According to the theory, a conserved quantity
implies that the equations don’t care where
you set your zero.
For instance, for conservation of energy,
the equations can’t care what moment you
set as time zero.
It could be just over two thousand years ago.
It could be the moment you were born, or it
could be this very second.
If the laws of physics don’t care about
that choice, energy will be conserved.
But an additional requirement that is never
mentioned is that space and time must be static
and unchanging.
But, of course, in general relativity, that
last requirement is not satisfied.
Space and time can change and warp and distort.
Accordingly, the law of conservation of energy
doesn’t necessarily apply.
So that’s the reason that it appears that
energy is lost.
It’s because non-conservation is not only
allowed, it’s expected.
Now, the description I’ve given here is
the gist, but, because of the limited time
we have, it’s very brief.
So I’ve put links to two more thorough and
technical explanations in the video description
below.
If you want to understand this better, you’re
going to have to read those.
Cronos804 and many others wants to know why
iron is the heaviest element that can be made
by fusion.
First, let me say that obviously iron isn’t
the heaviest element that can be made by fusion,
but it >>IS>AND<< get energy
out of it.
Let me give you two different explanations.
To start out with, two forces govern atomic
nuclei – the strong force that holds protons
and neutrons together and the electrostatic
repulsion pushing the positively charged protons
apart.
The strong force is basically a contact force
like Velcro, while the electrostatic repulsion
has an infinite range.
As nuclei get bigger, the electrostatic repulsion
becomes more important because it applies
over larger distances.
The strong force of only adjacent nucleons
holds it together, while the electrostatic
force of all protons pushes it apart.
This is the reason that nuclei with more than
120 protons or so don’t exist.
But it’s also why iron is the heaviest element
that can be made by fusion and have energy
come out.
For elements lighter than iron, the strong
force causes the nuclei to nestle together
neatly, and, above iron, electrostatic repulsion
starts to become important.
This graph shows the energy per nucleon for
many elements.
The element with the lowest energy is iron.
Elements with lower mass release energy as
they fuse.
Elements with higher energy release energy
as they split.
In the sun, light elements fuse together,
releasing energy until they hit iron.
Heavier than that and it takes energy to make
them.
Elements heavier than iron are made from the
energy of a supernova or when neutron stars
merge.
Heavy element fusion needs energy to proceed.
So that’s why iron is the final stage of
ordinary stellar fusion.
Good question.
Nick Fontaine asks if we had a superconducting
and super strong wire, could we use it to
lower a camera below the event horizon of
a black hole and see what is going on.
Hi Nick.
No.
We can’t.
And the reason is simple.
The event horizon is the point where gravity
grows so strong that light cannot escape.
Light is, of course, electromagnetism.
In your superconducting wire, the information
would come out along the wire, using electromagnetism
to transmit the signal.
Electromagnetism is also what holds the wire
together.
But we’ve already said that the gravity
of the black hole is too strong to let electromagnetism
escape.
And that’s true, even on a wire.
So no go.
I’m afraid that the black hole’s secrets
are still safe.
Mohit Soni notes that I have an unusually
great sense of humor for an astrophysicist.
Well thank you Mohit.
I appreciate that.
But it’s entirely understandable that this
would be so, because I’m not an astrophysicist.
I’m a particle physicist, and we’re known
for our clever and dazzling wit.
We even have to do a standup comedy routine
on our final exams.
Astrophysicists, on the other hand, generally
aren’t nearly so funny.
It’s music that seems to be their thing.
Theultrapixel asks if we have enough data
to work out a theory of everything if we were
smart enough or if we’re missing important
pieces.
Hi ultra.
I guess it’s possible that some smart whiz
kid might figure things out, but I totally
doubt it.
There are many things we don’t understand,
like dark energy, dark matter, and a bunch
of other things.
In fact, this video series is about to pivot
to topics exactly like those, which is to
say, unsolved mysteries.
We talked in this episode about the Planck
energy, which is the energy at which the laws
of physics as we know them must break down.
That energy is about a quadrillion times higher
than what the most modern particle accelerator
can achieve.
It’s inconceivable to me that as we explore
higher energies, we won’t encounter phenomena
we can’t even imagine now.
I think we’re talking thousands of years
of research before we can talk about a realistic
hope of finding a theory of everything.
Sadly, I won’t be here to see it.
Naveen James asks me my viewpoint about tachyons,
which are particles that go faster than light.
Hi Naveen.
The answer is simple.
I don’t.
There is zero evidence that they exist.
Of course, it’s possible that they actually
do exist, and people should continue to think
about ways to look for them.
But one thing I’m certain about is that
there has been a lot of ridiculous thing written
about them.
Totally ridiculous.
People talk about tachyons as having imaginary
mass, or going back in time, or breaking causality,
or all sorts of nonsensical things.
All of those ideas arise from applying Einstein’s
theory of relativity to particles going faster
than light.
But Einstein’s equations are explicitly
valid only for objects moving slower than
light.
So they just don’t apply.
If tachyons do exist, it will require new
theories to describe their motion.
It’s very much like how Newtonian physics
applies fine for the familiar slow and large
world we inhabit, but we had to invent relativity
and quantum mechanics to describe the world
of the fast and the small.
If we ever exceed the speed of light, Einstein’s
equations will just not apply.
People who try to apply them are like those
who try to use Newton’s laws to describe
a black hole.
It’s a foolish endeavor and it just doesn’t
work.
OK, so that’s all the time we have for questions
today.
You know the drill.
Please like, subscribe, and share.
As I just mentioned, after this video, I’m
going to turn my focus to mysteries and speculative
physics.
It’s going to be great fun.
I’m sure you agree, because, even at home,
physics – both the understood and the speculative
– is everything.
