impunv [sssbbg@gmail.com]

• Physics: Extreme stupidity or deliberate fraud?

Is it extreme stupidity, or is it deliberate fraud?

Why billions of dollars of your money are being wasted in order to prevent the advance of physics

Is it extreme stupidity, or is it deliberate fraud? These are some of the major topics in modern “physics”, being worked on by the most famous “physicists”, in the most prestigious schools, being published in the journals most successful in bragging how important they are, and which are supported by billions of dollars of the taxpayer’s money. Some are listed below and details are given in the main text and far more in the books, especially the OAIU book. Physicists: extreme stupidity or deliberate fraud?

A large number of "physicists" are working, at great cost to the taxpayer, on string theory. This requires that the dimension of space be 10 or 11. Since string theory violently disagrees with reality it is very attractive to "physicists". However it is well known that physics is possible only in dimension 3+1 (which Physicists (it seems almost all) who cannot distinguish reality from pictures used to keep the bookkeeping straight in an approximation scheme (as shown for example by all the nonsense about the energy of the vacuum) badly need professional help, obviously. Or is it all lies? What are they doing about it? Of course trying to keep it covered up so they can keep producing nonsense and wasting taxpayer money. What else could this be besides deliberate fraud?

Academic freedom is very important in educational institutions. Is it a special privilege or is it essential for searching for truth? Much of modern "physics" is not a search for truth but a search for nonsense, for ways to avoid truth. Could those (all too few) physicists who really want to find truth be able to do so if important formation (like what they are doing is known to be wrong)is withheld from them? If the leaders of the physics community, and government officials, deliberately and knowingly suppress and destroy knowledge, don't they show contempt for academic freedom? Clearly it is a special privilege for those in power in those educational institutions that are most successful in convincing people of their importance. What is the purpose of tenure? Doesn't the behavior of the leaders of physics show that it should be abolished?

Physicists believe quantum mechanics is nonlocal, that measuring the spin of a particle here affects the spin of a particle in another galaxy, instantaneously. Competent scientists know that if a result is strange something is being done wrong. And of course it is. Those who understand quantum mechanics know that the argument does not apply to it. What it shows is that classical physics is nonlocal. Physicists: extreme stupidity or deliberate attempt to confuse?

There are physicists (yes there are!) who believe that gravity is weak (yes it is) because it leaks out of the universe (!), undoubtedly helping large amounts of government money to leak out of the universe with it. Physicists: severe mental illness or deliberate fraud?

A leading belief of present-day “physicists” (leading ones!) is that our universe started when another universe (!) smashed into it, and that this might happen periodically. It seems that “physicists” to be taken seriously must act as if they are mentally ill. Or is it deliberate fraud?

Belief (unless it is all lies) in the cosmological constant shows that physicists need high-school students to help them. Or is it deliberate fraud?

Do physicists really believe (as their work on the cosmological constant shows) that a gravitational wave can be detected an infinitely long time before being emitted, or is all the research on the cosmological constant just fraudulent?

Physicists (it seems almost all) who cannot distinguish reality from pictures used to keep the bookkeeping straight in an approximation scheme (as shown for example by all the nonsense about the energy of the vacuum) badly need professional help, obviously. Or is it all lies?

These absurdities result from the same corrosive mixture of hubris and incompetence, and contempt for others, that made George Bush such an outstanding president --- outstandingly bad.

Index

Archive for June, 2007

The cosmological constant (confusion)

Posted by impunv on June 29, 2007

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

Posted by impunv on June 13, 2007

randomabsurdities.wordpress.com

Why we cannot expect gravitation to be weird

Posted by impunv on June 10, 2007

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;
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,
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

Why we cannot expect gravitation to have weird properties

Posted by impunv on June 9, 2007

SSSBBG@GMAIL.COM

Posted by impunv on June 3, 2007

Why we cannot expect gravitation to have weird properties

Posted by impunv on June 3, 2007

\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

Posted by impunv on June 3, 2007

\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}
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