Wednesday, February 22, 2017

Perhaps no-one understands Maxwell's equations

"Microsoft CEO Satya Nadella spoke at a public event in India on Monday ...

"The first time I put on a HoloLens was to see something Cleveland Clinic [a non-profit academic medical center] had built for medical innovation... As an electrical engineer who never understood Maxwell's equations, I thought if I had a HoloLens, I would have been a better electrical engineer. Overall I feel that augmented reality is perhaps the ultimate computer," he said.
From here.

Actually, the article was entitled, "Microsoft CEO says artificial intelligence is the 'ultimate breakthrough'", but I was struck by his confession of ignorance about the foundational theory of classical electromagnetism.

Maxwell's equations

This looks bad, of course. But let's cut the CEO some slack: Maxwell's equations are notoriously unintuitive, as I observed in this post.

You can use the equations, solving them for particular physical configurations. But what picture do they give of the nature of the field(s) themselves?

What are we to make of the fact that a stationary observer of a motionless charged ball sees a static spherical electric field E, while an observer moving past that same ball sees electric and magnetic fields (E' and B')?

The magnetic field is a relativistic effect.

The charge is at rest in frame F, so this observer notes a static electric field. An observer in another frame F′ moves with velocity v relative to F, and notices the charge to move with velocity −v with an altered electric field E due to length contraction and a magnetic field B due to the motion of the charge. (Wikipedia).

That's implicit in Maxwell's equations, but don't tell me it's obvious. For that, you need to write the equations in a manifestly covariant form, but they don't teach you that in undergraduate electrical engineering.


Oh, and he's surely right about augmented reality being the main deliverable from the current state of the art in artificial neural net technologies. The Holy Grail of AGI will be a product of mastering situated social cognition, a post for another day (but see here).

1 comment:

  1. Actually the Divergence based laws for E and B are referring to the sources rho (charge) and 0 for E and B respectively. Thus E comes from charge density and B seems to have no source. So one might ask "where does B come from?".The answer "from Relative motion!".

    The Newtonian Gravitational field is also described by a Divergence:

    Del.g = -4(pi)G(rho) (from Wikipedia!)

    Here the source is the matter density rho.
    The corresponding Curl equation would be:

    Del X g = 0

    Though if Gravitational Torsion existed this might not be correct.

    I see that there is an ambiguity over the definition of AGI in Wikipedia. Perhaps I should write about that another time.


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