Are the Quantum Numbers real ?

[Valery]

I've been wondering about reality of the quantum numbers: n, l, ml and ms. We know that they are variables discovered by Balmer, Bohr, Stoner and Pauli respectively and if you plug them in the certain formula the results will match with the atomic spectrum. Well, the spectrum is certainly is the real thing, but what about those numbers. We also know that those numbers follow certain set of rules like: n can not be equal to 0, l<n, ml=-l, ..., 0, ..., +l, ms= -1/2, +1/2. We know that each chemical element has specific set of the quantum numbers, thanks to Pauli. That means that we need four such numbers to define the element. We also know that quantum number l defines orbitals s, p, d and f and, therefore, the regions of the Periodic table. However, the Periodic table in its present format does not completely and clearly reflect quantum numbers n, ml and ms.

When I re-arranged the Periodic Table, so it strictly follows those four numbers, strange things started to occur. The perimeters of the s, p, d and f blocks became equal ! It became symmetric with the point of symmetry located right in the middle of the precious metals ! I called it ADOMAH PT, or it also is called The Perfect Periodic Table.

Then I have deduced that it naturally folds into the regular tetrahedron and significance of the quantum numbers in geometric terms have become apparent. But what does it all mean? Most textbooks compare the quantum numbers with the wave harmonics, etc. It is all true, but what about the Madelung or n+l rule which is central to the aufbauprinzip suggested by Bohr, as well as to the process of ionization, which follows the opposite order. As far as I know, no one knows, except that ADOMAH Tetrahedron PT provides nice explanation. So, are quantum numbers real? Do they physically exist? What are they?

 

[malawi_glenn]

the numbers are the way we label the different states. The states "exists".

Does the number "3" exist? that is a philosophical question.

 

[Valery]

Well, I think that the quantum numbers are not just the labels that we label the states with. I think word "we" shoudn't be used. They were not chosen subjectively. We certainly use them but we did not invent them. They had to be discovered along with the rules that relate them to each other. So, they are objective entities, right?

 

[malawi_glenn]

when i say "we" I mean physisits. But as i said, this is a more a philosphical question. "Does prime numbers exists?". Is mathematics invented or discovered? That is your ultimate question.

For me, mathamatics is the language invented to describe the physical world, hence my position is that math is invented. But I know that other opinions exists...

 

[Valery]

There are as many languages as nations in this world, but, as far as I know, there is only one mathematics and there is nothing else out there that can describe the world in such wonderful way. Isn't it amazing?
Is anyone up to a task to invent another, alternative way to describe the world? I really don't think so.

 

[malawi_glenn]

Well mathamatics have many diciplines. For example there exists ALOT of quantum mechanics representations..

And you can't win a philosophical debate by just saying "Is anyone up to a task to invent another, alternative way to describe the world? I really don't think so." (I don't have time to take that debate altough, have too many things to do right now) ;)
but the problem is not that simple as you might think.

And not everything in nature can be described by the mathematics we have today (calculus etc). Also the "inventors" of calculus where also physicics, so of course their mathamatical machinery was to be used by their physical investigations and vice versa. This is also why we can think that their math (and our minds) can't really grasp quantum field theory etc. We there use virtual particles etc as mathamtical TOOLS.

In the same way I use my native language to describe how I feel etc, it can never describe it 100%. I must project my thoughts and feeling into swedish, since our human languages have developed to fit our daily needs and conversations. And as I argued above, math has been developed to fit our needs for describing nature.

 

[Valery]

Of course, we invent symbols, methods, etc. to represent the concepts and principles. But, do we invent concepts and principles ? I really do not think so, they exist objectively around us and we must discover them. Do integers, using your example, exist in the real world? Of course! Just look at the stars or sand! Balmer had to discover certain integers and the formula to be able to describe part of the spectrum of the hydrogen, not just invent them. And Bohr had to do the same. It took quite some time too. Instead of searching for one set of the universal quantum numbers n and l they could use any numbers that fit this or that part of the spectrum and have number of formulas to describe it. (Many scientists do that, by-the-way). And why would we search for the unifying principles anyway? And why wouldn't we use couple of integers to describe the "spin" (or phase), instead of weird -1/2, +1/2? What about concept of quantum? Can you explain physical reality of the hydrogen spectrum with something other then the concept of quantum? Those concepts are embedded in reality and have to be discovered before we can describe them with our symbols and methods and we invent the symbols and the methods of description after we learn the concepts and the principles from the world around us. Therefore, the quantum numbers and their relationship with each other are the objective and permanent concepts of the physical world. That is my humble opinion, anyway. I do not require immediate response. Please, respond when you have time.
Valery.

 

[malawi_glenn]

The quantum numbers are just the number of nodes in the wave function you get when you solve the shrodinger eq, and the spin Q# just follows from SU(2) etc..so they are not discovered, they are a consequence of the mathamatics evented in the 17th century by Newton and leibniz. the same holds for prime numbers, which is a consequence of algebra. and the number e, which is a consequence of limits. etc etc

And of course nature must have elements of properties and relations, but not nessicarely "mathematical". Math is the language we use to describe of nature "communicates" with itself, while our ordinary language has developed to describe or daily life experiences. I.e we use math to projcet the properties of nature into our human mind. And nature is always bigger than whatever math or physical formalism that we can come up with (philosphical principles), so we cannot fully describe nature with math.

If quantum physics was know back in Newtons days when modern mathamatics was invented, then I think that the math we learn today would be totaly different.

I only have sources about philosophical debates about the nature of math in swedish, but i promise that the reasoning there is at a much much higher level than you and me have shown here;)

 

[Gigi]

Well, I think that these quantum numbers do exist. How? In the sense that they are part of the underlying symmetries of the quantum world.

If we talk about the O(3), SU(2) groups, whose generators- that are conserved quantities- are the orbital angular momentum and spin respectively, then the quantum numbers associated with them are also a result of the symmetries of the quantum world and are also conserved.

The idea that you mentioned about the regular tetrahydron sounds interesting- albeit I have not seen it before.
Can you relate the properties of that geometric shape to a certain symmetry that would leave it invariant?
What would that symmetry be? If it is the symmetry of the groups I mentioned above, then you have the right answer I guess.