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Language: en
Imagine you're in empty space and you
fire off a stream of electrons. Well,
then according to most physics
textbooks, the only way to change how
those electrons behave is by applying an
electric or magnetic or gravitational
force to them. But most physics
textbooks are wrong. In the 1950s, two
physicists came up with a clever
experiment. You could have electrons
travel through a region with no electric
or magnetic fields whatsoever. And yet
by flipping a switch, you could change
their behavior. The magnetic field could
be just zero. And yet the presence of
some quantity could actually lead to
observable effects. That wasn't supposed
to happen, right? This experiment split
the physics community in two. It made
them question whether fields are
fundamental or whether something that
was supposed to be just an abstract
mathematical tool was actually more core
to reality. This tool was first
introduced in an attempt to solve one of
the hardest unsolved problems in
physics, the threebody problem.
That is, if you have three bodies and
you know their initial positions and
velocities, how will they move under the
influence of each other's gravity? It's
a juicy juicy problem which has occupied
literally generations, hundreds of
hundreds of years of incredibly
ambitious, talented mathematicians,
physicists, and astronomers and and and
beyond. The fact that this problem is so
difficult to solve should at least be a
little surprising because if you have
just two bodies, then the solution is
easy to find. In fact, the general case
was already solved over 300 years ago by
Newton himself. But when Newton added a
third body, well, that's when everything
fell apart. In the two-body case, the
forces behaved predictably, always
pointing toward the systems shared
center of mass. But with three bodies,
this is no longer the case. When you try
to calculate the forces, they end up
being extremely dynamic. In addition to
worrying about the magnitude of the
forces, you also have to worry about
their direction. So you end up with this
chaotic mess of vectors.
For the next 100 years, everyone who
tried to solve this problem failed. But
what if there was some other way to
approach it? A way to simplify the math
and not have to worry about these
three-dimensional vectors?
Well, that's where Joseph Louie Lrangee
comes in. In the 1770s, he was also
trying to solve the threebody problem
and he came up with a new approach. It
works something like this. Say you've
got a single mass like a star. Lrange
imagined assigning a value to each point
in space around the star. The value is
determined by the stars mass and the
distance from the star. You can think of
each value as a height. And if we then
turn this into an altitude map, you can
see how the star creates this sort of
well. What Lrange had developed was the
gravitational potential V. And what's
important to note is that V is a scalar.
It has a magnitude but no direction.
So the genius in Lrange's idea is this.
At any given point, we can draw an arrow
pointing directly downhill where the
size of the arrow corresponds to the
steepness of the hill at that point. We
can repeat this process at every point.
And if we then shift our perspective to
two dimensions, look what we've got is
the gravitational field of the star.
Mathematically, we say that the
gravitational field G is equal to the
negative gradient of V. So like Branchet
found a way to switch the problem back
and forth between one of vectors and one
of scalers. And while adding up vectors
is hard, adding scalers is a piece of
cake. To find the combined potential
landscape of any number of bodies, you
just add up their individual potentials.
And then you can always use that to get
back the forces if you want. For a
simple two-body system like the Earth
orbiting the Sun, that combined
potential looks something like this. If
you look closely, you see that there are
five points where the gradient is zero.
And so Lrange realized the forces there
are also zero. which means that at each
of these points you could place a tiny
third body and it would maintain a
perfectly stable orbit. That is if it
isn't disturbed. These points are now
known as the Lrange points. And while
they didn't help solve the free body
problem, Lrunch was developing more
sophisticated tools. In fact, he
developed an entirely new way of doing
mechanics. But for that to work, he
didn't just need the potential. He
needed the potential energy and the
kinetic energy, too. I think when people
hear potential, they think potential
energy. And while they're very similar,
there is a subtle difference. If you
have the potential, that's basically the
field corresponding to a single body.
Then it will have some potential field
around it, which is described as P =
minus G M over R, where this is the mass
of the sun. But to get the potential
energy, we need to add in a second body.
So let's say that's the Earth. The
potential energy, let's call it U, is
basically just the potential times the
mass of the second body. So they're very
similar, but they're slightly different.
And the kinetic energy of the Earth is
simple. That's of course 12 MV^ 2. So
now we have everything we need to try
this new method. In fact, we made a
whole video on this over a year ago. But
for now, all we need to know is that we
can write down the kinetic minus
potential energy to find what's known as
the lrunchion. Then you sub that in to
the so-called oiler lrunch equation and
out comes your solution. For example,
predicting the motion of a double
pendulum by using the standard forces
approach is infamously hard because as
one pendulum is swinging, it provides
the attachment point for the pendulum
hanging below it. And so that pendulum
is in this moving reference frame as
it's swinging. But if you pluck the
kinetic and potential energy into the
Oiler L Grunch equation, then you can
quickly get to a solution, at least
numerically. That's actually how we made
this simulation. I remember thinking,
man, force is like hard to get the right
answer. You can do it if you're good and
people who are good at mechanics can do
it. But with the Lrangeian approach, you
could just write down the energy, which
is a scalar, not a vector. Plug it into
the Oiler Lrange equation and you get
the right equation of motion. And you
don't have to be a good physicist.
>> But for all its usefulness, the
potential wasn't enough to help Lrangee
solve the three-body problem. In 1887,
mathematician Heinrich Brunes finally
proved that the threebody problem is
unsolvable.
There are simply too many unknowns and
no way to simplify the problem to reduce
them. So, the best we've got are
computer simulations which compute the
potentials from moment to moment and use
that to predict how the system will
evolve in time.
And so that's where we come to realize
that the three-body problem is beautiful
for what it's taught us, even though we
now recognize that we can't actually
solve for this exact problem as as many
folks had hoped to do. And in doing
that, they merely gave us the machinery
of modern mathematical physics. So I'm
pretty happy they tried. The potential
helped simplify a wide array of
problems. For many physicists, it even
replaced forces as their primary tool.
It became so useful that people started
to wonder if other forces in nature
might have a corresponding potential.
Starting with the electric force. If you
look at the formula for the electric
force, you notice that it's remarkably
similar to that for gravity just with
masses and charges swapped. In the
1810s, Simeon Deni Pon, one of Lranch's
students, also noticed this similarity,
and he realized that you can define an
electric potential fi in a very similar
way. But there is one important
difference and that is while two masses
can only attract, two charges can
attract or repel. So now with the
potential you don't only get pits, you
also get hills.
But one force was much trickier to find
the potential for and that was the
magnetic force. And that's because
magnetism is a fundamentally different
beast from the gravitational and
electric force. Take a bar magnet. We
can draw the magnetic field it produces.
It looks something like this. Now, at
first glance, this looks very similar to
the electric scenario where we have a
positive and negative charge. But this
picture doesn't look at what's going on
inside the magnet. So, if we reveal
what's inside, then you see that these
lines actually continue, but now they
point from south to north. So, magnetic
field lines are actually loops. They
don't have an origin or end point. And
that fundamentally changes things. So,
physicists needed a new way to describe
the magnetic potential. The breakthrough
came in the 1840s from an undergraduate
student named William Thompson. His day
job as an undergraduate was to learn as
much fancy calculus as possible. And
then when he learned all that, he
invented more. Thompson found that the
mathematics of his day was unable to
describe the relationship between a
magnetic field and its associated
potential. So he came up with an
entirely new function, the curl. To see
how this works, imagine the arrows of
this vector field are like currents in a
liquid. If we were to place a paddle
wheel right here, it would start to
rotate rapidly counterclockwise. As
Thompson defined it, this spot has high
positive curl. At this spot, it would
rotate clockwise, but not as rapidly, so
it has lower negative curl. And here,
the current pushes on it equally in both
directions. So, it wouldn't rotate at
all. This spot has zero curl. Thompson
realized that the magnetic vector field
B could be defined as the curl of some
other vector field. the magnetic vector
potential A. Now, even though they're
both vector fields, it turns out that A
is often much easier to work with than
the magnetic field itself, much like the
other potentials V and FI. Thompson was
showing there was a kind of underlying
mathematical structure one could use
that would streamline the calculations.
But even Thompson thought this was a
kind of device, a helpful device and not
um a substitute for like the real
physics. Decades later, Thompson was
elevated to the House of Lords for his
contributions to science, where he
received a new title, Lord Kelvin. With
Kelvin's latest edition, there were now
three fundamental equations relating the
potentials to their respective fields.
Thanks to each of these, you could now
solve problems much easier. And so, ever
since, professional physicists often use
potentials instead of forces or fields
to solve the problems they're working
on. Potentials even show up in some of
our best physical theories of the
universe. But that raises an important
question. If potentials pop up
everywhere, then do they actually
represent anything physical? That is,
can they have a direct influence on
reality? Well, to most physicists, the
answer was a resounding no. Take the
gravitational potential of a single
star, for example. Well, we could just
add 10 to each value of the potential,
and this would shift the overall
landscape. But the change in landscape
from one point to the next remains the
exact same. So the field is the same as
the one we had before. And the force an
object would experience at any point
would remain unchanged. In fact, we can
add any constant 10, 100, a million, and
the field doesn't change. And so the
forces an object would experience going
around it also don't change. There are
an infinite number of ways we could
write the gravitational potential for
any gravitational field and get the
system to evolve in the same way. And
the same is true for electricity and
magnetism. The value of the field and
thus the force is fixed. But the value
of the potential is arbitrary. So from
this most physicists concluded that
potentials can possibly have any
physical significance. It must just be a
trick that makes the math easier. But
most physicists might be wrong.
>> In 1942, 23-year-old David Bow was hard
at work on his thesis in particle
physics when one day he received an
unexpected visit. Robert Oppenheimer,
who was David Bow's PhD adviser, wanted
to bring him squarely onto the new
Manhattan project efforts. This was a
life-changing opportunity. Bow would be
working sidebyside with some of the top
minds in physics. But there was a
problem. The project's military
director, General Leslie Groves, had to
approve Oppenheimer's recruits, and when
he ran a background check on Bow, he
didn't like what he saw. He briefly
joined the American branch of the
Communist Party when he was in
California. By his own recollections, he
quit pretty quickly cuz he got bored. He
said, "These people just sit around
talking all day and don't do anything."
Even so, Groves deemed Bow a security
risk and banned him from working on the
Manhattan project. But things got even
worse. Just as he was about to finish
his dissertation in Berkeley, the topic
was then classified. He did not have
clearance. So he couldn't even work on
or even write up his own dissertation.
So Oppenheimer had to certify that Bow
had done good work. And in 1943 in
wartime, that was sufficient for Bow to
actually get a PhD. After the war, Bow
became an assistant professor at
Princeton University. But fear
surrounding his communist sympathies
followed him wherever he went. In 1949,
he was brought before the House
Unamerican Activities Committee for
questioning. While Bow was under
investigation, Princeton let his
professorship lapse. And even after he
was acquitted, the university refused to
reinstate him. It seemed that Bow was
destined for obscurity.
And so, Oppenheimer gave him a firm
recommendation. Leave the country and
start fresh somewhere else. Oenheimer
was no stranger to political
persecution, and he didn't want Bow to
suffer the same fate. So Bow took the
advice. His journeys brought him to
Brazil and then Israel. And though he
was free from the political pressures he
had felt in America, he still found
himself an outcast. Many of Bow's
academic peers were put off by his more
unorthodox ideas, including his radical
interpretation of quantum mechanics and
his new theory of human consciousness.
But there was one student who was
enthralled by Bow's approach, and that
was Yakir Aharanov. He was first of all
extremely extremely bright and also very
nice personality.
So it was beautiful to interact with
him.
>> When Bow relocated once more, this time
moving to the University of Bristol in
England, Aaronov chose to come with him.
And it was there in Bristol in the 1950s
that Aaronov and Bow stumbled upon
something huge. For a long time I was
thinking more more deeply about the
interpretation of quantum mechanics. It
was not to solve any problem. It was
just curiosities.
>> According to quantum mechanics at the
smallest scales particles behave like
waves and this behavior is governed by
the Schroinger equation. The solution to
this equation is called the wave
function p. If you take its modulus
squared, you get the probability density
of finding a particle at a given point
at a given time. The left side of this
equation tells you how the wave function
changes over time and space. And the
right side tells you that this change
depends on H, what is known as the
Hamiltonian. It's basically just the
total energy of the system. In the case
where we have both an electric and
magnetic potential, the solution to the
shredding equation looks something like
this. where this is just a constant and
this term describes the complex phase.
It looks complicated but it's actually
quite easy to get a feel for it. So
let's plot it in two dimensions for an
electron moving to the right. The
different colors here represent the
different phases and you can see how the
phase evolves over time and space. Thank
you to Richard Beil for inspiring this
approach. Now if you look closely at the
original phase term you see a and phi
the magnetic and electric potentials. So
watch what happens if we add a magnetic
vector potential that points in the same
direction as the electron is traveling.
You can see that the wave stretches out.
So now the phase changes more slowly
over space than it did before. And if
the potential points the other way then
now the wave gets more compressed and
its phase changes faster over space. And
a similar thing would happen if you
change the electric potential phi. Now
this by itself I think wasn't shocking
to most physicists just as you would
always use the potentials to make the
math easier. That's also why you use it
in the shredding equation. But really
what's responsible for these you know
even phase changes were still the
fields. But you spoke to aarov.
>> Yeah.
>> And that wasn't his take.
>> No. If you look at the Schroinger
equation, you can't just replace the
potential fi with the electric field E.
>> Why not?
>> Because you're losing information.
>> Okay?
>> Because remember, you can define any
number of potentials for a specific
electric field because you can pick an
arbitrary height. But that information
is lost when you go and swap it out for
the electric field. There's another way
to think about it.
>> Okay. Okay. This getting real. So if you
have an expression like 5x^2 + 5, you'd
think you could just write this as the
integral of 10 x dx, right? Because the
integral is 5x^2
plus c, right? C is a constant. So it
includes five, but it also includes any
other number. But importantly, C is not
five or at least not in every case. So
you lose this specificity when you go
from a potential to an electric field.
And Aharanov wasn't comfortable with
that. So he thought what if every
quantum system was actually influenced
by the potential and not by the field,
>> right? So it's the potential that shows
up in the Schroinger equation. So it is
what influences wave functions. He had
to find a way to prove that what we're
observing is always because of a
potential and not because of the field.
>> How do you do that? Complicated.
See, Aharonov had to design an
experiment that would send a particle
through a region where there's no
electric or magnetic field, but there is
a potential. In such a setup, if the
phase of the particles wave function
started changing slower or faster, that
had to be the direct result of the
potential itself because there are no
fields.
But that's where you run into a problem
because there's no way to directly
measure the phase of a particle's wave
function. So how do you devise an
experiment that can yield a measurable
result? Well, Aharanov enlisted the help
of his mentor Bow and together they came
up with the following theoretical
experiment. It starts with a beam of
electrons which is split into two. In
the middle of these two beams is a
tightly coiled wire known as a solenoid.
Now solenoids have an interesting
property. When you run a current through
one, it produces a strong magnetic field
inside the coil and a very weak field
outside the coil. The longer the
solenoid, the weaker the field in the
surrounding space. For simplicity,
Haronovan Bomb imagined a setup with an
ideal infinitely long solenoid. One
where the magnetic field outside the
coil is exactly zero. After traveling on
opposite sides of the solenoid, the
electron beams are redirected back
towards each other by the researchers.
And here at this point, they intersect.
Now, since electrons behave as waves,
the waves from the intersecting beams
overlap and produce an interference
pattern. bright fringes with gaps in
between them. The exact pattern depends
on the phase of each of these waves.
When the solenoid is off, there is no
magnetic field in the region the
electrons are traveling through. And
there is no magnetic potential. The
phase of the electrons changes in the
same way across both beams, regardless
of whether they pass above or below the
solenoid. And so you get an interference
pattern that looks like this. But when
the solenoid is turned on, well, there
is still no magnetic field because it's
confined entirely within the coil. But
there is a magnetic potential. That may
sound strange, but remember the magnetic
field is the curl of the magnetic
potential. The curl of the potential can
be zero in some region even when the
potential itself is not. And that's
exactly what's happening here.
Now take a closer look at the vector
potential. In the space the upper beam
passes through, the potential points in
the opposite direction as the beam. So
here the phase changes faster. But below
the solenoid, it points in the same
direction as the beam. So the phase
changes slower. If the phase truly
depends on the potential alone and not
the field, then the phases of the two
beams should evolve differently. So as a
result, the interference pattern should
shift when the solenoid is on versus
when it's off. The magnetic field could
be just zero and yet the presence of
some vector potential could actually
lead to observable effects. That wasn't
supposed to happen, right? What I love
about this story is that it reminds me
that individual people can challenge
entire paradigms. For nearly 200 years,
many of the smartest minds in history
all believed that potentials were
nothing more than mathematical tools.
But then two outsider physicists came
along and defied that interpretation.
Confident in their approach, they took
on the entire scientific establishment.
That same belief in the power of the
individual is what motivated me to
partner with planet wild. Many of us can
feel helpless when we look at the huge
problems facing the earth today.
Deforestation, plastic pollution, and
the extinction of entire species. The
easy solution is just to wait around and
hope someone else will do something
about it. Planet Wild gets boots on the
ground to actually protect our planet.
And they make it easy for anyone to join
the cause, which is one of the reasons I
became a member. Another reason is that
every month we as a community fund new
projects to clean up oceans, rewests,
protect endangered species, and raise
awareness. You can think of Planet Wild
as crowdfunding for nature. My favorite
part, I get to see the impact of my
contributions through outstanding
monthly videos which are published right
here on YouTube. Take this for instance.
This is a Planet Wild mission in Mumbai.
It's a scalable technology that stops
plastic at the source, preventing 10
tons from reaching the ocean every
month. Planet Wild invested over
$100,000 in this. And that money didn't
come from governments or corporations.
It came from ordinary people like you
and me. You can sign up for whatever
amount feels right for you and cancel
anytime. The first 150 people to sign up
using my code, Veritassium 1, will get
their first month paid for by me. Just
scan this QR code or click the link in
the description. If you're interested in
the science behind their projects, then
go check out their YouTube channel. I'm
leaving the link to the plastic cleanup
mission in the description. And now back
to the mystery of the potential.
Aharanov and Bomb published their
findings in 1959 and the reception was
mixed.
>> Certainly at the beginning many people
thought that this can't be true. So
there were many people that tried to to
write articles against this.
>> Even Neils Boore, one of the founding
fathers of quantum mechanics found it
impossible to accept that a particle
could be influenced by a potential in
the absence of any force. But some
physicists supported a Heronovan bone.
Richard Feineman wrote, "The fact that
the vector potential appears in the wave
equation of quantum mechanics was
obvious from the day it was written. It
seems strange in retrospect that no one
thought of discussing this experiment
until 1959 when Bow and Aharanov first
suggested it and made the whole question
crystal clear." Fineman included himself
in that statement. He later wondered why
he had never noticed the effect.
Physicist Victor Viskoff had a similar
response. The first reaction to this
work is that it's wrong. The second is
that it's obvious.
Ultimately, there was only one way to
settle the debate. Someone had to
actually do the experiment. The first to
try was a colleague of Aharon Bombs at
the University of Bristol, Robert
Chambers. Chambers experiment largely
followed the setup Aaronovan Bomb
proposed with one notable exception. An
ideal solenoid would have to be
infinitely long, which is physically
impossible. So instead, Chambers used a
tiny needle-like piece of iron about a
millionth of a meter thick and 500 times
as long. When this iron whisker was
magnetized, it produced a magnetic field
that was strong within the metal itself,
but negligible outside of it, as well as
a magnetic potential in the surrounding
region of space. To get a baseline
interference pattern, Chambers fired two
beams of electrons around an empty
region of space. Then he added the
magnetic whisker. When he fired the
beams again, the interference pattern
shifted. It seemed that Aharanov and
Bomb were right. But critics were
unconvinced.
People objected to it because it since
the whis is finite. There is always some
magnetic fields that go out.
>> Maybe a stray field was responsible for
the effect, not the potential.
>> And that's showing throwing no shade on
their colleague who did these cool
experiments. It's like it's hard, right?
But it's really hard. And so it went for
several decades. Experimentalists
repeatedly tested the Aharana bomb
effect, but each trial had flaws that
left the result open to debate
until in 1986, a team of Japanese
researchers led by Akira Tonamura came
up with a new way to do the experiment.
See, they used a tiny donut-shaped
magnet to make their magnetic field.
With a perfect Taurus, all the magnetic
field is contained within the loop.
outside it it's absolutely zero. And as
an added layer of protection, the team
also coated the entire magnet in a layer
of superconducting nobbium, which would
block out any leaking fields. Now,
previous experiments relied on turning a
magnetic field on or off, but Tonamura's
team took on a different approach. In
their case, the magnet is always on. But
because of its unique shape, the
potential outside the Taurus is
different from the one in the center. It
points towards us on the outside and
away from us on the inside. And the team
realized they could take advantage of
this. They started by firing off an
electron beam which was actually wide
enough to be treated as two separate
beams. Part of it traveled along through
empty space and functioned as the
control whereas the other part washed
over the entire Taurus. And what's
important here is that the beam is wide
enough so that part of it passes around
the Taurus and part of it passes
through. Then at the end, a bip prism
deflects the electron beams toward each
other. They intersect and this is where
they create an interference pattern. Now
think about what this interference
pattern should look like. Well, for
starters, there should be a shadow of
the Taurus. So, we can fill that in. But
the rest, well, it depends on whether
the bomb effect is real or not. If it's
not real, we'd expect to see an
interference pattern that looks
something like this, where the pattern
outside the Taurus and in the center
match up. But if it is real, then the
electrons that traveled through the
center would have experienced a
different potential, which would have
shifted their pattern by half a phase.
So that should look something like this.
Now, here are the results from
Tonomora's experiment. You see these are
the interference fringes inside and
outside the magnet. And then if you
follow what is a peak outside the Taurus
lines up with
>> a trough inside the middle and then it's
a peak outside again.
>> And that's exactly what they predicted.
>> This is exactly what they predicted.
>> So it's real.
>> It's real.
>> Only the more experiment was really the
final proof experimentally.
>> And yet soon a new debate emerged. The
effect is real, sure, but how should we
interpret it? What is it really telling
us about the nature of the universe?
Today, physicists largely fall into one
of two camps. The first camp claims that
potentials aren't just mathematical
conveniences. They can influence
physical reality. This is the
perspective initially favored by
Aharonov and Bone. As they wrote in the
abstract of their paper, contrary to the
conclusions of classical mechanics,
there exist effects of potentials on
charged particles even in the region
where all fields vanish.
Some take this position a step further.
Since the potentials show up in the
Schroinger equation and the fields do
not, well, they argue that the
potentials are more fundamental to
physics than fields are. Richard Fineman
supported this idea. He wrote, "A is as
real as B, realer, whatever that means."
I mean, I kind of like that
interpretation, but something about the
potential bothers me, and that's the
fact that you can set the potential at
any arbitrary height. It can be plus
infinity. It can be minus infinity,
anything in between. So, wouldn't that
change, you know, how the potential
actually influences the wave function?
>> This bothered me too. So much so that I
actually ended up asking a professor
about this. But it turns out it can't.
It knows it's not just the potential
that's that's entering the observable.
It's the line integral. So, it's only a
that enters. It's not the magnetic
field. B vanishes. It's only a, but it's
not a alone. It gets a little technical
here but you know if I pull up you know
>> as one does
>> as one does a flip chart then we can
actually run this through. So if you
look at how the potential shows up then
what's measurable is not the phase
directly but it's the phase shift call
it delta theta then the phase shift is
the line integral of a over the path or
dotted with the path. So you get this.
Now you can imagine okay let's add a
constant to this and if our setup is
roughly you know we start here one
electron beam goes like this and the
other one goes like this and these are
symmetric then the potential here will
point let's say in this direction but
here it will point in that direction
let's say instead of a we do a plus c
some constant then when we're taking the
path this way we'll be adding that c and
we'll be dotting it with dx but because
that path is the exact same when we go
this way we just subtract it so it
cancels out so the potential yeah it
does show up but in such a way that all
the arbitrariness of the potential it
cancels out perfectly
>> okay
>> it's a geometrical quantity involving a
that has taken care of for which all
that residual ambiguity has has
literally canceled out
>> the potentials being physical might
sound strange but the Second
interpretation is even stranger.
Physicists in camp 2 maintain that
potentials really are just mathematical
objects and the fields are responsible
for the effect. But in Tonamura's
experiment, the magnetic field was
completely confined within the solenoid.
For this interpretation to be true, its
supporters are forced to assert that
fields can act non-locally. That is, a
field can influence things outside the
region of space where the field itself
exists. Many physicists find this idea
difficult to swallow. I think the idea
of saying that these fields act
non-locally undoes the reason why we
have field theory. Right? The great
triumph of field theory which has served
us so well for more than 100 years is
this notion stubborn notion that local
causes yield only local effects.
>> And yet Aharanov's own perspective has
shifted from camp one to camp 2.
>> When we publish the article we found
this the effect of potentials. when you
use potential and use the schedule
representation, it looks as if
everything is local, but it's misleading
because that local potentials are really
not physical. Later I decided that it
should be called a non-local effect of
the
electric magnetic field. The less field
the effect of a field that is not where
it is. While non-locality remains a
controversial idea, a sizable portion of
physicists do side with Aharanov and the
debate continues to this day.
>> I maybe have a third interpretation.
>> Good.
>> And I would love to get your thoughts
and if it's bad, please tell me
honestly.
>> Okay.
>> So, we did this other video about
particles essentially exploring all
possible paths all at once. And so right
now we're saying either the potentials
are real or fields are acting
non-locally. But what if there's a third
option where the fields are still local
and it is the fields that are affecting
the change but rather it's the particles
that are exploring all possible paths
all at once. You could potentially even
have some quantum tunneling effects
going inside an area where there are
fields. you know, as the electron or the
wave function at least explores all
possible paths gets influenced by those
slight bits where the wave function is
inside the field.
>> I actually don't think that's
ridiculous, Casper. That's how that's
for a strong ringing endorsement. I
think there's a lot to that. Um,
>> okay.
>> If we could think about these things as
it is indeed the quantum phase that's
being affected.
>> Yeah.
>> We can describe that phase in terms of
quantum mechanical path integrals. I
think that's a perfectly reasonable way
to to frame it. So yeah, I'd buy that.
>> That's awesome. I'm pretty sure this
isn't the complete answer, but one thing
which would be cool is if someone else
takes this idea, you know, or maybe it
gets inspired by it and they're like,
"Actually, that doesn't work, but here
is how it does work and now we're
closer."
>> That's right. That would be the best
possible outcome. Well, the best
possible outcome is is you're just
right. But the second best possible
outcome is that is that that nudges the
community more broadly to ask those to
ask new questions of familiar material.
That's right.
One new question the community asked
was, is there also a gravitational
version? In 2022, researchers at
Stanford tested this. A simplified
version of their experiment works
something like this. They shut up ultra
cold rubidium atoms into a tube-shaped
vacuum chamber at the top of which was a
tungsten mass. Now, atoms like electrons
are also governed by a wave function. So
they split each rubidium atom's wave
function into two distinct packets and
they launched them to different heights.
One was sent really high and got close
to the mass whereas the other didn't.
And then when the two collided at the
bottom this created an interference
pattern and when they let this interfere
and accounted for all other effects they
could clearly see the phase shift as
predicted by aarov and bomb. So it seems
like the gravitational aarov and bomb
effect is real. If the results hold up
the scrutiny, this is a huge finding
because it suggests that the
electromagnetic and gravitational
potentials can influence reality at the
most fundamental scale even when all the
fields are exactly zero. So, does that
mean that most physics textbooks are
wrong or need updating? Don't throw out
all the textbooks. They're beautiful. We
learn a lot, but that doesn't mean we're
done. And we should be open to surprise.
And just because things haven't changed
in let's say 200 years roughly between
say Lrange and Aaron Boom they still
could change right and they can
sometimes change in in beautiful and
surprising and very powerful ways. I
read somewhere that the reason you
decided to do the AB effect was uh that
you didn't really think potentials were
something that was just a mathematical
tool like most scientists believe.
>> That is correct. I was very ignorant.
Luckily, sometimes not to know too much.