The Universe Is Connected By Birkeland Currents

[Higgsy]

I think this is a extremely timely new video on this topic which delves into all the various questions/concerns (and a few more) that we've discussed in this thread. It talks about Scott's choice to not include boundary conditions, and the reasons for and limitations of that approach.

The author of the video does not understand the need to set appropriate boundary conditions in order to arrive at a unique and physical form of the solution for the problem under consideration. He talks about boundary conditions as though they should be imposed on the already determined form (in this case the Bessel function form of the axial and azimuthal components of B and current density with radial distance) in order to limit the non-zero extent of the variables beyond a finite radial distance. This is not how boundary conditions are properly used in the solution of physical problems described by partial differential equations; they should be used in setting up the problem so that the form of the solution is physical and unique. The very form of the paper's solution, J_0(αr) and J_1(αr), which is unphysical, is a consequence of improper boundary conditions.

[Michael Mozina]

I think this is a extremely timely new video on this topic which delves into all the various questions/concerns (and a few more) that we've discussed in this thread. It talks about Scott's choice to not include boundary conditions, and the reasons for and limitations of that approach.

The author of the video does not understand the need to set appropriate boundary conditions in order to arrive at a unique and physical form of the solution for the problem under consideration. He talks about boundary conditions as though they should be imposed on the already determined form (in this case the Bessel function form of the axial and azimuthal components of B and current density with radial distance) in order to limit the non-zero extent of the variables beyond a finite radial distance. This is not how boundary conditions are properly used in the solution of physical problems described by partial differential equations; they should be used in setting up the problem so that the form of the solution is physical and unique. The very form of the paper's solution, J_0(αr) and J_1(αr), which is unphysical, is a consequence of improper boundary conditions.

I still believe that you're still missing the key point with respect to boundary conditions. The azimuthal and axial magnetic field variations affect the different shells in different ways at different r values. It's important to have a large enough r value to allow for all the different variations to occur on different shells. Sure, once it's gets repetitive it might make sense to impose limits on r, but until all the variations play out, artificially restricting r only artificially limits your model.

You're also ignoring the fact that his Bessel model has support in the lab from Peratt's experiments. The actual experiments show the different shells working/moving differently at different r values.

Sure the model warrants improvement, including describing the electron flow, rather than just ion flow, logical limits on r, describing the affect of Marklund current, etc. More work on a Bessel model is certainly warranted, but the laboratory results and validation cannot simply be ignored only because the current model lacks some level of additional sophistication. It's still a *very* good start and it still enjoys laboratory support.

Compare and contrast that lab support with the complete lack of laboratory support for something like 'dark matter' or 'dark energy' where the math might be plenty sophisticated, yet its still totally useless at predicting anything observed in the lab.

[Higgsy]

The author of the video does not understand the need to set appropriate boundary conditions in order to arrive at a unique and physical form of the solution for the problem under consideration. He talks about boundary conditions as though they should be imposed on the already determined form (in this case the Bessel function form of the axial and azimuthal components of B and current density with radial distance) in order to limit the non-zero extent of the variables beyond a finite radial distance. This is not how boundary conditions are properly used in the solution of physical problems described by partial differential equations; they should be used in setting up the problem so that the form of the solution is physical and unique. The very form of the paper's solution, J_0(αr) and J_1(αr), which is unphysical, is a consequence of improper boundary conditions.

I still believe that you're still missing the key point with respect to boundary conditions. The azimuthal and axial magnetic field variations affect the different shells in different ways at different r values. It's important to have a large enough r value to allow for all the different variations to occur on different shells. Sure, once it's gets repetitive it might make sense to impose limits on r, but until all the variations play out, artificially restricting r only artificially limits your model.

No - you are missing the point about the need for proper boundary conditions when solving partial differential equations. The point is that if proper boundary conditions are applied in order to get a physical and unique solution, no "shells" need appear in the solution. The shells (cylindrical regions of positive and negative values for the axial and azimuthal magnetic field and for the current density) are an artefact of improper boundary conditions.

You're also ignoring the fact that his Bessel model has support in the lab from Peratt's experiments. The actual experiments show the different shells working/moving differently at different r values.

Do they? Do you mean the photo? There are certainly concentric features in that photo, but how can you tell that there are "different shells working/moving differently at different r values"?

[Michael Mozina]

No - you are missing the point about the need for proper boundary conditions when solving partial differential equations.

Define the term "proper" in this specific context.

The point is that if proper boundary conditions are applied in order to get a physical and unique solution, no "shells" need appear in the solution.

Nobody disputes that fact that by selecting an artificially small r value, you might only end up with a single shell/tube.

The shells (cylindrical regions of positive and negative values for the axial and azimuthal magnetic field and for the current density) are an artefact of improper boundary conditions.

Care to demonstrate that point mathematically and explain (clearly) why your choice of boundaries wasn't simply an artificial limitation in the model which ignores the other tubes/shells that might actually exist?

]Do they? Do you mean the photo? There are certainly concentric features in that photo, but how can you tell that there are "different shells working/moving differently at different r values"?

I can only tell from the photo that they're are different shells at different r values, each with their own unique sizes, shapes and features. I can only "presume" movement patterns based on the models and observations of the movement patterns around the poles of planets. I'd need more than a single image to determine movement patterns, but even a single images show different particle arrangements in different shells which are consistent with a Bessel function model.

[Higgsy]

No - you are missing the point about the need for proper boundary conditions when solving partial differential equations.

Define the term "proper" in this specific context.

As more than one person has said before, the solution should be unique and physical. Scott's solution is unphysical, and it is, moreover, not unique in that the simplification of eqn 12 by eqns 13 and 14 (setting j proportional to B everywhere) is unwarranted. Moreover, Scott himself admits that it is unwarranted. I can show how arbitrary functions appear in the solution of partial differential equations if you like.

The point is that if proper boundary conditions are applied in order to get a physical and unique solution, no "shells" need appear in the solution.

Nobody disputes that fact that by selecting an artificially small r value, you might only end up with a single shell/tube.

No - you miss the point. Boundary conditions do not arbitrarily truncate a solution to a partial differential equation. Rather they select the form of a solution from an infinite number of possible solutions. The point is that if proper boundary conditions are applied, the form of Scott's solution, the Bessel function illustrated in Fig 2 need not appear. The author of the video made the same mistake that you are making. A valid solution has to be of a form whereby the current density integrated over the area converges to a finite value as r goes to infinity.

The shells (cylindrical regions of positive and negative values for the axial and azimuthal magnetic field and for the current density) are an artefact of improper boundary conditions.

Care to demonstrate that point mathematically and explain (clearly) why your choice of boundaries wasn't simply an artificial limitation in the model which ignores the other tubes/shells that might actually exist?

My suggested boundary conditions are B=0 and ∂B/∂r = 0 for some finite R = 0<r<∞, where R can be as big as you like.

I also note that the parameter α in Scott's solution is a freely chosen scalar that determines the j:B ratio and the scale factor of the Bessel function j and B direction reversals without being at all predictive or being linked in any way to a physical property. α can range from infinitessimally small to infinitessimally large. For the same B_z(0), j_z(0) can be anything from infinitessimally small to infinitessimally large, and this is reflected throughout the field. Morever, Scott's condition that α can be infinitessimally small but not zero is not justified.

Do they? Do you mean the photo? There are certainly concentric features in that photo, but how can you tell that there are "different shells working/moving differently at different r values"?

I can only tell from the photo that they're are different shells at different r values, each with their own unique sizes, shapes and features. I can only "presume" movement patterns based on the models and observations of the movement patterns around the poles of planets. I'd need more than a single image to determine movement patterns, but even a single images show different particle arrangements in different shells which are consistent with a Bessel function model.

So you can't really tell. Scott's model is steady state (all partial derivatives with time = 0), magnetic potential energy stored minmised, zero Lorentz force, partial derivatives with respect to azimuth and z = 0, j proportional to B everywhere. Both figures 7 and 8, just by virtue of the fact that they terminated by a physical boundary in z, do not meet the criteria. Morever fig 8 is not steady state. You can't tell from these photos that they have anything to do with Scott's model.

[Michael Mozina]

No - you are missing the point about the need for proper boundary conditions when solving partial differential equations.

Define the term "proper" in this specific context.

As more than one person has said before, the solution should be unique and physical.

The whole point of his model is that there isn't just one tube with one unique set of physical attributes. There are multiple layers with different attributes at different radii.

Scott's solution is unphysical,

How can a model related to the movement patters of charged particles be "unphysical"? Dark matter isn't "physical" at all! Can you even name a physical source of "dark energy"? Inflation? How the heck is 'space expansion" a physical process? What "physically" is expanding in 'space expansion"?

and it is, moreover, not unique in that the simplification of eqn 12 by eqns 13 and 14 (setting j proportional to B everywhere) is unwarranted. Moreover, Scott himself admits that it is unwarranted. I can show how arbitrary functions appear in the solution of partial differential equations if you like.

Where did Scott "admit" to anything of the sort? We're not talking about *other* functions, just this one.

The point is that if proper boundary conditions are applied in order to get a physical and unique solution, no "shells" need appear in the solution.

The shells (cylindrical regions of positive and negative values for the axial and azimuthal magnetic field and for the current density) are an artefact of improper boundary conditions.

Demonstrate that claim. You keep asserting opinion as "fact".

My suggested boundary conditions are B=0 and ∂B/∂r = 0 for some finite R = 0<r<∞, where R can be as big as you like.

Woah. The moment that you preclude any changes to B with respect to r, (dB/dr=0) you preclude any possibility of changes in the B field, which precludes the whole concept that Scott is trying to demonstrate in the first place! More importantly, if current is flowing (and that's a given in his model), B cannot be 0. Come on. That's a purely *arbitrary* set of limitations that you've imposed and it's a completely different model entirely. You're comparing apples to oranges.

So you can't really tell. Scott's model is steady state (all partial derivatives with time = 0), magnetic potential energy stored minmised, zero Lorentz force, partial derivatives with respect to azimuth and z = 0, j proportional to B everywhere. Both figures 7 and 8, just by virtue of the fact that they terminated by a physical boundary in z, do not meet the criteria. Morever fig 8 is not steady state. You can't tell from these photos that they have anything to do with Scott's model.

There's an easy way to find out. Stop wasting money on DM experiments for a couple of years and put Scott's model to the test in the lab. You guys waste all of our tax dollars on stupid metaphysical nonsense which cannot even produce a valid falsification of the model in the first place. At least in Scott's case you have the possibility of verifying the model, or falsifying it outright.

[BeAChooser]

There's an easy way to find out. Stop wasting money on DM experiments for a couple of years and put Scott's model to the test in the lab. You guys waste all of our tax dollars on stupid metaphysical nonsense which cannot even produce a valid falsification of the model in the first place. At least in Scott's case you have the possibility of verifying the model, or falsifying it outright.

Yep. Higgsy fears that Birkeland Currents might actually be an explanation for many observation he can't explain except with unverified and unverifiable gnomes. Like the helically wound filaments I keep asking him about which he keeps ignoring.

[Zyxzevn]

Yep. Higgsy fears that Birkeland Currents might actually be an explanation for many observation he can't explain except with unverified and unverifiable gnomes. Like the helically wound filaments I keep asking him about which he keeps ignoring.

My experience with mainstream trolls is that they do not care.
They are too fixed into the box of belief, to even consider that something could be
wrong in the way they think.
They are not discussing about what is correct, but only want
to find easy attacks on people that think differently.

You can easily detect when they do not care, when like to use logical fallacies.
Sometimes mixed with actual reason.
Like adding a statement of how stupid you are, or how wrong you are.

It is hard for people to consider different ideas,
if they are locked into a certain way of thinking.

This generally happens to all people locked into theories, but not many decide
to use their theoretical background to troll other people about it.
A majority like to convert other people to their theories, though.
And some of them can be quite pushy.

Personally I like to explore different theories and I have a subreddit
specialized on changing your paradigm.
I do not accept everything and do not waste time on things that I think are completely wrong.
I also think that: if you are wasting your time, you are wasting your life.

[Michael Mozina]

Yep. Higgsy fears that Birkeland Currents might actually be an explanation for many observation he can't explain except with unverified and unverifiable gnomes. Like the helically wound filaments I keep asking him about which he keeps ignoring.

It's not just Higgsy, it's the entire astronomy community that fears empirical physics, and opposes the testing of empirical physical models. They're ultimately afraid that they might actually demonstrate that EU/PC theory is correct, and in doing so, destroy every existing astronomy funding channel that's currently in existence.

Just imagine if the government cut off dark matter and dark energy research tomorrow? It would throw the whole industry into complete chaos.

How much would it actually cost to fully fund SAFIRE, reconstruct Birkeland's full range of experiments, and/or conduct a series of experiments on Scott's BC model, and Birkeland current models in general? 30 million? 50 million? 100 million? 250 million? The mainstream has blown *billions* of dollars supposedly "testing" dark matter to date at LHC, LUX, PandaX., Xenon-1T, etc, etc, etc, and they have absolutely *nothing* to show for any of it, except perhaps a bunch of "constraints" where exotic matter cannot exist.

The really sad part of all this financial waste is that for mere *pennies on the dollar*, we could be doing *actual* physics and learning useful things, instead of throwing good money after bad, chasing metaphysical butterflies with metaphysical nets.

[Higgsy]

As more than one person has said before, the solution should be unique and physical.

The whole point of his model is that there isn't just one tube with one unique set of physical attributes. There are multiple layers with different attributes at different radii.

I understand that. I know exactly what his model predicts. Nevertheless, solutions should be unique and physical.

Scott's solution is unphysical,

How can a model related to the movement patters of charged particles be "unphysical"?

By predicting infinite current.

and it is, moreover, not unique in that the simplification of eqn 12 by eqns 13 and 14 (setting j proportional to B everywhere) is unwarranted. Moreover, Scott himself admits that it is unwarranted. I can show how arbitrary functions appear in the solution of partial differential equations if you like.

Where did Scott "admit" to anything of the sort? We're not talking about *other* functions, just this one.

Scott, p170, column 1: "...it is important to note that accepting (14) as a substitute for (12) assumes apriori that, for any non-zero α, a non-zero valued B at any point requires the existence of a current density j not equal to 0 at that same point. This is in general, an unwarranted presumption." Then he goes on to make exactly that presumption in setting up (26). (14), the unwarranted assumption, is a fundamental condition to get (26) (the differential equation of the form x^2(d^y/dx^2)+x(dy/dx)+(x^2)y=0 with a Bessel function as its solution; and then a fundamental condition to get (28) (which is that B_z follows a Bessel function of the first kind and zero order) and then to get (30) (that B_θ follows a Bessel function of the first kind and first order). The entire edifice depends on the unwarranted assumption. Without the unwarranted assumption, (14) is not necessarily true as being equivalent to (12); and (26), and everything which follows, is not a unique solution, because conditions other than (14) satisfy (12).

The point is that if proper boundary conditions are applied in order to get a physical and unique solution, no "shells" need appear in the solution.

The shells (cylindrical regions of positive and negative values for the axial and azimuthal magnetic field and for the current density) are an artefact of improper boundary conditions.

Demonstrate that claim. You keep asserting opinion as "fact".

See above. Also see Alfven, "Cosmic Plasma" pages 93 - 98 (a reference given to you earlier by Paladin). Alfven's (6) with a force free current is the same as Scott's (12), but the solution he gets has no reversing shells of magnetic field and current density.

My suggested boundary conditions are B=0 and ∂B/∂r = 0 for some finite R = 0<r<∞, where R can be as big as you like.

Woah. The moment that you preclude any changes to B with respect to r, (dB/dr=0) you preclude any possibility of changes in the B field, which precludes the whole concept that Scott is trying to demonstrate in the first place! More importantly, if current is flowing (and that's a given in his model), B cannot be 0. Come on. That's a purely *arbitrary* set of limitations that you've imposed and it's a completely different model entirely. You're comparing apples to oranges.

Nonsense. These are simply the Dirichlet and Neumann conditions for solving the Cauchy problem. These conditions only apply on the boundary which can be as far away as you like. You can set other boundary conditions which are appropriate for whatever problem you are trying to solve. For a steady state solution these are appropriate, but any boundary condition that converges total current will do.

[Higgsy]

Yep. Higgsy fears that Birkeland Currents might actually be an explanation for many observation he can't explain except with unverified and unverifiable gnomes. Like the helically wound filaments I keep asking him about which he keeps ignoring.

My experience with mainstream trolls is that they do not care.

So it's ok to call me a troll, is it? How does that sit with the forum rules?

[Higgsy]

Higgsy fears that Birkeland Currents might actually be an explanation for many observation he can't explain except with unverified and unverifiable gnomes. Like the helically wound filaments I keep asking him about which he keeps ignoring.

I have told you many times that I accept the existence of Birkeland currents, and braided filaments in the cosmic context, but that I do not do physics by looking at pretty pictures and making up stories. Several of the pretty pictures you presented have nothing to do with braided filaments produced by Birkeland currents. I explained why I thought that. You might disagree, but there is no point in asking me the same question over and over again. You're not going to get a different answer.

[Michael Mozina]

Higgsy fears that Birkeland Currents might actually be an explanation for many observation he can't explain except with unverified and unverifiable gnomes. Like the helically wound filaments I keep asking him about which he keeps ignoring.

I have told you many times that I accept the existence of Birkeland currents, and braided filaments in the cosmic context, but that I do not do physics by looking at pretty pictures and making up stories.

Oh *please*! You're handing us metaphysicalstories about exotic forms of invisible matter and energy, and "space expansion" based on nothing but pretty pictures.

Unlike all of your claims however, Scott's BC model *can and should* be put to the test in real experiments here on Earth. We've wasted *billions* of dollars are your dark matter snipe hunts with nothing to show for it, so why would you begrudge the use of tax dollars to be spent on testing Scott's model?

[Michael Mozina]

I understand that. I know exactly what his model predicts. Nevertheless, solutions should be unique and physical.

I think that you "believe" that you "know" what his model predicts, but your statements suggest otherwise.

By predicting infinite current.

Case in point. His model doesn't "predict" infinite current, it only predicts *consistent/persistent* current. Your understanding of his model is simply incorrect. The only way his model could produce "infinite current" is if the entire universe happens to be infinite and all of it is embedded into a single filament. He's not suggesting anything of the sort.

Scott, p170, column 1: "...it is important to note that accepting (14) as a substitute for (12) assumes apriori that, for any non-zero α, a non-zero valued B at any point requires the existence of a current density j not equal to 0 at that same point. This is in general, an unwarranted presumption." Then he goes on to make exactly that presumption in setting up (26).

Oh for goodness sake. He's noting that the *general* mathematical solution allows for a "zero" current, but he's then intentionally *restricting* his model to a simplified scenario where current exists and it's *constant over time*. This is simply a logical assumption in a *current carrying* scenario and he's only interested in movement of plasma in a current carrying scenario, otherwise there's no current to discuss, and no need of a Birkeland current in the first place!

All models are ultimately *simplified* and restricted to specific conditions where they are applicable. You're complaint is therefore irrelevant.

See above. Also see Alfven, "Cosmic Plasma" pages 93 - 98 (a reference given to you earlier by Paladin). Alfven's (6) with a force free current is the same as Scott's (12), but the solution he gets has no reversing shells of magnetic field and current density.

Alfven *restricts* r whereas Scott does not. It's entirely possible that both solutions are correct. In other words, if we limit the model to an r value that only includes the *first* tube, we get just *one* tube. If we don't restrict r, we might get *multiple* tubes. Both models can be correct in their own restricted sense.

We're going round and round over the same issue. You're complaining because Scott's model is restricted to current carrying environments, and it imposes no arbitrary limits on r values specifically and intentionally *so that it can explore what occurs in plasma at different r values*. Again, a restricted r value model can be correct within the limits of that r value, but a model based on larger (or unlimited) r values can produce different movement patterns at different r values. You can't compared the two directly and claim that only one of them is right. They can *both* be right in their own context.

[Higgsy]

I understand that. I know exactly what his model predicts. Nevertheless, solutions should be unique and physical.

I think that you "believe" that you "know" what his model predicts, but your statements suggest otherwise.

I know exactly what his model predicts. I have spent my adolescent and adult life understanding the physical implications of mathematical model predictions. Whereas you didn't seem even to understand what a Bessel function is at the start of this thread (you kept calling the B_z and B_θ functions sinusoidal).

By predicting infinite current.

Case in point. His model doesn't "predict" infinite current, it only predicts *consistent/persistent* current. Your understanding of his model is simply incorrect. The only way his model could produce "infinite current" is if the entire universe happens to be infinite and all of it is embedded into a single filament. He's not suggesting anything of the sort.

No this is not correct. His specific model prediction for currrent density integrated over a circular cross-section giving total current does not converge. That matters to a physicist - to you, perhaps not so much.

Scott, p170, column 1: "...it is important to note that accepting (14) as a substitute for (12) assumes apriori that, for any non-zero α, a non-zero valued B at any point requires the existence of a current density j not equal to 0 at that same point. This is in general, an unwarranted presumption." Then he goes on to make exactly that presumption in setting up (26).

Oh for goodness sake. He's noting that the *general* mathematical solution allows for a "zero" current, but he's then intentionally *restricting* his model to a simplified scenario where current exists and it's *constant over time*. This is simply a logical assumption in a *current carrying* scenario and he's only interested in movement of plasma in a current carrying scenario, otherwise there's no current to discuss, and no need of a Birkeland current in the first place!

It's not just a question of zero current. The steady state field aligned scenario occurs when the pressure gradient jxB is zero. Everyone agrees that that is the case, including Alfven in Cosmic Plasma. That results in (∇ x B) x B = 0, which is what Scott is trying to solve. Note that 12) is satisfied for any j parallel to B. Now Scott sets the condition that ∇ x B = αB where α is a freely chosen scalar which leads to μj = αB. This doesn't only exclude j = 0 for non-zero B. It sets a condition of current density proportional to magnetic field at every point, a constraint that is not required by field aligned currents and which is not warranted by any physical consideration. Note that Alfven merely says j_θ/j_z = B_θ/B_z which we recognise as a necessary condition for field aligned currents.

When you say "He's noting that the *general* mathematical solution allows for a "zero" current, but he's then intentionally *restricting* his model to a simplified scenario where current exists and it's *constant over time", you are misunderstanding my critique (and that of Scott himself when he calls his own assumptions "unwarranted"). No one is saying that there is no current at all - that would be, as you say, not very interesting (we get that if α=0 for example). But we need to consider j and B as vector fields; in effect we are talking about j(r,θ,z) and B(r,θ,z). So when we say that Scott's conclusion excludes j=0 for non-zero B, we are referring to a point in the field - that could but might not apply elsewhere in the field. Scott's constraint precludes the current density from falling to zero at any point in the field where B is non-zero, even though we know of situations where non-zero B coincides with zero j at some points in a field. But more worrying is the fact that Scott constrains |j| to be proportional to |B| everywhere in the field - this is not at all a constraint required by the physical situation, which merely requires one of j = 0, B = 0 or j and B to be parallel at every point. Finally, I don't know why you introduce "constant over time". Everyone agrees that it's a steady state model so all derivatives with respect to time are zero.

All models are ultimately *simplified* and restricted to specific conditions where they are applicable. You're complaint is therefore irrelevant.

But Scott's simplification isn't warranted by any physical consideration. Why should |j| be proportional to |B| everywhere?

See above. Also see Alfven, "Cosmic Plasma" pages 93 - 98 (a reference given to you earlier by Paladin). Alfven's (6) with a force free current is the same as Scott's (12), but the solution he gets has no reversing shells of magnetic field and current density.

Alfven *restricts* r whereas Scott does not. It's entirely possible that both solutions are correct. In other words, if we limit the model to an r value that only includes the *first* tube, we get just *one* tube. If we don't restrict r, we might get *multiple* tubes. Both models can be correct in their own restricted sense.

Does Alfven "restrict" r? Where does he do that?