Dirac's equation

Why does Dirac’s equation hold? Despite an all too prevalent belief it is not some strange property of nature. It is a trivial property of geometry. Considering only space transformations, ignoring interactions and internal symmetry, objects (thus free) belong to states of the Poincaré group. This has two invariants (like the rotation group has one, the total angular momentum). For a massive object these are the mass and spin in the rest frame. Knowing these the object is completely determined. Thus two equations, not one, are needed to determine an object. For spin- 1/2 , only, these two can be replaced by one, Dirac’s equation. Why is this? The momentum, p_µ is a four-vector. There is another four-vector, g_ µ. Thus µpµ is an invariant. It is a property of the object, and we give that property the name mass. Thus g_µp_µ = m, (1) which is Dirac’s equation. It gives the mass of the object, and the spin, 1/2 . This is only possible because of the g_µ’s. These form a Clifford algebra and there is (up to inversions) only one for each dimension. This is then the reason for Dirac’s equation, and only for a single spin.1/2

Fallacies from string theory

The issue of Physics World on string theory contains much material that is not only wrong, but obviously incorrect. Perhaps the most spectacular is the cosmological constant. It is trivially 0. Putting it in Einstein's equation sets a variable equal to a constant. A variable cannot equal a constant. Even a high school student knows that. There is no cosmological constant, which is unfortunate. If there were gravitation would have a fascinating property. A gravitational wave would be detected an infinitely long time before it is emitted. See the MRPG book (with further discussion in OAIU) or those who want to show this themselves can use the example in MTW. It is amazing that there have been so many esoteric explanations for such a trivial mistake. This is something that sociologists and philosophers of science should study, as should psychiatrists. In physics if a theory makes a wrong prediction just say that it has not advanced to the stage at which it can make predictions. Despite what its adherents say string theory has made a prediction --- the dimension, and that is wildly wrong (which is a reason string theory is so attractive). What is worse it has long been known that physics would be impossible in any dimension but 3+1, quite boring since it agrees with reality. See the OAIU book (and also GTFQM) for a rigorous proof. String theory has been proven with mathematical rigor to be impossible, thus physicists are quite enthusiastic about it. Of course string theory has no rationale (like Bush's Iraq policy) except for the excitement, wishful thinking and daydreaming it stimulates. The proper criteria for a theory in physics are not experiment, not mathematics, but wishful thinking and fantasy. With that criteria it does quite will. (The requirement for truth is tricky. Theories can be complete nonsense but necessary as classical physics and Bohr's theory show. See the OAIU book for discussion. But string theory does not fit into that either. Nor is it simple. It is wildly complicated and hideously ugly. Perhaps that is why so many physicists are so obsessed with it. Occam would be furious that anyone is considering such a theory.) It is strange that anyone would consider investing in a theory that has been proven to be nonsense. Of course no physics journal would consider publishing the proof that the dimension must be what experiment gives. That would spoil all the fun. Physicists are very concerned about ethics. Yet they find it perfectly acceptable to allow people to waste their careers and much public money working on something that is known wrong. Nor do they care about misleading the public (look at the best selling books that are nonsense) which will eventually undermine the support of science. (Of course no one cares about academic freedom. Those who do not want to waste their careers producing nonsense do not have that freedom since they are not allowed to know that what they are doing must be wrong.) As Goldhaber points out this is all quite unscientific. So why isn't it being fought more rigorously? Rather than fighting it "physicists" accept it enthusiastically! Another example of physicists' desire to find the most esoteric, complicated, convoluted explanation for simple results is quantum mechanics. Why nature must be quantum mechanical is almost trivial. See the GTFQM and OAIU books, plus QM,QFT. Then there is the daydream that string theory will produce a quantum theory of gravity. This ignores the fact that there is already one, the only possible one since it is required by geometry: GR. See MRPG. Where did the confusion that it is not quantum mechanical come from? It is completely quantum mechanical, including having uncertainty principles. What more does anyone want? But GR, while correct, isn't much fun. David Gross says we still don't know what string theory is. Sure we do. It is complete nonsense. The best thing that could be done to advance physics would be to bring Occam back to life. For further discussion and other problems with these see the books and my blog.

Peer review

Peer review (censorship) results in the destruction of knowledge undermining the rationale for schools (the creation and dissemination of knowledge), some badly needed, even resulting in many deaths. These papers that are destroyed, with knowledge suppressed, are generally correct and useful. This is not doubted. Their suppression is often purely arbitrary. In academic institutions, like in authoritarian societies, knowledge is not something to be treasured, but is dangerous, something to be carefully controlled, often suppressed. This is the very opposite of what these institutions supposedly exist for. Suppressing knowledge is a highly anti-social act, obviously. Why do presumably decent people do such things, even when they know (as they must) that what they are doing is wrong? There has been work in social psychology (by people like Milgram and Zimbardo) showing that with even a little situational pressure ordinary well-behaved, people will do awful things. The relevance of this to the damage that people are willing to do as referees and editors is quite clear. The society that they are in demands such evil, and they comply, and happily. If schools really cared about knowledge, which obviously they do not, they would be very careful to prevent this. Yet they actually encourage it, rewarding it. The ethics of those engaged in such behavior and their institutions is very obvious. In such institutions ethics is very important --- except when it prohibits what people want to do, what profits them.

Inertia

Some people are confused about inertia regarding it as a force or as something caused by distant matter in the universe. Why is there inertia? A consequence of it is that the velocity of an object does not change unless there is a force acting on it. Suppose that this were not true. Then objects would just move randomly, starting and stopping for no reason, moving erratically, unpredictably. There would be no law. But if there were no laws how can we say that inertia is due to distant matter? That would be meaningless since it would be impossible to predict or explain anything. Explanations like a fictitious force or distant matter would be meaningless. Nothing could be said. There has to be inertia otherwise there could be no physics. For related discussions see the OAIU book. Physicists like to take the obvious and develop convoluted and impossible theories to explain what is beyond explanation. This explains nothing about physics but much about physicists.

The reason for gauge invariance

Why is there gauge invariance? Despite the opinion of many physicists it is not because God likes it. Rather it is the form Poincaré transformations take for massless objects and are possible for these only. This has been discussed in depth in the book Massless Representations of the Poincaré Group (see booklist). It can be explained trivially. Consider an electron and photon with momenta parallel and spins along the momenta (so parallel). There are transformations that leave the momenta unchanged, changing the spin direction of the electron, but cannot change that of the photon. EM waves are transverse. (This is required by the Poincaré group, not God). Thus there are transformations acting on the electron but not on the photon, which is impossible. What are these transformations? Obviously gauge transformations. And that is exactly what the Poincaré group gives; all their properties follow. They are not possible for massive objects but are a required property of massless ones.

Little green men (they really are)

One of the faddish issues in physics is gender inequality. Females are strongly underrepresented. Of course those in power try to exclude people different from themselves. This is glaring in physics in which anyone who is not a crackpot like the leaders is pushed out. But gender inequality has become a faddish issue so there is great concern about it. One person trying to deal with it is Jocelyn Bell Burnell. She is well known for her work as a graduate student, which won her advisor a Nobel Prize. He was given the award for his brilliance in finding a student who discovered pulsars. These are now known to be rapidly rotating neutron stars but the signals were then thought to be communications from little green men (gender inequality goes back a long way; little green women were never considered). Of course she was never given an award. But why should she? She never found a student who made a major discovery. It turns out however that little green men were involved. They were on the Nobel Prize committee. What they were communicating can only be guess at.

How to determine crackpots

There are many strange ideas that are masquerading as science. How can crackpots be determined? There is a way that tells if a person is a crackpot. Someone who brags about all the great discoveries he is about to make is clearly a crackpot. Reading what they say shows that string theorists are screaming at everyone that they are crackpots. It is not necessary to look at string theory, which is glaringly crackpot, to tell, string theorists are screaming that they are crackpots. Of course string theory has nothing to with science, nor is it meant to. It is purely a religion (and like a religion ignores what experiment --- reality --- requires). Replacing science by religion is not unusual in physics. A half century ago, for example, there was much excitement about ideas extended from dispersion relations, involving smoothness of surfaces. Its center was at Berkeley and its leader was Geoffrey Chew. There was so much excitement that people at Berkeley asked each other "are you a member of the Chewish religion?". That idea had no real rationale and was wrong but was not crackpot. String theory is crackpot. That is why it lasted so much longer. It is still the leading religion of physicists. And the problem is not only in physics. One particularly cruel example is autism, a devastating neurological disorder, now known to be due to brain abnormalities. However the experts decided that it was do to the coldness of mothers, named refrigerator mothers. The way the mothers held the baby in the first 30 seconds caused devastating abnormalities. Of course there was no evidence of this but that was unnecessary. They were experts so qualified to decide even with no evidence at all (and, like string theorists, no matter how absurd their views). There is one thing experts know: how expert they are. And this was particularly cruel, adding to the burden of a parent with a severely sick child the extra burden of (nonexistent) guilt. But experts responsibility is to their expertness, not to facts, not to patients, not to those with grievous misfortune, but to themselves. And they were allowed to get away with it. All too often experts are so proud of their expertise their heads swell up in pride so much that it causes brain damage. This is quite clear in physics, especially with string theory, and in so many other places. Experts are dangerous.

Does physicists' choice of an approximation scheme determine the laws of nature?

Certainly. That is what many "physicists" believe, that is the foundation of much work in "physics". For example in the most widely used approximate calculational method, perturbation theory, certain integrals in intermediate steps have a lower limit of 0 so are infinite. This perturbs "physicists" immensely, so they try to revise nature (which is why they developed string theory which has the great attraction of being known wrong) to eliminate thus "problem". However when all steps of the algorithm are completed the result is finite and correct. The infinities are meaningless and are purely the result of stopping in the middle. If another approximation scheme were used this "problem" would never have arisen. Nevertheless "physicists" feel that this make-believe problem is so important that nature must be changed (for example by changing particles, which do not appear in the theory and have nothing to do with these integrals, to strings). Then there are the absurd beliefs about the vacuum. There is a way of drawing pictures to keep the bookkeeping straight in this particular way of approximating. Some of these pictures can be fancifully interpreted to imply absurdities about the vacuum. But there is a difference between bookkeeping and physics. Unfortunately "physicists" do not understand this. They will claim it is just their extreme incompetence. Reading the "physics" literature shows so many examples of the difficulties "physicists" have in dealing with the world of reality (or maybe it is just fraud).

A SUBVERSIVE VIEW OF MODERN "PHYSICS"

This discussion is carefully designed to infuriate as many people as possible. Since all statements here agree with reality it undoubtedly will. Even worse the statements have been mathematically proven to be correct. These proofs cannot be given in this short space but are easily available in books. As this column does not allow references the books' author must remain anonymous. We start then with the most popular subject of modern "physics". String theory is designed to solve the problems caused by point particles. However there is nothing in any formalism that even hints at particles, let alone point particles. Where did this idea of particles come from? Could it really be that thousands of physicists are wasting their careers to solve the problems caused by particles with not a single one even noticing that there are none? Don't dots on screens in double-slit experiments show that objects are points? Obviously not, they are consequences of conservation of energy. Moreover there are no problems. There are infinities in intermediate steps of a particular approximation scheme, but they are all gone by the end. With a different scheme the idea of infinities would never have arisen. The laws of physics are not determined by physicists' favorite approximation method. But these are not the real problems. What could be worse? String theory requires that the dimension be 10 or 11, in slight disagreement with reality. If predictions of your theory do not agree with experiment just say that it is not yet able to make any, while the ones it does make are carefully ignored. It has long been known that physics (a universe) is impossible in any dimension but 3+1. Why? Coordinate rotations give wavefunction transformations. If the wavefunction gives spin up along an axis it must be transformed to one giving it at some angle to a different axis. Coordinates being real are transform by orthogonal (rotation) groups; wavefunctions being complex require unitary groups. These groups must be homomorphic. They are not as shown by counting the numbers of generators and of commuting ones. Fortunately there is one exception, else there could be no universe: dimension 3+1. Why 3+1, not 4? The rotation group in 4 dimensions, SO(4), is unique in splitting into two independent SO(3) groups. It is not simple, only semisimple; SO(3,1) is simple. Whether God wants it or not the dimension must be 3+1. It is mathematics that is omnipotent. God, Nature and we, and even string theorists, must do what mathematics wants: accept dimension 3+1. Thus string theory is a mathematically impossible theory, in violent disagreement with experiment, designed to solve the terrible nonexistent problems caused by nonexistent particles. Perhaps that is why "physicists" are so enthusiastic about it. Next is the object that billions of dollars are being spent looking for: the nonexistent Higgs. There has been much interest in gauge transformations and in trying to extend them. These are the form that Poincar‚ transformations take for massless objects, and only these. This is trivial. Consider a photon and an electron with parallel momenta and spins along their momenta. We transform leaving the momenta unchanged but the spin of the electron is no longer along its momentum. The spin of the photon is unchanged (electromagnetism is transverse). Despite the opinion of physicists to the contrary this is required not by God but (omnipotent) mathematics, the Poincar‚ group. Here are transformations acting on the electron but not the photon, which cannot be. What are these? Obviously gauge transformations. So massless objects --- only --- have gauge transformations. The belief in Higgs bosons comes from the wish that all objects be invariant under gauge transformations, strongly disagreeing with experiment. However physicists are so enthusiastic about gauge transformations they try to apply them to massive objects. There are reasons for the laws of physics, like geometry and group theory, but these do not include physicists' emotional reactions. So all objects are massless. Nature does not agree. Physicists believe that if their theories do not agree with Nature, then Nature must be revised. Instead of giving that belief up it is kept --- physicists are emotionally attached to it --- and a new field, that of Higgs bosons, is introduced to give objects mass. This is like saying that since orbital angular momentum has integer values all angular momentum has. Since this is not true a new field is introduced to produce half-integer values. That would make no sense and neither do Higgs bosons. This introduces a new particle designed to make Nature agree with physicists, and also a force to make objects massive, which should have other effects and should show up elsewhere. This introduces (at least) two unnecessary, unsupported assumptions. Occam would be very upset. Actually if he knew what is going on in modern "physics" he would be furious. There are no Higgs. Why isn't there a cosmological constant? It sets a function (the left side of Einstein's equation) equal to a constant which is like saying that x^3 + 5x = 7 for all values of x. The cosmological constant must be 0, unfortunately. With one gravity would have a fascinating property: a wave would be detected an infinitely long time before being emitted. Let us quantize gravity, replacing a quantum theory with wild assumptions. Why must general relativity be the theory of gravity, thus the quantum theory of gravity? It is required by geometry (the Poincar‚ group) being its only massless helicity-2 representation. It is a quantum theory (consistent) not classical (inconsistent), having a wavefunction and uncertainty principles. It is different being necessarily nonlinear. Why don't people like it? Then ${\it times up}$

The cosmological constant (confusion)

Einstein's equation for gravitation G(x,y,z,t; m,l) = 0 (where m and l are usually written as subscripts) is often written as G(x,y,z,t; m,l) = L(m,l) where L is a constant, the cosmological constant, the energy of the vacuum (!). (While nothing thus has a lot of energy physicists do not have enough energy to see absurd errors.) What could possibly be wrong with this; the subscripts match. There are many things (see the MRPG and OAIU books), such as equating terms from different representations, which is like equating a vector and a scalar, and predicting that a gravitational wave would be detected an infinitely long time before being emitted. Here we just mention one. The right-hand side has been calculated to be huge (in physics, nothing has a lot of energy) but it must experimentally be small even unfortunately 0. Physicists have come up with the wildest explanations for the discrepancy involving extra dimensions and other very ridiculous nonsense. This shows how brilliant they are (which is the major aim) since only very brilliant people are able to come up with such extreme nonsense. Of course the reason the cosmological constant is 0 is trivial, so of no interest to physicists since it doesn't allow them to show great brilliance. One side of the equation is a function, which varies, the other side a constant which does not, obviously wrong. This is like saying 4x^3 + 7x^4 = 5 for all values of x. High-school students know that this is wrong but professional physicists do not. Clearly physicists should hire high school students to help them with their work so they won't make so many stupid mistakes.

Politics

For discussion of current issues see randomabsurdities.wordpress.com

Why we cannot expect gravitation to be weird

Why we cannot expect gravitation to have weird properties R. Mirman, sssbbg@gmail.com November 16, 2006 Abstract General relativity seems to have unphysical solutions, like closed time-like curves. This does not follow and is quite unlikely: the Einstein equation is a necessary condition for a gravitational field but not sufficient. There are additional requirements and before we can conclude that there are fields with strange properties we must show that all conditions are satisfied. This is implausible for weird fields. Are there closed timelike curves, wormholes, ..., in gravitational theory? Doesn’t Einstein’s equation gives these? Satisfaction of the equation is a necessary condition for a gravitational field, but not sufficient. There are further conditions. Abnormal solutions imply that not all conditions are satisfied. We cannot conclude that there are these unless it is shown that all are satisfied for the strange solution. This does not imply anything wrong with general relativity —it is almost certainly correct. It just means that it is applied incorrectly. What are other conditions ([2]; [3]; [4])? The field must be produced, else it does not exist. What produces a gravitational field? A sphere, a star, dust? But there are no spheres, stars, dust. These are merely collections of protons, neutrons, electrons and such — which are what creates and is acted upon. Such a collection must give a strange field. However these objects are governed by quantum mechanics. The uncertainty principle applies. Can a collection of such objects produce strangeness? Before it is claimed that there are closed timelike curves, wormholes, ..., it must be shown that there is a collection of quantum mechanical objects capable of producing them. Would we expect a single proton, a single electron, to give closed timelike curves? If not why would we expect a collection to? This implies that the formalism is being used incorrectly. This can be tricky because we often 1 think in ways different than the ones nature thinks in, like using classical physics as a formalism while nature uses quantum mechanics, or using large objects while nature produces gravitational fields from collections of quantum mechanical ones. Using the proper formalism is essential. There is another condition which is especially interesting since it requires that general relativity be the theory of gravity (thus the quantum theory of gravity, as it so clearly is ([2])). All properties of gravitation come from it. This has been discussed in depth, with all the mathematics shown and proven ([2]; [3]). Here we summarize. A physical object, like a gravitational field, must be a representation basis state of the transformation group of geometry, the Poincar´e group. (The Poincar´e group is the transformation group, not the symmetry group, although it is interesting that it is the symmetry group also ([4], sec. VI.2.a.ii, p. 113)). To clarify consider the rotation group and an object with spin up. Its statefunction (a better term than wavefunction since nothing waves) gives the spin as up. A different observer sees the spin at some angle, thus a different statefunction. The statefunction of the first must be transformed to give that of the second. Thus for each set of coordinates there is a statefunction and these are transformed into each other when the coordinates are. For each rotation there is a transformation of the statefunction. Moreover the product of two transformations must correspond to the product of the two rotations that they go with. Also a rotation, being a group element, can be written as a product of two, or ten, or 1000, or in any of an infinite number of ways. Each such product has a product of transformations on the statefunction going with it, with each term in the product of transformations corresponding to a term in the product of rotations. Thus the transformations on the statefunction form a representation of the rotation group, and each statefunction generated from any one by such a transformation is a basis state of the rotation group representation. This does not require that space or physics be invariant under the group. Rotations are a property of geometry whether space is invariant under them or not. Thus a state can be written as a sum of rotation basis states (spherical harmonics) and is taken into another such sum by a rotation. Each term in the latter is a sum of terms of the former (with coefficients functions of the angles). Each term is a sum only of terms from the same representation (states of angular momentum 1 go only into states of angular momentum 1, and so on). This is true whether space is invariant under rotations or not (say there is a direction, simulated by the vertical, that is different). An up state may go into a down one, but that is irrelevant since these (mathemat- 2 ical) transformations are considered at a single time. Also no matter how badly symmetry is broken there cannot be an object with spin- 1 3 . These would not be true if we expanded in unitary group states. The rotation group is a property of our (real) geometry. It is only a subgroup. The transformation group of space thus of the fields is the Poincar´e group. Statefunctions (including those of gravity, the connections) must be basis states of it. The Poincar´e group is an inhomogeneous group so very different from the simple rotation group. Gravitation is massless. The entire analysis depends on this. Massless and massive representations are much different. The little group of massive representations is semisimple (the rotation group), while that of massless ones is solvable. Thus massless objects have difficulty in coupling to massive ones. There are only three that can. Scalars apparently can. Helicity 1 gives electromagnetism (with its properties completely determined). For helicity 2 the indices do not match. Fortunately the formalism gives a nonlinear condition, the Bianchi identities, that allow gravitation to interact with massive objects. Gravitation must be nonlinear else it could not couple, so could not exist. Einstein’s equation then follows from the formalism, but is not all of it. A supposed gravitational field must be shown to form a representation basis state of a massless helicity 2 representation of the Poincar´e group or it is not a gravitational field. Unless ones with strange properties are shown to be that then they are results of the wrong or incomplete formalism, so nonexistent. Since the Poincar´e group is inhomogeneous the momentum operators (the Hamiltonian is one) must commute. There would be many problems if not ([2],sec. 6.3.8, p. 110). It must be checked for a proposed field that the momenta commute on it. The proper way to find fields is thus to find functions satisfying these properties — extremely difficult. To see if a field can be produced we must find if the momentum operators of the entire system commute. These consist of three sets of terms, for the field, for massive matter and for the interactions. Thus we have to find a (quantum mechanical) distribution of matter which, with the fields it produces, gives these operators, and such that they commute. It is likely to be very rare that we can do this. Great caution is required; we cannot jump to conclusions about the existence of strange solutions. Appendix: To illustrate the importance of proper formalism, properly applied, we consider other related topics ([2]). 3 Are there ”graviton”’s ([2],sec. 11.2.2, p. 187)? We are used to taking electromagnetic fields as sets of photons so try to apply it to gravity. But electromagnetism is linear, gravitation nonlinear. What is a photon? It is not a little ball, a ridiculous idea. If we Fourier expand an electromagnetic potential (a solution of the equations) each term is a solution. Each term is then a photon. A solution is a sum of solutions. If we do the same for a field that is a solution of the gravitational equations the terms are not solutions. A gravitational field is a collection of ”graviton”s each producing a collection of ”graviton”s, each ... . Obviously the concept is useless. Consider a gravitational wave extending over a large part of the universe. That single wave is a ”graviton”. The concept is not likely useful. Are there magnetic monopoles ([2],sec. 7.3, p. 131)? Maxwell’s equation have an asymmetry. But these are classical, so irrelevant. Quantum electrodynamics does not have such an asymmetry. There is no hole to be filled and, using the correct formalism, there is no way a magnetic monopole can act on a charge. There are no magnetic monopoles. What is the value of the cosmological constant? In Einstein’s equation one side is a function of space, the other a constant (obvious nonsense), that is one side is a function of a massless representation, the other a momentumzero representation. This is like equating a scalar and a vector. The cosmological constant is trivially 0, unfortunately else gravitation would have a fascinating property: a wave would be detected not only an infinitely long time before arrival but before emission ([2], sec. 8.1.4, p. 139). Are there Higg’s bosons? Gauge transformations are the form Poincar´e transformations take for massless objects, and these only ([2], sec. 3.4, p. 43). This is explained in one paragraph ([4], sec. E.2.1, p. 445). They cannot be applied to massive objects because of the mathematics, not because of some new field. People are entranced by gauge invariance and decided to apply it to objects where it cannot hold. This is like deciding that orbital angular momentum is integral so spins must be. They are not so there must be some new field that makes them half-integral. But the mathematics gives both types of spin, does not allow spin- 1 3 , gives gauge invariance for massless objects, and does not allow it for massive ones. This is a result of the mathematics, not of some new field. There are no Higgs bosons. References [1] Borstnik, Norma Mankoc, Holger Bech Nielsen, Colin D. Froggatt, Dragan Lukman (2004), ”Proceedings to the 7th Workshop ’What comes 4 beyond the Standard models’, July 19 – July 30. 2004, Bled, Slovenia”, Bled Workshops in Physics, Volume 5, #2, December. [2] Mirman, R. (1995c), Massless Representations of the Poincar´e Group, electromagnetism, gravitation, quantum mechanics, geometry (Commack, NY: Nova Science Publishers, Inc.; republished by Backinprint. com). [3] Mirman, R. (2004a), Geometry Decides Gravity, Demanding General Relativity — It Is Thus The Quantum Theory Of Gravity, in Borstnik, Nielsen, Froggatt and Lukman (2004), p. 84-93. [4] Mirman, R. (2006), Our Almost Impossible Universe: Why the laws of nature make the existence of humans extraordinarily unlikely (Lincoln, NE: iUniverse, Inc.) 5

No weirdness in gravitation

\documentclass[11pt]{article} \begin{document} \author{R. Mirman sssbbg@gmail.com} \title{Why we cannot expect gravitation to have weird properties} \maketitle \begin{abstract} General relativity seems to have unphysical solutions, like closed time-like curves. This does not follow and is quite unlikely: the Einstein equation is a necessary condition for a gravitational field but not sufficient. There are additional requirements and before we can conclude that there are fields with strange properties we must show that all conditions are satisfied. This is implausible for weird fields. \end{abstract} Are there closed timelike curves, wormholes, ..., in gravitational theory? Doesn't Einstein's equation gives these? Satisfaction of the equation is a necessary condition for a gravitational field, but not sufficient. There are further conditions. Abnormal solutions imply that not all conditions are satisfied. We cannot conclude that there are these unless it is shown that all are satisfied for the strange solution. This does not imply anything wrong with general relativity --- it is almost certainly correct. It just means that it is applied incorrectly. What are other conditions~(\cite{ml}; \cite{bna}; \cite{imp})? The field must be produced, else it does not exist. What produces a gravitational field? A sphere, a star, dust? But there are no spheres, stars, dust. These are merely collections of protons, neutrons, electrons and such --- which are what creates and is acted upon. Such a collection must give a strange field. However these objects are governed by quantum mechanics. The uncertainty principle applies. Can a collection of such objects produce strangeness? Before it is claimed that there are closed timelike curves, wormholes, ..., it must be shown that there is a collection of quantum mechanical objects capable of producing them. Would we expect a single proton, a single electron, to give closed timelike curves? If not why would we expect a collection to? This implies that the formalism is being used incorrectly. This can be tricky because we often think in ways different than the ones nature thinks in, like using classical physics as a formalism while nature uses quantum mechanics, or using large objects while nature produces gravitational fields from collections of quantum mechanical ones. Using the proper formalism is essential. There is another condition which is especially interesting since it requires that general relativity be the theory of gravity (thus the quantum theory of gravity, as it so clearly is~(\cite{ml})). All properties of gravitation come from it. This has been discussed in depth, with all the mathematics shown and proven~(\cite{ml}; \cite{bna}). Here we summarize. A physical object, like a gravitational field, must be a representation basis state of the transformation group of geometry, the Poincar\'e group. (The Poincar\'e group is the transformation group, not the symmetry group, although it is interesting that it is the symmetry group also~(\cite{imp}, sec.~VI.2.a.ii, p.~113)). To clarify consider the rotation group and an object with spin up. Its statefunction (a better term than wavefunction since nothing waves) gives the spin as up. A different observer sees the spin at some angle, thus a different statefunction. The statefunction of the first must be transformed to give that of the second. Thus for each set of coordinates there is a statefunction and these are transformed into each other when the coordinates are. For each rotation there is a transformation of the statefunction. Moreover the product of two transformations must correspond to the product of the two rotations that they go with. Also a rotation, being a group element, can be written as a product of two, or ten, or 1000, or in any of an infinite number of ways. Each such product has a product of transformations on the statefunction going with it, with each term in the product of transformations corresponding to a term in the product of rotations. Thus the transformations on the statefunction form a representation of the rotation group, and each statefunction generated from any one by such a transformation is a basis state of the rotation group representation. This does not require that space or physics be invariant under the group. Rotations are a property of geometry whether space is invariant under them or not. Thus a state can be written as a sum of rotation basis states (spherical harmonics) and is taken into another such sum by a rotation. Each term in the latter is a sum of terms of the former (with coefficients functions of the angles). Each term is a sum only of terms from the same representation (states of angular momentum 1 go only into states of angular momentum 1, and so on). This is true whether space is invariant under rotations or not (say there is a direction, simulated by the vertical, that is different). An up state may go into a down one, but that is irrelevant since these (mathematical) transformations are considered at a single time. Also no matter how badly symmetry is broken there cannot be an object with spin-${1\over 3}$. These would not be true if we expanded in unitary group states. The rotation group is a property of our (real) geometry. It is only a subgroup. The transformation group of space thus of the fields is the Poincar\'e group. Statefunctions (including those of gravity, the connections) must be basis states of it. The Poincar\'e group is an inhomogeneous group so very different from the simple rotation group. Gravitation is massless. The entire analysis depends on this. Massless and massive representations are much different. The little group of massive representations is semisimple (the rotation group), while that of massless ones is solvable. Thus massless objects have difficulty in coupling to massive ones. There are only three that can. Scalars apparently can. Helicity 1 gives electromagnetism (with its properties completely determined). For helicity 2 the indices do not match. Fortunately the formalism gives a nonlinear condition, the Bianchi identities, that allow gravitation to interact with massive objects. Gravitation must be nonlinear else it could not couple, so could not exist. Einstein's equation then follows from the formalism, but is not all of it. A supposed gravitational field must be shown to form a representation basis state of a massless helicity 2 representation of the Poincar\'e group or it is not a gravitational field. Unless ones with strange properties are shown to be that then they are results of the wrong or incomplete formalism, so nonexistent. Since the Poincar\'e group is inhomogeneous the momentum operators (the Hamiltonian is one) must commute. There would be many problems if not~(\cite{ml},sec.~6.3.8, p.~110). It must be checked for a proposed field that the momenta commute on it. The proper way to find fields is thus to find functions satisfying these properties --- extremely difficult. To see if a field can be produced we must find if the momentum operators of the entire system commute. These consist of three sets of terms, for the field, for massive matter and for the interactions. Thus we have to find a (quantum mechanical) distribution of matter which, with the fields it produces, gives these operators, and such that they commute. It is likely to be very rare that we can do this. Great caution is required; we cannot jump to conclusions about the existence of strange solutions. Appendix: To illustrate the importance of proper formalism, properly applied, we consider other related topics~(\cite{ml}). Are there "graviton"'s~(\cite{ml},sec.~11.2.2, p.~187)? We are used to taking electromagnetic fields as sets of photons so try to apply it to gravity. But electromagnetism is linear, gravitation nonlinear. What is a photon? It is not a little ball, a ridiculous idea. If we Fourier expand an electromagnetic potential (a solution of the equations) each term is a solution. Each term is then a photon. A solution is a sum of solutions. If we do the same for a field that is a solution of the gravitational equations the terms are not solutions. A gravitational field is a collection of "graviton"s each producing a collection of "graviton"s, each ... . Obviously the concept is useless. Consider a gravitational wave extending over a large part of the universe. That single wave is a "graviton". The concept is not likely useful. Are there magnetic monopoles~(\cite{ml},sec.~7.3, p.~131)? Maxwell's equation have an asymmetry. But these are classical, so irrelevant. Quantum electrodynamics does not have such an asymmetry. There is no hole to be filled and, using the correct formalism, there is no way a magnetic monopole can act on a charge. There are no magnetic monopoles. What is the value of the cosmological constant? In Einstein's equation one side is a function of space, the other a constant (obvious nonsense), that is one side is a function of a massless representation, the other a momentum-zero representation. This is like equating a scalar and a vector. The cosmological constant is trivially 0, unfortunately else gravitation would have a fascinating property: a wave would be detected not only an infinitely long time before arrival but before emission~(\cite{ml}, sec.~8.1.4, p.~139). Are there Higg's bosons? Gauge transformations are the form Poincar\'e transformations take for massless objects, and these only~(\cite{ml}, sec.~3.4, p.~43). This is explained in one paragraph~(\cite{imp}, sec.~E.2.1, p.~445). They cannot be applied to massive objects because of the mathematics, not because of some new field. People are entranced by gauge invariance and decided to apply it to objects where it cannot hold. This is like deciding that orbital angular momentum is integral so spins must be. They are not so there must be some new field that makes them half-integral. But the mathematics gives both types of spin, does not allow spin-${1\over 3}$, gives gauge invariance for massless objects, and does not allow it for massive ones. This is a result of the mathematics, not of some new field. There are no Higgs bosons. \begin{thebibliography}{99} \bibitem{nmb} Borstnik, Norma Mankoc, Holger Bech Nielsen, Colin D. Froggatt, Dragan Lukman (2004), "Proceedings to the 7th Workshop 'What comes beyond the Standard models', July 19 -- July 30. 2004, Bled, Slovenia", Bled Workshops in Physics, Volume 5, \#2, December. \bibitem{ml} Mirman, R. (1995c), Massless Representations of the Poincar\'{e} Group, electromagnetism, gravitation, quantum mechanics, geometry (Commack, NY: Nova Science Publishers, Inc.; republished by Backinprint.com). \bibitem{bna} Mirman, R. (2004a), Geometry Decides Gravity, Demanding General Relativity --- It Is Thus The Quantum Theory Of Gravity, in Borstnik, Nielsen, Froggatt and Lukman (2004), p.~84-93. \bibitem{imp} Mirman, R. (2006), Our Almost Impossible Universe: Why the laws of nature make the existence of humans extraordinarily unlikely (Lincoln, NE: iUniverse, Inc.) \end{thebibliography} \end{document}

No weirdness in gravitation

\documentclass[11pt]{article} \begin{document} \author{R. Mirman sssbbg@gmail.com} \title{Why we cannot expect gravitation to have weird properties} \maketitle \begin{abstract} General relativity seems to have unphysical solutions, like closed time-like curves. This does not follow and is quite unlikely: the Einstein equation is a necessary condition for a gravitational field but not sufficient. There are additional requirements and before we can conclude that there are fields with strange properties we must show that all conditions are satisfied. This is implausible for weird fields. \end{abstract} Are there closed timelike curves, wormholes, ..., in gravitational theory? Doesn't Einstein's equation gives these? Satisfaction of the equation is a necessary condition for a gravitational field, but not sufficient. There are further conditions. Abnormal solutions imply that not all conditions are satisfied. We cannot conclude that there are these unless it is shown that all are satisfied for the strange solution. This does not imply anything wrong with general relativity --- it is almost certainly correct. It just means that it is applied incorrectly. What are other conditions~(\cite{ml}; \cite{bna}; \cite{imp})? The field must be produced, else it does not exist. What produces a gravitational field? A sphere, a star, dust? But there are no spheres, stars, dust. These are merely collections of protons, neutrons, electrons and such --- which are what creates and is acted upon. Such a collection must give a strange field. However these objects are governed by quantum mechanics. The uncertainty principle applies. Can a collection of such objects produce strangeness? Before it is claimed that there are closed timelike curves, wormholes, ..., it must be shown that there is a collection of quantum mechanical objects capable of producing them. Would we expect a single proton, a single electron, to give closed timelike curves? If not why would we expect a collection to? This implies that the formalism is being used incorrectly. This can be tricky because we often think in ways different than the ones nature thinks in, like using classical physics as a formalism while nature uses quantum mechanics, or using large objects while nature produces gravitational fields from collections of quantum mechanical ones. Using the proper formalism is essential. There is another condition which is especially interesting since it requires that general relativity be the theory of gravity (thus the quantum theory of gravity, as it so clearly is~(\cite{ml})). All properties of gravitation come from it. This has been discussed in depth, with all the mathematics shown and proven~(\cite{ml}; \cite{bna}). Here we summarize. A physical object, like a gravitational field, must be a representation basis state of the transformation group of geometry, the Poincar\'e group. (The Poincar\'e group is the transformation group, not the symmetry group, although it is interesting that it is the symmetry group also~(\cite{imp}, sec.~VI.2.a.ii, p.~113)). To clarify consider the rotation group and an object with spin up. Its statefunction (a better term than wavefunction since nothing waves) gives the spin as up. A different observer sees the spin at some angle, thus a different statefunction. The statefunction of the first must be transformed to give that of the second. Thus for each set of coordinates there is a statefunction and these are transformed into each other when the coordinates are. For each rotation there is a transformation of the statefunction. Moreover the product of two transformations must correspond to the product of the two rotations that they go with. Also a rotation, being a group element, can be written as a product of two, or ten, or 1000, or in any of an infinite number of ways. Each such product has a product of transformations on the statefunction going with it, with each term in the product of transformations corresponding to a term in the product of rotations. Thus the transformations on the statefunction form a representation of the rotation group, and each statefunction generated from any one by such a transformation is a basis state of the rotation group representation. This does not require that space or physics be invariant under the group. Rotations are a property of geometry whether space is invariant under them or not. Thus a state can be written as a sum of rotation basis states (spherical harmonics) and is taken into another such sum by a rotation. Each term in the latter is a sum of terms of the former (with coefficients functions of the angles). Each term is a sum only of terms from the same representation (states of angular momentum 1 go only into states of angular momentum 1, and so on). This is true whether space is invariant under rotations or not (say there is a direction, simulated by the vertical, that is different). An up state may go into a down one, but that is irrelevant since these (mathematical) transformations are considered at a single time. Also no matter how badly symmetry is broken there cannot be an object with spin-${1\over 3}$. These would not be true if we expanded in unitary group states. The rotation group is a property of our (real) geometry. It is only a subgroup. The transformation group of space thus of the fields is the Poincar\'e group. Statefunctions (including those of gravity, the connections) must be basis states of it. The Poincar\'e group is an inhomogeneous group so very different from the simple rotation group. Gravitation is massless. The entire analysis depends on this. Massless and massive representations are much different. The little group of massive representations is semisimple (the rotation group), while that of massless ones is solvable. Thus massless objects have difficulty in coupling to massive ones. There are only three that can. Scalars apparently can. Helicity 1 gives electromagnetism (with its properties completely determined). For helicity 2 the indices do not match. Fortunately the formalism gives a nonlinear condition, the Bianchi identities, that allow gravitation to interact with massive objects. Gravitation must be nonlinear else it could not couple, so could not exist. Einstein's equation then follows from the formalism, but is not all of it. A supposed gravitational field must be shown to form a representation basis state of a massless helicity 2 representation of the Poincar\'e group or it is not a gravitational field. Unless ones with strange properties are shown to be that then they are results of the wrong or incomplete formalism, so nonexistent. Since the Poincar\'e group is inhomogeneous the momentum operators (the Hamiltonian is one) must commute. There would be many problems if not~(\cite{ml},sec.~6.3.8, p.~110). It must be checked for a proposed field that the momenta commute on it. The proper way to find fields is thus to find functions satisfying these properties --- extremely difficult. To see if a field can be produced we must find if the momentum operators of the entire system commute. These consist of three sets of terms, for the field, for massive matter and for the interactions. Thus we have to find a (quantum mechanical) distribution of matter which, with the fields it produces, gives these operators, and such that they commute. It is likely to be very rare that we can do this. Great caution is required; we cannot jump to conclusions about the existence of strange solutions. Appendix: To illustrate the importance of proper formalism, properly applied, we consider other related topics~(\cite{ml}). Are there "graviton"'s~(\cite{ml},sec.~11.2.2, p.~187)? We are used to taking electromagnetic fields as sets of photons so try to apply it to gravity. But electromagnetism is linear, gravitation nonlinear. What is a photon? It is not a little ball, a ridiculous idea. If we Fourier expand an electromagnetic potential (a solution of the equations) each term is a solution. Each term is then a photon. A solution is a sum of solutions. If we do the same for a field that is a solution of the gravitational equations the terms are not solutions. A gravitational field is a collection of "graviton"s each producing a collection of "graviton"s, each ... . Obviously the concept is useless. Consider a gravitational wave extending over a large part of the universe. That single wave is a "graviton". The concept is not likely useful. Are there magnetic monopoles~(\cite{ml},sec.~7.3, p.~131)? Maxwell's equation have an asymmetry. But these are classical, so irrelevant. Quantum electrodynamics does not have such an asymmetry. There is no hole to be filled and, using the correct formalism, there is no way a magnetic monopole can act on a charge. There are no magnetic monopoles. What is the value of the cosmological constant? In Einstein's equation one side is a function of space, the other a constant (obvious nonsense), that is one side is a function of a massless representation, the other a momentum-zero representation. This is like equating a scalar and a vector. The cosmological constant is trivially 0, unfortunately else gravitation would have a fascinating property: a wave would be detected not only an infinitely long time before arrival but before emission~(\cite{ml}, sec.~8.1.4, p.~139). Are there Higg's bosons? Gauge transformations are the form Poincar\'e transformations take for massless objects, and these only~(\cite{ml}, sec.~3.4, p.~43). This is explained in one paragraph~(\cite{imp}, sec.~E.2.1, p.~445). They cannot be applied to massive objects because of the mathematics, not because of some new field. People are entranced by gauge invariance and decided to apply it to objects where it cannot hold. This is like deciding that orbital angular momentum is integral so spins must be. They are not so there must be some new field that makes them half-integral. But the mathematics gives both types of spin, does not allow spin-${1\over 3}$, gives gauge invariance for massless objects, and does not allow it for massive ones. This is a result of the mathematics, not of some new field. There are no Higgs bosons. \begin{thebibliography}{99} \bibitem{nmb} Borstnik, Norma Mankoc, Holger Bech Nielsen, Colin D. Froggatt, Dragan Lukman (2004), "Proceedings to the 7th Workshop 'What comes beyond the Standard models', July 19 -- July 30. 2004, Bled, Slovenia", Bled Workshops in Physics, Volume 5, \#2, December. \bibitem{ml} Mirman, R. (1995c), Massless Representations of the Poincar\'{e} Group, electromagnetism, gravitation, quantum mechanics, geometry (Commack, NY: Nova Science Publishers, Inc.; republished by Backinprint.com). \bibitem{bna} Mirman, R. (2004a), Geometry Decides Gravity, Demanding General Relativity --- It Is Thus The Quantum Theory Of Gravity, in Borstnik, Nielsen, Froggatt and Lukman (2004), p.~84-93. \bibitem{imp} Mirman, R. (2006), Our Almost Impossible Universe: Why the laws of nature make the existence of humans extraordinarily unlikely (Lincoln, NE: iUniverse, Inc.) \end{thebibliography} \end{document}

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There are no Higgs

There has been much interest in gauge transformations and in trying to extend them to areas in which they do not apply. These are the form that Poincaré transformations take for massless objects, and are possible only for these. This has been discussed in depth in Massless Representations of the Poincaré Group: electromagnetism, gravitation, quantum mechanics, geometry: R. Mirman, although it can be explained in one obvious paragraph as given in Our Almost Impossible Universe: Why the laws of nature make the existence of humans extraordinarily unlikely: R. Mirman. For complete information see impunv.blogspot.com. The belief in Higgs bosons comes from the belief that all objects are invariant under gauge transformations, which strongly disagrees with experiment. Instead of giving that belief up it is kept, because physicists are emotionally attached to it, and a new field, that of Higgs bosons, is introduced to give objects mass. However gauge transformations are the form Poincaré transformations take for massless objects and are possible only for these. See Massless Representations of the Poincaré Group: electromagnetism, gravitation, quantum mechanics, geometry, although it can be explained in one obvious paragraph as given in Our Almost Impossible Universe: Why the laws of nature make the existence of humans extraordinarily unlikely: R. Mirman. For complete information see impunv.blogspot.com. They cannot be applied to massive objects and it makes no sense to so apply them. That would be like saying that since orbital angular momentum has integer values all angular momentum has. Since this is not true a new field is introduced to produce half-integer values. That would make no sense and neither do Higgs bosons. There are no Higgs bosons.

Nobody noticed? Highly unlikely! --- the irrationale for string theory

String theory is designed to solve the problems caused by point particles. However there is nothing in any formalism that even hints at particles, let alone point particles. Where did this idea of particles come from? Could it really be that thousands of physicists are wasting their careers to solve the problems caused by particles with not a single one even noticing that there are none? What objects are is discussed in Our Almost Impossible Universe: Why the laws of nature make the existence of humans extraordinarily unlikely, R. Mirman. This also has a rigorous proof, verified by others, that physics is possible only in dimension 3+1 so string theory must be wrong. Don't the dots on the screen in, say, the double slit experiment show that objects are points? Of course not, they are consequences of conservation of energy. See the OAIU book and also Quantum Mechanics, Quantum Field Theory: geometry, language, logic, R. Mirman. There are infinities in intermediate steps of a particular approximation scheme, but they are all gone by the end. If a different scheme was used the idea of infinities would never have arisen. The laws of physics are not determined by physicists' favorite approximation method. Further information is at impunv.blogspot.com. Thus string theory is a mathematically impossible theory, in violent disagreement with experiment, carefully designed to solve the terrible nonexistent problems caused by nonexistent particles. Perhaps that is why physicists are so enthusiastic about it.

Nonlocal; QM or classical physics?

While it is the general belief from the EPRB experiment that quantum mechanics gives that spatially separated objects exhibit correlations, it is wrong. It violates an uncertainty principle (number-phase). Quantum mechanics is a statistical theory. It cannot be applied to a single event, thus the argument is not relevant to quantum mechanics. What that argument shows is that classical physics is nonlocal. Consider a spherical shell which explodes into two objects spinning in (of course) opposite directions. When the spin direction of one is measured that of the other is forced into the opposite direction, even though it is now in a different galaxy. Hence those who say that the argument shows quantum mechanics is nonlocal are actually saying that classical physics is nonlocal. See the QM,QFT book for detailed discussions.

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