De Broglie actually proposed that ALL matter was essentially waves (of what material – he did not conjecture).  The waves all ‘grouped’ together close to a point that we consider to be the material particle.

This is different from Schrodinger’s wave for a particle – which is neither real – nor does it represent the actual particle’s position.

However, both these physicist were correct. De Broglie’s waves can be applied to photons and other massless particles – as their position essentially coincides with the grouping of their ‘waves’

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For electrons and other material particles, this begs the question – what is E in the equation below?

1. Is E equal to the rest energy ?
2. Or is it equal  to the rest energy plus the binding energy (electron in an atom)?
3. Or it is equal to rest energy plus binding energy plus it’s kinetic energy?

Actually, it could be any of the three above. Hence, one must be careful what one means by E=h\nu when applied to electrons and other mass bearing particles.

The Resolution?

The actual E in the equation above is not important. What’s important are the Energy differences. When the electron jumps from an allowed state to another allowed state, it emits photons of energy equal to E. And that is exactly what the E in the   represents for an electron.

The Fundamental disagreement between Relativity and QM

I spent a lot of time studying this paper on the Fundamental Disagreement of Wave Mechanics with Relativity

These kind of paradoxes can be resolved when one keeps in mind that the E above is not really the energy of the material particle, but rather, the energy emitted when the particle changes between states. The paper above is still legit – and highlights a slightly different issue.

Pilot wave Theory DeBroglie

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It was obviously going to be the wave function amplitude. Amplitudes take the place of probabilities, in Quantum Mechanics. This single mathematical fact is responsible for ALL the weirdness that comes about (interference, entanglement…).

Feynman proceeded – if amplitudes are to be added, how about adding ALL the amplitudes for a particle to get from A (emitter) to B (screen)? This seemed like a ridiculously infinite sum, but Feynman proceeded undaunted. And sure enough, several amplitudes canceled themselves out  – leading to the now famous Feynman Integral approach to Quantum Mechanics.

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This means that there should be FEWER waves of long wavelengths (low frequencies).

Hence, most of the energy (as you heat the blackbody) SHOULD go into the shorter wavelengths.

This, in effect, was not observed.

Lower frequencies were found in a HIGHER proportion. And after a frequency cutoff, no higher frequencies were even found!

Planck to the rescue

Planck prosposed that instead of thinking of ‘equipartition of energies’, what if one thought of a special distribution of frequencies. Only frequencies that absorbed a constant ‘quanta’ of energy were allowed.

E  = hf –> Where f is the frequency.

Lower frequencies should actually participate more in the energy absorption process, as only a slight amount of energy is required to be completely absorbed. The higher the frequency, the more energy would be required, making higher frequencies rarer. This is what was observed experimentally as well.

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If indeed, a particle is a PROCESS (one in which several pulses combine to appear at a point and then dissolve away…), then this provides at least a starting point to understand entanglement of two distant particles.

They were never particles in the first place. They were pulses (essentially superposition of several waves), that were ALWAYS entangled, in the way that two threads would tie around each other. Unless explicitly UNWRAPPED, the threads would stay entangled. A simple separation of the two threads, WITHOUT unfolding the entangled portions, would accomplish nothing.

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As per Bohm  (from the book Quanta and Reality)  – An electron is a thing that is always forming and dissolving.

Think of a medium such as a field, and a ‘process’ within that field. Imagine a pulse within this field. It moves inward, coverges at a point and then dissolves away. Imagine a series of such pulses all converging on a single point. These series of pulses will be so close together, that they will appear like a particle.

When you ask how an electron passes through one hole or the other, Bohm’s response was ‘An electron is not the kind of thing that passes through one hole or another. It is something that is always forming and dissolving and in effect, moves through both holes.

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Raw Count leads to probabilities

Instead of talking about PROBABILITIES of a magnetic moment getting through,  let us talk about the NUMBER of magnets (raw count) that get through.

Think of two possible exits for a Stern Gerlach apparatus. Half of ALL incoming will go through EXIT 1 and half of ALL incoming will go through EXIT 2. This leads to PROBABILITY 0.5 of the moment going through any one exit.

Now, that it has gone through a certain exit (say EXIT 1), let us focus on all those coming out of EXIT 1 (and ignore the ones from EXIT 2).

If we now ASK The SAME question again (send ALL these OUTGOING into another INCOMING apparatus) – we get the same answer. 100% pass through EXIT 1.

If we ASK a DIFFERENT QUESTION (rotate the apparatus by say 90 degrees), we get an UNKNOWN answer. The reason is that we are now asking a DIFFERENT QUESTION – and the state for this SECOND question is AS UNCERTAIN as the state for the FIRST question was prior to the FIRST experiment.

EACH VARIABLE is a different question – and just because ONE apparatus has answered ONE question,  it doesn’t mean the other  questions have been asnwered?

SINGLE Stern Gerlach

Consider a SINGLE stern gerlach appartus.

A Spin Entering this apparatus can have any orientation – including a ZERO degree orientation with respect to the axis of the apparatus. The ZERO degree is the ‘pass through’ case – and  the most common orientation possible.

Other orientations are up down – and anywhere in between UP and DOWN.

So – a natural expectation would be for the SPIN to take any of those orientations.

Back to Back (Double) Stern Gerlach Apparatus – Same Orientation

Back to Back (Double) Stern Gerlach Apparatus – Reverse Orientation

The reverse orientation provides the first clue that something isn’t quite normal about the way these experiments work.

If the axis is inverted, the result is also inverted. You may wonder – how did the spin that was pointing up – suddenly – and with 100% accuracy, point DOWN? The simplest answer is that the result responds to the question (the axis being measured).

But wait, it gets weirder still…

Back to Back (Double) Stern Gerlach Apparatus – Angled Orientation – 90 degrees to start with

Back to Back to Back (Triple) Stern Gerlach Apparatus –

Angled Apparatuses  – And John Bell’s Insights into the Predicted Results

When we say that the probability for angled exits is proportional to cosine ( angle between the axes), what does that mean?

That means – ON AVERAGE  (i.e. when you send a WHOLE BUNCH of particles in through successive detectors), the number that will come out with +1 (versus -1) is cosine ( angle).

Individual measurement  ALWAYS reveals +1 or -1. It is never a projection of any sort (like cosine theta). The result is always UP or DOWN. It is just that the overall distribution of the +1s and -1s follows a pattern – that of cos (theta)

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All energies are allowed.

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This is in an attempt to prevent the collapse, which only occurs when a particle is  ‘observed’

Understandably, many questions arise, such as ‘Who is observing’, Is it enough for a cat to be an observer? What about a fish? What if the observer has their back turned to the experiment but suddenly turns around just before the particle reaches the screen?

All these questions, though interesting, are meaningless.

As long as the particle’s PATH, is IN PRINCIPLE, detectable, it will NOT show an interference pattern (amplitudes will not interfere).

Only if it is not possible, in principle (using the existing experimental setup). to detect the path traversed, do we see an interference pattern.

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