Universal laws.

Laws of nature as expressed in physics as laws and theories are often said to be universal. This means that, so far as we have been able to test them, they apply everywhere and at every time, past, present and future.

Of course we haven't yet tested them everywhere and at every time. So how can we be so confident that they really are universal? Might there be an exception to one of them somewhere, that we haven't discovered yet? Could there be a strange form of matter for which the laws don't apply?

Let's examine these questions, first by looking at the past history of physics.

Historical examples.

In the pre-history of physics certain regularities of nature were noticed and formulated as principles or laws. The laws of mechanics (of levers and pulleys) were formulated and found useful for making mechanical devices. But no one supposed that these laws that apply to machinery might also apply to, say, the motions of bodies in the heavens. In fact it was conventional wisdom then that the laws of earthly matter (earth, water, air and fire) were distinctly different from the laws that governed celestial phenomena, beyond the earth. The celestial realm was supposedly not made of ordinary earthly stuff, but of something else, the quintessence (fifth essence). Goings-on in that realm were not expected to obey the same laws as the earthly stuff (the four essences).

But motions of luminous bodies in the heavenly realm were lawful, and the laws of the motion of sun, moon, and planets in the skies were soon forumlated, and developed into a complex mathematical system, the Ptoelmaic geocentric (earth centered) system. It was quite successful, for it could predict the positions of celestial bodies in past and future very accurately, and even predict eclipses. And it had a philosophical appeal, for it was based on circles, considered to be the "most perfect" geometric figure.

But as data improved, this system required tweaking, and had to incorporate more circles, and various gimmicks to modify the speed of objects around those circles. It became cumbersome, but it worked for its purpose, and that purpose was to predict planetary positions in the sky.

It still had problems, though. The position of the planet Mars was poorly modeled, and the system had to treat the planets Mercury and Venus in a manner different from the other planets.

This historical theme has been well treated in many books, so I need not write another book on it. These books tell us that the Ptolemaic system was "overthrown" by the Copernican heliocentric (sun centered) system. What motivated the new system, and why was it slow to be accepted?

Critics pointed out that the Copernican system wasn't much easier to use for planetary calculations. It still was based on circles, and only six fewer circles. It did treat Mercury and Venus in the same way as the rest of the planets, thereby eliminating one of the nagging aspects of the Ptolemaic system.

Johannes Kepler was able to get rid of the multiplicity of circles, epicycles and deferents by introducing elliptical planetary orbits.

The Copernican system differed from the Ptoelmaic system in a major way. The Ptolemaic system had a fixed and stationary Earth at its center. The Copernican system placed the Sun at the center and the Earth and planets moved around the sun. This difference should lead to an observable test. If the earth moved this way, there should be an observable "stellar parallax". Each star's position in the sky should show a yearly motion, a motion around small elliptical orbits due to the Earth's changing position. No such motion was observed. It was not until the 19th century that it was observed. The motion was very small because the stars are so very far away, at distances inconceivably larger than the critics of the Copernican system imagined.

The point in all of this is that the "Copernican revolution" was more than a philosophical shift. It did not succeed by emotional appeal. It was brought about by the experimental data and tested by experiments. All progress in physics is data-driven. The Ptolemaic system was quite successuful in that it could predict positions of planets in the sky. It could not, however, predict distances of objects from Earth. In fact, if those pretty pictures of the Ptolemaic system were taken seriously, they would predict ridiculously wrong distances. But at that time observational methods couldn't measure astronomical distances well at all. The distance to the Moon and Sun were fairly well measured by trigonometry, but pre-telescopic methods couldn't measure the distances to planets and stars.

Was the Ptolemaic model thereby shown to be "wrong"? Hardly. It worked for its very limited purposes, and still works. It is sometimes noted that optical-mechanical planetarium projectors operated using the Earth-centered model, for their only purpose was to show the positions of celestial bodies in the sky. Modern planetariums do things differently, and have the capability of showing the universe from any vantage point, not just from the Earth. Did the Copernican model settle the question of whether the Earth moved? Not really, it just assumed the Earth moved. Did the Copernican model improve the precision of predictions of planetary positions. No, as its critics were quick to point out.

Even today a few people maintain the fixity of the earth, just as some of them also declare the Earth to be flat as well as unmoving. There are even some who declare the Earth to be hollow shell with the entire universe inside, and we walk on the inside of this shell. By warping geometry to suit their prejudices they develop an elaborate system that they declare is just as reasonable as the conventional scientific fiew. Indeed they can, though few of the believers in these models are sufficiently versed in mathematics to work out the details. But they neglect the fact that there's physics to deal with. To sustain their warped geometry they would have to revise all of the fundamental laws of physics, force laws, gravitational laws, conservation laws, and even abandon the constancy of the speed of light. They haven't done this, for the task is beyond their abilities.

So why are the geocentric models now completely abandoned? Isaac Newton is responsible. The geocentric models were descriptive only, and applied only to the position of objects as seen in the skies. Newton introduced a more universal model of motion, using the concept of force, which included his three laws of motion and his law of universal gravitation. These laws applied to earthly as well as celestial phenomena, and they beautifully met the test of experiment. They fit the data provided by both earthly laboratories and astronomical observatories. And in the centuries since Newton they continue to meet the test of experiment and observation.

Newton can be credited with demonstrating that nature has underlying regularities that can be expressed as universal laws. Any model of the solar system is just a consequence of these laws.

What might future advances bring?

Science still has work to do. Unanswered questions abound, in cosmology, elementary particles, and quantum mechanics. Will progress in any of these areas cause us to abandon and replace Newtonian classical mechanics? I suspect not. Relativity did not invalidate classical physics. Quantum mechanics didn't, either.

Those who fantasize and hypothesize about wonderful advances in physics pin their hopes on finding exceptions to known laws. Possibile places to look:

  • Distant places in the cosmos where things might obey different laws.
  • As-yet-unobserved exotic phenomena.
  • As-yet-undiscovered strange particles that behave in different ways from ordinary matter.
We have examples already. Subatomic particles obey laws quite different from those of human-scale objects. But discovery of them and the laws they obey doesn't change in any way the behavior of billiard balls or any of the technological mechanisms and natural processes of our everyday experiences and our industrial technology. Newton's laws rule there.

Speculation about such exotic things is idle until someone shows experimental evidence for them. Until then it is philosophy, not physics.

Making hypotheses.

Non-scientists often suppose that scientists just sit around dreaming up hypotheses for others to test. If any are successful they then take credit for them. It doesn't work that way. Every hypothesis is motivated by a problem to be solved, a problem arising from nature and from experimental data—something observed that doesn't quite fit known laws.

Hypotheses are motivated by experimental data, and also shaped by it. The hypothesis is made with a clear intention that its consequences must account for that data. You don't just make a hypothesis without thinking about its consequences.

Pitfalls of Extrapolation.

Physics students often focus too narrowly on learning equations representing laws of nature. They may fail to appreciate that every law of physics is an idealization and approximation. Nature has no perfect straight lines or circles. Every measurement has experimental uncertainty. Calculus is based on the concept of a limit. But if you take a limit of any physical quantity as its size goes to zero, you are going beyond what is measurable by instruments, and even into the quantum realm where quantities are not infinitly divisible, nor smooth in behavior at small sizes. The very foundation of calculus is therefore imperfect (when applied to nature)— because nothing is infinitessimally divisible. Newton knew nothing of molecules and atoms. Yet the results of calculus operations are still perfectly good and useful, to the limits of measurement required. Mathematicians and physicists are well aware of these issues, they know under what conditions these processes might generate imperfect answers, and they know how to get around the problem. They realize that mathematics doesn't represent scientific truth, but is only a tool for expressing nature's behavior. Even an imperfect hammer can drive a nail when building a house.

Experienced scientists are practical people. They know that perfection is not only not possible, but not necessary for its purposes. They know when something is "good enough" to draw correct and confirmable conclusions and don't obsess about going for the ultimate decimal place.

For a mundane example, consider the law F = kΔx, representing applied force to stretch a wire an amount Δx. k is an elastic constant dependent on the metal the wire is made of. Now you can insert any value of force into the equation, but if the force is great enough, the wire will stretch beyond its elastic limit and break. The equation alone doesn't tell you about that. You have extrapolated the equation beyond its physical applicability.

Furthermore the equation represents a straight line, a linear relation. Yet some materials (rubber, for example) obey an elastic law that is non-linear. So it matters what material you are talking about.

This example is a law describing how materials behave. All materials are complex, with many conditions affecting them. Even temperature might be important in this case. (A metal wire lengthens with increasing temperature. If the temperature is too high the wire melts.) This is an example of a class of laws that are not fundamental or basic laws of physics (like Newton's laws).

Almost every equation in a physics textbook has such "gotchas", usually explained in the surrounding text that too many students skip.

    —Donald E. Simanek, 2004, 2014, 2017.

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