# Reflections in Einstein’s bubble

There’s something peculiar in this earlier post where I embroidered on Einstein’s gambit in his epic battle with Bohr.  Here, I’ll self-plagiarize it for you…

Consider some nebula a million light-years away.  A million years ago an electron wobbled in the nebular cloud, generating a spherical electromagnetic wave that expanded at light-speed throughout the Universe.

Last night you got a glimpse of the nebula when that lightwave encountered a retinal cell in your eye.  Instantly, all of the wave’s energy, acting as a photon, energized a single electron in your retina.  That particular lightwave ceased to be active elsewhere in your eye or anywhere else on that million-light-year spherical shell.

Suppose that photon was yellow light, smack in the middle of the optical spectrum.  Its wavelength, about 580nm, says that the single far-away electron gave its spherical wave about 2.1eV (3.4×10-19 joules) of energy.  By the time it hit your eye that energy was spread over an area of a trillion square lightyears.  Your retinal cell’s cross-section is about 3 square micrometers so the cell can intercept only a teeny fraction of the wavefront.  Multiplying the wave’s energy by that fraction, I calculated that the cell should be able to collect only 10-75 joules.  You’d get that amount of energy from a 100W yellow light bulb that flashed for 10-73 seconds.  Like you’d notice.

But that microminiscule blink isn’t what you saw.  You saw one full photon-worth of yellow light, all 2.1eV of it, with no dilution by expansion.  Water waves sure don’t work that way, thank Heavens, or we’d be tsunami’d several times a day by earthquakes occurring near some ocean somewhere.

Here we have a Feynman diagram, named for the Nobel-winning (1965) physicist who invented it and much else.  The diagram plots out the transaction we just discussed.  Not a conventional x-y plot, it shows Space, Time and particles.  To the left, that far-away electron emits a photon signified by the yellow wiggly line.  The photon has momentum so the electron must recoil away from it.

The photon proceeds on its million-lightyear journey across the diagram.  When it encounters that electron in your eye, the photon is immediately and completely converted to electron energy and momentum.

Here’s the thing.  This megayear Feynman diagram and the numbers behind it are identical to what you’d draw for the same kind of yellow-light electron-photon-electron interaction but across just a one-millimeter gap.

It’s an essential part of the quantum formalism — the amount of energy in a given transition is independent of the mechanical details (what the electrons were doing when the photon was emitted/absorbed, the photon’s route and trip time, which other atoms are in either neighborhood, etc.).  All that matters is the system’s starting and ending states.  (In fact, some complicated but legitimate Feynman diagrams let intermediate particles travel faster than lightspeed if they disappear before the process completes.  Hint.)

Because they don’t share a common history our nebular and retinal electrons are not entangled by the usual definition.  Nonetheless, like entanglement this transaction has Action-At-A-Distance stickers all over it.  First, and this was Einstein’s objection, the entire wave function disappears from everywhere in the Universe the instant its energy is delivered to a specific location.  Second, the Feynman calculation describes a time-independent, distance-independent connection between two permanently isolated particles.  Kinda romantic, maybe, but it’d be a boring movie plot.

As Einstein maintained, quantum mechanics is inherently non-local.  In QM change at one location is instantaneously reflected in change elsewhere as if two remote thingies are parts of one thingy whose left hand always knows what its right hand is doing.

Bohr didn’t care but Einstein did because relativity theory is based on geometry which is all about location. In relativity, change here can influence what happens there only by way of light or gravitational waves that travel at lightspeed.

In his book Spooky Action At A Distance, George Musser describes several non-quantum examples of non-locality.  In each case, there’s no signal transmission but somehow there’s a remote status change anyway.  We don’t (yet) know a good mechanism for making that happen.

It all suggests two speed limits, one for light and matter and the other for Einstein’s “deeper reality” beneath quantum mechanics.

~~ Rich Olcott

# Is there stuff behind the stats?

It would have been awesome to watch Dragon Princes in battle (from a safe hiding place), but I’d almost rather have witnessed “The Tussles in Brussels,” the two most prominent confrontations between Albert Einstein and Niels Bohr.

The Tussles would be the Fifth (1927) and Seventh (1933) Solvay Conferences.  Each conference was to center on a particular Quantum Mechanics application (“Electrons and Photons” and “The Atomic Nucleus,” respectively).  However, the Einstein-Bohr discussions went right to the fundamentals — exactly what does a QM calculation tell us?

Einstein’s strength was in his physical intuition.  By all accounts he was a good mathematician but not a great one.  However, he was very good indeed at identifying important problems and guiding excellent mathematicians as he and they attacked those problems together.

Like Newton, Einstein was a particle guy.  He based his famous thought experiments on what his intuition told him about how particles would behave in a given situation.  That intuition and that orientation led him to paradoxes such as entanglement, the EPR Paradox, and the instantaneously collapsing spherical lightwave we discussed earlier.  Einstein was convinced that the particles QM workers think about (photons, electrons, etc.) must in fact be manifestations of some deeper, more fine-grained reality.

Bohr was six years younger than Einstein.  Both Bohr and Einstein had attained Directorship of an Institute at age 35, but Bohr’s has his name on it.  He started out as a particle guy — his first splash was a trio of papers that treated the hydrogen atom like a one-planet solar system.  But that model ran into serious difficulties for many-electron atoms so Bohr switched his allegiance from particles to Schrödinger’s wave theory.  Solve a Schrödinger equation and you can calculate statistics like average value and estimated spread around the average for a given property (position, momentum, spin, etc).

Here’s where Ludwig Wittgenstein may have come into the picture.  Wittgenstein is famous for his telegraphically opaque writing style and for the fact that he spent much of his later life disagreeing with his earlier writings.  His 1921 book, Tractatus Logico-Philosophicus (in German despite the Latin title) was a primary impetus to the Logical Positivist school of philosophy.  I’m stripping out much detail here, but the book’s long-lasting impact on QM may have come from its Proposition 7: Whereof one cannot speak, thereof one must be silent.

I suspect that Bohr was deeply influenced by the LP movement, which was all the rage in the mid-1920s while he was developing the Copenhagen Interpretation of QM.

An enormous literature, including quite a lot of twaddle, has grown up around the question, “Once you’ve derived the Schrödinger wave function for a given system, how do you interpret what you have?”  Bohr’s Copenhagen Interpretation was that the function can only describe relative probabilities for the results of a measurement.  It might tell you, for instance, that there’s a 50% chance that a particle will show up between here and here but only a 5% chance of finding it beyond there.

Following Logical Positivism all the way to the bank, Bohr denounced as nonsensical or even dangerously misleading any attachment of further meaning to a QM result.  He went so far as to deny the very existence of a particle prior to a measurement that detects it.  That’s serious Proposition 7 there.

I’ve read several accounts of the Solvay Conference debates between Einstein and Bohr.  All of them agree that the conversation was inconclusive but decisive.  Einstein steadfastly maintained that QM could not be a complete description of reality whilst Bohr refused to even consider anything other than inscrutable randomness beneath the statistics.  The audience consensus went to Bohr.

None of the accounts, even the very complete one that I found in George Musser’s book Spooky Action at A Distance, provide a satisfactory explanation for why Bohr’s interpretation dominates today.  Einstein described multiple situations where QM’s logic appeared to contradict itself or firmly established experimental results.  However, at each challenge Bohr deflected the argument from Einstein’s central point to argue a subsidiary issue such as whether Einstein was denying the Heisenberg Uncertainty Principle.

Albert still stood at the end of the bouts, but Niels got the spectators’ decision on points.  Did the ref make the difference?

~~ Rich Olcott