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Physics Has Its Principles

'Physics is about everything one can see, hear or think about in the whole world. Mathematics is about everything!' - Michael Kroyter

Abstract. Physicists and mathematicians have fundamentally different approaches to describing reality. The essential difference is that physicists adhere to certain logical principles, any violation of which would amount to a miracle; whereas the equations of mathematics generally are oblivious to physical constraints. This leads to drastically different views of what is, and what is not, possible for cosmology and the reality we live in. Physics that adheres to these logical principles is known as "deep reality physics".

Introduction

"Something is wrong with science - fundamentally wrong. Theories keep getting stranger and stranger.” [ref. 1; opening words of Preface] This is certainly true of physics, which has backed itself into apparent contradictions, leading directly to the dominant Copenhagen view that “there is no deep reality to the world around us”.

A reasonable person might ask, “What is the wrong turn that physics has taken to arrive at this predicament?” The answer proposed here is that physics has given up its principles. It has too long consorted with mathematicians, who have no such principles. Mathematics obviously has considerable value as a tool for describing the world. However, a strength of physics historically has been the discipline it brings to mathematics by relating directly to nature. Forgetting this has surely been to the detriment of progress in physics.

The Causality Principle

Perhaps most basic of all the principles of physics is the causality principle. In its simplest form, it reads: “Every effect has a cause.” In more precise language, it reads: “Every effect has an antecedent, proximate cause.” Let’s examine these components, and see why each is required.

First, why must every effect have a cause? The answer is so basic that it is practically a matter of definition. The “cause” is whatever makes the “effect” happen. If something in the universe changes (an effect), having no “cause” to make it happen is the logical equivalent of magic, a miracle, or the supernatural. Even then, we might think of the will of the magician, miracle worker, or supernatural being as the cause. However, we are not referring here to tricks or illusions, but to events that happen without something making them happen. Even the will of a powerful being cannot produce an effect without having the means to do so. The “means” is the cause, and typically involves force or energy in some form. This point will be clearer when we examine the other two parts of the causality principle.

No Time Reversal

“Antecedent” means that a cause must exist in time prior to the effect happening. If their order were reversed, we would still refer to the chronologically first as the cause and the second as the effect. This is because if something were able to change the past, it could create logical contradictions. For example, let A cause B, then let B directly or indirectly eliminate A in the past. Then B could never have come into existence because A, now gone, is what caused it; and so on, in an endless loop of contradiction. So logically, all causes must be antecedent to their effects.

(We ignored the possibility of simultaneous cause and effect because that would require change without benefit of the passage of time. But we consider time to be a measure of change in the universe, making change without time a meaningless concept. Of course, nothing prohibits a cause from operating so close to simultaneously that we lack the ability to measure the short interval by which it precedes the effect. For our purposes here, it is important only that the effect must precede the cause, by however miniscule an amount.)

It follows that time travel into the past is not possible. Imagine what it would mean for a person to time-travel into the past, as in an H.G. Wells story. As the person appears in a time where he did not previously exist, that instantly violates any hope for conservation of matter or energy in the universe. Not only has more of both just been added to the past (displacing any substance that existed in that place previously), but the universe continues to have this supplemental mass and energy until their progenitors disappear from the present.

Another problem is that time travel must also involve travel through space. For example, the Earth is continuously traveling through space in its orbit around the Sun, in the Sun’s orbit around the Galaxy, and in the Galaxy’s motion through the local supercluster. If one could suddenly pop into the universe at a past time, how could one expect to find the Earth in space at that time?

Of course, the main reason why time travel is impossible, and not merely technologically difficult, is that it leads to logical contradictions of the type we described above. Sometimes it is claimed in science fiction that time travel must constrain one’s freedom of choice, voluntarily or involuntarily, to prevent changes to the future that would cause a logical contradiction. For example, you might be forbidden or prevented from going back and killing your own grandfather.

However, this ignores that your mere appearance in the past has changed the entire universe forever. When you arrive on Earth in the past, you displace or absorb air molecules in some new way, which changes the course of countless numbers of air molecule collisions, which in turn change countless numbers of other similar events. Eventually, some critical event that depended on air molecules being just so - maybe the timing of when a leaf falls, or whether or not something rolls over a cliff, or whether a roll of dice turns up a one instead of a six - will happen differently than in the original time line. That causes the new time line to begin to diverge from the old at an accelerating pace. Each new event generates many other new events that did not happen before. After enough time, everything becomes affected. So it is impossible for time travel over non-trivial time intervals to avoid eventually changing something in a way that leads to a contradiction. Time travel is therefore disallowed by the principles of physics.

No True “Action at a distance”

“Proximate” means “physically in contact with”. An effect can have many remote causes, but must have at least one proximate cause. The alternative would be a condition that one thing be able to affect another without the passage of anything between the two. Once again, this would be the logical equivalent of magic, a miracle, or the supernatural. This condition is called “action at a distance”, and is forbidden by the causality principle because it is logically impossible.

Isaac Newton, whose Universal Law of Gravitation is implicitly based on action at a distance, left no doubt that he considered this a pragmatic approximation of reality when he said: “That one body may act upon another at a distance through a vacuum, without the mediation of any thing else, by and through which their action and force may be conveyed from one to the other, is to me so great an absurdity, that I believe no man who has in philosophical matters a competent faculty of thinking, can ever fall into it.” So reality requires that any action be conveyed from a remote cause to a target by means of some sort of action-carriers. It does not require that the carriers be visible or even detectable. But exist they must, and they, or some surrogate carriers, must come into contact with the target to transmit the action.

[Those familiar with the extended Zeno’s Paradox for matter might object that true contact is impossible when matter is infinitely divisible. However, it suffices that “contact” be the finite limit of an infinite series of increasingly close approaches as one goes ever deeper toward the infinitesimal. This is analogous to crossing a street half way, then half the remaining way, then half again, and so on forever. Although an infinite number of half-the-distance steps are needed, the series nonetheless reaches a finite limit (the other side) in a finite time. For a fuller discussion, see ref. 1, chapter 1.]

Modern physics has introduced the concept of “fields”, such as charge around a particle or gravitation around a mass. When the particle or mass moves, its entire field moves with it. However, this cannot happen acausally. For example, the mass may cause adjacent parts of its field to move, which in turn move more distant parts, and so on. This is what happens in any rigid body when one part of it is pushed: a pressure wave propagates through it, conveying the push to all parts of the rigid body. Therefore, fields are not a form of action at a distance. The fact that gravitational fields are seen to update faster than light can propagate [2] is an argument for faster-than-light propagation of forces, not an argument for action at a distance.

Another modern physics concept is “curved space-time”. If such a thing exists and can cause a body to move, then it must itself consist of something tangible or “solid”; i.e., able to act on a body. If so, then it simply constitutes another action carrier updated by other carriers back to the source of gravity. It is reasonable to admit that we know nothing about what constitutes “space-time” or how it carries actions. It is not reasonable to maintain that “space-time” needs no tangible connections to either the source or the target of gravity. Obviously, many mathematical physicists in the field today do not think about “space-time” as tangible in that way. This can lead to some frustrating conversations between people with incompatible perspectives about reality.

     

Rubber sheet Analogy - Click for an enlargement

Figure 1. Rubber sheet analogy for “curved space-time. Artwork by Starosta.

To be specific, consider a marble at rest in a curved space-time, as in Figure 1. If at rest, it must remain at rest unless some force acts on it. We are told to visualize that the marble will tend to roll downhill, and this is how “curved space-time” produces the effect we call gravity. However, from a causality perspective, if the rubber sheet or “curved space-time” were located in space without gravity already present under the sheet, the marble would just stay in place on the side of the hill. The existence of curvature, even when time is involved in the curvature, is not a cause of motion. Only a “force” (a conveyor of momentum) can induce new motion. The force is the proximate cause.

No “Creation ex nihilo”

“No creation ex nihilo” is the principle that something cannot come into existence out of nothing. In a sense, it is another manifestation of the causality principle because such creation would represent an effect without a cause. However, this is a particular case worth considering on its own merits because our primary cosmology today, the Big Bang, begins with the ultimate creation-from-nothing scenario - the mass, space, and time of the entire universe from nothing - as its first step.

Creation ex nihilo is forbidden in physics because it requires a miracle. Everything that exists comes from something that existed before, that has grown, or fragmented, or changed form. Growth requires accretion, nourishment, or energy input. Fragmentation ranges from chipping to evaporation to explosion into bits so tiny that we can no longer see or detect them. Changing form includes changes of state, such as solids, liquids, gases, or plasmas.

“Matter” and “energy” may be regarded as simply different forms of the same substance, convertible back and forth. It is easy to visualize matter as exploding into ultra-tiny bits that we might call “energy”. But part of that energy consists of the high speeds of bodies. Where does that energy come from? Bodies have small constituents inside atoms that already have high speeds. These constituents may be liberated by an explosion, just as high relative speeds of bodies can be converted into fast constituent motion (heat) during a head-on collision. Even if we could not be specific about how this happened, we could still be certain that energy is not created on the spot from nothing.

So-called spontaneous particle creation from vacuum need not violate this principle because the vacuum is not empty. So called “zero-point energy” is energy of the vacuum, implying that the vacuum is occupied by substance on a scale too small for us to yet detect in any form other than in Casimir-type experiments. The principle only requires that the ingredients from which something is made pre-exist, but not that we can discover them yet.

Religious people might wonder why physics does not admit creation ex nihilo as an “act of God”, and therefore a valid cause. However, this is a non-economical, and non-testable hypothesis, thereby violating two of the criteria of Scientific Method. Moreover, “acts of God” are a potential explanation for everything, ending the need to investigate further and discover predictable causes. As long as all observations and experiments can be explained without need of miracles - something that has so far remained true - this principle must remain an inviolate guideline. Even if an apparent exception arose, it is difficult to imagine circumstances where a more economical, and therefore more scientific, hypothesis than an act of a Supreme Being would not exist. See also the later section of this paper about “repealing physical principles”.

No “Demise ad nihil”

The counterpart of not allowing the creation of something from nothing is “No Demise as nihil”; i.e., something cannot become nothing. However finely a thing may dissolve, however undetectable the bits of “energy” into which a thing may explode, if all the individual bits were brought together again with the same ordering, the original thing would be recovered. In other words, nothing has ceased to exist; it has merely changed its appearance or form.

It is conjectured in general relativity (GR) that “black holes” might exist, in which case anything inside an event horizon would be out of communication with the rest of the universe. Such a condition might appear to be the practical equivalent of passing out of existence. However, even for black holes, indications of existence can still be found outside the event horizon in the form of a gravitational field, so the object does continue its influence on the universe.

Nonetheless, as we will shortly consider, objects such as the “black holes” presently attributed to GR are forbidden to exist by the principles of physics (such as the next principle below). A type of astrophysical object for which escape velocity exceeds the speed of light might exist, and we might choose to call that a “black hole”. However, such an object would presumably remain in two way communications with the rest of the universe through the action of faster-than-light particles, and eventually disperse in some way as everything eventually does. But it cannot provide an example of demise ad nihil.

The Finite Cannot Become Infinite

The last of the often-self-evident principles of physics we will consider here is “the finite cannot become infinite”, and of course vice versa. That is because, no matter how many finite things we may collect, their total number and total substance remain finite. Likewise, if something is truly infinite (such as the set of all integers), then no matter how we divide it, at least one piece must remain infinite. And no matter how many equal-sized pieces we divide it into, each will still have an infinite number of components.

A singularity is a point where something has become infinite. In astrophysics, it is a point where matter has collapsed to infinite density and infinitesimal volume. Singularities occur routinely in mathematics. But up to now, whenever a singularity occurs in an equation, some constraint always prevents a singularity from arising in nature. For example, Newton’s Universal Law of Gravitation, universal law of gravitation (1013 bytes), where a (830 bytes) is acceleration, GM is the product of the gravitational constant and the mass, and r is the distance from the center of mass, has a singularity at the origin, r = 0. The equation requires acceleration to become infinite at the origin. But in reality, no test particle can ever reach the origin at the center of mass without first entering into the mass itself, which then changes the acceleration formula in a way that limits acceleration.

A classic example of this principle operating in physics is the “ultraviolet catastrophe”. It appeared that the energy of re-radiation of absorbed light should become infinite until Planck realized that such energy must occur in discrete packets, called “photons”. In similar manner, every other potential infinity in physics has always led instead to new constraints and improved equations lacking accessible singularities.

Physicists have tended toward the soft view that such infinities have never yet arisen, so perhaps they never will. But the principle is really a logical necessity if energy, force, density, and all physical quantities are viewed as consisting of a finite number of discrete physical components, even if at an undetectable level. Then obviously, no finite sum, however large, can become infinite. This guarantees that any equation containing a singularity will not continue to represent nature in the immediate neighborhood of that singularity, and that some constraint enforcing singularity-avoidance remains to be discovered in connection with that equation.

Of course, mathematicians are unaccustomed to physical principles and are very comfortable in dealing with singularities in their equations. The mathematicians who have taken over the province of general relativity have therefore, not surprisingly, advocated the existence of real singularities in nature at the centers of “black holes”. Einstein himself, as a good physicist, never accepted the concept of black holes, and held that some new constraint would modify his equations in the future. His own words [3] written late in his career while he was at Princeton) are illuminating, showing as they do a respect for physical principles over purely mathematical reasoning:

“If one considers Schwarzschild’s solution of the static gravitational field of spherical symmetry …, [g44] vanishes for r = m/2. This means that a clock kept at this place would go at rate zero. Further it is easy to show that both light rays and material particles take an infinitely long time (measured in ‘coordinate time’) in order to reach the point r = m/2 when originating from a point r > m/2. In this sense the sphere r = m/2 constitutes a place where the field is singular.

“There arises the question whether it is possible to build up a field containing such singularities with the help of actual gravitating masses, or whether such regions with vanishing g44 do not exist in cases which have physical reality. …” [brief discussion of uncompressible liquids omitted]

“One is thus led to ask whether matter cannot be introduced in such a way that questionable assumptions are excluded from the very beginning. In fact this can be done by choosing, as the field-producing mass, a great number of small gravitating particles which move freely under the influence of the field produced by all of them together. This is a system resembling a spherical star cluster. … The result of the following consideration will be that it is impossible to make g44 zero anywhere, and that the total gravitating mass which may be produced by distributing particles within a given radius, always remains below a certain bound.” [core of analysis omitted; skipping to conclusions]

“The essential result of this investigation is a clear understanding as to why the ‘Schwarzschild singularities’ do not exist in physical reality. … The ‘Schwarzschild singularity’ does not appear for the reason that matter cannot be concentrated arbitrarily. And this is due to the fact that otherwise the constituting particles would reach the velocity of light.

“This investigation arose out of discussions [with Robertson and Bargmann] on the mathematical and physical significance of the Schwarzschild singularity. The problem quite naturally leads to the question, answered by this paper in the negative, as to whether physical models are capable of exhibiting such a singularity.” [End of Einstein quote]

Einstein wasn’t arguing that the Schwarzschild singularity doesn’t exist in the equations, but that it doesn’t exist in physical reality. Much as for the case of “the ultraviolet catastrophe”, he reasoned that the equations will be shown to be incomplete as observations or experiments approach that limit.

Tangible, Material Entities Cannot Occupy the Same Space at the Same Time

            This obviously means literally the exact same space. It does not exclude a body being surrounded or even saturated by granules, a liquid, a gas, or a plasma. But no nucleus from any atom of one material entity can occupy the same space as the nucleus of any atom in another material entity at the same instant. Of course, if atomic nuclei themselves contain empty space, that can be occupied by something small enough to fit into the gaps. The principle merely forbids occupation of the identical space at the identical time by two tangible entities, but does not forbid filling in otherwise empty space.

            Another caveat seems warranted. One property that distinguishes particles from waves is the ability of waves to pass through one another without any effect on each other. However, when a wave passes, the constituents comprising the medium that carries the wave do not travel with it, but rather just bob up-and-down or back-and-forth in place. And of course, the principle that no two tangible, material entities can occupy the same place at the same time very much applies to every constituent of the medium, whether part of a wave or not. The wave is transmitted by constituent collisions, which occur without co-location of constituents ever occurring.

Corollaries of Principles

Many matters of considerable importance follow immediately from the principles of physics. For example, nature has no singularities. If it did, matter could disappear from the universe, violating the no demise ad nihil principle while also violating the finite cannot become infinite. The continued action of an external gravitational field after the cause of that field has permanently ceased to communicate with the outside universe is an effect without a cause. And the strange temporal properties of black holes have led to the proposal of “worm holes”, which violate the no time reversal principle. Black holes and worm holes are fun science fiction concepts, and are much touted and discussed by mathematical relativists. But no physicist who understands the logical necessity of the principles of physics as descriptors of reality can take such concepts literally.

It follows from these principles that there are no black holes in the traditional relativity sense of event horizons centered on a singularity. This does not preclude highly collapsed states of matter generating a high redshift for light, or possibly no light escape at all. But such objects would continue to have normal gravitational and electrostatic forces and be in two-way communication with the rest of the universe. Some of the fantastic properties of black holes will therefore turn out to be fantasies after all.

Perhaps even more importantly, the physical principles immediately imply that there was no Big Bang at the origin of the universe. The “Big Bang” also violates several physical principles: an effect with no antecedent, proximate cause; no singularities in nature; and no creation ex nihilo. If the universe really is expanding - an assumption very much in doubt [ref. 1, 1999 ed., chapter 22; reprinted from ref. 4] - then something must limit how far back that expansion can be projected.

Of course, religions have long taught that the creation of the universe is at least the one major exception to no creation ex nihilo. This approach suffers from the difficulties mentioned earlier in connection with ascribing causes to acts of God. As long as it remains clear that viable explanations do exist that require no “acts of God” [ref. 1, chapters 1-2], science will always prefer these because they make reality testable and ultimately predictable, at least to the limits of our understanding.

Definitions of Dimensions

            While not a physical principle, the matter of defining dimensions touches on some similar issues in the arena of the mathematicians’ approaches versus that of physicists. Mathematicians, lacking physical constraints, are free to imagine or invent unlimited numbers of dimensions, and to ascribe any properties to them they wish. So one hears often of parallel dimensions, hyper-dimensions, multiple time dimensions, more than three space dimensions, etc. It is easy to forget that such ideas are fictional concepts. We have not a single observation or experiment that cannot be fully and completely explained with three dimensions of space, one of time, and one of mass or scale. And despite having many theories of extra dimensions, we have no theoretical requirement for any but the five that are part of our everyday reality. So it is easy to forget that Occam’s Razor then requires that we not invent extra physical dimensions unless and until some necessity arises – not convenience, but necessity. Extra mathematical dimensions are fine if they serve a purpose, but should not be confused with physical reality.

             A second point about dimensions is that they are scales for the measurement of intervals. As such, they are ordinarily defined to be smooth and linear. Why complicate dimensions unless doing so serves a useful purpose? Moreover, scales for measurement are insubstantial; i.e., they have no substance. Therefore, a dimension cannot be affected by matter or by a force. Consider a common example, often seen in general relativity texts: “curved space”. Think of a light ray following that curvature and bending as it passes the Sun’s mass. GR suggests we think of the ray path as straight and space as curved. But it would be simpler, as in classical physics, to think of the ray path as curved and the space as straight. In fact, wherever we are in the universe, we can always construct three mutually perpendicular lines, extend each of them to infinity in both directions, and have all observers in the universe agree that these lines are straight, uniform, and parallel to the straight lines of all other observers, even if they pass near or through large masses. There is clearly no necessity for having curved space, whatever masses or forces may do to light, the vacuum, or other matter. For example, any two points along the curved path of a light ray past a mass can be joined by a taut string, which (if it is strong enough to resist the pull of gravitation and other forces) describes a straight line through space, and a shorter path in space than the ray takes.

             Therefore, the term “space” should continue to be used with its classical meaning, the dimension for measuring separations. If we have a theory in which we might like “space” to expand or contract, we must choose a different word, because the meaning of the word “space” is reserved for a useful concept that can have no distortions. For example, we might then have to say that “a space-filling medium” expands or contracts. That grounds the discussion in reality, and eliminates the fantastic.

             Similar remarks apply to time. Clocks may change rates, and they apparently slow down when in a gravitational field or moving relative to such a field. However, the dimension of time can remain as smooth and linear as we please, so we choose define it that way. Then time is simply a measure of change. In much of the 20th century, it was thought that time could not be measured apart from the behavior of clocks. However, experience with the Global Positioning System (GPS) has shown that, even when clocks move with different relative speeds in different gravitational potentials, all can be synchronized in epoch and rate to hypothetical underlying non-moving clocks in a strictly inertial frame with the gravitational potential projected to any standard height. Then all such clocks will remain permanently synchronized, and make excellent measures of a form of “universal time”, compatible with other clocks throughout the universe.

             However, if time is not a physical thing that slows down with speed and stops for things moving at the speed of light (as is true in Lorentzian Relativity, but not in Special Relativity), then it follows that the speed of light is not a speed limit for the universe. A hypothetical spaceship traveling at the speed of light might see its atomic clocks stop at that speed, or perhaps even reverse if the spaceship moved faster yet. But time would march forward for the spaceship and the entire universe at the same rate as ever. If the spaceship used chemical propulsion, it might have as much difficulty propelling itself faster than light as a propeller plane would have trouble exceeding the speed of sound. But nothing prohibits this happening in principle if new methods of propulsion such as gravity, not limited by the speed of electromagnetic radiation, were employed for the purpose.

Repealing Physical Principles

It is fun to think of other dimensions, time travel into the past, magic, and numerous other mathematical and/or science fiction concepts. However, it is useful to make a distinction between concepts that are possible, although we are not yet technologically advanced enough to make them happen; versus concepts that are now and always certain to be impossible because they lead to logical contradictions. This is reminiscent of the old argument: Can God, who is omnipotent, invent a square circle? The normally accepted answer is that even omnipotence does not enable a Being to devise a contradiction in terms.

In considering this difference, we should acknowledge Clarke’s First Law: “Any sufficiently advanced civilization is indistinguishable from magic.” The wording of this law notwithstanding, we can tell the difference between advanced technological feats and logically impossible feats. For example, we would not be too startled by an advanced species that had perfected Star-Trek-like teleporters, although that possibility is far beyond what our technology is capable of doing. By contrast, we could rest assured that no species, however advanced, can alter the past. Time travel into the past is a logical impossibility.

Now suppose that we encountered an advanced species that did have the capability to alter the past or violate other physical principles. Ironically, this is not a logical impossibility. For example, we have seen Star-Trek-like holodecks create virtual realities that are essentially indistinguishable from our own reality. Clearly, the programmer can alter the virtual reality program to appear to defy physical principles. Nonetheless, the result is little different from watching a movie about time travel or black holes, even though we might have no awareness that what we sensed was fictional. So if we saw physical principles being violated, we could conclude with some certitude that we were experiencing a virtual reality.

This raises an interesting philosophical challenge: How do we know that our present reality is not a virtual one? The short answer is that, if it is programmed to be faithful to all principles of physics and in other ways realistic, we might well lack any means of being able to tell which type of reality we inhabit. But ultimately, we are forced to act pragmatically and behave as if this reality is non-virtual because the consequences of doing otherwise are painful and catastrophic, to the best of our ability to predict them. [See ref. 1, chapter 20, for a fuller discussion of “truth and reality”.] The discovery of a single, clear violation of a principle of physics would change that conclusion. So we can see that a great deal is at stake in adhering to the principles for as long as that remains possible.

Conclusions

The principles of physics are inviolate rules because any contradiction would be tantamount to magic, a miracle, or the supernatural. Allowing miracles into theories makes them non-falsifiable, and therefore unscientific. Adhering to these logical principles and accepting "no miracles" as the only valid "first principle" is now known as "deep reality physics". The following principles were discussed here:

  • Every effect has an antecedent, proximate cause
  • No time reversal
  • No true action at a distance
  • No creation ex nihilo
  • No demise ad nihil
  • The finite cannot become infinite
  • Tangible, material entities cannot occupy the same space at the same time

These corollaries flow from application of the principles:

  • Nature has no singularities
  • There are no black holes
  • There was no Big Bang
  • 2-way time travel is impossible

These corollaries follow from classical definitions of dimensions:

  • Extra dimensions are not needed to describe physical reality
  • The five ordinary dimensions are always uniform, linear, and universal
  • The speed of light is not a universal speed limit

Discovering a definite violation of a physical principle would bring into question the nature of the reality we inhabit.

 

Derived from conferences held at Cesena, Italy 1999/09/20

and Sutton, Montreal 2002/10/07

Minor update 2008/03/30

 

[1] Van Flandern, T. (1993; 2nd edition 1999), Dark Matter, Missing Planets and New Comets, North Atlantic Books, Berkeley.
[2] Van Flandern, T. (1998), Phys.Lett.A 250, 1-11.
[3] Einstein, A. (1939), Annals of Mathematics, 40, #4 (Oct.), 922-936.
[4] Van Flandern, T. (1994), Meta Research Bull. 3, 25-35; available through metaresearch.

 
 
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