For the last week or so I’ve been contemplating this question: What would it have taken for Aristotle to have come up with the iconic equation of the Theory of Relativity, E = mc2, two thousand years before Albert Einstein was born?
It’s a fun question to ponder. Without considering the details, it’s exciting to think that maybe, just maybe, the basic conceptual tools might have been there for Aristotle to work with. After all, the pieces of the equation seem like such basic ideas: matter, energy, light, speed. Is it really that crazy to think that, given the right intellectual nudge in a particular direction, Aristotle could have come up with an equation for a relationship between mass and energy? We know the ancient Greeks had a lot of ideas that were far ahead of later science. Some Greek philosophers even believed that the Earth was a sphere, and were trying to calculate its circumference! Wouldn’t it be at least possible that Aristotle could have had a similar “ahead-of-his-time” insight, given the right circumstances or inspiration?
Just for fun, let’s try to answer that question.
First, we should break down Einstein’s equation into the basic concepts that go into it.
Energy. Aristotle did have a concept of energy, or enérgeia (ἐνέργεια): the thing that causes matter to move. The concept wasn’t exactly like our concept of energy today, but it had some similarities. For Aristotle, the notion of energy had spiritual or metaphysical overtones: pleasure was considered to be a type of energy, since it drove people to action. Similarly, happiness is a kind of energy, because it also causes action.
He does talk about energy in the more “normal” sense of kinetic energy, or movement; however, there are still some radical differences. Aristotle saw causes and effects in a way that is the reverse of the way we think of them today. For Aristotle, building materials have the potential to be a building, and it is that potential that provides the driving force or “energy” for the change. From our perspective today, this is weird, to say the least.
We see prior events as causing later events; for Aristotle, most objects had idealized forms that they “desired” to take, or were somehow drawn toward, so that the end result was supplying the motive force for the change.
The simplest example of this is probably his explanation of gravity. Materials made primarily from the element Earth had a “natural location” that was at the center of the earth (planet). Because all Earth (element) had a kind of “goal state” of being at the center of the earth (planet), that goal provided the causal force or energy for the movement of the matter.
So all of that is pretty weird. Nonetheless, it’s not inconceivable that Aristotle could have come up with the idea of measuring a quantity, E, that represented the amount of motive force (even if that force is “happiness”) that drives matter into motion.
Mass. This one is the easiest, and the most promising. (That is, “promising” if you are on the team that is rooting for Aristotle to pre-invent the theory of relativity.) Aristotle believed that the world was made up of elements, and as such he was able to talk about the way the mass of different objects affected their behavior. Most of what he said was wrong, as it turns out. For example, he believed that heavier things would fall faster than light things. He also believed that the natural state of all matter was at rest (apart from the “natural tendency” for earth to go to the center of the planet, air to go up into the sky, and so on), and that it would only move while a force was acting on it.
But, he would have at least been able to conceptualize the idea of the “amount of mass” (or at least: the amount of matter, in the form of elements) an object had. Therefore, he could have come up with the idea for a quantity of mass, m.
The Speed of Light. This is the most difficult piece to imagine Aristotle using in his pondering about the universe. Aristotle didn’t think that light had a speed. He didn’t really think much about “light” at all, in fact. He found light itself to be pretty uninteresting. As far as he was concerned, the reason we are able to see is because air is transparent. At night time, the reason we cannot see is that the air is no longer transparent. (That is logical, right?) When the sun comes up in the morning, the sun causes the air to become transparent. You see? There is no need to think about the idea of light at all.
Moreover, Aristotle believed that when the sun comes up, all of the air becomes transparent at once. So even if we replaced the idea of “speed of light” with something like “the speed of a change in the transparency in the air,” we would still be out of luck with Aristotle: for him, this effect was instantaneous.
Could anything have changed his mind? It’s possible. As it turns out, there was a Greek philosopher who lived before Aristotle who believed that the speed of light was finite. His name was Empedocles of Acragas, and Aristotle believed that he was wrong.
What if, by some small historical chance or change in circumstance, something had convinced Aristotle to read the theories of Empedocles of Acragas and agree with him? It certainly doesn’t seem impossible that it could have happened. The idea of light having a finite speed was around, it even pre-dated Aristotle. So for the sake of our hypothetical exercise, let us suppose that Aristotle had decided to accept, instead of disagreeing with, Empedocles of Acragas.
With only this one small, and reasonable, re-writing of history, it would have been possible for Aristotle to come up with the concept of a quantity, c, that represented the speed of light.
Where does that leave us?
So, to review: Aristotle could have talked about a quantity of “mass” of an object, although for him it probably would have had to do with the number of atoms it was composed of. Aristotle could have talked about a quantity of “energy”, although it would have had more to do with spirit, pleasure, or the desire of a material to “become” the form that it was intended to be. Finally, Aristotle could have talked about the speed of light, if he had decided to accept the view of Empedocles of Acragas instead of disagreeing with him.
Those are the pieces of the equation. Could he have come up with the relationship between them?
This is where the plausibility begins to really wear thin. (Assuming that you, dear reader, don’t feel like we’ve reached that point already.)
Given the limitations of experiments and measurement of the time, the only way he could have come up with the idea of the relationship would have been through a thought experiment. That’s fine, it turns out that Einstein himself used a thought experiment to argue for the relationship E = mc2.
Here is the basic gist of Einstein’s thought experiment (you can read more about it in detail, including the mathematical parts, on this page):
Imagine a small particle of light (a photon) moving inside a box from one side to another. Photons have momentum, and momentum must be conserved, so when the photon leaves one side of the box it must “push” the box slightly in the opposite direction. Similarly, when the photon “hits” the other side of the box, it cancels the movement of the box (conservation of momentum again). However, in this small amount of time that the photon was traveling, the box has therefore moved. But according to other conservation laws, the center of mass of the system must be the same. The only way for the box to move and the center of mass to remain the same, is if the photon (which has moved in the opposite direction) has some equivalent amount of mass to cancel out the movement of the box.
This is the way we explain it to people today, using ideas from today’s physics.
Unfortunately, just within this short thought experiment, there are at least four ideas that were not around during Aristotle’s time:
Light comes in particles (photons). Remember that for Aristotle, light was simply a property of air that made it transparent. He didn’t really see light as a “thing” that could be made up of particles. We can stretch our imaginations and suggest that if he had thought of light as being a “substance” of some kind, it would only have been natural for him to think of the idea of “light particles” since he did, after all, believe in the existence of atomic elements. So maybe we could grant him that.
Law of Conservation of Momentum. Aristotle did not have a concept of momentum at all. He didn’t even have the concept of inertia (or its earlier variant, “impetus”). For Aristotle, the moment a force stopped acting on an object, the object would stop moving. No momentum, no conservation. How did he explain the fact that a ball would continue to move through the air after leaving your hand when you threw it? He believed that your hand motion disturbed the air and caused it to move, and it was the air around the ball that caused the ball to continue to move forward.
Light particles have momentum. Well, if Aristotle didn’t have a concept of momentum and didn’t have a concept of “light particles,” he certainly couldn’t have entertained a thought experiment that involved light particles having momentum. Indeed, the whole idea that photons have momentum is a very recent discovery: James Clerk Maxwell put forth the idea in the 1850’s… very late in the game, when looking at it from the point of view of the Ancient Greeks.
The Center-of-Mass Theorem. The idea that the center of mass will not change in a closed system is a consequence of Newton’s conservation laws. The closest we can come to Newton’s “conservation laws” in Aristotle’s philosophy was his belief that every action must have a cause, going all the way back to the “un-moved movers” from which all movement and change in the universe springs. But even if we somehow grant Aristotle belief in particles of light that move at a finite speed, and somehow also grant him the radical change in his philosophy to accept the idea of momentum, it would be yet an additional stretch to get him to re-invent (or “pre-invent”) Newton’s laws of mechanics.
So it looks pretty grim. It appears as though Aristotle simply would not have been able to come up with E = mc2, no matter how much of a “benefit of the doubt” and how many little cheats we give him.
What this little thought experiment really illustrates is the fact that science is progressive and incremental. In other words, discoveries really do build on one another, step by step. Each breakthrough of each century has been made possible because it was able to make use of the breakthroughs of the century before. As much as we like to give credit to the brilliant creativity of “outside of the box” thinkers, the fact is that science progresses in steps, each one learning from and extending the one before it.
Even the biggest discoveries are not “leaps” when you stand back far enough, and look at it from a historical perspective.