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We know the universe has stuff in it called "matter" that takes up space.
And the universe isn't just static - things happen, too!
To be more precise, matter interacts with other matter, like the pull of the earth and
the moon on each other, or the mutual repulsion of your feet and the ground.
We might think that these interactions are just traffic laws imposed by an obtuse pan-galactic
regulatory committee… but in fact, the real answer is much deeper, and more bizarre: interactions
happen simply because you (and by you I mean "the universe") can measure things differently
in different places.
But wait a second: regardless of whether I measure a person to be 6 feet or 183 cm tall,
they're still the same height!
So measurement, by itself, is meaningless, but as surprising as it sounds, that meaninglessness
is exactly what causes the fundamental forces of nature.
Now, often on MinutePhysics I use analogies to help simplify complicated physical phenomena
while still getting the essence of the point across.
But today we're going to witness a real live application of the theory behind the standard
model, and while for simplicity's sake we're going to ignore quantum effects and apply
it to economics instead, this is literally the same math as the standard model.
Ready, set, PHYSICS!
Suppose, for example, that I gave you $2 for a $2 sheep – nothing has really happened,
or no value has been transferred, because I could sell you the sheep back and end up
with my same $2 again.
Ignoring the fact that maybe I like sheep more than money, which is why we'd trade in
the first place, the real value as measured by our "value-ometer", which we call money,
is unchanged.
What's more, the amount of money we pay for things is really an arbitrary scale, which
is obvious when you remember that different countries have different currencies.
But of course countries can't interact financially without a way of converting the way they measure
value.
So, now suppose I want to buy a sheep in Canada – there are two things that'll affect the
price: first, Canadians may just value sheep less than I do, and second, their dollar may
be different from my US dollar… so perhaps the sheep will only cost $3 Canadian.
Which of course means I can go to Canada, convert my 2 US dollars to 4 Canadian dollars,
spend three of them on the sheep, and come back to the US with my sheep, plus one canadian
dollar (which converts to fifty US cents).
If I then sell the sheep back to someone in the US for the $2 it's worth, I'll now have
$2.50 instead of $2.00.
So I made money just by buying and selling a sheep!
This is very different from the case of buying and selling a sheep inside the US, where no
real value changed hands.
Here, just by making a "currency exchange" part of my sheepish journey, I was able to
transfer real value from Canada to the US, and this transfer of value happened solely
because we measure value differently in different places.
It's like stealing, only legal!
Now, don't all go running off to buy Canadian sheep and sell them in the US… in the real
world shepherds (and money exchangers) realize that they're losing out, and the price of
sheep (and CAD) will adjust to take this into account and minimize all transfers of real
value, or "stealing".
But "making money from nothing" does happen if you can act before the market adjusts – it's
called "Arbitrage," and anytime it's possible, it means that the economy isn't in an equilibrium,
or optimal, state.
So much for the "invisible-hand" of the market…
But anyway, in physics, this effect of stealing real value is called "momentum transfer"…
or in day-to-day terms, a force.
And now we'll see why!
Suppose, instead of one border and one exchange rate, we have a whole row of countries that
can each exchange money with their neighbors:
Now if I want to pull off my arbitrage shenanigans by selling a sheep in Iran, I'll have to transfer
the money back to the US, which in this case means it'll be exchanged at every border along
the way.
But this series of measurement conversions looks like it's "moving"… like, it's an
"exchange-rate-particle" that gets created in Iran, carries value from Iran to the US,
then disappears!
Wait, let's see that again: buy a sheep, bring it to Iran, sell it, money changes from rial
to rupee to mirian to rupee to pound to dollar to dollar… and I end up with more money
than I bought the sheep for to begin with!
So that's it: real standard model physics in your own barnyard.
And hopefully now you can see why measuring things differently in different places inevitably
gives rise to a long-range interaction mediated by a particle!
For example, the electromagnetic potential tells us how electric charge is measured differently
at different places… it's the "electron-exchange-rate", and the excitations in the electromagnetic
field are particles, which we call photons.
Instead of transferring monetary value, these photons transfer momentum from one electron
to another, and if you add up a whole bunch of these momentum transfers, you get something
that we call a force!
But isn't a photon a particle of light and not a "force"!?!
Well, once you have the idea of an "exchange-particle", you don't actually need the electrons at the
endpoints anymore… you could just have that particle moving through empty space on its
own.
That's why photons are both the particles that mediate the electromagnetic force, and
bonafide particles on their own!!
In fact, all the forces we know, like the electromagnetic interaction, the strong interaction,
weak interaction, and gravitational interaction, work this same way at a fundamental level:
an "exchange-particle," which physicists crazily call a "gauge boson", transfers momentum and
energy between two matter particles.
And this is what Newton was trying to get at when he said "for every action there is
an equal and opposite reaction"… we'll cut him some slack since he lived in the seventeenth
century, but what he really should have said was "for every interaction you need an exchange
particle."
And maybe if he had known this, he could have turned sheep into gold.