- Hey there, Jade here.
During my physics degree
one sentence that was repeated to me over and over
by numerous professors was that physics is a model.
Now I have to tell you
that this idea never really resonated with me.
To me, the physical laws of nature that we learned
weren't simply a way to describe reality
they were reality.
There really were forces and fields
influencing how an object moved.
But my professors kept trying to tell me
Jade, physics is just a model.
And I think one of the main reasons why
I couldn't internalize this idea
is because we're only really taught one model,
Newtonian mechanics
you know, Newton's three laws of motion.
Objects move at a constant velocity
unless acted upon by a force.
Force equals mass times acceleration
and every action has an equal and opposite reaction.
It wasn't until I started to get deeper into quantum physics
and learned some really abstract math
that this whole physics is a model idea
really started to make sense to me.
So today, without talking about quantum physics
or abstract math
I'm going to try to convey to you the gravity
of this statement, that physics is indeed a model.
I'm going to share with you an alternative model
for Newton's laws, which is actually mathematically simpler.
So that's nice.
This, it's very interesting because it messes completely
with our intuition about how the past affects the future
and it extends right down
to the fundamental building blocks of physics.
But before we jump right into that
I want to first outline a particular scenario.
You've got a presentation in half an hour
but you're running late.
You can't bear the thought of not being able
to give your talk on the Promethea silkmoth
you worked so hard on.
So you're driving as fast as you can.
In other words, you want to get from point A, your house
to point B, work in the fastest time possible.
What path would you take?
Hopefully most of you said a straight line
since that's the part that takes the least amount of time.
Now, what if we make the problem a little harder
and say that point A is on nice, smooth, concrete
and point B is sitting in a big muddy puddle
where your car will move slower
compared to on the concrete.
Is the fastest path still a straight line?
Common sense will tell you that
if you go further on the concrete
you can spend less time in the slow mud
and save time overall.
However, spending more time on the concrete
makes the total distance you traveled longer.
So to get from A to B in the shortest amount of time
there seems to be a trade off
between creating the shortest possible path
and minimizing the time spent in the slow mud
which results in a path, something like this.
So what is all of this have to do with fundamental physics?
Good question.
So instead of you driving a car,
imagine a particle of light
and instead of traveling on concrete and mud
the light is traveling through it and water.
Water is denser than air so light travels slower
in the water.
The question is now
what Path will the light take between point A and point B?
Amazingly it was Pierre de Fermat
Sorry, I can't say that
Lemme get my husband to say it he's French.
- Pierre de Fermat.
- Amazingly it was
- Pierre de Fermat
- Who in 1662 noticed that light behaves the exact same way
you do when you're late for a presentation
on the Promethea silkmoth.
So math found that between any two points
light will take the path
that takes the least amount of time,
meaning that it bends around the boundary
making the same trade off between total distance traveled
and time spent in the slower water,
just like you did with your car.
Now, if you take the view that I once did
that this is what's really happening.
It's kind of freaky, right?
I mean, you knew where you wanted to go
and chose the path that would take the least amount of time.
Is that what light is doing?
Does a beam of light really choose anything?
We'll come back to this
but so far we've looked at lights
and seeing how it takes the path that minimizes travel time.
But what if I told you that all physical objects
in the universe, protons, electrons, stars,
planets, galaxies all follow a similar rule
that given a starting point and an end point
they all take the path that minimizes something.
Now, given the sneaky way that I said something
you'll hopefully wondering what that's something is.
Now, obviously it can't be travel time
as it is in the case with light
because that would mean that matter moves the same way
light does only in straight lines
and although matter does sometimes move in straight lines
it also moves in curves and arcs
and spirals and basically any way at all.
So what is this something that matter wants to minimize
when it goes from one path to another?
Well, it's a number that physicists call, the Action.
So what is this action thing?
Well, the action for a particular path
is found by taking the kinetic energy
and subtracting the potential energy
of the object along the entire path.
That's what this integral sign means.
If we break this equation down even further
we can get a better idea of what we're talking about.
The kinetic energy is the energy associated
with a particles motion, how fast it's going.
And the potential energy is the energy associated
with its position.
The action therefore depends on the kind of system
that the particle is traveling along.
A gravitational field, empty space,
attached to a spring, et cetera.
What this means is for any crazy trajectory we can think of
between point A and point B
we can assign that trajectory a number
and that is the action.
We do that by imagining an object moving along the path.
And at every point you take the kinetic
minus the potential energy
and add them up for all the points along the path
and that's the paths action.
Now, the path that the particle will actually take
is the one which has the smallest action.
This phenomenon is very appropriately called,
The Principle of Least Action.
This should make you think back to our example
of our particle of light
taking or choosing the path of least time.
The idea of minimizing things relates
to a lot of rich ideas in physics,
from circuits to electrostatics to quantum mechanics
to general relativity.
But the key way of looking at things that I want to focus on
is that all objects in the universe
behave in the same way that our light beam did.
Now compare this to the picture that Newton's laws paint
where what tells us how an object moves
are the forces that are present at each moment.
What the Principle of Least Action seems to tell us
is they seem to choose ahead of time what path to take
given some future location.
So an interesting question is
can the fundamental building blocks of matter
somehow see into the future?
No, Anticlimactic, Yes.
But the answer is no
because the predictions that you get
from the Principle of Least Actions
are exactly the same as the ones you get from Newton's laws.
You can actually derive the Principle of Least Action
from Newton's laws and vice versa.
This means that they're equivalent descriptions
and so they inherit these kinds of fundamental properties
like causality and determinism from one another.
Put in other way, if you had some particle
with initial conditions,
let it move according to Newton's law
so that it traces some trajectory
and finishes at some final outcome
you would get the exact same trajectory
if you fit the particles, initial conditions
and final outcome into the Principle of Least Action.
So to a physicist, the Principle of Least Action
is just another way of representing
the same classical Newtonian laws of motion.
On top of that since Newton's laws are large-scale
approximations of small-scale quantum mechanical laws
so too is the Principle of Least Action
the large-scale approximation of a quantum analog
the Feynman Path Integral,
which also display similar seemingly
future pathfinding weirdness.
So right now the younger more naive me
would be full of all kinds of questions like
which one is right, Newton's laws of physics
or the Principle of Least Action
and if the Principle of Least Action is right,
how do we explain all the paths
that the particle didn't take?
This is where we come back to that idea
that physics is a model.
To a lot of modern day physicists asking what is real,
isn't really an important question.
what's important is that this is a new mathematical tool
that makes calculations easier.
At least that's what Richard Feynman taught.
However, if you're somewhat of a romantic
and are not satisfied with that answer
a more philosophical interpretation
dates back as far as at Aristotle
and is that nature does in fact have goals.
Things move in such a way to satisfy nature's goals
and the Principle of Least Action
is a manifestation of this idea.
Other physicists like Fermat, Euler
and Leibniz saw the Principle of Least Action
as a kind of example of the perfection of God
for creating such economic and efficient laws of nature.
A few years ago, I would have probably been more inclined
to agree with the likes of Aristotle and Euler
in that the Principle of Least Action does imply
some kind of Supreme elegance of nature.
But I think over the years, cynicism have sunk in
and now I'm more on the same page as Richard Feynman
maybe embracing the whole physics is just a model idea
a little too much.
Then again, the two views don't necessarily
have to be mutually exclusive
but I want to know what you think.
Do you think that this is some kind of example
of the perfection of God or it's just a interpretation?
Lemme know in the comments
I am open to having my mind changed.
Just like the idea of physics being a model
didn't really sink in for me until I experienced it myself,
hearing about a concept in a video usually isn't enough
to really understand it.
True intuition comes from spending hours
agonizing over problems
and taking the time to form new pathways in your brain.
If you're interested in getting a firmer grasp
on some of the concepts we talked about today
I would highly recommend a course
by today's sponsor on Classical Mechanics.
This interactive course by brilliant.org
features a quiz on an alternative model
to Newtonian mechanics called Lagrangian Mechanics,
which is based on the same system of thought
as the Principle of Least Action we learnt about today.
You'll learn when it's useful to apply this mode of thinking
and how in some situations
you can make mathematical calculations much simpler
and more intuitive
as well as just learning a different way
to think about things
which is always a valuable thing to do.
Richard Feynman said he would try to think of
at least six different ways
to think about a physical concept
and that seemed to get him pretty far.
Brilliant methodology is to learn by doing
which as someone who completed a physics degree
having not taken any sciences in high school
I can say that's really the only way to do it.
It's free to sign up, but Brilliant is giving a 20% discount
to their premium membership
which includes unlimited access to all their courses
and they have a lot to the first 200 people
to use the link on screen.
Just go to brilliant.org/upAndAtom.
Thanks for watching until after the ad guys.
So in the past few weeks
I've become kind of more of a recluse
like I've been spending a lot of time in my room
just kind of buried in physics textbooks
and I'm watching like online physics lectures.
It's been like old physics and I've kind of become
a bit out of touch with the outside world.
And I just want to make sure
that my videos are still accessible to all of you.
The whole point of Up and Atom
is to make hard things less hard.
So I would hate to be kind of spreading the myth
or the idea that physics is just for really smart,
super elite, geniuses or something like that
because I'm definitely not like that.
But as I said, I've been kind of
out of touch with the outside world
so it's very hard for me to kind of know where everyone is
in terms of like what you know, your background.
So I just wanna make sure
that my videos aren't kind of going over your heads.
So please lemme know if that is the case
and how I can help make it better
and help make the videos more understandable.
Let me know and I'll see you next time.
Bye.
(upbeat music)