Spin Explained for the "Wikipedia Physicist" - No QM Needed!

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I don't understand electron spin. What is it? Does spin have units? Does it do anything like electric charge or gravitation does? What does it represent? Any help for a "wikipedia physicist" (as I call myself) would really help. Just keep in mind: I haven't taken a class in QM.
 
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It's one of the fundamental attributes of a quantum system. It's in the same category with mass/energy. From a rigorous viewpoint, it's linked to the global rigid symmetry of a flat space-time. To put spin in general relativity requires some advanced tricks in differential geometry.
 
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Yes, of course, but, for example, what does spin measure, and in what units? Mass has kg, and energy has J...
 
If you haven't studied QM, you won't understand this, but you should look at it anyway, because it might give you an idea why no one is going to be able to explain it to you in a way you'll be entirely satisfied with. The extremely short version is that it's a property that we can see that particles must have if we combine the principles of QM with the assumption that space is rotationally invariant.

The result of a measurement of a spin component operator is expressed in the same units as angular momentum. In terms of units of mass, length and time, it's kg m2/s, but you could also express it as Js (Joule-seconds).
 
Spin is the angular momentum (therefore it has units) of a quantum object calculated/measured in a reference system in which that object has 0 orbital angular momentum. One such system of reference is, of course, the one attached to the object itself.
 
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You can think of spin as the intrinsic angular momentum of a particle (rather than say, orbital angular momentum).

E.g. If the Earth is moving around the sun, and rotating, the orbit is the regular angular momentum, while the rotation is the "spin" angular momentum.

This is JUST a tool to help you make the concept a bit more concrete. DON'T take it literally. Particles, as far as we know are point particles and therefore can't really spin like the Earth does. Also, if you take an upper limit for the size of the electron, and try to find out how fast it must "spin" then a "point" at the electron's equator would need to be moving faster than the speed of light. This is no good! So don't think of this analogy in the literal sense.
 
Thanks for all of these. My first mistake, I think, is that I thought of spin as literal, and couldn't figure out how electron clouds could "spin". Now I see the truth: I will not understand without much more background knowledge than wikipedia can provide. (it might help to know more about eigenstates than I can figure out from German, for example)

Thanks!
 
Char. Limit said:
I don't understand electron spin. What is it?

It is very difficult for you to consider electron spin as real spinning.

The main reasons are as follows,
1 The electron size is too small, so by equating the angular momentum of the spinning sphere of the electron to 1/2hbar, the electron sphere speed leads to more than 100 times the speed of light.

2 The spinning electron will not go back to their original forms when they are rotated by an angle of 2 pi.
(This is called "two-valued", so when the angle is 4 pi, they go back.)

To speak simply, Spin is "a magnetic moment", because the magnetic moment can be measured by the real experiment.

But why we call it "spin"? To know that reason, we have to understand the spin history.
The most important phenominon of this was "an anomalous Zeeman effect", I think.

Because it is possible that the Stern-Gerlach experiment and the fine structure (energy difference between 2P1/2 and 2P3/2) can be explained also by the Bohr-Sommerfeld model. (For example, see this.)

They tried to explain about the many spectrum lines under the magnetic field using the spin-orbital interaction.
(But to be precise, the one electron atom hydrogen usually shows the normal Zeeman effect. and Lithium tend to show Paschen-Back effect. So the anomalous Zeeman effect is a little complicated to explain.)

Sorry for a little long story.
 
Char. Limit said:
Thanks for all of these. My first mistake, I think, is that I thought of spin as literal, and couldn't figure out how electron clouds could "spin". Now I see the truth: I will not understand without much more background knowledge than wikipedia can provide. (it might help to know more about eigenstates than I can figure out from German, for example)

Thanks!

As others have said, spin is intrinsic angular momentum, and is assigned discreet values (unlike continuous values for orbits or rotation). The electron, eg, has two discreet (key word) values: 1/2 and -1/2 spin.

Please understand that the guy who coined the intrinsic angular momentum of a particle as "spin" is a complete imbicile. The term is misleading.

For the electron, "spin" is synonymous with "charge." You have a positive charge (same as +1/2 spin) and a negative charge (same as -1/2 spin).
 
  • #10
ytuab said:
It is very difficult for you to consider electron spin as real spinning.

The main reasons are as follows,
1 The electron size is too small, so by equating the angular momentum of the spinning sphere of the electron to 1/2hbar, the electron sphere speed leads to more than 100 times the speed of light.

2 The spinning electron will not go back to their original forms when they are rotated by an angle of 2 pi.
(This is called "two-valued", so when the angle is 4 pi, they go back.)

To speak simply, Spin is "a magnetic moment", because the magnetic moment can be measured by the real experiment.

But why we call it "spin"? To know that reason, we have to understand the spin history.
The most important phenominon of this was "an anomalous Zeeman effect", I think.

Because it is possible that the Stern-Gerlach experiment and the fine structure (energy difference between 2P1/2 and 2P3/2) can be explained also by the Bohr-Sommerfeld model. (For example, see this.)

They tried to explain about the many spectrum lines under the magnetic field using the spin-orbital interaction.
(But to be precise, the one electron atom hydrogen usually shows the normal Zeeman effect. and Lithium tend to show Paschen-Back effect. So the anomalous Zeeman effect is a little complicated to explain.)

Sorry for a little long story.

Why isn't your log-on name ytuaeb? Just asking...
 
  • #11
Neo_Anderson said:
As others have said, spin is intrinsic angular momentum, and is assigned discrete values (unlike continuous values for orbits or rotation). The electron, eg, has two discrete (key word) values: 1/2 and -1/2 spin.

Please understand that the guy who coined the intrinsic angular momentum of a particle as "spin" is a complete imbicile. The term is misleading.

For the electron, "spin" is synonymous with "charge." You have a positive charge (same as +1/2 spin) and a negative charge (same as -1/2 spin).

Wait, electrons with positive 1/2 charge?
 
  • #12
It's just a convention that they have -1/2. They could have very well had +1/2 and their antiparticles -1/2.

There are, probably, 10 or more places in physics where "sign" conventions occur. Surely, one is forced to reconcile them all to get a clear picture.
 
  • #13
Don't electrons have both positive (up) and negative (down) spins? I seem to remember that from AP Chem...
 
  • #14
up and down spins are just the 2 "degrees of freedom" afforded to the electron. The electron's spin can either be directed in the direction of the positive Z axis or the negative Z axis - giving you both up and down. This is completely dependent on how you define your Z-axis.
 
  • #15
The "up" versus "down" issue is probably linked to a convention to disseminate the 2 independent eigenvectors for the spin operator of a spin 1/2 system:

\left|\uparrow\right\rangle =\left|\frac{1}{2},\frac{1}{2}\right\rangle and, of course,

\left|\downarrow\right\rangle =\left|\frac{1}{2}, -\frac{1}{2}\right\rangle
 
  • #16
OK, I think I might be getting a (very) basic idea now. One thing confuses me though: how can electron "spin" be synonymous with charge, if an electron has one possible value for charge, and two for "spin"?

Also, in the equation for the post above, what are those strange | and > symbols?
 
  • #17
Spin is not synonymous with charge. It is, however, linked to the magnetic moment.

That's bra-ket notation he's using. Those | > symbols represent a "ket". It's a vector in Hilbert space.
 
  • #18
OK... I looked up the magnetic moment, and found that the unit for that is J/T. Soo...

If magnetic moment and angular momentum are related by a g-factor of 2 (why 2?), does this g-factor have a value of 2 T/s?

Or am I just insane?

(Also, what is a "magnetic moment" in macroscopic, or at least understandable terms?)

Progress is being made, I'm closer to understanding than I was before. Don't give up on me now! (Not that you would)
 
  • #19
Char. Limit said:
I don't understand electron spin. What is it?

If you want another way of looking at it, you are doing the natural thing of thinking of the electron as a spinning ball. But instead, how about thinking of a point particle as a location that arises by the kinds of questions we ask.

So to start with, anything might be "there". Then we narrow down the there-ness to what might exist at a point.

It is a little like coralling sheep into a pen perhaps. First they are possibly all over the place, and then we constrain their location.

Then having located there-ness to a 3D point, there are still aspects of this point that remain as yet unconstrained. Like a potential to be rotating on the spot. Further questions can then polarise this point - fix a direction and quantity of spin.

So just see spin as the last refuge of freedom for something that has already been restricted to a spatial point. Then we can go in and constrain that aspect of its freedom as well.

With the sheep in a pen analogy, you can see we may have confined them to a point, yet we have not yet stopped them milling about. And maybe we can imagine polarising the state of those sheep by some kind of measurement, like having the sheep dog go in or do something else that makes them line up in some coherent circular fashion.

The sheep could potentially be going in many directions (well not many as the pen is a 2D plane rather than 3D sphere) and then measurement limits the action - it imposes a further constraint on the system's naked freedoms.
 
  • #20
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That sheep-in-a-pen analogy may be (no offense to the others) the best I've seen yet. Just one thing. An electron is an area of high probability, not a particle, so it's... not a 3-D point? Or am I assuming something stupid again?
 
  • #21
Matterwave said:
Spin is not synonymous with charge. It is, however, linked to the magnetic moment.

That's bra-ket notation he's using. Those | > symbols represent a "ket". It's a vector in Hilbert space.

I'm pretty certain that with the electron, spin is the same thing as charge.
 
  • #22
Char. Limit said:
OK... I looked up the magnetic moment, and found that the unit for that is J/T. Soo...

If magnetic moment and angular momentum are related by a g-factor of 2 (why 2?), does this g-factor have a value of 2 T/s?

Or am I just insane?

(Also, what is a "magnetic moment" in macroscopic, or at least understandable terms?)

Progress is being made, I'm closer to understanding than I was before. Don't give up on me now! (Not that you would)

G-factors are actually quite complicated, and to really understand them you'd need to go into relativistic quantum mechanics. For a normal Q.M. understanding, just take the g-factors as given.
 
  • #23
Neo_Anderson said:
I'm pretty certain that with the electron, spin is the same thing as charge.

Charge and spin are 2 completely separate concepts. I don't see why they would be "the same" for an electron.

The units of Charge is coulombs, and the units of Spin is J*s.
 
  • #24
I just thought that since charge had one possible value (-1) and spin had two (1/2, -1/2), they can't be EXACTLY the same. Can they?
 
  • #25
Neo_Anderson said:
I'm pretty certain that with the electron, spin is the same thing as charge.

Don't neutral particles have spin?
 
  • #26
Does the neutrino have spin? It's neutral (and elementary)...
 
  • #27
Char. Limit said:
That sheep-in-a-pen analogy may be (no offense to the others) the best I've seen yet. Just one thing. An electron is an area of high probability, not a particle, so it's... not a 3-D point? Or am I assuming something stupid again?

The view I am taking would be the top-down, condensed matter approach - solitons, Laughlin, etc.

The electron "is" just a persistent resonance or standing wave in this way of thinking.

And it is not - as yet - an official QM model. Although clearly the argument would go that we can only get Planck-close to a 3D point-like constraint.
 
  • #28
apeiron said:
The view I am taking would be the top-down, condensed matter approach - solitons, Laughlin, etc.

The electron "is" just a persistent resonance or standing wave in this way of thinking.

And it is not - as yet - an official QM model. Although clearly the argument would go that we can only get Planck-close to a 3D point-like constraint.

What argument says that? And what is Planck-close? 6.6*10^-34 m?
 
  • #29
OK, you guys are correct; charge is not synonymous with spin. I just found out that charge is a classical concept, not a quantum one.
 
  • #30
Char. Limit said:
What argument says that? And what is Planck-close? 6.6*10^-34 m?

Now you are asking far more difficult questions. And I would have to get too speculative.

Though one concrete example to google would be the mass of the proton. Consider how much of a proton's mass is due to the confinement of the quarks (most of it), and how much due to the mass of the quarks themselves (hardly any). Because we "know" the small space in which each quark resides, its momentum or average kinetic energy increases to match.

An electron is of course thought to lack such internal structure. Though if you take knot approaches or others arising from gauge symmetry, you could take these being about the way that symmetrical (when unconfined) QM potential becomes symmetry-broken when constrained sufficiently in soliton or quasiparticle fashion by an observing context.
 
  • #31
What is Planck-close, though? Are you talking about h?
 
  • #32
Char. Limit said:
What is Planck-close, though? Are you talking about h?

Yes, I did mean Planck-scale, so values yo-yoing around that limit on locatedness.
 
  • #33
Heisenberg said you can't exactly locate anything. Thus, the electron's position is a permanent unknown.
 
  • #34
Char. Limit said:
Heisenberg said you can't exactly locate anything. Thus, the electron's position is a permanent unknown.

That's a misstatement of the uncertainty principle. And what's it got to do with the topic?
 
  • #35
A poster was talking about the position of the electron... ah, never mind. I even forgot to consider "and momentum" in my reasoning. I think I'm not thinking well at 12:30 A.M.
 
  • #36
Just my two cents:

Spin is intrinsic angular momentum - in some regards a completely classical concept, although very hard to imagine because it is very unfamiliar in the classical context. (For the experts, nothing prevents you doing a classical field theory with dirac spinor fields - the representation structure of the Poincare symmetry is the same as ever)

Because the world is quantum mechanical, the possible values of this intrinsic angular momentum are quantised. The quantisation structure is as follows:
The total intrinsic angular momentum squared is always found to be s(s+1)\hbar^2. (hbar has units of angular momentum) where the value of s depends on which particle you are studying, but is always an integer or half integer.
For the electron, proton, neutron, s = 1/2. People will say 'the electron is spin 1/2' which means, the total intrinsic angular momentum is
\hbar\sqrt{\frac{1}{2}(\frac{1}{2}+1)}
Obviously it is easier to refer the the value 's', and just say spin 1/2 (since physicists always know how to relate the value of 's' back to the measured angular momentum). The value 's' is called the spin quantum number.

(A good quantum number is a symbol (not necessarily a number) which labels quantum mechanical stationary states according to the value of a conserved quantity).

Charge is also a quantum number, but it is complicated to explain why.

If something has a 'magnetic moment' it means it behaves like a tiny bar magnet. If you know about solenoids, hopefully you'll remember that when charge moves in a circle, it creates a magnetic field - when a charge has some angular momentum it creates a magnetic field.

It's not obvious, but this property is true of intrinsic angular momentum also. The intrinsic angular momentum of the electron creates a magnetic field - the magnetic moment of the electron.

In general, there will be some relation between the intrinsic angular momentum of some particle, and the magnetic moment it has, but this is complicated to work out. The relation is the g-factor.
 
  • #37
This also explains it to me very well. Thanks.

The property is true of intrinsic angular momentum because the particle itself has a charge, right?
 
  • #38
peteratcam said:
Just my two cents:

Spin is intrinsic angular momentum - in some regards a completely classical concept, although very hard to imagine because it is very unfamiliar in the classical context. (For the experts, nothing prevents you doing a classical field theory with dirac spinor fields - the representation structure of the Poincare symmetry is the same as ever)

There's no reason to talk of spin in the context of classical physics. Of all the fields we know, only 2 (em and gravitational) have a classic-level existence (they are the only interactions with infinite range). They're interaction fields to be more precise.

If you apply the Noether theorem to the e-m Lagrangian for the restricted Lorentz invariance, you get the angular momentum tensor composed of 2 parts: the orbital one and the "intrinsic" one. The "intrinsic" can be thought of "spin" only when discussing the quantization of the e-m field. Without the quantization, one doesn't have the <particle> interpretation any classical field (as I said above, there are only 2 classical fields altogether), thus can't talk about the spin of a particle, or total spin of a system of particles.

As I said in another thread, there's no spin outside flat space relativity, there's no spin outside quantum mechanics.
 
  • #39
Char. Limit said:
The property is true of intrinsic angular momentum because the particle itself has a charge, right?

No, charge is a separate property. Neutrons have no charge and half spin. So do neutrinos. Photons have no charge and integer spin.
 
  • #40
Char. Limit said:
This also explains it to me very well. Thanks.

The property is true of intrinsic angular momentum because the particle itself has a charge, right?

I think this is the state of affairs, although high energy physics is not my thing, so I hope someone will correct me if they know otherwise:
If a particle has charge, and has spin, then it will have a magnetic moment.
If a particle has charge and no spin, then it will not have a magnetic moment.
If a particle has no charge, but does have spin, then it might have a magnetic moment.
 
  • #41
bigubau said:
There's no reason to talk of spin in the context of classical physics. Of all the fields we know, only 2 (em and gravitational) have a classic-level existence (they are the only interactions with infinite range). They're interaction fields to be more precise.

As I said in another thread, there's no spin outside flat space relativity, there's no spin outside quantum mechanics.

In the context of classical physics, I agree. But in the context of understanding classical field theory in Minkowski space (which in principle, a mathematician in 1905 might have done, well before the Stern-Gerlach experiment), then the spinor representations of the Lorentz symmetry are still interesting.
 
  • #42
alxm said:
No, charge is a separate property. Neutrons have no charge and half spin. So do neutrinos. Photons have no charge and integer spin.

What I mean is that if a charged object is spinning, it exerts a magnetic field, right? So an electron with angular momentum would have a magnetic moment, because it is charged.

Does a neutron have a magnetic moment?
 
  • #43
Char. Limit said:
I don't understand electron spin. What is it? Does spin have units? Does it do anything like electric charge or gravitation does? What does it represent? Any help for a "wikipedia physicist" (as I call myself) would really help. Just keep in mind: I haven't taken a class in QM.

according to milo wolff. in an all wave model, electron spin is as a spherical rotation...

http://www.youtube.com/watch?v=uKrM...2E390874&playnext=1&playnext_from=PL&index=42


Spherical Rotation

Rotation of the inward quantum wave at the center to become an outward wave is an absolute requirement to form a particle structure. Rotation in space has conditions. Any mechanism that rotates (to creates the quantum "spin") must not destroy the continuity of the space. The curvilinear coordinates of the space near the particle must participate in the motion of the particle. Fortunately, nature has provided a way - known as spherical rotation - a unique property of 3-D space. In mathematical terms this mechanism, according to the group theory of 3-D space, is described by stating that the allowed motions must be represented by the SU(2) group algebra which concerns simply-connected geometries.

Spherical rotation is an astonishing property of 3-D space. It permits an object structured of space to rotate about any axis without rupturing the coordinates of space. After two turns, space regains its original configuration. This property allows the electron to retain spherical symmetry while imparting a quantized "spin" along an arbitrary axis as the inward waves converge to the center, rotate with a phase shift to become the outward wave, and continually repeat the cycle.

The required phase shift is a 180o rotation that changes inward wave amplitudes to become those of the outward wave. There are only two possible directions of rotation, CW or CCW. One choice is an electron with spin of +h/4pi, and the other is the positron with spin of -h/4pi.

It is an awesome thought that if 3-D space did not have this geometric property of spherical rotation, particles and matter as we know them could not exist.
 
  • #44
watcher said:
according to milo wolff. in an all wave model, electron spin is as a spherical rotation...

http://www.youtube.com/watch?v=uKrM...2E390874&playnext=1&playnext_from=PL&index=42

Spherical Rotation

Rotation of the inward quantum wave at the center to become an outward wave is an absolute requirement to form a particle structure. Rotation in space has conditions. Any mechanism that rotates (to creates the quantum "spin") must not destroy the continuity of the space. The curvilinear coordinates of the space near the particle must participate in the motion of the particle. Fortunately, nature has provided a way - known as spherical rotation -
After two turns, space regains its original configuration. This property allows the electron to retain spherical symmetry while imparting a quantized "spin" along an arbitrary axis as the inward waves converge to the center, rotate with a phase shift to become the outward wave, and continually repeat the cycle.

The required phase shift is a 180o rotation that changes inward wave amplitudes to become those of the outward wave.
It is an awesome thought that if 3-D space did not have this geometric property of spherical rotation, particles and matter as we know them could not exist.

I think it is quite natural for us to dream of a real particle and a real spinning of the electron. (These are inseparable.)
Your statement is very interesting, but I'm afraid it is imposibble to treat the spin as a real spinning in the quantum mechanics(QM).

You said the electron spin is "a spherical rotation". But how fast is the electron rotating(spinning) ?

Foundations of Quantum Physics by Charles E.Burkhardt (in page 264)
------------------------------
They imagined that the electron is a spherical shell having total charge e uniformly smeared over its surface, reminiscent of the model used to derive the classical radius of the electron in Section 1.2.5.
This spinning sphere creates a magnetic moment identical with that of a bar magnet.
Is this model consistent with the classical radius of the electron? No-- as can be seen by
equating the angular momentum of the spinning sphere to 1/2 hbar. Solving for the speed of a point on the sphere leads to a speed that is roughly 100 times the speed of light.
--------------------------------

So If the spinning speed does not exceed the speed of light, the electron must be 100 times bigger than the classical radius size(2.8 x 10^-15 m) or an proton (10^-15 m).

But of course, by the scattering experiment or the fact of the electron capture, the electron size must be much smaller than that. (In any state and any process, the electron always has spin 1/2, doesn't it?)

And in your model, after two turn, suddenly the electron field seems to regain its original configuration by returning the fully-twisted field to the untwisted original field artificially. This does not seem to be changing continuously like e^{i\phi/2} . Is this contradictry to the experimental results of rotating the spinning neutron in this thread ?

Do I misunderstand something?

I think if we can consider an electron as a real particle with real spinning in QM, we could have already done this a long time ago (in 1920's ~1930's). If you use some "new instruments" which could not be made at that time, this is a different matter.
 
  • #45
watcher said:
according to milo wolff. in an all wave model, electron spin is as a spherical rotation...
...
Spherical rotation is an astonishing property of 3-D space. It permits an object structured of space to rotate about any axis without rupturing the coordinates of space. After two turns, space regains its original configuration. This property allows the electron to retain spherical symmetry while imparting a quantized "spin" along an arbitrary axis as the inward waves converge to the center, rotate with a phase shift to become the outward wave, and continually repeat the cycle.
You should be more careful about what sources you're referring to at Physics Forums. This Milo Wolff doesn't seem to be an actual physicist, and more importantly, he doesn't seem to publish in peer reviewed journals. Also, the things you said about electron spin and rotations are very misleading.
 
  • #46
Nobody knows EXACTLY whan quantum mechanical spin is, anymore than we know exactly what "charge" is...both do have real world macroscopic effects we can observe/measure. In general spin is a degree of freedom of a particle. The polarization of light is a physical manifestation of quantum mechanical spin.

Roger Penrose notes:
Photons are indeed particles that possesses spin, but being massless, their spin behaves in a way that is a little different from the more usual spin of a massive particle (electron or proton) as necessarily spinning about its direction of motion.

From his book, THE ROAD TO REALITY, where he also goes into a lot of math related to spin ...too much of which is over my head...
 
  • #47
ytuab said:
I think it is quite natural for us to dream of a real particle and a real spinning of the electron. (These are inseparable.)
Your statement is very interesting, but I'm afraid it is imposibble to treat the spin as a real spinning in the quantum mechanics(QM).

what do you mean by real? you probably meant non-classical spin.

You said the electron spin is "a spherical rotation". But how fast is the electron rotating(spinning) ?

sorry if my post mislead you. let me try again.
space is what rotates in a spherical way. spin is the result of phase shift ( from up spin to down spin, vv) due to the meeting of the so called advanced and retarded emf waves (feynman),
the electron is the particle effect at the center of these waves or the amplitude of these quantum waves.

I think if we can consider an electron as a real particle with real spinning in QM, we could have already done this a long time ago (in 1920's ~1930's). If you use some "new instruments" which could not be made at that time, this is a different matter.

yes i think it is misleading to think of electron spin as a classical spin, that is a spinning spherical particle. but i thought i mentioned that the model i am referring is an all wave model as proposed by Schrodinger. whereas the particle does not spin but space spins and in turn "create" a particle ...

During this period Schrödinger turned from mainstream quantum mechanics' definition of wave-particle duality and promoted the wave idea alone causing much controversy. - wiki


The particle can only appear as a limited region in space in which the field strength or the energy density are particularly high. (Albert Einstein, Metaphysics of Relativity, 1950)

.
 
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  • #48
Fredrik said:
You should be more careful about what sources you're referring to at Physics Forums. This Milo Wolff doesn't seem to be an actual physicist, and more importantly, he doesn't seem to publish in peer reviewed journals. Also, the things you said about electron spin and rotations are very misleading.

fredrick and folks,

i don't like to appear like i am pitching for milo but his biography is in the internet, judge for yourselves if his "not so mainstream science idea of all wave model of matter" is not worthy of physics forum.

perhaps my reply to ytuab clarify some of the confusion.
 
  • #49
watcher said:
i don't like to appear like i am pitching for milo but his biography is in the internet, judge for yourselves if his "not so mainstream science idea of all wave model of matter" is not worthy of physics forum.
I sympathize with this to some degree, but the policy here at PF is to only discuss things that have already been judged, by well-known and respected science journals. So this is actually against the forum rules. The James Randi Educational Foundation has a good forum for those who want to discuss material that isn't allowed here.
 
  • #50
Fredrik said:
I sympathize with this to some degree, but the policy here at PF is to only discuss things that have already been judged, by well-known and respected science journals. So this is actually against the forum rules. The James Randi Educational Foundation has a good forum for those who want to discuss material that isn't allowed here.

understood
 
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