## 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:
http://arxiv.org/abs/hep-th/0401208
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…