Thoughts about Bell, Bohm, Christian, et al.

[Joy Christian]

Hi Jay,

I read your 5 page draft about Pythagoras with interest. While I appreciate and sympathize with the spirit of your argument, I find your use of the Pauli matrices language quite clumsy and confusing. There exists a much more powerful language to reveal the same light, introduced long ago by Grassmann. This was later improved upon by Clifford, who also incorporated Hamilton's insight of quaternions into Grassmann's framework. The result is of course what we now call Clifford or geometric algebra. As I mentioned, it is a much more powerful language than the language of matrices you are using. But more importantly, I do not see a clear cut analysis of the question of locality in your argument. The conceptual clarity on this issue in Bell's work is far superior. The issue of locality in quantum physics is so subtle that it is not good enough to have some vague intuitions about it. A systematic analysis is necessary. This is why, despite being so critical, I very much admire and appreciate Bell's contributions to the debate.

On a different note, you mention that you take the idea of quantum or guiding potential very seriously, and think that it is "real." If so, then you are stuck with non-locality in your work. Unless you interpret the guiding potential epistemically as Michel has suggested, you will not be able to get rid of non-locality from your work.

[minkwe]

Rick,

The cross section measurement does not imply there is nothing outside its dimension. Not saying it is responsible, but what do you think about the scope of the electric field for an isolated electron?

Surely there is stuff outside its dimension -- everything else. The scattering cross section tells you the maximum extent of interaction of the electron itself with anything. That tells you the electron cannot scatter from two slits at the same time that are separated by a distance outside the cross section. As concerns the mechanics of scattering, see viewtopic.php?f=6&t=51.

[Yablon]

Hi Jay,

I read your 5 page draft about Pythagoras with interest. While I appreciate and sympathize with the spirit of your argument, I find your use of the Pauli matrices language quite clumsy and confusing. There exists a much more powerful language to reveal the same light, introduced long ago by Grassmann. This was later improved upon by Clifford, who also incorporated Hamilton's insight of quaternions into Grassmann's framework. The result is of course what we now call Clifford or geometric algebra. As I mentioned, it is a much more powerful language than the language of matrices you are using. But more importantly, I do not see a clear cut analysis of the question of locality in your argument. The conceptual clarity on this issue in Bell's work is far superior. The issue of locality in quantum physics is so subtle that it is not good enough to have some vague intuitions about it. A systematic analysis is necessary. This is why, despite being so critical, I very much admire and appreciate Bell's contributions to the debate.

Hi again Joy,

I am well aware of Grassmann algebras, and I was not intending to present a magic argument about locality. I just wanted to point out that the basic structural issues of two-valued eigenstates date all the way back to Pythagoras if you really dig into it. If that had been known for 2500 years, maybe people would have approached the wake of Planck differently than they ended up doing.

On a different note, you mention that you take the idea of quantum or guiding potential very seriously, and think that it is "real." If so, then you are stuck with non-locality in your work. Unless you interpret the guiding potential epistemically as Michel has suggested, you will not be able to get rid of non-locality from your work.

Then I would have to think that my work does require non-locality, and I am OK with that because it seems to me to introduce the rudiments of "knowledge" into the quantum vacuum. And importantly, because I have proposed how this guiding potential can be measured photovoltaically and what should be quantitatively and qualitatively expected from taking such measurements as I stated in reply to Minkwe, I may not have to endlessly argue the point. That is because this guiding potential, if it exists, should really be accessible to measurement, especially if one does micro-scale slit experiments where the potential is predicted to be larger and thus more detectable.

I actually am gaining a sense for how you are handling non-locality in EPR for states which are prepared by interaction, and then separated and no longer interacting, and may write up some brief notes and figures to focus that discussion further.

I am curious, though: as simply stated as possible, how do you explain double slit results based on a strictly local theory, using spinors and curved space and torsion which you say are the real basis for your results? I am not able in my thinking to draw the line between handling double slit, and handling the separation of interactively-prepared states.

Jay

Jay

[minkwe]

I disagree. I believe the guiding potential is real. Not only that, as I start to develop in section 20 of http://jayryablon.files.wordpress.com/2 ... mplete.pdf with specific voltage drops, I believe that it can be directly detected by measuring the photovoltaic activity at a slit experiment detector as the individual photons strike the detector. I elaborated this in one of my posts here, a few days ago. And this is likely to be the precise topic of my next paper.

Bottom line: I propose to establish that the guiding potential is very real, by having it be directly observed to be what I have predicted it to be, on the detectors used in slit experiments.

Good luck with that. You may succeed in detecting the ether before you succeed in detecting your "guiding potential".

Maybe. I would say it this way:

Each particle does take a definitive path from its emission by a known source at X to its observed detection at Y on a detector. But we do not know what that path is without interrupting that path by making the particle strike a detector and thus "sinking" that particle somewhere between X and Y. The path integral tells us all possible paths, as well as the probability for each. But -- and this is central to my theory -- this probability amplitude is tied on a one-to-one basis with a definitive guiding potential which guiding potential a) is caused by the probability amplitude of the source, b) causes the probability amplitude of the sink, c) is a function of, not independent of, the particles which are propagating as well as the slit configuration, and d) provides the underlying least-action basis for explaining why individual particles strike detectors with the observed wavelike probabilities that they do.

You lost me at the "But ...". With what I know about the meaning of "probability",the rest doesn't make sense to me. Words like "probability", "potential" are epistemological. It doesn't make sense to talk of a "probability" causing anything. A probability is a number that encapsulates the likelihood of something happening, it does not cause anything to happen.They are not real things by their very definition. This is why I kindly suggested that you carefully examine your distinction between ontology and epistemology.

This then leads to my view that another example of confusion is: "light is both a wave and a particle -- duality." And clear thinking: "light is a particle which strikes detectors in wavelike patterns due to least action propagation through a guiding potential in the quantum vacuum."

I agree with you somewhat. I believe light is a particle with wave-like dynamics. Simply a distinction of dynamics and kinematics. There is no contradiction between "particle" and "wave". A spinning soccer ball is a particle and a wave.

The one question I then see in play, is whether the configuration of this very real and directly-measurable guiding potential can be explained based on strict locality, or requires some non-local explanation.

I'm still puzzled what the "essence" of this "guiding potential" is supposed to be. Have you given it much thought beyond what pops out of your equations. Is it a particle field, is it an ether, how does it affect particles, does it impart a force on electrons, photons, etc? How does it interact with photovoltaics? What is the mechanics of your "guiding potential"? These are all ontological questions.

I'm not convinced that your "guiding potential" is real. But that's just my opinion, don't let me discourage you from your efforts.

[FrediFizzx]

Rick,

The cross section measurement does not imply there is nothing outside its dimension. Not saying it is responsible, but what do you think about the scope of the electric field for an isolated electron?

Surely there is stuff outside its dimension -- everything else. The scattering cross section tells you the maximum extent of interaction of the electron itself with anything. That tells you the electron cannot scatter from two slits at the same time that are separated by a distance outside the cross section. As concerns the mechanics of scattering, see viewtopic.php?f=6&t=51.

This brings up a problem that I have with modern particle physics. Surely the electron "drags" along electric and magnetic fields associated with it. Of course particle physics relegates those fields to virtual photons. I see those fields as more of a disturbance of the quantum "vacuum". Now, we have an electron going through one slit. Surely part of the electron's electromagnetic field is going through the other slit. What effect is that going to have on the build up of the interference pattern?

[Yablon]

This brings up a problem that I have with modern particle physics. Surely the electron "drags" along electric and magnetic fields associated with it. Of course particle physics relegates those fields to virtual photons. I see those fields as more of a disturbance of the quantum "vacuum". Now, we have an electron going through one slit. Surely part of the electron's electromagnetic field is going through the other slit. What effect is that going to have on the build up of the interference pattern?

Fred, good query, I want to think about that further, but what you said may help me solve my non-locality problem with the guiding potentials because those potentials are all activated, i.e., "lit up" by the particles which travel through them.

The question I have is this: You said electron. What if you had said real (not virtual) photon? Because both electrons and photons (and all other particles shot through slits) have similar interference patterns. If a "real" photon carries virtual photons with it, you may have given me exactly what I am looking for.

I am now thinking of all these field quanta as "hurricanes" passing through the quantum vacuum which "create their own weather." When a hurricane hits land then different things happen with their weather; so too when these particle hurricanes hit slits.

Jay

[FrediFizzx]

This brings up a problem that I have with modern particle physics. Surely the electron "drags" along electric and magnetic fields associated with it. Of course particle physics relegates those fields to virtual photons. I see those fields as more of a disturbance of the quantum "vacuum". Now, we have an electron going through one slit. Surely part of the electron's electromagnetic field is going through the other slit. What effect is that going to have on the build up of the interference pattern?

Fred, good query, I want to think about that further, but what you said may help me solve my non-locality problem with the guiding potentials because those potentials are all activated, i.e., "lit up" by the particles which travel through them.

The question I have is this: You said electron. What if you had said real (not virtual) photon? Because both electrons and photons (and all other particles shot through slits) have similar interference patterns. If a "real" photon carries virtual photons with it, you may have given me exactly what I am looking for.

I am now thinking of all these field quanta as "hurricanes" passing through the quantum vacuum which "create their own weather." When a hurricane hits land then different things happen with their weather; so too when these particle hurricanes hit slits.

My viewpoint is that the quantum "vacuum" is a relativistic medium composed of fermionic pairs and is so perfectly nulled out that it can't be directly detected (it just becomes an interpretation). Photons are merely phonons (wavicles) of that medium so I don't have any problem with photons creating interference patterns. Now to your question about if real photons carry virtual photons with it keeping in mind that "virtual" in particle physics simply means "off mass shell". I not sure if we can look at it that way but perhaps a little bit if we realize that a photon is just a wavicle due to the fermionic pairs of the quantum "vacuum" being excited by the original energy conversion source. I would think that there would be some "off mass shell" situations happening but I don't think it matters much at all until the photon is destroyed at the detector. But even then, it all has to balance out somehow. Is there any effect of this regarding the slits? Still, it all has to balance out. And... if there are virtual photons involved with photons, what would be any practical spatial extent regarding the slits?

[Yablon]

. . . And... if there are virtual photons involved with photons, what would be any practical spatial extent regarding the slits?

That is the question, but let me re-frame it a bit:

Photons and electron and protons and neutrons and mesons and alpha particles and other particles all exhibit similar interference patterns from a double slit.

So, if whatever virtual particles surround an electron are involved with bringing about the observed diffraction pattern, it would seem that one would have to have some analogous virtual entities for all of these other particles. This is whether you have a charged electron, a neutral photon or neutron, a charged proton, or a charged or neutral meson, etc. What is good for one has to be good for the rest.

So, my question is whether all of this is plausible? My initial thinking was that is was not. Thus, I could not regard some "aspect" of a field quantum as going through the other slit. Thus, I was driven to non-locality. And thus I am driven to see if there is something in what Joy is doing that might flag me off of non-locality. Thus I am asking Joy and you and anyone else how what Joy is doing to find locality for distant entangled EPR states might be applied to double slit.

Jay

[Yablon]

So are you saying, Joy, that by putting our three space dimensions on a sphere not unlike what Freidmann did in his cosmological model, and by recognizing the fashion in which a three-dimensional Pythagorean space can be spinorially deconstructed (about which I will have much more to say in the next few days), we are able to locally explain apparent non-locality?

Exactly, Jay. Please see my latest paper: http://arxiv.org/abs/1405.2355 (I know you are not too keen on simulations, but this one supports the claim in my paper).

OK, Joy, let me now take a stab at how this might be plausible based on a spherical (I will say, more generally, curved) space, via some use of parallel transport.

Having not studied the details of how you do this, let me see how I would approach this once told that using a space curvature and torsion is part of the recipe.

Once I am in curved space, then there is no objective way to discuss whether two vectors (read: spin orientations) prepared in an oppositely-aligned singlet remain oppositely aligned when they are separated by a distance at points A and B in the curved space. There are paths I can choose via the curved space to parallel transport the orientation at B back to the one at A and find that they are indeed oppositely aligned once they are brought back together. And if I am on a sphere, I believe that I am guaranteed to have available at least one such path. On the other had, there are many paths by which I can parallel transport the orientation from B back to A and find that the orientations are not oppositely aligned. So the maintenance of the singlet system as a whole, is highly dependent on the path I take.

Now, if the physics I observe tells me that I will always have oppositely aligned states, this would seem to suggest that in some way, via least action, nature herself moves the particles only along paths for which the parallel transport maintains the opposite alignment. Or, perhaps, the torsion provides something of a "transformation" parameter to ensure that the singlet system remains invariant irrespective of the path we use to compare.

But no matter how you slice it, because there is no universal "right" answer by which one can compare alignments between two vectors separated by finite space because the parallel transport result is path-dependent, the orientation-at-a-distance is not an invariant physical observable. Unless it is made such by absorbing the range of possibilities into some other non-observable parameter, such that we can find an invariant way to discuss this. So we should look for some natural conspiracy by which the singlet system remains invariant irrespective of the nature of the spatial curvature.

I am reminded by all of this that in curved spacetime, not even energy conservation can be discussed on a global basis. It can only be discussed on a local basis.

Then we go question the usual suspects: what is the symmetry principle, what are the invariants, what are the non-observable, not absolute parameters under which this symmetry exists?

Am I cold, getting warm, or getting hot?

Jay

[Joy Christian]

So are you saying, Joy, that by putting our three space dimensions on a sphere not unlike what Freidmann did in his cosmological model, and by recognizing the fashion in which a three-dimensional Pythagorean space can be spinorially deconstructed (about which I will have much more to say in the next few days), we are able to locally explain apparent non-locality?

Exactly, Jay. Please see my latest paper: http://arxiv.org/abs/1405.2355 (I know you are not too keen on simulations, but this one supports the claim in my paper).

OK, Joy, let me now take a stab at how this might be plausible based on a spherical (I will say, more generally, curved) space, via some use of parallel transport...

Am I cold, getting warm, or getting hot?

Hi Jay,

You are all over the place. Please read the paper. It is only 4 pages long. It won't take you more than 10 minutes to read it. If you do read it, you will see that the precise meaning of what is meant by local (as specified by Einstein and Bell) is of paramount importance. Intuitive ideas of how it ought to be are not good enough.

Joy

[FrediFizzx]

Fred, the sedenions are not a division algebra because you can only define 8 of 15 octonion subalgebras with consistent quaternion subalgebras, of which there are 35.

Yes Rick, that is correct. Sorry I didn't make that more clear. But I was just presenting the certain rules for math in an order that I think how they came about in Nature. Sedenions have less rules than octonions.

[Rick Lockyer]

Rick,

The cross section measurement does not imply there is nothing outside its dimension. Not saying it is responsible, but what do you think about the scope of the electric field for an isolated electron?

Surely there is stuff outside its dimension -- everything else. The scattering cross section tells you the maximum extent of interaction of the electron itself with anything. That tells you the electron cannot scatter from two slits at the same time that are separated by a distance outside the cross section. As concerns the mechanics of scattering, see viewtopic.php?f=6&t=51.

Looked at the referenced thread, you wrote

A few comments about the misconceptions:
Constructive/destructive interference:
We now know that quanta/electrons are discrete particles of energy/mass, they cannot disappear at one location and appear instantaneously at another. Constructive and destructive interference, as much as it suggests that photons or particles magically disappear from some locations and appear instantaneously at other locations is inconsistent with physical evidence about electrons and photons. It is not that particles disappear from the minima and appear at the maxima, rather it is that, there are more particles going to the maxima to begin with than the minima. Nothing is "constructed" or "destructed". Then you may ask, why do particles prefer to go into the maxima rather than the minima, and that is what my explanation will answer (in fact it is not my explanation, it has been known but ignored since the beginning of quantum theory. I guess it was not mysterious enough for the copenhageners).

A single particle goes through both slits. (Hawking, Feynman, Brian Greene etc have all repeated this falsehood)
Simply nonsense. Quanta and electrons are indivisible. No need to explore this one further, it is clearly nonsense.

A single particle interferes with itself
Just as nonsensical. Why do you need slits if particles can interfere with themselves? We should be seeing diffraction from a single beam without any slits. Besides, a single particle does not produce a diffraction pattern, you need many particles, as the video you referenced clearly shows.

A single particle produces an interference pattern
Nonsense.

Knowing which way the particle went, disrupts the pattern
More nonsense. It is obvious that disturbing the path of the particles, disrupts the pattern. This is commonsense and not mysterious.

One more misconception:
The importance of the slits
Most attempts to explain diffraction patterns, focuses on the particles, and ignores completely the most important component, the slits. As you will see, my explanation will take into account all the components.

Any clarifications of the above needed, before I proceed?

Bold statement in the second item. You have an opinion. You can't say with any certainty your claim is true. It certainly is a critical link in your logic chain though, and you certainly are welcome to your opinion. I just don't share it.

Social comment: I found the argumentative style in the thread quite tedious.

[Rick Lockyer]

Quantum mechanics as you have said, demonstrates the cosine function is relative to the difference in Alice's and Bob's orientation angles. What this means is it really does not matter what the two absolute angles are. You could move both keeping the same relative difference and expect the results not to change.

What good would that do? If say you kept the relative difference at 60 degrees, you will only get results for just 60 degrees in the final plot. That will not tell us anything. And... QM results are always about averages. Will those average results be nearly the same? I would think so and the simulations show that they are.

What makes it interesting is quantum mechanics would predict a straight line for constant setting difference over a range of absolute settings, so a model and its simulation would be required to provide the same. Thus it is a test of whether or not the model is valid. Simple test for you to perform: in Joy's http://rpubs.com/jjc/16415, change beta for the first plot from 0 degrees to 30 degrees. If the model/simulation was true, the plot should be the -cos function with a 30 degree offset. It isn't because at the very least, the simulation is not true to expected results. The jury is out on the model.

[Joy Christian]

What makes it interesting is quantum mechanics would predict a straight line for constant setting difference over a range of absolute settings, so a model and its simulation would be required to provide the same.

This simulation produces exactly what quantum mechanics predicts in all conceivable physical scenarios. Your confusion arises because you have not understood what I have explained here: viewtopic.php?f=6&t=69#p3225.

Simple test for you to perform: in Joy's http://rpubs.com/jjc/16415, change beta for the first plot from 0 degrees to 30 degrees. If the model/simulation was true, the plot should be the -cos function with a 30 degree offset. It isn't because at the very least, the simulation is not true to expected results.

Incorrect. It is very easy to modify any simulation so that it stops working. Changing from 0 degrees to 30 degrees corresponds to a counterfactual change in the setting of Bob, which in turn means a different physical experiment altogether. Why should a different experiment produce the same result?

One has to produce only one correct simulation, like this one, to prove Bell wrong. You cannot prove Bell right by producing a simulation that does not work.

The jury is out on the model.

Perhaps you haven't heard. My analytical model is impeccably true, and it has always been impeccably true. It has now been verified by a number of exceptionally qualified, knowledgeable, and competent physicists around the world.

[FrediFizzx]

What makes it interesting is quantum mechanics would predict a straight line for constant setting difference over a range of absolute settings, so a model and its simulation would be required to provide the same.

This simulation produces exactly what quantum mechanics predicts in all conceivable physical scenarios. Your confusion arises because you have not understood what I have explained here: viewtopic.php?f=6&t=69#p3225.

I think I did understand what you were trying to say, and what you missed within. cos(a) and cos(-b) are poor representatives of cos(a-b) since they are each functions of a single variable.

Simple test for you to perform: in Joy's http://rpubs.com/jjc/16415, change beta for the first plot from 0 degrees to 30 degrees. If the model/simulation was true, the plot should be the -cos function with a 30 degree offset. It isn't because at the very least, the simulation is not true to expected results.

Incorrect. It is very easy to modify any simulation so that it stops working. Changing from 0 degrees to 30 degrees corresponds to a counterfactual change in the setting of Bob, which in turn means a different physical experiment altogether. Why should a different experiment produce the same result?

One has to produce only one correct simulation, like this one, to prove Bell wrong. You cannot prove Bell right by producing a simulation that does not work.

If you were actually demonstrating the proper function of two variables, it would be quite correct to do what I did. The second plot in your program does not change the initial conditions vector set u and does allow beta to breeze right through 30 degrees without any problems, so clearly it is not that for some strange reason beta can't be 30. Your simulation simply will not work without one of alpha or beta being 0. This is not a demonstration of -cos(alpha - beta). The rub is you can't do this without making the set u be a function of both Alice's and Bob's settings, which is precisely and very clearly evident in your x-y plot simulation within the following code snippet

Code: Select all

x <- runif(M, -1, 1)
t <- runif(M, 0, 2 * pi)
r <- sqrt(1 - x^2)
y <- r * cos(t)

u <- rbind(x, y)  ## 2 x M matrix; the M columns of u represent the
## x and y coordinates of M uniform random points on the sphere S^2

eta <- runif(M, 0, pi)  ##  My initial eta_o, or Michel Fodje's 't'

f <- -1 + (2/sqrt(1 + ((3 * eta)/pi)))  ## Pearle's 'r' is arc cosine of 'f'

for (i in 1:K) {
    alpha = angles[i]
    a = c(cos(alpha), sin(alpha))  ## Measurement direction 'a'

    for (j in 1:K) {
        beta = angles[j]
        b = c(cos(beta), sin(beta))  ## Measurement direction 'b'

        ua <- colSums(u * a)  ## Inner products of 'u' with 'a'
        ub <- colSums(u * b)  ## Inner products of 'u' with 'b'

        good <- abs(ua) > f & abs(ub) > f  ## Sets the topology to that of S^3

        p <- x[good]
        q <- y[good]
        N <- sum(good)

        v <- rbind(p, q)  ## N spin directions pre-selected at the source

        va <- colSums(v * a)  ## Inner products of 'v' with 'a'
        vb <- colSums(v * b)  ## Inner products of 'v' with 'b'

        corrs[i, j] <- sum(sign(va) * sign(-vb))/N

        ## corrs[j] <- sum(sign(vb))/N

        Ns[i] <- N
    }
}



Alice's measurements sign(va) and Bob's measurements sign(-vb) are both functions of v which in turn is a function of good, which in turn is a function of both a and b which are Alice's and Bob's chosen orientation angles respectively. You need to explain how this could possibly be valid. I am sorry but "you do not understand" is non-responsive. Do not confuse me with someone trying to prove Bell right. I could not care less since I do not believe the true nature of the physics is represented.

The jury is out on the model.

Perhaps you haven't heard. My analytical model is impeccably true, and it has always been impeccably true. It has now been verified by a number of exceptionally qualified, knowledgeable, and competent physicists around the world.

Believe me when I say that I want you to be successful. You are not there yet. [Inflamatory comment deleted]

[FrediFizzx]

Ok guys, let's get back on topic here. There are other threads to discuss Joy's simulations or make a new thread. I believe in this thread we are assuming that Joy's model is correct and with that assumption Jay wants to know if that could help him in his theory with his non-locality involving the double slit scenario. Jay, can you explain in words how your quantum potential arrises?

[Yablon]

Ok guys, let's get back on topic here. There are other threads to discuss Joy's simulations or make a new thread. I believe in this thread we are assuming that Joy's model is correct and with that assumption Jay wants to know if that could help him in his theory with his non-locality involving the double slit scenario. Jay, can you explain in words how your quantum potential arises?

Yes Fred,

Well stated. I am trying to understand Joy's approach better from a conceptual standpoint, to see if and how it might be applied to double slit. I did read Joy's four-page paper yesterday as well as rereading Einstein-Podolsky-Rosen (EPR) which I had read years ago, and had planned to pen some questions to Joy over the weekend. But let me reply right now to Fred.

The quantum potential arises in the course of my 225-page paper at http://jayryablon.files.wordpress.com/2 ... mplete.pdf. Obviously I cannot ask anyone to read the whole thing, but I can steer you to the key places in the paper where the potential arises and is developed, as well as discussing the (still-ongoing) evolution in my thinking about this potential. And, Fred, I will say that I am also "cooking" the comment you made the other day about virtual photons going through one slit while the electron goes through the other, as a possible path to a local explanation.

I will write and post my reply to Fred in several parts. This part will be:

PART I: GENERAL BACKGROUND

My quantum potential arises from the path integral formulation of quantum field theory which started with Richard Feynman, so first you have to buy that formulation. In the first full paragraph on page 78 of the linked paper, five lines down, you will see the usual formulation of the path integral in terms of Z=.... One takes an action S(G) which is a function of a gauge field G and via the path integration turns it into a quantum amplitude W(J) which is a function of a current density J. But, W(J), just like S(G), has dimensions of angular momentum = Energy x time a.k.a. action, which is of course also the dimensionality of Planck's constant. So just to get our language straight, I refer to S(G) as a "classical action" because that action is connected to a classical field equation via the Euler-Lagrange equation, and I refer to W(J) as a "quantum action" because that action is what one gets only after doing the path integration, which means carrying out the full path integration over DG and d^4x in that equation I just referenced on page 78. One will appreciate that this "quantum action" W(J), although having the same dimensionality as the "classical action" S(G), will certainly manifest different physics properties. One will also appreciate that because the classical gauge field G is the variable of integration in the path integral, once the path integral is done, there will no longer be a gauge field G in any of the equations. All that remains behind is a current density J and a quantum action W(J). Finally, if one were to take a time density of the classical action in the form E(G)=S(G)/time, then one would have a "classical energy" which in some circumstances could be a potential form of energy. Similarly, if one were to take as I later do, the time density of the quantum action in the form E(J)=W(J)/time, then one would have a "quantum energy" which also could in some circumstances be a potential form of energy. That is to say, just as the "quantum action" is expected to manifest differently than the "classical action," if we end up dividing these by time somewhere along the way, we will get a "quantum energy" versus a "classical energy" which could in some instances be a "quantum potential" versus a "classical potential," and these will also have different physical properties and require different understandings and interpretations which will carry through directly from differences between the classical versus quantum actions. So that explains the language I am using when I refer to a "quantum potential" versus a "classical potential." The "quantum potential" which ends up being at the heart of my theory is in fact the result of a later E(J)=W(J)/time calculation. And once I apply this to double slit, this does eventually turn into my "guiding potential" which looks like the sort of thing that David Bohm proposed with "pilot waves." Bottom line for this paragraph: If one believes that W(J) that emerges from path integration is physically real and observable and not just some helpful but non-existent epistemological construct, then one must believe that its time density E(J)=W(J)/time is equally real and observable. And this, coupled with some other evidence I will review momentarily, is what provides me with a rock solid conviction that my quantum potential is part of observable physically reality as EPR defined that term.

Now, let's talk briefly about the place that path integration occupies in the overall scheme of modern physics. Simply put: path integration is what we use to convert a classical field theory into a quantum field theory. No more and no less. It is that simple. Take any classical theory you wish. Electrodynamics with mediating field A^mu. Weak or strong interactions with mediating field G^mu. Even gravitation with mediating field g_mu nu (which shows up in the Einstein-Hilbert action with g and R). Write down its classical field equation(s). Use Euler Lagrange to obtain an action S(mediating field). Then plug that into the path integral with the mediating field as the variable of integration, do the math, and out pops W(source) with the mediating field stripped out because it is the variable of integration. For EM and weak and strong, the source is J^mu. For gravitation it is T^mu nu. And that is it! W(source)=... is the quantum field equation, and these quantum field equations are totally parallel to Maxwell's equations and the Yang-Mills equations and the Einstein equation in classical field theory. But if a quantum action behaves and needs to be understood differently than a classical action, then a quantum field equation also behaves and needs to be understood differently than a classical field equation, in spades! In many ways, my own conceptual struggles at present are rooted in the fact that I have derived some quantum field equations for W(J) which have never before been found, and am trying to master what these equations teach us about the universe. I feel much as Dirac must have felt, when he said that his equation "is smarter than its author." And I am asking for insight from you all so I can become as smart as my equations, which is why I stared this thread. Specifically, these quantum field equations I obtained for W(J) dump right onto middle of the table, all of the other conceptual conundrums of quantum theory such as locality and entanglement. So I landed right in the middle of what you all have been passionately debating, but I came in through a different door via having analytically done a previously-thought-to-be intractable path integral (subject of the next paragraph), and found that understanding the resulting equations landed me smack into the middle of a locality conundrum. Which, by the way, I take as a sign that the equations I derived are very much on the right track, because any quantum field equations, if correct, should land their author right in the middle of all these quantum conundrums. But, at the same time, they may also give some previously unavailable guidance about how to work one's way through these quantum conundrums. This is another reason I am coming to you all for helpful insight.

Now, you may ask, if extracting a quantum field theory from a classical field theory is as simple as I said in the last paragraph -- just find your classical action from the classical field equation, plug it into the path integral, and pop out the quantum field theory -- then why do we not have complete quantum field equations for Yang-Mills gauge theories and for gravitation? Why do we really only have a complete quantum field theory for electrodynamics? In theory, it really is as simple as I said in the paragraph above. But in practice it is extraordinarily difficult. Why? One word: mathematics! The mathematics of doing a path integral analytically and exactly is extraordinarily difficult, and indeed, has been one of the most intractable challenges faced by anyone seeking to develop quantum Yang-Mills theory, and even more so, quantum gravitation. Why is this so difficult? Because a path integral is of the form (again, full paragraph on page 78 of the linked paper, five lines down, looks like I left out the discardable coefficient C in the paper):

C W(J) = $DG exp i ($d^4x S(G))

and only the QED action is quadratic in G, i.e., only the QED action has terms of the form G^2 + JG and nothing of higher order. The Yang-Mills action has terms up to G^4, and for gravitation, it is totally nuts if you unpack R and g into g_uv and so all bets are off. Why is this a problem? Not because of $DG and not because of $d^4x. Because of the higher-than-G^2 terms in the action. Why? Because for an action of the form S(G) = G^2 + JG, the above equation for W(J) fits the template of an ordinary Gaussian integral (see, e.g., http://en.wikipedia.org/wiki/Gaussian_i ... n_function), and we know how to solve those. The reason we can get a quantum field theory for electrodynamics, is because it obliges us by only having a quadratic action. Yang-Mills is not so courteous, and gravitation, forget about it. Specifically, as of 2014, with all of the mathematics that is known in the world, it is still not known even how to analytically perform a Gaussian integration if the exponential being integrated contains Ax^4 + Bx^3 + Cx^2 + Dx + E. If you want an exact analytical answer, you have to ditch the x^4 and the x^3 terms. But in physics, and in Yang-Mills theory specifically, the G^4 and G^3 terms which prevent us from doing the mathematics, are precisely the very same terms that make strong and weak interactions non-linear! So this means that to date, humankind has never really seen an exact analytical equation for a non-linear quantum field theory with a quantum action action W(J) obtained from a non-linear classical field theory. We only have an analytical quantum field theory for electrodynamics, and the reason for that, is that electrodynamics is a linear theory, and the reason for that is that the terms in its action go no higher than G^2. Now, to be sure, physicists do not easily give up on things like these, so there are inexact workarounds. "Perturbative gauge theory" is one such workaround. So too is "lattice gauge theory." And, it is a widely utilized trick to employ the operator variational G=(delta /delta J)(JG) to replace the G^3 and higher terms in an action with terms in J so that the Gaussian integration only needs to be done on the quadratic G^2 + JG, see the first full paragraph on page 79, but this only solves the path integral on term-by-term basis by popping out Green's and Wick's functions. It does not yield a closed form solution and putting the term by term results together into closed form is also an intractable problem. So these theories and approaches all make compromises and simplifications and forgo certain symmetries in order to get some picture of W(J), and in many cases, they use computers to help. In fact, lattice gauge theory requires enormous computing power, which helps explain why Kenneth Wilson, who developed lattice gauge theory, was also a pioneer in promoting the development of supercomputers which advanced many other good technological benefits flowing from improved computing capacity beyond being able to do lattice calculations. But I digress.

Humankind, and particularly the physicists who care about this stuff that puts the rest of the population to sleep, simply have never before seen what an exact analytical non-linear quantum field equation looks like. And because of that, they have not had a chance to struggle (and it is a struggle) with trying to understand what these "smarter then their author" equations would mean if they were to have such equations in front of their eyes. In my paper, I have been able for the first time to obtain some analytically-exact quantum field equation which are non-linear, based on the up-to-G^4 terms of classical Yang-Mills theory. And because of that, I have been the first person in the world to my knowledge who has has had to struggle through deciphering what these non-linear equations are teaching. And as best I can tell, all of the non-locality that people struggle with in quantum theory comes whooshing in as soon as one starts to apply these non-linear quantum field equations to such things as the slit experiments. And because this happens, that tells me that these equations are on the right track. And it also tell me that I need to be talking to you all who have been hotly debating locality and non-locality for as long as I have been a moderator and participant of this group.

How did I manage to find myself in this position? While I started this paper with the thesis that baryons are Yang-Mills magnetic monopoles which I adhere to strongly and have empirically supported by successfully retrodicting fifteen light nuclear binding energies from hydrogen through oxygen and the proton and neutron rest masses as previously posted and discussed at length in this space, the emergence of the non-linear analytical quantum field equations was entirely independent of the baryon / monopole thesis. Simply put: I figured out how to solve the Gaussian integral which has the form Ax^4 + Bx^3 + Cx^2 + Dx + E in the action, for the specific form that this polynomial takes on in the Yang-Mills gauge theories which are widely-accepted to govern the weak and strong interactions. I do this via a recursion which I first uncover in section 8 of my paper, and which I then apply to exactly and analytically perform the complete Yang-Mills path integral in section 11 of my paper. That result -- which solves the mathematical problem that had previously been considered intractable-- is equation (11.5). Put plainly, sections 8 and 11 are a breakthrough in the mathematics of exactly and analytically applying the physics of path integration to non-linear field theories. Later refined versions of (11.5) are in equations (13.20) and (13.21), with the amplitude / action density M(J) defined from W(J) in the first line after (13.6).

From there, it is on to applying these equations. When the W(J) becomes divided by time to obtain an E(J)=W(J)/time as occurs in some later calculations, and then we develop all of this in time-independent fashion, I end up with an energy E(J) which in the simplest case where the source J is a Dirac delta, is identically synonymous with the Coulomb potential, as developed mainly in sections 16 and 19. (I first developed the time-independent case just to keep life simple in the opening stages of dealing with a non-linear quantum field equation -- I would expect the time-dependent development to tell us some interesting things about signal propagation speeds like how a change in slit configuration propagates out to inform the rest of the world that the slits are changed.) Beyond believing that W(J) and thus W(J) / time is real in the EPR sense because I am a believer in the reality in the EPR sense of what one gets out of a path integration, the correspondence with Coulomb when the source is postulated to be a Dirac delta is what convinces me that this potential is very, very real in the EPR sense. (I have left out how I get from sources J to probability densities. That too is a trek worthy of its own story in sections 14 and 15. But for now, I simply remind you that in Dirac theory, the time component J^0 of a current density four-vector is a probability density.) So when I then take this potential and apply it to more complicated probability densities like those for the single and double slit experiments, I believe that the potentials I derive there must be just as EPR-real as the Coulomb potential. Then, when I see that these potentials to which I have ascribed this EPR reality seem to require some non-locality, I take this as a signal that these equations are doing something right, I know that I have plunged into the quantum quagmire that all of you have debated here forever, and that is again why I came here for help.

Final note: Like any attentive author, when I write something down to try to teach it to others, as a byproduct I teach myself more than I knew when I started writing. In writing this and giving emphasis to the fact that this is a non-linear quantum field theory, I remind myself that these field quanta passing through slits are doing so in a non-linear way. This has made me more believing, not less, that Fred was on the right track when he mentioned "virtual photons," at least "in spirit," as perhaps a way to explain the slit experiments without resort to non-locality. If the quantum potential is affected by the field quanta as it clearly is (will discuss why in a later PART), but the theory is non-linear, then the potential must itself affect the potential, and this means that the potential around the electron as the electron goes through one slit will affect the potential at the other slit because of the non-linearity. And if that happens, and the slits also affect the potentials as its would seem they must (remember, these are quantum potentials -- all the usual classical ways of thinking about a potential -- such as what happens with an insulator -- are changed), then you could have a field quantum interfering with itself, not by going through two slits which ain't in the cards, but by activating a non-linear cascade in the potential which can reach over to and propagate through the other slit and then condition the guiding potential on the other side of the slits. Stay tuned, still "cooking" that one; if it flies, Fred gets an acknowledgement.

That should do it for PART I.

Jay

[FrediFizzx]

Hi Jay,

I'm a little confused here; probably missing something that is maybe in Part II? Isn't E(J) = W(j)/time just the self-energy of the source J? Have you considered instead,

E(J) = W(J)*frequency?

That of course corresponds to E = hbar*omega for a quantum type of energy expression.

[Yablon]

Hi Jay,

I'm a little confused here; probably missing something that is maybe in Part II? Isn't E(J) = W(j)/time just the self-energy of the source J? Have you considered instead,

E(J) = W(J)*frequency?

That of course corresponds to E = hbar*omega for a quantum type of energy expression.

Fred, you may be overthinking this. All I am really laying out at this broad introductory level is a dimensional analysis. Frequency is 1 / time, so dimensionally speaking we are saying exactly the same thing. You are trying to anticipate some interpretive issues; it is best to wait until I get to part to to lay out exactly where the time variable enters the calculations. But if you want a brief preview, the introduction of time takes place right after equation (14.13), and in the deeper, non-abelian calculation, after equation (15.17). That is where the quantum action W becomes the quantum potential E. Jay

[FrediFizzx]

OK, I will wait for Part II. I did read through your Sect. 14 and 15. It just seems like to me that you would need to separate E into terms for the self-energy of the source J and the quantum potential. Which perhaps you will do in Part II? I going to re-read Sect 14 again as I think it has more explanation about what you are doing.