Stimulated by NASA's Gravity B probe which went up the other day, designed to further test Albert Einstein's general theory of relativity, Impearls continues its recent series which began with a piece on competing theories of gravity to general relativity, followed by consideration of what scientific theories more generally are.

People often recall from undergraduate physics that Einstein's special theory of relativity (promulgated 1905) provides for the “relativity” or equivalence of motion between “inertial reference frames,” which is to say, between unaccelerated or “free falling” platforms or moving points of view in space.  Not included in typical undergraduate curricula — and thus gradually forgotten about by most, however — is Einstein's later general theory of relativity (1915), which removes the limitation of “inertial” on allowed viewpoints or reference frames, in order to permit relativity-equivalence of motion between accelerated as well as inertial points of view.  As Einstein put it: ¹

We arrive at a very satisfactory interpretation of this law of experience, if we assume that the systems K and K′ are physically exactly equivalent, that is, if we assume that we may just as well regard the system K as being in a space free from gravitational fields, if we then regard K as uniformly accelerated.  This assumption of exact physical equivalence makes it impossible for us to speak of the absolute acceleration of the system of reference, just as the usual theory of relativity forbids us to talk of the absolute velocity of a system; and it makes the equal falling of all bodies in a gravitational field seem a matter of course.

All viewpoints, accelerated or not, are encompassed within Einstein's general theory, and since rotating points of view or reference frames are in actuality just another kind of accelerated viewpoint, rotating frames are fully instantiated under general relativity.  Thus, though it's frequently noted that Einstein's general relativity has displaced Newton's gravitation, a consequence less noticed by many, however, is that Copernicus has also been likewise dethroned.

Under general relativity, it's just as valid and “true” to consider the universe as rotating once a day about a fixed and stationary Earth (i.e., the Ptolemaic universe), as it is to regard a rotating Earth revolving about a Sun within a more or less stationary universe (the Copernican system).  When it is Earth that is considered motionless, it's gravitational fields induced by the universe spinning round it, rather than the inertia of a rotating Earth, that raises up the Earth's equatorial “bulge,” and so forth.  As Einstein pointed out in an illuminating 1913 letter to Ernst Mach, Foucault pendulums, hitherto regarded as nearly perfect and unassailable proof of the Earth's rotation, are swung about by such forces, known as “frame dragging,” thus neutering Foucault's perfect proof!  Einstein wrote: ²

[To Ernst Mach, concerning confirmation at an upcoming eclipse]
… If so, then your happy investigations on the foundations of mechanics, Planck's unjustified criticism notwithstanding, will receive brilliant confirmation.  For it necessarily turns out that inertia originates in a kind of interaction between bodies, quite in the sense of your considerations on Newton's pail experiment.  The first consequence is on p. 6 of my paper.  The following additional points emerge:  (1) If one accelerates a heavy shell of matter S, then a mass enclosed by that shell experiences an accelerative force.  (2) If one rotates the shell relative to the fixed stars about an axis going through its center, a Coriolis force arises in the interior of the shell; that is, the plane of a Foucault pendulum is dragged around (with a practically unmeasurably small angular velocity).

It's just this kind of general relativistic “frame dragging” that the new Gravity B experiment is designed to investigate.

Moreover, it's this sort of close uniting of seemingly contradictory, polar-opposite concepts (e.g., rotating universe vis-a-vis spinning Earth, matter = energy, light is both particles and waves, etc.) that is part and parcel of the basic process and progress of science, and what physicist Niels Bohr was talking about in the last century when he said, “A great truth is a truth whose opposite is also a great truth.”

¹ A. Einstein, 1911, “Über den Einfluss der Schwerkraft auf die Ausbreitung des Lichtes,” Ann. Phys. (Germany) 35, 898-908.  English translation in H. A. Lorentz, A. Einstein, H. Minkowski, and H. Weyl, 1923, The Principle of Relativity: A Collection of Original Memoirs, Methuen, London; paperback reprint, Dover, New York.

² “Albert Einstein's appreciation of Mach, written to Ernst Mach June 25, 1913, while Einstein was working hard at arriving at the final November 1915 formulation of standard general relativity.”  Quoted in Charles W. Misner, Kip S. Thorne, John Archibald Wheeler, Gravitation, 1973, W. H. Freeman and Co., San Francisco; pp. 544-545.

Labels: Albert Einstein, astronomy, Copernican Universe, Copernicus, Ernst Mach, general relativity, gravity, Niels Bohr, physics science, Ptolemaic Universe, Ptolemy, reference frames, scientific theories

Reader Mike Zorn writes in reply to Impearls' recent piece “Battle-tested General Relativity”:

“Query:  Why then bother to examine alternative theories of gravity?
Reply:  To have foils against which to test Einstein's theory.”

Exactly.  That's what makes a theory: it has to be capable of being disproved.

I think that one of the problems the public has with science is that the public's definition of “theory” is completely different from the scientist's.  […]  [T]he public [has a] perception of “theory” as “a really good guess,” vs. science's definition as “the best explanation we have so far that fits all the facts we have so far.”  (As in, “evolution?  It's just a theory — why should we pay so much attention to it?”)

Mike makes good points here.  Many people think of science as little more than a gathering or encyclopedia of facts and, as Zorn notes, there's a perception that a scientific “theory” is merely a vague hypothesis or guess, as good (or bad) as any other.

These common perceptions are actually quite far from science.  Looking back on the requirements for a “viable” theory of gravity as described in the previous posting (see the link above), it should now be clear that a good theory is vastly more robust than than a mere guess.  It must be internally self-consistent, incorporate all of physics (and chemistry, etc.) beneath its theoretical umbrella, agree with every experiment ever performed, and predict a vast spectrum of observable phenomena for the future.

As Mike says, it must be disprovable.  The public has this funny idea that science proves things.  Rather, science is only capable of disproving laws or theories.  The “best man” left standing after each candidate has been tested by “trial by combat” against all the criteria — including, last but not least, the searing fires of experiment, past and present — is (provisionally) considered to be the victor.

Nor does evolution in particular belong on a qualitatively different and lower plane than, say, physics.  The fact that evolution to an extent draws its information from out of the distant past is not important in this regard.  Geology and astronomy similarly derive much of their data from the far past, yet these are quite decidedly “true,” reliable sciences.  Every fossil dug up out of the ground is a newly-detected signal from the past, readily able to disprove evolution if new results show that the painfully built up pattern of relationships within the organisms of the past is but an illusion.  (I'll not hold me breath waiting for that to happen!)  Every science, in fact, deals with (and only with) signals from the past.  A physics or chemical experiment on a lab bench — any physical measurement — observes the past, as it takes time for light or whatever the medium to propagate from the site of the reaction or event into the measuring apparatus.

Physicist and philosopher of science Jacob Bronowski put it this way, in his book The Common Sense of Science: ¹

We are not merely observing and predicting facts; and that is why any philosophy which builds up science only from facts is mistaken.  We know, that is we find laws, and every human action uses these laws, and at the same time tests them and feels towards new laws.  It is not the form of these laws which matters.  The laws of science, like those which we use in our private behaviour, remain helpful and truthful whether they contain words like “always,” or only “more often than not.”  What matters is the recognition of the law in the facts.  It is the law which we verify: the pattern, the order, the structure of events.  This is why science is so full of the symbolism of numbers and geometry, which are the most familiar expressions of structural relations.

There is no sense at all in which science can be called a mere description of facts.  It is in no sense, as humanists sometimes pretend, a neutral record of what happens in an endless mechanical encyclopaedia.  This mistaken view goes back to the eighteenth century.  It pictures scientists as utilitarians still crying Let be! and still believing that the world runs best with no other regulating principles than natural gravitation and human self-interest.

But this picture of the world of Mandeville and Bentham and Dickens's Hard Times was never science.  For science is not the blank record of facts, but the search for order within the facts.  And the truth of science is not truth to fact, which can never be more than approximate, but the truth of the laws which we see within the facts.  And this kind of truth is as difficult and as human as the sense of truth in a painting which is not a photograph, or the feeling of emotional truth in a movement in music.  When we speak of truth, we make a judgment between what matters and what does not, and we feel the unity of its different parts.  We do this as much in science as in the arts or in daily life.

We make a judgment when we prefer one theory to another even in science, since there is always an endless number of theories which can account for all the known facts.  And the principles of this judgment have some deep appeal which is more than merely factual.  William of Ockham first suggested to scientists that they should prefer that theory which uses in its explanation the smallest number of unknown agents.  Science has held to this principle now for six hundred years.  But is there indeed any ground for it other than a kind of aesthetic satisfaction, much like that of sacrificing your queen at chess in order to mate with a knight?

We cannot define truth in science until we move from fact to law.  And within the body of laws in turn, what impresses us as truth is the orderly coherence of the pieces.  They fit together like the characters in a great novel, or like the words in a poem.  Indeed, we should keep that last analogy by us always.  For science is a language, and like a language, it defines its parts by the way they make up a meaning.  Every word in the sentence has some uncertainty of definition, and yet the sentence defines its own meaning and that of its words conclusively.

It is the internal unity and coherence of science which gives it truth, and which makes it a better system of prediction than any less orderly language.

¹ J. Bronowski, The Common Sense of Science, 1951, Harvard University Press, Cambridge, Mass.; pp. 130-131.

UPDATE:  2004-04-29 23:50 UT:  A follow-up “Copernicus Dethroned” has been posted.

Labels: evolution, general relativity, gravity, Jacob Bronowski, philosophy of science, physics science, scientific theories

There's been an interesting conversation in National Review Online's blog The Corner between commentators Peter Robinson and John Derbyshire with regard to the testing of Albert Einstein's general theory of relativity.  (A satellite will soon launch carrying what is called a “Gravity B” experiment designed to further test general relativity.)  You can read the pieces of the discussion here: R1, R2, D3, R4, D5, R6, R7.

While quite enjoyable, I was a little concerned by a tendency to overlook, as I perceive it, the degree to which General Relativity has been tested and has prevailed against its competitors.  An excerpt from Misner, Thorne, and Wheeler's classic tome Gravitation (1973) on the subject of competing theories of gravity is illuminating in this regard: ¹  (Ellipses in the text refer to omitted section cross-reference numbers where each topic is gone over in detail.)

§ 39.1.  Other theories

Among all bodies of physical law none has ever been found that is simpler or more beautiful than Einstein's geometric theory of gravity {…}; nor has any theory of gravity ever been discovered that is more compelling.

As experiment after experiment has been performed, and one theory after another has fallen by the wayside a victim of the observations, Einstein's theory has stood firm.  No purported inconsistency between experiment and Einstein's laws of gravity has ever surmounted the test of time.

Query:  Why then bother to examine alternative theories of gravity?  Reply:  To have “foils” against which to test Einstein's theory.

To say that Einstein's geometrodynamics is “battle-tested” is to say it has won every time it has been tried against a theory that makes a different prediction.  How then does one select new antagonists for decisive new trials by combat?

Not all theories of gravity are created equal.  Very few, among the multitude in the literature, are sufficiently viable to be worth comparison with general relativity or with future experiments.  The “worthy” theories are those which satisfy three criteria for viability: self-consistency, completeness, and agreement with past experiment.

Self-consistency is best illustrated by describing several theories that fail this test.  The classic example of an internally inconsistent theory is the spin-two field theory of gravity [Fierz and Pauli (1939) {…}], which is equivalent to linearized general relativity {…}.  The field equations of the spin-two theory imply that all gravitating bodies move along straight lines in global Lorentz reference frames, whereas the equations of motion of the theory insist that gravity deflects bodies away from straight-line motion.  (When one tries to remedy this inconsistency, one finds oneself being “bootstrapped” up to general relativity {…}.)  Another self-inconsistent theory is that of Kustaanheimo (1966).  It predicts zero gravitational redshift when the wave version of light (Maxwell theory) is used, and nonzero redshift when the particle version (photon) is used.

Completeness:  To be complete a theory of gravity must be capable of analyzing from “first principles” the outcome of every experiment of interest.  It must therefore mesh with and incorporate a consistent set of laws for electromagnetism, quantum mechanics, and all other physics.  No theory is complete if it postulates that atomic clocks measure the “interval”  dτ = (− g_αβ dx^α dx^β)^½  constructed from a particular metric.  Atomic clocks are complex systems whose behavior must be calculated from the fundamental laws of quantum theory and electromagnetism.  No theory is complete if it postulates that planets move on geodesics.  Planets are complex systems whose motion must be calculated from fundamental laws for the response of stressed matter to gravity.  {…}

Agreement with past experiment:  The necessity that a theory agree, to within several standard deviations, with the “four standard tests” (gravitational redshift, perihelion shift, electromagnetic-wave deflection, and radar time-delay) is obvious.  Equally obvious but often forgotten is the need to agree with the expansion of the universe (historically the ace among all aces of general relativity) and with observations at the more everyday, Newtonian level.  Example: Birkhoff's (1943) theory predicts the same redshift, perihelion shift, deflection, and time-delay as general relativity.  But it requires that the pressure inside gravitating bodies equal the total density of mass-energy, p = ρ; and, as a consequence, it demands that sound waves travel with the speed of light.  Of course, this prediction disagrees violently with experiment.  Therefore, Birkhoff's theory is not viable.  Another example:  Whitehead's (1922) theory of gravity was long considered a viable alternative to Einstein's theory, because it makes exactly the same prediction as Einstein for the “four standard tests.”  Not until the work of Will (1971b) was it realized that Whitehead's theory predicts a time-dependence for the ebb and flow of ocean tides that is completely contradicted by everyday experience {…}.

§ 39.2.  Metric theories of gravity

Two lines of argument narrow attention to a restricted class of gravitation theories, called metric theories.

The first line of argument constitutes the theme of the preceding chapter.  It examined experiment after experiment, and reached two conclusions:  (1) spacetime possesses a metric; and  (2) that metric satisfies the equivalence principle (the standard special relativistic laws of physics are valid in each local Lorentz frame).  Theories of gravity that incorporate these two principles are called metric theories.  In brief, Chapter 38 says, “For any adequate description of gravity, look to a metric theory.”  Exception:  Cartan's (1922b, 1923) theory [“general relativity plus torsion”; see Trautman (1972)] is nonmetric, but agrees with experiment and is experimentally indistinguishable from general relativity with the technology of the 1970's.

The second line of argument pointing to metric theories begins with the issue of completeness (preceding section).  To be complete, a theory must incorporate a self-consistent version of all the nongravitational laws of physics.  No one has found a way to incorporate the rest of physics with ease except to introduce a metric, and then invoke the principle of equivalence.  Other approaches lead to dismaying complexity, and usually to failure of the theory on one of the three counts of self-consistency, completeness, and agreement with past experiment.  All the theories known to be viable in 1973 are metric, except Cartan's.  [See Ni(1972b); Will (1972).]

In only one significant way do metric theories of gravity differ from each other: their laws for the generation of the metric.  In general relativity theory, the metric is generated directly by the stress-energy of matter and of nongravitational fields.  In Dicke-Brans-Jordan theory {…}, matter and nongravitational fields generate a scalar field φ; then φ acts together with the matter and other fields to generate the metric.  Expressed in the language of {…}, φ is a “new long-range field” that couples indirectly to matter.  As another example, a theory devised by Ni (1970, 1972) {…} possesses a flat-space metric η and a universal time coordinate t (“prior geometry” {…}); η acts together with matter and nongravitational fields to generate a scalar field φ; and then η, t, and φ combine to create the physical metric g that enters into the equivalence principle.

All three of the above theories — Einstein, Dicke-Brans-Jordan, Ni — were viable in the summer of 1971, when this section was written.  But in autumn 1971 Ni's theory, and many other theories that had been regarded as viable, were proved by Nordtvedt and Will (1972) to disagree with experiment.  This is an example of the rapidity of current progress in experimental tests of gravitational theory!

Notice that in all of these “trials by combat” against the searing fires of experiment, it is Einstein's general relativity that has consistently withstood the tests, like Daniel walking through the fiery furnace!

Quoting further from Misner, Thorne, and Wheeler's Gravitation (§44.2): ² 

No theory more resembles Maxwell's electrodynamics in its simplicity, beauty, and scope than Einstein's geometrodynamics.  Few principles in physics are more firmly established than those on which it rests: the local validity of special relativity {…}, the equivalence principle {…}, the conservation of momentum and energy {…}, and the prevalence of second-order field equations throughout physics {…}.  Those principles and the demand for no “extraneous fields” (e.g., Dicke's scalar field) and “no prior geometry” {…} lead to the conclusion that the geometry of spacetime must be Riemannian and the geometrodynamic law must be Einstein's.

To say that the geometry is Riemannian is to say that the interval between any two nearby events C and D, anywhere in spacetime, stated in terms of the interval AB between two nearby fiducial events, at quite another point in spacetime, has a value CD/AB independent of the route of intercomparison {…}.  There are a thousand routes.  By this hydraheaded prediction, Einstein's theory thus exposes itself to destruction in a thousand ways {…}.

Geometrodynamics lends itself to being disproven in other ways as well.  The geometry has no option about the control it exerts on the dynamics of particles and fields {…}.  The theory makes predictions about the equilibrium configurations and pulsations of compact stars {…}.  It gives formulas {…} for the deceleration of the expansion of the universe, for the density of mass-energy, and for the magnifying power of the curvature of space, the tests of which are not far off.  It predicts gravitational collapse, and the existence of black holes, and a wealth of physics associated with these objects {…}.  It predicts gravitational waves {…}.  In the appropriate approximation, it encompasses all the well-tested predictions of the Newtonian theory of gravity for the dynamics of the solar system, and predicts testable post-Newtonian corrections besides, including several already verified effects {…}.

No inconsistency of principle has ever been found in Einstein's geometric theory of gravity.  No purported observational evidence against the theory has ever stood the test of time.  No other acceptable account of physics of comparable simplicity and scope has ever been put forward.

¹ Charles W. Misner, Kip S. Thorne, John Archibald Wheeler, Gravitation, 1973, W. H. Freeman and Co., San Francisco; pp. 1066-1068.

² Ibid., p. 1199.

UPDATE:  2004-04-19 00:51 UT:  A follow-up on the nature of scientific theories has been posted.

UPDATE:  2004-04-29 23:50 UT:  A follow-up “Copernicus Dethroned” has been posted.

UPDATE:  2004-04-18 16:30 UT:  Fred Kiesche at the stimulating The Eternal Golden Braid blog has linked to this piece, noting, ”To follow up on my recently posted news item about the Gravity B probe (launch still on track for Monday), Michael McNeil's Impearls (a great site, by the way; I'm still in debt for his help with J.D. Bernal's The World, the Flesh and the Devil) talks about Battle-Tested General Relativity.”

Additional articles on the Gravity B probe may be found here in the New York Times, and here in the journal Science (requires subscription or pay-per-view).

UPDATE:  2009-09-08 14:20 UT:  The foregoing excerpt from Misner, Thorne, and Wheeler's Gravitation was written three and a half decades ago, and thus one might imagine that things might well have changed in the meantime.  A while back, however, in 2007, I had an exchange of personal correspondence with well-known general relativist Sean Carroll of Caltech — author of the graduate-level text Spacetime and Geometry: An Introduction to General Relativity (2003), who blogs at Cosmic Variance (now sponsored by Discover Magazine) — and I had occasion to ask him if the lofty status that Gravitation ascribes to Einstein's geometrodynamics has held up over all those decades.  Here's Carroll's reply, which he's granted me permission to publicly quote:

Hi Michael —

All of that is still completely true, yes.

These days we actually have better reasons to consider alternatives to GR — namely, the apparent existence of dark matter and dark energy.  They are only “detected” through their gravitational fields, so it's natural to wonder whether the evidence in their favor is actually evidence for a modification of gravity.  Sadly, the attempts so far to modify gravity in the right ways have fallen a bit short; see these posts:

http://preposterousuniverse.blogspot.com/2004/05/was-einstein-wrong.html
http://preposterousuniverse.blogspot.com/2004/05/was-friedmann-wrong.html
http://cosmicvariance.com/2006/11/08/out-einsteining-einstein/

So we still think that Einstein's theory has passed all of its tests, as the tests themselves keep getting better and better.  But who knows?  Tomorrow we might get a surprise.

Sean

Labels: Albert Einstein, Charles W. Misner, general relativity, gravity, John Archibald Wheeler, Kip S. Thorne, physics science, scientific theories, Sean Carroll