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Guest post: Rick Ryals, “Dirac’s holes and Einstein’s constant” October 18, 2007

Posted by dorigo in physics, science.

I continue to receive interesting contributions for this blog. Since I am happy to host both orthodox and unorthodox ideas here, please do keep them coming – no charge this month 😉 . I advocate that doing science does not necessarily require a PhD and a desk in a University office, and that ideas and theories are not crackproof or crackpotty, but just right or wrong (well, ok, some are not even that) although at times it is hard to say. The following text is from Rick Ryals, also known as island. Happy reading!

Island” is a true independent researcher, or a bona-fide crackpot theorist by any other name, IF you can legitimately shoot down his supported assertion that Einstein was dead-right all along, as there never was any “greatest blunder”, (except that he once tried to divide by zero), so he never lost any arguments in Copenhagen, and the universe is not infinite in nature.  At the very least, he was never disproven by Hubble’s observation, as he thought that he was, rather, he simply didn’t know about the particle potential of the quantum vacuum, or he never would have abandoned has finite model.

You be the fair and reasoned judge.  Don’t let Einstein down again. Stick your necks out for a change, (dear cutting-edge theorists who might be lurking), by making a *reasoned and clearly explained* call about this:

A little history

My story is that of your typical crackpot who made a simple observation about the highly efficient manner that we humans tend to increase entropy, so I started studying physics, (about 20 years ago, now), to see what was known and how this stacked up to the paradigm shifting worldview that falls from my new understanding of nature.  I hit the fundamentals very hard and sometimes sounded a lot like every other crackpot that you see on “usenet”, I’m sure, but this “inventive” tendency slowly diminished as I read these dumb books that I paid ungodly amounts of money for, that Baez and others always recommended.  Add to that those many too many hours of painful tutorials that included the kind of math that draws blood while leaving permanent scars on a guy like me, and I finally began to get a clue.  I started studying gravity like every other good amateur student of physics, following along as best as I could with all of the great conversation that was going on in the sci.physics.research group, and interjecting my thoughts occasionally in a somewhat less than crackpotish manner that actually made it past the moderators for a change.

But What About The Hole That The “Hole” Left Behind?

Then one day some years later the topic of gravity popped-up again, as it did quite often, except that this time someone asked a very naive question… “Does particle creation from vacuum energy change the gravity of the universe?”.   Anyway, I waited to no avail for one of the gurus to reply, and when they didn’t, I became a little flustered and confused, because, at that time, I was studying about Einstein’s cosmological constant as he developed his finite extension of GR, and when I looked at this simple model, there was a very easy answer to that question.  So I finally got enough nerve up to offer an answer by asking the gurus for help, and I said… “But what about the [real] hole that the “hole” leaves in the vacuum?”  (You know, if you rip a hole in the vacuum, then you’re going to leave a hole, right?… speaking of “naive” 🙂

Well, the reply that I got was less than satisfying, because it didn’t jibe with the model that I was studying, since pair production does very much affect the gravity of the universe in this model, because gravity is not just the curvature that caused by the energy that’s contained in a region of space.  In this case, pair production drastically changes the effect when… \rho+3P/c^2=0 in a finite universe, because you can’t take huge voluminous chunks of vacuum energy from Dr. E’s model and then contain the matter energy-density over a finite region of space without increasing negative pressure in proportion to the local increase in positive gravitational curvature, since the gravitational acceleration is zero when the density of the vacuum is -0.5 \rho_{matter} .

You can’t take vacuum energy from a finite universe and then contain the matter energy-density to a finite region of space without increasing negative pressure via vacuum *rarefaction*, and this gravitationally counterbalanced effect *drives* stabilized expansion, so I’m at least *apparently* not a crackpot when I say that… Einstein was right, and was *never* proven wrong!

You have no choice but to condense or compress Einstein’s finite spacetime structure in order to attain the matter density, because… P=-u=-\rho c^2.  So there is no net change on the gravity of the universe, because the effect is two-fold… an increasing anti gravitational *effect* is offset by the local increase in positive gravitational curvature that accompanies the created massive particle pair.

I immediately noticed that this “self-regulating effect” very simply resolves the flatness problem without runaway expansion, and further inspection indicates that growing tension between the vacuum and ordinary matter will eventually and inevitably compromise the forces, so we will at some point have *another* big bang.  Not only that, but the horizon problem is resolved without the monopoles problem when a causally connected structure of certain volume decides to “rethermalize”.  I also noticed that the matter/antimatter problem was too resolved with equally intuitive physics, since the “antimatter” exist only in a rarefied negative pressure state, and cannot become a real, positive mass particle, until it has been condensed out of the vacuum with great ***dis proportionality*** in volume… to the tune
of about 120 orders of magnitude of corrected difference from the quantum expectation at this current time in the history of the growing universe!

In fact *all* of the fine-tuning problems are apparently addressed and resolved by this simple physics, but that’s only a small part of what it accomplishes:

Unbelievably enough to me, I didn’t get much of a response to my point, and when I pressed people on it, I’d get stuff like, “that’s the same mechanism that some inflationary models use to generate matter from the vacuum during the early period of rapid inflation”. ‘So, who cares about inflation if it isn’t even necessary’, I wondered?  But it turns out that the biggest reason that people don’t get excited about this is that they *wrongly* think that it somehow contradicts quantum field theory, which is a very well tested theory, indeed, so they dismiss my point out of hand without going any deeper.  Well, I’ve got a little news for you quick dismissive doubters… this does *not* contradict anything that is right about quantum theory, rather, it fills in the gap, and fixes what isn’t right with gravity theory, albeit greatly simplified.  In point of fact, it works by the exact same mechanism, since, as with electric charge, the normal distribution of energy does not contribute to particle pair creation, only departures from the normal distribution can accomplish this task.

I thought, “No wonder there are no negative mass particles, eh, Mr.
Dirac, Sir?”…

So What Exactly Does This Say About Dirac’s Hole Theory?

Okay, around that same time period someone brought up one of John Baez’s negative mass puzzles for the umteenth time, and Baez was not exactly thrilled about the idea of rehashing the whole mess again, saying that “we’ve been through all of this before”, which was true, and “there is nothing new to be gained by this”… which was not entirely true, since I was suddenly able to resolve the problem via a vacuum state that “mimics” an object of negative mass.

Dirac unified Einstein’s Special Relativity Theory with Quantum Mechanics by way of what is known as the Dirac Equation. This was rightfully hailed as a great feat in the world of theoretical physics, and he won the Nobel Prize for this contribution.  A funny thing about this, though, was that there are four solutions of the equation. Two of them correspond nicely to the two spin states of the electron. The other two solutions, however, extend to a strange prediction that there is an infinite set of quantum states where the electron has negative energy.

The two equations, E=mc^2 and E^2=m^2 c^4 …are only different if there is a physical meaning to the negative mass and negative energy values, where the second equation allows for both positive and negative mass-energy solutions.  The expression arises from the fact that the magnitude squared of the momentum four-vector is given by, m^2 c^2=p^2-E^2/c^2 .  In the case of a body at rest, p=0, which leads to, m^2=E^2/c^4.  The concept of negative mass arises by analogy with electric charges, where the formula for the energy of a relativistic particle, E^2=m^2 c^4+p^2 c^2 derives that a particle with a certain positive energy but no momentum could theoretically have a positive or negative mass!

This brings us to Dirac’s “hole theory”, where he rationalized these negative energy solutions by reinterpreting the vacuum state so that all of the negative energy states are filled, and all of the positive energy states are empty.  Dirac’s theory was flawed though, in-spite its success at predicting the existence of the “positron”, because it can’t fully account for particles of negative energy, since it is restricted to positive energy particles, and yet, the quantum field theory representation for this is not an accurate representation of Dirac’s negative energy states.

For example:
Dirac’s hole theory and quantum field theory are generally thought to be equivalent. In fact field theory can be derived from hole theory through the process of second quantization. However, it can be shown that problems worked in both theories yield different results.

And therein lies the problem that has not been resolved by *any* “reinterpretation” of the vacuum state, and so the quantum expectation
for the energy density of the vacuum is about 120 plus orders of magnitude^ greater than it should be without the assumption of an “ad
hoc” suppression mechanism to cover this “little” discrepancy.  The problem goes back to the negative mass absurdity that falls from the Dirac equation, and QFT’s “ad hoc” assumption has also assumed the flaw, rather than to fix it, which only carries and compounds the problems when extended to quantum gravity theories of all varieties.

And in conclusion… What About The Higgs?

In Einstein’s static model, G=0 when gravitational pressure is absolutely offset by negative vacuum pressure.  He brought in the cosmological constant to counterbalance the runaway re collapse effect that occurs in this model because of the obvious fact that we do have matter, but in order to get \rho > 0 from Einstein’s matter-less spacetime structure, you have to condense the matter density from the zero pressure metric, and in doing so the pressure of the vacuum necessarily becomes less than zero, P < 0, which obviously causes vacuum expansion.

*Note that the mass-density of the background changes every time that
you do this.

Einstein didn’t introduce the counter-balancing cosmological constant with matter generation from the vacuum in mind, so he didn’t like it, because without this knowledge he naturally concluded that it added an undesirable extra entity, so the logic that was used to reject the cosmological constant when it was discovered that the universe is expanding was sound in context with the knowledge of the time, but this is not the case given knowledge that the vacuum has real, massive, particle potential.  It is plainly evident from this that most natural way to create new matter in Einstein’s model, (“the most compatible with the spirit of general relativity”), also holds it flat
and stable, (it is “self-gauging” like Eddington thought, in other words), so any other conclusions that have been made since Einstein abandoned his finite universe without this knowledge are therefore subject to suspect review!

Somebody please correct me if I’m wrong, but this physics predicts something like a higgs mechanism, but no higgs boson, (I don’t think), which isn’t to say that the playing field hasn’t already been narrowed significantly… 😉

I see this as vindication of 30 years of Einstein’s “allegedly wasted” time working on his classical unified field theory, and there is an obvious theory of quantum gravity embedded in a constantly changing, but semi-dependent background, so that’s my story and I’m stickin’ to it, until or unless somebody can give me a reasonable critique that categorically disproves the relevance of my point to the seemingly insurmountable problems that are encountered by modern theoretical physics.

The ball is in your court…

Some relevant references:


1. Modeling » Guest post: Rick Ryals, “Dirac’s holes and Einstein’s constant” - October 18, 2007

[…] unknown wrote an interesting post today onHere’s a quick excerptAt the very least, he was never disproven by Hubble’s observation, as he thought that he was, rather, he simply didn’t know about the particle potential of the quantum vacuum, or he never would have abandoned has finite model. … […]

2. Tony Smith - October 18, 2007

island (Rick Ryanls) said:
“… I was studying about Einstein’s cosmological constant … You have no choice but to condense or compress Einstein’s finite spacetime structure …”.

The 10-parameter Poincare group ( 3 spatial rotations, 3 boosts (timelike rotations), and 3 translations ) does not allow compression of spacetime. To get compressions (and preserve light-cone structure) you need to add 5 more transformations (1 dilation and 4 special conformal transformations) which gives you the Conformal Group Spin(2,4) = SU(2,2) that acts non-linearly on 4-dim spacetime.

That gives you a conformal picture of gravity on the cosmological scale, as was investigated by Irving Ezra Segal. It can be shown ( see gr-qc/9809061 by R. Aldrovandi and J. G. Peireira ) that combining the 4 special conformal transformations with the 6 Lorentz transformations you get what looks like a /\ cosmological “constant” (since it can vary, it is really more like what is now called “Dark Energy”).
Further, you can by a modified MacDowell-Mansouri mechanism use the conformal group to get an Einstein-Hilbert Lagrangian with cosmological “constant”,
it seems to me clear that the basic picture of island is not only realistic, but can be directly connected with more conventional formulations of gravity, and that people who “… dismiss …[island’s]… point out of hand …” are more to be pitied for their ignorance than paid attention to.

Also, island said;
“… particle creation from vacuum energy … you have to condense the matter density from the zero pressure metric … this physics predicts something like a higgs mechanism, but no higgs boson …”.

This is in line with the idea of the Higgs as a Tquark condensate ( see for example hep-ph/0311165 by Hashimoto, Tanabashi, and Yamawaki ), since a Higgs condensate of particle-antiparticle pairs from the vacuum would naturally be dominated by the heaviest component, that of the heaviest quark-antiquark pair, the Tquark.
again it seems to me clear that the basic picture of island is realistic (the Higg being, not an independent fundamental particle, but a result of a Tquark condensate). Further, island’s picture can be described in conventional physics terms (as in the paper cited above).

Tony Smith

PS – As to why John Baez might not have been receptive to the above interpretation (of the conformal group a la I. E. Segal), Segal was advisor for Baez’s 1986 MIT Ph.D., and (in an obituary for Segal in the Notices of the AMS 46 (June/July 1999) 659-668, Baez said:
“… In his later years Segal spent most of his time on … the … cosmology …[of]… conformal geometry … it never seemed right to me … I tried to get him to explain … His explanation did not convince me. Later I tried to explain what I thought was his error. He became quite angry … this was very difficult, and our relationship became strained … I eventually wound up avoiding him …”.

3. island - October 18, 2007

Wow, Tony, thank you very much. I will try to grasp everything that you’ve said.

4. island - October 18, 2007

As to why John Baez might not have been receptive

Oh, and I don’t know that John wasn’t receptive, he simply didn’t reply, and may have never even read what I wrote, so let’s not lay this on him. I have put this before many others who can take responsibilty for that, and I’m already mad at John for “other”, (read anthropic), forms of willful ignorace, so I don’t need to add this to his list… 😉

5. Kea - October 18, 2007

…in an obituary for Segal in the Notices of the AMS 46 (June/July 1999) 659-668…

That’s very interesting, Tony. You’re a mine of historical quotes! Just for the record here, let me point out the similarities (noted originally by Tony) between Segal’s ideas and Riofrio’s Machian no-DE cosmology. Island, from this Machian perspective one can view the classical spacetime as an emergent phenomenon with no /\, which is possible because the /\ is associated with levels of quantumness [multiple levels is a post-QFT notion of an hbar (N) heirarchy, including Dark Matter – see Pitkanen’s work, for instance] and for a large range of hbar, /\ can be replaced by a variable speed of light. Einstein’s intuition then works only as an effective description, relying on the ficticious vacuum of a single-level hbar QFT.

6. island - October 18, 2007

Thank Kea, and yes, I have often stated in public that it doesn’t take a rocket scientist to see that there is absolutely nothing wrong with her math, and she can provide certain empirical evidence to support her assertion that the speed of light is not constant, so there are other relevan factors that determine which is the preferred theory.

Best of luck to her.

7. Alejandro Rivero - October 18, 2007

Hmm, what I find disturbing is that even for a basic quantum [field] theoretical discussion people seems to feel the urge of dressing it in the argumental robes of cosmology and quantum gravity. It is a generic plague of QFT thinking; remember for instance the traditional excuse for nonrenormalizability, “Gravity will give us a natural cutoff”.

8. island - October 19, 2007

I’d like to add to the discussion that you can experimenally prove the validity of the asserted physics simply by removing all pressure from a sealed container before you start condensing virtual particles from what’s “not” left in it.


Which is supported by that region of pseudo-negative pressure density that gets produced by the Casimir effect, which is the closest known real representative for a real object that expresses the characteristics of the, (also pseudo), negative mass object that falls quite naturally from Dirac’s negative energy solutions.


9. Domenic - October 19, 2007

What is the canonical physicist’s answer for your motivating question, “Does particle creation from vacuum energy change the gravity of the universe?”

And, I don’t see any connection between your talk of the Dirac sea and your talk of gravitational effects on pair creation. Pair creation is generally viewed as creating particles and antiparticles; presumably when you work out the gravitational effects on such, you are doing so in the particle-antiparticle paradigm, and not in the Dirac sea paradigm. Or are you also looking at the gravitational influence of having an infinite number of negative-energy fermions at every point in space? If so, I missed that…

10. Qubit - October 19, 2007

I think space-time just ignores virtual particles (by doing this it has the greatest chance of a real existence), when they become real they lower their entropy and the entropy of the universe becomes higher to compensate. This makes it look like its always been here. In other words, if there is a glass slipper for only one foot and a determined carrier to take the slipper to its owner, then the object can fit in its correct place.
Virtual particles appearing in the vacuum are just purely imaginary (IMO), unless they come close to a black holes horizon, this is how the entropy is lowered and raised for each particle pair (without a black holes horizon the pair can never be said to exist as real and if they do happen to come across an horizon, no one can say that they never existed before, as the object will have always existed as real). The black hole is prince charming and he puts everything in its place, because of the shift in entropy the object has the greatest chance to exist as a real object without the universe knowing, but that would be exactly what the universe wanted. If a higgs exists and man find it, then it would allow for us to pick and choose our history (are news stories telling us two tales, digital TV and deception filters. Oh dear “it’s the end of the world as we know it” only kidding :), you don’t need the higgs to do that.)

“The balls it your court…”

Just remember to be home by midnight!

11. Qubit - October 19, 2007

In not it.

12. island - October 20, 2007

Domenic asked:
What is the canonical physicist’s answer for your motivating question, “Does particle creation from vacuum energy change the gravity of the universe?”

Although I didn’t realize it at the time, the answer that I got was out of context with the finite model that I was studying:

Aaron Denny answered that:
In GR gravitation is essentially curvature due to the energy contained in a region. Pair-production changes this energy from photons to the mass of other particle pairs, but the energy amount, and thus the curvature and gravitation should be the same.


Domenic asked:
Or are you also looking at the gravitational influence of having an infinite number of negative-energy fermions at every point in space?

Particle theory says that for every fermion type there is another
fermion type that has exactly the same mass, and therefore no priori
distinction between matter and anti-matter. I incorrectly concluded that the opposite value of all other charges (quantum numbers), indicates that the asymmetry between the two classes of particles is due to the fact that the anti-particle has -rho and negative mass until it becomes a real particle.


I latter figured out with the help of Nathan Urban that the antiparticle actually has negative pressure when the model is not static because the vacuum only has negative density when P=-u=-rho*c^2. In this static state, pressure is proportional to -rho, but pressure is negative in an expanding universe, and so energy density is positive, e.g., vacuum energy density is less than the matter energy density, but it is still positive.

Someone better than me needs to write down the basis of wave functions in this background, including an expansion of the field in corresponding creation and annihilation operators. Then compute the stress-energy tensor in that background and quantitatively describe the vacua. Then work out the matrix elements of the stress-energy tensor between the vacuum and the one-particle states.

Anybody wanna start a retro-revolution?… 😉

13. Cavendish experiment 3 at Freedom of Science - October 21, 2007

[…] free flow of information now made possible by this medium. Dorigo himself states that he is “happy to host both orthodox and unorthodox ideas” in his blog and puts that in practice by letting very interesting guest bloggers write about […]

14. Visual Physics Blog » Guest Post at Tommaso Dorigo’s Blog - November 21, 2007

[…] desk in a University office, and that ideas and theories are not crackproof or crackpotty, but just right or wrong” . (In this connection, he had also published in his blog a great story titled Cracked Pots […]

15. Psybertron Asks - December 11, 2007

[…] human identity, but “Freedom” responded to Island’s post mentioned in my previous post below. addthis_url = […]

16. Guest post: Rick Ryals - “The Anthropic Principle” « A Quantum Diaries Survivor - June 23, 2008

[…] anthropic principle, guest posts trackback Rick Ryals, a frequent visitor of this site, wrote a guest post here some time ago, on Dirac’s theory and the Einstein constant. He sent me today another […]

17. kikiki62 - December 1, 2008

We are facing the limits of knowledge in the twilight of the scientific age.We ask ourselves,WHAT IS GRAVITY ? :For some scientist it is an endless attracting force emanating from matter; for others it`s a mysterious warping of a 4-dimensional “SPACE-TIME”,or even more mysterious”SUPERSTRINGS” curled up in 10 dimensions,or perhaps “QUANTUM GRAVITY”,”GRAVITY WAVES”or “GRAVITON PARTICLES”,,that is no one really knows..How does a fridge magnet cling endlessly against Gravity ? A block of wood falls to the floor,but a magnet clings via magnetic energy..What is the source of this energy from within,,and what is it`s rate of power drain as it holds a heavy magnet up against gravity ? You will find no answer to this simple and obvious question in any physics course or textbook..Light slows down when it enters water or glass and just recently has been slowed to as little as 3ft.per sec in laboratory experiments,,but why and how does it know to resume it`s normal light speed opon exit of the medium it was subjected to,No clear explanation could account for this surprising ecceleration in the laboratory.We do not know anything.Everything about Gravity is mysterious,,So says Michael Martin nieto,Theoretical physicist, Los Alamos National Laboratory,Discover magazine Oct.2003,,We are living in an era beyond Newton and Einstien,Rethinking our scientific Lagacy;;THE FINAL THEORY; by Mark McCutcheon //A book even Newton and Einstien would have enjoyed!!

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