Mike Smith Cosmos

The overlay is really in the physical interpretation of the mathematics. Spin is due to a rotation, but it is not as simple as rotation of a particle about some axis. This "extra rotation" manifests itself in nature as the intrinsic spin of a particle.

 

More generally, you are asking if mathematics is invented or discovered? This has been discussed on these forums before, have a search. The question is rather philosophical in nature. I doubt it would shed much light on the question of spin.

Yes I like that expression " the physical interpretation of the mathematics. Yes by all means we need to venture into the depths to gain an quantitative or predictive view but in the end the maths has to provide some mechanism for physical reality.

WHAT REALLY is going on at the Electron level. Be it that you chaps know the deep maths but what is the physical interpretation of the maths , and don't just say angular momentum and spin , because there is charge involved , there is some mass, there are some abilities for movement, and swapping with photons. Draw me a mental picture of whats going on down there. Wolfgang Paul and Hans Dehmelt Nobel prize winners 1989( not Pauli ) trapped an electron in a TRAP, it didn't like it. They kept it trapped for an hour then a few days , a month, finally a year, then it got out. May be it was quantum tunneling by the wave function ! Loose, trapped in atoms, ionized, converted to photons, full of charge ,conducting all sorts of Spin, happy in pairs within the shells. What kind of a tethered animal have we got here?

Thanks ! But there must be some overlay to the maths, unless you are saying like Mr Tegg that Maths is the bedrock rather than human constructs.

AJB

Have you a book or two ( name and author) that you can give me that I can order up , or was that the one you referred to a few days ago .

And can you possibly tell me how to attatch my comments to other peoples, as I seem to be making statements in isolation. ?

Are we not arriving at the difficulty of facing the crossing over from classical to quantum as if it were a different realm and out of bounds apart from the few. Surely the whole universe "exists" from the smallest point to the whole shebang . All that changes are different rules or approaches as we move through the scales. Maths does have a habit of becoming a barrier for many who approach this crossover territory. Surely it relies on those who have crossed over to make the understanding of the quantum region accessible. Otherwise we are surely in danger of sounding like priests who tell the lay people of old that the "deeper things" are our province only .

Roger Penrose one of the great current gurus of maths, gave a lecture to one of the American universities ( Princetown I think ) where he described it as classical above the waterline and quantum below the waterline. Different medium, different rules , different experience but still approachable none the less.

I appreciate the maths in whatever form will be a new pair of underwater goggles. But you that have gone there , tell us what you see !

STEEVEY

Not all lines of scientific research are following the same approach to the fabric of space time. Some view it as a blank canvass others a void seething with activity. Frank Wilczek a Nobel prize winner and professor involved with the Large Hadron Collider, calls it Grid The which has several layers of activity including the virtual particles commented on earlier. However these are separate to the particles such as the electron pairs we were discussing . Professor Frank Close also involved with the large hadron collider speaks of it as the Void. The idea that space is empty seems to be fading fast. Neutrinos also seem to be teeming across space; from the sun ; from power stations ; through the earth ; through you by the billion; even from the Big bang. So the small though not tiny electron with its SPIN whatever that is , is quite a significant happening in amongst all this other stuff.

I can visualize these pairs of electrons in some way being coupled and being particularly comfortable doing their angular momentum bit in some form of balancing "up" and "down" opposite direction. This is exactly how tuning fork prongs move. Touch one the other stops. Tap one the other moves but in an opposite direction. Try to make one vibrate on its own. It will but not as balanced and comfortable as the pair. This has striking resemblance to the electron pairs. Also if you try to bring in a third prong. No deal. Exclusion. This is only a model, but as I mentioned in a previous posting Prof Frank Wilczec says its good to have toy models untill you knock them down for something better.

Steevey, I may have something for you to visualize . I am working on some research at this very moment concerning WHY the pauli exclusion principle is invoked by two electrons in the same orbit or energy band. My area of research is to an extent looking for analogue models in the classical world where two tightly coupled particles behave in both an attractive/ repulsive coupling yet behave in opposite modes exactly. One such analogue is the tuning fork, where two similar prongs of a tuning fork vibrate in opposite directions IE one going exactly west when the other prong is going exactly east. This is irrelevant of initial striking of one prong of the tuning fork. Although this may sound crude as an equivalence of quantum mechanics , however ref:The new Quantum Universe Hey and walters 2009 edition page 58,59 shows violins bodies and drum surfaces as analogues to quantum mechanics wave functions , standing waves etc.

So if we find electrons coupled in pairs as they appear to be in orbitals the equivalence of coupling and movement ( angular momentum ) may yet become evident.

It is unreasonable to think of some formula or rule (pauli exclusion principle ) floating about in space , so as to impose a rule on two electrons in proximity, rather the fabric of space time and all particles and forces that such space consists of, having within itself the coupling necessary to facilitate the orientation we find happening with two coupled electrons in a given energy band or orbital.

Prof Lee Smolin of Princetown University Institute in Canada, has been proposing for years that space time is not a backdrop on which thing playout thier lives (particles , forces etc) but rather Space time comes out of / or is indemically part of the particles and forces themselves. ( Quantum Gravity the road to reality By Lee Smolin).

Hope this is of some help . !

Sorry Steevey I seem to have no got the method of attaching postings of mine to the members questions. Its there somewhere in the overall listing of postings

But when I'm picturing an electron, I'm not picturing it as this particle, I'm picturing it as a wave which is the undetirmination of an electron with relative shapes. They have regions, but the regions get weaker or "less probable" as the distance increases from its most probable place, which is more or less where on a wave, it would be the crest, just like in the double slit experiment where the most probable place corresponded to being hit on a wall as a wave on the wave crest or top of the wave.

How exactly do scientists know "spin" exists if there is no determined path for an electron and it pops up in different random places?

Is it that classically, an electron still does have a physical spin or physical movements, but because of quantum mechanics, an electron is also undetermined and follows mathematical probability? It would make a lot more sense for electrons exist in the same state but still avoid each other as waves.

Understanding Spin in a Popular Science Form.

I raised a few questions on the 23 Feb 2011 09:14 Mike Smith Cosmos , hoping that this would initiate a few comments for discussion along the lines that some of the old masters undertook during the early years of atomic Physics. Its true that this resulted in the Copenhagen agreement that some were told to " shut up and calculate " while others continued to discuss, argue, debate, think , propose, experiment and think again and help move atomic physics through to its present advanced form . Although many of the breakthroughs were made by maths orientated scientists. That is not true of all breakthroughs. Even Einstein was not the best of mathematicians but he was an expert in using lateral thought processes and thought experiments. I appreciate that the Science Forum ethos is, to not let speculative thought processes run wild , or to cloud current science understanding. However there may be scientists out there who can maintain and share with us, some form of model in their mind that is not pure maths. Although I have gone through the A level Maths, University Maths , Physics , Electronics, Satellite Communications Path, and taught physics , I still like to keep my feet on the ground to some extent when explaining either to myself or others physics concepts. I, along with a few others, would appreciate having some of these models ( be that not easy in quantum mechanics ), verbally offered, if at all possible .

I have gone some way to reading around the subject in the last three days . One or two things seem to be coming home to me. Angular momentum is a very fundamental thing for the operation of the atom thus elements. The orbital angular momentum is slightly easier to understand and visualize to some extent as demonstrated by the diagram on previous postings. Although even their uncertainty or probability still tempts wonder. Despite their fuzzy clouds one can form a mental picture however approximate or inaccurate these diagrams appear. Then we come to the electron spin itself which is said to have angular momentum of two discrete values up spin and down spin. Here comes the rub! If NOT a simple spinning Top for reasons of maths inconsistencies or problems what is the nearest or nearer approximate model that we can visualize, even if it one to shoot down and move on to a more accurate model. Frank Wilczek in his recent book " the lightness of being" page 114 " in trying to understand complicated concepts or equations its good to have toy models". So is there anyone out there who has a good toy model of :- an electron

A) its movement generally , say in orbit , B) its movement in or by itself including the spin bit , C) its reality as a point, charge swirl, wiggling small mass energy or whatever lepton

D) its ability or lack of to stand still E) any possible exclusion or coupling with another electron.

It seems to have originated way back as a fundamental particle within the plasma or shortly after the inflationary start to the Big Bang.

It has been mooted that one needs to penetrate maths to get the full picture. But surely we must cloth maths models with some form of philosophical idea !

I have started to do literature search on "Angular Momentum ". This often leads back to spin , which is inevitable. However often circular orbits, having set circumference as a constrain for standing waves and hence leading to quantum mechanical ideas as supported by Bhor, are quoted as the classical angular momentum from orbitals. The angular momentum for electrons and other particles is said to be an additional element to the overall angular momentum of the system or atom. I am currently reading the Cambridge University Press book THE NEW QUANTUM UNIVERSE by Tony Hey and Patrick Walters which has some good explanations. The fact that the term angular momentum is applied directly to spin, still seems to infer that something ( even if it is ill defined by locality and non locality issues ) is generating a "force" be it by a principle of equivalence or some other mathematical transform. Can anyone share more ideas on the difference between classical angular rotation giving rise to standing waves, and Spin ( angular momentum) again in quantum terms of up and down spin?

Thank you Mr Shaken not stirred "swansont". For your succinct comment. Surely we are moving from one simple statement like "spin" to another like "angular momentum". Perhaps I need to go and do some homework on angular momentum. But I thought it had something to do with mass and velocity not in a straight line but in some form of curved path. Perhaps this curved movement is more of a partial arc rather than a complete circle. This would infer more of a vibration than a spin. Is this leaning more toward string theory? I am aware that residual spin is the result of the sum of all spins within the system. However I still struggle to visualise (fatal comment) what is being summed and whats going on.

Is that a gun that you are holding in your picture ? I suggest you use it on me while I am still sane !

Sorry! I did not realise there was a second page. Clearly this topic of spin, has a few persons with the sort of conceptual problems that I have. I must say I think it is a defeat if we give in to the oft quoted comment ." If you think you understand it , you have got it wrong" Feynman .

Some famous maths person once said something to the effect that "if you cant jump off the back of a bus and go up to the first person you meet and explain in simple terms your theory, it is likely that it is not understood by yourself or others correctly " or something to that effect. Surely the fact that spin is so difficult to explain means , it is likely we don't yet fully and simply understand the subject of "Spin ". Is this not at the root of maths ( beautiful equations ) itself and symmetry.

I would still like a simple and beautiful explanation of " spin " as applied to quantum mechanics . If possible .

Thank you for your comments. I, perhaps foolishly, would like to do some research around the subject of "spin". Perhaps as Frank Wilczec voiced I am making trouble for myself. However I have a hunch ( eek ! ) that some goodies lay deep within this particular aspect of quantum mechanical arena.

I for one would enjoy, hearing in a little more detail, how two identical things( electrons, states, atoms whatever ) are inherently prohibited from existing.

I have been absent over the Xmas and new year, but am returning to the subject of spin. Surely the early founders of quantum mechanics such as Pauli used spin to derive the exclusion principal necessary for orbital or energy band structure for all ( the entire universe ) atoms. If the spin was not there, surely the universe would fall apart ! Although spin appears in all studies on quantum theory and is indeed used in ideas leading to quantum computing. It seems less spoken about in connection with quantum mechanics than perhaps the other aspects. Is this due to the fact that there is less understood about spin in the way that "wave particle duality " seems to leave many mystified ?

I find this subject interesting , yet at the heart of quantum theory. If anyone has any eureka feelings about " spin" at the quantum level please could you share them !