Ancient Physics – What Causes Tides? The Earth Moves!

I am feeling reasonably pleased with myself because I now have book 2 of my Gaius Claudius Scaevola trilogy, Legatus Legionis, out as an ebook on Amazon. This continues the story set during the imperium of Caligulae, and the early imperium of Claudius, and concludes during the invasion of Britain. I shall discuss some of the historical issues in later posts, but the story also has an objective of showing what science is about.

In my last post, I showed how the ancients could “prove” the Earth could not go around thy Sun. Quite simply, orbital motion is falling motion, and if things fell at different rates depending on their mass, the Earth would fall to bits. It doesn’t. So, what went wrong? Quite simply, nobody checked, and even more surprisingly, nobody noticed. Why not? My guess is that, quite simply, they knew, it was obvious, so why bother looking? So the first part is showing the Earth moves around the Sun is to have my protagonist actually see three things fall off a high bridge, and what he sees persuades him to check. I think that part of success in science comes from having an open mind and observing things despite the fact that you were not really intending to look for them. It is the recognizing that which you did not expect that leads to success.

That, however, merely permits the Earth to go around the Sun. The question then is, how could you prove it, at the time? My answer is through the tides. What do you think causes the tides? Quite often you see the statement that the Moon pulls on the water. While true, this is a bit of an oversimplification because it does not lift the water; if it did, there would be a gap below. In fact, the vector addition of forces shows the Moon makes an extremely small change in the Earth’s gravity, and the net force is still very strongly downwards. To illustrate, do you really think you can jump higher when the Moon is above you? There is a second point. In orbital motion (and the Earth goes around a centre of gravity with the Moon) all things fall at the same acceleration, but the falling is cancelled out because the sideways velocity takes the body away at exactly the correct rate to compensate. This allowed my protagonist to see what happens (although the truth is a little more complicated). The key issue is the size of the Earth. The side nearest the Moon is not moving fast enough, so there is a greater tendency to fall towards the Moon; the far side is moving too fast, so there is a greater tendency for water to be thrown outwards. There is, of course, still a strong net force towards the centre of the Earth, but when not directly under the Moon, the two forces are not exactly opposed, and hence the water flows sideways towards the point under the Moon. The same thing happens for the Sun. This is admittedly somewhat approximate, but what I have tried to capture is how someone in the first century who did not know the answer could conceivably reach the important conclusion, namely that the Earth moves. If it moves, because the Sun stays the same size, it must move in a circle. (It actually moves in an ellipse, but the eccentricity is so small you cannot really detect the change in the size of the Sun.)

 What I hope to have shown in these posts, and in the two novels, is the excitement of science, how it works and what is involved using an example that should be reasonably comprehensible to all. The same principles apply in modern science, except of course that once the basic idea is obtained, the following work is a bit more complicated.     

 

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Ancient theory: dynamics proved the Earth was stationary!

Aristotle was one of the greatest minds of all times, but when he came to formulate his theories of dynamics, he got it all wrong. What I find interesting is why he went wrong, and the answer is surprising: he failed to follow his own methodology! Why was that? The reason may be a little mundane, and that is, his book Physica was apparently one of the first he wrote, and he may not have developed his method of logic properly by then. If so, why did he not correct it later? In my view, probably because he was not that interested in physics. Even now, the fraction of the population who find physics interesting is probably rather small. One of the most important features of Aristotle, though, is that he really did believe that experiment and observation were the key, and only theories that complied with observation were valid.

The first problem might be called sloth. He was not one of the most active experimenters, and in fairness to him, much of which he should have done would have been very difficult to do with the very limited equipment that was available. Nevertheless he could have done better in many ways. His first problem was that believed things like energy “came into being and passed away”. For example, suppose you throw a stone up in the air. It starts moving rapidly, then it slows, stops at the top, then turns around and comes back down. What happened to the initial energy when it reached the top? He said, it had passed away. We say the kinetic energy is turned into potential energy, but you cannot see potential energy. We have it because otherwise the law of conservation of energy would be falsified, but who says energy is conserved? (There are very good reasons for why it must be, but these would be beyond Aristotle’s ability to see, bearing in mind what information was available to him.)

The next problem lay in the theory of contraries, which was established before Aristotle. Thus cold was a material that was the contrary of heat. What Aristotle failed to see was that the contrary was the opposite or absence of the other, thus cold is the absence of heat, and this is odd because Aristotle did recognize that dark was the absence of light. When we got to motion, Aristotle failed to see that the contrary of a force was another force in the opposite direction. Instead, he believed that bodies contained their own internal contrary to motion, thus if you had a cart, you needed a horse continually pulling on it to overcome the contrary inherent in the cart. Why was it inherent to the cart? Because different carts would require different forces to keep them going. See the way you can fall into a trap? He just did not carry his thoughts further. The problem was probably the cart, as everybody knew it would stop unless pulled. Nevertheless, had he used his fabled logic, he would have arrived at the correct conclusion. As I put it in my ebook novel, Athene’s Prophecy, what he had to say was, either the contrary was the property of the body, or it was the property of its environment. Back to the cart, it is a lot easier to pull it on a stone road than on boggy earth. He should have been able to identify restraining forces, but he did not.

An even worse problem lay in the assertion that heavy things fall faster than light things. The problem here lay in the contraries. Had he recognized that air provided a restraining force, which he could have determined by watching wind blow leaves, he could drop different weights that were compact. He did not, because to him, the answer was “obvious”. Just because it is obvious does not make it right!

Why was this important? Apart from the fact that it strangled the development of the theory of mechanics, which in turn placed limits on what could be invented, it also provided proof that the Earth did not orbit the Sun. Can you see why? The answer lies in the nature of orbital motion. The ancient Greeks realized that orbital motion required the earth to move sideways, but fall back towards the Sun, and thus stay at the same distance as it went around. If it falls, since heavier things fall faster than light ones, the Earth would fall to pieces, or at the very least, light things would form a stream towards the rear. This was not observed, so the Earth did not move. Simple really, but a wrong premise led to the wrong conclusion.

An ancient theory: how does the sun work?

One of the peculiarities of forming theories is that there is tendency to try to explain everything. For Aristotle, one of the most peculiar aspects of nature was the power of the sun. Where did the heat and light come from? An important observation was that the Sun’s output was known to have been constant for several thousand years, and a quick calculation showed that had it been powered by combustion, such as burning coal, it should have faded. It had not. Now there was a questionable issue here: how far away was the sun? Some time after Aristotle, Aristarchus measured this distance, and was the first to realize how big the solar system really was, and since his measurement was somewhat error-prone, he seriously underestimated the size of the star. Nevertheless, the argument was correct in another sense: if the star was further away, the power had to be correspondingly greater, so qualitatively the argument stood. So, what powered the sun?

There was only one possible explanation that Aristotle could see: the Sun had to be moving, and by moving, it generated a lot of friction, because such friction would be the only physical means of powering the star. The earth did not generate heat, therefore it was not moving. Note that it was not Rumford who established that friction generated heat, in fact the first would be the one who discovered how to start a fire by rubbing one stick in the cavity of another. Aristotle knew that, but somehow in the middle ages the knowledge got overturned by the concept that heat was some subtle fluid called caloric. So, what Aristotle did was to take the only explanation he had that was possible, and also one that helped his theory. It would be too much to expect the ancient Greeks to guess nuclear fusion, but it shows that when developing a theory, every now and again something turns up that should not be explained. There is no fault in admitting you do not know everything.

So, what was the weakness in that theory? The first one might be the phases of the moon. The moon was moving as well, but the phases of the moon were to be explained in terms of reflected sunlight, which is correct, but it meant that the moon was moving approximately as fast, but generating trivial amounts of heat and light. Why was this? Yes, you could find an explanation, but the problem then became, a new explanation was required for one additional fact.

Another interesting fact is that Aristotle and other ancient Greeks considered stars to be other suns, but a long way away. Again, true, but their light was considered to come from the same source: friction. The problem with that is that for those on the equatorial regions their angular velocity was very close to the same as that of the sun, which meant that if they were x times further away, they were going x times faster across whatever was providing the friction, and hence they would emit x times the energy. They should be a lot brighter than they are. A second problem was that those near the poles are travelling much slower, and in principle, the pole star does insignificant travelling. If so, there should be a general dimming from equator to pole, but there was not. Finally, since they have different degrees of brightness, it was argued (correctly) that they were different distances away, but if that were the case, they all had to be travelling on separate disks, all with the same periodic time, but all with different velocities. At the very best, an incredibly complicated scenario. Now the interesting fact is that these difficulties were recognized, but were swept under the carpet. That habit may not have died out just yet. 

 

What is involved in developing a scientific theory? (2)

In my previous post, I showed how the protagonist in Athene’s Prophecy could falsify Aristotle’s proof that the earth did not rotate, but he could not prove it did. He identified a method, but very wisely he decided that there was no point in trying it because there was too much scope for error. At this stage, all he could do was suggest that whether the earth rotated was an open question. If it did not, then the planets could not go around the sun, otherwise the day and the year would be the same length, and they did not. At this point it is necessary, while developing a theory, to assume that as long as it has no further part to play in the theory it does, if for no other reason than it is necessary. By doing so, it creates a test by which the new theory can be falsified.

The logic now is, either the earth moves or it does not. If it does move, it must move in a circle, because the sun’s size was constant. (Actually, it moves in an ellipse, but it is so close to a circle that this test would not distinguish it. If you knew the dynamics of elliptical motion, you could just about prove it did follow an ellipse. The reason is, it moves faster when closer to the sun, and the solstices and the equinoxes were known. A proper calendar shows the northern hemisphere summer side of the equinoxes is longer than the southern hemisphere’s one by about 2 – 3 days, and is the reason why February is the shortest month. We, in the southern hemisphere, get cheated by two days of summer. Sob! However, if you have not worked out Newton’s laws of motion, this is no help.) So, before we can prove the earth moves, we must first overturn Aristotle’s proofs that it did not, and that raises the question, where can a theory go wrong?

The most likely thing to go wrong in forming a scientific theory can be summarized simply: if you start with a wrong premise, you may draw a wrong conclusion. Your conclusion may agree with observation, because as Aristotle emphasized, a wrong premise can still agree with observation. One of Aristotle’s examples of false logic is as follows:

Man is a stone

A stone is an animal

Therefore, man is an animal.

The conclusion is absolutely correct, but the means of getting there is ridiculous. A major problem when developing a theory is that a wrong premise that brings considerable agreement with observation is extremely difficult to get rid of, and invariably it has pervasive effects for a long time thereafter.

One reason why, in classical times, it was felt that the Earth must be stationary was because of Aristotle’s premise that air rises. If so, the fact that we have air at all must be because the Universe is full of it. If so, then if the earth moves, it must move through air. If so, there would be a contrary wind, the speed difference of which on either side would depend on the rate of rotation. There was no such wind, therefore no such orbit. We can forgive Aristotle here, but we forgive those who followed Archimedes less well. Had Aristotle known of Archimedes Principle, this argument would probably never have been made. According to Archimedes, air rises to the top because it is the least dense, but it still falls towards the earth. Space is empty. There were clues in classical times that space was empty. One such clue was that when a star went behind the moon, it did so sharply, which indicated there was no air to refract it. It was also known there were no clouds on the moon.

This shows another characteristic that unfortunately still pervades science. Once someone establishes a concept, evidence that falsifies that concept tends to be swept under the carpet as long as by doing so, it does not affect anything else. No clouds on the moon might mean anything. So, perhaps, you will now begin to see how difficult it was to get the heliocentric theory accepted, and how difficult it is to find the truth in science when you do not know the answer. That applies just as much today as then. The intellectual ability of the ancients was as great as now, and Aristotle would have been one of the greatest intellects of all times. He just made some mistakes.

What is involved in developing a scientific theory? (2)

In my previous post, I suggested that forming the theory that the Earth was a planet that went around the sun was an interesting example of how a scientist forms a theory. When starting, the first task is to review the literature, which at the time, was largely determined by Aristotle. Since Aristotle asserted that the earth was fixed, it therefore follows that you must first overturn his assertions. One place to start is to decide why we have day and night. Let us use Aristotle’s own methodology, which is to break the issue down into discrete issues. Thus we say, either the Earth is fixed and everything rotates around it, or everything is more or less fixed, and the Earth rotates. Aristotle had reached that step, and had “proven” that the Earth did not rotate. Therefore the day/night must occur through the sun orbiting the Earth. The heliocentric theory, despite its advantages, is falsified unless we can falsify Aristotle’s proofs.

At this point, we should recognize that Aristotle was very clear on one point, and he has been badly misrepresented on this ever since. Aristotle clearly asserted that logic must be applied to experimental observations, and that observation alone was critical. So, what was his experiment? Aristotle argued that if you threw a stone vertically into the air, it always came back to the same place. Had the earth been rotating, the path length of a rotation increased with height, in which case the stone should drag back westwards. It did not, so the earth did not rotate. Note that at this point, Aristotle was effectively arguing for the conservation of angular momentum, similarly to the ice skater slowing her spin by extending her arms. Before reading any further, what do you think about Aristotle’s experiment? What is wrong, and how would you correct it, bearing in mind you have only ancient technology?

In my ebook, Athene’s Prophecy, my protagonist dismisses the experiment by arguing that vertical is defined as the point where the stone falls back to the same place. By defining the point thus, if the stone does not come back to the same place, it was not thrown vertically. He then criticizes Aristotle by arguing that the correct way to do the experiment is to simply drop the stone from a high tower. The reason is that while Aristotle would be correct in that there should be a drag to the west going up, exactly the opposite should occur on the way back down. What should happen if dropped from a tower is that the stone would strike the ground slightly to the east of the vertical position, and in Rhodes, where this was being discussed, also slightly to the south. Can you see why?

That the stone should go east follows from the fact that the angular velocity is constant, but the path length is longer the higher you are, so it is going east faster higher up. The reason it goes south is because the stone falls towards the centre of the earth, and thus very slightly decreases its latitude, but the point at the base of the tower does not. In my ebook, however, my protagonist wisely refused to carry out the experiment, because it is not that easy to carry out, even with modern equipment, and in those days the errors in measurement would most likely exceed the effect. Notwithstanding that, the logic is correct in that any effect like that going up will be exactly countered coming down, and consequently Aristotle’s “proof” is not valid. Thus one can falsify an experiment through logic alone. Of course, disproving Aristotle does not prove the earth is rotating, but it leaves it open as a possibility. Carrying out the dropped stone experiment would, provided you could guarantee that what you saw was real and not experimental error. That is not easy to do, even now.

What is involved in developing a scientific theory?

Everyone knows about people like Galileo, Newton, etc, but how are such theories discovered? Now obviously I have no idea exactly how they did it, but I think there are some principles involved, and I also think some readers might find these of interest. I hope so, because therein lies the third task for my protagonist in my novel Athene’s Prophecy.

The reason that is in the novel is because the overall plot requires a young Roman to get help from superior aliens to avoid a disaster in the 24th century. The reason for the time difference is, of course, relativity. Getting to the aliens involves being abducted by other aliens, but once taken to another world, the protagonist has to be something more than a specimen that can talk. To get the aliens to respond, he has to be someone of interest to talk to. Suppose you had the chance to talk to someone from the 16th century, or to Galileo, who would you choose? My proposition is, Galileo, so the task for my young protagonist is to prove the heliocentric theory, i.e. that the earth moves around the sun. That is similar to what was in the film Agora. The big problem was, everybody was so sure the earth was fixed and everything else went around it. Not only were they sure, but they could also use their theory to calculate everything that mattered, such as when the solstices and equinoxes would be, when Easter would be, and when various planets would be where in the sky. What else did they need?

The alternative theory was due to Aristarchus of Samos. What Aristarchus maintained was that the earth was a planet, and all planets went around the sun, the moon went around the earth, and the solar system was huge. This latter point was of interest, because Aristarchus measured the system. His first measurement was to obtain the size and distance of the Moon, and what he did was to get two people to measure the angle at the exact moment an eclipse of the moon started. These two people were separated by as much distance as he could manage, and with one distance and two angles he had a triangle that would permit the measurement of the distance to the moon. The size then followed from its solid angle. The method is completely logical, although the amount of experimental error was somewhat large, and his answer was out by a factor of approximately two. He then measured the distance to the sun by measuring the angle between the sun and moon lines when the moon was half shaded, and used his moon distance and Pythagoras’ theorem. His error here was about a factor of five, and would have been about a factor of ten had not the error in the moon distance favoured him. The error range here was too great (to see why, check how tangents get very large as they approach 90 degrees) but he was the first to realize that the solar system is really very large. He also showed that the sun is huge compared to the earth.

Aristarchus, following Aristotle, also postulated that the stars were other suns, but so far away, and they would have to be going at even greater speeds. This did not make sense, so he needed an alternative theory. In my opinion, this is invariably the first step in forming a new theory: there is some observation that simply does not make sense within the old theory. Newton’s theory was born through something that did not make sense. If you believed Copernicus, or Aristarchus, if you had heard of him, or of Galileo, then the earth and the other planets went around the sun, but there was a problem: Mars could only be explained through elliptical orbits, and nobody could explain how a body could orbit in an elliptical path with only a central force. Newton showed that elliptical orbits followed from his inverse square law of gravity. Relativity was also born the same way. What did not make sense was the observation that no matter what direction you looked, the speed of light was constant. What Einstein did was to accept that as a fact, and put that into the classical Galilean relativity, and came up with what we call relativity.

So we now get to the second step in building a new theory. That involves reading about what is known, or thought to be known, about the subject. If we think about the heliocentric theory in classical times, we now know that much of what was thought to be correct was not. So, here is a challenge. If you had to, could you prove that the earth goes around the sun, while being restricted to what was known or knowable in the first century? Answers in the next few posts, but feel free to offer your thoughts.