A question about the observer effect

[bilby]

Sorry for the delay in responding - I was in the process of reading it when you PMed me, and I have deliberately been avoiding reading this thread until I finished in case of spoilers.

As I see it, Liu was employing the observer effect as a plot device - a way for the researchers to realize that they were being spied upon. When Ball Lightning is considered as a kind of prequel to Three Body, this makes a lot of sense from the narrative perspective. My first thought was that in such a 'noisy' environment, an uncollapsed waveform would be hugely implausible - but then, so is an electron the size of a soccer ball, or atomic nucleii that fuse at low temperatures and emit energy that effects very specific materials while leaving others unaffected. In short, it's science fiction, and the laws of physics can be whatever the author wants them to be. Liu has an excellent core of hard science in his work, but it necessarily takes a back seat to telling the story he wants to tell.

When a major thread of your novel is the exploration of quantum weirdness at macroscopic scales, it would be difficult and surprising to waste something as strange as the observer effect, by not having it too act rather differently and on a rather larger scale from its real world behaviour. I think it's excusable in this case, just as are the changes he makes to the other effects he appropriates. He isn't writing a textbook; He's speculating about how things would be if things were just a bit different. All SciFi does that - and IMO he does it better than most.

But saying it's "the observational apparatus itself that causes wave function collapse" isn't changing the effect or having it act a bit differently from its real world behavior. It matches the observed real world behavior to a T. That's why the infamous "it takes consciousness to collapse wave functions" interpretation of quantum mechanics is an interpretation, not a case of playing fast and loose with the science for the sake of the story, or for the sake of love of mysticism. A lot of hard-nosed first rate physicists have accepted that interpretation, most famously Eugene Wigner, who won a Nobel Prize. The consciousness interpretation is named after John von friggin' Neumann, although it's not clear whether he actually favored it or merely considered it an equally viable possibility. The physicists who accept that view do not do so because they're under the spell of new age woo peddlers. They do so because they feel pushed into it, much against their natural inclinations, by all the severe difficulties with all the alternative interpretations.

Of course it's shocking that something so prima facie ridiculous could come from serious science. But anybody who thinks that's all it takes to settle the matter should heed Niels Bohr's dictum: anybody who isn't shocked by quantum mechanics has not understood it. Not saying the consciousness hypothesis is right -- what do I know? Just saying people who treat the idea with the contempt it's getting in this thread are de facto claiming Wigner and von Neumann were idiots. They weren't idiots. They were smarter than all of us put together.

Liu goes somewhat outside the lines though. But only slightly. And for sound narrative reasons.

In some parts of the book, superposition takes considerable time to 'fade' after an observer is introduced. It works within the story, and he's not trying to write a textbook. IMO it's excellent science fiction, and doesn't stray far from reality (to the best of my ability to tell - I suspect he knows a lot more than I do on the subject). I am not aware of any observations of gradual wave function collapse. But then, there are lots of real things that I am not aware of.

 

[steve_bank]

No. There is no psi-function for flippin a coin. That is just macroscopic probability due to fact that we dont have enough knowledge about the forces in that specific system at that time.

The psi-wave is something else. Its an actual entity.

A wave function is a probability distribution. It describes behavior in a system. The coin is an example of what is meant by a wave function collapsing into a measurable state.

Nothing nautical or complicated. Using the words wave and collapse are loaded words conjuring up images, as with 'imaginary' numbers. Get past the jargon and underlying QM is basic math. It is the endless possibilities of interpretation that lead to confusion.

As Irember the rectangular potential well from a modern physics class. The solution to the wave equation is sines and cosines. In a gas laser as a one dimensional potential well the wave function leads to the probability of a photon being in an area dydx. When wavelength of the photons are integer multiples of the well resonance occurs and a standing wave results, a sine wave. The wave function says the probability of a photon at an antinode, sine zero crossing, is low. The probability of a photon at a node or peak high.

As in probability distribution functions integrate the PDF ovr dx to get the cumulative distribution of a photon in the well..

The derivation in the link shows results in complex phasor form.

Theoretically a wave function could be developed for every particle in the universe, ignoring arguments over cosmology. I belive a wave function can be derived for a coin toss.

https://en.wikipedia.org/wiki/Rectangular_potential_barrier

Scroll down to where it is normalized, a statistical technique, to be a probability distribution function, integral over infinity = 1.

https://en.wikipedia.org/wiki/Wave_function

There are probably some holes in how I presented it, I think it covers it.

 

[Bomb#20]

How can quantum physics be any more weird than anything else? People once thought radio waves passing through their house was weird, and scary.

I.e., you don't understand quantum physics. That's not from me; that's Niels Bohr saying you don't understand.

As the saying goes, for every complex problem there is an answer that is clear, simple, and wrong. The many reassuring pictures people draw for themselves of quantum phenomena to make it feel no weirder than anything else are clear, simple, and wrong. Wave function collapse is not merely the effect of any physical interaction with the object. If you hit a superposed atom with a photon it doesn't collapse the atom's wave function -- you just get a more complicated superposed wave function for the whole atom+photon system. So if we suppose it's not the observer's mind but the Geiger counter's click that collapses the wave function, then we have the problem of explaining how a trillion elementary particle interactions are collectively able to do what no single interaction can do. Quantum mechanics proclaims the universe follows two rules: the Dirac equation describes how quantum objects interact with each other, and the Born rule describes how they interact with classical objects. The trouble is, the two rules are different, so what QM predicts will happen in an interaction depends on whether one of the objects is quantum or classical, even though a classical object is nothing but an amalgam of trillions of quantum objects. So how does nature "decide" which rule to apply?

Likewise, the wave function can't be merely not knowing the status of the unobserved particle. Ignorance does not generate interference patterns. Not knowing which hole the electron goes through cannot account for the fact that removing an obstruction can reduce the chance of the electron reaching the target.

Contrariwise, the wave function can't be a normal physical object like a radio wave either. Radio waves wave in normal physical space, in three dimensions, and exert forces on charged objects in three dimensional space when part of the wave passes over their locations in 3-d space. But quantum wave functions, in contrast, wave in "configuration space" -- the wave function of the atom+photon system has to be computed in a space of at least six dimensions -- the coordinates of the atom and of the electron are treated as a single 6-d position of a single object because if you treat them as two 3-d positions you get wrong answers -- and you need more dimensions if you want more accuracy because the atom has electrons that have their own independent coordinates. This is why there are "entanglement" effects, where two particles that interacted in the past keep interfering with each other long after they separated. So where is this space of a large but indeterminate number of dimensions, that mediates every interaction of particles that happen to meet in 3-space?

Entanglement is real. It's so weird that Einstein proposed an experiment that he intended would prove quantum mechanics was only an approximation, by showing the particles don't continue to interfere with each other over macroscopic distances, and showing the wave function really is just a statistical model, a description of our ignorance. But when technology advanced to the point that his experiment could be carried out, it did not come out the way Einstein predicted -- the way it would have had to come out if the quantum world were no weirder than radio waves. It came out the way Bohr predicted.

 

[bilby]

As classical entities, humans are ill equipped to understand quantum effects. We have a built in tendency to try to make analogies with the classical ideas that dominate our understanding; And that tendency is demonstrably wrong.

Mermin gives us the only rigorous way out so far - Shut up and calculate.

Liu gives us the only other option - Write fiction, and accept that it is just storytelling.

There's nothing wrong with make-believe, as long as we keep in the back of our minds the knowledge that it's all just stories.

 

[Treedbear]

... Wave function collapse is not merely the effect of any physical interaction with the object. If you hit a superposed atom with a photon it doesn't collapse the atom's wave function -- you just get a more complicated superposed wave function for the whole atom+photon system. So if we suppose it's not the observer's mind but the Geiger counter's click that collapses the wave function, then we have the problem of explaining how a trillion elementary particle interactions are collectively able to do what no single interaction can do. ...

Likewise, the wave function can't be merely not knowing the status of the unobserved particle. Ignorance does not generate interference patterns. Not knowing which hole the electron goes through cannot account for the fact that removing an obstruction can reduce the chance of the electron reaching the target.
...

Perhaps the double slit experiment is producing "a more complicated superposed wave function for the whole atom observer+photon system.", as you might phrase it. What appears to be the destruction of the interference pattern is actually just a much more complex one. Like a raw hologram imprint. It might re-appear if a coherent reference image was superimposed. Filtering or sorting the data in a way analogous to how the delayed choice quantum eraser method works.

 

[steve_bank]

How can quantum physics be any more weird than anything else? People once thought radio waves passing through their house was weird, and scary.

I.e., you don't understand quantum physics. That's not from me; that's Niels Bohr saying you don't understand.

As the saying goes, for every complex problem there is an answer that is clear, simple, and wrong. The many reassuring pictures people draw for themselves of quantum phenomena to make it feel no weirder than anything else are clear, simple, and wrong. Wave function collapse is not merely the effect of any physical interaction with the object. If you hit a superposed atom with a photon it doesn't collapse the atom's wave function -- you just get a more complicated superposed wave function for the whole atom+photon system. So if we suppose it's not the observer's mind but the Geiger counter's click that collapses the wave function, then we have the problem of explaining how a trillion elementary particle interactions are collectively able to do what no single interaction can do. Quantum mechanics proclaims the universe follows two rules: the Dirac equation describes how quantum objects interact with each other, and the Born rule describes how they interact with classical objects. The trouble is, the two rules are different, so what QM predicts will happen in an interaction depends on whether one of the objects is quantum or classical, even though a classical object is nothing but an amalgam of trillions of quantum objects. So how does nature "decide" which rule to apply?

Likewise, the wave function can't be merely not knowing the status of the unobserved particle. Ignorance does not generate interference patterns. Not knowing which hole the electron goes through cannot account for the fact that removing an obstruction can reduce the chance of the electron reaching the target.

Contrariwise, the wave function can't be a normal physical object like a radio wave either. Radio waves wave in normal physical space, in three dimensions, and exert forces on charged objects in three dimensional space when part of the wave passes over their locations in 3-d space. But quantum wave functions, in contrast, wave in "configuration space" -- the wave function of the atom+photon system has to be computed in a space of at least six dimensions -- the coordinates of the atom and of the electron are treated as a single 6-d position of a single object because if you treat them as two 3-d positions you get wrong answers -- and you need more dimensions if you want more accuracy because the atom has electrons that have their own independent coordinates. This is why there are "entanglement" effects, where two particles that interacted in the past keep interfering with each other long after they separated. So where is this space of a large but indeterminate number of dimensions, that mediates every interaction of particles that happen to meet in 3-space?

Entanglement is real. It's so weird that Einstein proposed an experiment that he intended would prove quantum mechanics was only an approximation, by showing the particles don't continue to interfere with each other over macroscopic distances, and showing the wave function really is just a statistical model, a description of our ignorance. But when technology advanced to the point that his experiment could be carried out, it did not come out the way Einstein predicted -- the way it would have had to come out if the quantum world were no weirder than radio waves. It came out the way Bohr predicted.

Depends on what you mean by understand. In the 19th century it was understood that time was absolute and matter was 'solid'.

QM is a deeper model than classical/Newtonian physics but still just a model. Whether there is something deeper who knows.The best example is Planck's explanation of BB radiation for which classical physics did not work.

The Fourier Transform is what it is regardless of application to QM or electronics, same with probabilities and statistics.I am with the shut up and calculate crowd to a degree. Imagination and what ifs based on existing theory leads to possible new science. AE and relativity. Maxwell and electromagnetics.

Speculation on things like multi universe and the nature of quantum reality is philosophy and entertainment. The flood of scifi.

Science is modeling observation. Because Bohr was a scientist doesn't mean he was an emotionless Vulcan.

Entanglement is an experiment and observation...is there some great human revelation and shattering truth in the experiment? Reality is what it is. You are churning QM into woo. I posted a link on an application of the WE and how it ends being a probility distribution.

Flip a coin in the dark. As It moves through space there is a probability of being in a given orientation. Flash a light and take a picture and the wave function collapses into an observable state.

Systems of particles are more complicated, but the same principle. Do you understand?

I go back to Popper's book on objective knowledge. His point was that the only thing we can reasonably consider is an experient. As debate even within the bounds of science expands around the experiment it becomes increasingly subjective. In the extreme we call it woo.

Hawkinga ar times drifted into the phantasmagorical. Mako's pop science shows spinning scince into the mystical.

 

[Jokodo]

Flip a coin in the dark. As It moves through space there is a probability of being in a given orientation. Flash a light and take a picture and the wave function collapses into an observable state.

It most certainly doesn't. A copper coin is not a particle, its very much a macroscopic object. 1 gram of copper contains about 9.5 (short scale) sextillion atoms. There's no wave function to collapse because its tumble could always be described adequately in deterministic terms.

A wave function collapse is not just a removal of uncertainty.

 

[steve_bank]

Flip a coin in the dark. As It moves through space there is a probability of being in a given orientation. Flash a light and take a picture and the wave function collapses into an observable state.

It most certainly doesn't. A copper coin is not a particle, its very much a macroscopic object. 1 gram of copper contains about 9.5 (short scale) sextillion atoms. There's no wave function to collapse because its tumble could always be described adequately in deterministic terms.

A wave function collapse is not just a removal of uncertainty.

Big grin. You continue to conflate Newtonian/continuum mechanics with QM. A coin is made of atoms made of particles. From a QN view ut is a system of particles. You continue to reject quantization of matter into discrete units despite existing theory.

A wave function can be developed that describes the probabilities of each copper atom as a system in space. It is not a physical wave, a wave equation is a mathematical model of particles. The word collapse is metaphor.

You know the probabilities of of the state of a system of particles, you can only know a state by measurement. It is no more complicated than that.

To the OP question the problem with particles is the energy represented by the measurement can be in the range of the energy of the particles being measured, so it can be difficult to separate measurement and effect of measurement on the system being measured.

Any measurement adds or subtracts energy with the system being measured. A small thermocouple has little effect on the thermal equilibrium of the ocean when measuring ocean temperature. A smasll thermocouple upsets the thermal equilibrium of a thimblefull of water.

 

[Jokodo]

Flip a coin in the dark. As It moves through space there is a probability of being in a given orientation. Flash a light and take a picture and the wave function collapses into an observable state.

It most certainly doesn't. A copper coin is not a particle, its very much a macroscopic object. 1 gram of copper contains about 9.5 (short scale) sextillion atoms. There's no wave function to collapse because its tumble could always be described adequately in deterministic terms.

A wave function collapse is not just a removal of uncertainty.

Big grin. You continue to conflate Newtonian/continuum mechanics with QM. A coin is made of atoms made of particles. From a QN view ut is a system of particles. You continue to reject quantization of matter into discrete units despite existing theory.

A wave function can be developed that describes the probabilities of each copper atom as a system in space. It is not a physical wave, a wave equation is a mathematical model of particles. The word collapse is metaphor.

You know the probabilities of of the state of a system of particles, you can only know a state by measurement. It is no more complicated than that.

To the OP question the problem with particles is the energy represented by the measurement can be in the range of the energy of the particles being measured, so it can be difficult to separate measurement and effect of measurement on the system being measured.

Any measurement adds or subtracts energy with the system being measured. A small thermocouple has little effect on the thermal equilibrium of the ocean when measuring ocean temperature. A smasll thermocouple upsets the thermal equilibrium of a thimblefull of water.

I something don't get the impression I'm the one conflating stuff.

Atoms are macroscopic objects for Most practical purposes, QM does not mean conservation of momentum can be violated, and stochastic processes do lead to deterministic outcomes.

 

[Jokodo]

When you cast a fair die once, the result can be anything from 1-6 with equal probability. When you cast the Same die a septillion times, the summed result will inevitably be, to within a very narrow margin, 3.5 septillions.

And that's just the you don't understand stochastics part.

 

[steve_bank]

When you cast a fair die once, the result can be anything from 1-6 with equal probability. When you cast the Same die a septillion times, the summed result will inevitably be, to within a very narrow margin, 3.5 septillions.

And that's just the you don't understand stochastics part.

Toss a coin and on each trial the probability is always 50/50. On any given die toss the probability is 1/6. It is why it is called random.

In statistics random means events are uncorrelated. The last event does not affect the probability of the next event.

Put 9 red and 1 blue ball in a box. Pick one and the odds of blue are 1/10. Put it back in, shake the box, and the odds of picking the blue ball are still 1/10. Repeat the process say 1000 times and red will appear 90% of the time and blue 10% of the time. That is the basis of quality control by sampling. That is an experiment I did 30 years ago to convince myself. Same with flipping a coin. .


The idea that previous random events affect future random events is called subjectivism. It is what gamblers at craps do when they think they see predictive patterns.

In my first incarnation I was reliability and quality control engineer.

Do you really want to discuss stochastic systems? Go ahead. In reliability Failure Modes And Criticality Analysis can be in part stochastic modeling. Given a set of component failure probilities what is the probilities of of the resultant state given one or more ecvents.

Or in nan deterministic control systems. Given the system is one sate what is the probability of one of several next sates. Probabilities and sate variables.

 

[Bomb#20]

... Wave function collapse is not merely the effect of any physical interaction with the object. If you hit a superposed atom with a photon it doesn't collapse the atom's wave function -- you just get a more complicated superposed wave function for the whole atom+photon system. So if we suppose it's not the observer's mind but the Geiger counter's click that collapses the wave function, then we have the problem of explaining how a trillion elementary particle interactions are collectively able to do what no single interaction can do. ...

Likewise, the wave function can't be merely not knowing the status of the unobserved particle. Ignorance does not generate interference patterns. Not knowing which hole the electron goes through cannot account for the fact that removing an obstruction can reduce the chance of the electron reaching the target.
...

Perhaps the double slit experiment is producing "a more complicated superposed wave function for the whole atom observer+photon system.", as you might phrase it. What appears to be the destruction of the interference pattern is actually just a much more complex one. Like a raw hologram imprint. It might re-appear if a coherent reference image was superimposed. Filtering or sorting the data in a way analogous to how the delayed choice quantum eraser method works.

And that's the sort of thinking that leads people down the path to Many-Worlds. An awful lot of first rate physicists accept that interpretation too. But inevitably, like every other interpretation, it has its own set of problems.

Probably the most severe is that it denies that the wave function ever collapses at all. But the only thing quantum mechanics has to offer to turn wave function amplitudes into empirically measurable probabilities is the Born rule, the rule that when the wave function collapses the universe throws away its phase, squares its absolute value, and picks an outcome. No collapse means no squaring means no way to get from the computed amplitude to the experienced frequency. When the photon hits the glass and the wave function is reflected with amplitude .2 and refracted with amplitude .8, the universe divides, and now there's an observer who sees a reflection and an observer who doesn't. Do it 25 times in a row and now there are 33 million observers -- and an awful lot more of them saw twelve photons reflected than saw only one. But .2 squared is .04 and experience tells us we'll typically see only one reflected photon out of 25.

 

[Jokodo]

When you cast a fair die once, the result can be anything from 1-6 with equal probability. When you cast the Same die a septillion times, the summed result will inevitably be, to within a very narrow margin, 3.5 septillions.

And that's just the you don't understand stochastics part.

Toss a coin and on each trial the probability is always 50/50. On any given die toss the probability is 1/6. It is why it is called random.

In statistics random means events are uncorrelated. The last event does not affect the probability of the next event.

Indeed. And that's part of why applying QM reasoning to a macroscopic object like a coin consisting of ~1e22 copper atoms, or 1e24 particles, is unreasonable. The standard deviation of the outcome around the expected mean with n tosses of a fair six-sided dice is calculated by sqrt(n * 35/12). Plugging 1e24 into this formula gives a value of just about 1/1e12 the total range of possible outcomes of 1-6 septillions, well within the expected error range of any measurement we could hope to make. In other words, if we don't know the current position and orientation of a tumbling coin, it's not because of QM, and bringing in QM shows that you either don't understand probabilities, or QM, or both.

 

[steve_bank]

When you cast a fair die once, the result can be anything from 1-6 with equal probability. When you cast the Same die a septillion times, the summed result will inevitably be, to within a very narrow margin, 3.5 septillions.

And that's just the you don't understand stochastics part.

Toss a coin and on each trial the probability is always 50/50. On any given die toss the probability is 1/6. It is why it is called random.

In statistics random means events are uncorrelated. The last event does not affect the probability of the next event.

Indeed. And that's part of why applying QM reasoning to a macroscopic object like a coin consisting of ~1e22 copper atoms, or 1e24 particles, is unreasonable. The standard deviation of the outcome around the expected mean with n tosses of a fair six-sided dice is calculated by sqrt(n * 35/12). Plugging 1e24 into this formula gives a value of just about 1/1e12 the total range of possible outcomes of 1-6 septillions, well within the expected error range of any measurement we could hope to make. In other words, if we don't know the current position and orientation of a tumbling coin, it's not because of QM, and bringing in QM shows that you either don't understand probabilities, or QM, or both.

Again, read the link on potential wells. In the case of a rectangular well the wave equation is a second order differential equation. The arbitrary constants are solved from the boundary-initial conditions. To generate the wave function for coin toss would require a set of initial conditions. If you do not understand that than you are just shooting in the dark.


Means and sd....sounds pretty esoteric. Intriguing. I'll have to read up on it. Don't Have a clue what you are trying to prove.

What is the underlying justification for using the arithmetic mean as an estimator?

Developing a wave function for the moon can be done, but it has no practical value. The moon is an aggregate of the quantum states of each particle in the moon. Practicality is not the question. Newtonian reality is the sum of probabilities of particles. In an electronics metaphor reality is noisy, always fluctuating.

As the degrees of freedom and density of states get large from particle to an object like the moon the energy difference between states becomes continuous in the limit. Which is why we treat Newtonian variables as continuous.

The coin toss was an example of the collapse of a wave function.

 

[bilby]

Obligatory SMBC:

 

[steve_bank]

To be precise and even a bit picaune, there are three states for a coin if you count landing upright. For a die add the edges and points to the flat surfaces.

 

[Treedbear]

... Wave function collapse is not merely the effect of any physical interaction with the object. If you hit a superposed atom with a photon it doesn't collapse the atom's wave function -- you just get a more complicated superposed wave function for the whole atom+photon system. So if we suppose it's not the observer's mind but the Geiger counter's click that collapses the wave function, then we have the problem of explaining how a trillion elementary particle interactions are collectively able to do what no single interaction can do. ...

Likewise, the wave function can't be merely not knowing the status of the unobserved particle. Ignorance does not generate interference patterns. Not knowing which hole the electron goes through cannot account for the fact that removing an obstruction can reduce the chance of the electron reaching the target.
...

Perhaps the double slit experiment is producing "a more complicated superposed wave function for the whole atom observer+photon system.", as you might phrase it. What appears to be the destruction of the interference pattern is actually just a much more complex one. Like a raw hologram imprint. It might re-appear if a coherent reference image was superimposed. Filtering or sorting the data in a way analogous to how the delayed choice quantum eraser method works.

And that's the sort of thinking that leads people down the path to Many-Worlds. An awful lot of first rate physicists accept that interpretation too. But inevitably, like every other interpretation, it has its own set of problems.

Probably the most severe is that it denies that the wave function ever collapses at all.

But you said:

... Wave function collapse is not merely the effect of any physical interaction with the object. If you hit a superposed atom with a photon it doesn't collapse the atom's wave function -- you just get a more complicated superposed wave function for the whole atom+photon system. ...

So why isn't it possible that in the double slit experiment the interference produced by the wave function is not visible simply because it has become much too complex to recognize? I'm not entertaining the MWI (or other woo).

The following part of your post is beyond my depth of understanding:

But the only thing quantum mechanics has to offer to turn wave function amplitudes into empirically measurable probabilities is the Born rule, the rule that when the wave function collapses the universe throws away its phase, squares its absolute value, and picks an outcome. No collapse means no squaring means no way to get from the computed amplitude to the experienced frequency. When the photon hits the glass and the wave function is reflected with amplitude .2 and refracted with amplitude .8, the universe divides, and now there's an observer who sees a reflection and an observer who doesn't. Do it 25 times in a row and now there are 33 million observers -- and an awful lot more of them saw twelve photons reflected than saw only one. But .2 squared is .04 and experience tells us we'll typically see only one reflected photon out of 25.

 

[Jokodo]

Indeed. And that's part of why applying QM reasoning to a macroscopic object like a coin consisting of ~1e22 copper atoms, or 1e24 particles, is unreasonable. The standard deviation of the outcome around the expected mean with n tosses of a fair six-sided dice is calculated by sqrt(n * 35/12). Plugging 1e24 into this formula gives a value of just about 1/1e12 the total range of possible outcomes of 1-6 septillions, well within the expected error range of any measurement we could hope to make. In other words, if we don't know the current position and orientation of a tumbling coin, it's not because of QM, and bringing in QM shows that you either don't understand probabilities, or QM, or both.

Again, read the link on potential wells. In the case of a rectangular well the wave equation is a second order differential equation. The arbitrary constants are solved from the boundary-initial conditions. To generate the wave function for coin toss would require a set of initial conditions.

Any prediction requires knowledge of the initial conditions. In the case of a coin toss, if you were to know the initial conditions with sufficient precision, a purely deterministic Model of reality is sufficient to predict its behavior with a much higher accuracy than you could ever hope to measure. No need to refer to QM at all.

If you do not understand that than you are just shooting in the dark.


Means and sd....sounds pretty esoteric. Intriguing. I'll have to read up on it. Don't Have a clue what you are trying to prove.

The range of hypothetically possible outcomes for the sum of a septillion dice is from one to six septillions. In that range, you only ever need to concern yourself with values between 3.4999999999 and 3.500000001 septillions, and probably several orders of magnitude narrower. The same Holds for a tumbling coin consisting of a septillion particles. Even is every particle has an uncorrelated chance of being in any arbiträre state along its range of possibilities, itself, I believe, a misunderstanding, the sum is everything but unpredictable. QM or the observer effect Play no role in explaining our inability to predict the outcome.

What is the underlying justification for using the arithmetic mean as an estimator?

Developing a wave function for the moon can be done, but it has no practical value. The moon is an aggregate of the quantum states of each particle in the moon. Practicality is not the question. Newtonian reality is the sum of probabilities of particles. In an electronics metaphor reality is noisy, always fluctuating.

As the degrees of freedom and density of states get large from particle to an object like the moon the energy difference between states becomes continuous in the limit. Which is why we treat Newtonian variables as continuous.

The coin toss was an example of the collapse of a wave function.

It doesn't work as such.

 

[steve_bank]

Any prediction requires knowledge of the initial conditions. In the case of a coin toss, if you were to know the initial conditions with sufficient precision, a purely deterministic Model of reality is sufficient to predict its behavior with a much higher accuracy than you could ever hope to measure. No need to refer to QM at all.

If you do not understand that than you are just shooting in the dark.


Means and sd....sounds pretty esoteric. Intriguing. I'll have to read up on it. Don't Have a clue what you are trying to prove.

The range of hypothetically possible outcomes for the sum of a septillion dice is from one to six septillions. In that range, you only ever need to concern yourself with values between 3.4999999999 and 3.500000001 septillions, and probably several orders of magnitude narrower. The same Holds for a tumbling coin consisting of a septillion particles. Even is every particle has an uncorrelated chance of being in any arbiträre state along its range of possibilities, itself, I believe, a misunderstanding, the sum is everything but unpredictable. QM or the observer effect Play no role in explaining our inability to predict the outcome.

What is the underlying justification for using the arithmetic mean as an estimator?

Developing a wave function for the moon can be done, but it has no practical value. The moon is an aggregate of the quantum states of each particle in the moon. Practicality is not the question. Newtonian reality is the sum of probabilities of particles. In an electronics metaphor reality is noisy, always fluctuating.

As the degrees of freedom and density of states get large from particle to an object like the moon the energy difference between states becomes continuous in the limit. Which is why we treat Newtonian variables as continuous.

The coin toss was an example of the collapse of a wave function.

It doesn't work as such.

You can not compute probilities of a coin toss based on the particles without a wave function.

1...
1...
2...
4 Therefore probability is ..

Show the steps in your reasoning. I do not see it'

Whether the uncertainties represented by QM that appear to underly reailit are a property of reality or a function of our limitations is an old question'

Are there hidden variables we can not detect? I believe QM is incomplete as Newtonian mechanism was before Q

https://en.wikipedia.org/wiki/Hidden_variable_theory

Physicists supporting De Broglie–Bohm theory maintain that underlying the observed probabilistic nature of the universe is a deterministic objective foundation/property—the hidden variable. Others, however, believe that there is no deeper deterministic reality in quantum mechanics.[citation needed]




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


The Copenhagen interpretation is an expression of the meaning of quantum mechanics that was largely devised in the years 1925 to 1927 by Niels Bohr and Werner Heisenberg. It remains one of the most commonly taught interpretations of quantum mechanics.[1]

According to the Copenhagen interpretation, physical systems generally do not have definite properties prior to being measured, and quantum mechanics can only predict the probabilities that measurements will produce certain 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.

There have been many objections to the Copenhagen interpretation over the years. These include: discontinuous jumps when there is an observation, the probabilistic element introduced upon observation, the subjectiveness of requiring an observer, the difficulty of defining a measuring device, and the necessity of invoking classical physics to describe the "laboratory" in which the results are measured.

Alternatives to the Copenhagen interpretation include the many-worlds interpretation, the De Broglie–Bohm (pilot-wave) interpretation, and quantum decoherence theorieThe Ensemble interpretation is similar; it offers an interpretation of the wave function, but not for single particles. The consistent histories interpretation advertises itself as "Copenhagen done right". Although the Copenhagen interpretation is often confused with the idea that consciousness causes collapse, it defines an "observer" merely as that which collapses the wave function.[55] Quantum information theories are more recent, and have attracted growing support.[69][70]

Under realism and determinism, if the wave function is regarded as ontologically real, and collapse is entirely rejected, a many worlds theory results. If wave function collapse is regarded as ontologically real as well, an objective collapse theory is obtained. Under realism and determinism (as well as non-localism), a hidden variable theory exists, e.g., the de Broglie–Bohm interpretation, which treats the wavefunction as real, position and momentum as definite and resulting from the expected values, and physical properties as spread in space. For an atemporal indeterministic interpretation that “makes no attempt to give a ‘local’ account on the level of determinate particles”,[71] the conjugate wavefunction, ("advanced" or time-reversed) of the relativistic version of the wavefunction, and the so-called "retarded" or time-forward version[72] are both regarded as real and the transactional interpretation results.[71]

Many physicists[who?] have subscribed to the instrumentalist interpretation of quantum mechanics, a position often equated with eschewing all interpretation. It is summarized by the sentence "Shut up and calculate!". While this slogan is sometimes attributed to Paul Dirac[73] or Richard Feynman, it seems to be due to David Mermin.[74]

 

[Bomb#20]

And that's the sort of thinking that leads people down the path to Many-Worlds. An awful lot of first rate physicists accept that interpretation too. But inevitably, like every other interpretation, it has its own set of problems.

Probably the most severe is that it denies that the wave function ever collapses at all.

But you said:

... Wave function collapse is not merely the effect of any physical interaction with the object. If you hit a superposed atom with a photon it doesn't collapse the atom's wave function -- you just get a more complicated superposed wave function for the whole atom+photon system. ...

So why isn't it possible that in the double slit experiment the interference produced by the wave function is not visible simply because it has become much too complex to recognize?

As far as I know, that is a possibility.

I'm not entertaining the MWI (or other woo).

I'm not following why you aren't entertaining the MWI, and why you're calling it woo. MWI basically takes the "the interference produced by the wave function is not visible simply because it has become much too complex to recognize" hypothesis as its premise, and follows it all the way to the end. And earlier you wrote "a more complicated superposed wave function for the whole atom observer+photon system.", which seems to be implying the conscious observer himself goes into a superposed state. If that isn't MWI you were entertaining, it's pretty darn close, and I'm not picking up on the distinction you're drawing.

The following part of your post is beyond my depth of understanding:

But the only thing quantum mechanics has to offer to turn wave function amplitudes into empirically measurable probabilities is the Born rule, the rule that when the wave function collapses the universe throws away its phase, squares its absolute value, and picks an outcome. No collapse means no squaring means no way to get from the computed amplitude to the experienced frequency. When the photon hits the glass and the wave function is reflected with amplitude .2 and refracted with amplitude .8, the universe divides, and now there's an observer who sees a reflection and an observer who doesn't. Do it 25 times in a row and now there are 33 million observers -- and an awful lot more of them saw twelve photons reflected than saw only one. But .2 squared is .04 and experience tells us we'll typically see only one reflected photon out of 25.

It's a technical criticism of MWI due to Ballentine -- more heavyweight than typical philosophical Occam's Razor sorts of objections. MWI proposes to explain apparent randomness in a deterministic theory by including the observer in the superposed state, so one version sees outcome A and the other version sees outcome B, and to both of them it looks perfectly random because they aren't aware of each other's outcomes and neither sees any reason for why he got his own outcome and not the other. Ballentine pointed out that that's lovely when A and B are equally probable, but it gives no explanation for why a typical observer would see A more often than B in phenomena where that's what happens. (I offered the partial reflection of light off of ordinary window glass as an example of such a quantum phenomenon.)