Schrödinger local and deterministic?

[Gerenuk]

That'd be great. I just want to mention that I've seen Bell's-inequality-like proofs, but they use a different model/language, so that I still don't know at which point locality is lost. Ideally I'd like to see something which states why the mathematical form of the R process is non-local. Maybe $f(x)=\sum_{x'}g(x,x')$? Whatever the correct definition of non-local is :)

 

[Demystifier]

There have been many QM Interpretation thread, but I haven't found this question answered:

Taking aside the fact that a complex probability amplitude is not something we can picture, is the Schrödinger equation local and deterministic at once?

Schrödinger equation is certainly deterministic, there is no doubt on it. However, the question whether it is also local is more subtle. Since wave function lives in the configuration space and not in the ordinary 3+1 space, what does it even MEAN to be "local"?

However, the locality of the Hamiltonian (which is an important ingredient of the Schrödinger equation) is a well defined concept. So we can say that Schrödinger equation is "local" in the sense that realistic quantum systems are based on a local Hamiltonian. On the other hand, we can also say that the Schrödinger equation is "nonlocal" in the sense that the quantity it describes - the wave function - is not a local object. An even more precise terminology is not that the wave function is "nonlocal", but that it is NONSEPARABLE.

 

[Gerenuk]

On the other hand, we can also say that the Schrödinger equation is "nonlocal" in the sense that the quantity it describes - the wave function - is not a local object. An even more precise terminology is not that the wave function is "nonlocal", but that it is NONSEPARABLE.

Can you write this down mathematically? I believe in physics you should never trust words alone unless both parties know exactly which mathematics stands behind it. Because once I learned the maths for some advanced topics I started noticing how much rubbish me and other people were talking before, when we knew only words, i.e. popular science.

Edit: preferably using non-locality and not non-separability. Unless you can find a very good proof to draw the connection.

 

[Naty1]

Post # 7 by the OP
"Now I'm trying to get some ideas to understand how determinism gets lost."

Here is how Roger Penrose describes the issue, and it adds a bit of detail to Pio's post #21 above:
(from his talk commemorating Stephen Hawking 60th birthday)

Either we do physics on a large scale, in which case we use classical level physics; the equations of Newton, Maxwell or Einstein and these equations are deterministic, time symmetric and local. Or we may do quantum theory, if we are looking at small things; then we tend to use a different framework where time evolution is described... by what is called unitary evolution...which in one of the most familiar descriptions is the evolution according to the Schrödinger equation: deterministic, time symmetric and local. These are exactly the same words I used to describe classical physics.

However this is not the entire story... In addition we require what is called the "reduction of the state vector" or "collapse" of the wave function to describe the procedure that is adopted when an effect is magnified from the quantum to the classical level...quantum state reduction is non deterministic, time-asymmetric and non local...The way we do quantum mechanics is to adopt a strange procedure which always seems to work...the superposition of alternative probabilities involving w, z, complex numbers...an essential ingredient of the Schrödinger equation. When you magnify to the classical level you take the squared modulii (of w, z) and these do give you the alternative probabilities of the two alternatives to happen...it is a completely different process from the quantum (realm) where the complex numbers w and z remain as constants "just sitting there"...in fact the key to keeping them sitting there is quantum linearity...

 

[yoda jedi]

Consistent yes, but with not as much predictive power. They do not predict the violation of the inequality without completing decoherence with the last part of the R process, which consists in picking one of the possible results out of many, in an undeterministic way.

right, an adscititious "collapse" unlike of intrisic.
because superpositions persist, MWI is deterministic.

Because the R process makes experimental predictions that the U process doesn't. Example, that YOU will get this or that result when you measure a given system in a given way¹ If you keep the U process only and use it to built a many world interpretation², you loose the definition of "you", and the above experimental prediction is no more defined.

1.-Forced.
2.-or you can reduce R.

 

[Naty1]

And here's how Carlo Rovelli describes a related issue: QM vs GR:

(http://www.cpt.univ-mrs.fr/~rovelli/book.pdf) thanks to Marcus...

QM was formulated using an external time variable (the “t” in the Schrödinger equation) or a FIXED non dynamical spacetime (the spacetime on which Quantum field theory is defined). But this external time variable and fixed background spacetime are incompatible with general relativity. In turn GR was formulated in terms of Riemannian geometry assuming that the metric is a smooth and deterministic dynamical field. But QM requires that any dynamical field be quantized: at small scales it manifests itself in discrete quanta and is governed by probabilistic laws. We have learned from GR that spacetime is dynamical and we have learned from QM that that any dynamical entity is made by quanta and can be in probabilistic superposition states.

 

[Pio2001]

I don't see a sandbox in the forums, and LaTeX behaves strangely in the preview form. Let me try and see if it works.

Gerenuk, it is easier for me to describe the EPR experiment with spin 1/2 particles because I have alreay all the equations written in LaTeX.

I start from the following initial state vector :

$$|\Psi\rangle = \frac{1}{\sqrt{2}} ( {|+\rangle_1} \otimes {|-\rangle_2} - {|-\rangle_1} \otimes {|+\rangle_2} )$$

Is it displayed properly ?

 

[Gerenuk]

You have to use small letters for the (tex] tag.

Let me try again:
$$|\Psi\rangle = \frac{1}{\sqrt{2}} ( {|+\rangle_1} \otimes {|-\rangle_2} - {|-\rangle_1} \otimes {|+\rangle_2} )$$

But really don't forget to introduce a definition of non-local and show why the R process explicitely is non-local. Because I know the Bell-type derivations. I just don't know where the non-locality creeped in.

 

[Pio2001]

Here is a description of an EPR experiment with two particles of spin 1/2.

I'll point out the non-locality mathematically. However, I won't use Schrödinger's equation at all and show that it is not even possible to give a local objective description of what happens using the usual conventions. The non-locality will appear in the wave function itself, even before the R process takes place.

1 Notations, framework.

The two observers, Alice and Bob, are labeled 1 and 2. The measurement results are noted + and - (using $$\hbar/2$$ units). No angle is mentionned when the measurement occurs along the Oz axis. The measurement devices can rotate inside the yOz plane. Their angle with Oz is noted $$\phi$$ when the observer is not mentionned, $$\alpha$$ when it is Alice, who is observer number 1, and $$\beta$$ when it is Bob, who is observer number 2.

$$|M+\phi\rangle_i$$ and $$|M-\phi\rangle_i$$ are the state vectors of the measurement devices of observer i (i=1 for Alice and i=2 for Bob), when they form an angle $$\phi$$ with Oz and show the results + and - respectively.

We may also use the letter O for observers who read the result on the measurement device and give them the state vectors
$$|O+\phi\rangle_i$$ and $$|O-\phi\rangle_i$$

Here is what you proposed :

Why can't I say B knows about A's complete state and her measurement apparatus completely, and thus is able to model all of A's measurement from an external view with U processes only?

I won't follow this proposition, because I can't check for Bell's inequality with one measurment only. I prefer to adopt the point of view on an omniscient observer. Getting the probabilities for all possible outcomes, I can check for Bell's inequality at once.

When you say "with U processes only", I assume that you modelize a measurement by intricating the measurement device with the particle measured.

2 The EPR Experiment

At time t0, a source emits two particles in the state

$$|\Psi\rangle = \frac{1}{\sqrt{2}} ( {|+\rangle_1} \otimes {|-\rangle_2} - {|-\rangle_1} \otimes {|+\rangle_2} )$$

This answers the question you were asking to Demystifier above. When you take two particles, labeled 1 and 2, you can write their wave function by taking the tensorial product of their respective wave functions.
The above wave function is non-separable because it can't be written as a tensorial product with only states of particle 1 on one side and only states of particle 2 on the other side. This case only occurs with quantic superpositions, but it does not involve non-locality in itself.

The particles reach the detectors at time t1.

After t0 and before t1, Alice turns her measurment device until it forms an angle $$\alpha$$ with Oz, and Bob does the same until his device forms an angle $$\beta$$ with Oz.

These actions restrict the possible states of Alice, Bob and their devices after t1 to the linear combinations of the following state vectors :

Alice :
$$\{ |O+\alpha\rangle_1, \, |O-\alpha\rangle_1 \}$$

Bob :
$$\{ |O+\beta\rangle_2, \, |O-\beta\rangle_2 \}$$

Alice's device :
$$\{ |M+\alpha\rangle_1, \, |M-\alpha\rangle_1 \}$$

Bob's device :
$$\{ |M+\beta\rangle_2, \, |M-\beta\rangle_2 \}$$

In order to intricate these states with the measured system, we must rewrite the system in the new basis.
The first step is easy. Since the initial wave function is symmetric under any rotation around the Ox axis, we can rewrite it

$$|\Psi\rangle \, = \, \frac{1}{\sqrt{2}} ( {|+\alpha\rangle_1} \otimes {|-\alpha\rangle_2} - {|-\alpha\rangle_1} \otimes {|+\alpha\rangle_2} )$$

We can start with Alice's intrication (measurement without reduction). The order has no importance. It gives

$$\frac{1}{\sqrt{2}} <br /> ( <br /> {|+\alpha\rangle_1} \otimes {|M+\alpha\rangle_1} \otimes {|O+\alpha\rangle_1} <br /> \otimes <br /> {|-\alpha\rangle_2}$$

$$- <br /> \,<br /> {|-\alpha\rangle_1} \otimes {|M-\alpha\rangle_1} \otimes {|O-\alpha\rangle_1} <br /> \otimes <br /> {|+\alpha\rangle_2} <br /> )$$

But now, in order to account for Bob's intrication, we must rewrite the vectors of his particle using the follwing substitutions :

$${|+\rangle}<br /> =<br /> cos{\frac{\phi}{2}} <br /> {|+\phi\rangle}<br /> -<br /> sin{\frac{\phi}{2}} <br /> {|-\phi\rangle}$$

$${|-\rangle}<br /> =<br /> sin{\frac{\phi}{2}} <br /> {|+\phi\rangle}<br /> +<br /> cos{\frac{\phi}{2}} <br /> {|-\phi\rangle}$$

which gives

$$\frac{1}{\sqrt{2}} <br /> (<br /> {|+\alpha\rangle_1} \otimes {|M+\alpha\rangle_1} \otimes {|O+\alpha\rangle_1} <br /> \otimes <br /> (<br /> sin{\frac{\beta-\alpha}{2}} <br /> {|+\beta\rangle_2} <br /> +<br /> cos{\frac{\beta-\alpha}{2}} <br /> {|-\beta\rangle_2}<br /> )$$

$$- <br /> \,<br /> {|-\alpha\rangle_1} \otimes {|M-\alpha\rangle_1} \otimes {|O-\alpha\rangle_1} <br /> \otimes <br /> (<br /> cos{\frac{\beta-\alpha}{2}} <br /> {|+\beta\rangle_2} <br /> -<br /> sin{\frac{\beta-\alpha}{2}} <br /> {|-\beta\rangle_2}<br /> )<br /> )$$

Then, Bob's intrication leads to

$$\frac{1}{\sqrt{2}} <br /> (<br /> {|+\alpha\rangle_1} \otimes {|M+\alpha\rangle_1} \otimes {|O+\alpha\rangle_1} <br /> \otimes$$

$$(<br /> sin{\frac{\beta-\alpha}{2}} <br /> {|+\beta\rangle_2} \otimes {|M+\beta\rangle_2} \otimes {|O+\beta\rangle_2}<br /> +<br /> cos{\frac{\beta-\alpha}{2}} <br /> {|-\beta\rangle_2} \otimes {|M-\beta\rangle_2} \otimes {|O-\beta\rangle_2}<br /> )$$

$$- <br /> \,<br /> {|-\alpha\rangle_1} \otimes {|M-\alpha\rangle_1} \otimes {|O-\alpha\rangle_1} <br /> \otimes$$

$$(<br /> cos{\frac{\beta-\alpha}{2}} <br /> {|+\beta\rangle_2} \otimes {|M+\beta\rangle_2} \otimes {|O+\beta\rangle_2}<br /> -<br /> sin{\frac{\beta-\alpha}{2}} <br /> {|-\beta\rangle_2} \otimes {|M-\beta\rangle_2} \otimes {|O-\beta\rangle_2}<br /> )<br /> )$$

Rearranging the different terms, we get

$$\frac{1}{\sqrt{2}} <br /> (\,<br /> <br /> sin{\frac{\beta-\alpha}{2}} <br /> ({|+\alpha\rangle_1} \otimes {|M+\alpha\rangle_1} \otimes {|O+\alpha\rangle_1}<br /> \otimes <br /> {|+\beta\rangle_2} \otimes {|M+\beta\rangle_2} \otimes {|O+\beta\rangle_2})$$

$$+<br /> \,<br /> cos{\frac{\beta-\alpha}{2}}<br /> ({|+\alpha\rangle_1} \otimes {|M+\alpha\rangle_1} \otimes {|O+\alpha\rangle_1} <br /> \otimes <br /> {|-\beta\rangle_2} \otimes {|M-\beta\rangle_2} \otimes {|O-\beta\rangle_2} )$$

$$- <br /> \,<br /> cos{\frac{\beta-\alpha}{2}}<br /> ({|-\alpha\rangle_1} \otimes {|M-\alpha\rangle_1} \otimes {|O-\alpha\rangle_1} <br /> \otimes <br /> {|+\beta\rangle_2} \otimes {|M+\beta\rangle_2} \otimes {|O+\beta\rangle_2} )$$

$$+<br /> \,<br /> sin{\frac{\beta-\alpha}{2}}<br /> ({|-\alpha\rangle_1} \otimes {|M-\alpha\rangle_1} \otimes {|O-\alpha\rangle_1}<br /> \otimes <br /> {|-\beta\rangle_2} \otimes {|M-\beta\rangle_2} \otimes {|O-\beta\rangle_2} )<br /> <br /> )$$

 

[Pio2001]

3 Non locality and Bell's inequality violation

This final expression is the key. You can see both non-locality and the inequality violation in it.

The non locality is mathematically represented by the fact that the amplitude of Alice's state vectors depends on $$\beta$$, and the amplitude of Bob's state vectors depends on $$\alpha$$, in a non-separable way, while $$\alpha$$ was chosen in a space-time region spatially separated from Bob, as he is represented here, and $$\beta$$ in a space-time region spatially separated from Alice, as she is represented here.

To put it short, Alice's complete description is a function of $$\beta$$, and Bob's complete description is a function of $$\alpha$$.

You may argue that this is only one possible representation among others, and that we may find another one that is local. I challenge you to find one, and then to calculate Bell's inequality violation from it.

Here how Bell's inequality violation is calculated from the above. Since you're already familiar with it, I skip the normalization part, the local mean values, and directly get to the calculus of $$<{S_{1 \alpha}}\otimes{S_{2\beta}}>$$

With or without involving an R process, we must assume that the frequency at which we observe a given pair of result is proportional to the squared modulus of the amplitude of the matching state vectors.

For (+,+), the product of the two measurements is 1, and the probability to get it is

$$(\frac{1}{\sqrt{2}} <br /> \,<br /> sin{\frac{\beta-\alpha}{2}})^2 <br /> \,<br /> =\,\frac{1}{2}sin^2{\frac{ \beta-\alpha}{2}}$$

For (+,-), the product is -1, and the probability is

$$(\frac{1}{\sqrt{2}} <br /> \,<br /> cos{\frac{\beta-\alpha}{2}})^2 <br /> \,<br /> =\,\frac{1}{2}cos^2{\frac{ \beta-\alpha}{2}}$$

For (-,+), the product is -1, and the probability is

$$(-\frac{1}{\sqrt{2}} <br /> \,<br /> cos{\frac{\beta-\alpha}{2}})^2 <br /> \,<br /> =\,\frac{1}{2}cos^2{\frac{ \beta-\alpha}{2}}$$

For (-,-), the product is 1, and the probability

$$(\frac{1}{\sqrt{2}} <br /> \,<br /> sin{\frac{\beta-\alpha}{2}})^2 <br /> \,<br /> =\,\frac{1}{2}sin^2{\frac{ \beta-\alpha}{2}}$$Thus $$<{S_{1 \alpha}}\otimes{S_{2\beta}}>$$ equals :

$$sin^2{\frac{ \beta-\alpha}{2}} - cos^2{\frac{ \beta-\alpha}{2}}$$

Which, after trigonometric simplification, leads to

$$<{S_{1 \alpha}}\otimes{S_{2\beta}}> \,=\, -cos(\beta-\alpha) \,=\,-cos(\alpha-\beta)$$

Which is enough to get

$$S = 2\sqrt{2}$$

For $$\alpha$$ = 0°, $$\beta$$ = 45°, $$\alpha'$$ = 90°, et $$\beta'$$ = 135°

 

[Pio2001]

Note : in the above conclusion, S is Bell's parameter and the inequality violated is S <= 2.
The S in $$<{S_{1 \alpha}}\otimes{S_{2\beta}}>$$, on the other hand, are the projections of the spin operator.

 

[Gerenuk]

I'll go through it in detail tomorrow.

Could you just point out how the full wavefunction would look like including position coordinates and time-dependence? Maybe you can also confirm that all the derivation stays valid if you do it correctly with a full wave-function. A spin function alone might not mean much. Some people were even surprised that it's impossible to find a fully antisymmetric three-spin state.

Is there a derivation which does not use spins only? Because otherwise that suggests that the funny spin states are the reason for trouble.

At first guess I even think it's hard to do such a derivation with position wavefunctions only and still use some notion of particles clearly flying apart?!

Anyway, I try to work through it.

PS: I once had the feeling that non-locality in QM could be connected with permutations of particles only somehow. Has anyone made a theory about this?

 

[yoda jedi]

I don't see a sandbox in the forums, and LaTeX behaves strangely in the preview form. Let me try and see if it works.

Gerenuk, it is easier for me to describe the EPR experiment with spin 1/2 particles because I have alreay all the equations written in LaTeX.

i know a model with spin 1/2 particles (but not MWI)
http://arxiv.org/PS_cache/quant-ph/pdf/9505/9505025v1.pdf

....A parametrized model, "Q", for the state vector evolution of spin-1/2 particles during measurement is developed...is local, deterministic, nonlinear and time asymmetric...that Q is not constrained by Bell’s inequality, locality and determinism notwithstanding.

 

[Demystifier]

Can you write this down mathematically? I believe in physics you should never trust words alone unless both parties know exactly which mathematics stands behind it. Because once I learned the maths for some advanced topics I started noticing how much rubbish me and other people were talking before, when we knew only words, i.e. popular science.

Edit: preferably using non-locality and not non-separability. Unless you can find a very good proof to draw the connection.

I know that you already know a lot about this, and I don't want to write you the stuff that you already know. Thus, you would help me if you could specify what EXACTLY you want me to write down mathematically.

 

[Pio2001]

i know a model with spin 1/2 particles (but not MWI)
http://arxiv.org/PS_cache/quant-ph/pdf/9505/9505025v1.pdf

....A parametrized model, "Q", for the state vector evolution of spin-1/2 particles during measurement is developed...is local, deterministic, nonlinear and time asymmetric...that Q is not constrained by Bell’s inequality, locality and determinism notwithstanding.

Thanks for the link.
I read the abstract and the introduction. This model is anti-realistic. Therefore the statement I wrote earlier stands true, until proven otherwise :

No modelization of the experiment have been given yet that
1) Describe what happens in terms of realistic objects
2) Predicts the violation of the inequality by means of the above description

 

[Pio2001]

Oops ! My mistake.

Interpretations that include backwards causality fit in the above statement :)

 

[Pio2001]

Could you just point out how the full wavefunction would look like including position coordinates and time-dependence?

For this purpose, I suggest to imagine ion traps positionned at the output paths of the spin measurment devices. We would use 1/2 spin ions, and they would be trapped into a given box if they get out of the measurment device from one way, and into another box if they get out the other way. The boxes would isolate completely the ions from their environment, preventing them to decohere.
This way, position would be trivially entangled with spin and all the math stuff would be essentially the same.

By the way, when you measure spin with a Stern-Gerlach device, you don't measure the spin of the particule, you measure its position at the output of the device !

Maybe you can also confirm that all the derivation stays valid if you do it correctly with a full wave-function.

I don't know how to write a full wave function. So I can't confirm that. However, the calculus that I made seem correct to me.

Is there a derivation which does not use spins only? Because otherwise that suggests that the funny spin states are the reason for trouble.

There is at least the one with photons polarisation, used to modelize 1982 Aspect's experiment.
And it seems to me that the superposition principle, combined with Heisenberg's inequalities, allows to do this with any pair of measurment.

For example in the delayed choice experiment, a Bell inequality must have been violated measuring the position of the impacts on the screen on one side (Alice), and the quantum eraser output on the other side (Bob). But the two events did not occur in spatially separated regions, so I guess it was not worth checking for Bell's inequality.

 

[yoda jedi]

I'd be very, very careful with such a statement ;-)
Usually the guys crying out "it's so easy!", don't have the slightest clue what the problem is about.
This observation doesn't apply here, but it is one thing to remember :)

To my knowledge the R process is ill-defined, so it's hard to use it for arguments. I mean when is an observation an observation? Why don't we consider the human being as quantum objects and thus have U processes only?
And how does this R process lose locality or determinism?
For me it's very important not to just know a keyword, but to really understand where mathematically either locality or determinism is lost. Or why at all some people say it is lost, whereas all the theory seems to be based on local and deterministic concepts?

Right ! irrelevant refutations or endorsing or spurious justifications...
or things like "is an old study, outdated" (Special Relativity dates back to 1905 ! so ?)

or the guys say solemnly "SHEER VOLUME OF EVIDENCE !", "is NOT generally accepted", "In probably 500+ papers in the past year alone" (ah ! then truth is matter of the number of papers, more papers, more truth), "ALL (and I mean 100%) of the experiments !", "I don't see the issue as being relevant"

hell ! they are cheer leaders or parrots ?

Thanks for the link.
I read the abstract and the introduction. This model is anti-realistic. Therefore the statement I wrote earlier stands true, until proven otherwise :

No modelization of the experiment have been given yet that
1) Describe what happens in terms of realistic objects
2) Predicts the violation of the inequality by means of the above description

what is a realistic object ?

 

[Gerenuk]

Hmm, that question seems really interesting to me:
What is the full (position and time dependent) wave-function of that singlet state, where the particles fly apart?

 

[DrChinese]

...or the guys say solemnly "SHEER VOLUME OF EVIDENCE !", "is NOT generally accepted", "In probably 500+ papers in the past year alone" (ah ! truth is matter of the number of papers, more papers, more truth), "ALL (and I mean 100%) of the experiments !", "I don't see the issue as being relevant"
hell, thay are cheer leaders or parrots ?

As Einstein said his critics, and to paraphrase: it only takes 1.

But your criticism misses the mark soundly (since I "parrot" all of the above frequently). This board is not for alternative science. End of the story. I have my own web site, and you can too. On that site, I say whatever I want. So could you. But this site is intended to discuss mainstream science. It is not a place to trumpet your homespun agenda.

Further: it DOES matter what 500+ papers say. It is patently absurd to claim otherwise. They could still be wrong, but the likelihood is low. Hey, they thought the human body had a temperature of 98.6 degrees for years. That has been adjusted. Were all those others "wrong" ?

Make a good argument and the rest will follow.

 

[DrChinese]

i know a model with spin 1/2 particles (but not MWI)
http://arxiv.org/PS_cache/quant-ph/pdf/9505/9505025v1.pdf

....A parametrized model, "Q", for the state vector evolution of spin-1/2 particles during measurement is developed...is local, deterministic, nonlinear and time asymmetric...that Q is not constrained by Bell’s inequality, locality and determinism notwithstanding.

Another meaningless reference. These are a dime a dozen. As Pio2001 says, this is actually anti-realistic and rests on semantic interpretation.

As with all candidate models: show me the realistic dataset! If you don't have one, please go back to the drawing board.

 

[Pio2001]

what is a realistic object ?

Among other things, it is an object that obeys physics' laws. For example, its position can't change faster than the speed of light. Or its properties can't be affcted by what is done outside its past light-cone.

 

[Frame Dragger]

Right ! irrelevant refutations or endorsing or spurious justifications...
or things like "is an old study, outdated" (Special Relativity dates back to 1905 ! so ?)

or the guys say solemnly "SHEER VOLUME OF EVIDENCE !", "is NOT generally accepted", "In probably 500+ papers in the past year alone" (ah ! then truth is matter of the number of papers, more papers, more truth), "ALL (and I mean 100%) of the experiments !", "I don't see the issue as being relevant"

hell ! they are cheer leaders or parrots ?

Wow, I take it someone pissed in your oatmeal this morning? Really yodajedi:

1.) WHO is "They"?
2.) What theory is it that you're pushing exactly?
3.) What part of the forum guidelines is hard to grasp?

As DrChinese has said, you're free to say what you want, but not everywhere you want to. If people such as Galileo can get their theories out in the face of politics and the (then) church, a patent clerk can produce E=MC^2, a quiet brit can produce (a LOT) of QM (Dirac), and a man trapped in his own body can share theories... you can manage.

Maybe the issue is the theory, and not the vehicle, or the "Them" those in the tinfoil deflector beanie crowd seem to blame for all of their ills.

As for what a realistic object is, most times that people use the term "Realism", they're speaking in terms of what Pio is saying, or more generally the Realism of EPR.

 

[Gerenuk]

Hey, anyone of you experts mind answering my last question #53? ;)

 

[Frame Dragger]

Hey, anyone of you experts mind answering my last question #53? ;)

Wouldn't it just be the usual time-dependent equation? a la http://www.britannica.com/EBchecked...ics/77513/Time-dependent-Schrödinger-equation

?

 

[Gerenuk]

I'm sure about the full form of the wavefunction which is connected to that singlet spin state.

So far it has been useful textbook quotes and references only, but no self-made thinking. Maybe someone can help me figure out the full wavefunction. Something like a plane wave position part and a time-dependent part which is connected to some energy? I mean really a full solution at least for the initial state
$$\Psi=?$$

It's important to make own thoughts. I once asked theoretical QM physics experts, what is the equivalent solution to singlets/triplet, but for three spins. They didn't have a clue and were even perplexed when I finally showed them the solution (no antisymmetric state and also you need an additional quantum number to distinguish degenerate states). So it seems its important to stroll around beyond textbook stuff.

PS: still trying to unpack the information in Pio's post. Maybe I miss some knowledge :)

 

[Frame Dragger]

I'm sure about the full form of the wavefunction which is connected to that singlet spin state.

So far it has been useful textbook quotes and references only, but no self-made thinking. Maybe someone can help me figure out the full wavefunction. Something like a plane wave position part and a time-dependent part which is connected to some energy? I mean really a full solution at least for the initial state
$$\Psi=?$$

It's important to make own thoughts. I once asked theoretical QM physics experts, what is the equivalent solution to singlets/triplet, but for three spins. They didn't have a clue and were even perplexed when I finally showed them the solution (no antisymmetric state and also you need an additional quantum number to distinguish degenerate states). So it seems its important to stroll around beyond textbook stuff.

PS: still trying to unpack the information in Pio's post. Maybe I miss some knowledge :)

Hmmm... that's beyond me frankly, but I wish you luck! Like you I'm still wading through Pio's posts (which are great btw, thanks Pio!). The amount of time I spend with reference books is truly sad.

Edit: This might be useful... https://www.physicsforums.com/showthread.php?t=147650

 

[ManyNames]

My posts where deleted for some reason.

Does this happen a lot round here?

 

[Pio2001]

The forum went offline for hours yesterday. It seems that they lost some posts. Mine are gone too.

 

[Frame Dragger]

Actually, I believe staff cleaned up the thread before the server had downtime.