Balmer's series and other guessworks in physics

[exponent137]

Balmer's series was firstly obtained by a guesswork. Do you maybe know any other physical formula, which was obtained by a guesswork?

This is a quantum formula, so I send to quantum physics. But I think also other areas of physics. I suspect that many of "y=kx+n" dependicies were also obtained by guesswork, after measurements (x₁,y₁...x_n,y_n) were found?

It seems to me that Planck's formula was also partially obtained by guesswork?

 

[tom.stoer]

The law for black body radiation was first guessed by Planck.

There were two formulas for the UV- (Wien approximation)and the IR-domain (Rayleigh-Jeans) respectively, which were in excellent agreement with experimental results, but incompatible with each other. Afaik Planck first found his famous Planck law first by interpolating between the Wien and the Rayleigh-Jeans formula and by fitting data.

Then Planck found a way (the quantum hypothesis for field oscillations in cavities) to derive the formula mathematically. Later Einstein and Bose showed that the formula can be derived by statistical mechanics applied to massless photons (which were not "known" when Planck started his work; Planck's derivation was not based on the idea of quantized el.-mag. fields but on quantized interaction of the field with the cavity; it was years later that the idea of the quantization of the field itself entered the stage)

 

[unusualname]

Heisenberg's "guess" that a 1-d electron system could be described by a matrix of probabilities of observable transitions is pretty spectacular, his 1925 paper which initiated quantum mechanics seems to have "magical" inspiration:

Understanding Heisenberg's 'Magical' Paper of July 1925: a New Look at the Calculational Details

Dirac said that after Heisenberg's 1925 paper the rest of the development of QM was, essentially, trivial (but Dirac was being modest, for example it required considerable imagination to "guess" the form of the Dirac Equation)

 

[ZapperZ]

Balmer's series was firstly obtained by a guesswork. Do you maybe know any other physical formula, which was obtained by a guesswork?

This is a quantum formula, so I send to quantum physics. But I think also other areas of physics.


I suspect that many of "y=kx+n" dependicies were also obtained by guesswork, after measurements (x₁,y₁...x_n,y_n) were found?

It seems to me that Planck's formula was also partially obtained by guesswork?

The phrase "guess work" is a bit too flimsy. What you are actually describing is what is often called "phenomenology". It is where we don't have a First Principle understanding of a phenomenon, but we have data or characteristics of that phenomenon. So one tries to describe the behavior of the data FIRST. In this way, any subsequent theory that wants to describe that particular phenomenon only has to match the phenomenological description of the phenomenon.

Zz.

 

[exponent137]

Thank you for both examples, guessworks and phenomenology.
A think than Balmer's example is more a guesswork than phenomenology.
It is a lot of guessworks when they try to describe the fine structure constant with a simple and precise formula. This is a guesswork, not phenomenology.
But, I think that dividing zone of guessworks and phenomenology is statistics. If you can give hypothesis and then tests it, this is phenomenology. I think to test hypothesis before you can physically explain a phenomenon. After you can test hypotesis, this is further no more a guesswork. I am interested if such guessworks (without hypotheses) work in physics.
In the all three examples above, I think that this was not happened. Or I am wrong?

Do you have still any successful examples of guessworks and phenomenology?

 

[tom.stoer]

I am not satisfied with the dualism "guesswork and phenomenology". What about abstract principles and deductive methods?

 

[Cleonis]

Balmer's series was firstly obtained by a guesswork. Do you maybe know any other physical formula, which was obtained by a guesswork?

Kepler found his First and Second law without the help of being guided by an underlying principle. (Well, Kepler had this belief that the Sun was key to all motion in the solar system.)

As I understand it Kepler tried a number of things. If I recall correctly, among Kepler's attempts was an off center circle, with the demand that equal areas are swept out in equal intervals of time. But the fit was not good enough. Kepler tried a non-circular shape, somewhat egg-shaped. Again the fit was not good enough. But among the attempts was also an ellipse, with the Sun at one focus, and equal areas swept out in equal intervals of time.

The search took many years. Again and again Kepler ended up with no result for his efforts. Still he kept trying variations. I find Kepler's perseverence absolutely incredible.