Re: What does Planck's constant really mean?

franklinhu@xxxxxxxxx wrote:
Planck's constant is said to be the smallest amount of heat which can
be radiated at the vibration frequency v. (See.
http://www.hypertextbook.com/physics/modern/planck/)

Can't you read? What the page *actually* says is that hv, i.e. Planck's constant *times the frequency*, is that "smallest amount of heat". (BTW, I would prefer using "energy" here instead of "heat").


This is in
accordance with the formula Energy = (any integer value representing
number of photons) X (Planck's constant 6.63 X 10^-34 J*s) X (frequency
in cycles/second).


And where exactly did you get this formula from?


My question is whether this also means that this is also the smallest
amount of energy difference between any frequencices.


What is "energy difference between frequencies" supposed to mean?



In other words,
the amount of energy has to be some whole number multiple of 6.63 X
10-34.

If you didn't notice: in physics, quantities have *units*. h isn't simply 6.63 x 10^-34. It is 6.63 x 10^-34 Js (Joule times seconds)!

Since energy is measured in J, not in Js, the answer to your question
should be obvious...


The formula does not place any quantization limits on
frequencies, so an infinity of frequencies is allowed.


Indeed. As long we talk about free particles...


This would also
imply that an infinity of energy amounts would also be allowed. But
this would seem to be in contradition with the whole idea that energy
only come in quantized packets.

No, that is in no way in contradiction with that idea. Why do you think so? Perhaps you should educate yourself a bit on what is meant when one says that energy comes in "quantized packets"...


It would seem that one possible solution is that frequencies would also
have to be quantisized, meaning that only certain frequencies would be
allowed 

For bound systems, yes. For free, no.


and if you were to closely examine a spectra which
theoretically contained all possible frequencies, you would actually
see frequency bands corresponding to energy spacings equal to Planck's
constant.

"energy spacings equal to Planck's constant" makes no sense. Again, see my comment about units above.


For example, if we simply the formula by using 1 as the integer amount
in the formula (energy of a single photon) and assume that the
frequency is 1 cycle/second,

Why don't you say "1 Hz", like everyone? And why do you use that frequency? What's so special about it?


It appears that the seconds terms cancel
out leaving just Joules which is a measure of energy of 6.63 X 10-34
Joules.


BFD!


Now the question is, can I modify the frequency to produce any
arbitrary amount of energy like 6.64 X 10-34 J,


YES!


or would I have to
modify the frequency enough to produce another Planck constant worth of
energy or 13.38 X 10-34 Joules?


NO!

Why on earth do you even call 6.63 x 10^-34 J "a Planck constant wort
of energy"???



If frequency can only come in particular quanta, some rough
calculations show that the frequency would have to differ somewhere in
the magnitude of 1 X 10-21 meters for such a small jump to occur.

Huh? What has the units meters to do with frequency? You apparently mean the wavelength?

Could you show that calculation, please?


This
would also imply that this would correspond to the maximum frequency
possible (based on the smallest possible weavelength of 1X10-21m) or
about 3 X 10^29 cycles/second. It might also imply that this is the
smallest possible unit of distance in the universe, since nothing can
seem to act at smaller distances that this. Going even further into
speculation, this could mean that space itself is quantized in 1 X
10-21 m cubes and explains why we see quantized amounts of energy &
frequency and why we see Planck's constant. (Lots of speculation, but
an interesting idea, I think).


Sorry, I don't see how your space quantization idea leads to the known
formula E=hv.


There is some experimental evidence from the dropping of neutrons in a
gravitational field that would suggest that the neutrons cannot take
arbitrary positions in space, but must drop in specific quanta,
indicating that space is quantized.
(See:http://www.users.csbsju.edu/~frioux/neutron/neutron.htm)

That has *nothing* to do with space quantization!!! These are simply the energy eigenstates of the neutrons in this bound state!!!


So this is not a wild idea.

It is. Could you please get a basic education before talking about topics you understand only superficially?


Bye,
Bjoern

fhuplanck

.

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