
#1
Apr311, 09:16 AM

P: 41

I'm not quite sure which forum I should post this in; it's related to my school work but I don't have any homework questions about it. Rather, I am just confused about what it really is and what it means. Hopefully it goes here.
I get that the projection of the angular momentum along some reference axis is quantized. My question is what does this mean physically and how does it lead to the band splitting in the SternGerlach experiment? Also, why is it called space quantization rather than angular momentum quantization? I read that the angular momentum is quantized against some reference axis, which may be arbitrary. This is precisely why I am confused about the SG experiment. If the reference axis is arbitrary, then there is no reason to apply the same reference axis to all atoms in a collection. Therefore, why does the SternGerlach experiment only show two bands, rather than a dispersion as each atom travels to a location on the plate as dictated by its own angular momentum projection? Finally, if it is "just" the angular momentum projection that's quantized, why is it called space quantization? Is this some sort of mild misnomer, or are the implications of angular momentum quantization going over my head? Does a.m. quantization imply something about quantization of position (or something else) across all coordinates in space? Thanks for any replies; I'm pretty confused on this topic. 



#2
Apr311, 11:47 AM

Sci Advisor
Thanks
P: 3,846

An atom does not keep a history. It does not remember the axis from the last time it was quantized. The SternGerlach apparatus imposes an axis and all the atoms must use it, and they will all have spin projection either +/ 1/2 along that axis. 



#3
Apr411, 11:08 AM

P: 90

Just as a circle cannot have an exact area (because pi is irrational) a perfect curve cannot exist  it must always be incremented in units and thus at some level be 'pixellated' you could even say quantized in a certain sense. This has consequences for our metric that we call space. Is it continuous?
(I thought this thread was about space quantization...) 



#4
Apr411, 04:46 PM

P: 41

What is space quantization? 



#5
Apr411, 05:16 PM

P: 267

Doesnt really describe why space itself is quantized, but maybe its more of a definition problem? 



#6
Apr511, 05:42 AM

P: 90





#7
Apr511, 10:56 AM

P: 41

The quantization of the angular momentum IS the quantization of the curve. Is this the case? If so, why? And what is "curve" referring to? The wavefunction by which the particle whose angular momentum is quantized is bound? 



#8
Apr511, 01:26 PM

P: 90

angular momemtum formula contains pi which is an irrational number and cannot have an exact value, so neither can angular momemtum  correct?
Is it a question then of what precision is being used before quantization occurs? 



#9
Apr511, 02:32 PM

Emeritus
Sci Advisor
PF Gold
P: 16,101

But these are issues for a different thread  they are a discussion of philosophical biases rather than anything else. There are honest, scientific reasons to explore theories involving the quantization of spacetime. (but I'm not entirely sure any of this has to do with the question in the opening post!) Back to the OP: could "space quantization" just be an abbreviation of "phasespace quantization"? Wiki's page on the latter was the second hit when I googled the phrase. 



#10
Apr511, 02:38 PM

Mentor
P: 11,221

The "space quantization" that Roo2 originally asked about is simply a short name for "quantization of the component of angular momentum along a specified direction." I don't know how that name came to be, but it goes back all the way to the days of the SternGerlach experiment in the 1920s, perhaps even earlier. [I now see that Hurkyl has suggested that it's short for "phasespace quantization" which sounds plausible to me.] The notion of space (and time) quantization in terms of Planck units or whatever, that people often ask about here on PF, is something different. It's a speculative concept and is not related to the "space quantization" of the preceding paragraph, as far as I know. 



#11
Apr511, 07:58 PM

P: 267

Thanks for clearing that up jtbell.




#12
Apr611, 08:49 AM

P: 41

Thanks jtbell, that clears things up for me!




#13
Apr611, 04:49 PM

P: 90

Its a question of precision. The precision of universal quantities must be limited. Thats also why we cannot get to zero separation and so get infinite forces. Suppose there will be no sensible reply to this. 



#14
Apr711, 08:36 AM

Sci Advisor
P: 1,867

Wavenspop, everything you said is a load of nonsense. You seem to be into computers, and trying to shoehorn both physics and mathematics into that kind of thinking.
The universe isn't a computer. As far as anyone knows, it doesn't work with discrete math. It doesn't have a special preference for integers. Space is not made up of 'pixels' or voxels, AFAIK not even in the more speculative theories jtbell mentions. In fact I believe that would violate a number of quite fundamental assumptions about how everything does work. (e.g. Noether's theorem). There is no 'question of precision'. The universe isn't a computer that needs to store digits somewhere, making exact representations of irrational numbers impossible. Besides which, every single integer can trivially be represented by an any number of infinite sums (e.g. 1 = 0.9999..)  just as pi can. So you're basically defying logic by claiming that integers are exact and things represented by an infinite series sum cannot be. There are also basic factual errors in what you're saying. There's an infinite number of curves whose area can be squared. A trivial example is the area under the parabolic curve 3x^{2} on the interval [0,1], which is unity. It's just that a circles and ellipses are not among those which can have an integer area with integer radii. That doesn't prove at all that they don't exist. It proves you can't draw a perfect circle on a computer screen, but as I already said, the universe doesn't work that way as far as anyone knows. Besides which, why should area specifically have to be integral? Every square with integer sides has an irrational diagonal, so you might as well argue that squares don't exist either. And you can "go to zero separation and get infinite forces". In an atom, two electrons (with opposite spin), modeled as point charges with a 1/r coulomb potential, will still have a nonzero probability of being in the same place at the same time. Because the infinity in the potential is canceled out by the infinity in the kinetic energy. (Here's a detailed and rigorous proof of that fact as well as some important properties of those cusps). Just because something might not be intuitive doesn't mean it's not logical. And if there's anything we know, it's that the universe obeys logic, not human intuition. 


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