A question about Quantum mechanics

[Severian]

If they predict different outcomes, but present technology cannot differentiate them, is that science?

 

Sure it is. Just because we are not technologically advanced enough to distinguish two different theories doesn't make them indistinguishable in principle. String theory, for example, can't be tested at the moment, but it can be tested in principle, so it is valid science.

[aommaster]

That's one way of interpreting the original statement, yes.

 

Do you mean that there are other ways of interpreting it?

[Conceptual]

The idea of parallel universes or extra dimensions is a mathematical artifact and should be taken literally with a grain of salt. Mathematics draws a picture on the plane of reason, i..e, cause and effect. Just like in art, one can create 3-D images on a flat piece of paper. If one looks at the artwork just the way the artist intends, it can look 3-D. If one looks at it from another angle one will notice is it actually 2-D. It may still be a good logical theory but does not reflect a 3-D integration of the universe.

 

To create 3-D from 2-D one needs a large number of rational planes each intersecting at different angles but with a common origin or common line. The line is better because it implies all good theories need to be to explain all the known data points instead of just one common data point. All these different planes reasoning will create a 3-D volume. They all together are helping us express an integrated understanding of the universe but none alone seem to be able to do whole thing. A 3-D theory would need to blend them all into one model.

[swansont]

Do you mean that there are other ways of interpreting it?

 

I haven't changed my mind since post #18.

[J.C.MacSwell]

Sure it is. Just because we are not technologically advanced enough to distinguish two different theories doesn't make them indistinguishable in principle. String theory, for example, can't be tested at the moment, but it can be tested in principle, so it is valid science.

 

Fair enough, although I did not realize String Theory had made any predictions.

 

My follow up question was with regard to the modelling stage. Prior to making predictions (while the model is not complete enough to form any, not merely noone actually making any) is that science?

 

I apologise if this seems trivial, just if you had a definite idea of where you draw the line I would like to hear it. (I'm interested, not just trying to be a pain)

[Mart]

Originally Posted by Swansont

Consider a spin 1/2 particle - the two states are "spin up" and "spin down." I can prepare that particle such that it is in both states, so that the wave function is a linear combination of the two. The particle is then said to be in a suerposition of the two states - the wave functions add together, following the principle of superposition. When I measure the particle's state, it can only be spin up or down, but it is not the case that it was in that one state all along.

Consider it considered. It seems like you're saying that the particle has no spin while it is not being measured. If so, how does the wave function "give" the particle a spin?

[Severian]

The idea of parallel universes or extra dimensions is a mathematical artifact and should be taken literally with a grain of salt. Mathematics draws a picture on the plane of reason' date=' i..e, cause and effect. Just like in art, one can create 3-D images on a flat piece of paper. If one looks at the artwork just the way the artist intends, it can look 3-D. If one looks at it from another angle one will notice is it actually 2-D. It may still be a good logical theory but does not reflect a 3-D integration of the universe.

[/quote']

 

It isn't just conceptual. It is a matter of how many coordinates you need to decribe an event. In 4 dimensions, each even has 4 numbers associated with it telling you where it happens. In 11 dimensions they will have 11 numbers. That is a fairly concrete difference.

[swansont]

Consider it considered. It seems like you're saying that the particle has no spin while it is not being measured. If so, how does the wave function "give" the particle a spin?

 

No, that's not what I'm saying. The particle is in both states, in the basis we are using. It is a spin 1/2 particle - that doesn't stop.

[Mart]

Originally Posted by swansont

The particle is in both states, in the basis we are using. It is a spin 1/2 particle - that doesn't stop.

Do you mean that it's spinning permanently and when we measure the spin we get the answer 1/2?

[Locrian]

He's saying the particle is in both states until it's measured. Remember, an object has spin, but it isn't "spinning" in any usual sense of the word, so it doesn't make sense to say that it's "spinning permanently."

[Mart]

Originally Posted by Locrian

He's saying the particle is in both states until it's measured. Remember, an object has spin, but it isn't "spinning" in any usual sense of the word, so it doesn't make sense to say that it's "spinning permanently."

Both states of what? Answer :spin. But if spin is not your everyday spin then what is it?

[5614]

Both states, as in it has up and down spin.

 

Spin in QM = http://en.wikipedia.org/wiki/Spin_%28physics%29

[Mart]

Thanks for the link 5614. So since particles like electrons are considered to have no volume (point particles) it's not easy to say how they can be spinning. Nevertheless QM uses the notion of spin as angular momentum to describe the behaviour of the electron. Sounds to me like a dodgy accounting device but if it delivers the goods who cares!

[5614]

Sounds to me like a dodgy accounting device but if it delivers the goods who cares!

It only sounds dodgy from a classical point of view.

[swansont]

Thanks for the link 5614. So since particles like electrons are considered to have no volume (point particles) it's not easy to say how[/i'] they can be spinning. Nevertheless QM uses the notion of spin as angular momentum to describe the behaviour of the electron. Sounds to me like a dodgy accounting device but if it delivers the goods who cares!

 

AKA intrinsic angular momentum - the particles are not physically spinning, as has been noted. It does sound dodgy at first, but after you do the experiments, you find that it's correct. The quantum world does not necessarily behave as the macroscopic world does, so you get into trouble assuming macroscopic behavior will hold.

[BhavinB]

Actually spin is a correction of something that quantum mechanics does not predict. You can call it dodgy, but the angular momentum interpretation is complete in that it describes all the properties we have noticed about spin.

 

More interestingly, the Dirac equation DOES predict spin.

[5614]

You can't really say QM does not predict spin.

 

When QM was originally being discovered anomalies in the results from experiments were noticed. The only way to patch up all of these anomalies was to say that spin does exist.

 

The only time QM didn't predict spin was when it wasn't fully discovered and even at that point anomalies in results were noticed, these anomalies were caused by spin. QM notices and the experiments predict something is there, this something we know as spin. So you could say QM does predict spin.

[BhavinB]

I say QM doesn't predict spin in the fact that you can't start with the Schroedinger equation and derive some property of particles that implies it has internal angular momentum (ie spin).

 

However, if you use the not so used, and incorrect Dirac equation, you can derive the concept of spin theoretically. The same goes for any of the proposed string theories...they all must theoretically explain spin.

 

If you look in any quantum mechanics book, they will always say a particle total wavefunction is the multiplication of its spatial distribution and its spin distribution. What they are doing is correcting for the fact that QM cannot derive spin.

[5614]

I say QM doesn't predict spin in the fact that you can't start with the Schroedinger equation and derive some property of particles that implies it has internal angular momentum (ie spin).

You're saying that QM doesn't predict spin just because you can't derive spin from Schrödinger's equation???

 

I'm sure you know that there's more to QM than Schrödinger's equation! So you can't say that just because Schrödinger's equation doesn't show spin neither does QM.

 

It's like looking at 1 human who is male and concluding that all humans are male. Just because 1 part of QM (Schrödinger's equation) doesn't predict spin, doesn't mean none of QM predicts spin.

[BhavinB]

Alright, I'll concede that SE is not all of QM. But the obvious major part of QM is solutions of the quantum mechanical hamiltonian which we can describe for any system. There is in effect no way to derive spin from any hamiltonian...which is exactly why there is no QM derivation of spin shown in ANY quantum mechanics book.

 

The true 'proof' of spin is in experiment, and we correct all our particle wavefunctions accordingly.

[5614]

Just for some info of when "spin" was first introduced.

 

In the 1920's physicists were trying to explain different parts of physics and part of this explanation came from Pauli who assigned electrons 4 different quantum numbers.

 

Three of these from the Bohr model (angular momentum, the shape of its orbit & its orientation). The 4th number was some other property of the electron that could only be one of 2 possible values.

 

Ralph Kronig proposed that electrons had instrinsic spin of 1/2, and the spin would either be aligned to the magnetic field of the atom or antiparallel to it. However Pauli strongly disagreed with this strongly, so Kronig gave up the idea.

 

Less than 1 year later the same idea occurred to 2 other physicists who published papers on it and the idea was excepted. The idea was slightly refined and was then accepted by all, even by Pauli.

 

In 1932 Bohr proved that "spin" cannot be measured by any classical experiment. It is a property that only appears in QM and has no classical meaning.

[5614]

There is in effect no way to derive spin from any hamiltonian...which is exactly why there is no QM derivation of spin shown in ANY quantum mechanics book.

 

The true 'proof' of spin is in experiment' date=' and we correct all our particle wavefunctions accordingly.[/quote']

The idea of 'spin' certainly came from an experimental problem. However spin only occurs in quantum interactions. It has nothing to do, in any way, anything to with classical physics.

 

As far as classical physics go, spin doesn't exist.

 

As far as quantum interactions and thus QM goes, spin must exist.

 

It is because of that that I say that QM does predict spin. Maybe it was originally from an experiment, but so what?

 

To have a fully working and correct quantum model you need spin. If you don't have spin then QM doesn't work, it says something is wrong, something is missing, it predicts something you don't know. This something is spin and QM says it must exist, so I say QM predicts spin.

[BhavinB]

lol...ok. Lets look at the word "predict".

 

'To state, tell about, or make known in advance, especially on the basis of special knowledge.'

 

Based on everything quantum mechanics derives about spatial and energy relations, it does not in advance predict spin. For example, quantum mechanics predicts the energy levels in a quantum well. Quantum mechanics predicts the spatial distribution of electrons in the hydrogen atom. Quantum mechanics predicts that the H2 molecule will form but the He2 molecule won't. QM also derives the quantization of angular momentum.

 

However, QM cannot in advance predict the existance of spin. Fortunately for us, Spin is a type of angular momentum and scientists have found that appending all spatial functions with spin angular momentum functions is the correct answer.

 

Perhaps you are confusing the fact that we can use our knowledge of spin and angular momentum in quantum mechanics to predict new things like spin transistors. But don't be confused in thinking that it is derived in quantum mechanics...it never was. Saying its not classical doesn't mean it was derived quantum mechanically.

[5614]

Ah, I see what you mean.

 

So for example; using our knowledge of electron configuration we know that H2 forms and He2 doesn't.

 

Whereas in regards to spin; something is missing which leads to observed results.

 

The missing thing is spin. It is not actually predicted by QM, more we have a set of observed results from which we can deduce that spin exists.

 

The true 'proof' of spin is in experiment, and we correct all our particle wavefunctions accordingly.

So if we didn't correct out wavefunctions by including spin then the wavefunctions would be incorrect. However this is not as such deriving it, more it is proving that it must exist.

 

You say that predict means:

'To state, tell about, or make known in advance, especially on the basis of special knowledge.'

Well QM does make spin known because we have our experiment which returned 'dodgy' results ('dodgy' if you exclude spin), from which we conclude that spin must exists. But I suppose you are saying that this is not a prediction because you didn't predict it would happen you noticed that it did.

 

The true 'proof' of spin is in experiment

Okay, point taken.