Gerard 't Hooft so states in his Imperial College Lecture. In the same lecture he said:
"We furthermore conjecture that information is not conserved in the deterministic description."
Furthermore he asserts:
The notion of ‘free will’ is given a meaning that deviates from most standard views on the subject;[5][6][7] ours[8] appears to go back as far as Benedict de Spinoza: an individual’s actions are completely dictated by laws of Nature, yet this does not exempt us from our responsibilities for our actions. The ‘free will postulate’ is presently seen as an axiom in the reconstruction of the interpretation of quantum mechanics. This postulate will not be needed in the form usually given. We replace it by the condition that a theory or model of Nature should give appropriate responses for every conceivable initial state.
So, in investigating our model, we have the ‘freedom’ to choose our initial state at will; whatever that state is, the model should tell me what will happen next. This is referred to as the ‘unconstrained initial state’ requirement.[9]"
He goes on to state that:
"Because of the periodicity, we must have
e−iHT = 1 → H = 2πn/T = ωn ; n = 0, ±1, ±2, . . . . (3.2)
This is exactly the spectrum of a quantum harmonic oscillator, except for the emergence of negative energy states. The states with n < 0 are forbidden, for some reason. Of course, we also do not have the ‘vacuum energy’ 1/2 ω , which would have emerged if we would have required e-iHT = −1 . This minus sign is as harmless as an overall addition of 1/2 ω to the hamiltonian, but perhaps it will mean something in a more complete theory; we will ignore it for the time being."
Maybe we will know the meaning of negative energies with the work of Professor 't Hooft.
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Yeah, like if he ever figures out that the correct model is finite, because negative energy only exists when the vacuum has negative pressure *because* rho is less than zero.
It's not that diffucult.
Like I said, it always comes down to the negative energy solutions, that nobody interprets as described above.
Instead, they "ignore it for the time being"... just like the WMAP anomalies, "the time being" has no limit.
It's not that diffucult.
In fact, it's so simple that you and I could write a paper about it:
In Einstein's model pressure is zero when there is no matter.
Think of this as a perfectly flat spacetime metric using the flexible rubber sheet analogy.
Now, stick a fork in it and spin it in circles until the matter density is attained over a finite region of space around the fork.
Note that the rubber sheet pulls back proportionally as negative pressure increases with matter generation.
Ta-Da
Note also that the vacuum mimics the negative mass solutions, since negative pressure has an antigravitational **effect**
Note that ALL of the problmes are now resolved.
You can get all of this from Ned Wright's website if you take what I've said now and previously into account:
http://www.astro.ucla.edu/~wright/cosmo_constant.html
It seems that I have to take you seriously. If even after reading a bit of 't Hooft, you are convinced that you have something to say, that intrigues me. I was trying to work with him during my post-doc, but it was not to be. He answers my e-mails, I think he will consider a comment on his recent work.
I have read all of his papers on determinisitic quantum mechanics, and I know exactly where we differ. I have also written about this on my blog in the past, but here's a new one from the talks at the recent Imperial College event in honor of Abdus Salam, which, uncoincidentally, Steven Weinberg boycotted:
http://www.phys.uu.nl/~thooft/gthpub/Salam_07.pdf
Injecting quantum mechanics into Einstein's theory of General Relativity turned out to be a vastly more stubborn problem than most of us had anticipated. We thought that this was a problem very similar to the riddles we have been facing in the past.
Injecting quantum mechanics into Special Relativity had also been hard, and it too at ¯rst looked like an impossible assignment. Various approaches using as much experimental input as we could put our hands on, in combination with pure logical reasoning, were tried; and we vindicated: the \Standard Model" was the most precise and complete answer that was uncovered. So should we not do the same thing again, sharpen our theoretical and experimental techniques, produce more precise formalisms, and yes, quantum gravity will be there. Will it? History also shows us that procedures that have proven very successful in the past, do not always guarantee success in the future. To crack this problem, we
might ¯rst have to step back. And if that does not help, perhaps step back further. By itself, this is a risky thing to say. I receive letters every day from crackpots who give me the same advice: forget all that mathematical gibberish, read the Bible, go meditate, or something of that sort. This is clearly not what I have in mind. What I do have in mind is that we have to improve our mathematics, but we might
have to start at places where we thought everything was secure. My own hobbyhorse is quantum mechanics.
-g.thooft
I'd reccommend a step back in history to look at the problem in the light that I've described it, but like I've said, people typically take too many assumtions for granted, so he might just take me for another crackpot, which is not true.
But it is a fact that Einstein did not know about the particle potential of the quantum vacuum or he never would have abandoned his finite model because matter generation from vacuum energy causes stable, counterbalanced, expansion... and that is more than just a little bit significant.
There IS something important to be said.
I read the Salam piece also.
As I said, if I write something clear, I expect 't Hooft, to at least answer politely. Maybe now he gets more e-mails and won't answer, but in the past he used to.
On the other hand, if the idea is clear, it can be posted in the Los Alamos archive. Maybe somebody will pick it up.
My problem is that I never believe the ideas I have, so I have only published two theory papers, and as it was, it was more the interests of my co-authors than mine. That is in part the reason why they still get money for writing papers, and I don't.
I do not mean to say that what we published was wrong, my concern is more with the question, so what?
In any case before I get into writing any paper, I have to be convinced that it matters.
Whatever you do, don't mention the anthropic principle, unless you just want to start a war... ;)
I think that it would be important to point out that this does not conflict with QFT because it works by the same process. As you can see from the example that I gave, and as with QFT, the normal distribution of energy does not contribute to particle creation. You have to condense or compress the energy down over a finite enough region of space to attain the matter density in before the virtual pair can be made real.
You can also see from the example why observed antimatter doesn't have negative mass. The vacuum has negative density when, P=-u=-rho*c^2
In this model, pressure is proportional to -rho, but pressure is negative in an expanding universe, and so energy density is positive, but it is less dense than the matter density.
You can also see how it resolves all of the problems listed on the page that I've linked, below, but like I said... I wouldn't mention the anthropic principle.
It could, however, be introduced as the dynamical structure principle that David Gross says is 'the biggest failure of science in the last 20 years that would make the landscape go away'.
http://zebu.uoregon.edu/~imamura/209/mar31/anthropic.html
Let me get your point. 't Hooft builds a toy model:
e−iHT = 1 → H = 2πn/T = ωn ; n = 0, ±1, ±2, . . . . (3.2)
His universe is very little, odd and even poimts, he gets negative solutions.
How do you go from there to negative pressure?
Okay, I wasn't sure if you were asking me to do this, or if you were saying that you were going to do it yourself, based on what has been already been said. Frankly, I think that you are more qualified, but I'm not as easy to understand as I think that I am, so...
The "extra" 1/2 in the eigenvalues of the harmonic oscillator Hamiltonian can be thought of as having a phase factor of -1, which represents vacuum energy as being equal to mass energy.
The magnitude of the negative pressure needed for energy conservation is easily found to be P=-u=-rho*c^2 where P is the pressure, u is the vacuum energy density, and rho is the equivalent mass density using E=m*c^2
But in General Relativity, pressure has weight, which means that the gravitational acceleration at the edge of a uniform density sphere is not given by g=GM/R2=(4*pi/3)*G*rho*R, but is rather given by g=(4*pi/3*G*(rho+3P/c2)*R .
This describs a quasi-static model, where g=0. We know that rho > 0, so by setting rho(vacuum) =0.5*rho(matter) we have a total density of 1.5*rho(matter) and a total pressure of -0.5*rho(matter)*c^2, since the pressure from ordinary matter is essentially zero (compared to rho*c^2). Thus rho+3P/c^2=0 and the gravitational acceleration is zero; g=(4*pi/3)*G*(rho(matter)-2*rho(vacuum))*R=0
Matter generation from vacuum energy drives expansion via vacuum rarefaction, and the quantum oscillator evolves 'backwards' from the normal expectation when tension between the vacuum and ordinary matter increase when the increasing matter density is off-set by increasing negative pressure.
This leads to a statement about causality and inflationary theory, because neither, a first cause, nor inflation, are necessary when a universe with certain volume has periodic big bangs when tension becomes so great that the forces that bind the finite structure are compromised.
The "initial state" is perpetually inherent, in other words, but the imbalanced system *evolves* closer to absolute symmetry each time that we have a big bang, so the next universe will be infinitesimally more-"flat" than this one is, via the above described "asymmetric transitions".
Of course, there is more that can be said to justify this against cutting edge assumptions, but I hope that I am in the park with what you wanted me to say.
I am the student, here, and I am wide-open to any help that you can offer.
I reposted my last reply with some minor clarification in, "The Negative Energy States", thread.
It seems that I have to take you seriously.
This is completely speculative, but I want to tell you where my confidence and persistence come from, just so that you are able to see what a true "epiphany" means:
Somebody once asked a group of theorists if pair creation affects the gravity of the universe, and nobody could answer... so I finally asked a very naive question; "But what about the hole that the hole left behind". The answer that I got did not make any sense in context with the cosmological model that I was studying at that time, so I kept asking questions that nobody could answer.
I had no idea that this leads to an "evolutionary" cosmology, nor did I even know what the anthropic principle was at that time, I just wanted to study gravity.
My anthropic observation was that our contribution to the universe is mainly entropic, (which I can prove that I have been saying for years before Susskind jumped on this as a means to "predict the cc and solve the coincidenc problem").
But it was much later, (maybe 6 years after devoting my reasearch time to the anthropic phyisics), that I figure out that this evolutionary cosmology is actually inherent to any true anthropic cosmological principle, and I am thinking that this is no coincidence!
There is an inherent prediction to any true anthropic cosmological principle that tells physicists that they should look for a mechanism that enables the universe to "leap"/Bang/"evolve"... and I literally stumble over both of these... "anthropic coincidences"... ???
This is why I know that this is it.
We can teach each other. Both are the students here. Your answers to my questions help me understand your proposal.
I am thinking both, about this answer, and the one in negative energy.
I know it is not easy to build a toy model like 't Hooft, and see how it solves or not old problems. It is just that I like that way of thinking. Maybe in a simple context I can understand your point. I see that you tried to follow my proding in both cases. I thank you for that. I'll get back to you when I understand a little more.
Thank you Eduardo. I will keep studying this so that I might hopefully be able to say more about it.
Hi Eduardo,
e−iHT = 1 → H = 2πn/T = ωn ; n = 0, ±1, ±2
How do you go from there to negative pressure?
Maybe I misunderstood you, but "vacuum energy" 1/2ω, which equates to negative pressure, (-0.5*rho(matter)*c^2), necessarily arises if we require that e-iHT=−1.
This doesn't just happen to coincidentally fit Einstein's finite static model.
Like 't Hooft said... we have the "freedom" to choose this, but I claim that we can justify that this "initial state" is perpetually inherent via the process that I described... in that model.
What am I missing?
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