Every Force in Nature (Theory of Everything, Part III)

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.