Buzz about a quantum gravity theory that sends space and time back to their Newtonian roots I read that autumn begins this year September 23. I am forced to make a break in my post until at least this day. Here is the reason:
I am interested in understanding the phenomenon of light propagation. I am not completely sure what light is, but it is somehow related to electromagnetism, quantum theory and the concept of a photon. At least so they say. So I read what is known about the subject. Actually I am studying the monograph "Geometry of Quantum Theory" by V.S. Varadarajan, 2nd edition Springer 2007.
The last chapter there:
Here is content of this chapter:
CHAPTER IX
Relativisitic Free Particles 322
1. Relativistic Invarince 322
2. The Lorentz Group 330
3. The Representations of the Inhomogeneous Lorentz Group 343
4. Clifford Algebras 348
5. Representations in Vector Bundles and Wave Equations 356
6. Invariance Under the Inversions 372
7. Localization 377
8. Galilean Relativity 391
Notes on Chapter IX 399
Photons are discussed on p. 371. The last paragraph of this chapter, p. 371, reads as follows
" For all of us seeking to find the true nature of photons, this invites us to look ever deeper into the mysteries of light. In 1917, Albert Einstein said, “For the rest of my life, I will reflect on what light is.” Likewise, light continues to motivate us to take on new challenges."Mr. Takhashi - The mysterious behavior of individual photons
P.S.6 27-09-23 09:11 Prompted by the discussion with Bjab in the comment section below, this morning I ordered the book
The cover tells us:
"This book shines bright light into the dim recesses of quantum theory, where the mysteries of entanglement, nonlocality, and wave collapse have motivated some to conjure up multiple universes, and others to adopt a "shut up and calculate" mentality. After an extensive and accessible introduction to quantum mechanics and its history, the author turns attention to his transactional model. Using a quantum handshake between normal and time-reversed waves, this model provides a clear visual picture explaining the baffling experimental results that flow daily from the quantum physics laboratories of the world. To demonstrate its powerful simplicity, the transactional model is applied to a collection of counter-intuitive experiments and conceptual problems."
Should come the first week of October. Will be waiting impatiently.
P.S.7. 9:40 Which reminded me of the books by Eric Berne on Transactional Analysis that I have avidly studied in my youth. Dealing with longitudinal photons now.
P.S.8. 11:50
P.S.9 12:13 Have calculated the longitudinal photon boost cocycle. It came out unbelievingly simple! It is just the redshift ratio E'/E where E' is the energy of the photon emitted by the moving source. The cocycle property translates simply into""I'm a time traveler," said George. "I came from the future, or perhaps I should say one possible future."
- Jantzen, "Spacetime splitting techniques and gravitoelectromagnetism in general relativity"
- Horawa, "Topological Quantum Gravity of the Ricci Flow"
- Hoprava, "Lifshitz Gravity for Lifshitz Holography"
- Scientific American 2009: "Splitting Time from Space—New Quantum Theory Topples Einstein's Spacetime - Buzz about a quantum gravity theory that sends space and time back to their Newtonian roots" (except: change Hoava into Horava)
- Horava, "The Geometry of Time in Topological Quantum Gravity of the Ricci Flow"
- Horava, "Surprises with Nonrelativistic Naturalness"
- Blas, "Models of non-relativistic quantum gravity: the good, the bad and the healthy"
- Jacobson, "Extended Horava gravity and Einstein-aether theory"
- Landsman - "The 3+1 split of space-time", Chapter 8 from: Landsman - Foundations of General Relativity_ From Einstein to Black Holes-Radboud University Press (2021). in particular: 8.11 Epilogue: The problem of time. P. 217:
"This Pre-Socratic opposition between “becoming” and “being”, or “change” and “existence”, continued with Aristotle. This had disastrous consequences for mathematical physics. In his Metaphysics, Aristotle organized knowledge into something like a 2×2 matrix, where the axes are “changing/permanent” and “dependent/independent”(that is, of man). He put physics in the change & independent entry, whereas mathematics was supposed to be permanent & independent (the latter against Plato). See e.g. Gaukroger (2020). This classification held back the interaction between physics and mathematics for 2000 years, until initially Kepler and Galilei and subsequently Huygens and especially Newton recombined them and thus provided the basis for modern science.
These implication were all proposed by McTaggart (1908, 1927). See also Dainton (2010). The only implication that really counts for our technical discussion is “time ⇒ B-series”, or rather its contrapositive “no B-series ⇒ no time”, but the chain in (*) is convenient in order to frame the overall problem of time. The first implication goes back at least to Aristotle (Physics, Book IV, chapter 11), see Shoemaker (1969) for a nice philosophical analysis. It would be denied by Newton (Rynasiewicz, 2014), but GR can deny it, too, as it admits static solutions (see §8.4).
The point, however, is that according to the arguments reviewed and critiqued below GR admits no flow of time whether or not time requires change. Similarly, the second implication needs to be argued for, as McTaggart does at some length, but his target is the A-series, whose alleged incoherence allows him to disprove the existence of time.
Instead, the argument in our main text concerns the B-series. It is remarkable that of the two great twentieth-century philosophical treatises about existence and time, both of which are hard-core specimens of “armchair” philosophy based on pure speculation, McTaggart (1921, 1927) has been very influential on discussions that are informed by modern science, whereas Heidegger (1927) has, rightly, been completely sidelined in the philosophy of science.
This is the version of the problem addressed in Callender (2017), whose opening sentences deserve to be quoted: ‘Time is a big invisible thing that will kill you. For that reason alone, one might be curious about what it is.’"
"What did this enzyme do? She considered this, and the answer became startlingly clear. In normal cells each strand of DNA had a special noncoding segment on each end, like the plastic tips of a shoestring. She could see that each time a cell divided this special end segment became shorter. And finally, when the segment length went to zero, the cell could not divide again, the natural cell renewal processes stopped, and the body began to age. The new enzyme systematically restored the end segments to human DNA. It did not require cells to divide, but it allowed them to when the body's repair mechanisms made the request. "Wow!' said Alice aloud. "It's the Fountain of Youth!"John G. Cramer, "Einstein's Bridge"
P.S.18 15:45
""You mean that we can go back to a time when Alice is still alive?" George asked. He looked a bit wild-eyed, Roger thought.
"Yes," Iris replied, "of course."
"Wait a moment," said Roger. "Are you talking about moving back to some alternate-branch Everett-Wheeler universe?"
Iris laughed. "Since we established contact with your culture, many Individuals of our world, particularly our science meta-historian specialists, have derived great amusement from your quantum mythology, that area which you call the 'interpretation of quantum mechanics.' They were particularly amused by your Copenhagen interpretation, with its state vectors that are altered by the thoughts of intelligent observers, and by your Everett- Wheeler interpretation, with its splitting and resplitting into multiple universes. In this regard, your culture is unique among those that we have encountered. No other has provided such a remarkable demonstration of fertile creative desperation in seeking to understand physical behavior at the quantum level. We find these myths of yours quaint and charming."
"In other words, 'wrong'?" asked Roger.
Iris looked troubled. "No more wrong, say, than your Greek or Norse myths. Your excursions of scientific fantasy are an interesting manifestation of your culture, but they are not an accurate portrayal of the behavior of the universe. Human observers, for example, are not demigods with the ability to collapse a wave function with an act of measurement or of insight. It is better that they are not, believe me." "
John G. Cramer, "Einstein's Bridge"
"Roger nodded. "We're going to need that technology. Tern's team at Iris Institute Europe has been making real progress in understanding the Makers' maths. It's now clear that the mathematics used by the Makers is a variant of Clifford algebra. It's like finding the Rosetta stone. We have the code key to their formalism."John G. Cramer, "Einstein's Bridge" (at the very end of the book)
Contradictions at the very foundations of my knowledge. I can't hope to build anything solid and lasting when there are contradictions at the very base. Need to uproot them first.
ReplyDeleteContradiction resolved. On the road again. Back to the Varadarajan's unfinished problem that even Krishna, for some reason, wouldn't be of much help.
ReplyDeleteLongitudinal photons were bad to me yesterday. Today they behave like nothing ever happened. Now transversal photons. They are more complex and probably a little bit unpredictable with their behavior. Lot of patience needed, and determination as well.
ReplyDeleteI am preparing my list of publications for my profile on Math-Net.Ru.. While doing so I realized that long ago I have set a program of my future work. Surprisingly the program is still valid. It is on my web page with the title that I am sure tells very little (if anything) to the Reader. Here it is
ReplyDeleteOn Berry's phase.
Back in June you mentioned the 8-dim phase space in relation to future physics and I tended to think of you morphing it with your anti-spacetime, Kaluza-Klein-like, and degenerate metric ideas which sounds really interesting. Berry phase I've seen before but probably at best only ever thought of it as part of an overall Feynman propagator phase.
DeleteI have some problem with the Schrödinger equation modeling reality. It is not symmetrical.
ReplyDeleteVery good! Explain your problem in details. I am interested. Perhaps together we can learn something new.
DeleteP.S. Now I see that my own photon problems will penetrate well into autumn, so there will be no new posts probably for a month at least.
For example for free particle QM has:
Deleteiℏ ∂/∂t ψ(x,t) = -ℏ/2m ∂²/∂x² ψ(x,t)
I think that there should be ± at the very beginnig
OK. Give me some time to think about it.
DeleteLet us work in momentum representation ane let h=1.
DeleteWith the energy operator H=p^2/2m the Schr. eq. is
iℏ ∂/∂t ψ(x,t) = H ψ(x,t)
Calculate average velocity, I denote average by [[ ]]
d[[x]]/dt =(d/dt) (ψ x ψ)=(ψ iHx-ixH ψ)=i(ψ,[H,x]ψ)=[[p/m]]
If we would take instead
iℏ ∂/∂t ψ(x,t) = -H ψ(x,t)
then the same way we would get
d[[x]]/dt = - [[p/m]]
thus a wrong sign.
Is my reply clear enough, or should I expand?
DeleteExpand please.
Delete(Every equality in:
d[[x]]/dt =(d/dt) (ψ x ψ)=(ψ iHx-ixH ψ)=i(ψ,[H,x]ψ)=[[p/m]]
)
Expanded as a postscript at the bottom of the post above - so that I could use LaTex for mathematical symbols.
DeleteBardzo dziękuję za pracę którą dla mnie wykonałeś (za postscript).
DeleteBędę musiał ją przestudiować.
Na razie utrudnia mi to:
Brak nawiasu w (4).
Jakieś h w (8).
Brak (t) w (9)
Niejasne jest dla mnie dlaczego w (5) pochodna nie poprzedza x z daszkiem.
Niejasne jest dla mnie przejście z (7) do (8).
Replaced the version. Corrected typos. Thanks.
DeleteIn (5) we calculate time derivative of the expectation value of the position at time t.
Concerning (7) to (8) tarnsition we use the fact that H is Hermitian, H=H*, which means
(H psi, phi)= (psi, H phi)
and, of course,
(-H psi, phi) = - (H psi, phi) = (psi, -H phi)
for any psi, phi.
And concerning (5) - we are working in Schrodinger's picture. The operator x does not depend of time. In Heisenberg's picture operator x would become x(t), but ψ would be independent of time. The end result would be the same.
DeleteThe we use ->
DeleteThen we use
Nawias w (8)
the we must ->
then we must
Dzięki za wyjaśnienia.
Muszę to wszystko sobie poukładać.
Corrected. Thx!
DeleteFrom the route:
Deletewhat is the expectation value of the position of the free particle, because if it does not exist, does its time derivative exist? Is it a flaw?
Expectation value of any operator depends on a state. Different states will give different expectation values. The explicit formula for the expectation value in state ψ is
Delete∫ (x |ψ(x)|^2) dx from - ∞ to +∞.
It exist and is finite for a dense set of states, as is usual in quantum mechanics for unbounded observables.
w ostatnich trzech wzorach (14a) , (15), (16) d chyba powinno być kręcone.
DeletePerhaps one explanation: it will certainly not exist for plane waves, that is why we build "wave packets".
DeletePracujemy w jednym wymiarze, więc d kręconego nie trzeba. A iloczyn skalarny i zależność funkcji falowej jest od x. Dla różnych czasów t mamy różne funkcje falowe, co czasem piszemy jako ψ(x,t), ale to może być, jak widać, mylące
DeleteJednak należy to rozumieć jako ψ_t(x). Czas jest jedynie parametrem, nie zaś zmienną funkcji falowej. Zatem winno być zwykłe d a nie kręcone - i tak jest.
Operatory działają w przestrzeni funkcji od x, a nie w przestrzeni funkcji od (x,t)! W szczególności dla wyliczania iloczynu skalarnego nie całkujemy po t a jedynie po x.
"Operatory działają w przestrzeni funkcji od x, a nie w przestrzeni funkcji od (x,t)!"
DeleteTego nie rozumiem.
Poza tym czy Wikipedia się myli względem tego d kręconego:
https://en.wikipedia.org/wiki/Momentum_operator
A dlaczego zatem stosujesz d kręcone np. we wzorze (14)
(Co to za jakaś pochodna funkcji po parametrze?)
Tak, Wikipedia mąci, piszą ją różni studenci i "delegowani", jedni lepiej rozumieją, inni mniej.
DeleteDlaczego kręcone w (14)? Kręcone zawsze jest dobre, a Ty użyłeś kręconego.
Zauważ, że gdy używam zwykłego d/dx to zawsze w stosunku do ψ lub &\psi;(t).$. W samej rzeczy w (6) winienem był napisać &\psi(t).$ Zostawiłem zależność od czasu domyślną. Niepotrzebnie.
Gdy piszę ψ(t) oznacza to, że dla każdego t mamy inną funkcję falowa (ψ(t))(x).
W tym sensie t jest parametrem wektora stanu. Wektor stanu to funkcja od x. Ta funkcja zmienia w czasie i staje się inną funkcją - innym wektorem. Wektor satnu zmienia się z czasem./ A wektor stanu to cała funkcja od x. Ewolucja ma miejsce w przestrzeni funkcyjnej - w przestrzeni, której wektorami są funkcje od x. Niektórzy piszący Wikipedię ( i
autorzy podręczników dla fizyków i inżynierów) mogą z tego nie zdawać sobie sprawy. Matematyk takiego niedopatrzenia raczej będzie unikał. Matematyk chce zrozumieć. Fizyk chce stosować. Do stosowania często rozumienie nie jest potrzebne. Oczywiście są wyjątki. Zależy od kogo i gdzie ktoś pobierał nauki.
"W samej rzeczy w (6) winienem był napisać &\psi(t).$"
DeleteW (6) przecież napisałeś.
Czy w (15) i (16) brakuje 1/2m ?
Corrected. Thank you. And replaced ψ(t) by ψ_t - as it should be for clarity.
DeleteIn formulas (10) (13) (15) (16):
Deletem ->
|m|
and then we would not have to choose a = -1
Negative mass concept in Galilei-Newtonian physics? Interesting.
DeleteOnly in quantum physics, or also in classical mechanics?
Shouldn't we start with rewriting classical dynamics before we jump into the quantum world?
@Bjab
DeleteIs something like this that you have in mind?
" There is a curious corollary of this result, which Bondi pointed out in his paper. Consider a pair of equal and opposite positive and a negative mass placed close to each other. The negative mass is attracted to the positive mass, while the positive mass is repelled by the negative mass. Thus the two masses will experience equal forces and accelerations in the same direction (in violation of Newton's third law) and the system of two particles will accelerate, seemingly without limit. The negative mass will chase the positive mass with constant acceleration."
Anti-Gravity and Anti-Mass
by John G. Cramer
Classical mechanics does not require rewriting because it concerns the world of everyday matter and not the world of antiparticles. It is possible that quantum mechanics requires a slight correction, which will make it finally understandable.
DeleteI disagree. Rewriting quantum mechanics cannot be done without rewriting classical mechanics. First because quantum mechanics cannot be understood without relating it to the world of experience, and the world of experience is mathematically treated by classical mechanics. Second, if negative mass exists in any "real" sense, then it should be detectable, so we need to know how would a macroscopic body made of anti-matter behave. Which includes the notion of time flowing backward, whatever that may mean.
Delete
Delete"Is something like this that you have in mind?"
Rather not. I don't know if gravitational mass equals inertial mass.
What you propose is essentially, as I understand, adding the complex conjugate Schrodinger wave function, which is kind of equivalent to reversing the direction of time. This is a part of "transactional interpretation of quantum mechanics", eleborated John G. Cramer - whose article in Analog I quoted above.
Delete@Bjab.
Delete"Rather not. I don't know if gravitational mass equals inertial mass."
Good. So there is something to think about.
"I disagree. Rewriting quantum mechanics cannot be done without rewriting classical mechanics. First because quantum mechanics cannot be understood without relating it to the world of experience, and the world of experience is mathematically treated by classical mechanics."
DeleteI don't understad why you disagree.
Consider an analogous situation related to special relativity. No one rewrites Newton's classical mechanics, but only states that it applies to low speeds (i.e. the speeds with which humanity has been dealing for centuries). Similarly, no one has to rewrite classical mechanics, but only state that it applies only to the world of ordinary particles and not antiparticles (i.e. particles (matter) that humanity has been dealing with for centuries).
"Similarly, no one has to rewrite classical mechanics, but only state that it applies only to the world of ordinary particles and not antiparticles (i.e. particles (matter) that humanity has been dealing with for centuries)."
DeletePerhaps my wording did not express exactly what I meant. Instead of "rewrite" I should have said: write a new classical mechanics that include antiparticles. Of course people were contemplating this idea for a long time. If there are anti-particles, then it is a necessity to search the laws that govern their behavior. This includes modifying the framework of classical mechanics, where normally such a possibility is not being considered.
Of course here the term "particle" or "antiparticle" may be misleading if, for instance, we take the point that "there are no particles", only "waves". That would require a lot of work to invent physics based exclusively on the concept of "waves".
"What you propose is essentially, as I understand, adding the complex conjugate Schrodinger wave function, which is kind of equivalent to reversing the direction of time."
DeleteAdding the complex conjugate not to the Schrodinger wave function but to the Schrodinger equation - (That plus/minus). It mathematically is kind of equivalent to reversing the direction of time but I would rather think of it like changing handedness.
OK. I will think of it. It seems to me that it should be related to the "transactional interpretation" of quantum mechanics:
Deletehttps://en.wikipedia.org/wiki/Transactional_interpretation
@Bjab
DeleteAnd thank you very very much for bringing this possibility to my attention by asking your question about Schrodinger's waves!
and the kind of quite classical path integral formulation too with its time reversed antiparticles which are also spin "reversed" in the all neutrinos are left-handed and antineutrinos right-handed kind of sense. Doing a path integral does seem to require a Cramer transaction and GRW or many worlds-like additions are possible too and even a Bohm-like addition in the EEQT center algebra "classical" sense could work. It's a smorgasbord out there.
DeleteOnly for free particles? What about particles in some very very small force field?
ReplyDelete"...very very small..."
DeleteI don't know yet. Do you?
I checked particle(s) in an infinite well (-L,L)
The solution is:
ψ(x,t) = cos kx (cos ωt - i sin ωt)
but
ψ(x,t) = cos kx (cos ωt + i sin ωt) is not (but should be. So ± in Schrödinger Eq. would be handy also in this case).
Somewhat on the subject: a new preprint appeared on arxiv last night:
ReplyDeletePhysical unambiguity of the definition of the photon position operator and its special eigenstates, by Grzegorz M. Koczan
We (GMK and AJ) were extensively exchanging our views on the subject and shared results of our calculations since the end of July