I. The scientific method
David Berlinski once said:
Where science has a method, it is trivial – look carefully, cut the cards, weigh the evidence, don’t let yourself be fooled, do an experiment if you can. These are principles of kennel management as well as quantum theory. Where science isn’t trivial, it has no method. What method did Einstein follow, or Pauli, or Kekulé? Kekulé saw the ring structure of benzene in what he called a waking dream. Some method.
My real view is that there is only one science, and that is mathematics, and that the physical sciences are really forms of experimental mathematics. The idea that there is out there a physical world which just happens to lend itself to mathematical description has always seemed to me to be incoherent. There is only one world – the universe, in fact, and it has the essential properties of a mathematical model. For reasons that we cannot even begin to understand, that model interacts with out senses, and so without measuring devices, allowing us to pretty much confirm conclusions antecedently reached by pure thought.
https://docs.google.com/document/d/1GWum5O7pSlFVu8V5P5HciOnVxbSl5Jg67ZRwf1IZAGo/edit?pli=1
This claim is worth exploring. For one thing, questions of scientific method crop up in debates over the relation between theology and science. Do theological claims violate the scientific method? Is there a scientific method?
It's easy to find statements of the scientific method on the Internet. According to one source:
The scientific method has four steps
1. Observation and description of a phenomenon or group of phenomena.
2. Formulation of an hypothesis to explain the phenomena. In physics, the hypothesis often takes the form of a causal mechanism or a mathematical relation.
3. Use of the hypothesis to predict the existence of other phenomena, or to predict quantitatively the results of new observations.
4. Performance of experimental tests of the predictions by several independent experimenters and properly performed experiments.
http://teacher.nsrl.rochester.edu/phy_labs/appendixe/appendixe.html
Sounds very straightforward and uncontroversial. But if you study works on the philosophy of science, that summary proves to be deceptively simple and overly confident. If you consult Gary Gutting's entry on "Scientific Methodology" in the Blackwell Companion to the Philosophy of Science, the scientific method is very much up for grabs.
II. The Divine foot in the door
One reason debates over scientific methodology are significant is that atheists like to invoke "the scientific method" to preemptively disqualify theological claims. In a refreshing moment of candor, one exponent famously or infamously admitted that:
http://www.drjbloom.com/Public%20files/Lewontin_Review.htm
Lewontin is half right. Admitting the possibility of miracles, admitting the existence of an interventionist God, introduces an element of unpredictability into science. That's because personal agents exercise rational discretion, unlike inanimate natural process which are uniform–absent interference from an outside agent.
If, however, science is a quest for a true description or true explanation of natural events, and if an interventionist God does, indeed, exist, then like it or not, scientists have no choice but to bend to reality, however unwelcome that may be.
In addition, Lewontin overstates his case. Granting God's existence doesn't have the destabilizing consequences he imagines. God is not a gremlin who tampers with laboratory experiments to throw off the results. Christian theology typically has a strong doctrine of providence.
III. The tortoise and the hare
Is there a scientific method? One difficulty is the diversity of science. Given all the different branches of science, is there one method that captures what every scientific discipline does?
But another difficulty is the difference between two different kinds of scientists. On the one hand you have the plodders. They are patient observers and chroniclers of nature. They conduct tedious experiments. They proceed in steps.
This is not to be disdained. It produces a lot of useful science. It's how most scientific practitioners must proceed–given their intellectual limitations.
On the other hand, the greatest scientific minds tend to proceed in skips. They have flashes of insight. Physical intuition. They resort to analogies and thought-experiments. They have no method. They can't be emulated. Darwin was a tortoise to von Neumann's hare. Edison was a tortoise to Feymann's hare. To take some examples:
During my stay in London I resided in Clapham Road....I frequently, however, spent my evenings with my friend Hugo Mueller....We talked of many things but most often of our beloved chemistry. One fine summer evening I was returning by the last bus, riding outside as usual, through the deserted streets of the city....I fell into a reverie, and lo, the atoms were gamboling before my eyes. Whenever, hitherto, these diminutive beings had appeared to me, they had always been in motion. Now, however, I saw how, frequently, two smaller atoms united to form a pair: how a larger one embraced the two smaller ones; how still larger ones kept hold of three or even four of the smaller: whilst the whole kept whirling in a giddy dance. I saw how the larger ones formed a chain, dragging the smaller ones after them but only at the ends of the chains....The cry of the conductor: "Clapham Road," awakened me from my dreaming; but I spent a part of the night in putting on paper at least sketches of these dream forms. This was the origin of the "Structural Theory.(6)
During my stay in Ghent, I lived in elegant bachelor quarters in the main thoroughfare. My study, however, faced a narrow side-alley and no daylight penetrated it....I was sitting writing on my textbook, but the work did not progress; my thoughts were elsewhere. I turned my chair to the fire and dozed. Again the atoms were gamboling before my eyes. This time the smaller groups kept modestly in the background. My mental eye, rendered more acute by the repeated visions of the kind, could now distinguish larger structures of manifold conformation; long rows sometimes more closely fitted together all twining and twisting in snake-like motion. But look! What was that? One of the snakes had seized hold of its own tail, and the form whirled mockingly before my eyes. As if by a flash of lightning I awoke; and this time also I spent the rest of the night in working out the consequences of the hypothesis. (6)
http://dwb4.unl.edu/Chem/CHEM869E/CHEM869ELinks/www.woodrow.org/teachers/ci/1992/Kekule.html
http://www.fdavidpeat.com/bibliography/essays/divine.htm
Linus Pauling was lying in bed with a cold when he managed to build accurate models of protein structure, largely based on his unmatched feel for such numbers. And every chemist can learn from the incomparable intuition of Enrico Fermi who tossed pieces of paper in the air when the first atomic bomb went off, and used the distance at which they fell to calculate a crude estimate of the yield.
http://blogs.scientificamerican.com/the-curious-wavefunction/2013/05/24/what-is-chemical-intuition/?print=true
Within a week I was in the cafeteria and some guy, fooling around, throws a plate in the air. As the plate went up in the air I saw it wobble, and I noticed the red medallion of Cornell on the plate going around. It was pretty obvious to me that the medallion went around faster than the wobbling.
I had nothing to do, so I start to figure out the motion of the rotating plate. I discover that when the angle is very slight, the medallion rotates twice as fast as the wobble rate - two to one [Note: Feynman mis-remembers here---the factor of 2 is the other way]. It came out of a complicated equation! Then I thought, ``Is there some way I can see in a more fundamental way, by looking at the forces or the dynamics, why it's two to one?''
I don't remember how I did it, but I ultimately worked out what the motion of the mass particles is, and how all the accelerations balance to make it come out two to one.
I went on to work out equations of wobbles. Then I thought about how electron orbits start to move in relativity. Then there's the Dirac Equation in electrodynamics. And then quantum electrodynamics. And before I knew it (it was a very short time) I was ``playing'' - working, really - with the same old problem that I loved so much, that I had stopped working on when I went to Los Alamos: my thesis-type problems; all those old-fashioned, wonderful things.
It was effortless. It was easy to play with these things. It was like uncorking a bottle: Everything flowed out effortlessly. I almost tried to resist it! There was no importance to what I was doing, but ultimately there was. The diagrams and the whole business that I got the Nobel Prize for came from that piddling around with the wobbling plate.
http://www.physics.ohio-state.edu/~kilcup/262/feynman.html
- Salviati: If we take two bodies whose natural speeds are different, it is clear that on uniting the two, the more rapid one will be partly retarded by the slower, and the slower will be somewhat hastened by the swifter. Do you not agree with me in this opinion?
- Simplicio: You are unquestionably right.
- Salviati: But if this is true, and if a large stone moves with a speed of, say, eight, while a smaller stone moves with a speed of four, then when they are united, the system will move with a speed of less than eight. Yet the two stones tied together make a stone larger than that which before moved with a speed of eight: hence the heavier body now moves with less speed than the lighter, an effect which is contrary to your supposition. Thus you see how, from the assumption that the heavier body moves faster than the lighter one, I can infer that the heavier body moves more slowly...
- And so, Simplicio, we must conclude therefore that large and small bodies move with the same speed, provided only that they are of the same specific gravity.
Another possible action of the demon is that he can observe the molecules and only open the door if a molecule is approaching the trap door from the right. This would result in all the molecules ending up on the left side. Again this setup can be used to run an engine. This time one could place a piston in the partition and allow the gas to flow into the piston chamber thereby pushing a rod and producing useful mechanical work. This imaginary situation seemed to contradict the second law of thermodynamics.
http://www.auburn.edu/~smith01/notes/maxdem.htm
Newton looked at these two formulas for the distance a cannonball would travel horizontally and vertically, and he noticed that the distance the cannonball would fall in a given time interval t was constant, since a is constant. However, the distance the cannonball travels horizontally is dependent on its speed --- something he could control. So, if he changed the speed of the cannonball, he could change its trajectory, as illustrated below
Then Newton realized that if he chose just the right velocity, the trajectory of the cannonball would curve at exactly the same rate the Earth (being spherical) curves, and therefore the cannonball would always stay the same height above the ground. In doing so, he balances the inertia of the cannonball (which makes it want to continue traveling in a straight line, and therefore away from the Earth) against the acceleration due to the Earth's gravity (which pulls the cannonball toward the center of the Earth).
The result is that the cannonball orbits the Earth, always accelerating toward the Earth, but never getting any closer. That may sound like a strange statement, but remember acceleration is the change in velocity, which is both the speed and direction of an object. In this case, the cannonball's direction is changing, and therefore it experiences an acceleration even though its speed doesn't change. (You experience this kind of acceleration when you go around a corner at constant speed in a car.)
Newton figured out that the speed of the cannonball was related to the acceleration due to the Earth's gravity (a) and the radius of the orbit (r; measured from the center of the orbit; i.e., the center of the Earth) as follows:
One cool thing about this relation is that even though Newton figured it out for a cannonball orbiting the Earth, it applies to any object in circular motion. Because of inertia, objects always want to travel in straight lines; in order to make them curve into circular motion, they have to be accelerated somehow. For Newton's cannonball, the Earth provided the acceleration. For a ball on a string, the tension in the string provides the acceleration. For your car going around a corner, the engine, through the tires and the friction between the tires and the road, provide the acceleration. In all cases, the amount of acceleration you'll need is described by the above equation, and is dependent on how fast the object is moving, and how tight a circular path it needs to travel on.
http://www.eg.bucknell.edu/physics/astronomy/astr101/specials/newtscannon.html
Now imagine that a (very fast) train is travelling along the track in the direction from A toward B and it so happens that the lightning flashes at A and B hit the ends of the train. The question is: “Do the flashes hit the train simultaneously?” As far as our observer Mike is concerned, as he saw the flashes together the answer must be “yes”. If the flashes hit the ends of the train, the ends must have been at A and B at the moments of the flashes. But what of an observer N, Nina, inside the train, let us say at the mid point of the train?
The same definition of simultaneity applies in the train’s frame of reference. If the observer sees two flashes which have travelled equal distances at the same time they must have been simultaneous in that frame of reference.
So, do observers in the train also see the two lightning strokes A and B as simultaneous? Imagine that Nina happens to be opposite Mike, that is, also half way between A and B at the moment the flashes occurred (as determined in the embankment frame). See diagram M1. This is NOT the time at which Mike and Nina see the flashes. They see them a little after this moment when the light reaches them – we need to take into account the ‘look-back time’, that is, the time taken for light to travel from the flashes to the observer.
For Mike to see the events as simultaneous, the light must have come from A and B and met at his position. Remember that Mike is at rest relative to the embankment. Nina in the train, however, is racing away from A and towards B and so will see the flash from B first (diagram M2) because it will have less distance to travel. Note that we could not take a photo and see what is represented in the diagrams! (The camera only ‘sees’ the light when it enters the lens.) They must be seen as ‘reconstructions’ of what must have been. Diagram M3 shows the moment that Mike sees both flashes and diagram M4 shows the moment a little later again when Nina sees the flash from A.
http://www.vicphysics.org/documents/teachers/unit3/EinsteinsTrainGedanken.pdf
Isaac Newton conducted an experiment with a bucket containing water which he described in 1689. The experiment is quite simple and any reader of this article can try the experiment for themselves. All one needs to do is to half fill a bucket with water and suspend it from a fixed point with a rope. Rotate the bucket, twisting the rope more and more. When the rope has taken all the twisting that it can take, hold the bucket steady and let the water settle, then let go. What happens? The bucket starts to rotate because of the twisted rope. At first the water in the bucket does not rotate with the bucket but remains fairly stationary. Its surface remains flat. Slowly, however, the water begins to rotate with the bucket and as it does so the surface of the water becomes concave. Here is Newton's own description:-
... the surface of the water will at first be flat, as before the bucket began to move; but after that, the bucket by gradually communicating its motion to the water, will make it begin to revolve, and recede little by little from the centre, and ascend up the sides of the bucket, forming itself into a concave figure (as I have experienced), and the swifter the motion becomes, the higher will the water rise, till at last, performing its revolutions in the same time with the vessel, it becomes relatively at rest in it.Soon the spin of the bucket slows as the rope begins to twist in the opposite direction. The water is now spinning faster than the bucket and its surface remains concave.
What is the problem? Is this not precisely what we would expect to happen? Newton asked the simple question: why does the surface of the water become concave? One is inclined to reply to Newton: that is an easy question - the surface becomes concave since the water is spinning. But after a moment's thought one has to ask what spinning means. It certainly doesn't mean spinning relative to the bucket as is easily seen. After the bucket is released and starts spinning then the water is spinning relative to the bucket yet its surface is flat. When friction between the water and the sides of the bucket has the two spinning together with no relative motion between them then the water is concave. After the bucket stops and the water goes on spinning relative to the bucket then the surface of the water is concave. Certainly the shape of the surface of the water is not determined by the spin of the water relative to the bucket.
Newton then went a step further with a thought experiment. Try the bucket experiment in empty space. He suggested a slightly different version for this thought experiment. Tie two rocks together with a rope, he suggested, and go into deep space far from the gravitation of the Earth or the sun. One certainly can't physically try this today any more than one could in 1689. Rotate the rope about its centre and it will become taut as the rocks pull outwards. The rocks will create an outward force pulling the rope tight. If one does this in an empty universe then what can it mean for the system to be rotating. There is nothing to measure rotation with respect to. Newton deduced from this thought experiment that there had to be something to measure rotation with respect to, and that something had to be space itself. It was his strongest argument for the idea of absolute space.
Now Newton returned to his bucket experiment. What one means by spin, he claimed, was spin with respect to absolute space. When the water is not rotating with respect to absolute space then its surface is flat but when it spins with respect to absolute space its surface is concave. However he wrote in the Principia:-
I do not define time, space, place, and motion, as they are well known to all. Absolute space by its own nature, without reference to anything external, always remains similar and unmovable.He was not too happy with this as perhaps one can see from other things he wrote:-
It is indeed a matter of great difficulty to discover and effectually to distinguish the true motions of particular bodies from the apparent, because the parts of that immovable space in which these motions are performed do by no means come under the observations of our senses.
Leibniz, on the other hand, did not believe in absolute space. He argued that space only provided a means of encoding the relation of one object to another. It made no sense to claim that the universe was rotating or moving through space. He supported his argument with philosophical reasoning, but faced with Newton's bucket, he had no answer. He was forced to admit:-
I grant there is a difference between absolute true motion of a body and a mere relative change of its situation with respect to another body.For around 200 years Newton's arguments in favour of absolute space were hardly challenged. One person to question Newton was George Berkeley. He claimed that the water became concave not because it was rotating with respect to absolute space but rather because it was rotating with respect to the fixed stars. This did not convince many people that Newton might have been wrong. In 1870 Carl Neumann suggested a similar situation to the bucket when he imagined that the whole universe consisted only of a single planet. He suggested: wouldn't it be shaped like an ellipsoid if it rotated and a sphere if at rest? The first serious challenge to Newton, however, came from Ernst Mach, who rejected Neumann's test as inconclusive. However, he wrote in 1872 in History and Root of the Principle of the Conservation of Energy:-
If we think of the Earth at rest and the other celestial bodies revolving around it, there is no flattening of the Earth ... at least according to our usual conception of the law of inertia. Now one can solve the difficulty in two ways; either all motion is absolute, or our law of inertia is wrongly expressed ... I [prefer] the second. The law of inertia must be so conceived that exactly the same thing results from the second supposition as from the first.We quote from an 1883 work by Mach on Newton's bucket:-
Newton's experiment with the rotating water bucket teaches us only that the rotation of water relative to the bucket walls does not stir any noticeable centrifugal forces; these are prompted, however, by its rotation relative to the mass of the Earth and the other celestial bodies. Nobody can say how the experiment would turn out, both quantitatively and qualitatively, if the bucket walls became increasingly thicker and more massive -- eventually several miles thick.Mach's argument is that Newton dismissed relative motion too readily. Certainly it was not rotation of the water relative to the bucket that should be considered but rotation of the water relative to all the matter in the universe. If that matter wasn't there and all that there was in the universe was the bucket and water, then the surface of the water would never become concave. He disagreed with Newton's thought experiment based on two rocks tied together in completely empty space. If the experiment were carried out in a universe with no matter other than the rocks and the rope, then the conclusion one can deduce from Mach's idea is that one could not tell if the system was rotating. The rope would never become taut since rotation was meaningless. Clearly since this experiment cannot be performed it is impossible to test whether Mach or Newton is right.
http://www-history.mcs.st-and.ac.uk/PrintHT/Newton_bucket.html
No comments:
Post a Comment