>Anyway, from what I understand, Andrei and you are debating different settings:

Andrei is referring to two (today) space-like separated regions, which according to the deterministic evolution of classical EM are correlated, since they inevitably share a past light cone (if not later, than at least starting with Big Bang). Correct IMHO.

No, Georg, not correct at all: you are wrong.

The key error that you make is:

>which according to the deterministic evolution of classical EM are correlated, since they inevitably share a past light cone

That is false.

In classical EM, lots of stuff inside your past light cone has **no effect on you at all in the present**.

Indeed, the only thing you can “see” at all via EM fields is what happens precisely **on** your past light cone: anything **inside** your past light cone but not on it cannot be “seen” at all.

This is supposed to be obvious to anyone who passed undergrad physics. In fact, I could remove the “scare quotes” around “see” and it would still be true. With your actual visual system — your eyes! — you can only see things **on** your past light cone, but nothing **inside** the light cone that is not on it.

This is just another way of saying that light moves “at the speed of light.”

Most of the “surface” of observer B’s light cone is not part of the “surface” of observer A’s light cone. So, most of the past events that observer B can “see” right now cannot be “seen” by observer A right now. Most of the surface of B’s light cone that has an EM effect on B at present has **no effect on A at present at all.** No “correlation,” nada.

I know that you will be quite sure that I am not saying what I seem to be saying. Surely I am not **really** saying that **everything** inside (but not on the surface) of A’s light cone has absolutely no EM effect **at all** on A right now!

But, yes, I am saying that because it is obviously true once you realize that EM effects travel at (and only at) the speed of light.

Really: get a piece of paper, draw your past light cone, put a point down for an event inside but not on the past light cone, and then try to draw a line from that event to you at the apex of the cone which represents the EM effect — such a line must be light-like, of course.

I think if you actually try to do this, the “light bulb will go on,” and you will see why what I am saying is not only true but obviously true.

I know that you and most STEM people **think** they were taught that anything inside the past light cone does in fact affect your present. But you misunderstood: that is not how it works.

By the way, there are formulations of EM (e.g.,using the Feynman-Heaviside formulae) where this fact is obviously built into the math via a Dirac delta function restricted to the surface of the past light cone. But it is true regardless of which formulation you use, and this is supposed to be obvious when you understand what the “**light** cone” actually is.

I think part of the problem here is that the phrase “light cone” can be ambiguous in English. In technical math language, “light cone” refers only to the “surface” (technically “hyper-surface” since we are in 3+1 dimensions) of the light cone, but people often use it also to refer to the interior “volume” (technically, “hyper-volume”) inside the light cone.

And, thus people confuse themselves. Badly.

Funny how hard it is for people to overcome the erroneous conceptions they picked up from their initial physics classes!

Anyway, there is no deep subtlety here: what you and Andrei believe is unquestionably false. It is one of those common misconceptions that physics students pick up such as that an object released from circular motion continues on a curved path.

It seems almost impossible to correct this sort of misconception: as carefully as I have explained this here, I bet you yourself still do not believe that you are mistaken on this, do you? And I am quite sure Andrei will *never* believe it.

Dave

P.S. Apologies to everyone for failing to close an HTML tag and unintentionally bolding half of my previous comment — hopefully I’ll do better this time.

]]>Thanks for the explanation. I am unable to comment on EE education styles, and I am not even sure if there is a US vs European (i.e. mine) way. I would expect that EEs get a more technical introduction to the subject than physicists, and this may blur some of the founding principles for us EEs.

Anyway, from what I understand, Andrei and you are debating different settings:

Andrei is referring to two (today) space-like separated regions, which according to the deterministic evolution of classical EM are correlated, since they inevitably share a past light cone (if not later, than at least starting with Big Bang). Correct IMHO.

You are stating, that you can (today) change one of these regions (B) arbitrarily without immediately affecting the other (A). Also correct.

The apparent contradiction is resolved by recognizing that “your”change of region B cannot come about without changing conditions all the way back to Big Bang – again according to classical, deterministic EM – but such that region A remains “unchanged” and region B takes on the “new” state.

But this is a counterfactual situation, by positing different initial conditions than in Andrei’s case and therefore does not remove the correlation between regions A and B.

It’s just a different correlation than in Andrei’s case.

However, I agree that “superdeterminism” is a bit over the top. There is determinism and there is causality. “Superdeterminism” and “supercausality” are unscientific terms.

The hypothesis that non-locality is the result of “superdeterminism” is correct if the paper describes the mathematics of the field structure that is responsible for the “superdeterminism”. I have scanned the paper very fast but I couldn’t recognize the conceptual framework. Nevertheless, I am glad that the authors have published their paper (and I agree with the idea that “superdeterminism” and non-locality are identical at a fundamental level).

With kind regards, Sydney

]]>>Therefore I was asking for a pointer to that theorem …

I did more than that: I proved the theorem. And, if you have forgotten the background material, I told you where to brush up on that.

By the way, unless you underwent a much more rigorous introduction to Maxwell’s equations than any of the electrical engineers I have known who were educated in the US (and I have worked with a very large number of such guys), you were not exposed to the background material I described.

The problem with explaining the theorem is that most STEM people take it for granted: **of course** you can freely specify initial conditions at different points of space and change them in one region without having to change them everywhere! It hardly bears mentioning. Everyone — except our friend Andrei — just takes this for granted. So, yes, you will have trouble finding this theorem spelled out explicitly in textbooks, simply because the textbook author assumes that any student has enough brains to see that it is obvious.

But, since Andrei does not, I spelled the theorem out explicitly.

And, if my explanation is not clear to you, you really do not recall much about Macwell’s equations: again, at least in the States, EEs learn very little about all this.

And, again, the point is so obvious that it should not require an explicit proof: I merely provided the proof for those who do not see that it is obvious. But the proof does require background in diff equs and Maxwell’s equations beyond the education of many EEs.

Dave

EDIT [Mateus]: Fixed your HTML tag.

]]>I would not mind some mathematics, I am an electrical engineer and familiar with Maxwell’s equations (or was so, some years back;-) Therefore I was asking for a pointer to that theorem …

Georg ]]>

> The region B past light cone then inevitably overlaps the region A past light cone at some time, and therefore also A will change.

> Can you point me to that theorem?

Georg: the theorem is there in what I wrote.

I’m afraid that you may not understand the underlying math and physics that I assume, and I do not know how to explain all that here in a comment thread: indeed, I do not know how to explain *all* of that in less than a few hundred pages!

If you really are interested, get a copy of J. David Jackson’s *Classical Electrodynamics* and master it all the way through, with special concentration on the sections concerning time-varying fields, Maxwell’s equations, and time reversal (this is specifically Chapter 6 in the second edition, but chapters are, I believe, relabeled in later editions).

I’ll try to give you hints as to what you need to understand. The basic points are:

First, the E and B fields and charges and the velocity of charges (and hence the currents) **at one point in time** (and everywhere in space) can be specified to be **anything at all** (provided they are consistent with the divergence equations) as the “initial conditions.”

Second, once you have done that, then Maxwell’s equations and the Lorentz force law **uniquely** determine the future **or past** values of the E and B fields and charges and currents.

A reasonable person would say, “Wait, what about non-electromagnetic forces on the charges??” but Andrei in his presentation of his views elsewhere has said he wants to rule those out, so I have followed his desire.

How do we know that just specifying E and B and charge locations and velocities at one point in time (and throughout space) suffice to determine future **and past** values of all of these things? It follows from basic facts about differential equations and specifically the fact that Maxwell’s equations are first order in the time derivatives of the E and B fields.

What about your and Andrei’s concern about the light-cones?

The differential equations control everything. The differential equations say that I can alter values in one region of space **and not another** in the present and then run time backwards and produce earlier conditions that will produce **exactly** those specified results in the present.

Light-cone considerations are relevant to looking to see what you might have to check to see what **might**influence your state in the present. It does not guarantee that **everything** in your past light-cone **does** influence your present state, and it is easy to come up with counter-examples: e.g., imagine a pulse of light that cuts through your past light-cone but happens not to hit **you** in the present but rather somewhere else in the present.

How do I know that you can run Maxwell’s equations and the Lorentz force law backwards in time? Well, that is just obvious mathematically to anyone who understands differential equations. Formally, there is a time-reversal invariance (see Table 6.1 in Jackson’s second edition): the one possible surprise is that you have to replace B by -B (basically because the B field is a so-called “axial vector”).

Again, what I have presented against Andrei’s views is not just a hand-waving, suggestive argument but rather a mathematical proof. However, an ordinary grade-school child cannot understand a completely valid mathematical proofs involving calculus, simply because he does not know calculus.

Similarly, to understand my proof, you need to understand physics and math at an advanced undergrad physics major’s level.

I know this violates the Web’s “no background knowledge required / everything can be explained in 500 words” ethos.

But, alas, math and physics are not consistent with that ethos.

Dave

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