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Anchovyforestbane

Copenhagen Interpretation?

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I've always been extremely skeptical of the Copenhagen interpretation. I'm aware of its use in explaining the probability distribution of subatomic particles, but the extent to which the idea has been taken, simply seems unrealistic. 
I'd very much like to see a mathematical/scientific proof of some kind which more adequately affirms/debunks the veracity of this interpretation.

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Copenhagen ( or Bohr ) interpretation is simply wavefunction ( probability distribution ) collapse to single ( observable ) state on interaction/observation. There is plenty of math that confirms that.

Are you going to reply/discuss any of the many questions you posted ?
Or are you just tossing sh*t at the wall.

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9 minutes ago, MigL said:

Copenhagen ( or Bohr ) interpretation is simply wavefunction ( probability distribution ) collapse to single ( observable ) state on interaction/observation. There is plenty of math that confirms that.

I know what it is. I'm simply asking for mathematical proof for the seemingly fantastical conclusions which have been drawn from it.

 

 

9 minutes ago, MigL said:

Are  you going to reply/discuss any of the many questions you posted ?

Or are you just tossing sh*t at the wall.

The reason I'm posting so frequently, is because there is another scientific forum I'd been using up until now; currently, my posts here are reposts of currently unanswered submissions there. Once I'm done submitting them I will go through them and answer whatever comments I was not notified about.

Edited by Anchovyforestbane

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It is an interpretation of the mathematics.
There are other interpretations also.

How exactly would you mathematically prove the interpretation of specific mathematics ?

There is something to be said for well-posed questions.
And could be the reason your questions were ignored on the other forum.

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1 minute ago, MigL said:

It is an interpretation of the mathematics.
There are other interpretations also.

How exactly would you mathematically prove the interpretation of specific mathematics ?

I'll phrase it this way; specifically what are the mathematics that have been used to reach these unrealistic corollaries?

 

4 minutes ago, MigL said:

There is something to be said for well-posed questions.
And could be the reason your questions were ignored on the other forum.

Perhaps they lack context... perhaps people would be more willing to actually think about these things if they had some real-world reason to do so. In many cases, however, there are none present; and to manufacture one, it might have to be altered to the point of no longer being the same idea.
Either way, I don't think its crucial that people listen to my scientific pontifications. I simply want to express them, and if someone finds it thought-provoking then it's all for the better.

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I'll re-phrase also.

The standard mathematics of quantum mechanics are probabilistic.
The 'interpretation' of the square of the amplitude of the wave function is as the probability of observation.
The mathematical model, then, reinterpreted in the context of real-world scenarios, leads to a cat being both alive and dead before wave function collapse, in the Copenhagen interpretation. Or the universe 'splitting' so that the cat is dead in one universe, and alive in the other, for the Many Worlds interpretation. Do you also want mathematical proof that the universe is splitting every time a quantum particle interacts ?

And that is all that they are, trying to interpret probabilistic-world math, to real-world scenarios.
And yes, the math model works spectacularly well.

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The Copenhagen interpretation simply can be intuitively understood as another striking property of the Hermitian operator. 

In QM every observable has an associated operator. This operator is Hermitian because the observable value need to be real.

Now this Hermitian operator, say Q, has the property to return eigenvalues, say q, when operating on a function, called the eigenfunction or eigenstate. In a determinate state, the measurement of Q will always produce a certain eigenvalue q. Putting it other way might help. If measuring a physical quantity returns a certain value q, then we can be sure that it was in the state |q>, the associated eigenstate of q. Thus, you can draw the conclusion that "immediately" after the measurement,  the state collapsed to |q>. 

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33 minutes ago, Sriman Dutta said:

The Copenhagen interpretation simply can be intuitively understood as another striking property of the Hermitian operator. 

In QM every observable has an associated operator. This operator is Hermitian because the observable value need to be real.

Now this Hermitian operator, say Q, has the property to return eigenvalues, say q, when operating on a function, called the eigenfunction or eigenstate. In a determinate state, the measurement of Q will always produce a certain eigenvalue q. Putting it other way might help. If measuring a physical quantity returns a certain value q, then we can be sure that it was in the state |q>, the associated eigenstate of q. Thus, you can draw the conclusion that "immediately" after the measurement,  the state collapsed to |q>. 

I see, I see. Is there a source you know of that discusses this in more detail?

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2 hours ago, Anchovyforestbane said:

Either way, I don't think its crucial that people listen to my scientific pontifications. I simply want to express them, and if someone finds it thought-provoking then it's all for the better.

This is a science DISCUSSION forum. Nobody is here to listen to you do anything but discuss science WITH us, not at us. 

I think you need to learn more science before you pontificate. This is what makes your questions seem strange. You propose some very unphysical things as if it's important, like it matters to anyone anywhere. 

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6 minutes ago, Phi for All said:

This is a science DISCUSSION forum. Nobody is here to listen to you do anything but discuss science WITH us, not at us. 

It's easy to find throughout my posts here that I encourage discussion as much as I can. All I'm saying is that, if others choose not to do so, it isn't the end of the world for me.

 

8 minutes ago, Phi for All said:

I think you need to learn more science before you pontificate. This is what makes your questions seem strange. You propose some very unphysical things as if it's important, like it matters to anyone anywhere. 

You can also easily find that my submissions to not consist exclusively of these pontifications. I also discuss very real matters, some even related to future work. These pontifications are merely ideas I've had that I'd like to share and discuss with other scientifically minded folks. 

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4 hours ago, Anchovyforestbane said:

I know what it is. I'm simply asking for mathematical proof for the seemingly fantastical conclusions which have been drawn from it.

The math is the math of QM.

Interpretations are ways to help understand the physics. If you don’t like an interpretation you can use a different one. The QM is the same.

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5 hours ago, Anchovyforestbane said:

I'll phrase it this way; specifically what are the mathematics that have been used to reach these unrealistic corollaries?

Every interpretation seems unrealistic. We're wired to think more classically...but the evidence doesn't support it.

Edited by J.C.MacSwell

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6 hours ago, Anchovyforestbane said:

I've always been extremely skeptical of the Copenhagen interpretation. I'm aware of its use in explaining the probability distribution of subatomic particles, but the extent to which the idea has been taken, simply seems unrealistic. 
I'd very much like to see a mathematical/scientific proof of some kind which more adequately affirms/debunks the veracity of this interpretation.

You can live a long, healthy, happy life without going down that road. Are you sure you want to go where the buses don't stop?

It depends on what you want QM for.

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1 hour ago, joigus said:

You can live a long, healthy, happy life without going down that road. Are you sure you want to go where the buses don't stop?

It depends on what you want QM for.

I'm into QM, and science in general, because I have a passion for understanding and utilizing the complex systems and structures composing our universe. The Copenhagen Interpretation is the most popular way of understanding the probabilistic nature of nuclear physics, but I do not find the Many-Worlds Corollary to be a reasonable conclusion.

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6 minutes ago, Anchovyforestbane said:

I'm into QM, and science in general, because I have a passion for understanding and utilizing the complex systems and structures composing our universe. The Copenhagen Interpretation is the most popular way of understanding the probabilistic nature of nuclear physics, but I do not find the Many-Worlds Corollary to be a reasonable conclusion.

The Many Worlds Interpretation isn't a corollary of the Copenhagen Interpretation.

They're alternative interpretations.

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2 hours ago, J.C.MacSwell said:

The Many Worlds Interpretation isn't a corollary of the Copenhagen Interpretation.

They're alternative interpretations.

Is that so? Any book I've read matches them together as though one must necessarily imply the other.

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13 minutes ago, Anchovyforestbane said:

Is that so? Any book I've read matches them together as though one must necessarily imply the other.

Then your books are crap or you’re reading them wrong

https://en.m.wikipedia.org/wiki/Many-worlds_interpretation

Quote

The many-worlds interpretation (MWI) is an interpretation of quantum mechanics that asserts that the universal wavefunction is objectively real, and that there is no wavefunction collapse.[2] This implies that all possible outcomes of quantum measurements are physically realized in some "world" or universe.[3] In contrast to some other interpretations, such as the Copenhagen interpretation, the evolution of reality as a whole in MWI is rigidly deterministic.[2]:8–9Many-worlds is also called the relative state formulation or the Everett interpretation, 


https://en.m.wikipedia.org/wiki/Copenhagen_interpretation

Quote

According to the Copenhagen interpretation, material objects, on a microscopic level, generally do not have definite properties prior to being measured, and quantum mechanics can only predict the probability distribution of a given measurement's possible results. The act of measurement affects the system, causing the set of probabilities to reduce to only one of the possible values immediately after the measurement. This feature is known as wave function collapse.

You’ll notice that the many worlds hypothesis is listed in the “Alternatives” section of that 2nd link, clearly indicating there is no implication of sameness.

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1 hour ago, Anchovyforestbane said:

Is that so? Any book I've read matches them together as though one must necessarily imply the other.

The many world interpretation is not pecular to QM. It can be seen as an interpretation of probability itself (although I don't like it).

If you toss a coin, it can be either head or tail. Suppose you get head. There was an equal probability of getting tail before the start of the experiment. Thus, why one event is partially favoured when tossed randomly ? This might raise the thought that there exists another world( read universe), where you tossed the coin and got a tail.

Since QM is all about probabilistic nature of the world, people interpret it using this argument. Such theories naturally go to multi-verse concepts and scifi.

.

.

But I don't consider this uncertainty in QM to be a source of theorising multiverse. Rather it is a fundamental property of the Fourier transform! Take an example of a signal. If you squeeze its time period, it's frequency curve is flattened. The Fourier transform has a remarkable property. If you try to squeeze or localise a signal( or a wve or any function) in one domain, it will not be localised in its conjugate domain (not a good terminiology, but I am using it to illustrate the property). Conjugate domains or variables simply mean two domains or variables whose functions form  a Fourier transform pair. For example, take time and frequency. 

The uncertainty in QM comes from the fact that position x and its associated conjugate variable wavenumber k form a Fourier pair. By de Brogile's hypothesis, you have p=hk/2pi, or the momentum is directly proportional to k. This thus clearly forms another pair of conjugate variables, with just another constant in the exponentials. Indeed I actually kind of believe that the entire mysteries of QM can be dragged down to this fact that p and x are conjugate pairs.

If you want maths, just google about it and there's plenty of lecture notes. If you are a beginner, I would suggest get a good textbook or try an online course. 

 

Hope I cleared your doubts :) .

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8 hours ago, Sriman Dutta said:

The many world interpretation is not pecular to QM. It can be seen as an interpretation of probability itself (although I don't like it).

If you toss a coin, it can be either head or tail. Suppose you get head. There was an equal probability of getting tail before the start of the experiment. Thus, why one event is partially favoured when tossed randomly ? This might raise the thought that there exists another world( read universe), where you tossed the coin and got a tail.

Since QM is all about probabilistic nature of the world, people interpret it using this argument. Such theories naturally go to multi-verse concepts and scifi.

.

.

But I don't consider this uncertainty in QM to be a source of theorising multiverse. Rather it is a fundamental property of the Fourier transform! Take an example of a signal. If you squeeze its time period, it's frequency curve is flattened. The Fourier transform has a remarkable property. If you try to squeeze or localise a signal( or a wve or any function) in one domain, it will not be localised in its conjugate domain (not a good terminiology, but I am using it to illustrate the property). Conjugate domains or variables simply mean two domains or variables whose functions form  a Fourier transform pair. For example, take time and frequency. 

The uncertainty in QM comes from the fact that position x and its associated conjugate variable wavenumber k form a Fourier pair. By de Brogile's hypothesis, you have p=hk/2pi, or the momentum is directly proportional to k. This thus clearly forms another pair of conjugate variables, with just another constant in the exponentials. Indeed I actually kind of believe that the entire mysteries of QM can be dragged down to this fact that p and x are conjugate pairs.

If you want maths, just google about it and there's plenty of lecture notes. If you are a beginner, I would suggest get a good textbook or try an online course. 

 

Hope I cleared your doubts :) .

This was the kind of explanation I was looking for, I thank you.  : )

Edited by Anchovyforestbane

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3 hours ago, Anchovyforestbane said:

This was the kind of explanation I was looking for, I thank you.  : )

You're welcome :)

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On 11/18/2020 at 2:17 AM, Anchovyforestbane said:

I'm into QM, and science in general, because I have a passion for understanding and utilizing the complex systems and structures composing our universe. The Copenhagen Interpretation is the most popular way of understanding the probabilistic nature of nuclear physics, but I do not find the Many-Worlds Corollary to be a reasonable conclusion.

I agree with you, basically, that the Copenhagen interpretation is not satisfactory, and neither it is the many-worlds interpretation. But the Copenhagen interpretation works like a dream. That's the problem, actually. It works like a dream and mathematically, it cannot be the whole story. As Bell said, Copenhagen's interpretation is good FAPP (for all practical purposes.)

As Bell also said,
 

Quote

 

The question at issue is the famous 'reduction of the wave packet'. There are, ultimately, no mechanical arguments for this process.

J. Bell, M. Nauenberg, The Moral Aspect of Quantum Mechanics, Preludes in Theoretical Physics, ed. by A. De Shalit, H. Feshbach, and L. Van Hove. North Holland, Amsterdam, (1966) pp. 279-86.

 

Mind you: He didn't mean classical-mechanical arguments; he meant quantum-mechanical arguments.

I'm working on a miniature of explanation in 2-dimensional quantum mechanics, if you're interested.

The many-worlds interpretation is not a corollary of the Copenhagen version. It's more like what @Sriman Dutta says:

On 11/18/2020 at 6:35 AM, Sriman Dutta said:

The many world interpretation is not peculiar to QM. It can be seen as an interpretation of probability itself (although I don't like it).

If you toss a coin, it can be either head or tail. Suppose you get head. There was an equal probability of getting tail before the start of the experiment. Thus, why one event is partially favoured when tossed randomly ? This might raise the thought that there exists another world( read universe), where you tossed the coin and got a tail.

I totally agree with this.

On 11/18/2020 at 1:09 PM, Anchovyforestbane said:

Indeed I actually kind of believe that the entire mysteries of QM can be dragged down to this fact that p and x are conjugate pairs.

Conjugate variables are certainly peculiar. Their properties cannot be simulated by any finite-dimensional space of states and thereby cannot be completely understood with discrete mathematics. They are the domain of transcencental mathematics. Unlike the famous \( J_x \), \( J_y \), \( J_z \) that people use in all the completeness theorems, they always pair in couples, one of which is conserved, the other is not. ;)

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10 minutes ago, joigus said:

I agree with you, basically, that the Copenhagen interpretation is not satisfactory, and neither it is the many-worlds interpretation. But the Copenhagen interpretation works like a dream. That's the problem, actually. It works like a dream and mathematically, it cannot be the whole story. As Bell said, Copenhagen's interpretation is good FAPP (for all practical purposes.)

I'm working on a miniature of explanation in 2-dimensional quantum mechanics, if you're interested.

I would indeed be very interested. 

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8 hours ago, joigus said:

I agree with you, basically, that the Copenhagen interpretation is not satisfactory, and neither it is the many-worlds interpretation. But the Copenhagen interpretation works like a dream. That's the problem, actually. It works like a dream and mathematically, it cannot be the whole story. As Bell said, Copenhagen's interpretation is good FAPP (for all practical purposes.)

etc

 

Yes QM is still very much a work in progress/unfinished business.  +1

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10 hours ago, joigus said:

Conjugate variables are certainly peculiar.

Was in response to:

On 11/18/2020 at 6:35 AM, Sriman Dutta said:

Indeed I actually kind of believe that the entire mysteries of QM can be dragged down to this fact that p and x are conjugate pairs.

Not in response to @Anchovyforestbane. Sorry. It was the quote of a quote, and the quote function doesn't, or didn't, embed the quotes.

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The “mysteries of QM” aren’t really part of the Copenhagen interpretation. The main issue between interpretations is how you think about what’s going on when you make a measurement of an undetermined quantum state.

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