How is realism understood in QM?

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Summary:

I'm trying to get a better understanding of Realism in QM.

Main Question or Discussion Point

It seems that with every discussion I engage in, new thoughts and questions about QM keep popping up. I'm sure this is pretty standard but I hope that my questions haven't crossed the line into being excessive.

I know that in the EPR paper the authors set out a criterion that, if fulfilled, would (in their opinion) qualify something as being real. The criterion being:
EPR said:
If, without in any way disturbing a system, we can predict with certainty (i.e., with probability equal to unity) the value of a physical quantity, there exists an element of physical reality corresponding to this physical quantity. It seems to us that this criterion, while far from exhausting all possible ways of recognizing a physical reality, at least provides us with one such way
Am I correct in thinking that there is a theorem which demonstrates that quantum systems do not have these "physical quantities" prior to being measured? Does this make QM anti-realist by necessity?

I've also heard statements about QM (I think in terms of the Copenhagen Interpretation) which says that it is meaningless to talk about the state of the system prior to being measured. This is partly where some of the confusion arises for me. Does that [particular] interpretation mean that there is no system prior to being measured? I presume that it doesn't but I find it difficult to understand the position from there. Does this have relevance to the charge of incompleteness?

I was thinking about the idea that quantum systems do not have "physical quantities" prior to being measured and the analogy that I came up with was that of water. Generally, we think of "wetness" as being a property of water but is water actually wet? I imagine that "from the perspective of water" it wouldn't consider itself to be wet. Wetness is just a "property" that manifests when it comes into contact with other objects i.e. when it is measured. Can realism be thought of in that way in QM?
 

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  • #2
WWGD
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I dont know if this has to see with Quantum. In my understanding wetness is an emergent property, arising from the internal organization of the molecules, etc. But hope those more knowledgeable than me ( many here) can chime in.
 
  • #3
PeroK
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Summary: I'm trying to get a better understanding of Realism in QM.

It seems that with every discussion I engage in, new thoughts and questions about QM keep popping up. I'm sure this is pretty standard but I hope that my questions haven't crossed the line into being excessive.

I know that in the EPR paper the authors set out a criterion that, if fulfilled, would (in their opinion) qualify something as being real. The criterion being:


Am I correct in thinking that there is a theorem which demonstrates that quantum systems do not have these "physical quantities" prior to being measured? Does this make QM anti-realist by necessity?

I've also heard statements about QM (I think in terms of the Copenhagen Interpretation) which says that it is meaningless to talk about the state of the system prior to being measured. This is partly where some of the confusion arises for me. Does that [particular] interpretation mean that there is no system prior to being measured? I presume that it doesn't but I find it difficult to understand the position from there. Does this have relevance to the charge of incompleteness?
You're making the usual beginner's mistakes in confusing "state" with "measurement outcomes".

In QM we may know the state of a system perfectly but the state only tells us the probabilities for measurement of dynamic quantities, such as spin, angular momentum, energy etc.

Orthodox QM says that these quantities simply do not have well defined values before a measurement. It's only the measurement process that forces the system to take a stand and return a definite value.

Again, the Stern-gerlach experiment exemplifies this.

You really ought to learn some QM; rather than only learning about QM!:wink:
 
  • #4
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I dont know if this has to see with Quantum. In my understanding wetness is an emergent property, arising from the internal organization of the molecules, etc. But hope those more knowledgeable than me ( many here) can chime in.
I was just trying to use it as an analogy to describe the idea of a property which only manifests upon contact with something else alá measurement.
 
  • #5
PeroK
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I was just trying to use it as an analogy to describe the idea of a property which only manifests upon contact with something else alá measurement.
There are analogies in the classical world, but they do not go as deep as QM.

A quantum system could be thought of as a die before you throw it. The measurement process is throwing the die.

You know everything about the die, but you don't know what number will come up.

But this analogy can only be pushed so far.

Einstein's argument regarding realism is that the electron must have a definite spin before we measure it. It can't "really" have a probabilistic uncertain spin. It's just we don't know what it is until we measure it.

For most people the Bell theorem and quantum entanglement become the battleground.

But, IMHO, the simple spin of a single electron seriously undermines this realism. Stern Gerlach again.

That's partly why people like Bohr were so convinced by QM before the Bell theorem. It wasn't just a whim. The behaviour of the spin on a single electron already fits better with orthodox QM than realism with an array of hidden variables.

In summary, the behaviour that militates against realism is there in the most basic quantum phenomenon.
 
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  • #6
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You really ought to learn some QM; rather than only learning about QM!:wink:
It might just be my preconception of what that would entail but I've tried reading some textbooks on other physics topics and I've struggled with them. I usually end up looking for interpretations of them and an explanation of the consequences.

You're making the usual beginner's mistakes in confusing "state" with "measurement outcomes".

In QM we may know the state of a system perfectly but the state only tells us the probabilities for measurement of dynamic quantities, such as spin, angular momentum, energy etc.

Orthodox QM says that these quantities simply do not have well defined values before a measurement. It's only the measurement process that forces the system to take a stand and return a definite value.
Ah ok, so they have the properties prior to measurement just not well defined values? I thought I had read (I thought on here but maybe not) that quantum systems don't have certain properties until they are measured. Not necessarily that they had ill defined values but that they didn't have those properties. I've heard that is what Neils Bohr meant by the following:

Neils Bohr said:
Nothing exists until it is measured.

When we measure something we are forcing an undetermined, undefined world to assume an experimental value. We are not measuring the world, we are creating it.
Again, the Stern-gerlach experiment exemplifies this.
When the particles are prepared are they prepared in a specific spin state, prior to being measured? Do they have position and momentum prior to being measured?

I was under the impression that QM doesn't specify this information prior to measurement, which is why EPR levelled the accusation of incompleteness at QM.
 
  • #7
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It might just be my preconception of what that would entail but I've tried reading some textbooks on other physics topics and I've struggled with them. I usually end up looking for interpretations of them and an explanation of the consequences.


Ah ok, so they have the properties prior to measurement just not well defined values? I thought I had read (I thought on here but maybe not) that quantum systems don't have certain properties until they are measured. Not necessarily that they had ill defined values but that they didn't have those properties. I've heard that is what Neils Bohr meant by the following:




When the particles are prepared are they prepared in a specific spin state, prior to being measured? Do they have position and momentum prior to being measured?
You can prepare a state with a relatively well defined value of some observable. But, QM has incompatible observables. There is a limitation on how well you can define the value of incompatible observables, in any given state. It's called the uncertainty principle.

Position and momentum are an example of two mutually incompatible observables.

Spin about the x-axis, y-axis and z-axis are three mutually incompatible observables.

You can prepare an electron with a definite value of spin in one direction. In the sense that a measurement of spin about that axis will certainly, with 100% probability, return the one value. But, in that state a measurement of spin about either of the other two axes will give a 50-50 split.
 
  • #8
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You can prepare a state with a relatively well defined value of some observable. But, QM has incompatible observables. There is a limitation on how well you can define the value of incompatible observables, in any given state. It's called the uncertainty principle.

Position and momentum are an example of two mutually incompatible observables
Thanks Perok. I'm familiar with the uncertainty principle and the idea that the more precisely you measure something like position, the less precisely you can measure momentum. Am I correct in saying that the more precisely you can determine the time a particle leaves an emitter, the less precisely you can determine the energy of the particle?


Spin about the x-axis, y-axis and z-axis are three mutually incompatible observables.

You can prepare an electron with a definite value of spin in one direction. In the sense that a measurement of spin about that axis will certainly, with 100% probability, return the one value. But, in that state a measurement of spin about either of the other two axes will give a 50-50 split.
I'm having a little trouble reconciling a couple of things: the idea that we can prepare an electron with a definite value of spin in one direction - this to me sounds like the EPR claim of incompleteness i.e. the notion that the particle has a definitive spin when it is created but the equations of QM don't define/describe this.

with this
Einstein's argument regarding realism is that the electron must have a definite spin before we measure it. It can't "really" have a probabilistic uncertain spin. It's just we don't know what it is until we measure it.
How can we prepare an electron with a definite value of spin in one direction if the spin is probabilistic and uncertain. I get that QM gives us the probability of the measurement outcome, and when we actually measure the electron it will give a definite value, but I don't see how it can be said that the electron is prepared with a definite spin. I think that speaks to the heart of the question on realism.

But, IMHO, the simple spin of a single electron seriously undermines this realism. Stern Gerlach again.

That's partly why people like Bohr were so convinced by QM before the Bell theorem. It wasn't just a whim. The behaviour of the spin on a single electron already fits better with orthodox QM than realism with an array of hidden variables.

In summary, the behaviour that militate against realism is there in the most basic quantum phenomenon.
This is what I'm asking about, the anti-realism of QM (or certain interpretations of QM), namely the anti-realism of Bohr. The idea that:

Bohr said:
Nothing exists until it is measured.

When we measure something we are forcing an undetermined, undefined world to assume an experimental value. We are not measuring the world, we are creating it.
That is what I was trying to convey with the analogy of water. That "wetness" only exists when it is measured i.e. when it comes into contact with something else. In terms of that analogy it would seem as though anti-realist interpretations would deny the existence of water until such point as its wetness is measured (with water representing the quantum system prior to measurement). That is how the position appears to me, but I am open to correction.

I would tend to think that water (the quantum system) exists prior to its wetness (physical property) being measured, with wetness being a property that manifests only upon measurement i.e. contact with another system. Is this interpretation of realism compatible with any of the interpretations of QM?
 
  • #9
atyy
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I was thinking about the idea that quantum systems do not have "physical quantities" prior to being measured and the analogy that I came up with was that of water. Generally, we think of "wetness" as being a property of water but is water actually wet? I imagine that "from the perspective of water" it wouldn't consider itself to be wet. Wetness is just a "property" that manifests when it comes into contact with other objects i.e. when it is measured. Can realism be thought of in that way in QM?
No, the lack of realism is more fundamental than that. The water molecules, electrons etc themselves are not necessarily real in QM (in the standard interpretation). Only the measurement results or the measurement outcomes are real. Whether something is real or not has to be subjectively determined by the observer. This can be motivated by Schroedinger's cat. It is obviously absurd to think the cat is dead and alive at the same time, so we say who cares, we don't know anything about what we don't observe. So the superposition of the cat being dead and alive is not necessarily real, just a formal step in a calculation that predicts the correct probabilities of measurement outcomes. Only the measurement outcome of the cat being dead or alive is real. If you are good enough to measure and observe the cat being dead and alive, then that will be real for you.
 
  • #10
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Thanks Perok. I'm familiar with the uncertainty principle and the idea that the more precisely you measure something like position, the less precisely you can measure momentum. Am I correct in saying that the more precisely you can determine the time a particle leaves an emitter, the less precisely you can determine the energy of the particle?


I'm having a little trouble reconciling a couple of things ....
First, that is not the uncertainty principle. That is, at best, a popular science version of the principle.

The uncertainty principle says nothing about how precisely you may measure any observable. That depends only on your measuring apparatus.

The uncertainty principle is about state preparation, not measurement precision.

It is also a statistical law, so it says nothing about particular measurements. Uncertainty in this context is the variance (or standard deviation) on a set of measurements on an ensemble of identically prepared systems. It has nothing to do with the precision of any measurement, in the usual sense of that word.

In general it applies to any pair of incompatible observables.

Second, time is not an observable in QM. There is no uncertainty in a measurement of time in the sense above.

The time-energy uncertainty principle is something very different. What it says is that the more uncertainty you have in the energy of a system, the less time the systems takes to change significantly. In the extreme care where the system is prepared in an energy eigenstate, where the is no uncertainty in energy, nothing changes over time. This is called a stationary state.

By contrast, if there is a large uncertainty in the energy, then the expected value of measurements of other observables will change significantly over a short time.

Finally, the rest of your post is philosophical objections to QM based largely on a lack of any depth of understanding of the foundations or principles of QM.

One of the easiest intellectual exercises is to imagine philosophical objections to something you don't understand. That's fundamentally the problem with debating the foundations of QM when you don't know what QM really says.
 
  • #11
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No, the lack of realism is more fundamental than that. The water molecules, electrons etc themselves are not necessarily real in QM (in the standard interpretation). Only the measurement results or the measurement outcomes are real. Whether something is real or not has to be subjectively determined by the observer. This can be motivated by Schroedinger's cat. It is obviously absurd to think the cat is dead and alive at the same time, so we say who cares, we don't know anything about what we don't observe. So the superposition of the cat being dead and alive is not necessarily real, just a formal step in a calculation that predicts the correct probabilities of measurement outcomes. Only the measurement outcome of the cat being dead or alive is real. If you are good enough to measure and observe the cat being dead and alive, then that will be real for you.
Thank you atyy, this is how I had interpreted the different explanations that I have heard with regard to the standard interpretation, I just wanted to be sure that I was understanding them correctly because I don't find them compelling.

Sticking with the water analogy: if we take a step back and instead of presupposing that there is "water" in the box (borrowed from Schroedinger's cat thought experiment), lets say that we don't know what is inside the box but we perform a measurement and our measurement reveals the property of "wetness". The standard interpretation would seem to say that there is nothing real inside the box prior to the measurement. I struggle to see how this can be the case though. Surely, there must be some real "thing" inside the box prior to measurement. If there wasn't then surely our measurement of an empty box simply wouldn't yield any results?

I can understand how a property only "comes into being" through measurement, in the analogy the "wetness" of water only arises when water comes into contact with something else. But I don't see how it can be said that there is nothing real in the box prior to being measured.

Are there any interpretations of QM which challenge the standard anti-realist interpretations?
 
  • #12
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so they have the properties prior to measurement just not well defined values?
They have uncertain values. Of course an electron must be in the beam measured even before the measurement, but you cannot tell precisely where in the beam. Its position before the measurement is (by preparation) ''somewhere in the beam'' rather than definite coordinates, whereas at the time of the measurement it is "at the fairly precise place where the impact is recorded", well approximated by definite coordinates.

Are there any interpretations of QM which challenge the standard anti-realist interpretations?
My thermal interpretation is an intuitive, realist interpretation.
 
  • #13
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First, that is not the uncertainty principle. That is, at best, a popular science version of the principle.

The uncertainty principle says nothing about how precisely you may measure any observable. That depends only on your measuring apparatus.

The uncertainty principle is about state preparation, not measurement precision.

It is also a statistical law, so it says nothing about particular measurements. Uncertainty in this context is the variance (or standard deviation) on a set of measurements on an ensemble of identically prepared systems. It has nothing to do with the precision of any measurement, in the usual sense of that word.

In general it applies to any pair of incompatible observables.
Thank you for the clarification Perok. I have encountered the uncertainty principle a number of times (most recently in this video). I was under the [mistaken] impression that the uncertainty principle related more to measurements. I had heard it in terms of state preparation but one of the contexts that I have heard about it is in that of the EPR paper. I must have misinterpreted it though because it sounded like the EPR paper talked about exploiting the phenomenon of entanglement to ascertain the position and momentum information for particles, through measurement.


Second, time is not an observable in QM. There is no uncertainty in a measurement of time in the sense above.

The time-energy uncertainty principle is something very different. What it says is that the more uncertainty you have in the energy of a system, the less time the systems takes to change significantly. In the extreme care where the system is prepared in an energy eigenstate, where the is no uncertainty in energy, nothing changes over time. This is called a stationary state.

By contrast, if there is a large uncertainty in the energy, then the expected value of measurements of other observables will change significantly over a short time.
Ah, so there is a time-energy uncertainty principle it's just not Heisenberg's uncertainty principle, is that correct?

Finally, the rest of your post is philosophical objections to QM based largely on a lack of any depth of understanding of the foundations or principles of QM.

One of the easiest intellectual exercises is to imagine philosophical objections to something you don't understand. That's fundamentally the problem with debating the foundations of QM when you don't know what QM really says.
I'm not necessarily looking to debate the foundations of QM, I'm trying to understand them bettter. The issue of anti-realism is one such issue. I have heard it characterised in a pretty specific way, as how atyy has done above, and I find that this leaves me with some glaring questions. That is the purpose for posting, to try and get a better understanding and to maybe better define my own position with regard to QM or to see if there is an interpretation that fits with my own reasoning.
 
  • #14
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My thermal interpretation is an intuitive, realist interpretation.
Thank you A. Neumaier, I've saw a link for this last night and had a quick glance at it. I am looking forward to getting into it in more depth - or at least, to the depth that I am capable of.

I think I would tend towards realism myself but I'm not sure yet if it is the kind of realism that is aligned with any particular interpretation of QM.

They have uncertain values. Of course an electron must be in the beam measured even before the measurement, but you cannot tell precisely where in the beam. Its position before the measurement is (by preparation) ''somewhere in the beam'' rather than definite coordinates, whereas at the time of the measurement it is "at the fairly precise place where the impact is recorded", well approximated by definite coordinates.
Am I right in saying that this appears to slightly different to the anti-realist position that atyy has espoused here and that is usually associated with the Copenhagen Interpretation?

You seem to be implying that the electron does have a precise position, "somewhere in the beam", and the uncertainty lies in our ability to determine that. Is this not what EPR claimed in their paper?
 
  • #15
A. Neumaier
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You seem to be implying that the electron does have a precise position, "somewhere in the beam"
No. Position is (like any observable in quantum mechanics) an imprecise notion, which in principle cannot be made arbitrarily precise except under special circumstances (such as measurement).

It is like the position of a car on a road. It is meaningless to specify this position to millimeter accuracy since the car is extended over a region in the meter range. Thus the position of a car is intrinsically uncertain and imprecise.

The Copenhagen interpretation idealizes position to three exact coordinates. This idealized position does not exist except at the moment of (idealized) measurement.

The thermal interpretation does not idealize and defines the meaning of quantum uncertainty in such a way that it is analogous to the intrinsic uncertainty in the position of a car. According to the thermal interpretation, the ''size'' and "shape" of an electron depend on its preparation, and a typical electron in a typical beam has the size and shape of the beam itself. So even in principle one cannot say (without special preparation) more than the electron is where the beam is.
 
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  • #16
atyy
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Are there any interpretations of QM which challenge the standard anti-realist interpretations?
The standard interpretation is not anti-realist. It is pragmatic.

It is possible to have a purely pragmatic or operational view of quantum mechanics. However, many physicists, have thought that quantum mechanics is incomplete because it gives the observer a special status, whereas common sense seems to suggest that the observer should be just another physical system, subject to the laws of physics. This is the famous measurement problem of quantum mechanics. There are no completely satisfactory solutions to the measurement problem at the moment, but two famous approaches are Bohmian Mechanics and the Many-Worlds Interpretation. The problem with Bohmian Mechanics is that it is not clear whether it can be extended from non-relativistic quantum mechanics to the relativistic standard model of particle physics. The problem with Many-Worlds is that it is not clear how probability should arise from deterministic evolution of the wave function.

https://m.tau.ac.il/~quantum/Vaidman/IQM/BellAM.pdfAgainst 'measurement'
John Bell

https://arxiv.org/abs/0712.0149The Quantum Measurement Problem: State of Play
David Wallace

https://arxiv.org/abs/1906.11510On the CSL Scalar Field Relativistic Collapse Model
Daniel Bedingham, Philip Pearle
 
  • #17
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Thank you for the clarification Perok. I have encountered the uncertainty principle a number of times (most recently in this video). I was under the [mistaken] impression that the uncertainty principle related more to measurements. I had heard it in terms of state preparation but one of the contexts that I have heard about it is in that of the EPR paper. I must have misinterpreted it though because it sounded like the EPR paper talked about exploiting the phenomenon of entanglement to ascertain the position and momentum information for particles, through measurement.
The uncertainty principle (UP) relates to the spread of measurements you would get if you made them. It's not about the precision of those measurements.

1) Wrong: the particle has a definite position, but the UP limits how precisely you can measure its position.

2) Correct: the particle has no definite position and the UP imposes a minimum "spread" or "variance" of measurements of position on an ensemble of identically prepared systems. (The variance in position measurements is inversely proportional to the variance in momentum measurements.)

Warning: you will find a lot on line to the contrary.

The die analogy is of some use: every throw of the die represents a totally precise measurement. The measurement values are equally spread across 1-6. The expected value is actually 3.5 if you throw a die repeatedly. It's not the case that the die was "really 3.5" before you threw it, but you got imprecise measurements. The die is actually never 3.5, it's only ever 1-6 with complete precision after a throw.

Ah, so there is a time-energy uncertainty principle it's just not Heisenberg's uncertainty principle, is that correct?
Yes, but it is a "very different beast" from the UP as above.

I'm not necessarily looking to debate the foundations of QM, I'm trying to understand them bettter. The issue of anti-realism is one such issue. I have heard it characterised in a pretty specific way, as how atyy has done above, and I find that this leaves me with some glaring questions. That is the purpose for posting, to try and get a better understanding and to maybe better define my own position with regard to QM or to see if there is an interpretation that fits with my own reasoning.
I thought you might like the following. This is from one of the standard undergraduate QM textbooks, by Griffiths. This sort of thing is why I love his book. The underlines are mine:

Note first that every measurement of an electron spin about any axis always returns the same precise value ℏ/2ℏ/2. Except, the spin can be clockwise or anticlockwise, represented by ±ℏ/2±ℏ/2. Note that this is always 1/3 of the "total" spin. Unlike a classical object, you can never find an axis of spin rotation: and, of course, according to QM there is no axis of spin. Whatever axis you choose, you always get 1/3 of the total spin. If we measure spin about the z-axis, then we get ±ℏ/2±ℏ/2 and after the measurement the electron is said to be in the state z+z+ or z−z−, depending on the measurent value. Similary, if we measure spin about the x or y axes.

Anyway, what Griffiths has to say is this:

***

Let's say we start out with an electron in the state z+z+. If someone asks "what is the z-component of the electron's spin?", we could answer unambiguously +ℏ/2+ℏ/2. For a measurement of spin about the z-axis is certain to return that value. But, if our interrogator asks instead, "what is the x-component of the electron's spin?" we are obliged to equivocate. If you measure spin about the x-axis the chances are 50-50 that you will get either +ℏ/2+ℏ/2 or −ℏ/2−ℏ/2. If the questioner is a "realist" he will regard this as an inadequate - not to say impertinent - response. "Are you telling me you don't know the true state of that particle?" On the contrary, we know precisely that the state of that particle is z+z+. "Well then, how come you can't tell me what the x-component of its spin is?" Because it simply does not have a particular x-component of spin. Indeed it cannot, for if both the z-spin and x-spin were well-defined, the UP would be violated.

At this point our challenger grabs the test tube and measures the x-component of spin. Let's say he gets +ℏ/2+ℏ/2. "Aha!" (he shouts in triumph), "this particle has a perfectly well-defined value of x-spin." Well, it does now, but that doesn't prove it had that value prior to your measurement. "What has happened to your UP? I now know both the z-spin and the x-spin." But you do not: your measurement altered the particle's state; it is now in the state x+x+, and you no longer know the value of its z-spin. Check it out: measure the z-spin. If we repeat this scenario over and over, for the measurement of z-spin we will get +ℏ/2+ℏ/2 or −ℏ/2−ℏ/2 with equal probability.

(Note: that is to say after the measurement of x-spin, we no longer know the z-spin, which has become "uncertain".)

To the layman, philosopher or realist, a statement of the form "this particle does not have a well-defined position or momentum or spin or whatever) sounds vague, incompetent or (worst of all) profound. It is none of these. But, its precise meaning , I think, is almost impossible to convey to anyone who has not studied QM in some depth.

Electron spin is the simplest and cleanest context for thinking through the conceptual paradoxes of QM.

***

Vis-a-vis this thread I agree with Griffiths. It is almost impossible for you to grasp the precise nature of the UP or any of the apparent conceptual paradoxes of QM without having formally studied at least electron spin. You can read all the papers on EPR that have ever been written, but if you do not know electron spin thoroughly then you're just chasing shadows.
 
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  • #18
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The standard interpretation is not anti-realist. It is pragmatic.
I understand the pragmatism of the standard interpretation but is it anti-realist in its pragmatism? Your characterization of it above would seem to suggest that it is.

The part that jars with me is the idea that there is nothing real prior to measurement. To my mind, if there was nothing real there before measurement, then there would simply be nothing to measure and our attempts to make a measurement would simply not yield any results. It sounds like saying there is nothing real.

It is possible to have a purely pragmatic or operational view of quantum mechanics. However, many physicists, have thought that quantum mechanics is incomplete because it gives the observer a special status, whereas common sense seems to suggest that the observer should be just another physical system, subject to the laws of physics. This is the famous measurement problem of quantum mechanics. There are no completely satisfactory solutions to the measurement problem at the moment, but two famous approaches are Bohmian Mechanics and the Many-Worlds Interpretation. The problem with Bohmian Mechanics is that it is not clear whether it can be extended from non-relativistic quantum mechanics to the relativistic standard model of particle physics. The problem with Many-Worlds is that it is not clear how probability should arise from deterministic evolution of the wave function.
Thanks atyy, I'm familiar with the points you raise there but definitely need to develop my understanding of them.

With regard to incompleteness, one of the arguments I've come across a few times is the idea that QM doesn't predict the outcomes of individual experiments, instead it predicts the probability distribution over a number of experiments. I'm thinking this is linked to the notion of realism but I can't quite formulate how.

https://m.tau.ac.il/~quantum/Vaidman/IQM/BellAM.pdfAgainst 'measurement'
John Bell

https://arxiv.org/abs/0712.0149The Quantum Measurement Problem: State of Play
David Wallace

https://arxiv.org/abs/1906.11510On the CSL Scalar Field Relativistic Collapse Model
Daniel Bedingham, Philip Pearle
Thank you atyy, I will give these a read.
 
  • #19
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The uncertainty principle (UP) relates to the spread of measurements you would get if you made them. It's not about the precision of those measurements.

1) Wrong: the particle has a definite position, but the UP limits how precisely you can measure its position.

2) Correct: the particle has no definite position and the UP imposes a minimum "spread" or "variance" of measurements of position on an ensemble of identically prepared systems. (The variance in position measurements is inversely proportional to the variance in momentum measurements.)
Thank you Perok, explanations like this are exceptionally helpful.

Am I correct in thinking , with #2, that the minimum "spread"/"variance" of measurements imposed by the UP relates to the probabilistic predictions of QM? Is this directly related to the wavefunction of the particle? Is this what the wavefunction is?


Warning: you will find a lot on line to the contrary.
Thank you for the heads up!!

The die analogy is of some use: every throw of the die represents a totally precise measurement. The measurement values are equally spread across 1-6. The expected value is actually 3.5 if you throw a die repeatedly. It's not the case that the die was "really 3.5" before you threw it, but you got imprecise measurements. The die is actually never 3.5, it's only ever 1-6 with complete precision after a throw.
Relating this analogy to realism, we might ask the question what was the die showing before the throw, or what was it showing before we measured it? To me it sounds like the standard interpretation says it is meaningless to talk about the die until after its been thrown and the measurement taken.

Yes, but it is a "very different beast" from the UP as above.
I see. Thank you.


I thought you might like the following. This is from one of the standard undergraduate QM textbooks, by Griffiths. This sort of thing is why I love his book. The underlines are mine:

Note first that every measurement of an electron spin about any axis always returns the same precise value ℏ/2ℏ/2. Except, the spin can be clockwise or anticlockwise, represented by ±ℏ/2±ℏ/2. Note that this is always 1/3 of the "total" spin. Unlike a classical object, you can never find an axis of spin rotation: and, of course, according to QM there is no axis of spin. Whatever axis you choose, you always get 1/3 of the total spin. If we measure spin about the z-axis, then we get ±ℏ/2±ℏ/2 and after the measurement the electron is said to be in the state z+z+ or z−z−, depending on the measurent value. Similary, if we measure spin about the x or y axes.
This is incredibly helpful Perok. Thank you!!

Am I understanding correctly when I think that when we measure the spin of a particle, we are essentially measuring whether it is clockwise or anti-clockwise (is this the same as up and down?) along a given axis? Is this what the Stern-Gerlach does, it deflects the particle according to its orientation thereby allowing us to ascertain whether it was anti-clockwise or clockwise?

Is it the case that we can choose to measure along any of the 3 axes and we will get an answer of either clockwise or anti-clockwise?


Let's say we start out with an electron in the state z+z+. If someone asks "what is the z-component of the electron's spin?", we could answer unambiguously +ℏ/2+ℏ/2. For a measurement of spin about the z-axis is certain to return that value. But, if our interrogator asks instead, "what is the x-component of the electron's spin?" we are obliged to equivocate. If you measure spin about the x-axis the chances are 50-50 that you will get either +ℏ/2+ℏ/2 or −ℏ/2−ℏ/2. If the questioner is a "realist" he will regard this as an inadequate - not to say impertinent - response. "Are you telling me you don't know the true state of that particle?" On the contrary, we know precisely that the state of that particle is z+z+. "Well then, how come you can't tell me what the x-component of its spin is?" Because it simply does not have a particular x-component of spin. Indeed it cannot, for if both the z-spin and x-spin were well-defined, the UP would be violated.
Just trying to parse this. Is it the case that we can prepare an electron in the state z+z+, which is why we can unambiguously answer that it's z-component is +ℏ/2+ℏ/2? Or, do we have this unambiguous answer only after we measure the particle? The above seems to suggest that we can prepare it in the z+z+ state.

Let's say someone prepares the particle but doesn't tell us what it is. Am I correct in saying that if we measure spin about the x-axis, we will calculate the chances as being 50-50 that we will get either +ℏ/2+ℏ/2 or −ℏ/2−ℏ/2, with the same 50-50 chance if we chose either of the other two axes?

At this point our challenger grabs the test tube and measures the x-component of spin. Let's say he gets +ℏ/2+ℏ/2. "Aha!" (he shouts in triumph), "this particle has a perfectly well-defined value of x-spin." Well, it does now, but that doesn't prove it had that value prior to your measurement. "What has happened to your UP? I now know both the z-spin and the x-spin." But you do not: your measurement altered the particle's state; it is now in the state x+x+, and you no longer know the value of its z-spin. Check it out: measure the z-spin. If we repeat this scenario over and over, for the measurement of z-spin we will get +ℏ/2+ℏ/2 or −ℏ/2−ℏ/2 with equal probability.

To the layman, philosopher or realist, a statement of the form "this particle does not have a well-defined position or momentum or spin or whatever) sounds vague, incompetent or (worst of all) profound. It is none of these. But, its precise meaning , I think, is almost impossible to convey to anyone who has not studied QM in some depth.

Electron spin is the simplest and cleanest context for thinking through the conceptual paradoxes of QM.
Again, thank you Perok, I feel like this helps to clarify a lot. Personally don't think that the idea that "a particle does not have a well-defined position or momentum or spin or whatever" is all that vague. I think the trade-off between the pieces of information makes sense. I would think that in order to be exact about the position of a particle you would need to stop it dead. In so doing you clearly kill its momentum and so lose that information. I do have trouble reconciling some of the statements that are sometimes made in relation to the UP, some of which you have mentioned yourself. I have emboldened them above and it might bring some clarity to outline where my conflict lies.

Even if my characterization of the UP above isn't exactly accurate, we can simply work from the notion of the particle having a well defined z-spin; as you mentioned we can start with a particle in the z+z+ or z- z- state with precise values of ±ℏ/2±ℏ/2. If we take this as our definition of well defined, then we can see that it presupposes that the spin component must have an assigned value. But, how can it have an assigned value without making a measurement? Measurement is essentially the process by which we assign values.

Just taking out the emboldened statements, I will try to outline my reasoning and if you feel so inclined you can highlight where I am going wrong:

In your example above of the person choosing to measure the x-spin of the particle and the precise value is returned, you state that that doesn't prove it had that value prior to your measurement. This is somewhat of a tautology, because measurement is the process by which we assign values. You make a somewhat different, but more definitive statement before that: it simply does not have a particular x-component of spin.

There is a distinction to be made here between saying that the particle didn't have a particular value for spin (in the given direction) prior to measurement and saying that it simply does not have a particular component of spin (in that direction).

Measuring the precise x-spin value of the particle doesn't prove that it had that value prior to measurement because it is meaningless to talk about values prior to measurement. It is also true to say that measuring the x-spin value doesn't prove that it had an x-component of spin either but - here is the point of contention - it equally doesn't prove that it didn't have an x-component of spin prior to measurement. It is possible that it did have an x-component.

The UP - as far as I understand it - tells us that both the z-spin and the x-spin can't be well defined because to be well defined implies having precise values, which itself implies measurement. The UP specifies the trade-off between measuring the two spin components. However, measuring the spin in the z direction doesn't allow us to conclude that it simply does not have a particular x-component of spin. It may well have an x-component, we cannot be certain that it does or doesn't

To say that the particle simply does not have a particular x-component of spin would, to my mind, violate the UP because it seems to be a pretty definitive, pretty certain statement about the x-component of the spin of the particle. How do we know that it doesn't have an x-component?

(Note: that is to say after the measurement of x-spin, we no longer know the z-spin, which has become "uncertain".)
This is an example of the point. The z-spin has become "uncertain" but that doesn't mean that we can say with certainty that it simply does not have a particular z-component of spin.


Hopefully the error in my reasoning is easily identifiable there.
 
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PeroK
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Hopefully the error in my reasoning is easily identifiable there.
There's too much there to answer! One general point is that if you (try to) reject QM and impose classical ideas then you have two problems:

1) To explain the observed phenomena. Even if QM were wrong, the experiments don't go away! You still have Stern Gerlach; double-slit; the humble hydrogen atom to explain.

2) You still have to propose laws of nature to support your classical view. It's not enough to say, for example, it's possible an electron has an all components of spin simultaneously (just like a classical spinning object). Of course, in principle it's possible, but what laws of nature govern this fully determined spin? Why can't you ever find the axis of rotation, if it really exists?

And then you have the critical question: what does it even mean for an electron to have a definite axis of rotation if there are no experimental means of ever identifying it? On this the experimental evidence is clear, you never find an axis of rotation. You say: possibly it exists. Well, then I'd say: go and find it!

My advice is to try reading the introduction on that pdf I sent the link to. I had a read this evening and it is very good. You might have to skip the maths, but it explains a lot about the wavefunction, for example.
 

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