Sometimes, seemingly crazy ideas in physics lead to the most profound advances.
For example: the idea that every electron in the universe is really the one same electron..
traveling forwards and backwards in time.
In the spring of 1940 the great physicist John Archibald Wheeler had a flash of insight.
He picked up the phone and called Richard Feynman.
The fateful conversation began...
"Feynman! I know why all electrons have the same charge and the same mass"
"Why?" asked Wheeler's former graduate students.
Because...
They are all the same electron.
Wheeler went on to describe. Here's one electron universe idea: that there exists only one electron
and that electron traverses time in both directions.
It bounces in time eventually traversing the entire past and future history of the universe in both directions
and interacting with itself countless times on each pass.
In this way it fills the universe with the appearance of countless electrons.
When the electron is moving backwards in time, it's a positron, the antimatter counterpart of the electron.
Whether or not we should take Wheeler's ideas seriously is debatable.
However, Richard Feynman did take at least one aspect very seriously:
the mathematical equivalence of antimatter as time-reversed matter.
In fact, it was Swiss physicist, Ernst Stueckelberg, who first proposed this idea in the 1930s.
But Wheeler's 'One-Electron Universe' idea inspired Feynman to build this
representation of antimatter into his path integral formulation and the following
Space-Time interpretation of quantum mechanics,
which won him the 1965 Nobel prize for physics.
The 'One-Electron Universe' was motivated by an odd fact about electrons that had troubled Wheeler:
that they are all identical.
Exactly the same charge, exactly the same mass, exactly the same everything,
there was no satisfying explanation for this.
Wheeler's notion was that if electrons behave as though they are identical,
perhaps they truly are to the point of being identically the same entity.
Let's think about the electron as its "worldline". It exists as a line traced by its passage through space and time,
rather than as a point-like particle, at one instant in time.
The point-like electron is just a segment of that worldline if we take a slice, through space-time, at one instant in time.
The direction of an electron's worldline can shift as the electron is scattered by photons;
but, what if it were possible to deflect an electron back the way it came...
Temporally?
If an electron can revert its course in time,
then its worldline looks like a zigzag; at any one point there can be multiple instances of the same electron.
Think about it as though you are flying over a giant "S" bend in a river:
You can only see the straight parts of the flow; that one river looks like three rivers.
That one electron...
is zigzagging back-and-forth 10 ^ 80 times
looks like all of the electrons in the universe
This "winding river" analogy is actually pretty useful.
If you are observant you might notice that between zigs and zags of the river the direction of the current changes.
Well, moving charged particles also produce a current: an electric current.
The direction or sign of that current depends on the direction of motion,
but also on the sign of the charge.
For example, if a negatively charged electron is moving to the left, it produces some current "I";
then, an electron moving to the right produces the same strength of current, but with the opposite sign: "-I"
and a positively-charged positron moving to the left
also produces the same opposite-signed "-I" currents.
So, you get the same flipped sign whether you reverse the direction of the motion of the electron
or if you give it the opposite charge by turning it into a positron.
But reversing a particle's motion is mathematically the same as watching it in reversed time.
That doesn't mean that time actually goes backwards;
just that if you reverse the ticking of the clock in the particle's coordinate frame,
its direction of motion appears reversed, which has the same effect as flipping its charge.
Actually, it's slightly more complicated than that.
In a quantum field theory that's consistent with Einstein special relativity, all particles must be symmetric under what we call:
CPT transformation.
C is charge conjugation; so, flipping the sign of the charge.
T is time reversal; changing the direction of the coordinate clock.
P is parity inversion; which can be thought of as reflecting the particle, like in a mirror.
So, if you make all of these changes at the same time...
Flip the charge, invert the parity, reverse time, a particle should end up back where it started.
But if you just flip the charge and invert parity - so do a CP transformation -
you still have to reverse time again to get back where you started.
So that means CP transformations leave an object time-reversed.
So that's equivalent to a T transformation.
But a charge-flip just turns a particle into its antimatter counterpart.
A parity inversion still leaves it as antimatter.
CP transformations alone turn matter into mirror reflected antimatter,
so T transformations must do the same thing.
In the sense of these fundamental symmetries, antimatter is time-reversed matter.
We already saw how expressing antimatter as time-reversed matter is extremely useful in simplifying Quantum field theory calculations,
because it massively cuts down the number of Feynman diagrams you need.
For example, this one diagram for electron and photon scattering,
represents both the double deflection of an electron, or of a photon producing
an electron-positron pair before the positron annihilates with the first electron.
That virtual particle in the middle
may be an electron traveling forwards or backwards in time; the latter is a positron.
So, how does this work with Wheeler's one electron hypothesis?
We can think of the annihilation of an electron and positron as just the electron being deflected back in time.
Similarly, the creation of a particle pair is the electron being scattered forward in time.
If we draw a Feynman diagram for the whole universe we can have only one electron
undergo countless scattering events, some of which change its course through time.
At some point in the middle of the diagram we see many many electrons...
Wheeler's idea was that they are the same electron.
Now there are some big problems with the One-Electron Universe idea.
The biggest is that we should see equal numbers of electrons and positrons at any time.
After all, when that first electron makes it to the end of time,
it needs to travel back again as a positron in order to have any more electrons.
But clearly there are more forward propagating electrons than positrons.
Wheeler suggested, perhaps half jokingly, that all the positrons may be hiding in protons.
Ultimately though he didn't pursue this idea particularly seriously.
It's certainly not widely accepted that there's only one electron in this universe,
nor whether that's even a meaningful statement.
We now think of electrons as oscillations; as waves in the more fundamental electron field.
It doesn't really make sense to think of an electron as a thing that carries an identifying label.
However, the insight was a critical step in Feynman's later work...
and the notion is nonetheless rather poetic;
imagine that every electron, indeed every particle, in our bodies
- in everyone's bodies - is the same particle,
separated from itself by countless passages across the cosmos and across all of time.
That makes each of us a tangled knot in the one single thread,
weaving back-and-forth, across the reaches of Space-Time.
Hey everyone; now that we completely understand the fundamental nature of antimatter,
let's go back and look at the solution to the Feynman diagram challenge question.
I asked you to draw all of the two-vertex and four-vertex diagrams
for the interaction where electrons and positrons scatter off each other.
Using the simple rules I laid out for building Feynman diagrams, well here are the two-vertex diagrams.
These are really interesting
because the processes seem so different.
In one case we have a positron and an electron influencing each other's momentum by exchanging a virtual photon,
similar to electron-electron scattering.
But in the second case, the electron and positron
actually annihilate each other, producing a virtual photon, which then creates a new
electron-positron pair.
As long as the incoming and outgoing particles have the same momenta
these two are part of the same overall interaction.
The four-vertex diagrams look like this:
We randomly selected five correct answers.
If you see your name below, you're a lucky winner, and we have a "Space-Time" t-shirt for you;
Email us PBSspacetime@gmail.com with your name, address,
U.S. t-shirt size - small, medium, large, etc.- also, let us know which t-shirt you want.
That includes our brand-new shirt:
"the heat death of the universe is coming".
In fact, this shirt is available to anyone to purchase. Link in the description.
We also have a new shirt that's exclusive to challenge winners and Patreon supporters...
Introducing: Astro Chicken von Neumann, Conqueror of the Galaxy.
Last week we talked about the controversial evidence that many galaxies in the observable universe are drifting very slightly
towards a point beyond the cosmic horizon...
We call it "Dark Flow".
You guys had some great comments.
OxFFF1 comments that Dark-Flow must have a constant velocity and not be accelerating...
and is absolutely right in commenting that.
Assuming Dark-Flow is real, and assuming it's caused by a gravitational influence beyond the edge of the observable universe,
then yeah, it no longer exerts a force on us.
That force would have been exerted by a high-density patch of space in the pre-inflationary period at the beginning of the universe.
Now, that patch has been thrown so far away that it cannot influence us, or us it.
However the residual drift remains
Daniel Grass asks about how we can measure the direction of dark-flow
given that we can only really measure the velocity components that are towards us or away from us.
And yeah, that's a limitation and a challenge of this method.
However, if all galaxies have a slight preferred direction to one point on the sky,
then the way those velocity vectors map onto our line of sight to those galaxies
should change in a very particular way over the entire sky.
This is why you need so many galaxies across the sky to do this.
M Paulson poked fun at astronomers for using "dark" to describe anything they don't understand:
Dark Matter, Dark Energy, Dark Flow...
It's true, we're kind of stuck on the word.
To be fair, we did workshop lots of other words, but
"Huh?"-matter, discombobulating-energy, and "WTF-flow" just didn't do as well in the focus group.