Quantum field theory in curved space time, quantum gravity....They are one and the same.
    By Hontas Farmer | August 7th 2009 05:29 PM | 31 comments | Print | E-mail | Track Comments
    Robert Wald has formulated QFT in curved space time in terms of it's algebra of observables on a manifold.  In doing so he has, perhaps unintentionally, provided framework in which very different theories of quantum gravity look very similar. 

    Schrodinger, Heisenberg, Feynman...there is more than one formal development of quantum physics.  The problem of this day is integrating quantum physics with gravitational physics.  The Algebraic construction described by Robert Wald in a recent paper could be a fourth such formalism.  The well constructed theories of quantum gravity conform to what he wrote in his paper (or chronologically his paper inadvertently describes the general formalism that has gone into LQG, String/M-theory, and even my little theory of quantum gravity).
    There are a number of axiomatizeations of quantum theory.  Schrodingers wave mechanics, Heisenberg's matrix mechanics, and Feynman's path integral formulation (which while used mostly for interacting field theory can be used for quantum theory as well) and some physicist such as the man I learned quantum theory from like to mix their own set of axioms.  The following construction could be used for all of quantum mechanics but I will focus on quantum gravity.  

    Wald's algebraic construction:
    I have worked on quantum gravity independently for quite some time.  I have also dabbled in traditional quantum field theory in curved space time.  In loop quantum gravity, M(atrix) theory, and my theory, each proposes what seem to be very different things.  Then I read a paper by Robert Wald of the university of Chicago "The Formulation of Quantum Field Theory in Curved Spacetime" arXiv:0907.0416v1.  In which he proposes the following. 
    The algebraic approach: In the algebraic approach, instead of starting with a Hilbert space of states and then defining the field observables as operators on this Hilbert space, one starts with a *-algebra, A, of field observables. A state, ω, is simply a linear map ω : A → C that satisfies the positivity condition ω(A∗A) ≥ 0 for all A ∈ A. The quantity ω(A) is interpreted as the expectation value of the observable A in the state ω. If H is a Hilbert space which carries a representation, π, of A, and if  then the map ω : A → C given by
    defines a state on A in the above sense. 
    Dr. Wald then explains how a Hilbert space representation of A can be found by way of the Gelfand–Naimark–Segal construction. He states that 

    The key difference is that, by adopting the algebraic approach, one may simultaneously consider all states arising in all Hilbert space constructions of the theory without having to make a particular choice of representation at the outset. It is particularly important to proceed in this manner in, e.g., studies of phenomena in the early universe, so as not to prejudice in advance which states might be present.
    This statement makes me think of the various theories of quantum gravity. 

    In his paper he goes on to take on the remaining assumptions that go into quantum field theory in flat space-time and postulate replacements for each of them.  

    •   Spectrum condition --->micro local spectrum condition

    • Global poincare invariance ---> local poincare invariance*

    • "...the condition that at spacelike separations quantum fields either commute or anticommute generalizes straightforwardly to curved spacetime."

    I am going to say that this construction of quantum field theory in curved space time is more than just a QFT for a fixed curved space-time.  Wald has set out a recipe for the quantization of space-time itself, which is what is done in two seemingly incompatible ways in Loop Quantum Gravity, and in my theory Quantum Space-time dynamics.  Even string theory could likely be formulated in a way which would conform to Walds recipe! All any fundamental theory of physics is just a algebra of field observables.  Once one has an acceptable algebra of field observables the rest follows naturally if one knows of this.   

    Examples LQG and Quantum Space-Time Dynamics:

    According to Carlo Roveli  Loop Quantum Gravity is a algebra of fields defined on a manifold one of which is space-time.
    One can still describe spacetime as a (differentiable) manifold (a space without metric structure), over which quantum fields live. A classical metric structure will then be defined only by expectation values of the gravitational field operator.
    With the algebra of the field being a loop algebra.

    I wrote in my book on Quantum Space-Time Dynamics about an operator S the eigenvalues of which are equivalent to possible metrics, s, in general relativity.   The metric does not make an appearance in the theory until that point.  It is derived from the algebra of the operators which I discovered after I had worked out the physical consequences of the theory as being the lie group and algebra F(4).  It could be more orthodoxly formulated in terms of Hurwitz quanternions.  However the representation seen in my book, I feel, has the advantage of seeming familiar and being more physically intuitive.

    I am certain that string/M theory can also be shown to conform to Dr. Walds general prescription.

    The payoff

    Wald has done something that I suspected was possible, that LQG theorist have thought was possible, he has provided the framework in which non string quantum gravity and string theory can look the same. Perhaps LQG and string theory could be unified using this construction.  LQG/or my theory describing gravity and space time, String theory describing every thing else.   My own theory already has room for this because in this theory "everything else" already has an operator T to describe it.  

    A theory of quantum gravity and possibly everything else that may be in the universe is close at hand.


    ... the physical consequences of the theory as being the lie group and algebra F(4).  It could be more orthodoxly formulated in terms of Hurwitz quaternions.
    Is that algebra really 52-dimensional, as the following suggests?
    Apparently one can use the octonions to build all five of the exceptional complex simple Lie algebras, not just g2. The easiest of the others is probably the construction of the 52-dimensional Lie algebra f4 using an exceptional Jordan algebra.
    Hurwitz quaternions, perhaps, might be somewhat easier to grasp (I like quaternions, so perhaps I'm biassed).  Adolf Hurwitz was quite a productive chap, getting 11 entries in Wolfram Mathworld.

    But envisaging how group theory relates to physics is not easy.  Pauli called it the 'Gruppenpest', and it was only Eugene Wigner who really got hold of it[1]; moreover it had to wait until Gell-Mann and Neeman forced the issue in 1960s that the widespread skepticism dissipated [2].

    I'm more of a historian, and if one were to ask me to explain it in the context even of the electron and SU(2), I wouldn't know how to start.


    Robert H. Olley / Quondam Physics Department / University of Reading / England
    Yes it is 52 dimensional, though the dimension of a lie algebra, or a group, are not the same as for a space.  To add to the confusion, to actually compute with a algebra one often has to resort to a representation, often a matrix representation, the dimensionality of which means something else all together!  It can be hard to keep all of these things straight. 

    As for the history of group theory in physics a very early paper in which it appears is "Invariant Variation Problems" by Emmy Noether.  A fundamental and foundational paper by a woman.  In which she proves two theorems (that's right two not just one).  One of which is known simply as noethers theorem in which she wrote:  

    If the integral I is invariant with respect to a G, then ρ linearly independent combinations of the Lagrange expressions become divergences —and from this, conversely, invariance of I with respect to a G will follow. The theorem holds good even in the limiting case of infinitely many parameters.

    Wikipedia, and most physics books, state it simply as this....

    To every differentiable symmetry generated by local actions, there corresponds a conserved current.

     Thus turning all of the then known conservation laws from being practical magic into derivable facts, As well as providing a way to derive new conserved currents. 

    Science advances as much by mistakes as by plans.
    Emmy Noether!  Now there's a mathematician and a half!  If one regards learning mathematics as being like climbing a mountain, then her algebra represents the point where one has to start carrying oxygen.

    In Unknown Quantity: A Real and Imaginary History of Algebra by John Derbyshire, she is given a whole chapter to herself, entitled The Lady of the Rings.  Now Derbyshire writes for the National Review, so he can hardly be sympathetic to feminism or anything like that.  Nevertheless, he is very forthright in his condemnation of how she was put down because she was a woman.  (He's very good on the algebra too.) 

    She eventually found a position at Bryn Mawr College in Pennsylvania.  "Bryn Mawr" means "great hill" in Welsh.  Certainly apt when one finds studying maths an uphill struggle!

    Robert H. Olley / Quondam Physics Department / University of Reading / England
    Yes she was deserving of the Nobel prize. One would think that male chauvinism was dead among enlightened physicist.  However I personally have witnessed it.  For example a very smart colleague once gave an answer in a class.  She was told she was wrong.  A male then said the same thing and was told he was right.  I have sent emails to physicist who did not know or know of me who would refer to me in the masculine.  I correct them and they say they assume all physicist are male. No wonder only one woman won a nobel prize in over 100 years.   
    When asked to draw a scientist, little children, even college freshmen still overwhelmingly draw lab coated men holding flask.   

    Science advances as much by mistakes as by plans.
    Are you certain that the continuous differential geometry implicit in general relativity's curved spacetime is appropriate to model the physics of quantum fields in gravity, where discrete graviton interactions will cause accelerations not as a smooth spacetime curvature, but as a lot of little quantum leaps? I'm not debunking the use of curvature for approximating on large scales the resultant of loads of small discrete graviton interactions, but it will be a failure on very small scales where individual graviton interactions become important, and where the actual physics of quantum gravity is best studied. If you start with a false model that's merely good classical approximation on large scales outside what you are interested in (the actual dynamics of graviton interactions, i.e. quantum gravity), are you not building on quicksand?

    "There are a number of axiomatizeations of quantum theory. Schrodingers wave mechanics, Heisenberg's matrix mechanics, and Feynman's path integral formulation (which while used mostly for interacting field theory can be used for quantum theory as well) and some physicist such as the man I learned quantum theory from like to mix their own set of axioms."

    Quantum mechanics (first quantization) is a confidence trick. Schroedinger, Heisenberg, et al. in ordinary quantum mechanics not only contradict special relativity, but they quantize the wrong stuff. All first quantization approaches model the uncertainty in position and momentum using a wave equation, but include a classical Coulomb interaction for the field. This is a lie! You have to quantize the field, if your math is representing physical reality. The randomness of the field quanta interacting with an electron in an atom causes the uncertainty in the position of the electron. There's no big mystery. There's no wavefunction collapse on measurement: just a discontinuity between switching from time independent to time dependent Schroedinger equations when an electron is measured.

    You can use a wave equation to model the way that a random, quantized electromagnetic field interferes with the motion of an electron on small scales, but you can't legitimately just use a wave equation for electron motion and a classical (non-random) Coulomb field. Claims about entanglement by Aspect et al. are not supported by the data.

    Second quantization, although it makes the math harder, is physically the only correct way to go in quantum mechanics, e.g. Dirac's equation, the Klein-Gordon equation, and the treatment of field quanta in Feynman's path integral. The field is quantized, not classical. In quantum tunnelling, for example, the second quantization treatment makes the mechanism very clear and simple: the Coulomb field when replaced by random exchange of field quanta is no longer a "classical barrier". Instead, an alpha particle (or whatever particle you choose) can penetrate the electromagnetic field because the field is statistical in nature, like random bombardment of air molecules in causing random brownian motion. There is a small chance that field quanta simply won't happen to interact with the alpha particle for a time sufficient for the alpha particle to get through the "coulomb barrier". That's quantum tunnelling, just field quanta randomness, no magic. On large scales, air pressure gives rise to a classical deterministic force. On small scales, it gives way to randomness. If you use the steady air pressure equation, it will not be a perfect model on the smallest scales due to the randomness of individual air molecules which becomes important on very small scales. Feynman explains this clearly with path integrals in his 1985 book QED.

    ‘When we look at photons on a large scale – much larger than the distance required for one stopwatch turn [i.e., wavelength] – the phenomena that we see are very well approximated by rules such as “light travels in straight lines [without overlapping two nearby slits in a screen]“, because there are enough paths around the path of minimum time to reinforce each other, and enough other paths to cancel each other out. But when the space through which a photon moves becomes too small (such as the tiny holes in the [double slit] screen), these rules fail – we discover that light doesn’t have to go in straight [narrow] lines, there are interferences created by the two holes, and so on. The same situation exists with electrons: when seen on a large scale, they travel like particles, on definite paths. But on a small scale, such as inside an atom, the space is so small that [individual random field quanta exchanges become important because there isn't enough space involved for them to average out completely, so] there is no main path, no “orbit”; there are all sorts of ways the electron could go, each with an amplitude. The phenomenon of interference becomes very important, and we have to sum the arrows [amplitudes in the path integral for individual field quanta interactions, instead of using the average which is the classical Coulomb field] to predict where an electron is likely to be.’

    - Richard P. Feynman, QED, Penguin Books, London, 1990, Chapter 3, pp. 84-5.

    I took a course in quantum mechanics in 1996-7 and they completely omitted QFT and just presented wrong stuff like Schroedinger's equation, which is fine as an approximation but lacks the physical integrity of representing the quantum Coulomb field. It's actually more accurate in some ways to look at the Bohr atom and just explain that because the Coulomb field is quantized and particularly chaotic on subatomic distances, and this is binding the electron to the positive nucleus, so the randomness of the Coulomb field makes the electron's motion chaotic. For many electrons or for long periods of time, the average location may be described by a wave equation, but that leads to metaphysical ideas about wavefunction collapse.

    I'm angry to have been cheated of QFT reality when studying "QM", and being fed lies which were OK in 1926 but obsolete in 1929. I understand that Dirac's equation or path integrals are not suitable for convenient treatment of electron orbits at undergraduate level, but that's purely a mathematical objection, not physical. There should be an effort to teach the physics of QFT and to honestly admit that the non-relativistic Schroedinger equation is just a physically wrong (but mathematically helpful) approximation to QM (just as epicycles were mathematically helpful for Ptolemy to predict apparent 2-d planetary positions around the sky seen from earth, although they didn't represent the correct 3-d motions of the planets around the sun). I'm only now starting to understand the real physics behind QFT, and have had to go through Ryder (too brief on key details of the SM), Weinberg (vols 1-2, better at maths than at making the hard physical facts clear, although the early history of QFT is nicely summarized in vol. 1), Zee (makes a big effort to appear physical in dealing with QFT math, but actually introduces confusion and misses all the points Feynman made in QED about the physics of path integrals), Penrose 2004 (no useful math, but some interesting physical speculations), and MaMahon's 2008 book (which is badly organized, has some typographical errors and is not very physical, but very clearly explains all the key maths). If physical understanding does not precede mathematical speculation, you have the risk of the mess Schroedinger made. Even the path integral is physically flawed because the finite universe clearly contains large numbers of interactions, not infinite numbers. The path integral even for an interaction between just two real particles leads to a perturbative expansion with a infinite number of field correction terms, each having a different Feynman diagram. Clearly, a sum over histories should physically be a discrete summation, not the integral over an infinite number of interactions, which is just a statistical approximation valid for averaging the interaction over an infinitely long period of time, or else averaging an infinite number of such interactions:

    ‘It always bothers me that, according to the laws as we understand them today, it takes a computing machine an infinite number of logical operations to figure out what goes on in no matter how tiny a region of space, and no matter how tiny a region of time. How can all that be going on in that tiny space? Why should it take an infinite amount of logic to figure out what one tiny piece of spacetime is going to do? So I have often made the hypothesis that ultimately physics will not require a mathematical statement, that in the end the machinery will be revealed, and the laws will turn out to be simple, like the chequer board with all its apparent complexities.’

    - R. P. Feynman, The Character of Physical Law, November 1964 Cornell Lectures, broadcast and published in 1965 by BBC, pp. 57-8.

    Are you certain that the continuous differential geometry implicit in general relativity's curved spacetime is appropriate to model the physics of quantum fields in gravity, where discrete graviton interactions will cause accelerations not as a smooth spacetime curvature, but as a lot of little quantum leaps? I'm not debunking the use of curvature for approximating on large scales the resultant of loads of small discrete graviton interactions, but it will be a failure on very small scales where individual graviton interactions become important, and where the actual physics of quantum gravity is best studied. If you start with a false model that's merely good classical approximation on large scales outside what you are interested in (the actual dynamics of graviton interactions, i.e. quantum gravity), are you not building on quicksand?
    No.  If you read my book (Quantum Space Time Dynamics find it on google books) you will see what I mean.  In my theory curvature is quantized and not continuous.  Mass-energy curves spacetime in integer multiples of the planck length.  Where by curving space time would mean:makes the invariant interval calculated different from the flat space-case by n planck lenght's.   If you work through the mathematics this ends up implying that the smallest gravitating mass is the planck mass.  If my own theory has a weak point that is it.  While my theory allows less massive particles to react to a gravitational field, only those with a gravitational field of the planck mass or larger could have a field of their own. 

    That is the hardest conceptual stumbling block I suspect.  People are used to thinking of space-time as smooth, and that any arbitrarily small bit of mass or energy would have a gravitational field.  I on the other hand think that deeply held assumption stands to be proven.

    Science advances as much by mistakes as by plans.
    Hi Hontas,

    Thanks, that sounds interesting. I found your book online and it seems well organized and interesting, although it is a bit pixillated there and not easy to read particularly as it is technical and will take quite a bit of study so I'll try to get a print version or download it.

    Thanks, You'll be one of the select few who bought it if you do.  May I ask did you find it on google books?  They have the full copy on there.   Here is a link.  
    Quantum Space-Time Dynamics (Via Google Books)
    Science advances as much by mistakes as by plans.

    I believe your approach is a step in the right direction, but wonder if it has gone far enough to predict the outcome of something the can be tested in a laboratory.

    Considering the extremely small size of the Planck length, space can be quantized and still qualify as a continuous function for most of cosmology strictly in conformance with continuous functions as they are defied in the calculus books.

    A continuous differential in calculus doesn't get infinitely small, it just gets small enough that its size make no difference in the calculation.

    Classical science gave up totally smooth space and time when it adopted the new mathematics based on set theory.

    So quantum theory can easily expect to treat space discreetly, and still not need to challenge the work of classical cosmology.

    A second topic is the prediction that a sufficiently small mass produces no gravitational field, but still interacts with the gravity fields of local curvature. I guess you are predicting electromagnetic interactions, unless the intention was for nuclear interactions weak or strong type.

    At last count I only found 4 forces and 4 varieties of interactions.

    Are you predicting masses smaller than the Planck mass, and is so, how would they be measured.?

    As far as I know the neutrinos are the only real candidates, and they are rather hard to measure. Then the weak interaction might be what you intended. Is that correct?

    The third point is my main concern with your theory and its limitations. I don't believe you mentioned the cosmological constant, and the magnitude of the vacuum energy, which would seem to be the biggest difficulty in unifying Cosmology, gravity and Quantum mechanics.

    Johannes referred to this difficulty in his article:

    to which I replied with a way of reconciling the energy of zero point with the cosmological constant and not compromising any principle.

    "This message is about vacuum energy and a way of looking at space curvature with regard to the cosmological constant in general relativity".


    "EQUAL PARTITION OF VACUUM ENERGY unifies cosmology with quantum mechanics, putting an end to 'the biggest embarrassment in theoretical physics' ".

    I really would like to see something like equal partition, and the departures from it expressed in terms of wave mechanics as a continuation of your work.

    So maybe you could complete the picture with a second volume, or some articles.

    You are right about differential calculus.  The thing is in the regime in which this theory and others like it would apply we can't ignore the fundamental crinkelyness of "smooth" space-time anymore.
    What my theory predicts which could be tested with a sensitive enough measurement is that masses smaller than the planck mass not not have a gravitational field of their own, they merely react to the gravity of larger masses.  IF we can measure two neutrons in isolation interacting with eachother by gravity that would disprove (but not prove) my theory.    

    My theory has nothing to say about, the other forces, or cosmology per-se.  That said If my theory is applied to the early universe there could be observable consequences.  

    The question I have about my theory, is how does it predict somenthing different from Loop Quantum Gravity/Cosmology, or String/M Theory and the related cosmology.  The answer is right now I don't really know.  It's sort of a work in progress.   

    As for a second volume.  When I have some time.  After I am done with my MS thesis I will work on a more formal formulation of this.  I wrote the first book as I was learning the methods of theoretical physics.  What I know now is exactly which lie group and algebra I was in fact working with, and it's matrix rep ( in terms of Hurwitz and /or lipschits quaternions).  

    In terms of the subject of this article ,  what I know now is the algebra of the observables in my theory, and I have a framework I can put it in that will make sense to other people... not just me.  :-)
    Science advances as much by mistakes as by plans.
    IN STRING THEORY I WOULD EXPECT THE STRINGS TO REPRESENT SOMETHING SUBSTANTIAL, like the wave lengths of the zero point oscillators.

    Has string theory really predicted anything that can be tested?

    I don't think so.   The difference between my theory loop gravity and string theory lies in the details.  My theory of quantum gravity, says that only an integer multiple of a Planck mass will have a gravitational field.  Any particle smaller than that will not have a g field.  The particles have to bind by some other force before they begin to gravitate.  
    Science advances as much by mistakes as by plans.

    Taking the Planck mass from John D. Barrow, Vintage Press, 2002 page 26. it seems like something that could be tested with a first class laboratory torsion balance.

    For a particle that large the electromagnetic force is the only other force I know of to hold a particle together. Nuclear forces don't operate on a scale that large.

    There is a problem with molecules in a gas. None of them are as large as a Planck mass. Then there are the tiny dust particles that tend to settle downward on top of everything.

    So I believe there is a way to test that part of your theory.

    Cosmology treats gravitational force as the interaction of two gravitational fields. When there is only one field, there curvature but no acceleration.

    I would suggest a slight change in your explanation to distinguish real mass from virtual mass.

    With Planck mass you are dealing with virtual particles and virtual mass. So if that is how your theory is written, the claim might only apply to virtual particles.

    Then if you claim that a virtual pair like electron and positron have no gravitational mass, its a theoretical question.

    To make the claim for a real pair would find serious objections.

    Even with the virtual pair there is some doubt. In that case you might find help in the EQUAL PARTITION reference.

    It can be argued that a virtual pair is close to equilibrium between mass creation and electric charge creation. The two properties cancel out when they are equal, leaving no net gravitational field.

    I believe your approach has merit, and would benefit from additional work, especially editing to remove as many objections as possible.

    55 Miligrams!  The Planck mass is nowhere near 55 miligrams.  It is more like 2.17 MIRCOgrams.   The reduced Planck mass is slightly larger at about 4.3 MICROgrams. ( Those are the CODATA values and universally accepted. )
    The rest of your argument relies on using the wrong number for the planck mass.  

    I will ignore that and address your confusion further.
    There is a problem with molecules in a gas. None of them are as large as a Planck mass. Then there are the tiny dust particles that tend to settle downward on top of everything. 
    The gas particles, and tiny dust particles could be explained as settling down on  due solely to the gravity of the massive body (planet, asteroid, moon) they come to rest on.  In classical standard physical theories we usually  convert a system which has a small mass and a huge mass into center of mass coordinates, and use the reduced mass.Which works out to be virtually the same as the mass of the planet, moon.. etc in question.  It's virtually the same as totally ignoring the mass of the gas or dust particle all together.   In a certain sense my theory is saying is that gravity does not cut on until you have a total non-gravitationally bound mass of at least 4.3 micrograms.  It is saying that you can without any loss of precision at all totally ignore any gravity such small objects may have... they have none.  
    Consider the following.    The radius of a black hole is defined by the Schawarzchild radius formula  
    (where c=hbar=1).  If we write the planck length in terms of the constants which define it the Planck length is   .  Now consider Einstein's less famous energy relation   .

    Set the wavelength lambda equal to the planck length then use that energy as the mass for the black hole


    An integer times the planck length is the resulting radius.  In a four dimensional universe the planck mass is the minimum mass a black hole may attain.  Furthermore suppose you have a beam of light of wavelength equal to the Planck length... what happens?  Such a wave of light would gravitationally collapse into a micro black hole!  Effectively there is no way to measure even in principle any length shorter than the planck length.  (The ultimate measureing stick we have is a ray of light, and as I just explained the marks on this meter stick can be no shorter than the Planck length which relates to mass.)  

    For this reason I assert that no mass smaller than the planck mass can have a gravitational field of it's own.  Such a particle if it is totally neutral (no ionizeation, no electrostatic charge noting) will not effect another mass by way of gravity either.    Such particles may only couple to the gravity of other more massive objects.


    Science advances as much by mistakes as by plans.

    My own model of EQUAL PARTITION works out to be 2.73 micrograms for the Planck mass in flat space, and not significantly different on Earth, but I don't really expect anyone to take my version as a quotable reference at this point.

    The rest of my argument still stands firm for gas molecules and to some extent for dust particles, although it is harder to prove for tiny dust particles. So the torsion balance would probably not be able to measure the gravity of one dust particle.

    The remainder of your reply is very familiar to me.

    With the reduced mass you are claiming that a dust particle of one microgram has no gravitational field of its own, but still adds to the gravity of a larger mass if it is close enough to be influenced by the field of the other mass.

    My EQUAL PARTITION MODEL agrees with you on that point but only for virtual masses. Furthermore I give a reasonable explanation of how the induction mechanism operates, based on three very well established principles of science. My model does not attempt to describe real particles except as the distant source of macro gravitational fields..

    Your calculation example gives a different method of coming to the same conclusions as mine, as far as virtual particles are concerned.. So I am very interested in it. I really wonder if it can be applied to real particles.

    Induced gravity is a good topic to write about, so I am open to a wide variety of opinions. At this point I could argue that you are right about virtual particles, but express a lot of doubt about real particles. The question is important and worth exploring further.

    Then in a very low density interstellar dust cloud, your model can exist in two different states, separated by a very small energy barrier. If the density is sufficiently low, then there is no gravity field from any dust particle, and no gravity field for the entire cloud.

    On the other hand if a small region of the cloud became slightly denser for a moment, then the entire cloud could acquire a macro gravity field at light speed.

    On the other hand the macro gravity could be lost at light speed if one region of a marginally low density cloud became slightly less dense for a moment.

    It's an interesting concept and one that could be observed in astronomy.

    For gas clouds of low density the same issues apply, and in some cases might be observed.
    Thanks for your reply.

    IT"S NOT 55 micrograms either. The reduced Planck mass is 4.3 micrograms,  2.44*10^19 GeV/C^2.  [1] The mass of the proton is 0.938 GeV/C^2.  [2]  The Planck mass is 2.6*10^19 protons.  Sounds like allot. If those protons were in hydrogen molecules that would be 10^-4 of a Mol  (1 Mol=6.022*10^23).  That would not even be close to a gram of water.. not at all.   
    Measuring with the precision needed to know if there was any gravity due to these masses would be extremely difficult. But it has to be done.  Because not only my little theory, but string theory, and loop quantum gravity rely to an extent on the fact that space-time is fundamentally different at the Planck scale. 

    Science advances as much by mistakes as by plans.
    VERY GREAT POWER WOULD BE REQUIRED TO CREATE FLAT SPACE IN A LABORATORY FIELD GENERATOR ON EARTH. Your experiment might be done in one of the space missions. A lot of people have recommended scientific tests to be done in space at all levels of complexity.

    A great many tests from less famous scientists have been done in space. One recent proposal was to measure whether or not a positron is attracted to gravity or repelled by it. So your experiment is in the right category for space testing.

    The 55 number is not my favorite, but there are at least 10 published varieties of Planck mass with somewhat different coefficients of the dimensional group. You are quoting one of them. I quoted Barrow because it is a classic that many people will be able to find and read. Also Barrow explains why the Planck units are important on a level that most people can understand.

    Depending on how vacuum zero point energy is partitioned, the Planck mass gets shifted by a percentage, that really doesn't change any conclusions you made about it.

    Your theory could probably be tested by astronomy. Then it would fit in well with topics about dark energy, dark mass, and acceleration of galaxies.

    I have become very interested in the outcome of your theory, and hope it can be proven, because that would open up a lot of new science and go a long way toward reconciling facts with theories.

    To be complete and balanced I believe you will need to add the electromagnetic induction to your theory.

    If a small particle resides in flat space it is dominated by the flatness (in your theory) and does not have enough energy of its own to bend space one way (or the other).

    Then if the particle is subjected to a field of positive curvature (gravity) or negative curvature (electromagnetic field) the result will be an induced polarization to align the particle with the dominant field.

    If the electromagnetic fields are dominating, then the small particle of less than Planck mass should express negative curvature and repel other masses. That is a dangerous thing to say in public. so maybe you could find a more technical way to handle the electromagnetic excess that pushes galaxies apart.

    Thanks for your response.

    I"m sorry to tell you the CODATA value is the generally accepted value for the Planck mass.  Not 55 anything anywhere.  Where ever you read that can be safely discarded. 
    Science advances as much by mistakes as by plans.
    DON'T BE SORRY FOR HAVING A DIFFERENT OPINION, but please do read the fine print before you take a constant out of CODATA or NIST to use in your work.

    The number you quoted is for energy measured per radian, as is often used in the physical sciences, but not always. The choice was arbitrary by CODATA and the results are recommended for the situations where it applies.

    My reference was to John D. Barrow (Cambridge University), “THE CONSTANTS OF NATURE” Vintage Press, 2004, page 26. It was chosen for a reason.

    Barrow expresses the Planck mass on the basis of energy per wave length., which is perhaps less popular, but more firmly based on measurements in physical science.

    Calculations might be easier in terms of radians, but wave length measurements are a lot easier to do.

    S suggest to you that a wave length is a fundamental quanta of the physical world, but a radian is not. A radian is an abstract mathematical construction.

    So if you are planning to measure radians of a partial wave many light years away through a special telescope, the CODATA is fine.

    On the other hand if you intend to measure wave lengths of something at a distance, it would be wise to the correct constant. CODATA and NIST would not object to that.

    Thanks for your reply.

    ENGERY USED PER RADIAN...  The non redueced Planck mass is <s>about half of the reduced planck mass</s> . 
    The non reduced planck mass is 2.176*10-8 kg.  NO where is it ever 55 (any)grams ever.  
    I did dash off the number 2.2 micrograms for the non-reduced planck mass.  Like all my errors it is one which does not change any of my physical claims. I APOLOGISE IF I SOUNDED TO COARSE. In theory the scaling argument I and practically every other physicist researching quantum gravity has made still holds.  Masses smaller than the Planck mass just don't have a gravitational field of their own. 
    Science advances as much by mistakes as by plans.
    I GUESS THE ANSWER TO YOUR COMMENT IS THAT TO UNIFY QUANTUM MECHANICS WITH COSMOLOGY, the quantum mechanical community should find ways to predict things that can be measured on a large scale from a far distance. I'm coming from the cosmology side of science.

    Your theory looks like one that might fit into a unified theory.

    I have Barrow's book in my hand now and am reading 55.6 micrograms on page 26.

    The astronomer who will test your theory in a gas cloud with a telescope will be measuring wavelengths, not radians.

    Your comments were a great help to me.

    Best wishes.

    According to Codata the current value for the Planck mass is about 22 micrograms.  It is possible that this is different than what you have in that source because of more precise measurements of the gravitational constant.  
    Science advances as much by mistakes as by plans.

    If it does then you need to be very precise about which Planck mass you are using and why it was chosen.

    The reduced mass formula you sent in a different message is saying that a sufficiently dense gas cloud will have all of the molecules induced to gravitate by their mutual field strength. Then there should be some smaller density at which it doesn’t happen and there is no gravitational field from the cloud. If these both occur there should be a critical density at which the change occurs, and it should be observable by astronomy.

    Barrow quoted Max Planck from 1899 and the constants are slightly different now, but not by much.

    The main difference is a factor of SQRT(1/ 2 Pi) that CODATA has multiplied to Planck's mass for easier calculations of energy in radians that has become popular in much of science.

    Reduced Planck mass has another factor SQRT(1/ 8 Pi) multiplied by the one above also for easier calculations and simpler mathematics in general relativity.

    Max Planck did not use either of these modifications. He based his mass on the energy of a complete wavelength.

    You could get a lot of different opinions about which constant has physical significance. Ease of calculations is probably not a good argument.

    I hope your theory can make a prediction. Then you should make some type of statement about which version of Planck mass you are using and why that choice has physical significance in the measurements.

    Thanks again.

    The density of the matter/energy as such never fell out of my equations, however the interaction of the particles did.  The particles have to be in a bound state of some non-gravitational force of nature.  (EM, Strong or weak atomic force) before they will "emit" a quantum of curvature/graviton.
    The above is the Quantum Mechanical explanation.  What you have seems to be a good classical deduction.  I took a course on Astrophysics last year.  If I recall correctly what keeps a cloud from condensing is a combination of thermal excitations, and magnetic currents in the cloud.  There is as you deduced a critical density at which a cloud will collapse and form stars.   

    So we are both quite right thanks for the sanity check. 

    As for the actual # of the planck length, mass, and such, that will depend entirely on the work of the experimentalist.  In the orthodoxy of physics someone with my credentials is not likely to get funding to do any experiment which could measure the things we have discussed. 

    My messages with you have been a productive sanity check.  Keep any questions you have coming.  :-)
    Science advances as much by mistakes as by plans.
    Hello Blogger,

    I’m sending a brief news release regarding Earth's magnetic field that you can use on your blog. You may take more information from the website if you like. Please consider using it. You can also find images on my website.


    Contact: Dennis Brooks

    Earth’s Magnetic Field Is Produced By An External Dynamo System, Not An Internal Dynamo.

    Earth’s magnetic field is not produced by an internal dynamo within the planet.
    By Dennis Brooks, Image By NASA
    New Theory: (Excerpt) Earth’s magnetic field is not produced by an internal dynamo. The magnetic field and the planet are parts of a complex dynamo system surrounding the planet. The system includes the planet, the magnetic field, radiation belts, and ring current. The same is true of the other planets. Saturn, Jupiter, Neptune, and Uranus are visible components of otherwise invisible planetary dynamo systems, which are all housed within a magnetosphere. According to this new theory, there is no internal dynamo within the planet itself. Planet Earth does not have a unique way of producing its magnetic field. Nor do the other planets. Each magnetic field of each planet is produced in exactly the same way, by its planetary dynamo system. Visit the researcher’s website to learn more. Read more at

    I'm not a planetary scientist.  However based on basic physics I see a few things wrong, and a few things right about your theory.  Here are the things that are wrong first.  
    • You say that the earth's outer core is too hot to produce a magnetic field.  Consider the sun.  The sun has a very strong magnetic field and it is many times hotter than earth's inner core.  
    • You say that the ring current of the radiation belts is the true source of a planetary magnetic field.  How does the field start in your theory?  Which comes first the radiation belts or the core geomagnetic field?  It's simpler for the geomagnetic field to be the cause of the radiation belts. 

    Here is what I see that is right.

    •  As far as I know no one has considered the induced magnetic field due to the charges in the radiation belts. I don't know of observations or calculations which have tried to quantify any magnetic field that could exist due to the current in the van allen radiation belts.  I know one belt is mostly protons, and the other mostly electrons.  In any case there must be billions of Coulombs of charge in total in those belts.  It makes sense that they should have a magnetic field of their own.  The question is just how does that magnetic field interact with and possibly modify the magnetic field of the earth.  The earth's field transfering energy  to the belts and the belts back to the field of the earth by way of their dipole field.   How would the earth's B field be different without the radiation belts. 

    My opinion of this work is that you should pursue it.  First review all the literature you can and be sure no one else has done this before.  Learn how to state your theory quantitatively.  If you don't know calculus already, learn it, then learn basic physics, and a first course in electrodynamics.  Then learn about geology and learn how planets work.  You don't necessarily have to go to school to do this but that's the simplest way.  If you have a bachelors degree you can go to many colleges as a non-degree seeking student and learn what you need. 

    Then write this all up as a scholarly paper and publish it.  I have read and see things that were patent nonsense published so as far as I am concerned anything that is not patent nonsense deserves to be published even more. 


    Science advances as much by mistakes as by plans.

    You said, "I'm not a planetary scientist.  However based on basic physics I see a few things wrong, and a few things right about your theory.  Here are the things that are wrong first.  You say that the earth's outer core is too hot to produce a magnetic field.  Consider the sun.  The sun has a very strong magnetic field and it is many times hotter than earth's inner core."

    But if his theory is that the temperature of the Earth is too hot to produce a magnetic field, the same would go for the sun. If he is right (and I am not a planetary scientist either) the sun's size could be the contributor for its larger magnetic field, as it is "many times" larger than the Earth. So in fact, (again if this is true) the temperature of the sun would not play a role anymore than that of the Earth.

    Just a thought...

    The sun produces a magnetic field.  We have measured it directly.  Measurement is the heart, and soul of science.  Once those measurements are taken and verified that's it.  Theory must accommodate them. 
    Science advances as much by mistakes as by plans.
    I wonder what Lee Smolin of the Perimeter institute would say about Wald's theory.
    An old but remarkably originally thinking professor Mendel Sachs has recently written some books on the unification of gravity and the other fields. See

    I also tried to give my own contribution. I discovered the quaternion waltz and to my humble conviction it belongs to the fundamentals of quantum physics. I wrote my vision down in a short article There also exist a .htm version of this article. It also shows how the waltz forms the source of special relativity and how quaternions introduce items that are no longer quaternions and have a Minkowski metric. These items can properly be handled with Clifford algebras. I used the freedom to used higher dimension 2n-ons as eigenvalues of operators. In this way can curved manifolds be handled and comes general relativity into the picture.
    If you think, think twice
    Sonds interesting.  I think I'll check those out. 
    Science advances as much by mistakes as by plans.