Thoughts about Bell, Bohm, Christian, et al.

[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.

[FrediFizzx]

Hi Jay,

I think I found the source of my confusion. Right before and in eq. (14.11) you drop out the J-sigmas so when you get to eq. (14.13, 14.14) it looks like there is only one J source when they are in fact still expressions for interactions between two J sources.

[Yablon]

Hi Jay,

I think I found the source of my confusion. Right before and in eq. (14.11) you drop out the J-sigmas so when you get to eq. (14.13, 14.14) it looks like there is only one J source when they are in fact still expressions for interactions between two J sources.

Yes, Fred. The J-sigmas which I drop out are fields in spacetime; and the remaining J sources are in momentum space which I treat a few equations later by transforming to the rest frame.

In your earlier posts you commented on the electron self-energy, so let me discuss that for a moment. I want to condition you and anyone else who studies my paper, as well as myself, to keep remembering that we are dealing now with field equations for non-linear quantum field theory. That fact cannot be repeated too often; I want to drum it into my head and everyone else's. So we all need to think about things differently than we do when we are dealing with, e.g., QED which for all the efforts to treat non-linear aspects of nature e.g., Schwinger and the magnetic moment anomaly, is still a linear field theory. So working against the background of a linear field theory, people have had to "add in" non-linear features of nature which we expect need to be accounted for, and that often calls for some clever, heavy lifting.

Electron self-energy is one such example. If we ignore the self-energy, then we have a linear problem, and we can think of an electron moving through an external field without affecting that external field. That is, we neglect the electron's own contribution to the field, and thus neglect some non-linear terms. If we do not ignore the self-energy, then in a linear field environment,the problem is very difficult. But once we have a non-linear quantum field theory which includes accounting for non-linear behaviors in the quantum vacuum, then we have to trust the mathematics of our theory to properly handle various non-linear behaviors including the electron self-energy.

In other words: when we talk about an electron in a linear theory, and if we want to account for everything that goes on, then we must talk about the electron as well as its self energy. When we talk about electrons in a non-linear theory, then we only need to talk about electrons, and we don't worry ourselves about the self-energy. We then trust the non-linear theory to inherently take care of anything non-linear that the electron does including create a self-energy which modifies the external field, and in fact that seems to be exactly what happens.

This is why I continue to think that you may have instinctively hit the nail on the head when you made the recent comment about virtual photons, as regards being able to explain the double slit experiments on a local basis. I believe it impossible to explain the double slit results locally with a linear quantum field theory that uses a Bohmian potential. But I believe that a non-linear quantum theory with a Bohmian guiding potential and field quanta obeying least action principles does provide the tools to do exactly that: achieve a local, least action-based explanation of the double slit results. This should make Einstein and Bohm and Christian very happy.

Jay

[FrediFizzx]

A funny thing about non-linear quantum field theory is that the electron that goes through the slits isn't necessarily the same one that hits the detection screen. It can swap with one from the quantum "vacuum" in a virtual electron-positron pair. But I suppose that doesn't matter much as all electrons are the same.

Anyways, looking forward to your Part II when you get a chance.

[Yablon]

Fred and all, I can put in a few sentences what will be the lengthier outcome of Part II and Part III etc.: There is a one-to-one (i.e. isomorphic) relationship between any given probability density, and a related quantum potential (or the quantum action in the most general case). If you know one, you know the other. When you take the observed probability density for particles to strike the double slit detector and plug it into the quantum field equations (a specific application among an unlimited variety of applications of the non-linear quantum field equation), out pops a uniquely-related potential. That is how the mathematics for the quantum field equation works for any posited probability distribution.

Once you have obtained this potential for the double slit detector example, then you are into interpretation of how this potential works, and that is where questions of the particles themselves affecting the potential (an offshoot of self-energy), least action, and locality versus non-locality, arise. The lengthier materials I intend to write after I finish writing up a large patent I am working on for a client right now, will a) outline the foundations and premises via which one arrives at the underlying non-linear quantum field equation, b) summarizing the five examples, i.e., five probability densities, to which I have applied that equation thus far, c) describe how the lessons from each of these examples helps us to better understand and interpret and apply the non-linear quantum field equation, and d) elaborate the precise reasons why the double slit potential raises the core quantum issues that it does and the challenges of interpretation that this presents.

The quantum field equation I have uncovered does not by itself answer all of the difficulties people have with quantum theory: rather, it simply brings them onto a different stage and views them in a different light and so provides yet another tool for approaching these problems. The advantage this does provide, is that normally people approach explaining double slit and entanglement "seat of the pants," by trying to find any explanation they can without a disciplined, rigorous physical theory for doing so behind them. That leads to idiosyncratic approaches and explanations, which usually does not work for physics. My work provides a broadly-applicable field equation through which these problems can be analyzed, and so enforces a very orderly discipline on how one thinks about these problems. That sort of discipline can make all the difference in the world. Jay

[Yablon]

Fred and all, I can put in a few sentences what will be the lengthier outcome of Part II and Part III etc.: There is a one-to-one (i.e. isomorphic) relationship between any given probability density, and a related quantum potential (or the quantum action in the most general case). If you know one, you know the other. When you take the observed probability density for particles to strike the double slit detector and plug it into the quantum field equations (a specific application among an unlimited variety of applications of the non-linear quantum field equation), out pops a uniquely-related potential. That is how the mathematics for the quantum field equation works for any posited probability distribution.

Once you have obtained this potential for the double slit detector example, then you are into interpretation of how this potential works, and that is where questions of the particles themselves affecting the potential (an offshoot of self-energy), least action, and locality versus non-locality, arise. The lengthier materials I intend to write after I finish writing up a large patent I am working on for a client right now, will a) outline the foundations and premises via which one arrives at the underlying non-linear quantum field equation, b) summarize the five examples, i.e., five probability densities, to which I have applied that equation thus far, c) describe how the lessons from each of these examples helps us to better understand and interpret and apply the non-linear quantum field equation, and d) elaborate the precise reasons why the double slit potential raises the core quantum issues that it does and the challenges of interpretation that this presents.

The quantum field equation I have uncovered does not by itself answer all of the difficulties people have with quantum theory: rather, it simply brings them onto a different stage and views them in a different light and so provides yet another tool for approaching these problems. The advantage this does provide, is that normally people approach explaining double slit and entanglement "seat of the pants," by trying to find any explanation they can without a disciplined, rigorous physical theory for doing so behind them. That leads to idiosyncratic approaches and explanations, which usually does not work for physics. My work provides a broadly-applicable field equation grounded in path integration and acquiring its non-linearity from Yang-Mills, through which these problems can be analyzed, and so enforces a very orderly discipline on how one thinks about these problems. All of the Fourier analysis is already fully baked in to the general case field equation, that is, one does the Fourier transforms once for the general case, and then plugs in the specific cases and gets out direct answers without having to do anything Fourier again. That sort of discipline can make all the difference in the world. Jay

[Schmelzer]

So you believe
1. The "guiding potential" definitely exists as a physical thing (in the real world) rather than just an information manipulation device of your theory.
2. It is impossible to explain (as differentiated from "I cannot explain").

Won't you need to believe both of those in order to believe non-locality is required? Otherwise, maybe the "guiding potential" is not real (1 out the door), and/or maybe somebody else can explain it even if you can't (2 out the door), then your belief is irrational/premature.

First of all, if one follows Popper, then anyway all scientific research is, in a certain sense, premature: It never gives absolute certainty. Theories may be corroborated by observation, but this does not prove them. Moreover, (less well-known, but also Popper) even an experimental falsification cannot be certain, and remains open to criticism.

What would be clearly irrational is the refusal to use some very plausible hypothesis simply because it is not certain, not proved or so. In this case, we would have to reject science completely - because it never gives absolute certainty. Thus, the two possibilities you have listed make the belief only premature - which it is in some sense anyway - but not at all irrational.

What is, instead, rational, is to look the most plausible explanation. For a scientist, this would be an explanation which is compatible with the existing mathematical apparatus. It may contain additional elements (like the dBB guiding equation), but should not contradict the existing apparatus. The existing mathematical apparatus describes the quantum state with a wave function on the configuration space - but the configuration is, from the very start, a global object. One can, of course, look for modifications to get rid of this wave function. But this is something one has, yet, to do. I'm very much in favour of interpreting the wave function, at least in part, as epistemical. But this is something one has yet to realize.

Moreover, there is Bell's theorem, which tells us that a local realistic explanation is not possible. Of course, as everything in science it is open to criticism - and is criticized here. But I don't see yet that this criticism has been successful. Therefore there seems not much hope for others finding local realistic explanations.

[Brad Johnson]

Ilja, isn't this a Hamiltonian function? If so then the space in
consideration is a phase space and not a global object.
So what we have is a wave function associated with a mass
In motion. IOW restraints on degrees of freedom.

[Schmelzer]

Ilja, isn't this a Hamiltonian function? If so then the space in
consideration is a phase space and not a global object.
So what we have is a wave function associated with a mass
In motion. IOW restraints on degrees of freedom.

The wave function is something different from a Hamilton function. There are representations of the Hilbert space on the phase space. But even if one uses this representation, so that the wave function is a function on phase space, it is not yet a Hamilton function, simply the mathematics is yet very different.

Of course, one can think about making the similarity greater, but this is, again, work in progress. And the phase space is, except for a single point particle, also a global object.

[minkwe]

First of all, if one follows Popper, then anyway all scientific research is, in a certain sense, premature: It never gives absolute certainty. Theories may be corroborated by observation, but this does not prove them. Moreover, (less well-known, but also Popper) even an experimental falsification cannot be certain, and remains open to criticism.

And if you don't follow popper? I don't know where you got the idea from my year old post that only certainty is permitted. There comes a point when we can't even begin to have useful discussions because, even the language is babel. For example:

For a scientist, this would be an explanation which is compatible with the existing mathematical apparatus. It may contain additional elements (like the dBB guiding equation), but should not contradict the existing apparatus.

I hope you are not suggesting that what is going on, is an "equation" (see "like the dBB guiding equation"). Because this is precisely the kind of thing that is not even wrong. An equation can only represent one perspective of what is really going on, an abstraction of it at best. The folly comes from thinking that those equations themselves are objects, doing things like guiding other objects.

The existing mathematical apparatus describes the quantum state with a wave function on the configuration space - but the configuration is, from the very start, a global object.

The configuration is not an object. The configuration contains global information about all the objects in the system. It is a description of the system, not the system itself. It is epistemology not ontology. The configuration could not possibly exist, unless the system actually existed by itself. The (x, y, z, t) coordinates of a particle represents a configuration of the particle in one particular space time representation. But those coordinates are information, not objects. I could pick a different set of basis vectors, or a different type of representation and be able to provide a different but complementary perspective about the position of the particle. The only thing that is real, is the fact that the particle really exists, not the configuration I chose to ascribe to it.

One can, of course, look for modifications to get rid of this wave function. But this is something one has, yet, to do. I'm very much in favour of interpreting the wave function, at least in part, as epistemical. But this is something one has yet to realize.

Our problem is not the inability to "get rid of the wave function". Our problem is our inability to understand, or be clear about what exactly the wave function represents. To the extend that we start ascribing ontological status to fictions of our imagination, however useful they are as calculation devices.

Moreover, there is Bell's theorem, which tells us that a local realistic explanation is not possible.

And you believe it? My response to that will be to quote Bell's own statement about von Newmann's own hidden variable no-go theorem. Feel free to search and replace "von Newmann" with "Bell", because Bell proceeded to make a very similar error, and many have been gullible enough to believe it without thorough verification, exactly like Bell himself described in that interview:

Bell:Then in 1932 [mathematician] John von Neumann gave a “rigorous” mathematical proof stating that you couldn’t find a nonstatistical theory that would give the same predictions as quantum
mechanics. That von Neumann proof in itself is one that must someday be the subject of a Ph.D. thesis for a history student. Its reception was quite remarkable. The literature is full of respectable
references to “the brilliant proof of von Neumann;” but I do not believe it could have been read at that time by more than two or three people.
Omni: Why is that?
Bell: The physicists didn’t want to be bothered with the idea that maybe quantum theory is only provisional. A horn of plenty had been spilled before them, and every physicist could find something to apply quantum mechanics to. They were pleased to think that this great mathematician had shown it was so. Yet the Von Neumann proof, if you actually come to grips with it, falls apart in your hands! There is nothing to it. It’s not just flawed, it’s silly. If you look at the assumptions it made, it does not hold up for a moment. It’s the work of a mathematician, and he makes assumptions that have a mathematical symmetry to them. When you translate them into terms of physical disposition, they’re nonsense. You may quote me on that: the proof of von Neumann is not merely false but foolish.

Bell's error is hidden in plain sight in his very first paper on this subject, for anyone who can read to see.

Therefore there seems not much hope for others finding local realistic explanations.

The is no polite response that is fitting, so I'll leave this one as is.

[Schmelzer]

The is no polite response that is fitting, so I'll leave this one as is.

I think similarly about your response.