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Frank Wilczek about Penrose's new book

Frank Wilczek did not allow his first Nobel prize to reduce his activity, and one of the many things he recently did was to read the new book The Road to Reality by Roger Penrose, even though it has about 1100 pages. Wilczek wrote an excellent review of this book for a recent issue of Science. Unfortunately, you need a subscription to access the article, or you need to buy the paper version.



Although I have not read the whole book, it does not seem necessary to determine that I completely agree with 's comments. First of all, is a highly original thinker. Among his discoveries, we find

  • Various methods and solutions of GR related to dynamics of black holes (which includes his method to gain energy from the Kerr black hole)
  • The Penrose (BMN) limit of geometries, a kind of pp-waves
  • The Penrose causal diagrams
  • The esoteric Insect formalism for GR: tensors are bugs and indices are their legs
  • The Penrose tilings and quasicrystals
  • The twistors (1967)
  • Spin networks that he invented decades before they became fashionable in loop quantum gravity which was another framework that people were proposing as an approach to quantum gravity
If I paraphrase him, Wilczek argues that Penrose's book should rather be called Fifty Sidewalks Around Reality. It is a physics-oriented book, but otherwise another eclectic interdisciplinary work with many layers, different ideas, and viewpoints. Wilczek looks at the book from three different perspectives. Penrose is most successful from the viewpoint of a teenager who is interested in math and physics: the book will make such readers excited about the complex numbers, relativity, and spinors. (Although it is unlikely that they will learn what a line bundle on the twistor space is.)




However, the perspective of a professional physicist is less encouraging. Penrose proposes
  • that the wavefunction collapse is a real process that is somewhat connected with quantum gravity and perhaps time-asymmetry of the fundamental physical laws; I guess that Wilczek and I are not the only people who think that these ideas are misguided
  • the initial conditions for the Big Bang are, according to Penrose, unlikely - the gravitational field must be very ordered while the matter is in thermal state which is an unlikely state; well, I would say that these things are explained well in Brian Greene's The Fabric of the Cosmos
Penrose also talks about particle physics which is the most problematic part of the book. Wilczek has found several huge errors, for example
  • Penrose believes that the Cabibbo angle governs the mixing of K0 and K0bar into K0-short-lived and K0-long-lived.
  • Penrose apparently talks about some non-existing alternative directions in electroweak symmetry breaking
  • Penrose believes that at this transition, some new kind of disorder arises
Peter Woit loves Penrose's book because it is also critical about string theory: Peter Woit's reaction is more predictable than the Hydrogen atom. Wilczek does not say much about these topics, but according to the available data
  • Penrose believes that there is something wrong with the black hole entropy calculations - which must definitely be a misunderstanding on his side (I don't have the book so it's not clear what the misunderstanding is)
  • We've been informed that Penrose protested that something had to be wrong with all theories with extra dimensions because the moduli spaces of Calabi-Yau spaces have singularities such as the conifold; Penrose obviously has not been explained that the conifold singularity is exactly one of the physical questions that has been best understood in the 1990s, and physics of string theory around this point is completely non-singular. It's an example of a triumph of string theory. See the paper by Strominger and its 400 citations. ("Conifolds in string theory" is a larger field than "loop quantum gravity", and the former makes sense.) Roger Penrose also does not like higher-dimensional theories because they make his twistor ideas less important.
To summarize with Wilczek: there's much to admire and profit from in this book, but judged by the highest standards The Road to Reality is deeply flawed.

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reader Quantoken said...

As I pointed out, the blackhole entropy in the Hawking form, i.e., proportional to horizen area divided by planck length squared, can easily be fixed using nothing more than merely some dimensional analysis technique. So it is NOT a big deal at all for super string theory or LQG to have derived the BH entropy. Any theory at all which does derive a formula for BH entropy, and which does the math correctly and does not result in the wrong physical units (an elementary school level mistake), would have arrived at the Hawking BH entropy formula, give or take a trivial dimentionless factor. Getting that 1/4 factor right is just numerology.

See this for a simple gedanken expperiment:
http://quantoken.blogspot.com

As for Roger Penrose. He is as infamous as Eddington for two things he repeatedly lied. One is he kept boasting Eddington's 1919 solar eclipse experiment as one of the greated experiment (in supporting the GR), knowing full well that that experiment has long be discredited for data manipulation and untrustworthy of data accuracy.

Eddington's experimental setting simply could have produce the kind of data accuracy needed to prove or disprove GR or see any effect at all. I do not know why the scientific community keep brainwashing young people by torting the 1919 experiment.

Another ingamous thing for Penrose is he repeated mislead the public by torting the binary pulsar observation data as "proving GR to the accuracy of 12 decimal places." The truth is the raw observation data needed to be averaged over long time to achieve an accuracy of 12 decimal places, before any tiny GR effect would show up at all, instead of being buried in noises.

So the 12 decimal places figure was not something to boast about the accuracy of GR, but was actually a reason to suspect the experiment result that whether it was possible to achieve that kind of accuracy, through massive data average and computation, using the 1970's computer technology, when there wasn't even a 32 bits CPU, and the precision of floating point numbers on computers was no more than just 7 or 8 decimal places.

Even with today's computing technology, it would be hard pressed to achieve a systematic error due to computer floating point data round-offs, which is accurate to better than 12 decimal places.

Quantoken


reader Anonymous said...

I don't mind the notion that deterministic wave function collapse be associated with sub planckian regimes. T'Hooft has a few interesting ideas about that.

I mean its really the only place that such a thing could occur by quick inspection of Bells theorems. Since various cherished local symmetries may no longer be present at that regime, it *may* get by the inequalities.

Still thats speculative in nature, and not scientific unless a suitable self consistent theory was available that allowed for such a thing


reader Quantoken said...

Speaking of book reviews, some one on Peter's blog posted this link:

http://schwinger.harvard.edu/~motl/rovelli.html

It would be amazing if as Lubos claimed his review of the Rovelli book has become more popular than the book itself. And it's good that Lubos provided a URL to the book as free in PDF.

But I guess Rovelli would have known Lubos's review, which is not kind of all. Rovelli must have written a rebuttal to Lubos's review and published it some where. Would any one be kind enough to provide the link to Rovelli's rebuttal to Lubos's review, and/or any Lubos rebuttal to Rovelli's rebuttal?

Since I would like very much to see those rebuttals first before I read Lubos' review, and then the actual book. It would be more fun than just straight read the book first and then the reviews and rebuttals :-)

Quantoken


reader Anonymous said...

Lubos,

Can you go in to more detail on what is wrong with Penrose's entropy arguments? Wilzcek, for instance says that Penrose "argues forcefully that the standard initial state assumed in big bang cosmology, which posits thermal equilibrium for matter but near-perfect order in the gravity field (i.e., uniformity), is highly unlikely--in the precise sense of having extremely low entropy relative to the maximum available."

Thanks,
Vish


reader Anonymous said...

Quantoken, look up the reviews on amazon for Rovelli's book and you will find what you are looking for, sort of.


reader Anonymous said...

The best book reviews are always written without reading the book!

I doubt if Rovelli has bothered to answer Lubos's review, which was more a rant than review. Rovelli did publish the linked rather amusing (fictional) Dialog on Quantum Gravity though. It (and Lubos's review) did inspire me to buy Rovelli's book, though. Anything in physics that could inspire so much fury *had* to be interesting. I can't say that I agree with many of LM's comments, and I sometimes wondered if we were reading the same book.


reader Lumo said...

Dear Vish,
thanks for your feedback!

First of all, we definitely NEED a low-entropy beginning of the Universe. This is the only way how the arrow of time emerges: this is why the people are getting older but usually not younger. A low-entropy beginning of the Universe is what's necessary for the second law of thermodynamics to make sense.

Just like the entropy may be expected to be large in the future, it must be small in the past. So if someone like Penrose assumes that the entropy right after the Big Bang must be maximized, then it directly contradicts the 2nd law of thermodynamics.

In the standard Big Bang theory, we must *assume* that the beginning had a low entropy, and I will try to justify it later. The entropy then grows to the present value. Note that the matter entropy is maximized for uniform densities (like for gas). On the other hand, the gravitational entropy is maximized when the gravitational field is inhomogenious - if the matter is clumped.

This is what allows the early gas to clump (and seemingly create a more order state) without violating the 2nd law of thermodynamics: the gravitational entropy overcomensates the decrease of the entropy.

OK, so why was the beginning of the Universe a low-entropy state? The best explanation we have is inflation. It simply explodes the size of the Universe. During inflation, the total entropy of the Universe grows, but much more slowly than how it would grow otherwise, without inflation.

Because of inflation, you can even imagine that the Universe before the inflation was a pretty high-entropy state, which is what you probably prefer (although it's not clear whether it can really be a "maximal" entropy state). The inflationary era then dillutes the entropy to a superlarge volume; the density decreases.

Congratulations to the reader who bought Rovelli's book - great deal and a very rational reason why you bought it! :-) You never know whether I am paid for attracting readers like you. ;-)

All the best
Lubos


reader Anonymous said...

Sorry, bad link in previous post: Dialog on Quantum Gravity


reader Anonymous said...

Lumo - You never know whether I am paid for attracting readers like you. ;-)Well, I certainly hope so. You certainly worked pretty hard at it. Actually, it was the dichotomy between Rovelli's calm, witty discussion and your "off his meds" passion that intrigued me. Though to be honest, I had already read other stuff by Rovelli.


reader Lumo said...

Happy ends are great - especially if everyone is happy.

You bought a great book. You will learn that the space is made of Lorentz-violating atoms and even afterwards, you will have toilet paper for $70.

Also, by having bought this text, you improved the amazon.com ranking of this great book from #379,554 to #202,665, and all people who have worked on the book will get a part of your money.

This is how things should work. ;-)


reader Anonymous said...

Lumo - You bought a great book....

And an even better deal - it only cost me $48! I'm going to bed now, so I'll put it back on the shelf, right between Polchinski and GS&W. It does look a bit lonely though - I'll be looking forward to your review of Thiemann's complementary volume. If you ever write a book, and the price is right, I'll put you between the two of them.

:-)


reader Anonymous said...

Lumo - Just like the entropy may be expected to be large in the future, it must be small in the past. So if someone like Penrose assumes that the entropy right after the Big Bang must be maximized, then it directly contradicts the 2nd law of thermodynamics.
...

You are distorting Penrose's argument. Of course he doesn't make the elementary error of assuming that the overall entropy is high initially. He is saying that if you consider the particle content in isolation, it is a maximally entropic state - a hot dilute gas with only the minimal clumping forced by quantum fluctuations. On the other hand, if you consider the gravitational field in isolation, it is the opposite - maximally flat and minimum entropy.

I'm sure he realizes that inflation is supposed to produce this state and cure the paradox, but as you well know, that only happens when the inflation is exquisitely fine tuned. The paradox isn't really cured, just swept under a different rug.

And since you mentioned Greene's book (and vetted it), you doubtless recall that there is nothing necessary about the universe starting in a low entropy state - it's far more likely that our current low entropy is just a fluctuation. Of course that would make history and physics (and life) a bit pointless.


reader Quantoken said...

Lubos said: "First of all, we definitely NEED a low-entropy beginning of the Universe. This is the ONLY way how the arrow of time emerges: this is why the people are getting older but usually not younger. A low-entropy beginning of the Universe is what's necessary for the second law of thermodynamics to make sense."

Wrong! The time arrow would emerge if the entropy of the universe increases. But that is definitely NOT the only way time arrow can emerge. There are plenty of ways time arrow emerges with a none-increasing entropy.

The computer is a good example. If you a little bit of computer science you know that any computation do NOT yield more information than the input. Some computation processes are irrevesible and that would yield the time arrow, like one way hash. You can generate incredibly complicated and seemingly random sequence from very simple inputs. But still the information or entropy never increase, and we all know that a computing process does NOT generate true randomness. It only generate pseudo random sequences.

Seth Lloyd suggested that our universe is a giant quantum computer. See his "computational universe".

The truth is the total quantum entropy of the universe never increases or decreases. That's the basis of the GUITAR theory.

For entropy to grow, you would have to inject true randomness. The God would have to toss a dice. Even a physical dice would roll according to the physics of dynamics. But the dice the God tosses would have to roll in a completely random way that does not obey any physics law in its movements. It's unthinkable how such randomness could have been generated in the first place.

That's why Einstein said "God does not toss a dice."

As for the second law of thermal dynamics, one has to keep in mind it's only a possibility law and not an absolute law. There are chances that all gas molecules in a room would be collected on half of a room and the other half happen to be vacuum, although such possibility is astronomically small, it is yet not zero.

The second law is not the most fundamental ones of physics laws and it must have been derived from something more fundamental, and is only good statistically. The most fundamental law is the conservation of quantum information of the universe, which means the observed universe must be of fixed size and limited, and that causes effects like Hubble red shift and spacetime curvature etc, all are needed to conserve quantum entropy.

Quantoken


reader Quantoken said...

The GUITAR theory has been amazingly successful in deriving tons of extremely precise results, including the correct CMB temperature of 2.724K, the neutron to electron mass ratio up to 10 decimal places, calculated using the best known netron decay lifetime 885.4 +- 0.4 seconds.

Recently I further derived the characteristic mass responsible for weak interactions. We know the fundamental quantum of mass M0 = Me/alpha, or about 137.036 times the mass of an electron.

When the electromagnetic field of an electron expands to the whole universe, it results in a mass which is alpha times the mass quantum, alpha*M0, which is Me. Oppositely, when we push the field inward, it would result in a mass equal to (4*PI/alpha)*M0, which is
4*PI*137.036^2*Me. And that is about 120.6 GeV.

Once you project that characteristic mass of 120.6 GeV on the two sides of a right angle triangle, whose longest and shorted sides are 3 and 2, then you get two component masses:
M1 = M*sin(theta) = M * 2/3 = 80.4 GeV
M2 = M*cos(theta) = M * sqrt((9-4)/9) = 89.89 GeV

And that two masses are the masses of the so called W and Z particles responsible for weak interaction.

Very precise, isn't it?

Quantoken


reader Leucipo said...

89.89 is a bit of from 91.18

Still you can rewrite your formula as
3/8 M_W= pi/alpha^2 m_e

and blame GUT for the 3/8 value.


reader Leucipo said...

Better yet, you could join HdV in noticing that the value M_e/M_W is very close to the difference between muon and electron magnetic anomalies.It could be fine tuning or it could be the same coincidence. I have never calculated the muon magnetic anomaly, but a term such as (3/8pi) alpha^2 does not seem very surprising in such context.


reader Quantoken said...

Leucipo said:
"Better yet, you could join HdV in noticing that the value M_e/M_W is VERY CLOSE to the difference between muon and electron magnetic anomalies.It could be fine tuning or it could be the same coincidence."

You need to take general physics again! The "coincidence" you discussed is the same coincidence that muon and electron happen to have the SAME charge and them also happen to have the same spin, and when their charges spins they happen to generate magnetic field following the same QED laws!!!!

It's a known physics fact that the magnetic momentum has got to be inverse proportional to the particles mass. No new physics here. Too bad you don't know it.

Quantoken


reader Quantoken said...

BTW, who is this HdV guy who also thought of the same "coincidence"? I hope he is not a famous guy or Harvard professor something. Otherwise: Too bad a famous guys could be SO ignorant of basic physics training.

Quantoken


reader Lumo said...

Dear Quantoken,

I encourage you to reduce your self-confidence, especially when you're attacking others (not just me!), to a level that more accurately reflects the other participants' judgement of your intellectual capacity.

Thanks,
Lubos


reader Quantoken said...

Lubos:
One's self confidence is based on his basic training. It took me less that half a second to see that the mass ratio and magnetic momentum ratio has to be the inverse of each other, from known physics laws. How long does it take you to realize it? It would be disgraceful for any established one to fail to be unable to see that fact.

Have you verified my claim of neutron mass calculation up to 10 decimal places? There can be no coincidence when you reach 10 decimal places. And if they provided me the wrong neutron lifetime I could not have obtained the correct result. So at least I have pointed out a correct empirical relationship between delay lifetime and mass difference. That could also be used to explain why the actual W, Z mass is slightly higher than my calculated values.


Quantoken


reader Leucipo said...

Quantoken, I am surprised of knowing that the mass of the W particle (not the muon) is now a concept of general physics primers. Please recommend me your university.

As for HdV, as far as I know hr is an engineer, and I quoted it to you because you could consider him more a "peer" than other physicists, even if his numerology is usually better expressed than yours. And he knows what the anomalous electronic moment is.

But just compare my way of writing your own formulae with the original one. You must improve formal presentation in order to transmit your ideas.


reader Leucipo said...

Incidentaly, the Quantoken webpage could be a good example of the problems with landscapes. He claims to have a six parameter space where he can pinpoint two three vectors (a,b,c),(x!,y!,z!) and then by choosing some basic algebra operations, he gets exactly a six decimal digits measurement. Obviously we could give the six digits directly and the information content is even better.

Then, Q. takes the precaution of claiming that a secret analysis of his landscape selects (he does not say "uniquely", but it is implied) the vectors to be (1,3,3) and (1!,5!,7!).

It reminders me of a letter from Newton to Leibniz, where N. does not want to give a detail of calculus, but at least he chooses to give a checksum of the detail he is hidding, so in the future he will be able to proof he already know the occult detail. If Q. really had a theory, he could use public key encoding to make it available, then to publish the deciphering key when he feels ready.

And of course, Lubos could strongly suggest this to be done in Quantoken blog, not his :-)


reader Quantoken said...

You mis-quote my (1,3,1) as (1,3,3), and I mis-read your M_w as muon mass. fifty-fifty.

But still your said coincidence is probably in the known of physics. The magnetic anormaly was NOT calculated, but MEASURED, Find them here:
http://www.physics.nist.gov/cuu/Constants/index.html

The measured magnetic moment anormaly difference between muon and electron is 6.26762(62)x10^-6. That is indeed close to the mass ratio of electron to W boson, but not a very impressive closeness.

I would say that the magnetic moment anormaly difference must be due to some process that the weak interaction is involved, so surely the heavier the particle involved in the interaction, the smaller the difference will be.

It would be reasonable to say that both the W and Z bosons will participate in that interaction. There will be a mixing angle. To figure out the mixing angle, draw a right angle trangle of side equals to 3, and one edge equals to 1, so
sin (theta) = 1/3
cos (theta) = sqrt(8/9)

The mixing would be:
(M*)^2 = (M_w*cos(theta))^2 + (M_z*sin(theta))^2

Using my calculated mass of W and Z:
M_w = 80.4 GeV
M_z = 89.89 Gev
You get:
M* = 81.51 GeV

So the ratio is:
Me/M* = 0.510998 MeV/81.51Gev
Me/M* = 6.2691x10^-6
Not a bad conincidence at all with
delta U = 6.26762(62)x10^-6
The difference is only 2 sigma.

Quantoken


reader Anonymous said...

And speaking Brian Greene's book (FotC), I just started reading his section on the expanding universe. Boy does he make a dog's breakfast of his attempt to discuss co-moving coordinates. I was counting on you to catch that type of conceptual blunder, Lubos.


reader JesseM said...

Lubos, if chaotic inflation is the answer to the arrow of time problem, then would you predict there would be an equal number of regions of the universe where the arrow of time operates in reverse, which finally shrink down to tiny patches of space via reverse-inflation? If not, then it seems inflation does not really answer the question of how the arrow of time can emerge from time-asymmetric laws. You're probably aware of Sean Carroll's recent proposal which says that at some distant point in the past long before our own Big Bang there were plenty of time-reversed universes, so that on the largest scale spacetime is completely time-symmetric, but this is the only inflation-based theory I know of that has this feature (and Carroll says he was influenced by Penrose in coming up with this proposal).


reader Quantoken said...

Virtually all equations of all known physics are exactly time reversible. So from a microscopic theory point of view, it's extremely difficult for a time arrow to emerge from those known time reversible physics laws.

Seth Lloyd is making a step towards the right direction, I think. Time arrow NATURALLY arises once you consider the whole universe as a giant quantum computer. One needs to know that the computation processes are normally IRREVERSIBLE: you can not execute a piece of computer code in reverse order. Many of the mathematics algorithms are also irreversible, like one way hash.

Such irreversibility is directly responsible for the occurence of the time arrow. And it does NOT require an entropy increase to do that.

Quantoken


reader Quantoken said...
This comment has been removed by a blog administrator.

reader Lumo said...

Well, I don't remember a discussion of the co-moving coordinates in Brian's book. Even though I found other errors in this discussion - how pressure and energy density affects the evolution of the shape of the Universe; signs of different pressures and energy densities; and so on, it is entirely possible that I've neglected an error related to co-moving coordinates especially because I did not understand that this coordinate topic was discussed. But could you be more specific what's the alleged error?

The arrow of time is a source of infinite discussions - and we had long discussions with Brian, too. It is partly a matter of philosophical preference. Most people including Quantoken! - well, except for Penrose - agree that the elementary dynamical laws of the Universe are CPT-symmetric and/or very close to T-symmetric laws, so that they can't explain the big asymmetry from the thermodynamic point of view.

The thermodynamic arrow of time has its origin in the special low-entropy beginning of the Universe. I actually think that there is a more fundamental arrow of time inserted to the interpretation of quantum mechanics where one is suppose to insert the initial density matrix or state and predict the probabilities in the future, not the other way around. I am convinced that all the pictures of the Universe where different parts have different arrows of time are inconsistent, but I don't really know how to convince others about it.


reader Lumo said...

Well, I don't remember a discussion of the co-moving coordinates in Brian's book. Even though I found other errors in this discussion - how pressure and energy density affects the evolution of the shape of the Universe; signs of different pressures and energy densities; and so on, it is entirely possible that I've neglected an error related to co-moving coordinates especially because I did not understand that this coordinate topic was discussed. But could you be more specific what's the alleged error?

The arrow of time is a source of infinite discussions - and we had long discussions with Brian, too. It is partly a matter of philosophical preference. Most people including Quantoken! - well, except for Penrose - agree that the elementary dynamical laws of the Universe are CPT-symmetric and/or very close to T-symmetric laws, so that they can't explain the big asymmetry from the thermodynamic point of view.

The thermodynamic arrow of time has its origin in the special low-entropy beginning of the Universe. I actually think that there is a more fundamental arrow of time inserted to the interpretation of quantum mechanics where one is suppose to insert the initial density matrix or state and predict the probabilities in the future, not the other way around. I am convinced that all the pictures of the Universe where different parts have different arrows of time are inconsistent, but I don't really know how to convince others about it.


reader CapitalistImperialistPig said...

In FotC, pages 234 and 235, with talk of motion in excess of the cosmic flow of spatial expansion and similar "ether drift" type notions.

Contrary to what he states, in our reference frame, clocks of distant galaxies *do* run slow, just like the clocks of a local observer with the same speed. In fact, a local observer, moving at the speed of the distant galaxy, would find the distant galaxies clocks synchoronized with him, but not our clocks.


reader Quantoken said...

Lubos said:
"I am convinced that all the pictures of the Universe where different parts have different arrows of time are inconsistent, but I don't really know how to convince others about it."

That notion is surely inconsistent not because it is physically inconsistent, but because it is logically inconsistent. It's logically inconsistent to observe any time reversed process, because time arrow is a very strongly perceptual thing.

Let you give you one example. What would you think when you see some one walking BACKWARDS on the street?

Penrose would say: see! here is a good example of time reversed processes. This guy is actually walking normally forward. But his time arrow is exactly opposite to ours, so we see him walking backwards.

But virtually every one else other than Penrose would say: No, his time arrow is forward. He is merely doing funny thing by walking backwards.

Physically, whether the guy is walking backwards with a normal time arrow, or he is walking forward but his time arrow is reversed. The two are in-distinguishable. We can not do physics experiment to distinguish the two different cases, because virtually all of our physics laws are time symmetric.

But we strongly attach ourself to the percepual idea that the time for every thing all tick forward, not backward. Because of that, we could never observe any time reversed process. Even if we observe something that seems to be time reversed, we explain it not as time reversal, but as reversal of the actual physics process!

Nuclear decay process could be such a "time reversed" process. We look at a nuclear and it simply releases an electron and an anti-neutrino at a totally un-predictable time. The thing is completely random and with no cause at all, which defies logic.

In principle, if it were not for our strong conviction of time arrow always move forward, we could consider the decay as a time reversed process of particle collision: An incoming electron and anti-neutrino hits the nuclear and be absorbed. This way we removed the randomness and give the event that happens a proper cause and proper predictability.

We no longer have the predictability problem here: Things happen exactly when we obser an electron and anti neutrino hit the nuclear at almost the same time. But we face a probability problem instead: how could such a low probability event happen at all?

You see what happened when we do time reversal? We have traded the difficulty of predictability, with the difficulty of probability.

The "predictability" and "probability" are twin brothers that convert between each other in time reversal! And they both have a natural explanation when you introduce the concept of total quantum entropy of the universe. Once you fix that total amount of quantum entropy, it leads to the time symmetry between predictability and probability of events!!!

Quantoken


reader Lumo said...

Dear Capitalist pig,

I think that you are very confused. By "our reference frame", Brian and other physicists obviously mean the standard coordinate "t" in the Fridman-Robertson-Walker solution.

The same value of "t" means the same proper time from the big bang, or the same historical era of the Universe. By definition - and assumption of homogeneity - this time "t" is going with the same speed at all places of the Universe, while the objects that are moving relatively to the CMB frame would be time-dilated according to the usual rules of special relativity.

I disagree that you have found an error in FOC.

All the best
Lubos


reader CapitalistImperialistPig said...

Lubos - I know what Greene was trying to say, but it's what he *did* say that I find wrong.

Greene - Recall from Chapter 3 that Einstein discovered that clocks that move though space in different ways tick off time at different rates...But the clocks we are now disussing are not moving though space at all.Brian Greene seems to have rediscovered absolute space! Is that a feature of string theory? Because those clocks sure as heck are moving though space in a reference frame fixed in our galaxy. And compared to our clocks they tick slower.

Greene - It is precisely these clocks - clocks whose only motion comes from the expansion of space - that provide the syncronized clocks needed to measure the age of the universe. What I object to is this notion of absolute space, and the fact that he makes it sound like these clocks are sychronized with ours. Each of these clocks has only local validity. What bothers me the most is that he makes it sound as if an Astronaut zipping thru space (in, say, our galaxy) with the same velocity as some distant galaxy would not find his clocks ticking at the same rate as those in the distant galaxy.

And don't call me confused till you get the facts in your posts within a couple of orders of magnitude of right.


reader CapitalistImperialistPig said...

Lubos - One more point. The point he is making is that at each point in our local universe, there is a preferred reference frame with respect to the isotropy of the local universe. The mumbo-jumbo about points at rest with respect to space make it sound like Lorentz invariance doesn't apply.

Though maybe you have converted to the LQG religion and don't believe in that anymore :-]


reader Anonymous said...

CIP said:
Because those clocks sure as heck are moving though space in a reference frame fixed in our galaxy. And compared to our clocks they tick slower.

No, they aren't moving at all. They are stationary. The space between us and them is changing with time, and this is why they are redshifted. But they are *not* moving with respect to us at all. In fact Greene is one of the few popularizers who gets this right.


reader Lumo said...

Dear CIP,

I also agree with Greene. Technically what Greene (and we) have in mind are the usual coordinates for the FRW Universe.

While local physics in the approximation of special relativity is Lorentz invariant and there is no preferred frame, in cosmology (which needs general relativity), of course, there *is* a preferred frame - you can call it "absolute space" if you wish to be provocative :-) - and it is the frame associated with the cosmic microwave background.

You can determine whether something is moving with respect to it, or not. Note that this breaks Lorentz invariance only by a small amount - amount corresponding to the weak CMB radiation, or alternatively, amount that only becomes apparent when you consider regions comparable to the Universe.

But once again, yes, a cosmological solution (big bang) spontaneously breaks most symmetries including the Lorentz symmetry, and picks a reference frame.

The "same point in space" is the point with the same (usual) FRW spatial coordinates. As this "same point" moves through time, we therefore say that it does not move through space at all. However, the metric is being scaled by a factor that depends on time - again, this is a universal cosmic time, if you wish.

There is definitely no error in the quotes you listed.

Does it help?
Lubos


reader CapitalistImperialistPig said...

I think Lubos understands my point*, but just won't admit that Greene's presentation is misleading, but that Anonymous is genuinely confused, probably due to reading Greene :-) In any case, I have a short true-false test for you each:

a) The relativistic Doppler effect can be thought of as the product of two factors, one due purely to the recession and the other due to the relativistic time dilation (the gamma factor). This is clearly explained, for example, in The Feynman Lectures, vol I, chapter 34. When we compute the Doppler shift from a distant galaxy, we should neglect this time dilation factor, since it isn't moving with respect to space, and its clocks are synchronized with ours. True or False?

b) We can think of each galaxy as carrying with it a little clock, measuring proper time elapsed since the big bang. (A precise measurement of the temperature of the CMB can be thought of as the measurement principle for such a clock.) Suppose we have a telescope powerful enough to read the clock of a distant galaxy moving rapidly away from us. If we allow for the travel time of the light from the distant galaxy we will find that its reading is just the same as our would have been when that light started out. True (because our clocks are synchronized) or False (because their clock ran slow due to time dilation)?

Eagerly awaiting both your answers.

Cheers!



*Based on his more or less apropos mumbling about FRW coordinates. Though the universe seems to be pretty darn flat, so I'm not sure GR is really the point.


reader eppur si non muove said...

a) The relativistic Doppler effect can be thought of as the product of two factors, one due purely to the recession and the other due to the relativistic time dilation (the gamma factor). When we compute the Doppler shift from a distant galaxy, we should neglect this time dilation factor, since it isn't moving with respect to space, and its clocks are synchronized with ours. True or False?

True. There is no Doppler shift in cosmology, though unfortunately it is often called that. The red-shift is due to something that happens to the light *after* it leaves the distant galaxy, namely the fact that it passes through a region where the spacetime geometry is dynamic. No time dilation, no recession either.

b) We can think of each galaxy as carrying with it a little clock, measuring proper time elapsed since the big bang. Suppose we have a telescope powerful enough to read the clock of a distant galaxy moving rapidly away from us.

It isn't moving......

If we allow for the travel time of the light from the distant galaxy we will find that its reading is just the same as our would have been when that light started out. True (because our clocks are synchronized) or False (because their clock ran slow due to time dilation)?

There are various subtleties here, but to cut to the chase, in essence the answer is "True" because to say otherwise would give you the idea that time dilation is somehow relevant here. How can there be any time dilation when the speed of that galaxy relative to us is [leaving aside peculiar motions] precisely zero? I repeat, the galaxies are not *moving*. The geometry is dynamic, a purely general relativistic effect that cannot be understood in terms of SR. Look for the phrase "dynamic geometry" in MTW.


*Based on his more or less apropos mumbling about FRW coordinates. Though the universe seems to be pretty darn flat, so I'm not sure GR is really the point.

If you think that GR is not relevant to cosmic redshifts, then it is you who are confused my friend. And our spaceTIME is very far from being "pretty darn flat", though 3D SPACE is. Indeed if spaceTIME were pretty darn flat there would be no redshift!


reader CapitalistImperialistPig said...

One vote in! One vote for the Chandrasekar theory of MTW*! But we still haven't heard from our critics. Let's turn those answers in folks. Your best chance to prove (not merely state) that one or more of us is deeply confused.

*For later elucidation.


reader CapitalistImperialistPig said...

After some reflection and study, I have to concede that eppur si is right, a conclusion that took some movement on my part. Of the several sources I consulted, I would like to mention Peeble's Physical Cosmology, which reinforced my confusion, Sean Carroll's Intro to GR, which was very helpful, Weinberg's G&C, which pointed out that the true and false answers are not necessarily mutually contradictory, and expecially John Baez's short article.

I believe my most important confusion was in not realizing that the flatness cosmologists refer to was the just in the three-geometry. Further clarification might be appreciated. Or not.


reader Anonymous said...

Well, you don't have to feel bad about getting confused about this matter, because a hell of a lot of professionals are confused about it too. I really don't know of any reference that sets out the facts clearly and unambiguously. Maybe the best thing to do is to stare at the FRW metric for a cosmology with flat spatial sections. What do you see? You see Pythagoras's theorem with a time-dependent multiplicative factor. What has happened is NOT that things have started to move --- rather, Pythagoras has become time-dependent!


reader Jack Sarfatti said...

Loop Quantum Gravity and Superstrings?
Who ordered them.

Jack Sarfatti
http://stardrive.org
sarfatti@pacbell.net

Previews of Coming Attractions

1916 GR is like an old man with an enlarged prostate - a mere trickle of stress-energy density currents between gravity and matter fields because of the Bianchi identities with zero torsion and zero non-metricity.

Loop quantum gravity and superstrings? Who ordered them? They are both not even wrong.

Since the metric for the Hodge duality is Minkowski in the Yang-Mills spin 1 substratum of Einstein's emergent (A. Sakharov, 1967 "metric elasticity") we can cleanly separate positive and negative frequency parts for a good Fock occupation number space fiber with creation/destruction ladder operators for the virtual bosons inside the "Higgs Ocean" vacuum at each "coincidence" P. We never have to worry about quantum gravity foam because gravity is simply the smooth ODLRO phase modulation with a little bit of quantum noise in the Bu^a field.

Let a(x) and a*(x) destroy and create a VIRTUAL boson inside the post-inflation vacuum then

|Post-Inflation Higgs Ocean>

= e^(w*aa - wa*a*)e^(za* - z*a)|Massless Pre-Inflation Dirac Sea>

a|z> = z|z> Glauber macro-quantum state (displaced circular Gaussian in phase space).

|w,z> = squeezed elliptical displaced Gaussian. The squeeze parameter is the eccentricity of the ellipse and the orientation of its major axis in phase space (N,theta). The area of the Gaussian random noise is preserved.

The inflation noise is Gaussian obviously and this is actually observed in WMAP. We should also look for variable squeezing across the sky related to galaxy and star formation?


On Jun 12, 2005, at 2:55 PM, iksnileiz@earthlink.net wrote:


I agree with you that the non-trivial part B of the tetrad field may be the key to separating observer-dependent and objective aspects of the Einstein field, and arriving at a satisfactory understanding of gravitational energy.


J: Rovelli starts from there, but he has no idea that ALSO the dimensionless

Bu^a ~ BuLp Grad(Vacuum ODLRO)

4D Grad in a indices.


for the 4D Diff(4) macro-quantum supersolid world crystal is analogous to

v = (h/m)Grad[arg(Ground state ODLRO) for the 3D macro-quantum superfluid

g(curved metric)uv ~(flat)uv + B(uIv) + B(uBv) for "spin 2"

Note the elastic linear B term and the plastic nonlinear B^2 term.

Also, B while is not a spin-2 Diff(4) first rank tensor field all by itself, it is a Minkowski spacetime spin-1 Yang-Mills vector field.

Z: No surprise, since he is working with a different model.

Personally, I think you are way ahead of him.

J: I do explain many puzzling anomalies now observed!


J: Lubos is probably correct about the lack of contact of loop quantum gravity with observation and that it cannot even reproduce GR. Baez admitted that at GR 17. Of course string theory has its weaknesses too, but may be closer to observation? We also have to look at Wilczek's objections to some of Penrose's statements.

Z: Also, as I've mentioned, spacetime coordinate transformations, as *mathematically* defined, do not change any observer's world line.


J: That's what I call a kind of gauge freedom.

Z: You can call it that, and I appreciate your analogy, but I think the problem goes much deeper.

J: Too vague. Show how.

J: That is, all GCTs that do not change the state of motion of a detector are physically equivalent. An example of a physical GCT is starting in the rest LIF of a detector in space and then firing a rocket engine attached to the detector. The transformation, in that case, tetrad eu^a(P), that describes the relation between the momentarily coincident LIF with indices a & LNIF with indices u at same P. But you see here a complete local equivalence of the inertial force to the gravity since the physical difference is Bu^a in

eu^a(P) = Iu^a + Bu^a(P)

i.e. Bu^a(P) encodes the information of switching on the rocket engine!

You cannot locally distinguish inertial force from gravity force!

Z: But actually you can, as shown by Ohanian & Ruffini.

J: No, you still don't get it! You keep getting hung up on that. You do not understand what the word "locally" means. It means DO NOT MEASURE GEODESIC DEVIATION. Indeed, geodesic deviation is irrelevant to gravity force. The measurement procedures are orthogonal.

Obviously you can measure the local tidal curvature tensor at P in either an LIF or a LNIF makes no difference.

EEP means, YOU DO NOT MEASURE THE GEODESIC DEVIATION CURVATURE AT P because even if you do, then you STILL cannot tell the difference between an inertial force and a gravity force! Suppose the curvature is not zero so what? Think of y = y(x) and dy/dx. Measure y at xo. That does not tell you anything about dy/dx at xo if you have no prior knowledge of y(x). Indeed IN ALL CASES GRAVITY FORCE IS ALWAYS 100% INERTIAL FORCE. GRAVITY FORCE IS 100% INERTIAL FORCE in EVERY CASE IMAGINABLE.

Here inertial force is the NON-GRAVITY REACTION FORCE needed to PUSH the test particle OFF a timelike geodesic (relative to LC connection - I only do 1916 GR here).

The measurement of tidal curvature geodesic deviation is most cleanly done in the LIF where all gravity forces are strictly ZERO and special relativity applies locally to a good approximation.

Consider the SSS metric in only the radial direction to keep it simple

ds^2 = (1 - 2rs/r)(cdt)^2 - (1 - 2rs/r)^-1dr^2


This metric is only good for those HOVERING LNIFs at FIXED r > rs. Some NON-GRAVITY FORCE is pushing those HOVERING LNIFS off timelike geodesics. For the LIF observer the effective LOCAL metric is always to lowest order approximation

ds^2 = (cdt')^2 - dr'^2

even though geodesic deviation for the LIF observer is not zero!

The key is

(1/2)c^2Gradgoo = (1/2)c^2Grad(1 - 2rs/r) = c^2rs/r^2 = GM/r^2

= APPLIED UNIVERSAL NON-GRAVITY INERTIAL FORCE PER UNIT TEST MASS POINTING OUTWARD NEEDED TO KEEP THE HOVERING LNIF DETECTOR AT FIXED r.

IN FACT GRAVITY FORCE IS ELIMINATED 100%. What we call "gravity force" is 100% INERTIAL FORCE logically independent of curvature.

Of course in flat space-time you do not need any non-gravity force at all to keep a test particle "still" relative to a marker (neglecting their weak gravity of course).

Therefore, Paul you have been working on a non-problem! The gravity energy is also a non-problem, but much more subtle.

Similarly, I mean a local event as a coincidence of at least two processes, like Rovelli's "collision" of two point particles, that is clearly an active Diff(4) invariant "object".


Z: Spacetime "events" are addressed by coordinates,

This is wrong.


Z: Wrong?

J: Yes, wrong.

Z: Obviously "events" occur at definite locations on the spacetime manifold, and these 4D locations (points on the spacetime manifold) are assigned unique addresses by spacetime coordinate systems.

J: Not even wrong until you give an operational definition for "definite locations on a spacetime manifold". Rovelli is good on this issue.

Z: Mathematically, at least, changing CS *addresses* has to be sharply distinguished from changing *locations*.

J: Prove that with a mathematical example. Your words are too vague.


Rovelli is correct on that part. Events are coincidences like the collision of two point particles (toy model).


Z: Yes, but these coincidences occur at *definite locations in spacetime*

J: Wrong. Read Rovelli again on this. There is no such thing as

*definite locations in spacetime*

Define what you mean. Do you mean a collision of two point particles? If so, see Rovelli's discussion of the "Einstein hole problem" with the nice pictures.

that are merely assigned addresses by
spacetime coordinate systems.

Z: If Rovelli thinks that there is no mathematical distinction between an active Diff(4) rearrangement of manifold points (an actual deformation of the manifold) on the one hand, and a mere reshuffling of CS addresses, on the other, then
he is quite mistaken IMHO.

J: I do not understand what you just wrote. Your words are not even wrong. Give a mathematical example of what you mean here. If you cannot do that you have not really said anything worth saying on the issue.

You seem to think that the Diff (4) group creates physical deformations. That is not true at all. Only stress-energy density currents and self-interactions of the geometrodynamic field create physical deformations of the manifold. That's why we have Diff(4) covariance in the first place! That's why in

Guv(Gravity) + /\(ZPF Vacuum Energy)guv(Gravity) + (8piG/c^4)Tuv(Matter) = 0

We only have Diff(4) COVARIANT TENSORS!

Diff(4) is the LOCAL SYMMETRY GROUP it DON'T MAKE ANY PHYSICAL or "actual deformations". You have the wrong idea entirely!

Diff(4) is the LOCAL GAUGING of T4 with Bu^a as the induced compensating gauge potential. Also, you have Vacuum ODLRO in the inflation phase transition from the unstable rest-massless gravity-free conformal false vacuum to the stable curved vacuum with rest masses from Higgs ODLRO coherence and gravity and even dark energy/matter in which T4 is SPONTANEOUSLY BROKEN to allow CURVATURE! You do not get Gennady Shipov's torsion until you LOCALLY GAUGE so(1,3) in addition to T4. If IN ADDITION you spontaneously break so(1,3) in the vacuum then you will also get preferred velocity effects. Whether that happens or not, apart from Hubble flow (maximal isotropy of CMB) is purely empirical.


Z: but are not defined by them. So it should be obvious that such "events", just like manifold points, are absolutes with respect to such transformations.

J: Too vague. Give a precise mathematical example.

You have the wrong idea here. I mean you have garbled things above.

Z: No, I just disagree with your your version of Rovelli.

J: Well you are so vague that your words have no meaning to me.

Physical events are invariants to be sure, but "manifold points" are not.


Z: Manifolds are not *deformed* by mere coordinate changes.

J: Right, but neither are they deformed in active diffeomorphisms! That's the point!


Z: So as far as I can see, the effect of GCTs on manifold points and events is similar. Addresses are simply re-shuffled.

J: Yes, but that is the case for both active and passive Diff(4). The mathematically distinct manifold points A & B in Rovelli's nice discussion are not physically distinguishable, i.e. the collision of particles 1 & 2 is PUSHED FORWARD (or is it backward?) from A to B so that NOTHING MEASURABLE has changed in the active Diff(4) from A to B. P includes both A & B in the same equivalence class!

Now your way of thinking will work to some extent in special relativity quantum field theory and in classical mechanics and classical electromagnetism, but it does not work in GR and it took the great Einstein what 3 years? to understand this and today most physicists still do not really understand it!


See Rovelli's explanation of Einstein's solution of the "hole problem".

For example, any transition overlap function between 2 local charts for same "coincident" P that leaves c^2(LC)00^i, i = 1,2,3 invariant is not physical. Note that points A & B in Rovelli's are same P = {~| A,B,C ...} That is A ~ B if B = active Diff(4) on A etc.

Z: In my POV, *none* of the mathematically defined coordinate transformations on the spacetime manifold has any physical meaning at all until such a meaning is attached to them, or to some subset of them.

Z: Chasing your own tail. Circular. Meaningless until you show an independent procedure.

Z: It's pretty obvious if you think about it.

J: Since I do not understand your English I do not know. If you cannot make your idea more mathematical or more specific in terms of gedankenexperiments you are not communicating to my mind at least.

Z: Mathematical coordinate changes in themselves do not change any observer's world line. But in order to change an observer's frame of reference, you must at the same time also change that observer's world line.

J: Yes, that I understand. I understand that if a LIF observer fires a rocket engine in space then she is transformed to a LNIF observer and that instant coincident local transformation (approximately to be sure) is not a Diff(4) thing at all but is a tetrad thing. But then if she changed the thrust it is a Diff(4) thing moving from one non-geodesic to another "instantly" at a "crossing point". But even then, the Diff(4) is a MERE DESCRIPTION of her PHYSICAL ACTION, e.g. throwing the switch or turning the dial on the thrust control panel.

Z: So there is a basic *contradiction* in the orthodox treatment that needs to be resolved. I'm resolving it.

J: No you have not. I just resolved it for you in my above remark - bull's eye!


I have no idea what you are talking about.


Z: I believe you. I'm afraid you'll have to wait until I write this up.

J: Read Andrew Marvel "To a coy mistress". Hal Puthoff has the same problem. Time and ET waits for no mortal. Promises, promises ...


That is, think of EM and weak and strong fields Au ... as animals living on Leviathan the Great White Whale Moby Dick, which is the geometrodynamic tetrad field e = I + B.


Note also Rovelli's remark that you cannot do spinors without using tetrads. See Kiehn's latest on MACRO spinor solutions of EM field solitons (if I got that right?).


Z: Fine.

* J: Kiehn thinks his spinor solitons explain Ken Shoulders EVOs. Perhaps, but I think I explain them with dark energy cores holding in the electric charge shell. On the other hand if the Vacuum ODLRO local field were itself some kind of macro-spinor field that could be interesting although I am not here sure if that idea makes any sense.


Z: This is *all* up in the clouds. Do you think Rovelli's indistinguishable points on the bare 4D manifold is not "up in the clouds"?

J: No, what he said there I find very clear. I have hardly read the rest of his book as yet.

Z: The abstract vector space that is constructed at each point on the manifold for which the tetrad forms a set of basis vectors need not have anything to do with the tangent bundle. Using a tetrad to span a tangent manifold is just a particular concrete interpretation of the abstract mathematical concept. All in the realm of pure mathematics, however.

J: So what? I don't see you saying anything important here.

Z: You can also choose a coordinate basis. That is not automatic either.


J:
e = eu^a&adx^u

e is a dimensionless Cartan 1-form

&a is a 1-co-form vector field basis in the tangent fiber with dimension 1/length

dx^u is a 1-form basis in base space with dimension length

Z: Yes, fine. I can see you've been studying this stuff.


J: Beginning to. There are some ambiguities in getting everything dimensionally consistent with factors of Lp. Mathematicans doing physics ignore all that setting everything = 1 and I think they make mistakes as a result e.g. mixed dimensions of the same components of the (LC) connection field for example. Some ~ r others ~ 1/r for SSS solution in some books. First rule in Physics 101 is that any equation should be consistent in units and physical dimensions.


Z: I think you may be right that at some point in the development the units should be put back in and careful attention should be paid to them.

J: I know I am right about that. Basic physics is being ignored by these mathematicians in physicist's clothing.

You can make them anholonomic (non-coordinate) sticking in Lie brackets - all well-known techniques.

e.g.

[dx^a,dx^b] = Wab^cdx^c

Wab^c = Jim Corum's object of anholonomy with dimension length

Yes, and what it represents physically is the state of linear elastic warping B(uIv) and nonlinear plastic cracking B(uBv) of the perfect Minkowski Planck lattice that is the pre-inflationary massless conformal false vacuum without any gravity and inertia at all!

Z: If you construct such a tetrad field, yes it can be interpreted that way.

J: It's very important - that's Hagen Kleinert's key idea. Tensors were invented for elasticity theory in the 19th Century.

Z: I'm simply pointing out that this is a particular interpretation of the abstract notion of a tetrad.

J: So? What then? Right but trite unless you say something surprising beyond that.
e.g. the state of warping and cracking of the 4D active Diff(4) invariant supersolid Higgs vacuum at P is given by the base space reciprocal lattice vector field

eu(P) = eu^a&a = (Iu^a + Bu^a)&a

where &a = nab&^b and [eu(P)] is a length^-1 i.e. eu - &u = Bu = crystal distortion reciprocal lattice "phonon" wave vector away from equilibrium along the u axis (u = 0,1,2,3), e^u - dx^u = B^u is the lattice distortion with dimension of length.

nab = flat Minkowski metric of pre-inflation unstable false conformal massless twistor vacuum without gravity and inertia because vacuum ODLRO = 0

Z: In the long-wave approximation this looks to me like a theory of continuous media in 4D.

J: That's Kleinert's idea. I have simply plugged into that with

Bu^a = Bu&^aargVacuumODLRO

Bu^a is a pure number. Therefore Bu is a length in that convention since &^a is 1/length

Z: OK.

J: Bu = Bu^adxa

dxa = (Mink)abdx^b

Bu = Bu&^aargVacuumODLROdxa

&^aargVacuumODLROdxa = 1

Z: OK.

J: What they are doing in loop gravity is overly-complicated (complexification of the tetrad, taking self-dual "instanton" part etc.) Where all the Pundits go wrong is not realizing that there even is a macro-quantum theory whose rules are different from micro-quantum theory. I get diff(4) invariance + background-independence non-perturbatively trivially!

J: Hawking made this error at GR 17. Susskind makes it also. So does Lubos. Of course, I could be wrong, but we shall see.

Z: If you're right they are all barking up the wrong tree.

J: Yes, All The Kings Horses and All The King's Men - even The Astronomer Royal!


Z: I'm inclined to agree.


J: Micro-QM is linear, nonlocal, unitary with signal locality. Macro- QM is nonlinear, local, non-unitary with signal nonlocality. Gravity + dark energy is a "More is different" macro-quantum phenomenon.

Vacuum ODLRO makes quantum theory (QT) and general relativity (GR) completely consistent with each other.


Z; I think it's an interesting and very promising approach.

J: BTW John Baez in Ch 5 last part also waffles on gravity energy problem, p. 452 Notes to Part III


Z: YES.

Z: So does Penrose in "Road to Reality".

J: I think I gave the real answer as to why this is really a pseudo-problem:
BTW from my "Rovelli Notes": The non-trivial warp part B of the Einstein-Cartan tetrad components e = I + B comes into being and becoming from the simultaneous local gauging and spontaneous vacuum symmetry breaking of the spacetime translation group T4, therefore there is no reason at all, from Noether’s theorem, to imagine that either total energy or total linear momentum of the pure gravity field as the spacelike integral of a local density should be conserved as the lapse function "time" pushes forward from one spacelike slice to another in the ADM 3+1 foliation. Indeed, the Hamiltonian of the pure gravity field is strictly zero because of the constraint structure of Einstein’s field equation.

The error you make Paul is to over-extend flat spacetime ideas to where they do not work.


Z: And from my POV you may simply be fetishizing curved spacetime, which may turn out to be simply a *geometric model* for the correct fundamental theory. That was Feynman's view.

J: Feynman's ideas here were not well developed. He was thinking only flat space-time background then as I recall. It was 25 years ago.

Z: In the discussion on "no curved spacetime" on Baez's web site, for example, you will see that even Steve Carlip admits that there is at present no local empirical basis for deciding between a flat-background model and a curved-spacetime model for
Einstein GR.

J: Of course most of the data are still weak field where the flat background works OK pragmatically.

Z: So it could be that a local flat-background model could exhaust the confirmed (and confirmable) empirical content of GR. The reality here is that we really don't know at this point how this will eventually shake down.


J: Conservation of total energy is simply a piece of T4 symmetry, i.e. time displacement invariance. It is certainly FALSE for the gravity vacuum.


Z: Depends on the theory. This is certainly the case in Einstein's theory. Inside Einstein GR, gravitational field energy isn't even *defined*.

J: GR is the only GOOD theory we have. There is no other. It works and so far has not been falsified. The whole attempt is wrong and that includes what Alex has proposed IMHO. Local conservation? Yes! Global conservation in general? No!


Z: I think the decomposition we are talking about is local, i.e., point by point.

J: What's your point? (Pun intended)

Z: As Einstein himself once said, "all physics is local". That's how he preserved his equivalence hypothesis.

J: See what I said above.


Z: Then in Einstein's theory, where physically does the energy carried away by gravitational waves go?


J: When there is the flat background in weak field there is no problem. Since "total energy" is meaningless in a curved spacetime, it need not go anywhere!


Z: Well, that could be viewed as a problem with the geometric model for GR. Einstein certainly regarded this as a serious problem in 1918, since he wrote several papers about it.

J: Simply a failure of nerve on his part perhaps? Not enough faith in his own equations? It happens frequently.

You know mathematically all they have is

Tuv^;v(Matter) = 0 locally

Then they make the split

Tuv^;v(Matter) = Tuv(Matter)^,v + parts that depend on products of the (LC) connection with Tuv(Matter)

They identify the sum of these products with tuv(Matter-Gravity)^,v.

LC is LC(Gravity) therefore LC(Gravity)Tuv(Matter) is dependent on both Matter & gravity.

Also note that Tuv(Matter) = &Action(Matter)/&guv

Where & is a functional derivative.

So what would tuv(gravity vacuum) even mean?

Does it mean

&Action(gravity)/&matter fields ?

Clearly not.

It must mean

&Action(Gravity)/&guv(Gravity)?

I suspect that is ZERO?

Back to original thread:

Where tuv(Matter-Gravity)^,v = 0 in an LIF since (LC) = 0 in an LIF by EEP.

Now we have something like the divergence theorem where

|||Div.Ad^3x = ||A.nd^2x

tuv(Matter-Gravity)^v is like DivA

So one can get an expression for tuv(Matter-Gravity). Does Pauli do this explicitly BTW? What's the equation number.

Z: You seem to be holding up the curved-manifold model as the measure of all things.

J: If it ain't broke don't fix it.

Z: I am saying it can itself be critically evaluated against other standards.

J: Show me. Hand waving not allowed.

Z: "No critical action without critical reaction". A metatheoretic "general relativity principle".:-)

J: Talk is cheap. Let's see the math.

"Total energy" conservation is an artifact of T4 symmetry. Gravity is the breaking of T4 symmetry. Without the symmetry there is no conservation law, e.g. Noether's theorem. Read Wigner.

Z: But your own tetrad/gauge field model shows how the effects of B and I can be separated.

J: So what? What's the connection?

e(curved) = I(flat) + B(curved)

Do a GCT X

e' = Xe

g(curved) = [I(flat) + B(curved)](flat)[I(flat) + B(curved)]

g'(curved) = X(I + B)(flat)X(I + B)

The globally flat case is B = 0 where

g'(curved) = XI(flat)XI

So what? What then? What's your next step?

recall e is a map from LIF to LNIF & back at SAME P (a "coincidence")

recall X is a map from LNIF to LNIF' & back again at same P

Note different manifold points A =/= B FORMALLY are same PHYSICAL P when

B = active Diff(4)A

So what?

Locally there is no problem of course.


Z: Yes there is -- Einstein's field stress-energy is not general covariant.

J: First write down the formula for that. Or if you cannot tell me which equation in Pauli shows the formula for that. I have Pauli with me here in NYC. First let's see what exactly you are talking about.

My B is also NOT a Diff(4) tensor Paul.

Only e = I + B is the Diff(4) tensor. So what?

Remember

e' = I + B'

But

e' = Xe = XI + XB

But

XI =/= I

Rather

XI = I' =/= I

Therefore

e' = I + XI + XB - I

Therefore

B' = XB + XI - I

Therefore,

XI - I is the INHOMOGENEOUS part of the Yang-Mills spin-1 FLAT vector potential in the tetradic substratum where

B(curved) ~ 4DGrad(Goldstone Phase of Vacuum ODLRO)

F = DB

D = d + B/\ = Cartan exterior gauge covariant derivative making p-forms into p+1 forms

where B is a 1-form and *B is a Hodge-dual 3-form relative to Minkowski metric that is the exact metric in the tetradic substratum.

Note that Stokes theorem is

|B = ||dB

| is over the closed loop boundary c of surface s

|B =/= 0 even though B ~ grad(Goldstone Phase) when the Higgs |Vacuum ODLRO| -> 0 at a Goldstone PHASE SINGULARITY making the effective manifold of the vacuum condensate MULTIPLY-CONNECTED like the normal fluid vortex cores in superfluid He4. This causes an ANHOLONOMY (mixed partial derivatives of the Goldstone phase do not commute). What is happening is that the line integral |B is no longer a over the outer closed loop that is also a boundary because of the "hole" where |Vacuum ODLRO| -> 0. That is, like the TWO 2D wormhole mouths in an Einstein-Bridge connecting two 3D parallel universes, there are TWO separated closed loops that together form the boundary over which Stokes theorem applies. If we only measure the outer line integral we get "flux-without-flux". Similarly in the wormhole mouth, if we only are in one universe we see a net charge (flux) coming out of the wormhole mouth even though the total flux is zero out of both wormhole mouths because in Gauss's law divE = 0 in vacuum.

To repeat: This, in effect, gives a phantom "Flux without flux" through the surface s IF we ignore the inner line integral enclosing the return flux in the hole that is something like a phantom string if the "vorticity" core penetration length area is small compared to the area of s.

Furthermore, since the Vacuum ODLRO field is single-valued, the fluxes are quantized.

DF = 0 are the "Bianchi identities" in this Yang-Mills self-interacting field.

D*F = *J is the source equation.

The topology here is analogous to a wormhole where the two closed surfaces are like the wormhole mouths.

The stress-energy current density is shared between the gravity and matter fields in

Tuv(Matter)^,v + tuv(Matter-Gravity)^,v = 0

in 1916 GR.


Z: Right.

J: So show me the explicit formula for tuv(Matter-Gravity) - cite equation in Pauli OK.

Note that here tuv(Gravity)^;v = 0 separately, therefore the sharing is not as direct as it could be when the (LC) Bianchi identities are violated by torsion and non-metricity.

What we really want is

tuv(Gravity)^;v + tuv(Exotic Vacuum)^;v + Tuv(Matter)^;v = 0

with none of the terms on LHS separately zero, but all sharing the currents!

1916 GR is like an old man with an enlarged prostate - a mere trickle of stress-energy density currents between gravity and matter fields because of the Bianchi identities with zero torsion and zero non-metricity.

You can get a global conservation approximately only with asymptotic flat space-times.


Z: Yes, and that's the best that can be done in Einstein's theory. So this problem was never actually solved by Einstein, even while he himself recognized it as a serious problem.

J: There is nothing to solve because of Noether's theorem. It's a false problem. Total global energy conservation breaks down when T0 symmetry breaks down in the Vacuum ODLRO and in the local gauging of T4 to Diff(4). Local conservation of stress-energy current densities still holds. What is true locally need not be true globally.

There is a theorem that U(1) gauge invariance demands that the photon have zero rest mass. U(1) is spontaneously broken in the superconducting ODLRO ground state and the photon inside that macro-quantum ground state has a rest mass

m = h/c(penetration depth of magnetic field)

Electric charge however is still conserved. The EM potential Au is the compensating field from locally gauging global U(1) on the electron field down to local U(1).

This is analogous to locally gauging global T4 down to local Diff(4) GCTs X with tetrad warp field Bu^a. Note that the tangent fiber index a is like the internal index of a self-interacting non-Abelian Yang-Mills spin-1 Poincare group first rank tensor (4-vector) field. The "internal" fiber group is so(1,3) in this Yang-Mills setting. The Lie algebra of so(1,3) is like TWO SU(2) groups one for the 3 space-space rotations and one for the 3 boost space-time rotations all at LOCAL FIXED P.

Bu^a has a coherent signal c-number ODLRO part and some random quantum noise because the Higgs vacuum is a macro-quantum squeezed Glauber state (like in quantum nonlinear optics). We can squeeze the orthogonal Higgs amplitude & Goldstone phase quadratures in the local phase space fiber (N, theta) at P.

Since the metric for the Hodge duality is Minkowski in the Yang-Mills spin 1 substratum of Einstein's emergent (A. Sakharov, 1967 "metric elasticity") we can cleanly separate positive and negative frequency parts for a good Fock occupation number space fiber with creation/destruction ladder operators for the virtual bosons inside the "Higgs Ocean" vacuum at each "coincidence" P. We never have to worry about quantum gravity foam because gravity is simply the smooth ODLRO phase modulation with a little bit of quantum noise in the Bu^a field.

Let a(x) and a*(x) destroy and create a VIRTUAL boson inside the post-inflation vacuum then

|Post-Inflation Higgs Ocean>

= e^(w*aa - wa*a*)e^(za* - z*a)|Massless Pre-Inflation Dirac Sea>

a|z> = z|z> Glauber macro-quantum state (displaced circular Gaussian in phase space).

|w,z> = squeezed elliptical displaced Gaussian. The squeeze parameter is the eccentricity of the ellipse and the orientation of its major axis in phase space (N,theta). The area of the Gaussian random noise is preserved.

The inflation noise is Gaussian obviously and this is actually observed in WMAP. We should also look for variable squeezing across the sky related to galaxy and star formation?

For example, the Wheeler-DeWitt equation in the superspace whose points are 3D geometries 3gij is

H(pure gravity)(BIT Wave Function of Multiverse) = 0

leading to the “problem of time” in idealistic non-Bohmian attempts at quantum gravity that are only thoughtlike BIT with no rocklike hidden variable IT. In the Bohmian interpretation, the super- geodesic equation of motion for the IT hidden variable is separate from the above Wheeler-DeWitt equation for the pilot BIT wave functional that need not depend on any time parameter.

Z: I would have to think about this.

J: Shelly Goldstein has shown this in detail.

Z: OK.

J: All you can say is

Sum of all Tuv = 0 locally, i.e. matter + gravity + exotic zpf vacua



Z: Yilmaz has worked out the detailed math for his particular implementation of this idea. For a scalar auxiliary field you get an exponential solution for the SSS problem, which agrees very closely with the Schwarzschild metric. It's all in his papers.

J: Yilmaz's theory is complete nonsense IMHO. Not even wrong. It solves nothing. It explains nothing. It leads nowhere. It is obscure.


Z: I'm simply pointing out that by definition a gravitational vacuum source field doesn't go away even when all gravitating matter is removed.

J: Right but trite. I said that long ago in both my books from 2002 on Amazon.com. It's obvious. What is not obvious is how to apply that to the observations and I have done that too.

Z: Of course, a zero point field that is always present in the vacuum falls in a grey zone.

J: Too vague. Examples of that are the galactic halo gravity lenses & flat stellar rotation curves, the Pioneer anomalies, the voids, and the interior of electrons and EVOs. Electrons look like points because of a huge space warp at scale of 1 fermi. Lubos Motl is wrong that GR is not important on scale of 1 fermi. Lepto-quarks are micro geons like Kerr-Newman vacuum solutions with effective G* from dark energy /\zpf cores ~ 10^40G (see also A. Burinski). They also mimic strings because they obey

J(Spin) ~ Regge Slope (Energy)^2

as I showed in 1973 which caused Abdus Salam to invite me to ICTP in Trieste. Ask Jagdish Mehra. He was there and knows what happened.

http://qedcorp.com/APS/ice9.wav


Residual zero point energy "exotic vacua" of both dark energy (Pioneer 10 & 11 anomaly a_g = -cH) and dark matter (Galatic Halos flat stellar rotation curves) & stability of extended electron Bohm hidden variable and Ken Shoulders mesoscopic "charge clusters" does give a local tuv(zpf) but that has nothing at all to do with classical gravity waves in weak field approximation on a flat background.

Z:Right.


J: You seem to contradict yourself.


Z: Nope.


J: In any case what you wrote above is so vague I do not know what you were trying to say.


Z: A vacuum source field means that R_uv =/= 0 in the vacuum, since this source field itself produces curvature. It also carries a "baseline" energy-momentum density.

J: Right but trite. In fact most regions of spacetime have /\zpf ~ 0 at most scales. This puts the base line at ~ ZERO!

Z: Thus it is natural to include it in the field Lagrangian, in which case it will show up in the field equations derived from this Lagrangian. Why is that "vague"?

J: Because you have not written a formula! Also you did not say anything like that at all to begin with. The Einstein-Hilbert action density with /\ is written down routinely as R + /\ (both have dim 1/Area - multiply by string tension c^4/8piG

Z: If you want to see a specific implementation of this idea, with detailed math, look at Yilmaz's papers.

J: Hogwash. I don't need no Yilmaz for that. Also he does not have the correct formulas. He does not have /\guv terms at all. Yilmaz's theory is a dead horse fly in your soup.


With

TOTAL Tuv^;v = 0

Therefore, any total energy-momentum = 0

Universe is a "free lunch".

In my view the search for quantum gravity is a serious error. Gravity is emergent in the inflationary vacuum phase from micro- quantum theory to macro-quantum theory. God plays dice in the unstable pre-inflationary micro-quantum vacuum that has no gravity and no inertia in it. The rules change completely in the Big Bang. God loads the dice significantly in order for gravity and dark energy to emerge into Being and Becoming. Our post-inflationary expanding accelerating universe in the multiverse of parallel worlds next door is a vibrating “super- solid” or “world crystal”.


Z: It's certainly a promising alternative to the usual perturbative approach. The macro-quantum ghost of the departed Maxwellian aether.


J: It's not "departed", we are fish swimming in it, or rather the "fish" are themselves phase ripples in it - solitons i.e. vacuum geons like Chapline & Laughlin's "dark energy stars" on micro- scale of "mass without mass" (Wheeler) in which the zero point energy false vacuum cores give effective strong short range gravity G* ~ 10^40G on the fermi scale of 10^-13 cm ~ e^2/mc^2.


Z: But we are not fish swimming in Maxwell's *classical mechanical* ether. Hence "departed".

J: This is where Rovelli's philofawzy is good. More on that later.


Z: The only flag I would raise here is about the stability of the vacuum LRO. According to your BEC model, why is the gravitational vacuum observed to be so stable? What exactly would it take to disrupt and destabilize this LRO?

J: This means you still do not understand the key idea. Ask why is the superconductor ground state stable? It's the same problem!

Z: OK. If it's really not a problem, then it's not a problem.


J: If you read PW Anderson you will see why. Actually I have explained it many times. It's the released binding energy when the ionized virtual e+-e- plasma of the false vacuum FUSES in the inflation to the vacuum ODLRO condensate of bound virtual positronium! The released energy heats up the real quark-gluon plasma post-inflation.

Z: OK.


J: The Goldstone phase of Vacuum ODLRO is "rigid" that's part of "More is different". That's why space-time is stiff. If you do not do your homework and read the key "superfluid" papers in PW Anderson's "A Career in Theoretical Physics" you will never really understand the idea here. Soft condensed matter physicists are very familiar with this idea.


Z: Yes, I know there is a lot of literature on this. I'll try and get hold of Anderson's "Career". And what about light propagation? How does light propagate through the vacuum BEC? Could the characteristics of the vacuum BEC be responsible for the permeability and dielectric constant of the vacuum?


J: That's Puthoff's dead end. I will not go there.

Z: Just a question.

J: "The Question is: What is The Question?" Not all questions need to be answered. Some questions are not worth answering because the question is not interesting. Theoretical physics is the art of asking good questions.

Z: Wouldn't it be reasonable to expect that the properties of your all-pervading positronium BEC would determine at least some optical characteristics of the vacuum?

J: Indeed it does. It makes guv!

Z: OK. What about vacuum light propagation speed?

J: That's like asking how to calculate Young's modulus in a crystal. Not interesting.

Z: Obviously gravitation has an effect on light propagation, so your BEC field must have some connection to the observed speed of propagation of light.

J: I get guv that's enough. Light is ds^2 = 0. I follow Einstein there.

Z: But you can't deny that if your vacuum BEC exists, then light has to travel through it to get from A to B.


J: Yes, but QED shows direct effects are MINISCULE!

Z: OK -- but that's not the same as "zero".

J: Quibble. Atomic BECs slow down speed of light, but they are real atoms on mass shell not virtual quanta inside the vacuum.

Hal has wasted 20 years or more on that and has gotten nowhere important. I think Ibison is finally persuading him to look in my direction?

Z:Hal's theory is a toy model that was designed to be used as a heuristic tool for "engineering".


J: Hal's toy is badly broken. It has not done anything important there at all. Where are the engineering plans for saucers that fly? They don't exist - I mean not based on PV.


Z: It's not an exact quantum theory of the physical vacuum, and it doesn't claim to be.

J: The truth is that PV has failed to deliver on any of its promises in 20 years! Time is up for Hal. The Devil will have his due! :-)


reader Jack Sarfatti said...

Correction: In the superconductor with U(1)EM spontaneously broken, total electric charge is not conserved in the sense that there is a violation of Wigner's superselection rule. The macro-quantum ground state is a coherent superposition of different total charge number eigenstates.