QM & Consciousness: Has Theory Been Disproven?

In summary, the theory of consciousness playing a fundamental role in quantum mechanics has been largely disproven, with decoherence being the current explanation for the measurement problem. The idea that consciousness causes collapse is not taken seriously and is seen as a weird thought. While it is difficult to eliminate the observer from the equation, this does not suggest that consciousness plays a role in collapse. The Hard Problem of consciousness remains a challenge in QM, but it can be circumvented by considering consciousness as a result of brain states. Many physicists strongly object to the concept of consciousness playing a fundamental role in quantum theory, and it is recommended to read works by Tegmark, Penrose, Chalmers, and follow the advances in neuroscience and philosophy to gain a
  • #1
Pete Hammand
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Just curious, but has this theory been completely disproven? Is it possible to even debate that this is the case? It seems to me that some of the founders of QM such as Heisenberg, Pauli, and even Max Planck toyed with this idea and considered it a possibility. Why is it not any more? I don't see any issue with it being plugged into the equation. If it helps solve the puzzle then why not?
 
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  • #2
Pete Hammand said:
Just curious, but has this theory been completely disproven? Is it possible to even debate that this is the case? It seems to me that some of the founders of QM such as Heisenberg, Pauli, and even Max Planck toyed with this idea and considered it a possibility. Why is it not any more? I don't see any issue with it being plugged into the equation. If it helps solve the puzzle then why not?

Well, there is absolutely no evidence for believing that a conscious observer has any different role in QM than a nonconscious recording device such as a camera. So I don't think there is any special role for consciousness.

I think decoherence has mostly replaced the role that conscious observation once played in QM.
 
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  • #3
stevendaryl said:
Well, there is absolutely no evidence for believing that a conscious observer has any different role in QM than a nonconscious recording device such as a camera. So I don't think there is any special role for consciousness.

I think decoherence has mostly replaced the role that conscious observation once played in QM.
I see. But I had this weird thought, that maybe the decoherence is simply the particle 'knowing' that a conscious observer is measuring it. Not the result of any phenomenon of interacting with the measuring device. It is also hard to eliminate the observer by the very fact that we look at the data...
 
  • #4
I think there is still disagreement on this issue. Here is Ed Witten saying it seems to be a problem (especially 3:00 - 3:10).

 
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  • #5
Of course it hasn't been disproven, nor can it be. Its like solipsism - inherently not provable. Its just a ridiculously weird view of the world that only those attracted to such would embrace.

If you want to know why it gained some adherents read Mathematical Foundations Of Quantum Mechanics by Von Neumann. But the key point is with our modern understanding of decoherence his argument no longer holds.

Thanks
Bill
 
  • #6
stevendaryl said:
I think decoherence has mostly replaced the role that conscious observation once played in QM.
I don't agree. The measurement problem has several aspects, and decoherence helps with some of them, such as how the measurement basis is selected. But the more fundamental ontological problem, if I understand correctly, goes something like this:
Is the wavefunction/ quantum state an entity that exists in space & time, or is it strictly a tool for calculating (probabilistic) results of measurements?
If it is not real, then what does exist between measurements?
But if it is real, then what happens to it after a measurement?
If it "collapses", & this is seen as an objective occurrence, then what could cause such a thing to happen?
Wigner & von Neumann suggested that since all of inanimate matter can be included in the quantum state, whose evolution does not allow for collapse, it must be that collapse as an objective occurrence is caused by interaction with something nonphysical- i.e. consciousness.
Nowadays this is not taken seriously, for one thing because few (scientifically-minded) people still believe that consciousness is nonphysical. Also, can you really believe that the universe was in a superposition of all possibilities for billions of years, until a conscious animal evolved in one tiny branch, at which point the whole thing suddenly collapsed?
The "orthodox" approach to the problem is that the state is not assumed to be real, but that the question of what does exist between measurements is outside the realm of science because, by definition, it has no observable effects.
Those who are not satisfied with this pursue "interpretations" such as many-worlds or bohmian mechanics, or alternative models such as dynamic collapse.
 
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  • #7
Pete Hammand said:
But I had this weird thought, that maybe the decoherence is simply the particle 'knowing' that a conscious observer is measuring it.
QM says that interactions with the environment will quickly change a quantum superposition into something that's indistinguishable from a classical superposition ("it's one of the options; we just don't know which one"). You're suggesting that the real reason isn't that matter behaves quantum mechanically, but that it knows what we're doing. That is a weird thought indeed.

Pete Hammand said:
It is also hard to eliminate the observer by the very fact that we look at the data...
This is true, but it doesn't in any way suggest that consciousness causes collapse.
 
  • #8
atyy said:
I think there is still disagreement on this issue. Here is Ed Witten saying it seems to be a problem (especially 3:00 - 3:10).
The Hard Problem remains hard in QM. However it is easily circumvented. In order to explain consciousness of outcomes one postulates that one's experience supervenes on the state of the brain. One should then follow up by asking why anyone would want to introduce metaphysics into physics.
 
  • #9
Pete Hammand said:
I see. But I had this weird thought, that maybe the decoherence is simply the particle 'knowing' that a conscious observer is measuring it. Not the result of any phenomenon of interacting with the measuring device. It is also hard to eliminate the observer by the very fact that we look at the data...

If you replace the concept of a particle 'knowing' that it is being observed with its state being relative to that of the observer then your line if inquiry will be more fruitful.

For the majorty of physicists consciouness is a concept from neuroscience and philosophy and they strongly object to it playing any fundamental role in quantum theory or cosmology so you will encounter much resistance here.

I suggest you read some Tegmark and Penrose, then for the philosophy
read Chalmers and try to follow the advances in neuroscience.
 
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  • #10
maline said:
I don't agree. The measurement problem has several aspects, and decoherence helps with some of them, such as how the measurement basis is selected. But the more fundamental ontological problem, if I understand correctly, goes something like this:
Is the wavefunction/ quantum state an entity that exists in space & time, or is it strictly a tool for calculating (probabilistic) results of measurements?
If it is not real, then what does exist between measurements?
But if it is real, then what happens to it after a measurement?
If it "collapses", & this is seen as an objective occurrence, then what could cause such a thing to happen?
Wigner & von Neumann suggested that since all of inanimate matter can be included in the quantum state, whose evolution does not allow for collapse, it must be that collapse as an objective occurrence is caused by interaction with something nonphysical- i.e. consciousness.
Nowadays this is not taken seriously, for one thing because few (scientifically-minded) people still believe that consciousness is nonphysical. Also, can you really believe that the universe was in a superposition of all possibilities for billions of years, until a conscious animal evolved in one tiny branch, at which point the whole thing suddenly collapsed?
The "orthodox" approach to the problem is that the state is not assumed to be real, but that the question of what does exist between measurements is outside the realm of science because, by definition, it has no observable effects.
Those who are not satisfied with this pursue "interpretations" such as many-worlds or bohmian mechanics, or alternative models such as dynamic collapse.
Thank you for that reply that really is interesting. To be honest, I think Von Neumann was on to something. The Von Neumann chain is 'cut' once it reaches it's final destination, which is the conscious observer who determines the final outcome-giving certainty. IMO certainty has no meaning without the observer. The particles alone don't bringing certainty.
 
  • #11
maline said:
Nowadays this is not taken seriously, for one thing because few (scientifically-minded) people still believe that consciousness is nonphysical.
Then they haven't thought about it.
maline said:
Also, can you really believe that the universe was in a superposition of all possibilities for billions of years
Why not? The state space defines all those possibilities. Why should the state vector have to hug a basis state?
 
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  • #12
maline said:
I don't agree. The measurement problem has several aspects, and decoherence helps with some of them, such as how the measurement basis is selected. But the more fundamental ontological problem, if I understand correctly, goes something like this:
Is the wavefunction/ quantum state an entity that exists in space & time, or is it strictly a tool for calculating (probabilistic) results of measurements?
If it is not real, then what does exist between measurements?
But if it is real, then what happens to it after a measurement?
If it "collapses", & this is seen as an objective occurrence, then what could cause such a thing to happen?
Wigner & von Neumann suggested that since all of inanimate matter can be included in the quantum state, whose evolution does not allow for collapse, it must be that collapse as an objective occurrence is caused by interaction with something nonphysical- i.e. consciousness.
Nowadays this is not taken seriously, for one thing because few (scientifically-minded) people still believe that consciousness is nonphysical. Also, can you really believe that the universe was in a superposition of all possibilities for billions of years, until a conscious animal evolved in one tiny branch, at which point the whole thing suddenly collapsed?
The "orthodox" approach to the problem is that the state is not assumed to be real, but that the question of what does exist between measurements is outside the realm of science because, by definition, it has no observable effects.
Those who are not satisfied with this pursue "interpretations" such as many-worlds or bohmian mechanics, or alternative models such as dynamic collapse.
I also see your point too, it is odd to think, but maybe consciousness DID exist somehow, but it isn't within our understanding currently of how it did. Because our paradigm says brain creates consciousness, but if it is indeed the other way around, then consciousness must have existed all the way back to the Big. Bang.
 
  • #13
Pete Hammand said:
Thank you for that reply that really is interesting. To be honest, I think Von Neumann was on to something. The Von Neumann chain is 'cut' once it reaches it's final destination, which is the conscious observer who determines the final outcome-giving certainty. IMO certainty has no meaning without the observer. The particles alone don't bringing certainty.
Sure, if you assert that the final destination is consciousness then consciousness has a special role. And if you assert that the final destination is The End of Time then we are in a Many Worlds superposition until then.
 
  • #14
Pete Hammand said:
IMO certainty has no meaning without the observer..
Why are you still saying this? You idea is based on a myth which several people here have shown you is outmoded and incorrect. If you don't understand then you should ask, or even challenge them! Please don't keep reiterating your own opinion when it has been refuted.
 
  • #15
Derek Potter said:
Sure, if you assert that the final destination is consciousness then consciousness has a special role. And if you assert that the final destination is The End of Time then we are in a Many Worlds superposition until then.
I think it scares physicists to think of the implications of consciousness being fundamental, because this worldview implies that there is no 'real world' out there, it's simply a construct of consciousness. It's much more neat and tidy to think of it as a great machine rather than a great thought. But as you said there are many interpretations, and most scientists seem to think that this is not the case.
 
  • #16
maline said:
few (scientifically-minded) people still believe that consciousness is nonphysical

Derek Potter said:
Then they haven't thought about it.
By "nonphysical" I mean "not describable in terms of physical processes", or, in your own words, not supervening on the physical state of the brain (& body).

maline said:
can you really believe that the universe was in a superposition of all possibilities for billions of years, until a conscious animal evolved in one tiny branch, at which point the whole thing suddenly collapsed?
Just to make clear: the unbelievability lies in the "until... suddenly". The many worlds interpretation, which Derek is very excited about, has an uncollapsed state that just continues for all time. That has its own difficulties, but not this particular absurdity.
 
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  • #17
Derek Potter said:
Why are you still saying this? You idea is based on a myth which several people here have shown you is outmoded and incorrect. If you don't understand then you should ask, or even challenge them! Please don't keep reiterating your own opinion when it has been refuted.
I'm not really saying this is a case in a scientific view. That was more of a philosophical statement that you need to think about. It's a silly argument , but a simple one. The only way we can be 'sure' anything exists is through conscious observation, this applies to science, or any area of life for that matter.
 
  • #18
Pete Hammand said:
I'm not really saying this is a case in a scientific view. That was more of a philosophical statement that you need to think about. It's a silly argument , but a simple one. The only way we can be 'sure' anything exists is through conscious observation, this applies to science, or any area of life for that matter.
"We don't do philosophy here" Regrettably this forum has a Philosophy Police who will close a thread even if it is still very active and productive if anyone veers off into something even slightly smelling of philosophy. QM is grounded in certainty and reality through the Postulate of Observations. Observation is imported directly, intact and unexplained into QM from everyday life. It would therefore be ridiculous and quite wrong to expect QM to do anything about "certainty" and "reality" that goes beyond what everyday experience provides.
 
  • #19
I think that it should be possible to formulate the empirical content of QM in a way that doesn't mention observations or observers or consciousness. Something along the lines of this:

Let [itex]\mathcal{S}[/itex] be the set of all macroscopically distinguishable states of the universe. One way to specify this might be to divide up the universe into tiny little cells, and for each cell, describe the contents of the cell in coarse-grained terms: the average number of particles of various types, their average kinetic energies, the total momentum and angular momentum, the average values of electrical and magnetic fields within the cell, etc.

Then we come up with the following mappings:
  1. If [itex]s[/itex] is the macrostate at some time, then assume we have some recipe for computing [itex]\rho_s[/itex], which is a corresponding quantum-mechanical density matrix for the universe (or just for the region of interest).
  2. As sort-of an inverse, if [itex]\rho[/itex] is a density matrix, then let [itex]P_\rho(s)[/itex] be a corresponding probability distribution on macroscopic states.
  3. If [itex]\rho[/itex] is any density matrix, then let [itex]\rho(t)[/itex] be the result of evolving [itex]\rho[/itex] using the Schrodinger equation for a time [itex]t[/itex]
Then in terms of these functions, we can formulate the empirical content of quantum mechanics in a way that doesn't mention observers or observations or measurements or consciousness by saying:
If the universe starts off in macroscopic state [itex]s[/itex], then after time [itex]t[/itex], it will be in state [itex]s'[/itex] with probability [itex]P_{\rho_s(t)}(s')[/itex]​
 
  • #20
maline said:
The many worlds interpretation, which Derek is very excited about, has an uncollapsed state that just continues for all time. That has its own difficulties, but not this particular absurdity.
I am prepared to defend MW from misrepresentation but I do not impose it on an argument, indeed in this case I am explicitly talking about collapse theories. I agree that the "until suddenly" aspect is a different one from the "great big superposition" one but the silliness of it is in assuming a causal role of consciousness at all, not the suddenness. Thank you for reminding me that MWI has its own difficulties, by the way. I must be getting old but I can't seem to remember what they are.
 
  • #21
Derek Potter said:
"We don't do philosophy here" Regrettably this forum has a Philosophy Police who will close a thread even if it is still very active and productive if anyone veers off into something even slightly smelling of philosophy. QM is grounded in certainty and reality through the Postulate of Observations. Observation is imported directly, intact and unexplained into QM from everyday life. It would therefore be ridiculous and quite wrong to expect QM to do anything about "certainty" and "reality" that goes beyond what everyday experience provides.

Hm ok. Is there a theoretical physics forum where this would fit?
 
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  • #22
stevendaryl said:
I think that it should be possible to formulate the empirical content of QM in a way that doesn't mention observations or observers or consciousness. Something along the lines of this:

Let [itex]\mathcal{S}[/itex] be the set of all macroscopically distinguishable states of the universe. One way to specify this might be to divide up the universe into tiny little cells, and for each cell, describe the contents of the cell in coarse-grained terms: the average number of particles of various types, their average kinetic energies, the total momentum and angular momentum, the average values of electrical and magnetic fields within the cell, etc.

Then we come up with the following mappings:
  1. If [itex]s[/itex] is the macrostate at some time, then assume we have some recipe for computing [itex]\rho_s[/itex], which is a corresponding quantum-mechanical density matrix for the universe (or just for the region of interest).
  2. As sort-of an inverse, if [itex]\rho[/itex] is a density matrix, then let [itex]P_\rho(s)[/itex] be a corresponding probability distribution on macroscopic states.
  3. If [itex]\rho[/itex] is any density matrix, then let [itex]\rho(t)[/itex] be the result of evolving [itex]\rho[/itex] using the Schrodinger equation for a time [itex]t[/itex]
Then in terms of these functions, we can formulate the empirical content of quantum mechanics in a way that doesn't mention observers or observations or measurements or consciousness by saying:
If the universe starts off in macroscopic state [itex]s[/itex], then after time [itex]t[/itex], it will be in state [itex]s'[/itex] with probability [itex]P_{\rho_s(t)}(s')[/itex]​
You're still ultimately left with probability though.
 
  • #23
Pete Hammand said:
Hm ok. Is there a theoretical physics forum where this would fit?
No idea. If you find one let me know will you? Thanks for taking the point graciously.
 
  • #24
Pete Hammand said:
You're still ultimately left with probability though.
Yes, but you can distinguish, if you want to, between probability that is caused by an actual random jump and probability in terms of likely (yes that's circular) statistics in a series of measurements, or, in MWI, of finding oneself in a particular branch. And so on. It's not a simple matter of "you're still ultimately left with probability".
 
  • #25
stevendaryl said:
I think that it should be possible to formulate the empirical content of QM in a way that doesn't mention observations or observers or consciousness. Something along the lines of this:

Let [itex]\mathcal{S}[/itex] be the set of all macroscopically distinguishable states of the universe. One way to specify this might be to divide up the universe into tiny little cells, and for each cell, describe the contents of the cell in coarse-grained terms: the average number of particles of various types, their average kinetic energies, the total momentum and angular momentum, the average values of electrical and magnetic fields within the cell, etc.

Then we come up with the following mappings:
  1. If [itex]s[/itex] is the macrostate at some time, then assume we have some recipe for computing [itex]\rho_s[/itex], which is a corresponding quantum-mechanical density matrix for the universe (or just for the region of interest).
  2. As sort-of an inverse, if [itex]\rho[/itex] is a density matrix, then let [itex]P_\rho(s)[/itex] be a corresponding probability distribution on macroscopic states.
  3. If [itex]\rho[/itex] is any density matrix, then let [itex]\rho(t)[/itex] be the result of evolving [itex]\rho[/itex] using the Schrodinger equation for a time [itex]t[/itex]
Then in terms of these functions, we can formulate the empirical content of quantum mechanics in a way that doesn't mention observers or observations or measurements or consciousness by saying:
If the universe starts off in macroscopic state [itex]s[/itex], then after time [itex]t[/itex], it will be in state [itex]s'[/itex] with probability [itex]P_{\rho_s(t)}(s')[/itex]​
How do you use all the Physics symbols? Lol. I'm typing on an ipad here and wanted to write out some math earlier but wasn't sure how to do it.
 
  • #26
Pete Hammand said:
How do you use all the Physics symbols? Lol. I'm typing on an ipad here and wanted to write out some math earlier but wasn't sure how to do it.
The toolbar over the reply box - the one which starts with B I U etc - click on the ∑ at the end
 
  • #27
Derek Potter said:
Yes, but you can distinguish, if you want to, between probability that is caused by an actual random jump and probability in terms of likely (yes that's circular) statistics in a series of measurements, or, in MWI, of finding oneself in a particular branch. and so on. It's not a simple matter of "you're still ultimately left with probability".
Thank you, I'm not very knowledgeable of physics beyond an AP physics class I took back in high school (which was over a decade ago), so if I'm wrong on anything feel free to correct me. I've been reading a lot of science/physics related books recently and thought it would be fun to throw some of my ideas on here and see what people who are well versed in physics have to say about it.
 
  • #28
Pete Hammand said:
How do you use all the Physics symbols? Lol. I'm typing on an ipad here and wanted to write out some math earlier but wasn't sure how to do it.

If you know the formatting language LaTex, then you can make mathematical symbols by writing [ itex ] some symbols [ / itex ] (without the spaces).

I don't know a whole lot of LaTex, but some basics are:

Greek letters:
[ itex ]\psi[ /itex ] [itex]\rightarrow \psi[/itex]

Calligraphic letters:
[ itex ]\mathcal{S}[ /itex] [itex]\rightarrow \mathcal{S}[/itex]

Super and subscripts:

[ itex ]A_{\alpha}^{\beta} [ /itex ] [itex]\rightarrow A_\alpha^\beta[/itex]
 
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  • #29
stevendaryl said:
If you know the formatting language LaTex, then you can make mathematical symbols by writing [ itex ] some symbols [ / itex ] (without the spaces).

I don't know a whole lot of LaTex, but some basics are:

Greek letters:
[ itex ]\psi[ /itex ] [itex]\rightarrow \psi[/itex]

Calligraphic letters:
[ itex ]\mathcal{S}[ /itex] [itex]\rightarrow \mathcal{S}[/itex]

Super and subscripts:

[ itex ]A_{\alpha}^{\beta} [ /itex ] [itex]\rightarrow A_\alpha^\beta[/itex]

Or, as Derek says, you can just click the symbols appearing above the edit box. That's a subset of what you can do with LaTex, though.
 
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  • #30
Pete Hammand said:
Thank you, I'm not very knowledgeable of physics beyond an AP physics class I took back in high school (which was over a decade ago), so if I'm wrong on anything feel free to correct me. I've been reading a lot of science/physics related books recently and thought it would be fun to throw some of my ideas on here and see what people who are well versed in physics have to say about it.
Ah, well if it's fun you want, this might not be the best place to look :). Actually it's well worth struggling with some of the papers people will link you to. Certainly there is at least one expert here who will point you to some heavy-duty maths without so much as a compass to guide you, let alone a Sat Nav. But there are others who try to spell stuff out and it's worth the struggle. That is indeed fun, if perhaps an acquired taste. Good authors, even if they condense the maths into an impenetrable block, often put in excellent readable discussion sections.
By the way, my physics degree is over forty years old. Most of measurement theory and decoherence theory hadn't been recognised and they were still trying to find the top quark. Not being a professional physicist (Copenhagen put me off QM and what's the point of physics without QM?!), I've had to forage and glean what I can.
 
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  • #31
bhobba said:
Of course it hasn't been disproven, nor can it be. Its like solipsism - inherently not provable. Its just a ridiculously weird view of the world that only those attracted to such would embrace.

If you want to know why it gained some adherents read Mathematical Foundations Of Quantum Mechanics by Von Neumann. But the key point is with our modern understanding of decoherence his argument no longer holds.

Thanks
Bill

Fredrik said:
QM says that interactions with the environment will quickly change a quantum superposition into something that's indistinguishable from a classical superposition ("it's one of the options; we just don't know which one"). You're suggesting that the real reason isn't that matter behaves quantum mechanically, but that it knows what we're doing. That is a weird thought indeed.This is true, but it doesn't in any way suggest that consciousness causes collapse.

Derek Potter said:
The Hard Problem remains hard in QM. However it is easily circumvented. In order to explain consciousness of outcomes one postulates that one's experience supervenes on the state of the brain. One should then follow up by asking why anyone would want to introduce metaphysics into physics.

I think what all these replies assume is that the measurement problem has at least one solution, ie. Bohmian Mechanics or MWI can be considered "consensus" quantum mechanics.

As long as the measurement problem has not been solved or is asserted not to matter, the observer retains fundamental status. One may argue whether the observer is the same as consciousness, but that is semantics. Neither are explained in terms of more fundamental things, so they are just names for objects that fundamentally postulated, so one can call it the "observer" or "consciousness" or "pink fairies". "Consciousness" is not a terrible term, because bhobba and Weinberg's preferred term is "common sense", and Witten calls it "consciousness".
 
  • #32
atyy said:
I think what all these replies assume is that the measurement problem has at least one solution, ie. Bohmian Mechanics or MWI can be considered "consensus" quantum mechanics.

As long as the measurement problem has not been solved or is asserted not to matter, the observer retains fundamental status. One may argue whether the observer is the same as consciousness, but that is semantics. Neither are explained in terms of more fundamental things, so they are just names for objects that fundamentally postulated, so one can call it the "observer" or "consciousness" or "pink fairies". "Consciousness" is not a terrible term, because bhobba and Weinberg's preferred term is "common sense", and Witten calls it "consciousness".
Exactly what I was thinking.
 
  • #33
atyy said:
As long as the measurement problem has not been solved or is asserted not to matter, the observer retains fundamental status.

I really don't see that. The empirical content of QM is just as well explained by saying that macroscopic quantities have definite values. Consciousness in the human brain would be just a particular instance of that.
 
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  • #34
stevendaryl said:
I really don't see that. The empirical content of QM is just as well explained by saying that macroscopic quantities have definite values. Consciousness in the human brain would be just a particular instance of that.

If you are using the orthodox flavour of Copenhagen, say Landau & Lifshitz's version, then we have a fundamental division of the universe into macroscopic and quantum. The thing that is placing this cut can reasonably be called the observer or consciousness. I suppose it is not so bad if the cut cannot be shifted, so the cut is objective. However, most people would consider the cut shiftable.
 
  • #35
atyy said:
If you are using the orthodox flavour of Copenhagen, say Landau & Lifshitz's version, then we have a fundamental division of the universe into macroscopic and quantum. The thing that is placing this cut can reasonably be called the observer or consciousness. I suppose it is not so bad if the cut cannot be shifted, so the cut is objective. However, most people would consider the cut shiftable.

Okay, if you want to conflate the macroscopic/microscopic distinction with the conscious/nonconscious distinction, then I agree with you. But the reason I like the macroscopic/microscopic distinction is that it doesn't rely on unmotivated distinctions between say, a conscious human and an unconscious recording device. I don't think that distinction serves any purpose. You can replace a human observer by a machine, and nothing about QM changes, as far as I can see.

On the other hand, I see the macroscopic/microscopic distinction as unsatisfying, for other reasons. For one thing, the cutoff is pretty arbitrary.
 

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