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Einstein’s “Scientific Testament”
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Posted by: Gunnar Tomasson
INTRODUCTION
In August 1954, Einstein made certain comments on the conceptual foundations of the General Theory of Relativity which have long intrigued me and, while I am well versed in the non-specialist literature on Einstein’s work, I have not come across any clarification of the points at issue or their possible resolution.
The occasion was “the last letter that he sent to his old friend [Michele Besso], and it provides us with a veritable scientific testament. It was written in reply to a letter that Besso (still intellectually very alive at eighty-one) wrote to the seventy-five-year old Einstein, asking for comments on a brief statement of his (Besso’s) view of the essential content of general relativity.”
“Your picture of the general theory of relativity characterizes its genetic aspects very well,” Einstein began his letter. “However, it is also valuable to analyse the whole thing from the standpoint of formal logic. For if the mathematical difficulties make the empirical content of the theory temporarily inaccessible, logical simplicity (even though it is not by itself sufficient) becomes the only criterion of the value of the theory.” (‘Einstein, A Centenary Volume’, ed. by A. P. French for the International Commission on Physics Education, Harvard University Press, 1979, p. 267)
The intriguing part came at the end, where Einstein advised his life-long friend and collaborator as follows:
“I concede, however, that it is quite possible that physics cannot be founded on the concept of field – that is to say, on continuous elements. But then, out of my whole castle in the air – including the theory of gravitation, but also most of current physics – there would remain almost nothing.”
SETTING THE STAGE
A few months later, Einstein was dead and, while we don’t know the specific grounds for his reservations about the field concept, they must have concerned “the empirical content of the theory” which the “mathematical difficulties” associated with its four-dimensional expression had made “temporarily inaccessible”, yet remained subject to analysis “from the standpoint of formal logic.”
In turn, such logical analysis must begin with what, apparently, had been Einstein’s own point of departure in the theory’s derivation, as indicated later by his approach to the conceptualization of the “cosmological problem” in ‘The Meaning of Relativity’ (Fifth Edition, finalized by Einstein in 1954, Princeton University Press, 1974).
“[The] so-called “cosmological problem” will be considered here in detail,” he wrote, “in part because of its basic importance, partly also because the discussion of these questions is by no means concluded. I feel urged toward a more exact discussion also by the fact that I cannot escape the impression that in the present treatment of this problem the most important basic points of view are not sufficiently stressed.
“The problem can be formulated roughly thus: On account of our observations of the fixed stars we are sufficiently convinced that the system of fixed stars does not in the main resemble an island which floats in infinite empty space, and that there does not exist anything like a center of gravity of the total amount of existing matter. Rather, we feel urged toward the conviction that there exists an average density of matter in space which differs from zero.
“Hence the question arises: Can this hypothesis, which is suggested by experience, be reconciled with the general theory of relativity?
“First we have to formulate the problem more precisely. Let us consider a finite part of the universe which is large enough so that the average density of matter contained in it is an approximately continuous function of (x1, x2, x3, x4). Such a subspace can be considered approximately as an inertial system (Minkowski space) to which we relate the motion of the stars. One can arrange it so that the mean velocity of matter relative to this system shall vanish in all directions. There remain the (almost random) motions of the individual stars, similar to the motions of the molecules of a gas. It is essential that the velocities of the stars are known by experience to be very small as compared to the velocity of light. It is therefore feasible for the moment to neglect this relative motion completely, and to consider the stars replaced by material dust without (random) motion of the particles against each other.” (Op. cit., pp. 110-111)
THE "COSMOLOGICAL PROBLEM"
When so conceptualized, the “cosmological problem” is reduced to that of analyzing the stability of an imaginary universal structure comprising point particles of matter distributed isotropically in finite space in an initial state of rest. On the assumption that gravity is an innate attribute of matter, of course, the particles would promptly collapse towards a common center of gravity.
His introduction of the “cosmological constant” into the equations of gravitation was Einstein’s response to this dilemma – “We may remark, by the way,” he added, “that in Newton’s theory there exists the same difficulty.” (Op. cit., p. 112)
I. NEWTON
Not quite!
In Newton’s case, the “difficulty” is rooted in the twin ASSUMPTIONS (1) that gravity is an innate attribute of matter and (2) that Newton’s gravitational equations may be construed in that respect as causal rather than descriptive in nature – Newton never embraced either of these assumptions and went to great lengths to make that clear.
“Several times in his Bentley letters,” Cornell philosopher E. A. Burtt reported in his “classic” 1920/1930s work, ‘The Metaphysical Foundations of Modern Physical Science’, “Newton took occasion to object to the doctor’s assumption that gravity is an essential quality of bodies. This his own experimental principles had led him to refuse to do […]. At the same time the prestige of his law of gravitation, and its apparent universality in the world of matter, had encouraged a general impression that gravity was innate in matter according to Newtonian principles, an impression that was further advanced by Cotes’ explicit championship of the doctrine in his preface to the second edition of the ‘Principia’. “You sometimes speak of gravity as essential and inherent to matter. Pray do not ascribe that notion to me; for the cause of gravity is what I do not pretend to know, and therefore would take more time to consider it.”” (Doubleday Anchor Books, 1954, pp. 290-291)
As for the second assumption, Newton was no less emphatic, writing with respect thereto in Definition VIII at the outset of ‘Principia’: “I likewise call attractions and impulses, in [a certain] sense, accelerative, and motive; and use the words attraction, impulse, or propensity of any sort towards a centre, promiscuously, and indifferently, one for another; considering those forces not physically, but mathematically: wherefore the reader is not to imagine that by those words I anywhere take upon me to define the kind, or the manner of any action, the causes or the physical reason thereof, or that I attribute forces, in a true and physical sense, to certain centres (which are only mathematical points); when at any time I happen to speak of centres as attracting, or as endued with attractive powers.”
II. HAWKING
Newton pleaded and cautioned in vain – the notion that his gravitational equations were somehow explanatory rather than descriptive of orbital phenomena within the Earth-Moon System took deep root and remains an unquestioned point of departure for modern cosmology despite the superior descriptive accuracy of Einstein’s General Theory of Relativity based on totally different “explanatory” principles.
For example, Stephen W. Hawking has summarized Newton’s seminal contribution to the foundations of modern physics in general and cosmology in particular as follows:
“An explanation [of Kepler’s orbital data] was provided only much later, in 1687, when Sir Isaac Newton published his ‘Philosophiae Naturalis Principia Mathematica’, probably the most important single work ever published in the physical sciences. In it Newton not only put forward a theory of how bodies move in space and time, but he also developed the complicated mathematics needed to analyze those motions. In addition, Newton postulated a law of universal gravitation according to which each body in the universe was attracted toward every other body by a force that was stronger the more massive the bodies and the closer they were to each other. It was this same force that caused objects to fall to the ground.” (‘A Brief History of Time’, Bantam Books, 1988, p. 4)
III. NEWTON'S LAW
In fact, it is NOT clear if Newton meant to postulate a law of “universal” gravitation in the sense that “each body in the UNIVERSE was attracted toward every other body” – while the fuzzy wording of his Rule III of ‘Reasoning in Philosophy’ may be so construed, Newton’s summary account of issues relating to the applicability of his gravitational equations within the SOLAR system at the end of the third edition of ‘Principia’ published in 1725/26 conveys the contrary impression:
“Hitherto we have explained the phenomena of the heavens and of our sea by the power of gravity, but have not yet assigned the cause of this power. This is certain, that it must proceed from a cause that penetrates to the very centres of the sun and planets, without suffering the least diminution of its force; that operates not according to the quantity of the surfaces of the particles upon which it acts (as mechanical causes used to do), but according to the quantity of solid matter which they contain, and propagates its virtue on all sides to IMMENSE DISTANCES, decreasing always as the inverse square of the distances. […] But hitherto I have not been able to discover the cause of those properties of gravity from phenomena, and I frame no hypotheses; for whatever is not deduced from the phenomena is to be called an hypothesis; and hypotheses, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy. In this philosophy particular propositions are inferred from the phenomena, and afterwards rendered general by induction.”
IV. THEORY AS AXIOMATIC CONSTRUCT
In 1933, Einstein commented on this passage as follows: “Newton, the first creator of a comprehensive, workable system of theoretical physics, still believed that the basic concepts and laws of his system could be derived from experience. This is no doubt the meaning of his saying, hypotheses non fingo [I frame no hypotheses].”
In contrast, echoing David Hume’s construction of the epistemological aspects of Newton’s work and drawing on his own experience, Einstein was persuaded that such basic concepts and laws “are free inventions of the human intellect, which cannot be justified either by the nature of that intellect or in any other fashion a priori” – that “the axiomatic basis of theoretical physics cannot be extracted from experience but must be freely invented.” (‘On the Method of Theoretical Physics’, reprinted in ‘Ideas and Opinions’, Dell Paperback, 1976, p. 266)
As ‘free inventions’ of Einstein’s intellect, the axiomatic foundations of the General Theory of Relativity are subject to analysis “from the standpoint of formal logic” – with drastic consequences if the least logical flaw is found therein. For, as Einstein observed in 1919: “The chief attraction of the theory lies in its logical completeness. If a single one of the conclusions drawn from it proves wrong, it must be given up; to modify it without destroying the whole structure seems to be impossible.” (‘What is the Theory of Relativity’, London Times, reprinted in ‘Ideas and Opinions’, p. 227)
(Alexander Friedman’s discovery in 1922 of an algebraic problem associated with the ad hoc “cosmological constant” led in due course to its removal and replacement by the notion that the equations of General Relativity were descriptive of a universal structure in which the expansion of space itself negates the “cosmological problem”; Friedman’s finding did not concern the axiomatic presuppositions of Einstein’s theory but paved the way for one ad hoc notion to be replaced by another.)
TESTING EINSTEIN'S AXIOMS
In formulating the “cosmological problem”, as noted earlier, Einstein “consider[ed] a finite part of the universe [or] subspace [which] can be considered approximately as an inertial system […] to which we relate the motion of the stars [which] for the moment [are] consider[ed] replaced by material dust [or point particles of matter] without (random) motion of the particles against each other.”
In this conceptual scheme, the Solar System is represented, “for the moment”, by one such point particle of matter insofar as its gravitational interaction with all other particles in the subspace are concerned. However, when it comes to evaluating the scheme’s applicability to the facts of experience, one must consider that the Solar System, while “without (random) motion” within the subspace by assumption, is in rotational motion around its axis.
The logical consistency of Einstein’s axioms in this respect may be tested by a simple thought experiment as follows:
1. Let A be the center of the Solar System, with B representing the center of a given Star System, such that a straight line between A and B passes through point C at the Solar System’s boundary towards which the Voyager 1 spacecraft is moving through the joint effect of its own motion and the Solar System’s rotational motion.
2. Now imagine a photon, P1, being emitted towards A from Voyager 1 at point D along its path, and a second photon, P2, being emitted from A along a path such that timing devices will record P1’s arrival at A when P2 impacts Voyager 1 at C.
3. Both DA and AC describe STRAIGHT paths of photon propagation relative to the Solar System's center A but CURVED paths relative to that of Star System B due to the Solar System’s rotational motion around its axis.
4. Since a given photon’s path of propagation cannot be BOTH straight and curved relative to a given inertial system, it follows that Einstein’s axioms are NOT those of a conceptual scheme which “can be considered approximately as an inertial system.”*
CONCLUDING REMARKS
Einstein may have suspected as much. For, in ‘The Evolution of Physics’ (1938) – a book which he co-authored with Leopold Infeld – he acknowledged that it remained an open question whether inertial systems did in fact exist.
Whether or not such systems exist - and in our dynamic Cosmos, the chances that they do appear vanishingly close to zero - it is CERTAIN rather than “quite possible that physics cannot be founded on the concept of field or continuous elements” as envisaged in the General Theory of Relativity.
It is a measure of Einstein’s greatness of spirit that he did not “egg-walk” around the harsh implications thereof for his own greatest achievement, but gracefully conceded that “then, out of my whole castle in the air – including the theory of gravitation, but also most of current physics – there would remain almost nothing.”
Gunnar
* ADDENDUM Nov. 9, 2003.
The above mechanics may be applied to the phenomenon of Stellar Aberration as follows:
5. Now consider Starlight emitted towards a telescope at A from Star System X located on the line XDA.
6. For the Starlight to be observed at A, the telescope must be aligned with the line ACB.
7. Hence Stellar Aberration commensurate with the angle at which lines XDA and ACB intersect at A.
Posted by: Philip Mintz
There exists much evidence that the mass of a body of matter increases when the body accelerates. Not only that, but the mass is absolute, not relative.
A particle in a particle accelerator arrives at its target with a mass that is several times as much as its rest mass. That can be understood if we recognize that all matter is made of the same kind of building blocks. I call them bits, and they come in pairs, neg bits and pos bits. The core of an electron is an aggregate of neg bits.
A particle is accelerated by being pushed by a source of bit pairs. The pusher emits bits that are received by the pushee.
Philip Mintz
http://philmintz.tripod.com
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