# Why fundamental quantization of energy is hv?

1. Jun 16, 2009

### janakiraman

Now this might seem to be a very stupid question. But neverthless, I dont understand why the fundamental quantization of energy must be hv? why not any value lower or higher like hv^2 or h/v^2. Is it possible to prove that this value of quantization is most favourable than any other value?

I'm not sure if I had put my question in an understandable form. But it would be great if someone could enlighten me on the same

2. Jun 16, 2009

### Pengwuino

I don't really know what you mean by "fundamental quantization of energy" but first of all, hv^2 or hv^3 isn't even dimensionally correct. I think the answer you're looking for is simply that's how it is. We didn't ask for it to be that but that's what it is. Energy is proportional to the frequency and h was a proportionality constant to be determined.

3. Jun 16, 2009

### janakiraman

Ok thats how i always get started off with, very dubious :). Well ok I can put it this way. I know E is proportional to frequency. Accepted. And why is the quantized part needs to be hv? Why can't I have some different value for 'h'? I think when Planck and Einstien proposed it, they had calculated the planck's constant based upon the existing experimental results of black body radiation and photo electric effect and so the value of 'h' perfectly fitted with the curves. My question is can we prove that indeed this is the most favorable value for energy to be quantized and not any energy above or below it?

4. Jun 16, 2009

### Fredrik

Staff Emeritus
Isn't Planck's constant defined as the number that makes $E=h\nu$?

5. Jun 16, 2009

### Pengwuino

Yes, that is the experimentally verified value. That's it. It's like gravity being approximately 9.8 m/s^2 near the surface of Earth. You can't ask it to be something else, that's simply what nature gave us.

6. Jun 16, 2009

### Count Iblis

In natural units this is:

energy = frequency

We also have that:

momentum = wavevector

If you combine the two relations into one relation between four-vectors, you get:

(energy, momentum) = four-wavevector

Can we have a different relation? You could speculate that at high energies gravity will become important. The Schwarzschild radius is proportional to the energy, while the characteristic length scale in quantum mechanics is the Compton wavelength which is inversely proportional to the total (rest) energy.

7. Jun 16, 2009

### Bob S

The present most precise value of the Planck constant is based on a measurement at NIST using a torsion balance, kilogram mass, a superconducting coil, and an induced voltage based on Faraday's Law. See
http://www.aip.org/png/html/planck.htm [Broken]

Last edited by a moderator: May 4, 2017
8. Jun 16, 2009

### sokrates

I think he's referring to the historical, initial definition, which as far as I know is correct.

Planck's constant was defined as the proportionality factor relating the energy of a photon to its frequency.

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9. Jun 16, 2009

### Fredrik

Staff Emeritus
As far I can tell (by taking a quick look at Wikipedia), I was right about the definition. The page that Bob S linked to describes how to measure Planck's constant, and suggests that this method might be used to find a better definition of a kilogram than the current one. It doesn't really say anything about the definition of Planck's constant.

10. Jun 16, 2009

### f95toli

Just to clarify:
The basic idea of the Watt balance is (or at least was) to measure Planck's constant with very high precision and then use that value for a new definition of the kilogram.
It is (was) essentially an attempt to improve the SI; i.e. it was in no way an experiment in "fundamental" physics so it is more or less irrelevant for this discussion.

11. Jun 16, 2009

### Count Iblis

The definition of Planck's constant can also be interpreted as a matter of defining units. I.e. allowing one to use inconsistent units (for energy, time, momentum, length etc.) and then having to introduce a conversion factor to compensate for that inconsistency.

Michael Duff has argued strongly in favor of this view, see e.g. here:

http://arxiv.org/abs/hep-th/0208093

12. Jun 16, 2009

### canoe

Planck's constant is a constant of nature. Historically (circa 1900), it was empirically derived by Max Plancks's examination of the emissive power of a black body. Planck originally fit the curve of black body radiation based on data obtained from the experiments of Lummer and Pringsheim. In order to do so he had to make the assumption that E=hf. Later, Planck went back and formulated his radiation law based on thermodynamic principles. However, he could never justify his original assumption that E=hf. Planck just thought it was a useful construct. In 1905 Einstein derived a linear relationship (in his explanation of the photoelectric effect) between the frequency and the energy of a light particle "(photon)" where h turned out to be the slope of the relationship. Einstein was basically saying that E=hf was more than a useful construct - that it was real. Millikan later proved Einstein's Theory regarding the photoelectric effect experimentally and also found Planck's constant within his results.

So we can assign it (h) a precise definition based on experiment, but we don't know where it comes from. It is a constant within nature that has never been explained or derived by theory.

I had read about this just recntly and actually found an old schematic of the device used by Lummer and Pringsheim. It consisted of a cavity oven, a focusing spectrometer, a bolometer darkened with lamp black, and a bridge circuit.

13. Jun 16, 2009

### Bob S

Early measurements of h, or actually h/e were done by measuring the end point (short wavelength limit) of the x-ray spectrum with a defined voltage on an x-ray tube. This is W. K. H. Panofsky's thesis in 1941:
http://etd.caltech.edu/etd/available/etd-06182004-143223/ [Broken]
There were also related wavelength measurements of x-ray lines using Bragg diffraction or reflection. The development of the Josepheson junction (and SQUIDS) in the late 1960s repaced the old Planck's constant measurement with a new fundamental constant, h/2e = magnetic flux quantum = 2.0578 x 10-15 tesla-m2. This changed h by about 60 parts per million. So the present value of Planck's constant does not depend on measuring the wavelength of photons.

Last edited by a moderator: May 4, 2017
14. Jun 16, 2009

### canoe

Yes. Planck's constant is ubiquitous. It pops up all over the place.

15. Jun 16, 2009

### janakiraman

Yeah that was my basic idea, how did it come up. But I have two important questions from the replies above

@Pengwuino

Well i dont know much about general relativity, but i had thought that based upon the mass of earth and other related values, you could calculate the gravity of earth to be 9.8 m/s^2. I'm surprised to know that its stilla fundamental constant like 'h'

@canoe
variation of 60 parts per million of 'h' is not a small value if i'm right. I have also read that based on qm, we were able to calculate the energy level of Hydrogen spectrum to a very very accurate value of around 1 part per million. If that was true, how did this change modify those results?

16. Jun 16, 2009

### Count Iblis

If you accept quantum mechanics as the absolute truth, then the explanation is simple, essentially given by Michael Duff in his article:

http://arxiv.org/abs/hep-th/0208093

So, it is simply a conversion factor. If the true laws of physics say that
X = Y, but for historic reasons you always measure X and Y in incompatible units (which have been assigned incompatible dimensions because we used to think that there was no way you could combine X and Y), then the equation X = Y will appear as X = r Y where r is some conversion factor that will have the dimensions of X/Y.

So, we see that Planck's constant as no physical meaning whatsoever in this picture. One can set hbar = 1. This then means that time is given the same dimension as inverse energy and momentum the dimension of inverse length. If we set c = 1 too, then time and length have the same dimensions. Then if we set G = 1, everything becomes dimensionless.

Of course, physics is only about dimensionless numbers, so this is the way it should be.

17. Jun 16, 2009

### canoe

I'm not sure. I was interested in Planck's derivation of his radiation law so I had delved into the Lummer and Pringsheim experiment. Although, I am certain that more recent experiments have refined h, I'm not acquainted with them and so I have no knowledge on their perceived variation. I say perceived variation (from some norm) because h is still a natural constant. It is what it is...and the only reason we get more refined values is that we are progressing in becoming less clumsy in its measure.

I am just now looking at a text book where the ground state equation of a Hydrogen atom has been derived from the Schrodinger equation. it would seem that there would be variation in not only h-bar but the coulomb constant, and the fundamental charge that would far outweigh 1 part per million. Where did you read that? Are you certain that [they] were not referring to a variation in measure?

18. Jun 16, 2009

### Phrak

There are at least two ways to read your question. The first way, is what almost everyone is answering--that energy is a different way of measuring 1/T.

For the second, what would happen if the proportionality constant between energy and frequency were to become everywhere different in the universe? Would the difference be physically measurable, or would some hypothetical outside observer simply notice that we were no longer using the same span for the length of a second anymore?

You could ask the same of c, units conversion factor for length and time, or the gravitational constant.

The second way to answer is to tell what physics would be like if h were a local variable--if it changed over spacetime regions. I don't know what the answer is, but I'm sure it's interesting.

Last edited: Jun 16, 2009
19. Jun 16, 2009

### canoe

You have just derived Planck units. If we set hbar=1, c=1, and G=1 then by definition length (space), time, and mass had to be unity (i.e. 1).

http://en.wikipedia.org/wiki/Planck_units

However, we still are pretty much rooted in anthropocentric units (kg, m, s) when performing experiments.

20. Jun 16, 2009

### Phrak

I don't know what you mean. I'm still free to pick any length as a unit length. I pick one lamp length, you pick 1 tree; they are not the same span.

21. Jun 16, 2009

### canoe

That is an imaginative and fascinating thought...and I mean that in a very positive way. If it weren't late and I have to work in the AM, I would kick that can around for awhile. I might want to get back to you on that.

22. Jun 16, 2009

### canoe

Just take a quick gander at this url...right under Table 2.

http://en.wikipedia.org/wiki/Planck_units

23. Jun 17, 2009

### janakiraman

@canoe

I dont remember exactly, but i definitely remember the precision of calculation was extraordinary. I'm trying to recollect it but not sure

@phrak

Its an amazing conception, you have put down things in a beautiful and a clear way about the vague things that i had thought, but it would be good if someone could think about it.

Also could someone answer my question related to gravity constant of 9.81 m/s^2. Is it not possible to derive it from general relativity? Also another interesting thing that emerges out of discussion (atleast in my understanding) is the linear relationship between the energy and frequency irrespective of the kind of vibration i.e., sinusoidal like EM radiations or the longitudinal vibrations like the lattice vibrations or phonons. its quite remarkable that this relationship also holds good for the entire frequency spectrum ranging from new hertz to order of gigahertz. It is something really fundamental and spectacular i guess.

24. Jun 17, 2009

### Staff: Mentor

9.8 ms-2 is not a fundamental value, but I think G - gravitational constant - is, in the same way h is. Both are proportionality constants that we can't calculate, we can only measure them.

25. Jun 17, 2009

### Bob S

Let's first list some quantities that are absolute identifiable quantities, except that they depend on the system of units:

1) speed of light, c
2) charge of electron, e
3) etc.

Now let's list some quantities that are absolute, meaning unitless:

1) fine structure constant α = 2 pi e2/hc =1/137.036
2) etc.

Now what is Planck's constant?

h= 2pi 137 e2/c; or h-bar = 137 e2/c

We could select a system of units where we define e = c = 1, then h-bar = 137.