|What Does Planck's Constant Really Mean?|
|eI am seeking what is the physical meaning of Planck's constant. I began this investigation since it didn't appear to be a unit of length measurement or of time. I have come to the following startling conclusion:
Planck's constant is the amount of energy contained in any single cycle of an electromagnetic wave, regardless of the wavelength.
This means that any single electromagnetic wave, no matter how long or short contains 6.63X10-34 Joules of energy at a minimum. A high frequency wave contains more energy by virtue of the fact that more waves can fit into any given time period, but the individual waves contain exactly the same energy as lower frequency waves.
I base this conclusion on what happens at .1hz. It was stated in an earlier post that if Planck's constant represented a minimum unit of energy, that this frequency would be impossible in that it would result in an amount of energy less than the minimum. However, in reality, a .1hz wave cannot actually physically exist since there is no wave which only goes up 1/10th of the way, and then repeats another 1/10th and so on. In order for a wave to be complete, it must go through an entire cycle and then repeat. So for a .1 hz signal, it actually takes 10 seconds for it to complete a full cycle. A .1hz signal cannot complete a full cycle in 1 second. It takes a full 10 seconds. So it doesn't make sense to speak of partial cycles. Nature only produces full wave cycles.
Now if we go back to the E=hv formula and we want to get the energy for a full wave cycle at .1 hz, we have to add together the energy contained in 10 seconds (which is the amount of time required to complete a full cycle). This should be a simple multiplication by 10. So we get E = h X .1hz X 10 = 6.63 X 10-34 Joules which is exactly the same amount of energy contained in a single cycle at 1 hz. We can play this game at any frequency. If we consider 1.5 hz, we need at least 2 waves to get 3 complete cycles. So E = h X 1.5hz = 9.94X10-34 (for a single wave). Multiply by 2 to get whole waves (19.89X10-34) and divide by 3 to determine the energy of any single wave = 6.63X10-34 J. No matter what frequency is used, the result is if you calculate the energy of a single wave, it is always equal to Planck's constant. These calculations do not rely on changing any of the units in the forumla. It is the result of simple logic using addition and multiplication. It is a simple logical consequence of the E=hv formula.
Intuitively, I think this makes sense since waves of equal amplitude will displace anything in their path in exactly the same way. A boat rises and falls the same amount in the sea no matter the frequency of the incoming waves. The amount of work or energy is based only on the mass of the boat and the displacement. It just happens more slowly or faster, but the same amount of work is done to lift and lower the boat, regardless of the wave frequency.
I have not seen Planck's constant expressed in terms of the energy of a single wavelength. But I think this gives a solid and intuitive feeling for what Planck's constant really is. It isn't a limit on wavelength, so any wavelength is possible, but it is a limit on the energy contained in any single electromagnetic wave. However, even this does not place limits on the range of observable energy. If you consider .999 hz instead of 1 hz, the energy over 1 second is 6.62X10-34 J (slightly less than Planck's constant). It doesn't need to jump integer multiples of Planck's constant. However, if you were to consider only full waves over the exact same period of time, this would mean that over a 1000 seconds, the 1hz signal would have 1000 waves and the .999 hz signal would have 999 waves and the difference in total energy over 1000 seconds would be exactly equal to Planck's constant, so in this way, energy would have to jump by Planck's constant.