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Sunday, May 09, 2010


Isaac Newton presented four simple equations (three laws of motion plus his law of gravity) which made it possible to predict where the planets would be to well within a small fraction of measurement error. He seems to have believed that each equation was just plain true. Certainly after 2 centuries almost all physicists believed that.

To get from the 4 hypotheses of interest to testable predictions, two auxialiary hypotheses were needed -- that no force but gravity affects the location of the planets and that the Sun and the planets are rigid spheres. These are good approximations and, as far as I know, they haven't been disproven by observations of the locations of planets.

Newton hypotheised that the four equations were true natural laws. Clearly the two auxiliary hypotheses were not true statements about planet Earth. Newton hypothesized another force which he called friction. We would now consider friction one of the effects of the electromagnetic force.

Newton inspired many people to try to be the Newton of this that or the other field of inquiry. Unfortunately, they tended to try to do this by keeping the form of Newton's work and changing the substance. Hence we have von Clauswitz advising that one strike at "the center of mass" of the adversary and Rousseau talking about "solidarity" and assuming that solidal polities act like solid bodies. The same words were used with different meanings based on trust in their magical powers. Sometimes, this was reckless but fruitful.

Unfortunately, one of the magical words was friction. In the Principia, the Latin word appears roughly in the context of a confession that what was written so far is clearly inconsisten with masses of easily available data. Newton wrote something allong the lines of, that's because I left out friction, nonetheless the chapters on motion without friction were useful.

Thus the magical power of "friction" was its ability to make refutation of hypotheses not matter at all, because models which were wildly inconsistent with the data might be like the earlier chapters of the Principia. Granting a word power over our minds is always a mistake and this was a very serious mistake whose damaging consequences still harm economic research (which is getting much better very quickly thank you (no thanks to me)).

However, note two things. Friction doesn't appear in the laws of motion. The first law describes motion with no forces and hence neither friction nor gravity. The second and third describe motion with forces including gravity friction and presumably other forces. Newton's law of gravity does not assert that there is no other force. In Newton's work on the solar system, there was a clear distinction between the hypotheses of interest and the two auxiliary hypotheses added to get testable implications.

Also the testable implications were accurate to well within measurement error.
Better measurements have since been made and Newton's law of gravity and f=ma are both known to be false. Newton merely asserted that, since we have excellent reason to believe the 4 equations apply out there (we now know they don't) we should hypothesize that they apply down here too.

The Newton's of this that and the other thing don't have any example of their model without "friction" working. The magic word "friction" is invoked the instant the theory confronts any data at all.

Now I think the real lesson is that if one takes a true statement and changes the meanings of the words, one is likely to get a false statement, that words don't have magical powers and that the forms of theoretical physics do not have value if it is separated from the substance. But the magic word "friction" has done more damage than the others and it's past time to insist that people rephrase arguments without using it before they are taken seriously.


Cosma Shalizi said...

(Pedantic corrections of no relevance to the actual argument follow)

Actually, Newton assumed that the Earth is a deformable body, and calculated the deformation from a spherical shape due to its rotation, which was confirmed (at great expense) by Maupertius in the 18th century. Likewise there is a lot of observational evidence for the non-rigidity of the other planets (especially the gas giants, obviously) and of the Sun, as one can, e.g., observe ripples in the surface of the Sun.

However, it can be shown that if one has a spherically symmetric extended body, the net gravitational force it exerts on other, external bodies is the same as a point mass located at its center. Rigidity doesn't enter into this. Whether this result was known to Newton, I don't know.

Robert said...

I'm pretty sure Newton knew that, according to his model, a Sphere would attract as if it were a point mass at the center.

I meant the motion of the moon was as if the earth were a rigid sphere. Indeed one amazing confirmation of Newton was that the earth is flatter near the poles.

The rigid part is because a sphere which is not rigid and (I think) isn't a gas either will bulge towards (and opposite) the other mass (the tides -- I'd guess Newton knew he predicted tides). Then as it rotates the bulge moves and pulls the other mass along.

Since a day is less than 28 days, the Earth tends to pull the moon forward in its orbit which means the moon gets further from the Earth. It is believed to have been much closer long ago. The moon pulls the bulge West so a day is longer than it used to be.

I think this is why the moon shows one face to the Earth (back when it was molten major tides on the moon)

I'm pretty sure this extra acceleration hasn't been measured so the rigid spheres approximation to the motion of centers of mass of the planets Sun and moon is not rejected by the data.

I'm pretty sure it only matters for the moon and the Earth as it must be some inverse r to the much more than 2 effect and it depends on both masses being big.

So I see your pedantry and raise it.