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Andrew Steane
Andrew Steane
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On the one hand this whole area is quite subtle so to understand how modern physics deals with it you need quite a lot of learning (university level and beyond). Having said that, modern physics does offer a perfectly coherent account of all such phenomena so they do not present paradoxes or puzzles in that sense.

The chief thing I would offer to someone asking who has not learned quantum measurement theory or quantum field theory is that you have to beware of the loose usage associated with terms such as "measurement" and "observe" in popular accounts of science. Rather than those terms it is better, in the first instance, to speak about interactions and entanglement. For an example, one physical system (called by us a measuring device) interacts with another physical system (called by us a particle) and the two become entangled. What happens next depends on the individual case. IfIt might be that the two subsequently become disentangled, or it might be that instead the larger one then interacts with further systems, spreading the entanglement out into many degrees of freedom, such that the disentanglement never occurs. In the latter case one finds that all the predictions of quantum physics are just as if a collapse of the wavefunction had occurred, but it is not necessary to pick any particular moment when the collapse takes place.

In hopes of clarifying a little, consider a sum such as $$ f = a + e^{i \theta} b $$ where $i^2 = -1$ and to follow this you will need either to know about complex numbers or just take it on trust. Suppose we wish to know the value of $|f|^2$. That's easy, it is $$ |f|^2 = |a|^2 + |b|^2 + \left(a b^* e^{-i\theta} + a^* b e^{i\theta}\right) $$ Now consider what happens when this $|f|^2$ is in fact a probability, as opposed to something like a length or a mass or a time. How do you measure a probability? You can't! Not in one go, at least. Rather you have to try some method such as run an experiment many times and take the average. But now the answers will depend on what happens with $\theta$. If $\theta$ always has the same value (and so do $a$ and $b$) then the average of $|f|^2$ is $$ \langle|f|^2\rangle = |a|^2 + |b|^2 + \left(a b^* e^{-i\theta} + a^* b e^{i\theta}\right) \tag{1} $$ but if $\theta$ varies randomly then the average of $|f|^2$ is $$ \langle|f|^2\rangle = |a|^2 + |b|^2. \tag{2} $$ The difference between (1) and (2) is what people are talking about when they discuss things like 'collapse of the wavefunction'. The reason is that any physical description leading to case (2) can here be replaced by a different physical description making the same prediction. The different description is that $|a|^2$ is the probability for one case and $|b|^2$ is the probability for another, and all we are doing is adding those probabilities.

When two different physical descriptions lead to the same physical predictions then you get debates about which physical description is the more elegant, and the debate cannot be resolved by experimental test. This does not mean the debate is without value, because it concerns things like elegance and coherence of ideas and these are important in science.

On the one hand this whole area is quite subtle so to understand how modern physics deals with it you need quite a lot of learning (university level and beyond). Having said that, modern physics does offer a perfectly coherent account of all such phenomena so they do not present paradoxes or puzzles in that sense.

The chief thing I would offer to someone asking who has not learned quantum measurement theory or quantum field theory is that you have to beware of the loose usage associated with terms such as "measurement" and "observe" in popular accounts of science. Rather than those terms it is better, in the first instance, to speak about interactions and entanglement. For an example, one physical system (called by us a measuring device) interacts with another physical system (called by us a particle) and the two become entangled. What happens next depends on the individual case. If might be that the two subsequently become disentangled, or it might be that instead the larger one then interacts with further systems, spreading the entanglement out into many degrees of freedom, such that the disentanglement never occurs. In the latter case one finds that all the predictions of quantum physics are just as if a collapse of the wavefunction had occurred, but it is not necessary to pick any particular moment when the collapse takes place.

In hopes of clarifying a little, consider a sum such as $$ f = a + e^{i \theta} b $$ where $i^2 = -1$ and to follow this you will need either to know about complex numbers or just take it on trust. Suppose we wish to know the value of $|f|^2$. That's easy, it is $$ |f|^2 = |a|^2 + |b|^2 + \left(a b^* e^{-i\theta} + a^* b e^{i\theta}\right) $$ Now consider what happens when this $|f|^2$ is in fact a probability, as opposed to something like a length or a mass or a time. How do you measure a probability? You can't! Not in one go, at least. Rather you have to try some method such as run an experiment many times and take the average. But now the answers will depend on what happens with $\theta$. If $\theta$ always has the same value (and so do $a$ and $b$) then the average of $|f|^2$ is $$ \langle|f|^2\rangle = |a|^2 + |b|^2 + \left(a b^* e^{-i\theta} + a^* b e^{i\theta}\right) \tag{1} $$ but if $\theta$ varies randomly then the average of $|f|^2$ is $$ \langle|f|^2\rangle = |a|^2 + |b|^2. \tag{2} $$ The difference between (1) and (2) is what people are talking about when they discuss things like 'collapse of the wavefunction'. The reason is that any physical description leading to case (2) can here be replaced by a different physical description making the same prediction. The different description is that $|a|^2$ is the probability for one case and $|b|^2$ is the probability for another, and all we are doing is adding those probabilities.

When two different physical descriptions lead to the same physical predictions then you get debates about which physical description is the more elegant, and the debate cannot be resolved by experimental test. This does not mean the debate is without value, because it concerns things like elegance and coherence of ideas and these are important in science.

On the one hand this whole area is quite subtle so to understand how modern physics deals with it you need quite a lot of learning (university level and beyond). Having said that, modern physics does offer a perfectly coherent account of all such phenomena so they do not present paradoxes or puzzles in that sense.

The chief thing I would offer to someone asking who has not learned quantum measurement theory or quantum field theory is that you have to beware of the loose usage associated with terms such as "measurement" and "observe" in popular accounts of science. Rather than those terms it is better, in the first instance, to speak about interactions and entanglement. For an example, one physical system (called by us a measuring device) interacts with another physical system (called by us a particle) and the two become entangled. What happens next depends on the individual case. It might be that the two subsequently become disentangled, or it might be that instead the larger one then interacts with further systems, spreading the entanglement out into many degrees of freedom, such that the disentanglement never occurs. In the latter case one finds that all the predictions of quantum physics are just as if a collapse of the wavefunction had occurred, but it is not necessary to pick any particular moment when the collapse takes place.

In hopes of clarifying a little, consider a sum such as $$ f = a + e^{i \theta} b $$ where $i^2 = -1$ and to follow this you will need either to know about complex numbers or just take it on trust. Suppose we wish to know the value of $|f|^2$. That's easy, it is $$ |f|^2 = |a|^2 + |b|^2 + \left(a b^* e^{-i\theta} + a^* b e^{i\theta}\right) $$ Now consider what happens when this $|f|^2$ is in fact a probability, as opposed to something like a length or a mass or a time. How do you measure a probability? You can't! Not in one go, at least. Rather you have to try some method such as run an experiment many times and take the average. But now the answers will depend on what happens with $\theta$. If $\theta$ always has the same value (and so do $a$ and $b$) then the average of $|f|^2$ is $$ \langle|f|^2\rangle = |a|^2 + |b|^2 + \left(a b^* e^{-i\theta} + a^* b e^{i\theta}\right) \tag{1} $$ but if $\theta$ varies randomly then the average of $|f|^2$ is $$ \langle|f|^2\rangle = |a|^2 + |b|^2. \tag{2} $$ The difference between (1) and (2) is what people are talking about when they discuss things like 'collapse of the wavefunction'. The reason is that any physical description leading to case (2) can here be replaced by a different physical description making the same prediction. The different description is that $|a|^2$ is the probability for one case and $|b|^2$ is the probability for another, and all we are doing is adding those probabilities.

When two different physical descriptions lead to the same physical predictions then you get debates about which physical description is the more elegant, and the debate cannot be resolved by experimental test. This does not mean the debate is without value, because it concerns things like elegance and coherence of ideas and these are important in science.

Source Link
Andrew Steane
Andrew Steane
  • 61.8k
  • 3
  • 86
  • 252

On the one hand this whole area is quite subtle so to understand how modern physics deals with it you need quite a lot of learning (university level and beyond). Having said that, modern physics does offer a perfectly coherent account of all such phenomena so they do not present paradoxes or puzzles in that sense.

The chief thing I would offer to someone asking who has not learned quantum measurement theory or quantum field theory is that you have to beware of the loose usage associated with terms such as "measurement" and "observe" in popular accounts of science. Rather than those terms it is better, in the first instance, to speak about interactions and entanglement. For an example, one physical system (called by us a measuring device) interacts with another physical system (called by us a particle) and the two become entangled. What happens next depends on the individual case. If might be that the two subsequently become disentangled, or it might be that instead the larger one then interacts with further systems, spreading the entanglement out into many degrees of freedom, such that the disentanglement never occurs. In the latter case one finds that all the predictions of quantum physics are just as if a collapse of the wavefunction had occurred, but it is not necessary to pick any particular moment when the collapse takes place.

In hopes of clarifying a little, consider a sum such as $$ f = a + e^{i \theta} b $$ where $i^2 = -1$ and to follow this you will need either to know about complex numbers or just take it on trust. Suppose we wish to know the value of $|f|^2$. That's easy, it is $$ |f|^2 = |a|^2 + |b|^2 + \left(a b^* e^{-i\theta} + a^* b e^{i\theta}\right) $$ Now consider what happens when this $|f|^2$ is in fact a probability, as opposed to something like a length or a mass or a time. How do you measure a probability? You can't! Not in one go, at least. Rather you have to try some method such as run an experiment many times and take the average. But now the answers will depend on what happens with $\theta$. If $\theta$ always has the same value (and so do $a$ and $b$) then the average of $|f|^2$ is $$ \langle|f|^2\rangle = |a|^2 + |b|^2 + \left(a b^* e^{-i\theta} + a^* b e^{i\theta}\right) \tag{1} $$ but if $\theta$ varies randomly then the average of $|f|^2$ is $$ \langle|f|^2\rangle = |a|^2 + |b|^2. \tag{2} $$ The difference between (1) and (2) is what people are talking about when they discuss things like 'collapse of the wavefunction'. The reason is that any physical description leading to case (2) can here be replaced by a different physical description making the same prediction. The different description is that $|a|^2$ is the probability for one case and $|b|^2$ is the probability for another, and all we are doing is adding those probabilities.

When two different physical descriptions lead to the same physical predictions then you get debates about which physical description is the more elegant, and the debate cannot be resolved by experimental test. This does not mean the debate is without value, because it concerns things like elegance and coherence of ideas and these are important in science.