The Wigner function helps to visualize entanglement in a system.  This has been used for a few years in coherent optics to this effect.  Several of the invited speakers at the upcoming Wigner workship (Low Wood Bay Hotel, Lake District, England, June 5) will highlight this aspect of Wigner functions.

Hi Peter:

Good to see you are still active (& in physics).

One of the deepest problems in ALL physics is the concept of momentum: it is a purely math idea with no experimental equivalence as no human can make two measurements with a zero time separation. 

Hello Herb,

Thank you for your friendly greetings! - Frankly, I have forgotten, where we have met us before :-(

Anyway, I am wondering about your answer, because neither Huygens', nor Newtons' results about momentum conservation are related to making "two measurements with a zero time separation" - or did i overlook something?

Hi Peter: We started corresponding in 2007 (until 2012) about EM I believe. Are you still reachable via Dekasges?  My email is now [email protected]. Both Huygens & Newton were primarily mathematicians and polished the older concept of momentum using Descartes new algebra.  Newton wanted Dt -> 0 so he could invent the simplicity of calculus and did not care about experimental verification of all of his concepts.  Since physics has been hijacked by mathematicians, no-one wants to give up calculus, even though it cannot be measured (physics as an empirical science?).  I have given it up for finite math - see my papers on Academia.edu.

Hi Profs. Enders, Perry, Spencer,

                                                          May we draw your kind attention to the papers Mallick (2011) , Mallick, Hamburger, Mallick (2016,2016) on the website www.researchgate.net/Soumitra K. Mallick where Quantum Stock Market Information systems Stock and Flow String Theoretic quantum algorithms, simulation and protocols have been mathematical-statistically developed conformal with management-engineering and quantitative finance applications on industrial engineered stock exchanges and Statistical Physics leading to the String Matching Field Theory of Econophysics have been developed using the Faye intrpretation of Quantum physics using ergodic as well as subjective probabilities and learning actions. So without meaning to intervene in your friendly exchanges we provide another solution which we believe is quite original and clear in its applications.

Earl Chair Prof. (CA) Dr. Soumitra K. Mallick QC, EPS Fellow (In),MES, MRES, MAICTE

for Soumitra K. Mallick, Dr. Nick Hamburger and Earl Prince Sandipan Mallick EPS Fellow (In) (designate from 2020)

Hello Herb,

(i) You wrote,

"Newton wanted Dt -> 0..."

I guess, he wanted to represent the continuity of motion through continuous space and time - as Huygens did, who invented his principle for that.

(ii) Further, you wrote,

"...he...did not care about experimental verification of all of his concepts."

IMHO, this is not correct, see his own experimental work and his reference to the rotating bucket.

(iii) Further, you wrote,

"Since physics has been hijacked by mathematicians..."

I would rather second Arnold's (that of KAM theorem) regret, that maths has developed along ways not being tightly related to physics [starting, perhaps, after Cauchy]. Moreover, since physics moved from Germany to USA, pragmatism overwhelmed axiomatics.

(iv) Do we need immediately subsequent measurents to determine momentum? IMHO, not: Let a body move towards a spring and measure the (finite!) time difference between hitting the spring and coming to rest.

What do you think?

PS: Charles Francis has developed an interesting theory baing on finite differences

Dear Soumitra K Mallick,

Please have a look at the market place in your city for finding answers to your comment ;-)

Dear Peter:

Yes, Newton wanted the APPARENT continuity of the motion of MACRO-sized objects (like planets & billiard balls AND BUCKETS of water).  Thus, his approach was 'good enough' for calculating human observations, like planetary periods. 

YES, finite time differences are central to the definition of the concept of velocity and momentum but there is no justification for assuming this is valid at the scale of electrons.  I have not heard of anyone experimentally observing electrons bouncing off springs.  Nice theory without any possibility of experimental verification. This is one of my core critiques of QM: continuum math but not continuum experimental validation. 

PS Any online links to Chas Francis's discrete work? (another name from my past). 

PS: "Indian Institute of Social Welfare & Business Management" - that sound very much like a 'contradictio in adjecto' - if not, I would be happy to know, why :-)

Herb,

I agree with "apparent", of course.

Please search for 'Charles Francis quantum gravity'.

Newton did not consider electrons. The classical concept of electrons can be applied to electrons at most in those situations, where its quantum properties play no role, ie, without interactions.

Anyway, quantum mechanics assumes the homogeneity of free space, hence, the conservation of total momentum. This can be mesured in quantum systems as well, see Moessbauer effect.

Sorry, Peter but your are retreating into math mysticism.  I was raising the issue of experimental verification of zero time separation (central to the differential definition). 

Physics really is still an empirical science, is it not? 

Dear Dr.Enders,

                             May I draw your attention to the Mallick (2011) paper on Pareto Optimality (Statistical) of India's Emerging Stock Markets where I have by Quantitative Finance developed the Statistical Econophysics of Stock Market Dynamic Equilibrium under Central Planning by using Statistical Equlibrium ideas of Physical Systems like Thermodynamics and have shown that systems do actually converge over time to steady state probabilistically by using Gauss-Markov Theory Econometrics and also in Developing the Cybernetic Insurance Market Network Field Theory drawing parallels with the work of Grossman & Stiglitz in the case of financial markets (Economic Sciences Nobel Laureate Prof. Stiglitz) along with my collaborators Dr. Nick Hamburger and Mr. Sandipan Mallick  laid down the Insurance Market Field Theory (Mallick, Hamburger, Mallick (2016)) as solution to String Theoretic SO(11) simple Strings with Management Engineering solutions. Both these fields are interactive fields between Business Management and Social Welfare in that they draw upon the same Network of Information and Energy, which we have also developed the Interaction Model.

SKM

for SKM, NH, SM

Christian:  The widespread use of Hamilton's formulation in mechanics ignores the static assumption: all parts are interacting instantaneously, so all the math can be developed at one time; Newton's differential approximation (OK for planets: not atoms).

Hence my reference to math mysticism, which invokes the symbolic over the empirical. 

Dear Profs. Enders, Baumgarten, Spencer,

                                                                             Just to clarify to the debate over the Hamiltonian time paths I have mentioned above, one of us has also modelled condensed matter analysis in the formation of coal and other mining reserves, even water, by using Dbranes String Theoretic conformal flows to analyse mining technologies Econophysics and the notion of efficiencies in mining where the Hamiltonian problems have been converted into Lie Group Homology by using scalar diffeotopies in differetial topologies with Kuhn Tucker Lagrangean actions using Lapalce transforms to generate Lorenz transforms to analyse spacextime forces which operate. This is neither particles nor planetary motion, perhaps somewhere in between having jump processes derivatives in Lie Brackets and conserving information and energy in paqrticular ways. Please refer to Mallick (2014, 2016) in www.researchgate.net/Soumitra K Mallick and also Mallick, Hamburger, Mallick (2016) proof of Millenium Problem #1 in certain econophysics fields. Thanks.

SKM

for SKM, NH, SM

Feynman, followed Dirac, and emphasized the Lagrangian approach to avoid the false assumption of a single time (instantaneous interactions).

Dear Christian: Fermi's scientific biography relates how even as late as 1920, Newtonian mechanics was taught by mathematicians; so how can you throw away the Dt -> 0 limit behind all differential equations.  This is NOT real, certainly not at the micro level (quantum mechanics). 

Hi Chris: The mathemystics will appreciate your defence of their symbolic fantasies.  Just because we can draw a curve on paper or in our imaginations does not make them real; so, neither are other operations on them like tangents.  I started this dialogue with the challenge that there is no EXPERIMENTAL measurements made at zero time difference.  It would help if people tried to clarify their thinking about the Nature of Reality. 

PS Please don't quote authorities (like Kant): they are just sounding off their opinions like everyone else; this is why science is neither an aristocracy nor a democracy. 

PPS Naive realism is how most people on the planet view the world - why do you think they are wrong?

Dear Herb,

"Yes, Newton wanted the APPARENT continuity of the motion of MACRO-sized objects (like planets & billiard balls AND BUCKETS of water).  Thus, his approach was 'good enough' for calculating human observations, like planetary periods."

It's just doubtful to invoke Newton's physics for objects, for which it has not been invented. Newton's mechanics - as described in '...de gravitatione' and 'Principia' - points at classical bodies. Hence, it should be tested for classical bodies, not for quantum particles.

PS Any online links to Chas Francis's discrete work? (another name from my past). 

arxiv.org/vc/gr-qc/papers/0508/0508077v2.pdf

Hi Peter: I checked out this paper; more field theory and only one new useful idea. 

Christian: Please don't fall into the Science-generates-Technology fallacy.  Sometimes  a new scientific/engineering discovery (e.g. semiconductors) leads to a new technology, very occasionally a 'pure' science discovery (Hertz) leads to a new tech but even in this case, Hertz stumble upon it and was NOT stimulated by a science theory.  Far more often, Science can investigate new phenomena AFTER a new technology is invented, such as various vacuum pumps.  

I cannot be anti-science as I have practised theoretical research for over 50 years.  But, more and more, I see science regressing into Old Bad Habits; with protection of the orthodoxy being the common thread, compounded by preservation of privileges.  These characteristics were rampant in the Catholic Church around 1600 and led to the reformation.  I believe we need strong pressure (& criticism) of today's science to avoid a similar demise. 

My critique of differential equations is based on it being used in research areas without critical thought.  It has run aground in providing useful insights at the discrete level of reality (atomic physics); no analytical solutions beyond the hydrogen atom.

Thus, Heisenberg's critique of the Bohr & Sommerfeld atomic models was based on the macro scale (classical) insistence that electrons cannot be viewed as particles "as we cannot view them continuously".  In his diatribe, Heisenberg ignored that we do NOT track photons continuously but he viewed them as real.  Furthermore. his uncertainty principle focuses on the ideas of measuring an electron's location and velocity both simultaneously.  So, the idea that measurement of velocity does imply the experimental need for experimenters to achieve the zero time separation (as in Newton's macro differential definition of velocity).  Thus, a key concept in my view (instantaneous velocity) in QM deserves a firmer empirical foundation.  

The ongoing popularity of Bohr's model in physics education (& imagery in the public's mind), plus the fact that wave mechanics only produces very small variants from Bohr's result shows me that the Bohr model is worth revisiting, perhaps to show powerful new ideas.  Meanwhile all physics undergrads are given a superficial intro to Schroedinger's solution of the hydrogen atom, without deep critical analysis while it provides no conceptual physical insights - math constraints on equations are not a firm foundation for further work at the atomic level that is stalled in 1925 thinking. 

Christian~

Don't knock yourself down; up until 1850 all physics was experimentally based.  Then some unemployed math boys were hired to teach mechanics.  This was when the rot set in; the cuckoos were brought into the nest of physics and the mathematicians have grown ever since (bureaucrats love them - they don't need any expensive equipment.)  This "hijacking" is never commented upon because people are now being trained as technicians, not educated to think for themselves. Few know the History of their field and fewer know the (Natural) Philosophical issues involved.

Soon Maxwell made a huge mistake and went off on a new path (fields = partial differential equations) for RELIGIOUS reasons (he was a fanatical Christian, like Faraday).  They hated the idea of particles with an empty void between them, so they believed that God would not have designed the Universe like that, so they filled the void with fields; thus, God was now everywhere (or in theological terms "immanent"). 

Maxwell's EM Equations (actually Heaviside's) were just a math transformation of the earlier integral (or flux equations summarizing 100 years of experimental results on macro electricity and magnets) into localized, point-level differential equations.  Not only were these blown out of the water by the Michelson experiments but the discovery of the particle nature of electricity (i.e. the electron) blew the foundations off Maxwell's aether.  For more details, see my paper UET2, available to all on my page on Academia.edu.

Einstein, steeped in late 19C physics invented his special theory of relativity to save all this nonsense.  So, Brave Bohr ignored them (but did not know why, because he too was steeped in the validity of math in physics).  I am deeply involved in extending the Bohr/Sommerfeld model to three dimensions (the only reason wave mechanics got finer details) by using discrete mathematics and a new view of the EM interaction, (grounded on the electron/electron interaction) which explicitly rejects "local' action for 'far' action (this is not 'Spooky' - that was Albert's rhetoric. 

Hi Christian:

I do not know how to upload onto RG? Can you suggest something?

I do not understand the RG HELP system's text on uploading. 

Anyway, I view Academia.edu as the best vehicle to reach the general public, which is accessible through Google. 

https://www.academia.edu/27948014/Continuous_Two-Electron_Theory_of_Electromagnetism_UET3_