Gravity Equation Discredits Lubos Motl

Louise Riofrio published some physics papers on a model of cosmology based on a simple relationship

GM = tc3

But then Assistant Professor Lubos Motl of Harvard University (a string theorist who religiously believes in 10/11 dimensional spacetime, but has no objective evidence for it whatsoever) made some rude sexist remarks about her being female on his Reference Frame blog, and claimed this equation to have no physical connection.  He dismissed it as merely dimensional analysis.  Being thus duped, I stupidly believed him at first, but now it is clear that he was not even wrong:

Simply equate the rest mass energy of m with its gravitational energy mMG/R with respect to large mass of universe M located at an average distance of R = ct from m.

Hence E = mc2 = mMG/(ct)

Cancelling and collecting terms,

GM = tc3

So Louise’s formula is derivable, while extra dimensional Lubos is as usual proved to be not even wrong (just like his beloved string theory).  But women physicists are more careful and so more likely to be correct.  They don’t go dismissing things they can’t understand by making a sexist remark, so they are more likely to get the physics correct.

In more detail:

To prove Louise’s MG = tc3 (for a particular set of assumptions which avoid a dimensionless multiplication factor of e3 which could be included according to my detailed calculations from a gravity mechanism):

(1) Einstein’s equivalence principle of general relativity:

gravitational mass = inertial mass.

(2) Einstein’s inertial mass is equivalent to inertial mass potential energy:

E = mc2

This equivalent energy is “potential energy” in that it can be released when you annihilate the mass using anti-matter.

(3) Gravitational mass has a potential energy which could be released if somehow the universe could collapse (implode):

Gravitational potential energy of mass m, in the universe (the universe consists of mass M at an effective average radius of R):

E = mMG/R

(4) We now use principle (1) above to set equations in arguments (2) and (3) above, equal:

E = mc2 = mMG/R

(5) We use R = ct on this:

c3 = MG/t

or

MG = tc3

Which is Louise’s equation. QED.

Christine Dantas has a PhD in astrophysics and studies Smolin’s very mathematical loop quantum gravity as an alternative to string theory.  However, after listing the evidence for loop quantum gravity, Lubos Motl then subjected her to dismissive rudeness (calling her guilty of ‘sloppy thinking‘ was horribly inaccurate and also hypocritical of Lubos, seeing his sloppy uncheckable claims for extra dimensions and string, and his errors such as the example above) combined with his usual loud sexist comments.  Lubos Motl seems determined to stop women rising to prominent positions in physics.  Why does he not want this?  Is it because the hot air of string hype may be reduced, I wonder?

Even his senior at Harvard, string theorist Professor Lisa Randall, states in the preface of her nicely caveated and polished book Warped Passages that she does not entirely agree with Lubos’ view of females, and she does admit the possibility that string may be not even wrong if it can’t be checked.

If Lubos is the role model of macho physics in action, then the future of physics certainly lies with female physicists who don’t allow such hormone driven prejudices to destroy their objective judgement on scientific matters.  It is largely because of pseudo-macho hype from male string theorists, such as Lubos et al., (I won’t mention Witten’s name here because he is nowhere near as rude as Lubos) mathematical physics gets ever less popular.  (More on the decline: here.)

I’m reading Woit’s course materials on Representation Theory as time permits (this is deep mathematics and takes time to absorb and to become familiar with).  Wikipedia gives a summary of representation theory and particle physics:

‘There is a natural connection, first discovered by Eugene Wigner, between the properties of particles, the representation theory of Lie groups and Lie algebras, and the symmetries of the universe. This postulate states that each particle “is” an irreducible representation of the symmetry group of the universe.’

Woit’s historical approach in his course notes is very clear and interesting, but is not particularly easy to read at length on a computer screen, and ideally should be printed out and studied carefully.  I hope it is published as a book with his arXiv paper on applications to predicting the Standard Model.  I’m going to write a summary of this subject when I’ve finished, and will get to the physical facts behind the jargon and mathematical models.  Woit offers the promise that this approach predicts the Standard Model with electroweak chiral symmetry features, although he is cautious about it, which is the exact opposite of the string theorists in the way that he does this, see page 51 of the paper (he is downplaying his success in case it is incomplete or in error, instead of hyping it).

By contrast, Kaku recently hyped string theory by claiming that it predicts the Standard Model, general relativity’s gravity, and lots more; but of course this is completely untrue, because in string theory, to get it to work, you first have to fiddle the dimensions to 10 just in order to produce particle physics and to 11 to produce gravity (although the 10-11 dimensions paradox was allegedly overcome by Witten’s M-theory in 1995, which is a kind of mathematical Holy Trinity).

In no case has the string theory – even once fiddled to a number of dimensions that makes it work “ad hoc” – then managed to make even a single checkable physical prediction!

This is why string theory is a complete disgrace as physics, although Woit (perhaps because he now works in a mathematical department) is always keen to kindly say that at least string theory has led to an increased mathematical understanding of extra dimensional manifolds like solutions to the Calabi-Yau manifold which gives about 10500 metastable ground states of the vacuum (and thus 10500 ‘dark energy’/cosmological constant levels, forming Susskind’s anthropic ‘cosmic multiverse landscape’ of universes!) in an oscillating string due to the many possible parameters of the 6 dimensional manifold’s size and shape dimensions (how elegant and how beautiful … I don’t think).

31 thoughts on “Gravity Equation Discredits Lubos Motl”

1. 09 22 06

Hello Nigel:
Thanks for the response at Louise’s blog. So one thing I noticed is that the set of equations works at the Planck scale, assuming it is locally Euclidean. However, within space with curvature, the assumption that R=ct breaks down. L=ct works for Planck scales, but R=ct does NOT work unless we consider the space to be locally Euclidean methinks. If you assume a metric like say, a p-adic metric (where we assume that all points of the universe can be labelled with primes) the calculations for distances will not be the same. What I am trying to figure out is if the equations should produce the same results (more or less a phase change) independent of the choice of metric, as a background independent, gauge invariant entity.

Regarding your derivation with the e^3 factor, can you point me to your paper? I will look around here for it.

Regarding looking at the equations where one object is at rest with respect to the other one, we are making the assumption that R=ct and that seems somewhat contradictory because relativistic energies are not equated with Newtonian energies. You guys are equating Newtonian energies with Newtonian energies which don’t describe the universe in entirety unless we are in the limit that v

2. 09 22 06

Uh oh, some of the comment got chopped off Nigel, I was just saying that you guys assumed v

3. Hi Mahndisa,

Welcome and thank you. Thank you also for your comment on Louise’s blog. Sorry for the problems. Regards the comment cutoff, I’m guessing that you typed the keyboard arrow symbol and WordPress here tried to read it and failed and that ended the comment. WordPress automatically reads and convert anything in comments straight into hyperlinks and html code for superscript etc, and since the arrow symbols are used for this, it creates problems. The arrows and other code symbols in comments on blogger sites don’t get converted into code, only on WordPress. (I’ve had problems with blogger being unavailable for long periods which is why I’m now using WordPress.)

The e^3 result is derived in a letter published in Electronics World in 2004. The essence is near http://feynman137.tripod.com/#h although it is not very well done. I’m modelling the spacetime effect by saying that mass continuity should apply for the divergence of mass due to the Hubble expansion relationship, applying spacetime. Mass continuity equation (for the galaxies in the space-time of the receding universe): dρ/dt + div.(ρv) = 0. Hence: dρ/dt = -div.(ρv). Now around us the universe looks the same in all directions, so: dx = dy = dz = dr, where r is radius. Hence divergence (div) term is: -div.(ρv) = -3d(ρv)/dx. For spherical symmetry Hubble equation v = Hr. Hence dρ/dt = -div.(ρv) = -div.(ρHr) = -3d(ρHr)/dr= -3ρHdr/dr= -3ρH. So dρ/dt = -3ρH. Rearranging:-3Hdt = (1/ρ) dρ. Solving by integrating this gives say: -3Ht = (ln ρ1) – (ln ρ). Using the base of natural logarithms (e) to get rid of the ln’s: e^[-3Ht] = density ratio. Because H = v/r = c/(radius of universe) = 1/(age of universe, t) = 1/t, we have: e^[-3Ht] = (density ratio of current time to earlier, higher effective density) = e^[-3(1/t)t] = e^-3 = 1/20. All we are doing here is focussing on spacetime in which density rises back in time, but the outward motion or divergence of matter due to the Hubble expansion offsets this at great distances. So the effective density doesn’t become infinity, only e^3 or 20 times the local density of the universe at the present time. The inward pressure of gauge bosons from greater distances initially rises because the density of the universe increases at earlier times, but then falls because of divergence, which causes energy reduction (like red-shift) of inward coming gauge bosons.

If this at any stage seems to make a massive leap and is unclear, that is probably my fault and not yours. I urgently need to rewrite the treatment to bring out the physical connections surrounding the mathematical calculations or the latter just look like fudged stuff. However, you get the same correction factor numerically by doing a calculation of the gravity mechanism proposed for a series of many shells around the observer, each containing the correct proportion of the mass of the universe, the effects of which (gravitons or whatever) are redshifted towards the observer. As you go to shells at greater distances, the spacetime density rises ever more, but the redshift also rises and offsets the density increase for local gravity effects we can observe.

By the way, I’m happy for Euclidean geometry with Lorentzian transformation occurring physically due to local physical contraction due to motion in a quantum field spacetime. You move against the physical medium, and you get compressed physically in that direction.

Always in special relativity, it is only the length of the object in motion which is really shortened, not spacetime itself. Cut aside the obfuscation, and FitzGerald’s idea that the aether actually causes the contraction is quite compatible with the Dirac sea picture of quantum field theory. Of course this would be dismissed by Lubos Motl as totally crackpot.

So I’d take a metric which is localized to the matter only, say the measuring ruler or whatever is actually in motion. It is quite easy to see how to correct relativity. Lunsford’s analysis http://cdsweb.cern.ch/search.py?recid=688763&ln=en seems to indicate that Einstein should have tried 6 dimensional unification where the 3 “extra” dimensions describe coordinated matter, since this unifies electromagnetism and general relativity properly (unlike the 5 dimensional Kaluza-Klein unification). Smolin’s work unifies the field equation of GR with path integrals QFT without assuming any particular metric. I think this is correct: the metric depends on what you are describing.

For cosmology, you have 3 uniformly expanding large scale timelike dimensions which describe vast distances (better described as times for obvious reasons), while for local predictions you are dealing with contractable matter, gravitational contraction, time dilation etc., ie, non-expanding (and indeed contractable) dimensions deal with matter. So I don’t think any particular metric is universally true. By the way, I’m not completely against string theory and I think the particle may well be a string, but without extra dimensions. The properties normally ascribed to imaginary extra dimensions should instead be supplied from physical dynamics.

(Please note that this WordPress site is running slow right now, it keeps returning time-out errors due to server overload. Sorry if it is wasting your time too!)

4. I just put a comment on Lubos Motl’s blog about this post and it was deleted. I’ve pointed out to Lubos before that string theory stripped of extra dimensions (using physical dynamics to deal with the problems now glossed over by extra dimensions) is quite a nice way to think about particles, particularly if you are a philosopher who doesn’t care primarily about calculating physical parameters in a checkable way from a theory whose dimensions are verified.
Personally, I’m less interested in philosophy than in checkable predictions, so I’m not really bothered if my comment gets deleted from the blog of Motl the physics philosopher whose main interests are political diatribes.

5. 09 22 06

Thanks for the comments Nigel. Yes, that is what I was hinting at was the fact that background independence needs to be a feature of any theory and that the equations need to fall out regardless of any metric used. However your point about the object being in motion suffering length contraction makes sense, but only when v is on the order of ‘close’ to c. I think that the LQGers have something when they talk about a discretized spacetime and in that sense, we could use padic quantization of spacetime and your equations should come out of that less a phase change or something, if it is background independent. I really appreciate your comments and the time you took to answer my questions. I hope you have a great weekend:)

6. Hi Mahndisa,

Agreed on background independence. In 1949 a spacetime fabric like a crystal was shown to mimic the SR contraction/energy formulae, see: C.F. Frank, ‘On the equations of motion of crystal dislocations’, Proceedings of the Physical Society of London, A62, pp 131-4:

‘It is shown that when a Burgers screw dislocation [in a crystal] moves with velocity v it suffers a longitudinal contraction by the factor (1 – v^2 /c^2)^1/2, where c is the velocity of transverse sound. The total energy of the moving dislocation is given by the formula E = E(o)/(1 – v^2 / c^2)^1/2, where E(o) is the potential energy of the dislocation at rest.’

Given this length contraction, the spacetime principle gives us an identical time-dilation factor (because distances and times must be both shortened by the same factor). Given the energy variation factor above, we get the mass variation formula because of E=mc^2 which is implies by electromagnetic theory (i.e., light with energy has momentum which implies that the way to relate energy and mass is E=mc^2).

This applies to the Dirac sea in its bound (ground) lowest energy state, because we know it can’t be free in the ground state or the entire vacuum would be polarized by an free charge, cancelling out the charge completely.

Only the strong electric field (see previous posts on this blog) ABOVE say 10^16 volts/metre which occurs at around 10^-15 metre from an electron is capable of causing pair production (freeing charges in the vacuum from their bound state, so that they can be polarized and shield electric fields; the energy of the shielded gauge bosons is conserved in this region and causes the short ranged nuclear forces, but that’s another story).

Below 10^16 volts/metre electric field strength, ie, beyond 10^-15 m from a charge, the vacuum charges in the Dirac sea must be incapable of polarization, according to renormalized quantum field theory. So this implies that the ground state to the vacuum is not a gas of free, polarizable charge, but is bound somehow to prevent polarization. Hence it is some kind of crystal form, and this explains why Frank’s model (quoted above) predicts the correct form of the Lorentz/FitzGerald/”SR” contraction formula.

Hope you have a great weekend too!

7. nc says:

Recent comments of mine to other blogs:

Quantum gravity solved and predicted general relativity’s dark energy (small positive cosmological constant) riddle in 1996, two years before Perlmutter’s supernovae recession data: see http://christinedantas.blogspot.com/2006/09/interesting-links.html for some equations and see

For other comments on this topic with a diagram see http://mrigmaiden.blogspot.com/2006/09/update-to-riofrio-equations-post.html

Comment on the problem of how life evolved: http://riofriospacetime.blogspot.com/2006/09/faint-young-sun.html

Comment on standard model modelled in low dimensions by representation theory:

http://www.math.columbia.edu/~woit/wordpress/?p=466

nc Says: Your comment is awaiting moderation.
September 29th, 2006 at 9:06 am

Stefan,

‘There is a natural connection, first discovered by Eugene Wigner, between the properties of particles, the representation theory of Lie groups and Lie algebras, and the symmetries of the universe. This postulate states that each particle “is” an irreducible representation of the symmetry group of the universe.’
http://en.wikipedia.org/wiki/Particle_physics_and_representation_theory

Clearly this is a more natural and simple approach to build an understanding of particle physics than by adding extra dimensions and superpartners. There is a difference in goal between http://arxiv.org/abs/hep-th/0206135 and string theory.

String theory is extremely arrogant and presumptive: adding extra dimensions to account for unobserved gravitons and adding the boson-fermion supersymmetry to achieve unobservable unification at 10^16 GeV, is just like taking a hammer to crack a nut. You simply don’t need such extravagant measures: there is no evidence that needs explaining by extra dimensions and superpartners, and you don’t make any predictions by it.

Now for the real problem: there is the standard model with its symmetry breaking mechanisms to be explained, and it seems that representation theory can make progress with this problem without requiring extra dimensions.

nc Says: Your comment is awaiting moderation.

September 29th, 2006 at 9:11 am

Even if string theory in 10 d could describe the standard model as well as representation theory in 4 d, Ockham’s razor tells you that representation theory in 4 d is the best choice:

‘entities should not be multiplied needlessly’

8. nc says:

The image link in the comment copy below should be to http://thumbsnap.com/v/96oFXbrG.jpg which shows the mass model more clearly. A rigorous prediction of the other constants besides alpha, and a rigorous physical analysis of how coupling can occur between uncharged boson and fermion: obviously a boson like a photon is electromagnetic radiation so it has electromagnetic fields associated with it, so is only uncharged as such as seen from a distance where the positive electric field is cancelled by the negative electric field. At shorter range a photon is a dipole field, and if it is a massive boson then it is moving slowly compared to c, and can be polarized about is axis by an electric field, which may account for the polarization of mass in renormalization?

http://www.math.columbia.edu/~woit/wordpress/?p=466#comment-16674

nc Says: Your comment is awaiting moderation.

September 29th, 2006 at 1:15 pm
Stefan,

Wikipedia provides a nice down-to-earth one sentence introduction to that:

‘There is a natural connection, first discovered by Eugene Wigner, between the properties of particles, the representation theory of Lie groups and Lie algebras, and the symmetries of the universe. This postulate states that each particle “is” an irreducible representation of the symmetry group of the universe.’

This is the kind of springboard you need to start with, to get enthusiastic. I’m interested in the way forces are modified by renormalization of charge and mass. Clearly, pair production of electron-positron loops (and heavier loops) in the strong field near any particle can be electrically polarized. This gives the ‘heuristic’ or trial and error interpretation for how electric charge is renormalized, see http://arxiv.org/abs/hep-th/0510040 p 71.

However, mass can’t be polarized, because there is only one type of mass (even antimatter falls downward). So mass and its force field (quantum gravity) can’t be directly renormalized by the same heuristic explanation used for electric charge!

So if vacuum polarization in strong (pair production producing) fields is the correct explanation for the need to renormalize electric charge, it can’t directly explain how mass can be renormalized.

My understanding is that both electron charge and mass need to be renormalized to calculate the magnetic moment of the electron by the Feynman, Schwinger, Tomonaga approach.

Therefore, mass can’t be completely independent of electric charge, otherwise mass renormalization wouldn’t work. Unfortunately, the charge/mass ratio changes with energy (mass increases with velocity, unlike charge). Therefore the way that mass couples to charge is not proportional to the charge, just to things like the motion of the charge.

So whatever gives mass to charges does so in a very special way. Since mass is the charge for quantum gravity, this is really the key problem. The Higgs field theory for electroweak symmetry breaking is not very impressive as it simply can’t predict masses as explained in Not Even Wrong page 99 (UK edition, I don’t know whether it is the same in the US edition, but it is near the beginning of chapter .

Trying to fiddle a semi-empirical theory that predicts mass is fun: http://thumbsnap.com/v/7TCsIwOz.jpg shows the polarized zones around particles. Each polarized zone has inner and outer circles corresponding to the upper (UV) and lower (IR) cutoffs for particle scatter energy in QFT. The total shielding of each polarization zone is the well known alpha factor of 1/137. If the mass-producing boson is outside this polarization zone, the charge shielding reduces the mass by the alpha factor. By very little numerology, this model works extremely well.

You would expect that semi-empirical relationships of the numerology sort would precede a rigorous mass predicting mechanism, just as Balmer’s formula preceded Bohr’s theory for it.

Obviously any as yet unorthodox idea may be attacked by the ‘crackpotism’ charge, but I think this one is particularly annoying to orthodoxy as it is hard to dismiss objectively.

9. nc says:

IMPROVEMENT TO MASS MODEL DISCUSSED IN COMMENT ABOVE

1. Mass is gravitational charge. To renormalize a mass field like inertial mass or gravitational mass is impossible to do directly, because mass can’t be polarized like charges which separate (polarize) in an electric field.

2. Renormalization of mass is possible however, using a mechanism. Fermion’s are conventional electric monopoles (+ or – charges) with a magnetic dipole field. Light photons are electromagnetic radiation which by Maxwell’s equations must contain exactly the same amount of positive as of negative electric field. This is how they induce oscillations of charges.

Because the photon is an electric dipole, it can in principle be polarized along its axis if it goes slower than light. We know from electroweak symmetry that the 91 GeV Z_o gauge boson of electroweak theory is a massive photon that goes more slowly than c due to its rest mass. This can therefore be polarized, which is UNIQUE.

Therefore, the Z_o gauge boson is particle of the polarizable mass field which is renormalized in quantum field theory such as QED. The polarization of the Z_o field is a rotation of its dipolar axis of electric field, rather than a separation of two charge monopoles as occurs when a fermion field is polarized.

10. nc says:

copy of comment to:

http://scienceblogs.com/islandofdoubt/2006/09/string_theory_testable.php

Hi Luke Lea,

I’m sure you have good intentions in promoting Lubos and string theory.

String theory starts off with a 1 dimensional line. This is the string. The word string is a misnomer really because a string is something physical, and the 1 dimensional line isn’t. Anyhow, forget this for now.

When it moves in spacetime, this 1-dimensional “stringy” line gains an extra dimension (time) and becomes a 2-dimensional world sheet.

Then to get particle physics they have to add either 8 or 24 dimensions to give the required vibrational degrees of freedom for the known particles using the Ramanujan function to satisfy conformal symmetry.

This results in 10 or 26 dimensions in total. These 8 or 24 dimensions come from supersymmetry (1:1 symmetry of superpartner bosons for each fermion) which uses 8 dimensions, and the older bosonic string theory which uses 24 dimensions. Supersymmetry is included to make the Standard Model forces unify at about 10^16 eV or something, way too high to ever check even in a particle accelerator as big as the solar system. So it is a load of unobservables being invented in order to “explain” a completely untestable, uncheckable hypothesis.

This is not explaining anything known, or anything real. It is like coming up with an explanation of the afterlife, which can never be checked in principle by anybody alive. It is not falsifiable, and makes no predictions. Rubbish.

Notice that bosonic (26-d) string theory became a heresy after Witten’s M-theory and people who develop 26-d string theory like Tony Smith are simply censored off arXiv by the simple act of deleting their work:

http://www.valdostamuseum.org/hamsmith/stringbraneStdModel.html

see http://valdostamuseum.org/hamsmith/ for Tony Smith’s blacklisting by the mainstream.

Anyway, with the M-theory 10-dimensional particle supersymmetry, you get the problem of explaining why there are 10 dimensions when general relativity only has 4 spacetime dimensions.

Easy! The Calabi-Yau manifold can roll up the 6 dimensions we can’t see, and it rolls them up at the Planck scale, very conveniently so we can never check them.

Plus, the Calabi-Yau manifold even constrained to 6-d has loads of unknown parameters to describe the size and shape of each of the 6-dimensions it has. The vibrational modes for it are extremely complex as a result, so the string has 10^500 possible ground states, the “cosmic landscape”.

This is explained in a brilliant manner in Peter Woit’s book “Not Even Wrong”. It is the end of theoretical physics. String theory either destroys Popperian falsifiability or Popperian falsifiability will destroy strings. There are only 10^80 fermions in the universe! You can’t have checkable science when the theory has 10^420 more states than there are particles in the universe.

Anyone who knows anything about numbers knows that these type of numbers kill string theory and make it complete drivel that says nothing useful whatsoever.

Anyway, M-theory also unifies 10 dimensional string theories (there are many variants, all crackpot in the sense of making no checkable predictions) with 11-d supergravity which is the classical limit. Lubos has a long list of things string theory says about information theory, black holes, branes, the holographic conjecture, and such like. There is not much observational data from black holes, nobody in the mainstream has worked out a falsifiable theory of quantum gravity, so all this stuff this is just fads of speculative hype.

String is a complete fraud. There is nothing there.

Consider the alternatives. One is Woit’s representation theory ideas which models the Standard Model with weak force chiral symmetries in ordinary low-dimensioan spacetime (see page 51 of Woit’s http://arxiv.org/PS_cache/hep-th/pdf/0206/0206135.pdf showing how the standard model can be produced with electroweak symmetry, without requiring extra dimensions).

Wikipedia shows the origin of representation theory:

‘There is a natural connection, first discovered by Eugene Wigner, between the properties of particles, the representation theory of Lie groups and Lie algebras, and the symmetries of the universe. This postulate states that each particle “is” an irreducible representation of the symmetry group of the universe.’

As for gravity, Lee Smolin’s loop quantum gravity (an alternative to string) is also ignored by the string theory obsessed mainstream of theoretical high energy physics. Peter Woit describes what loop quantum gravity is about very clearly in Not Even Wrong:

‘In loop quantum gravity, the basic idea is to use the standard methods of quantum theory, but to change the choice of fundamental variables that one is working with. It is well known among mathematicians that an alternative to thinking about geometry in terms of curvature fields at each point in a space is to instead think about the holonomy [whole rule] around loops in space. The idea is that in a curved space, for any path that starts out somewhere and comes back to the same point (a loop), one can imagine moving along the path while carrying a set of vectors, and always keeping the new vectors parallel to older ones as one moves along. When one gets back to where one started and compares the vectors one has been carrying with the ones at the starting point, they will in general be related by a rotational transformation. This rotational transformation is called the holonomy of the loop. It can be calculated for any loop, so the holonomy of a curved space is an assignment of rotations to all loops in the space.’ – P. Woit, Not Even Wrong, Cape, London, 2006, p189.

When you look at Smolin’s lectures, Smolin sums the graphs of Penrose spin network interactions to yield a path integral quantum field theory which equals general relativity without a metric (ie, background independent).

Since Yang-Mills quantum field theories like the standard model involve the exchange of gauge bosons between charges to produce forces, and since gravitational charge will be mass, evidently the “loops” of Smolin’s theory are the loops created by gauge bosons being exchanged back and forward across spacetime between masses. There is a lot to be explored here, with many possibilities.

Instead of working on the standard model and gravity using these low-dimensional real modelling strategies, the stringers are wasting everybody’s time and money on speculation which is now known to be hopeless due to the cosmic landscape problem. Mainstream string theory is both a fad and a fallacy.

11. nc says:

Recent comment of mine to another blog

This is dealing with the difference in force coupling constant between electromagnetism and gravitation. This is different in several details from the discussion of this on my home page, which will be updated. Some of the changes in details are simplifications (maybe not all justified). The main increase in clarity is the strong association with the line of gauge boson shielding by mass (for the gravity mechanism) with the straight line summation of charges.

I should have started the comment as follows with an explanation of Dr Thomas Love’s demonstration that the wavefunction collapse assumption in quantum mechanics is a mathematical artefact of the switch over from time-dependent to time-independent forms of the Schroedinger equation when a measurement is taken:

http://electrogravity.blogspot.com/2006/03/thomas-r.html States: Love … compares the two versions of the Schroedinger equation on page 10 [of the preprint, ‘Towards an Einsteinian Quantum Theory’]. The time independent and time-dependent versions disagree and this disagreement nullifies the principle of superposition and consequently the concept of wavefunction collapse being precipitated by the act of making a measurement. The failure of superposition discredits the usual interpretation of the EPR experiment as proving quantum entanglement. To be sure, making a measurement always interferes with the system being measured (by recoil from firing light photons or other probes at the object), but that is not justification for the metaphysical belief in wavefunction collapse.’

http://electrogravity.blogspot.com/2006/03/copies-of-my-comments-to-dr-dantass.html states: Dr Thomas Love … preprint, “Towards an Einsteinian Quantum Theory”, where he shows that the superposition principle is a fallacy, due to two versions of the Schroedinger equation: a system described by the time-dependent Schroedinger equation isn’t in an eigenstate between interactions.

“The quantum collapse occurs when we model the wave moving according to Schroedinger (time-dependent) and then, suddenly at the time of interaction we require it to be in an eigenstate and hence to also be a solution of Schroedinger (time-independent). The collapse of the wave function is due to a discontinuity in the equations used to model the physics, it is not inherent in the physics.”

http://countiblis.blogspot.com/2005/11/universe-doesnt-really-exist.html

… At every instant, assuming the electrons have real positions and the indeterminancy principle is explained by ignorance of its position which is always real but often unknown – instead of by metaphysics of the type Bohr and Heisenberg worshipped – so you have a vector sum of electric fields possible across the universe.

The fields are physically propagated by gauge boson exchange. The gauge bosons must travel between ALL charges, they can tell that an atom is “neutral” as a whole, they just travel between the charges.

Therefore even though the electric dipole created by the separation of the electron from the proton in a hydrogen atom at any instant is randomly orientated, the gauge bosons can also be considered to be doing a random walk between all the charges in the universe.

The random-walk vector sum for the charges of all the hydrogen atoms is the voltage for a single hydrogen atom (the real charges mass in the universe is something like 90% composed of hydrogen), multiplied by the square root of the number of atoms in the universe.

This allows for the angles of each atom being random. If you have a large row of charged capacitors randomly aligned in a series circuit, the average voltage resulting is obviously zero, because you have the same number of positive terminals facing one way as the other.

So there is a lot of inefficiency, but in a two or three dimensional set up, a drunk taking an equal number of steps in each direction does make progress. The taking 1 step per second, he goes an average net distance from the starting point of t^0.5 steps after t seconds.

For air molecules, the same occurs so instead of staying in the same average position after a lot of impacts, they do diffuse gradually away from their starting points.

Anyway, for the electric charges comprising the hydrogen and other atoms of the universe, each atom is a randomly aligned charged capacitor at any instant of time.

This means that the gauge boson radiation being exchanged between charges to give electromagnetic forces in Yang-Mills theory will have the drunkard’s walk effect, and you get a net electromagnetic field of the charge of a single atom multiplied by the square root of the total number in the universe.

Now, if gravity is to be unified with electromagnetism (also basically a long range, inverse square law force, unlike the short ranged nuclear forces), and if gravity due to a geometric shadowing effect (see my home page for the Yang-Mills LeSage quantum gravity mechanism with predictions), it will depend on only a straight line charge summation.

In an imaginary straight line across the universe (forget about gravity curving geodesics, since I’m talking about a non-physical line for the purpose of working out gravity mechanism, not a result from gravity), there will be on average almost as many capacitors (hydrogen atoms) with the electron-proton dipole facing one way as the other,

BUT NOT QUITE THE SAME NUMBER!

You find that statistically, a straight line across the universe is 50% likely to have an odd number of atoms falling along it, and 50% likely to have an even number of atoms falling along it.

Clearly, if the number is even, then on average there is zero net voltage. But in all the 50% of cases where there is an ODD number of atoms falling along the line, you do have a net voltage. The situation in this case is that the average net voltage is 0.5 times the net voltage of a single atom. This causes gravity.

The exact weakness of gravity as compared to electromagnetism is now explained.

Gravity is due to 0.5 x the voltage of 1 hydrogen atom (a “charged capacitor”).

Electromagnetism is due to the random walk vector sum between all charges in the universe, which comes to the voltage of 1 hydrogen atom (a “charged capacitor”) multiplied by the square root of the number of atoms in the universe.

Thus, ratio of gravity strength to electromagnetism strength between an electron and a proton is equal to: 0.5V/(V.N^0.5) = 0.5/N^0.5.

V is the voltage of a hydrogen atom (charged capacitor in effect) and N is the number of atoms in the universe.

This ratio is equal to 10^-40 or so, which is the correct figure.

12. nc says:

Just found the original source I saw for the equivalence: E = mc^2 = mMG/R. It can be viewed as formula 1 on the page http://www.gravity.uk.com/galactic_rotation_curves.html

Unfortunately, that page states that the entire mass of the universe M is located at the horizon radius of the universe R = c/H. This is obviously wrong. The average radius of the mass of the universe is less than c/H for various physical reasons.

For one thing, the observerable mass is located between us and c/H. It is therefore absurd to use a radius of c/H for it.

A second problem is that, whatever gauge bosons (gravitons??) are responsible for quantum gravity, they will have presumably have a de Broglie wavelength which will be REDSHIFTED by the cosmological expansion, reducing the coupling constant drastically wherever visible light redshifts are severe. This effect is ignored by the maths in general relativity and other cosmological models, and because it is ignored, the real effects from gravity gauge boson redshift in the data leads to ad hoc modifications or ‘epicycles’ which are false (such as dark energy models).

I take account of this effect dynamically in working on the mechanism for gravitation by exchange of radiation which causes force, and this gives me a way to work out the right dimensionless correction factor for distance R. Basically it is a factor of e^3 ~ 20. See http://feynman137.tripod.com/#h for gauge boson mechanism and prediction of G, which gives a formula which can be directly compared to that above.

My understanding of the dynamics for equating particle energy with gravitational potential energy is very simple. Physically, in the August 2002 Electronics World issue, the model is put forward that a fermion is a trapped energy current: gravity traps it (gravity is weak on large scales, but because of the inverse square law it becomes strong enough on small scales). This suggests that the orbital kinetic energy of the particle is exactly equal to its gravitational potential energy with respect to the universe. If the particle’s forward-directed (spin direction) kinetic energy of spin was greater than the gravitational energy confining it, then spin would not be a closed loop but would instead be a spiral outwards and fermions would grow in size; if the gravitational potential energy were bigger than the forward kinetic energy, then the particle would spiral inwards as gravity collapsed it. Hence there is an equilibrium which explains E = mc^2 = mMG/R physically, as long as you take a physically meaningful value for R based on the gravity mechanism. R is not equal to the radius of the universe, but is considerably smaller due to the mass distribution and the redshift dynamics (which cut off contributions to gravitational potential from the furthest distances, because the gravitons exchanged over such massive expanding distances are too far red-shifted to have the energy to contribute anything).

The New Scientist advertisement that Hunter published was semi-anonymous, giving as name only “The Gravity Group” and an address in Huddersfield to write to if interested. However the root of his page above is http://www.gravity.uk.com/ which is signed John Hunter.

The root page also states: “Conjecture: The attractive gravitational mass of an object varies, depending on the proximity of other matter, in order to keep its total gravitational potential energy equal to its rest mass.

“As the earth’s distance to the sun varies, the strength of the earth’s gravity would vary over a year – causing an annual 6cm variation of the moons orbit around the earth. This effect may have been measured by lunar laser ranging. If the conjecture is true, LISA (the space based gravitational wave detector) may be able to detect solar oscillations, which would change the sun’s gravitational mass.

“The shape of ‘galactic rotation curves’ may be explained by the conjecture.”

Although John Hunter’s equivalence E = mc^2 = mMG/R is a very important line of investigation, and some of his tests (such as the above) may bear fruit if anyone will listen, I disagree with his cosmological ideas: http://www.gravity.uk.com/cosmological_model.html

“In this model not only is space expanding, but the size of material objects is increasing too. This expansion is called rescaling to emphasis that, in this model, all length dimensions increase uniformly, i.e. the size of people, atoms, stars, distance between all objects – all these lengths increase uniformly according to dL/L = H.dt … giving L = L_o .e^(Ht).”

In addition to this weird idea that length grows exponentially, he thinks the speed of light and force vary in proportion to length, while his scaling tells him that energy and Planck’s constant increase by a faster exponent, e^(2Ht), and the universal gravitational constant G varies faster still, as e^(3Ht). In his model he has mass and the Hubble parameter remaining constant.

All his exponential scaling laws are wrong, as is the claim that the Hubble parameter is constant. The Hubble parameter is actually equal to 1/(age of universe) according to the way the universe is observed to be expanding at great distances (no net deceleration due to gravity, ie, any gravitational deceleration which exists – probably none at all because gravitons will be redshifted severely over cosmological sized distances and therefore expansion redshifts will negate long range gravitational retardation forces – is exactly offset by some kind of acceleration/dark energy), or it is equal to (2/3)/(age of universe) if you insist on ignoring observations and assuming that the Friedmann (gravitationally decelerating) solution to GR be accepted without a cosmological constant.

Therefore the Hubble parameter falls off inversely with time, whereas Hunter assumes it is constant and then has to vary lots of other things. This is all unphysical junk and the error he makes that the Hubble parameter is constant is nonsense (like string theory, it is mathematics disconnected too far from both physical evidence and physical mechanism).

The Hubble parameter H comes from v = Hr, where v is recession velocity and r is apparent distance of galaxy cluster or supernova giving the redshifted light.

The limiting velocity v is obviously c, so c = Hr where r is the limiting observable horizon radius of the universe, which ignoring gravitational deceleration is: r = ct where t is age of universe (with critical density gravitational deceleration and zero cc it would be r = 2ct/3). Therefore: H = c/r = c/(ct) = 1/t. This PROVES that the Hubble parameter H is falling with time and is not constant. (H is only a constant in the sense v/r = H where r is observable distance of galaxies receding from us at velocity v in the spacetime we observe where we observe increasing time past with increasing distance due to the travel time of the light coming to us.)

Going back to the page http://www.gravity.uk.com/galactic_rotation_curves.html Hunter makes some FAR more useful suggestions than his false cosmological scaling factor speculations:

“For a mass as big as a galaxy equation {E = mc^2 = mMG/R} should be amended to E = mc^2 = (mMG/R) + (m^2)G/r

“m = mass of galaxy within radius r

“giving

“G = c^2 /[ (M/R) + (m/r) ].”

Because M/R is a constant, this is a very important formula. However, I think R is not the true radius of the universe but needs a fairly large correction factor (correction factor of e^3 as explained earlier. With this correction, however, Hunter’s formula: “predicts a reduction in the effective gravitational constant for masses of high m / r ratio.”
This looks like good physics to me:

“For ‘ordinary’ masses the m / r ratio is insignificant compared to (c^2)/G, but for galaxies it is significant.

For a star orbiting a galaxy at radius r, with m being the mass of the galaxy within radius r,

“a = (v^2)/r = Gm/r^2

“v^2 = Gm/r

“So stars moving at a constant velocity at different radii means a constant m / r ratio.

“Equation {G = c^2 /[ (M/R) + (m/r) ]} predicts this constant ratio in the following way. For any given radius r, if the mass within this radius is such that the m / r value is higher than an average value (k), then the effective gravitational constant is lowered. This allows rotating matter to drift away from the centre, thus reducing the m / r ratio at this radius.

“If m / r {is smaller than} k (for any given radius r) then the effective gravitational constant is higher than average attracting more matter to within this radius, increasing the m / r ratio at this radius.

“In this way a constant m / r ratio for spiral galaxies can be maintained for different r, resulting in the constant velocity of stars and the flat shape of the rotation graphs.

“A reduction in the value of G at the centre of galaxies, equation {G = c^2 /[ (M/R) + (m/r) ]}, may lead to the phenomenon of active galactic nuclei and the emergence of jets.”

I have replaced Hunter’s equation 5 (which I disagree with because of his interpretation of distance R) with {G = c^2 /[ (M/R) + (m/r) ]} in the quotations above.

Here, R represents an effective distance obtained by normalizing the E = mc^2 = mMG/R to the gravity mechanism result at http://feynman137.tripod.com/#h

Hunter is probably correct in his solution of the galactic rotation problem, because his arguments are relatively strong both logically in his derivation and in terms of the results agreeing with experimental facts.

13. Pingback: Gravity
14. I don’t like Lubos Motl, but I agree with him here that the physics above is not even wrong.

15. nc says:

Dr Sarfatti, it isn’t a question of liking Lubos Motl, it’s a question of making checkable predictions. The physics above is making checkable predictions, which is a level better than the “not even wrong” (unpredictive) string theory which Lubos Motl hypes. Sadly, Louise Riofrio’s particular solution of varying velocity of light is likely the wrong one, and G increases with time instead (the usual objection to G rising being false since it assumes that the ratio of gravity to electromagnetic force coupling constant varies with G, instead of both forces remaining in the same ratio due to unification dynamics). You need to be a little more objective and precise about what you disagree with, please. There is a list of steps each based on well established physics, and if you dismiss them all it makes you look as if you are … well, as if you are not being scientific. The same equation comes from a gravitational mechanism: http://quantumfieldtheory.org/Proof.htm

16. nc says:

“In case people are wondering what alexis is referring to, in his latest posting, in the middle of supposedly explaining what is wrong with a list of achievements of LQG, Lubos includes a photo from the website of Louise Riofrio. The photo shows her with an impressive lizard. … trying to humiliate her … In his comment section he and his commenters speculate on which is Riofrio, the woman in the picture or the lizard, with Lubos explaining that he had thought of using a picture of her with a monkey, to better make the point.

“The guy is just completely grotesque and subhuman, it’s amazing that anyone takes him seriously.”

17. nc says:

Copy of a comment:

Louise has a new post showing that the person behind this latest attack is at Cornell, and he seems to be upset that Louise tried posting papers on arXiv. The previous time (last June) the critic was Dr Motl, and Dr Woit really fell out with him over his sexism, rudeness, etc.

I wrote a post showing that Louise’s GM = tc^3 far from being completely unphysical is really obtained simply:

Simply equate the rest mass energy of m with its gravitational potential energy mMG/R with respect to large mass of universe M located at an average distance of R = ct from m.

Hence E = mc^2 = mMG/(ct)

Cancelling and collecting terms,

GM = tc^3

So Louise’s formula is derivable.

The rationale for equating rest mass energy to gravitational potential energy in the derivation is Einstein’s principle of equivalence between inertial and gravitational mass in general relativity (GR), when combined with special relativity (SR)equivalence of mass and energy!

(1) GR equivalence principle: inertial mass = gravitational mass.

(2) SR equivalence principle: mass has an energy equivalent.

(3) Combining (1) and (2):

inertial mass-energy = gravitational mass-energy

(4) The inertial mass-energy is E=mc^2 which is the energy you get from complete annihilation of matter into energy.

The gravitational mass-energy is is gravitational potential energy a body has within the universe. Hence the gravitational mass-energy is the gravitational potential energy which would be released if the universe were to collapse. This is E = mMG/R with respect to large mass of universe M located at an average distance of R = ct from m.

I wrote several follow up posts about this because as a result of my post, Dr Thomas S. Love of the Departments of Mathematics and Physics, California State University, emailed me a derivation of Kepler’s law based on the similar reasoning of equating the relevant energy equations! See for example

https://nige.wordpress.com/2006/09/30/keplers-law-from-kinetic-energy/

When I explained all the above in a blog discussion on alternatives to string theory, I think it was one of the discussions at Asymptotia run by Professor Clifford V. Johnson (who is the most friendly and reasonable of the string theorists, I think), Professor Jacques Distler of the University of Texas ridiculed it because it didn’t use tensor calculus or something irrelevant.

I’m sympathetic with people who want alternatives to do an enormous amount and prove G = 8*Pi*T and SU(3)xSU(2)xU(1), but what these censors are doing is driving the early development of alternative ideas underground, minimising the number of people working on them, and generating a lot of needless heat and hostility. I’ve rarely seen a critic make a genuine scientific point, but whenever they do, these points are taken seriously and addressed carefully.

It’s all in Machiavelli’s description of human politics:

“… the innovator has for enemies all those who have done well under the old conditions, and lukewarm defenders in those who may do well under the new. This coolness arises partly from fear of the opponents, who have the laws on their side, and partly from the incredulity of men, who do not readily believe in new things until they have had a long experience of them. Thus it happens that whenever those who are hostile have the opportunity to attack they do it like partisans, whilst the others defend lukewarmly …”

That’s the mechanism by which new ideas traditionally have to struggle against those who are happy with the hype of string theory and the lambda-CDM ad hoc cosmology.

Some of the comments Clifford made recently on Asymptotia in trying to defend string theory by saying it is incomplete made me very upset. There is serious hypocrisy, and string theorists themselves just can’t see it:

“… this is an ongoing research program on a still rather underdeveloped theory. … how come you are willing to pre-suppose the outcome and discard all the work that is going on to understand and better develop string theory in so many areas? This is especially puzzling since you mention that lack of understanding.
How can you on the one hand claim that a theory is poorly understood, and then in the same breath condemn it as unworkable before it is understood?”
Clifford

They just can’t understand that mainstream string theory ideas that fail to make really checkable predictions can’t be defended like this, because mainstream pro-string censors (not Clifford, admittedly) go out of their way to attack alternatives like LQG for being incomplete, not to mention Louise’s theory.

(BTW, sorry this is a such a long comment, I’ll copy it to my blog so you are free to delete, if it’s clutter.)

18. nc says:

Two ways to get GM = tc^3:

(1)

Consider why the big bang was able to happen, instead of the mass being locked by gravity into a black hole singularity and unable to expand!

This question is traditionally answered (Prof. Susskind used this in an interview about his book) by the fact the universe simply had enough outward explosive or expansive force to counter the gravitational pull which would otherwise produce a black hole.

In order to make this explanation work, the outward acting explosive energy of the big bang, E = Mc^2, had to either be equal to, or exceed, the energy of the inward acting gravitational force which was resisting expansion.

This energy is the gravitational potential energy E = MMG/R = (M^2)G/(ct).

Hence the explosive energy of the big bang’s nuclear reactions, fusion, etc., E = Mc^2 had to be equal or greater than E = (M^2)G/(ct):

Mc^2 ~ (M^2)G/(ct)

Hence

MG ~ tc^3.

That’s the first way, and perhaps the easiest to understand.

(2)

Simply equate the rest mass energy of m with its gravitational potential energy mMG/R with respect to large mass of universe M located at an average distance of R = ct from m.

Hence E = mc^2 = mMG/(ct)

Cancelling and collecting terms,

GM = tc^3

So Louise’s formula is derivable.

The rationale for equating rest mass energy to gravitational potential energy in the derivation is Einstein’s principle of equivalence between inertial and gravitational mass in general relativity (GR), when combined with special relativity (SR)equivalence of mass and energy!

(1) GR equivalence principle: inertial mass = gravitational mass.

(2) SR equivalence principle: mass has an energy equivalent.

(3) Combining (1) and (2):

inertial mass-energy = gravitational mass-energy

(4) The inertial mass-energy is E=mc^2 which is the energy you get from complete annihilation of matter into energy.

The gravitational mass-energy is is gravitational potential energy a body has within the universe. Hence the gravitational mass-energy is the gravitational potential energy which would be released if the universe were to collapse. This is E = mMG/R with respect to large mass of universe M located at an average distance of R = ct from m.

19. nc says:

copy of a comment to

http://riofriospacetime.blogspot.com/2007/03/t-minus-3-days-conference-opening.html

I just looked up the blog post mentioned in the previous comment and the comments are shut down, preventing any response.

Tony Smith kindly quoted a little bit I wrote saying something like “the total gravitational potential energy of the universe is on the order E = MMG/R = MMG/(ct), which when equated to E=Mc^2 gives Louise’s equation”

However, this was then dismissed by another comment from somebody else, who did not go back and check my comment on the other blog. The point is, I also have a lot more justification, such as the reason why you need to equate the gravitational energy with the rest mass energy.

Consider a star. If you had a star of uniform density and radius R, and it collapsed, the energy release from gravitational potential energy being turned into explosive (kinetic and radiation) energy is E = (3/5)(M^2)G/R. The 3/5 factor from the integration which produces this result is not applicable to the universe where the density rises with apparent distance because of spacetime (you are looking to earlier, more compressed and dense, epochs of the big bang when you look to larger distances). It’s more sensible to just remember that the gravitational potential energy of mass m located at distance R from mass M is simply E = mMG/R so for gravitational potential energy of the universe is similar, if R is defined as the effective distance the majority of the mass would be moving if the universe collapsed.

This idea of gravitational potential energy shouldn’t bee controversial: in supernovae explosions much energy comes from such an implosion, which turns gravitational potential energy into explosive energy!

Generally, to overcome gravitational collapse, you need to have an explosive outward force.

The universe was only able to expand in the first place because the explosive outward force, provided by kinetic and radiation energy, which counteracted the gravitational force.

Initially, the entire energy of the radiation was present as various forms of radiation. Hence, to prevent the early universe from being contracted into a singularity by gravity, we have the condition that E = Mc^2 = (M^2)G/R = (M^2)G/(ct) which gives GM = tc^3.

****************

My earlier comment:

Two ways to get GM = tc^3:

(1)

Consider why the big bang was able to happen, instead of the mass being locked by gravity into a black hole singularity and unable to expand!

This question is traditionally answered (Prof. Susskind used this in an interview about his book) by the fact the universe simply had enough outward explosive or expansive force to counter the gravitational pull which would otherwise produce a black hole.

In order to make this explanation work, the outward acting explosive energy of the big bang, E = Mc^2, had to either be equal to, or exceed, the energy of the inward acting gravitational force which was resisting expansion.

This energy is the gravitational potential energy E = MMG/R = (M^2)G/(ct).

Hence the explosive energy of the big bang’s nuclear reactions, fusion, etc., E = Mc^2 had to be equal or greater than E = (M^2)G/(ct):

Mc^2 ~ (M^2)G/(ct)

Hence

MG ~ tc^3.

That’s the first way, and perhaps the easiest to understand.

(2)

Simply equate the rest mass energy of m with its gravitational potential energy mMG/R with respect to large mass of universe M located at an average distance of R = ct from m.

Hence E = mc^2 = mMG/(ct)

Cancelling and collecting terms,

GM = tc^3

So Louise’s formula is derivable.

The rationale for equating rest mass energy to gravitational potential energy in the derivation is Einstein’s principle of equivalence between inertial and gravitational mass in general relativity (GR), when combined with special relativity (SR)equivalence of mass and energy!

(1) GR equivalence principle: inertial mass = gravitational mass.

(2) SR equivalence principle: mass has an energy equivalent.

(3) Combining (1) and (2):

inertial mass-energy = gravitational mass-energy

(4) The inertial mass-energy is E=mc^2 which is the energy you get from complete annihilation of matter into energy.

The gravitational mass-energy is is gravitational potential energy a body has within the universe. Hence the gravitational mass-energy is the gravitational potential energy which would be released if the universe were to collapse. This is E = mMG/R with respect to large mass of universe M located at an average distance of R = ct from m.

****************

What’s interesting is that the mainstream doesn’t want to discuss science when it comes to alternatives, as Tony Smith makes clear in his discussion of censorship.

They use ad hominem attacks, which is a lazy approach whereby no careful science or disciplined checks are involved. The mainstream however objects if ad hominem attacks are used against it’s leaders. For example, Dr Ed Witten – M-theory creator – was misleading when he claimed:

‘String theory has the remarkable property of predicting gravity.’ – Dr Edward Witten, M-theory originator, Physics Today, April 1996.

Dr Peter Woit remarks that the prediction is just a prediction of an unobservable spin-2 graviton and not a prediction of anything to do with gravity that is either already experimentally verified or checkable in the future:

‘There is not even a serious proposal for what the dynamics of the fundamental ‘M-theory’ is supposed to be or any reason at all to believe that its dynamics would produce a vacuum state with the desired properties. The sole argument generally given to justify this picture of the world is that perturbative string theories have a massless spin two mode and thus could provide an explanation of gravity, if one ever managed to find an underlying theory for which perturbative string theory is the perturbative expansion.’ – Quantum Field Theory and Representation Theory: A Sketch (2002), http://arxiv.org/abs/hep-th/0206135

If you call mainstream M-theory hypers ‘liars’, ‘charlatans’, ‘crackpots’, etc., you find that you are then accused of being a ‘science hater’. So they don’t like criticism.

To give credit where due, Dr Ed Witten published a letter in Nature, Nature, Vol 444, 16 November 2006, stating:

‘The critics feel passionately that they are right, and that their viewpoints have been unfairly neglected by the establishment. … They bring into the public arena technical claims that few can properly evaluate. … Responding to this kind of criticism can be very difficult. It is hard to answer unfair charges of élitism without sounding élitist to non-experts. A direct response may just add fuel to controversies.’

So Dr Ed Witten at least doesn’t encourage attacks on critics, he just prefers to ignore them. Maybe this is worse for critics with alternative ideas, however, where the choice is controversy or being ignored altogether.

But the mainstream as a whole does go far out of its way to use ad hominem attacks on alternatives, hence Lubos Motl’s attacks, and many others.

20. nc says:

One new idea which occurs to me: the two types of derivation in the above comment could be combined to prove one or the other. If you can take the first type of derivation as experimentally sound, for example, then that would allow you to theoretically derive Einstein’s equivalence principle between inertial and gravitational mass.

21. nc says:

copy of a comment:

http://dorigo.wordpress.com/2007/03/29/confused/#comment-31696

3. nc – March 29, 2007

Regarding Louise Riofrio’s GM = tc^3:

Consider a star. If you had a star of uniform density and radius R, and it collapsed, the energy release from gravitational potential energy being turned into explosive (kinetic and radiation) energy is E = (3/5)(M^2)G/R. The 3/5 factor from the integration which produces this result is not applicable to the universe where the density rises with apparent distance because of spacetime (you are looking to earlier, more compressed and dense, epochs of the big bang when you look to larger distances). It’s more sensible to just remember that the gravitational potential energy of mass m located at distance R from mass M is simply E = mMG/R so for gravitational potential energy of the universe is similar, if R is defined as the effective distance the majority of the mass would be moving if the universe collapsed.

This idea of gravitational potential energy shouldn’t bee controversial: in supernovae explosions much energy comes from such an implosion, which turns gravitational potential energy into explosive energy!

Generally, to overcome gravitational collapse, you need to have an explosive outward force.

The universe was only able to expand in the first place because the explosive outward force, provided by kinetic and radiation energy, which counteracted the gravitational force.

Initially, the entire energy of the radiation was present as various forms of radiation. Hence, to prevent the early universe from being contracted into a singularity by gravity, we have the condition that E = Mc^2 = (M^2)G/R = (M^2)G/(ct) which gives GM = tc^3.

****************

Comparison of two ways to get GM = tc^3:

(1)

Consider why the big bang was able to happen, instead of the mass being locked by gravity into a black hole singularity and unable to expand!

This question is traditionally answered (Prof. Susskind used this in an interview about his book) by the fact the universe simply had enough outward explosive or expansive force to counter the gravitational pull which would otherwise produce a black hole.

In order to make this explanation work, the outward acting explosive energy of the big bang, E = Mc^2, had to either be equal to, or exceed, the energy of the inward acting gravitational force which was resisting expansion.

This energy is the gravitational potential energy E = MMG/R = (M^2)G/(ct).

Hence the explosive energy of the big bang’s nuclear reactions, fusion, etc., E = Mc^2 had to be equal or greater than E = (M^2)G/(ct):

Mc^2 ~ (M^2)G/(ct)

Hence

MG ~ tc^3.

That’s the first way, and perhaps the easiest to understand.

(2)

Simply equate the rest mass energy of m with its gravitational potential energy mMG/R with respect to large mass of universe M located at an average distance of R = ct from m.

Hence E = mc^2 = mMG/(ct)

Cancelling and collecting terms,

GM = tc^3

So Louise’s formula is derivable.

The rationale for equating rest mass energy to gravitational potential energy in the derivation is Einstein’s principle of equivalence between inertial and gravitational mass in general relativity (GR), when combined with special relativity (SR)equivalence of mass and energy!

(1) GR equivalence principle: inertial mass = gravitational mass.

(2) SR equivalence principle: mass has an energy equivalent.

(3) Combining (1) and (2):

inertial mass-energy = gravitational mass-energy

(4) The inertial mass-energy is E=mc^2 which is the energy you get from complete annihilation of matter into energy.

The gravitational mass-energy is is gravitational potential energy a body has within the universe. Hence the gravitational mass-energy is the gravitational potential energy which would be released if the universe were to collapse. This is E = mMG/R with respect to large mass of universe M located at an average distance of R = ct from m.

Analysis of what GM = tc^3 implies:

If you look at GM = tc^3, you see ‘problems’ right away. The inclusion of time on the right hand side implies that there is some variation with time of something else there, G, M, or c.

Louise has investigated the assumption that c is varying while GM remains constant. This tells her that c would need to fall with the inverse cube-root of the age of the universe. She has made studies on this possibility, and has detailed arguments.

I should mention that I’ve investigated the situation that c doesn’t vary, but that G increases in direct proportion to t. This increase of G is the opposite of Dirac’s assumption (he thought G may decrease with time, and was initially higher, a claim refuted by Teller who pointed out the fusion rate dependence on G which would have made the sun’s power boil the oceans during the Cambrian era, which clearly didn’t occur). G variation actually doesn’t affect fusion in starts or the big bang, because electromagnetism would vary in a similar way. Fusion depends on protons approaching close enough due to gravity-caused compression to overcome the Coulomb repulsion, so that the strong force can attract them together. If you vary both gravity and electromagnetism in the same way (in a theory unifying gravity with the standard model) you end up with no affect on the fusion rate: the increased gravity from bigger G doesn’t increase fusion because coulomb repulsion is also increased! Hence, variations in G doesn’t affect fusion in stars or the big bang.

Smaller G in the past doesn’t therefore upset the basic big bang model. What it does do is to explain why the ripples in the cosmic background radiation are so small: they are small because G is small, not because of inflation.

So this is another aspect of Louise’s equation GM = tc^3. It could turn out that something else like G is varying, not c. One more thing about this, some theoretical calculations I did suggest that there is a dimensionless constant equal to e^3 (the cube of the base of natural logs), due to quantum gravity effects of exchange radiation in causing gravitation. Basically, the exchange radiation travels at light velocity in spacetime (it doesn’t travel instantly), so the more distant universe is of higher density (being seen further in the past, and earlier in time after big bang, hence more compressed). Hence, gravity is affected by this apparently increasing density at great spacetime distances. Another factor stops this effect from going toward infinity at the greatest distances: redshift. Gauge bosons should get stretched out (redshifted in frequency) by expansion, so the energy they carry E=hf, decreases. Great redshift offsets the increasing strength of gravitational exchange radiation due to the density going towards infinity as you look to great distances.

This effects is easily calculated, and the result is G = ¾(H^2)/(Pi * Rho * e^3), which is a factor of (e^3)/2 or approx. 10 times smaller than the value implied by a critical density in pre-1998 cosmology (no cc), where you can rearrange critical density to give G = 3(H^2)/(8 * Pi * Rho).

This means that Louise’s equation becomes:

GMe^3 = tc^3.

The dynamics resolve the dark matter problem. I’m writing a paper on this. Previously I’ve had published 10 pages on it in the August 2002 and April 2003 issues of Electronics World because the mechanism for the gravity exchange radiation is linked to that for electromagnetism, but I’d like to try again to get a paper in Classical and Quantum Gravity. The editor of Classical and Quantum Gravity had my last submission refereed by a string theorist in who ignored the science and just said it didn’t fit into the mainstream speculation. (The editor of Classical and Quantum Gravity forwarded me the referee’s report, without giving the name of the referee: it was evident from the report that the referee would be happier if the paper was within string theory’s framework, which is why I suspect he/she is a string theorist.)

22. nc says:

copy of comment:

http://riofriospacetime.blogspot.com/2008/02/explorer.html

Louise,

I’d like to revisit the following scientific points:

1. There’s a lot of mass (galaxies, etc.) almost isotropically distributed around us in the universe. (I don’t think anyone disputes that.)

2. If it wasn’t receding, i.e., if it was static and nothing was keeping it there, from our reference frame it might be expected to collapse (we’d see it falling towards us).

3. The collapse would turn gravitational potential energy into kinetic energy of material coming together.

4. The average distance matter would fall would be some fraction of the radius of the universe, say half the radius of the universe for a very rough first approximation.

5. The argument used to get the potential energy of the universe can be compared to a collapsing star. If you had a star of uniform density and radius R, and it collapsed, the energy release from gravitational potential energy being turned into explosive (kinetic and radiation) energy is E = (3/5)(M^2)G/R. The 3/5 factor from the integration which produces this result is not applicable to the universe where the density rises with apparent distance because of spacetime (you are looking to earlier, more compressed and dense, epochs of the big bang when you look to larger distances). It’s more sensible to just remember that the gravitational potential energy of mass m located at distance R from mass M is simply E = mMG/R. In a supernova explosion, the gravitational collapse of distributed matter releases energy.

The gravitational potential energy released in the collapse would be on the approximate order of magnitude

E = (M^2)G/r = (M^2)G/(ct)

where t is age of universe, where r is the average distance the matter falls before it hits other matter.

6. The gravitational field energy needed to keep this from occurring is therefore a similar amount of expansion kinetic energy:

E = Mc^2.

The relativistic equation for total energy is:

E = Mc^2

where M is the actual mass (which is a function of velocity), and

E = M_0 c^2 (1 – v^2 /c^2)^(-1/2)

where M_0 is the rest mass (not the actual mass), because

M = M_0 (1 – v^2 /c^2)^(-1/2).

Since by the equivalence principle inertial mass (which increases with velocity by the formula just given) is equivalent to gravitational mass, it is the true mass M not the rest mass M_0 which we need to consider.

Hence

E = Mc^2

is the formula to use.

Since the energy of the big bang E = Mc^2 caused the expansion (against inertial and gravitation) in the first place, it must be at least equal to the approximate gravitational potential energy E = (M^2)G/(ct), or the universe wouldn’t have been able to expand in the first place because it would have become a black hole (Professor Susskind, in an interview about his book “The Cosmic Landscape” argued that the universe simply had enough outward explosive or expansive force to counter the gravitational pull which would otherwise have turned it into a black hole). So:

Mc^2 {is greater than or equal to} M^2G/(ct)

Hence at least as an approximation:

tc^3 = MG.

What part of the above “derivation” is wrong?

It’s pretty straightforward.

Let’s take a serious look at a comment which was abusively attacking my competence on 29 March 2007 by an anonymous commentator using the name “Guess Who” on Tommaso Dorigo’s blog (the same comment was copied that day to a posting on Mahndisa’s blog after she wrote after ignoring the content of a comment of mine: “We have gone over this already. You are not applying the equations correctly. The conclusions are incorrect due to a misapplication of physical law. See my comments above. I am turning comments off for this.” She then quoted the “Guess Who” comment I’m about to discuss as alleged evidence of my incompetence: “You are not defending science; you are defending misguided and incompetently performed calculations, which I cannot abide.”).

The “Guess Who” comment made a long series of ignorant claims, so let’s go through them all:

“You are using the expression for rest mass. That means literally mass at rest in some reference frame. But you know that the early universe was radiative: all particles were moving randomly and very close to the speed of light, so almost all their energy was in the momentum (p) part of the full expression E = sqrt((p*c)^2 + (m*c^2)^2). Because of the randomness, there was no reference frame in which p = 0.”

This is wrong, because the relativistic equation for energy only includes momentum where it is written in terms of rest mass. If you are dealing with the actual mass, which increases with velocity, which is what we’re concerned with, the E = Mc^2. So this person doesn’t know that the relativistic correction applies to rest masses (which are imaginary in practice, becauses masses are in motion and the energy of their motion adds to their mass!).

“> the gravitational potential energy E = MMG/R = (M^2)G/(ct).

Most quantities which you put in this expression are ill- or un-defined.”

I don’t think that energy, mass G, radius, c and t are ill-defined. The person just needs to bother to read the definitions.

“In general relativity, which you must (and claim to) use in this context, energy does not stand alone as a separately conserved quantity: it’s just one component of the 4×4 energy-momentum tensor.”

I know the 16 component energy-momentum tensor: it has components for energy density, energy flux, momentum density, momentum flux, pressure and vicosity. All of these quantities get translated into energy density. You can measure energy many ways, and all energy contributes to gravitation. For our purposes, the rest-mass energy of the universe includes all of these contributions.

“Your M is supposed to be the rest mass of the universe, which is neither at rest nor, to the best of our knowledge, finite. So you have an infinity squared there.”

No, M is the mass of the universe, which depends on velocity, M_0 is rest mass. (In any case, unless v is a significant fraction of c, the difference between M and M_0 is not major. You don’t know what you’re talking about. You’re just playing with things you don’t understand: physics concepts can always be extended to include more and more correction factors for known, factual physical processes. That’s not the issue. What’s the issue is whether the basic concepts are right. They are in this case.)

“Your R = c*t looks like it could be the Hubble radius (up to some factor of order unity, e.g. 2 in a radiative universe) but you say that it’s “defined as the effective distance the majority of the mass would be moving if the universe
collapsed”. Excuse me, but that would make R = 0.”

No, if the majority of the universe had zero distance to move if the universe collapsed, it would be here already. It isn’t. It’s at a great distance, and would have a fraction of the radius of the universe to fall to reach here.

“So, you are equating an incorrect expression for an ill-defined E with an undefined quantity containing a square of an ill-defined, presumably infinite M divided by 0.”

Wrong, E, M and the distance have all be precisely defined. In the case of the fall distance, the details are complex due to quantum gravity effects and density variation with distance/time past (see my calculations on my blog) and we’re using an approximation here just to get the basic principle across. The mass of the surrounding universe is located between radii of 0 to R where R = ct. This is because, as discovered by Perlmutter in 1998, gravity isn’t causing the universe to decelerate, so the old Friedmann solution to general relativity for the scale factor or effective radius of the universe, R = (2/3)ct is false; the (2/3) factor came from gravitation and this solution from Robertson/Walker/Friedmann’s metric is wrong empirically. The Hubble expansion rate shows that the gravitational deceleration is not occurring at that rate. Quantum gravity suggests that the reason is that gravitons exchanged between receding masses are redshifted to lower energy, reducing the effective gravitational coupling constant over cosmologically large distances, although the mainstream solution is to ignore quantum gravity, assuming that general relativity needs to instead be supplemented by dark energy to provide repulsion that over cosmologically large distances offsets the attractive force of gravity.

“General relativity fully contains special relativity. To do serious cosmology, you need to solve the equations of general relativity. You are not doing that.”

No, [special relativity] is incompatible with general relativity because it is a generally covariant theory and special relativity isn’t, and if you don’t believe me, try reading some papers on general relativity by someone called Albert Einstein:

‘The special theory of relativity … does not extend to non-uniform motion … The laws of physics must be of such a nature that they apply to systems of reference in any kind of motion. … The general laws of nature are to be expressed by equations which hold good for all systems of co-ordinates, that is, are co-variant with respect to any substitutions whatever (generally co-variant).’ – Albert Einstein, ‘The Foundation of the General Theory of Relativity’, Annalen der Physik, v49, 1916 (italics are Einstein’s own).

‘But … the general theory of relativity cannot retain this [SR] law. On the contrary, we arrived at the result according to this latter theory, the velocity of light must always depend on the coordinates when a gravitational field is present.’ – Albert Einstein, Relativity, The Special and General Theory, Henry Holt and Co., 1920, p111.

‘Special relativity was the result of 10 years of intellectual struggle, yet Einstein had convinced himself it was wrong within two years of publishing it. He rejected his theory, even before most physicists had come to accept it, for reasons that only he cared about. For another 10 years, as the world of physics slowly absorbed special relativity, Einstein pursued a lonely path away from it.’ – Einstein’s Legacy – Where are the “Einsteinians?”, by Lee Smolin, http://www.logosjournal.com/issue_4.3/smolin.htm

“Again ill-defined. But let’s say you take the standard FRW solutions of Einstein’s equations, put yourself in the comoving frame and compute the gravitational potential of a test particle according to your prescription. Since the FRW solutions are isotropic, your result will = 0. So now you’re saying that taking the square of an ill-defined, presumably infinite M and dividing by 0 yields 0.”

This is just trash. The FRW solutions to general relativity wrong by observation, and adding an epicycle in effect by unobserved dark energy, ignores graviton redshift energy degradation in quantum gravity.

Since gravitons will be redshifted towards zero energy as redshift goes towards infinity (recession velocities approaching c), there can be no “curvature” on the largest distance scales in the universe. Hence, apart form Perlmutter’s actual observations of no gravitational deceleration using automated CCD telescope observations of supernovas, quantum gravity itself tells you that general relativity is wrong when applied to cosmology, i.e. massive distances in an expanding universe.

A lot of personally-directed, ignorant, abusive garbage directed towards me follows in the comment which I need not quote here because it is just a list of quotes of me followed by sneers which ignore my work.

I’ll copy this to my blog, because I think it is a useful defense of the conceptual derivation of tc^3 = MG, and Mahndisa has closed the comments section on the relevant post on her blog, preventing any response being made there. I don’t agree with everything you suggest(I’ve investigated changes in G rather than c), but I agree with the general concept tc^3 = MG.

What’s interesting is that there are lots of other physicists around who could be investigating this critically and checking it.

I think that there should be a lot more support for people like Dr Peter Woit who standing up against the hypocrisy of physically vacuous mainstream M-theory which predicts nothing and is “not even wrong”. Dr Lee Smolin too, although in his case he’s been accused (unfairly) of being critical of the mainstream in order to get attention for his own ideas which are maybe not immensely better than string theory (although Smolin’s “doubly special relativity” does make some predictions than may be tested).

One interesting thing I’ve mentioned is the fact that general relativity is a failure at describing cosmology scientifically. There’s no curvature on cosmologically large scales (e.g., the scale of the universe or its effective radius) indicated by observations of redshifts. It also won’t occur theoretically, if quantum gravity involves exchange of gravitons between receding masses, because those gravitons will be received with lower energy due to the recession of gravitational charges in the universe.

I think from memory that the two critics of all this stuff have been Professor Distler commenting using his actual name on Professor Johnson’s Asymptotia blog, both people working on mainstream string theory, and “Guess Who”. Neither of them have come up with any physical discussion at all, if we discount the false claims by “Guess Who” and the claim by Distler that tensors are needed. Anyone can take tc^3 = MG and put into into a tensor field equation simply by writing it as a definition of G = (tc^3)/M and putting that into Einstein’s field equation. However, the equation tc^3 = MG relates to cosmology, where Einstein’s field equation fails to make falsifiable predictions (the small ad hoc cosmological constant wasn’t predicted). So Distler is missing the point.

What we have is a problem similar to a political innovation situation well explained in Nicolo Machiavelli’s classic work, published in 1531 A.D.:

http://www.constitution.org/mac/prince06.htm

“Because the innovator has for enemies all those who have done well under the old conditions, and lukewarm defenders in those who may do well under the new. This coolness arises partly from fear of the opponents, who have the laws on their side, and partly from the incredulity of men, who do not readily believe in new things until they have had a long experience of them. Thus it happens that whenever those who are hostile have the opportunity to attack they do it like partisans, whilst the others defend lukewarmly, in such wise that the prince is endangered along with them.”

Tony Smith quotes the problems which Feynman had at the Pocono Conference in 1948, where leading physicists Teller, Pauli and Bohr all dismissed Feynman’s work. See http://www.valdostamuseum.org/hamsmith/goodnewsbadnews.html

“… My way of looking at things was completely new, and I could not deduce it from other known mathematical schemes, but I knew what I had done was right.

… For instance,

take the exclusion principle … it turns out that you don’t have to pay much attention to that in the intermediate states in the perturbation theory. I had discovered from empirical rules that if you don’t pay attention to it, you get the right answers anyway …… Teller said: “….. It is fundamentally wrong that you don’t have to take the exclusion principle into account.” …..

….. Dirac asked “Is it unitary?” ….. Dirac had proved ….. that in quantum mechanics, since you progress only forward in time, you have to have a unitary operator. But there is no unitary way of dealing with a single electron. Dirac could not think of going forwards and backwards …… in time …..

….. Bohr ..… said: “….. one could not talk about the trajectory of an electron in the atom, because it was something not observable.” ..… Bohr thought that I didn’t know the uncertainty principle …..

….. it didn’t make me angry, it just made me realize that ….. [ they ] ….. didn’t know what I was talking about, and it was hopeless to try to explain it further.

I gave up, I simply gave up …..”.

– “The Beat of a Different Drum: The Life and Sciece of Richard Feynman”, by Jagdish Mehra (Oxford 1994) (pp. 245-248).

Feynman’s idea was explained to Oppenheimer by Dyson, who had no time for new ideas from youngsters and was abusive towards Dyson until Bethe intervened on Dyson’s behalf, as Dyson explains in an interview.

Tony Smith also mentions on his page http://www.valdostamuseum.org/hamsmith/ecgstcklbrg.html the work of Ernst Stückelberg who came up with Feynman’s key ideas about 5 years earlier, but had them rejected by the Physical Review in 1943.

Another example is George Zweig, whose quark model called Aces was rejected by Physical Review Letters.

It’s unsurprising that after his experience of 1948, with ignorant attacks from a consensus of the top physicists who were all certain Feynman was wrong, Feynman went on to write things like:

‘Science is the organized skepticism in the reliability of expert opinion.’ – R. P. Feynman (quoted by Smolin, TTWP, 2006, p. 307)

and

‘Science is the belief in the ignorance of [committees of speculative] experts.’ – R. P. Feynman, The Pleasure of Finding Things Out, 1999, p187.

The real challenge is overcoming groupthink:

’Groupthink is a type of thought exhibited by group members who try to minimize conflict and reach consensus without critically testing, analyzing, and evaluating ideas. During Groupthink, members of the group avoid promoting viewpoints outside the comfort zone of consensus thinking. A variety of motives for this may exist such as a desire to avoid being seen as foolish, or a desire to avoid embarrassing or angering other members of the group. Groupthink may cause groups to make hasty, irrational decisions, where individual doubts are set aside, for fear of upsetting the group’s balance.’ – Wikipedia.

‘[Groupthink is a] mode of thinking that people engage in when they are deeply involved in a cohesive in-group, when the members’ strivings for unanimity override their motivation to realistically appraise alternative courses of action.’ – Irving Janis.

This is virtually impossible to do. The tactic of mainstream (groupthink) people who have no evidence simply throwing up garbage and personal abuse from under cover of anonymity which others are misled into believing to be correct, is appalling.

There is very little that can be done against it. If you attack it as being ignorant, most bystanders will think you are the villain because they don’t know anything about physics. They can’t tell what’s right by looking at the facts, so they side with the majority instead.

I’m writing a book as time permits but don’t hold your breath. It’s a hell of an undertaking as there are thousands of details I must get right and if I do succeed scientifically, nobody will read it anyway. A book that is long enough to contain sufficient detail to convince people, will almost by definition be too long for anyone to bother reading.

I’m sticking to this project because there is factual evidence that nobody listens to, and I don’t like dictatorship. Dictatorship was supposed to have been ended by freedom-winning wars. Instead, there is dictatorship everywhere, even in science. You expect problems with democracy, but it’s just too much that in science – a subject where I was taught that facts are the things which count, not prejudices – fundamental physics is run by physically ignorant dictators who can’t tell apart facts of nature from orthodox wishful thinking.

23. nige cook says:

copy of comment:

http://riofriospacetime.blogspot.com/2008/02/explorer.html

Louise,

I’d like to revisit the following scientific points:

1. There’s a lot of mass (galaxies, etc.) almost isotropically distributed around us in the universe. (I don’t think anyone disputes that.)

2. If it wasn’t receding, i.e., if it was static and nothing was keeping it there, from our reference frame it might be expected to collapse (we’d see it falling towards us).

3. The collapse would turn gravitational potential energy into kinetic energy of material coming together.

4. The average distance matter would fall would be some fraction of the radius of the universe, say half the radius of the universe for a very rough first approximation.

5. The argument used to get the potential energy of the universe can be compared to a collapsing star. If you had a star of uniform density and radius R, and it collapsed, the energy release from gravitational potential energy being turned into explosive (kinetic and radiation) energy is E = (3/5)(M^2)G/R. The 3/5 factor from the integration which produces this result is not applicable to the universe where the density rises with apparent distance because of spacetime (you are looking to earlier, more compressed and dense, epochs of the big bang when you look to larger distances). It’s more sensible to just remember that the gravitational potential energy of mass m located at distance R from mass M is simply E = mMG/R. In a supernova explosion, the gravitational collapse of distributed matter releases energy.

The gravitational potential energy released in the collapse would be on the approximate order of magnitude

E = (M^2)G/r = (M^2)G/(ct)

where t is age of universe, where r is the average distance the matter falls before it hits other matter.

6. The gravitational field energy needed to keep this from occurring is therefore a similar amount of expansion kinetic energy:

E = Mc^2.

The relativistic equation for total energy is:

E = Mc^2

where M is the actual mass (which is a function of velocity), and

E = M_0 c^2 (1 – v^2 /c^2)^(-1/2)

where M_0 is the rest mass (not the actual mass), because

M = M_0 (1 – v^2 /c^2)^(-1/2).

Since by the equivalence principle inertial mass (which increases with velocity by the formula just given) is equivalent to gravitational mass, it is the true mass M not the rest mass M_0 which we need to consider.

Hence

E = Mc^2

is the formula to use.

Since the energy of the big bang E = Mc^2 caused the expansion (against inertial and gravitation) in the first place, it must be at least equal to the approximate gravitational potential energy E = (M^2)G/(ct), or the universe wouldn’t have been able to expand in the first place because it would have become a black hole (Professor Susskind, in an interview about his book “The Cosmic Landscape” argued that the universe simply had enough outward explosive or expansive force to counter the gravitational pull which would otherwise have turned it into a black hole). So:

Mc^2 {is greater than or equal to} M^2G/(ct)

Hence at least as an approximation:

tc^3 = MG.

What part of the above “derivation” is wrong?

It’s pretty straightforward.

Let’s take a serious look at a comment which was abusively attacking my competence on 29 March 2007 by an anonymous commentator using the name “Guess Who” on Tommaso Dorigo’s blog (the same comment was copied that day to a posting on Mahndisa’s blog after she wrote after ignoring the content of a comment of mine: “We have gone over this already. You are not applying the equations correctly. The conclusions are incorrect due to a misapplication of physical law. See my comments above. I am turning comments off for this.” She then quoted the “Guess Who” comment I’m about to discuss as alleged evidence of my incompetence: “You are not defending science; you are defending misguided and incompetently performed calculations, which I cannot abide.”).

The “Guess Who” comment made a long series of ignorant claims, so let’s go through them all:

“You are using the expression for rest mass. That means literally mass at rest in some reference frame. But you know that the early universe was radiative: all particles were moving randomly and very close to the speed of light, so almost all their energy was in the momentum (p) part of the full expression E = sqrt((p*c)^2 + (m*c^2)^2). Because of the randomness, there was no reference frame in which p = 0.”

This is wrong, because the relativistic equation for energy only includes momentum where it is written in terms of rest mass. If you are dealing with the actual mass, which increases with velocity, which is what we’re concerned with, the E = Mc^2. So this person doesn’t know that the relativistic correction applies to rest masses (which are imaginary in practice, becauses masses are in motion and the energy of their motion adds to their mass!).

“> the gravitational potential energy E = MMG/R = (M^2)G/(ct).

Most quantities which you put in this expression are ill- or un-defined.”

I don’t think that energy, mass G, radius, c and t are ill-defined. The person just needs to bother to read the definitions.

“In general relativity, which you must (and claim to) use in this context, energy does not stand alone as a separately conserved quantity: it’s just one component of the 4×4 energy-momentum tensor.”

I know the 16 component energy-momentum tensor: it has components for energy density, energy flux, momentum density, momentum flux, pressure and vicosity. All of these quantities get translated into energy density. You can measure energy many ways, and all energy contributes to gravitation. For our purposes, the rest-mass energy of the universe includes all of these contributions.

“Your M is supposed to be the rest mass of the universe, which is neither at rest nor, to the best of our knowledge, finite. So you have an infinity squared there.”

No, M is the mass of the universe, which depends on velocity, M_0 is rest mass. (In any case, unless v is a significant fraction of c, the difference between M and M_0 is not major. You don’t know what you’re talking about. You’re just playing with things you don’t understand: physics concepts can always be extended to include more and more correction factors for known, factual physical processes. That’s not the issue. What’s the issue is whether the basic concepts are right. They are in this case.)

“Your R = c*t looks like it could be the Hubble radius (up to some factor of order unity, e.g. 2 in a radiative universe) but you say that it’s “defined as the effective distance the majority of the mass would be moving if the universe
collapsed”. Excuse me, but that would make R = 0.”

No, if the majority of the universe had zero distance to move if the universe collapsed, it would be here already. It isn’t. It’s at a great distance, and would have a fraction of the radius of the universe to fall to reach here.

“So, you are equating an incorrect expression for an ill-defined E with an undefined quantity containing a square of an ill-defined, presumably infinite M divided by 0.”

Wrong, E, M and the distance have all be precisely defined. In the case of the fall distance, the details are complex due to quantum gravity effects and density variation with distance/time past (see my calculations on my blog) and we’re using an approximation here just to get the basic principle across. The mass of the surrounding universe is located between radii of 0 to R where R = ct. This is because, as discovered by Perlmutter in 1998, gravity isn’t causing the universe to decelerate, so the old Friedmann solution to general relativity for the scale factor or effective radius of the universe, R = (2/3)ct is false; the (2/3) factor came from gravitation and this solution from Robertson/Walker/Friedmann’s metric is wrong empirically. The Hubble expansion rate shows that the gravitational deceleration is not occurring at that rate. Quantum gravity suggests that the reason is that gravitons exchanged between receding masses are redshifted to lower energy, reducing the effective gravitational coupling constant over cosmologically large distances, although the mainstream solution is to ignore quantum gravity, assuming that general relativity needs to instead be supplemented by dark energy to provide repulsion that over cosmologically large distances offsets the attractive force of gravity.

“General relativity fully contains special relativity. To do serious cosmology, you need to solve the equations of general relativity. You are not doing that.”

No, [special relativity] is incompatible with general relativity because it is a generally covariant theory and special relativity isn’t, and if you don’t believe me, try reading some papers on general relativity by someone called Albert Einstein:

‘The special theory of relativity … does not extend to non-uniform motion … The laws of physics must be of such a nature that they apply to systems of reference in any kind of motion. … The general laws of nature are to be expressed by equations which hold good for all systems of co-ordinates, that is, are co-variant with respect to any substitutions whatever (generally co-variant).’ – Albert Einstein, ‘The Foundation of the General Theory of Relativity’, Annalen der Physik, v49, 1916 (italics are Einstein’s own).

‘But … the general theory of relativity cannot retain this [SR] law. On the contrary, we arrived at the result according to this latter theory, the velocity of light must always depend on the coordinates when a gravitational field is present.’ – Albert Einstein, Relativity, The Special and General Theory, Henry Holt and Co., 1920, p111.

‘Special relativity was the result of 10 years of intellectual struggle, yet Einstein had convinced himself it was wrong within two years of publishing it. He rejected his theory, even before most physicists had come to accept it, for reasons that only he cared about. For another 10 years, as the world of physics slowly absorbed special relativity, Einstein pursued a lonely path away from it.’ – Einstein’s Legacy – Where are the “Einsteinians?”, by Lee Smolin, http://www.logosjournal.com/issue_4.3/smolin.htm

“Again ill-defined. But let’s say you take the standard FRW solutions of Einstein’s equations, put yourself in the comoving frame and compute the gravitational potential of a test particle according to your prescription. Since the FRW solutions are isotropic, your result will = 0. So now you’re saying that taking the square of an ill-defined, presumably infinite M and dividing by 0 yields 0.”

This is just trash. The FRW solutions to general relativity wrong by observation, and adding an epicycle in effect by unobserved dark energy, ignores graviton redshift energy degradation in quantum gravity.

Since gravitons will be redshifted towards zero energy as redshift goes towards infinity (recession velocities approaching c), there can be no “curvature” on the largest distance scales in the universe. Hence, apart form Perlmutter’s actual observations of no gravitational deceleration using automated CCD telescope observations of supernovas, quantum gravity itself tells you that general relativity is wrong when applied to cosmology, i.e. massive distances in an expanding universe.

A lot of personally-directed, ignorant, abusive garbage directed towards me follows in the comment which I need not quote here because it is just a list of quotes of me followed by sneers which ignore my work.

I’ll copy this to my blog, because I think it is a useful defense of the conceptual derivation of tc^3 = MG, and Mahndisa has closed the comments section on the relevant post on her blog, preventing any response being made there. I don’t agree with everything you suggest(I’ve investigated changes in G rather than c), but I agree with the general concept tc^3 = MG.

What’s interesting is that there are lots of other physicists around who could be investigating this critically and checking it.

I think that there should be a lot more support for people like Dr Peter Woit who standing up against the hypocrisy of physically vacuous mainstream M-theory which predicts nothing and is “not even wrong”. Dr Lee Smolin too, although in his case he’s been accused (unfairly) of being critical of the mainstream in order to get attention for his own ideas which are maybe not immensely better than string theory (although Smolin’s “doubly special relativity” does make some predictions than may be tested).

One interesting thing I’ve mentioned is the fact that general relativity is a failure at describing cosmology scientifically. There’s no curvature on cosmologically large scales (e.g., the scale of the universe or its effective radius) indicated by observations of redshifts. It also won’t occur theoretically, if quantum gravity involves exchange of gravitons between receding masses, because those gravitons will be received with lower energy due to the recession of gravitational charges in the universe.

I think from memory that the two critics of all this stuff have been Professor Distler commenting using his actual name on Professor Johnson’s Asymptotia blog, both people working on mainstream string theory, and “Guess Who”. Neither of them have come up with any physical discussion at all, if we discount the false claims by “Guess Who” and the claim by Distler that tensors are needed. Anyone can take tc^3 = MG and put into into a tensor field equation simply by writing it as a definition of G = (tc^3)/M and putting that into Einstein’s field equation. However, the equation tc^3 = MG relates to cosmology, where Einstein’s field equation fails to make falsifiable predictions (the small ad hoc cosmological constant wasn’t predicted). So Distler is missing the point.

What we have is a problem similar to a political innovation situation well explained in Nicolo Machiavelli’s classic work, published in 1531 A.D.:

http://www.constitution.org/mac/prince06.htm

“Because the innovator has for enemies all those who have done well under the old conditions, and lukewarm defenders in those who may do well under the new. This coolness arises partly from fear of the opponents, who have the laws on their side, and partly from the incredulity of men, who do not readily believe in new things until they have had a long experience of them. Thus it happens that whenever those who are hostile have the opportunity to attack they do it like partisans, whilst the others defend lukewarmly, in such wise that the prince is endangered along with them.”

Tony Smith quotes the problems which Feynman had at the Pocono Conference in 1948, where leading physicists Teller, Pauli and Bohr all dismissed Feynman’s work. See http://www.valdostamuseum.org/hamsmith/goodnewsbadnews.html

“… My way of looking at things was completely new, and I could not deduce it from other known mathematical schemes, but I knew what I had done was right.

… For instance,

take the exclusion principle … it turns out that you don’t have to pay much attention to that in the intermediate states in the perturbation theory. I had discovered from empirical rules that if you don’t pay attention to it, you get the right answers anyway …. Teller said: “… It is fundamentally wrong that you don’t have to take the exclusion principle into account.” …

… Dirac asked “Is it unitary?” … Dirac had proved … that in quantum mechanics, since you progress only forward in time, you have to have a unitary operator. But there is no unitary way of dealing with a single electron. Dirac could not think of going forwards and backwards … in time …

… Bohr … said: “… one could not talk about the trajectory of an electron in the atom, because it was something not observable.” … Bohr thought that I didn’t know the uncertainty principle …

… it didn’t make me angry, it just made me realize that … [ they ] … didn’t know what I was talking about, and it was hopeless to try to explain it further.

I gave up, I simply gave up …”.

– “The Beat of a Different Drum: The Life and Sciece of Richard Feynman”, by Jagdish Mehra (Oxford 1994) (pp. 245-248).

Feynman’s idea was explained to Oppenheimer by Dyson, who had no time for new ideas from youngsters and was abusive towards Dyson until Bethe intervened on Dyson’s behalf, as Dyson explains in an interview.

Tony Smith also mentions on his page http://www.valdostamuseum.org/hamsmith/ecgstcklbrg.html the work of Ernst Stückelberg who came up with Feynman’s key ideas about 5 years earlier, but had them rejected by the Physical Review in 1943.

Another example is George Zweig, whose quark model called Aces was rejected by Physical Review Letters.

It’s unsurprising that after his experience of 1948, with ignorant attacks from a consensus of the top physicists who were all certain Feynman was wrong, Feynman went on to write things like:

‘Science is the organized skepticism in the reliability of expert opinion.’ – R. P. Feynman (quoted by Smolin, TTWP, 2006, p. 307)

and

‘Science is the belief in the ignorance of [committees of speculative] experts.’ – R. P. Feynman, The Pleasure of Finding Things Out, 1999, p187.

The real challenge is overcoming groupthink:

’Groupthink is a type of thought exhibited by group members who try to minimize conflict and reach consensus without critically testing, analyzing, and evaluating ideas. During Groupthink, members of the group avoid promoting viewpoints outside the comfort zone of consensus thinking. A variety of motives for this may exist such as a desire to avoid being seen as foolish, or a desire to avoid embarrassing or angering other members of the group. Groupthink may cause groups to make hasty, irrational decisions, where individual doubts are set aside, for fear of upsetting the group’s balance.’ – Wikipedia.

‘[Groupthink is a] mode of thinking that people engage in when they are deeply involved in a cohesive in-group, when the members’ strivings for unanimity override their motivation to realistically appraise alternative courses of action.’ – Irving Janis.

This is virtually impossible to do. The tactic of mainstream (groupthink) people who have no evidence simply throwing up garbage and personal abuse from under cover of anonymity which others are misled into believing to be correct, is appalling.

There is very little that can be done against it. If you attack it as being ignorant, most bystanders will think you are the villain because they don’t know anything about physics. They can’t tell what’s right by looking at the facts, so they side with the majority instead.

I’m writing a book as time permits but don’t hold your breath. It’s a hell of an undertaking as there are thousands of details I must get right and if I do succeed scientifically, nobody will read it anyway. A book that is long enough to contain sufficient detail to convince people, will almost by definition be too long for anyone to bother reading.

I’m sticking to this project because there is factual evidence that nobody listens to, and I don’t like dictatorship. Dictatorship was supposed to have been ended by freedom-winning wars. Instead, there is dictatorship everywhere, even in science. You expect problems with democracy, but it’s just too much that in science – a subject where I was taught that facts are the things which count, not prejudices – fundamental physics is run by physically ignorant dictators who can’t tell apart facts of nature from orthodox wishful thinking.