In Defense of Einstein
Very rough draft from my new book "Star Gate" under construction. "Z" will be a "fictional character" as in Plato's and Galileo's "Dialogues." The UFO and paranormal fields are littered with unreliable bad and bogus physics information that even affects US Defense policy along the lines of Sharon Weinberger's "Imaginary Weapons" and its sequel(s). This book, as are my other books, are intended to correct this deplorable situation.
Einstein allegedly wrote the following:
"XX. The Equality of Inertial and Gravitational Mass as an Argument for the General Postulate of Relativity
WE imagine a large portion of empty space, so far removed from stars and other appreciable masses that we have before us approximately the conditions required by the fundamental law of Galilei. It is then possible to choose a Galileian reference-body for this part of space (world), relative to which points at rest remain at rest and points in motion continue permanently in uniform rectilinear motion. As reference-body let us imagine a spacious chest resembling a room with an observer inside who is equipped with apparatus. Gravitation naturally does not exist for this observer. He must fasten himself with strings to the floor, otherwise the slightest impact against the floor will cause him to rise slowly towards the ceiling of the room.
To the middle of the lid of the chest is fixed externally a hook with rope attached, and now a “being” (what kind of a being is immaterial to us) begins pulling at this with a constant force. The chest together with the observer then begin to move “upwards” with a uniformly accelerated motion. In course of time their velocity will reach unheard-of values—provided that we are viewing all this from another reference-body which is not being pulled with a rope.
Note that the "ET" is exerting a non-gravity force on the chest, which then creates the gravitational field inside the chest that is objectively detected by an ordinary scale that the man in the chest stands on watching the pointer displace exactly as it would doing the same experiment locally on the surface of the Earth. Detecting intrinsic curvature as non-gravity force-free "geodesic deviation," i.e., Weyl stretch-squeeze & Ricci compressions/expansions from head to toe are irrelevant here even if they were large enough to notice. Z, and others simply garbles this key distinction raising an irrelevant bogus Red Herring objection to Einstein's "informal language" (David Bohm) on the physical meaning of general relativity.
"But how does the man in the chest regard the process? The acceleration of the chest will be transmitted to him by the reaction of the floor of the chest. He must therefore take up this pressure by means of his legs if he does not wish to be laid out full length on the floor. He is then standing in the chest in exactly the same way as anyone stands in a room of a house on our earth. If he releases a body which he previously had in his hand, the acceleration of the chest will no longer be transmitted to this body, and for this reason the body will approach the floor of the chest with an accelerated relative motion. The observer will further convince himself that the acceleration of the body towards the floor of the chest is always of the same magnitude, whatever kind of body he may happen to use for the experiment.
Relying on his knowledge of the gravitational field (as it was discussed in the preceding section), the man in the chest will thus come to the conclusion that he and the chest are in a gravitational field which is constant with regard to time. Of course he will be puzzled for a moment as to why the chest does not fall in this gravitational field. Just then, however, he discovers the hook in the middle of the lid of the chest and the rope which is attached to it, and he consequently comes to the conclusion that the chest is suspended at rest in the gravitational field."
By the actual non-gravity force provided by the "rope" that is equivalent to firing a rocket in space to keep at a fixed distance from a large gravitating mass like the Sun or the Earth or the Moon. We misinterpret this "non-gravity force" as the "gravity field" pushing us off the zero-g geodesic path that we would take in its absence. The heaviness we feel standing still on Earth is exactly equivalent to the astronaut firing his rocket engine to stay in fixed position above the surface of the rotating Earth below. In both cases there is a non-gravity external applied force, different in each instance, maintaining the non-geodesic path relative to the local curved space-time geometrodynamic field causing the heaviness that we inaccurately call "gravity force" as if it were an intrinsic force when in fact it is an "inertial force", i.e., an artifact of the off-geodesic non-inertial local reference frame we are at rest in. What confuses Z and others is the garbling of the informal language from Newton and Einstein that like oil and water do not mix even though they lead to the same mathematics and predictions in the appropriate limiting case of weak gravity fields (i.e., large radii of intrinsic curvature) and relative speeds of test particles to detectors small compared to the vacuum speed of light c. Z incorrectly objects to the following remark of Einstein's - The Grand Master of The Gedankenexperiment -- an art lost by mathematicians in theoretical physicist's costume tying themselves up in Gordian knots.
" Ought we to smile at the man and say that he errs in his conclusion? I do not believe we ought if we wish to remain consistent; we must rather admit that his mode of grasping the situation violates neither reason nor known mechanical laws. Even though it is being accelerated with respect to the “Galileian space” first considered, we can nevertheless regard the chest as being at rest. We have thus good grounds for extending the principle of relativity to include bodies of reference which are accelerated with respect to each other, and as a result we have gained a powerful argument for a generalised postulate of relativity.
We must note carefully that the possibility of this mode of interpretation rests on the fundamental property of the gravitational field of giving all bodies the same acceleration, or, what comes to the same thing, on the law of the equality of inertial and gravitational mass. If this natural law did not exist, the man in the accelerated chest would not be able to interpret the behaviour of the bodies around him on the supposition of a gravitational field, and he would not be justified on the grounds of experience in supposing his reference-body to be “at rest.”
Suppose that the man in the chest fixes a rope to the inner side of the lid, and that he attaches a body to the free end of the rope. The result of this will be to stretch the rope so that it will hang “vertically” downwards. If we ask for an opinion of the cause of tension in the rope, the man in the chest will say: “The suspended body experiences a downward force in the gravitational field, and this is neutralised by the tension of the rope; what determines the magnitude of the tension of the rope is the gravitational mass of the suspended body.” On the other hand, an observer who is poised freely in space will interpret the condition of things thus: “The rope must perforce take part in the accelerated motion of the chest, and it transmits this motion to the body attached to it. The tension of the rope is just large enough to effect the acceleration of the body. That which determines the magnitude of the tension of the rope is the inertial mass of the body.” Guided by this example, we see that our extension of the principle of relativity implies the necessity of the law of the equality of inertial and gravitational mass. Thus we have obtained a physical interpretation of this law.
From our consideration of the accelerated chest we see that a general theory of relativity must yield important results on the laws of gravitation. In point of fact, the systematic pursuit of the general idea of relativity has supplied the laws satisfied by the gravitational field. Before proceeding farther, however, I must warn the reader against a misconception suggested by these considerations. A gravitational field exists for the man in the chest, despite the fact that there was no such field for the co-ordinate system first chosen. Now we might easily suppose that the existence of a gravitational field is always only an apparent one. We might also think that, regardless of the kind of gravitational field which may be present, we could always choose another reference-body such that no gravitational field exists with reference to it. This is by no means true for all gravitational fields, but only for those of quite special form. It is, for instance, impossible to choose a body of reference such that, as judged from it, the gravitational field of the earth (in its entirety) vanishes.
Einstein here means over a region of space-time not at an isolated point.
"We can now appreciate why that argument is not convincing, which we brought forward against the general principle of relativity at the end of Section XVIII. It is certainly true that the observer in the railway carriage experiences a jerk forwards as a result of the application of the brake, and that he recognises in this the non-uniformity of motion (retardation) of the carriage. But he is compelled by nobody to refer this jerk to a “real” acceleration (retardation) of the carriage. He might also interpret his experience thus: “My body of reference (the carriage) remains permanently at rest. With reference to it, however, there exists (during the period of application of the brakes) a gravitational field which is directed forwards and which is variable with respect to time. Under the influence of this field, the embankment together with the earth moves non-uniformly in such a manner that their original velocity in the backwards direction is continuously reduced.”
It's quite obvious in the above paragraph, that Einstein's use of "gravitational field" is conceptually independent of intrinsic curvature and Z's attempt to fuse them is a fundamental misunderstanding leading to bogus objections against what Einstein is saying above. Appeals to pure mathematics of "differential geometry" with alternate connections are equally beside the point.
On Jan 5, 2007, at 7:50 PM, Jack Sarfatti wrote:
1. Z has used this forum to make allegations about defects in Einstein's theory of gravity (AKA General Relativity or GR) about the equivalence principle that are Red Herrings and really have nothing to do with what Einstein actually wrote when trying to explain his ideas to the public.
I will quote directly from Einstein's popular essays.
Part of Z's garbled not-even-wrong thesis revolves around the term "gravitational field." It is obvious from Einstein's actual words below that he does not mean "curvature" when he uses "gravitational field." Roughly speaking, in popular terms, the "curvature" is the inhomogeneity or variation in the gravitational field from place and time to another place at another time not too far away. Einstein's theory of gravity depends on "differential geometry", i.e., relationships between events not too far away. How far? Well that does depend inversely on the intensity of the curvature. Formally speaking for the mathematicians, Einstein by "gravity field" derives from the zero torsion symmetric "Levi-Civita connection field" (LC) for the self-parallel transport of vectors along paths or world lines in 4D space-time. Imagine an arrow in plane Euclidean geometry displaced by a small amount parallel to itself to get an initial rough intuitive idea of the concept.
The equivalence principle:
In contrast to electric and magnetic fields, the gravitational field exhibits a most remarkable property, which is of fundamental importance for what follows. Bodies which are moving under the sole influence of a gravitational field receive an acceleration, which does not in the least depend either on the material or on the physical state of the body. For instance, a piece of lead and a piece of wood fall in exactly the same manner in a gravitational field (in vacuo), when they start off from rest or with the same initial velocity. This law, which holds most accurately, can be expressed in a different form in the light of the following consideration.
Here Einstein is using the more familiar "common sense" Newtonian concepts where gravity is a force. In geometrodynamics the intrinsic gravity force is eliminated along the timelike geodesic paths of curved spacetime. What we experience as "gravity force" i.e. "heaviness" or "weight" is always 100% inertial force caused by some non-gravity force pushing the detector off its natural free float subluminal geodesic path. This is completely independent of the presence of intrinsic local curvature as we only focus on the exact point-like motion of the center of mass of the detector and choose not to measure the relative motions of the different parts of the detector so as not to add irrelevant noise to the signal i.e. Einstein's key organizing idea. The core method of theoretical physics, as explained by David Bohm, is the art of making significant abstractions weeding out secondary and/or orthogonal concepts interesting in their own right as they may be.
If now, as we find from experience, the acceleration is to be independent of the nature and the condition of the body and always the same for a given gravitational field, then the ratio of the gravitational to the inertial mass must likewise be the same for all bodies.
Therefore, the non-geodesic gravitational force must be, within Einstein's 1915 theory, 100% inertial in curved space-time always caused by some non-gravity force. For example, Alice and The Mad Hatter are at the North and South Poles of the Earth respectively. They are both accelerating radially away from the center of Earth in opposite directions at g ~ 9.8 meters/sec^2 yet they are standing still relative to each other! This would be a paradox in globally flat Euclidean space-time, but it is exactly what we expect in the topsy turvy uncommon-sensical curved space-time of Riemann, Lewis Carroll and Albert Einstein! In fact, the quantum electrical forces in the ground at the Earth's surface continually push Alice and The Mad Hatter away from each other off their otherwise weightless free-float local geodesic "straightest paths" in the curved local geometrodynamic field. Do not confound the intrinsic geometrodynamic field, the folded wrinkled cosmic fabric of space-time with Einstein's misnamed "gravitational force" - a remnant from Newtonian thinking where gravity is a conservative path-independent force field with an action-at-a-distance scalar potential similar to the electrical Coulomb potential with mass as gravity charge. This "common sense" analogy used by amateurs is very limited and quickly leads to false and not even wrong conclusions by the uninitiated into the real mysteries of Super Cosmos.
By a suitable choice of units we can thus make this ratio equal to unity. We then have the following law: The gravitational mass of a body is equal to its inertial mass.
It is true that this important law had hitherto been recorded in mechanics, but it had not been interpreted. A satisfactory interpretation can be obtained only if we recognise the following fact: The same quality of a body manifests itself according to circumstances as “inertia” or as “weight” (lit. “heaviness”). In the following section we shall show to what extent this is actually the case, and how this question is connected with the general postulate of relativity.
Given an extended test body whose self-gravity field can be ignored, what Einstein means here is the motion of its point center of mass. The complex possible relative motions of vibration and rotation and distortion of the parts of the extended body are ignored in this approximation. Therefore, the presence of local intrinsic curvature fields is completely irrelevant to the way Einstein uses "gravitational field" and applies it to formulate the equivalence principle. Because of this fact, Z's crank thesis that the gravitational field has a non-zero intrinsic tensor part plus the inertial force part is completely false within the 1915 Einstein theory without the Russian torsion field of Gennady Shipov first properly explained in 1961 by T.W.B. Kibble of Imperial College, University of London in terms of the local gauging of the 10-parameter Poincare group of Einstein's 1905 theory of special relativity for all source non-gravity field dynamical actions. Silly arguments by mathematicians that one can formally do so has no physical meaning and is simply "excess baggage" (J.A. Wheeler) of "less with more" rather than the other way round much preferred.
Z has made much noise with little signal about "uniform gravity fields." Here is what is what Einstein actually wrote about "the uniformly accelerated coordinate system (instead of an inertial system)" in the globally flat spacetime of 1905 special relativity:
"This gravitational field 'generated' by the acceleration of the coordinate system would of course be of unlimited extent in such a way that it could not be caused by gravitational masses in a finite region; however, if we are looking for a field-like theory, this fact need not deter us."
Z pulls this out of context completely and uses it to manufacture a bogus objection to Einstein's theory that there is some fundamental defect in Einstein's heuristic formulations of the equivalence principle that is the corner stone of the physical meaning of his theory.
An accelerated coordinate system in globally flat Minkowski spacetime requires a non-gravity force to accelerate it. This is Newton's 2nd Law F = ma. The "force of gravity" in Newton's sense is always in reality caused by some non-gravity force. That is, the "force of gravity" is really a kind of misnomer because it is only felt as "weight" or "heaviness" in non-inertial, i.e. "non-geodesic" frames of reference where "geodesic" means the straightest possible path in 4D spacetime relative to the symmetric Levi-Civita connection field, whether flat or curved makes no difference. All of this is only in the absence of the Russian torsion fields of course. Curvature is only detected in the relative motions of the different parts of the extended test body and that is completely irrelevant to the key idea which only describes the precise point motion of the center of mass of that test body. Relative motions about that center of mass are a different problem and there the curvature will play a key role. Z garbles this distinction to make irrelevant bogus objections.
to be continued
"If we knew what it was we were doing, it would not be called research, would it?"
- Albert Einstein