A lot of thanks Soren, for your prompt help. Also, the history of physics is always heart-warming. I am reading your references - very interesting.

The articles you recommended answer part of my questions. But, one question remains: what is the range of velocities of the atoms in such experiments? I mean the longitudinal velocity, i.e. the one with which the atoms enter the apparatus.

Best regards,

Sofia

Hi Sofia,

If you want spin 1, unlike the S-G expt's silver atom, then you'll need two unpaired electrons in a triplet state (spins parallel) rather than a singlet state, where they're paired.

As I understand it, molecular oxygen at room temperature is in a triplet state.

It would take a bit of research to locate a suitable atom in an electronic triplet state as in most (all?) cases it would have to be in an excited state, which is likely to decay into a singlet state unless, as in molecular oxygen, the transition is forbidden.

I'm not sure what the nuclear orientation in S-G's silver atoms would have been - presumably depending on the isotopic composition, but it may well be that the nuclear spin component plays an insignificant role in atom as heavy as silver. 

Hope this helps - Paul

Many thanks, Paul !

I am dealing with a thought-experiment, and although it's just a thought-experimentas I am checking it's feasibility. The experiment deals with spin 1 bosons, electrically neutral, and tests them with the Stern-Grlach (SG) apparatus. By the way, I need to split the incident beam, then merge back the components. The today SG technology is very bad, but I didn't find a better analogous.

A problem in my experiment is that I need to work with quite fast atoms, around 10Km/s. And I have no idea if at such velocities one can obtain the splitting of the beam, i.e. the three beams clearly separate.

With thanks and kind regards,

Sofia

Hi again, Sofia,

As far as your gas velocities go:

A hydrogen atom at room temperature is supposed to move at 2.7 km/sec (see 1st link), so it works for your original question, but for the 10 km/sec in your later post, you'd have to heat it up quite a bit (see third link, but that's for molecular hydrogen).

Here's a sample calculation for a heavier/slower molecule, copied from 2nd link:

Example #1: Calculate the rms speed of an oxygen gas molecule, O2, at 31.0 °C

Solution:

v = (3RT) / Mv = [(3) (8.31447) (304.0)] / 0.0319988

v = 486.8 m/s

Here is the above set-up done with units:

v = [(3) (8.31447 kg m2 s-2 K-1 mol-1) (304.0 K) / 0.0319988 kg/mol

Remember that kg m2 s-2 is called a Joule and that the unit on R is usually written J/K mol. The more extended unit of J must be used in this particular type of problem.

Best regards - Paul

(My point about silver atoms and nuclear spin in the previous post was that I started to wonder whether you could use the electron-proton spin triplet state of hydrogen, allowing highest velocities, and then deleted the paragraph as I wanted to check it again; but you picked up the post before I'd deleted the last para). 

http://www.teachastronomy.com/astropedia/article/Velocity-of-Gas-Particles

http://www.chemteam.info/GasLaw/gas-velocity.html

http://physics.stackexchange.com/questions/65251/escape-velocity-for-hydrogen-molecules

Dear Paul,

A lot of thanks for your help. I was quite deceived, because after a lot of work on a proof that I prepare, I suddenly realized that it may be totally non-realistic from technical point of view. The today Stern-Gerlach technique is quite bad, and I don't see a better alternative for my purposes.

But, the information you gave me, gives me hopes. I will use it.

With kindest regards,

Sofia

Dear Paul, Soren, and other friends,

I am interested to reduce as much as possible the length of the magnets in the Stern-Gerlach type of experiment with which I have to do. Though, I'd like to preserve the separation between the exiting beams. One of the possibilities is to work with atoms of low mass. I searched in internet, but what I found was either nuclear spin data of different elements and isotopes, or data about the electron shells. What I need is the total spin of the atom, as the input beam in my experiment consists in neutral atoms.

Can somebody help?  

Hi Sofia,

As you may recall, the interaction of electron and nuclear angular momenta results in hyperfine structure in atomic spectra; overview and refs in the link below should help. Beyond reading Herzberg, I never got involved in actual calculations myself. The attached file might suggest a shortcut.

As usual - hope this helps.

Best - Paul

https://en.wikipedia.org/wiki/Hyperfine_structure

Hi Sofia

your works is very interesting and i wish your success.

Sofia,

Not sure if it's entirely relevant, but have you seen the current Stack-Exchange discussion (link  below; refs via the link itself)? Robin Ekman writes:

"...can you distinguish between classical and quantum models [of spin]? Well, the Stern-Gerlach experiment [7] does that. The real story is a bit more complicated according to historians of science [8-10]. (I should add a disclaimer that I have not read these papers in detail as I've not had the time. But I think you will find them interesting.) On the other hand, Bell and GHZ experiments are rather convincing that we do live in a quantum world.

We can also look for Stern-Gerlach effects in the relativistic regime by using the Frenkel model/Tamm-Good equations and comparing to a calculation based on the Dirac equation. (To avoid having to use full QED, one should use the Foldy-Wouthuysen transformation [11-14].) This was done recently by Weng, Bauke, and Keitel [15], showing that strongly relativistic electrons in extremely intense laser fields have different motions according to the Frenkel and Foldy-Wouthuysen models. According to Weng, Bauke, and Keitel, the difference is plausibly within experimental limits at least with next-generation lasers."

Cheers - Paul

http://physics.stackexchange.com/questions/283137/dependence-of-spin-on-classical-vs-non-classical-physics/284274#283137

Dear Paul, and all the other friends,

First of all, many thanks for your help.

I am about proposing an experiment for testing on a very general level the de Broglie-Bohm mechanics. I deal there with the Stern-Gerlach apparatus. In general, this is a very big apparatus, which is a problem for me. I would be glad to refer to an apparatus with the same effect, but much smaller dimensions.

But, let me tell you a couple of other things:

There are people who strongly believe in Bohm's mechanics. I would have been glad if it were correct, because it offers a simple escape from the "collapse" hypothesis of von Neumann.

Unfortunately, as Prof. Partha Ghose proved, and I also proved, Bohm's mechanics contradicts the experiment.

Though, if we leave aside the formulas of the Bohmian mechanics and retain only the basic idea of particles with trajectories, this basic idea is very difficult to disprove. Thus, to refute this idea and stick to the Copenhagen interpretation which says that there is no substructure beneath the wave-function, is unfounded, at least for the moment.

So, it's on this that my investigations are focussed at present.

Best regards,

Sofia

Very useful to get your overview, Sofia.

But do I understand your position correctly:

1) You're aiming to support the idea of particles with trajectories, but not via the formulas of Bohmian Mechanics?

2) You do not believe in the von Neumann/collapse hypothesis?

3) You do not believe that wavefunctions have no substructure?

Regards - Paul

Dear Paul,

I tried hard to prove that the basic idea of particles and trajectories (of de Broglie-Bohm type) do not exist.

You see, it is not difficult to prove such a thing if reasoning according to moving frames. From the cellebrated Hardy's article “Quantum Mechanics, Local Realistic Theories, and Lorenz-Invariant Realistic Theories”, (Phys. Rev. Lett. 68, no. 20, page 2981, 1992), such a proof was already derived. Following the wave-function evolution according to one frame leads to a conclusion A, however, following the wave-function evolution according to another frame leads to a conclusion B, where the conclusions A and B clash.

But, what I wanted, was to judge according to one and single frame, because there are all sort of doubts about using moving frames. For instance the supporters of the de Broglie-Bohm ideas incline to believe that a preferred frame may exist. That would contradict the relativity, but they though try to bring all sort of justifications.

You see, the proof that Bohm's formulas contradict the experiment, was done, by Prof. Partha Ghose and by me, without moving frames. However, I have the feeling that about the general idea of particles and trajectories (leaving aside Bohm's formulas), there is some NO-GO, and only with moving frames we can disprove this idea. Again, for the moment it's just a feeling.

As to the von Neumann collapse, it's the same situation. Using moving frames, it's easy to show that the collapse hypothesis is wrong, i.e. wave-packets that didn't produce a click in a detector, do not disappear,they can have an observable effect.

Kindest regards,

Sofia

Dear Sofia,

Thanks for the clarification. I can't reach Hardy's 1992 paper for the present, though I've seen it cited frequently.

As regards the existence of quantum particles and waves: I tried recently (on Stack Exchange and ResearchGate) to make the case that the photon has no independent existence. My basic argument was that neither particles of light (photons) nor light waves exist, other than in the maths connecting emitter and absorber.

Although my initial 'short-cut' argument  [that the null-vector light-path in Minkowski Space constituted a “contact interaction” and therefore avoids the need for any intervening entity, so the photon has no existence] was effectively rebutted, no-one convinced me of the invalidity of my basic argument.

However, I learned subsequently that, according to two peer-reviewed articles, one co-authored in 1999 by the 2012 Nobellist Serge Haroche, it is possible to detect photons non-destructively. If so, then I must accept that the photon – and presumably other massless particles – do have some sort of independent existence:

1)       Seeing a single photon without destroying it [1] G. Nogues et al.

 See also the Haroche’s lengthy but more accessible Nobel Lecture [5]  

2)       Nondestructive Detection of an Optical Photon Andreas Reiserer, Stephan Ritter*, Gerhard Rempe [2].

Curiously, none of the critics of my suggestion cited either of these papers, which are, to my argument, 'killer' refs.

This whole discussion should not be confused with the larger literature asserting that while photons are not a necessary concept, nevertheless light waves do exist, (e.g. [3, 4] ).

I realise this isn't directly relevant to your original question, but is perhaps tangential to your points about the existence of Broglie-Bohmian particles and trajectories.*

Best regards - Paul 

* Incidentally, one of my prized possessions is a signed reprint that de Broglie sent me in the 1970s

http://www.nature.com/nature/journal/v400/n6741/full/400239a0.html

http://journals.aps.org/rmp/pdf/10.1103/RevModPhys.85.1083

https://arxiv.org/abs/1311.3625

https://arxiv.org/abs/1507.02113

https://arxiv.org/pdf/quant-ph/9711046v1.pdf

Dear Sofia!

Honestly I was not closely involved with the Stern-Gerlach-experiment. In my opinion it proves that the so-called „spin“ is not a rotary motion. The spin exists comparable to the elementary charge in two opposite states without spatial orientation. Electric or magnetic fields are disturbing the isotropy (of the space?) and therefore particles or atoms are separated.

Your project is interesting. I would try to icrease the inhomogeneity of the magnetic field by different shapes of the magnetic poles. The atom beam across to the symmetry plane of the magnet? Why do you want to work with smaller magnets? The idea to use different atoms espacially light aroms is good: Maybe you will incidentally discover spezific properties.

I wish you success!

Hans