marcus said:
You understand, Juan, that the vague general question "Does the Universe have a memory?" is not the issue. That is simply the provocative title of Atiyah's talk. Mathematically there are SEVERAL ways one could respond to this question. In this thread we are not interested in OTHER ways people have addressed this general question. We are interested in the SPECIFIC way that Atiyah has suggested in this talk. That is already hard enough to grasp, I find.
So far i know usual standard physics including the standard model is memoryless. String theory AND M-theory are also memoryless. In fact, all that string theorists are doing in this difficult question of irreversibility is -as it is typical in string theorists- copy the work done by others...
Moreover, they often copy incorrectly. The recent attempt to solve the problem of arrow of time using a radical generalization of standard string theory has been a joke, because string theorists are specialists on
nothing (except gargabe and propaganda in media). They believe that string theory IS difficult AND fundamental and the rest of disciplines a kind of second-class activity. Then they do some work on any speciality where they have no idea and the rest of people do jokes with the nonsense published...
In fact, string theorists used wrong tools developed in other fields by Prigogine and others 50 years ago, tools that the own Prigogine abandoned time ago by new more sophisticated tools that CANNOT be used in that trivial theory called string theory which relies in outdated aspects as Hilbert space mathematics.
I remark again that
string theory is both outdated and wrong.
You claim that mathematically there are SEVERAL ways one could respond to this question. Of course! but we need the correct physical way and in more than 100 years nobody found one still!
marcus said:
You seem to be implying that there is PRIOR WORK along the lines of Atiyah's talk. that would be interesting, if it were a fact.
There is a 100-years research in the problem of time even if you newer heard this. There has had several attempts to find an arrow of time in quantum gravity and also in string theory. All material published is from the perspective of a string theorists 'fascinating'; from the perspective of people has done research in this difficult question it is :zzz:
String theorists would read has been published in a specific topic before doing irrelevant comments and proposals. This is also advice for you, Marcus before doing grandilocuents claims about the last fad on string theory -and rest of insane disciplines- you would first read has been published in that topic by other people. It is a good thecnique.
Perhaps this was the reason of the 40 years failure of string theory community for obtain anything: the implicit -asummed- fact that string theory goes beyond any other theory...
********************************************
Now i explain my reading of Atiyah talk.
Firsts items are pure string theory marketing. Some of claims of Atiyah are very discussible, for exmaple the claim that string theory has provided Fields Medals is not correct.
In item 5 does a wrong claim about causality. It is talking about causality of a reversible unitary deterministic universe. Our universe is not that. That in QM the state IS an element of Hilbert space is false. This is valid only as approximation, for example for stable particles. For instable particles one needs to work with generalized states. There is a very large literature in the topic of generalized states beginning with the classical -not very adequate- Gamow states for instable particles and radioactive nuclei.
Item 6. Ignorance of our past does not explain Heisemberg uncertainty. This is an complete exageration. Heisemberg uncertainty relationshiphs are time-simmetric.
Item 7. Retatrded differential equations are well known in physics. i) They do not explain the arrow of time ii) They cannot be solved. In fact, people is doing is just the
contrary that Atiyah claims: the ABANDON of retarded differential equations. This is done, for example using powerful memory-kernel thecniques that eliminate the retardation in favor of the present state knowledge. Why are retarded differential equations ABANDONED? Because are computationally intractable. For example Zwanzig kinetic equation has been UNSOLVED until today except in the short memory regime when equation IS time local.
Item 10. Finite difference equations are also very, very, very, very well-known on physics of irreversibility. They do NOT solve arrow of time and do not work. The quantum of time is called chronon. Has has some attempt to derive decoherence and measurement quantum process from discrete approaches. Did not work.
The rest may be a joke. Unless that one remembers that 'quantization' for a mathematician can mean classical for a physicist. For example, in NC geometry mathematicians call 'quantum' to everything with a discrete structure and some models of NC geometry are really classical for physicists. Item 11 reinforces this opinion.
Item 11. Atiyah expresses his misunderstanding of what is time, what is evolution, and what is spacetime. To claim two copies of spacetime with different structure for pass and future and that is may explain the arrow of time is a pure nonsense.
Item 12. Perhaps is Atiyah asking by a Zubarev-like equation?
partial |phi(t)> / partial t = -iH |phi(t)> + e{|phi(t)> - |phi(t_0)>}
The infinitesimal source corresponds to the standard Abel kernel, it introduces an instantaneous memory kernel selecting retarded solutions (t > t_0) of the Schrödinger-like equations. This is known for decades. The memory kernel can be generalized for a finite decay of quantum correlations. It does not work!
Note In rigor the above state vector CANNOT be a Hilbert vector. In fact it is not. Atiyah again proves his ignorance of those topics.
Item 13.
Yes, superposition is approximated (a simple look to above Zubarev-like equation proves that). This is ALREADY known for decades. Zubarev equation was published in the 50s (??)
Nothing of this is new! BUT retarded equations like Zubarev one do NOT solve the measurement process even if are nonlinear equations breaking the supersposition principle of the linear Schrödinger equation of QM. It is all a 'bit' more complex that Atiyah claims...
Item 14.
Is there such one thing as 'curved spacetime'? Who has proven that? In sci.physics.research i asked by the Newtonian limit of GR and nobody replied still what is the curvature of spacetime on the Newtonian limit. Carlip has done a wrong attempt to derive the Newtonian limit using a wrong metric and a wrong understanding of basis of Newtonian physics. Carlip does not know the difference between a 'potential' and a 'field' (still do no replied to my question in sci.physics.relativity of why the island universe asumption is wrong in fields but experimentally proven for potentials. Carlip simply does not understand Penrose criticism), has asumed that time in Newtonian gravity is a dimension! work with covariant derivatives which is wrong (in Newtonian physics derivatives are FLAT), etc. Moreover, even in Carlip metric the curvature scalar R is zero because it contains an extra c term into g_00. Etc, etc.
Precisely the approaches without curved spacetime: FTG (worked by Feynman), spacetime calculus (discussed here in PF some time ago), teleparallel gravity, etc. are more powerful. There is no such one kind as 'curved spacetime' on those approaches. This solves many of classical GR problems: singularities, energy, systems of references, etc.
Atiyah's statement that retarded actions give "natural answer to wave equations" is WRONG. In fact, the usual Lienard Wiechert potentials taking only the retarded part of the wave equations are wrong (i already cited many literature on the topic many times in PF). It is also well-known that retarded solution is incomplete: self-action, impulse renormalization of mass, violation of conservation of momenta, etc.
There is NO Hamiltonian associated to retarded equations. This is the reason that Wheeler-Feynmann theory NEWER was posted in Hamiltonian form and famous promised talk newer arised...
In the point 2) It appears that Atiyah still thinks that the Dirac equation is a relativistic generalization of the Schrödinger equation, which is a pure nonsense.
See Weinberg volume 1 for a discussion of why the Dirac equation is NOT a wave equation (in fact it is not in QFT, it is an identity for field operators NEWER for wavefunctions). In sci.physics.research (thread about quantum fields) you can find some related information about why the Dirac equation is not a wavefunction equation by Eugene and myself. The proofs involves sophisticated math that Atiyah may unknow (one can prove that generator of time translations in Dirac equation does not have compact support).
Items 15, 16, and 17. Bla, bla, bla.
Item 18. Point 1. Yes, time reversiblity is not correct, but way proposed by Atiyah is simply wrong. The point now is the searching of some additional effect, for example Poincaré resonances in LPS in the Brushel School approach (which are NOT retarded differential equations). The Brushel School abandoned the search of the basis of the arrow of time in retarded equation in the 60s or 70s if i remember correctly. One would read material published for learning
WHY.
Point 2. Speculative. In fact some recent work in the topic suggests that momentum-positin duality holds, but a new kind of complementarity arises. Complementarity time-entropy. Precisely NC geometry of the time coordinate introduces nonunitarity.
About the ultimate description of Nature on geometrical terms, I doubt!
I believe -like Newton or Feynman- that the geometric approach is only approximated.
