Does e=hf contain an error ? A fresh look at Planck's constant of action

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Offline mxplxxx

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In a previous existence ( I described Planck’s action constant and showed its relationship to the quantum of action that is the basis of quantum physics.  It is tempting to think that this is where the tale ends, “and they lived happily ever after”. But, quantum physics has so many paradoxes and weirdness that it is hard not to get the feeling that something is seriously amiss. Einstein certainly thought so. That something may be contained in the hypothesis that the early physics pioneers may have displayed muddled thinking when it comes to the quantum of action. I hope to show, as many others are starting to do, that Planck’s action constant h is better defined with units of energy rather than action. In other words that all quanta of energy contain the same amount of energy, rather than action.

Firstly, action is a seriously weird concept. It may be that for it to form the basis of a complete theory of reality makes the theory itself weird. An extensive internet search for someone, anyone, who could describe what action is in relation to an electromagnetic wave, or explain the relationship of Planck’s quantum of action to reality, drew a complete blank. It seems that it is pretty true to say that noone knows what this constant really means. The unit of action is a mathematical entity only and bears little relation to reality. Finally, the fact that the energies derived from action can take on any value, masks the quantum nature of reality.

I believe that two values are important when it comes to a quantum of energy. My hypothesis is that:

  • Energy, which I regard as rest energy, is the same for all quanta of energy and has a value of hE joules. hE has the same numerical value as Planck’s action constant but with units of joules rather than the problematic joules.seconds.
  • Power is the rate at which a quantum of energy will be transferred or converted. It is related to the speed at which the quantum is travelling. It is given in the case of a cycle of an electromagnetic wave (i.e. a photon) by the equation P = hEf where P is the power in joules/sec , hE is the energy constant in joules (as above) and f is the frequency of the wave in hertz (cycles per second).

If we take this power equation and multiply both sides by 1 second we get Pt1=hEft1, where t1 is a 1 second constant of time. Given that E=Pt , the equation then becomes E1= hEft1 where E1 is per second energy in joules. Looking at the right side of this equation, hEt1 is just Planck’s action constant (joules times 1 second), so we can rewrite the equation as E1=hf.  It is a pretty fair bet that this is how the seminal E=hf equation evolved. So E = E1. But E1 is per second energy (i.e. derived from power) which cannot be the energy of a photon which is measured over a period of 1/f seconds. To derive the energy of a photon given E is per second energy, we need to multiply E by 1/f. This always results in a value of hE joules.

So, to summarise, it is hypothesised that:

  • A photon IS one cycle of an electromagnetic wave.
  • A photon contains 1 quantum of energy.
  • The energy of a photon, and therefore of a quantum of energy, is a constant hE joules where hE has the same numerical value as Planck’s constant of action (6.62606957(29)×10−34).
  • The power of a photon, and therefore of a quantum of energy, is given by the equation P=hEf where P is the power in joules/sec, hE is the constant energy of the photon in joules and f is the frequency in hertz (cycles per sec) of the photon’s associated electromagnetic wave.

A picture of what this implies is that the energy of a photon is rest energy and the power is derived from the speed of the photon (c). I can see two mechanisms whereby the speed of transfer of energy is affected.

  • The energy density of a quantum can vary. A gamma ray would have a higher energy density than a radio wave.
  • The shape of a quantum of energy may vary. A gamma ray may be a tall narrow shape which transfers quickly (with more power) and a radio wave may be a long thin shape which transfers slowly (with less power). Interestingly, shapes in this hypothesis relate to the shape of a cycle of an electromagnetic wave.

Of the two explanations, based on the Occam’s razor principle, the shape hypothesis appears the more likely because it is simpler.

« Last Edit: 24/09/2011 04:36:40 by mxplxxx »


Offline granpa

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Planck's constant has units of angular momentum

from Planck's constant we get alpha

alpha = 1/137 = v/c where v is teh speed of the electron an a bohr atom.