Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Alan McDougall on 18/06/2013 16:59:35
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How and why does measuring a particle make its wave-function collapse,
producing the concrete reality that we perceive to exist? The issue, known as
the measurement problem, may seem mysterious, but understanding of what
reality is, or if it exists at all, hinges upon the answer.
Thus can physics answer this question yet?
Alan
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No - we cannot answer this question. It is this lack that allows the many different interpretations of quantum mechanics. Whilst the interpretations are very interesting and sooner or later someone will find a way to experimentally test and disprove some of them - we do not need the interpretations to use quantum mechanics as the maths works fine without the more metaphysical side question of "what is really going on"
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No - we cannot answer this question. It is this lack that allows the many different interpretations of quantum mechanics. Whilst the interpretations are very interesting and sooner or later someone will find a way to experimentally test and disprove some of them - we do not need the interpretations to use quantum mechanics as the maths works fine without the more metaphysical side question of "what is really going on"
I am absolutely not interested in the metaphysical, science should come up with the answer at some point, so why can't we on this scientific forum propose our own scientific ideas on the topic
Alan
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A scientific explanation has some pretty hefty requirements: it has to be fully consistent with prior observations and be falsifiable by future experiments. Scientific explanations also generally need to apply Occam's razor: they should be pared down to the absolute essentials without extra untestable components.
We know the mathematics that describe quantum mechanics are scientific since the equations describe observations and have been tested experimentally. Going beyond that to what the mathematics "really" means on a deeper level leaves the realm of science, since no one has yet offered a falsifiable explanation. Moreover, all explanations of the "reality" behind the math involve some extra parts to the theory that can't be tested: multiverses, "collapse" of some entity, pilot waves, etc.
The Copenhagen interpretation is generally preferred, in my opinion, because it has the fewest extra parts. Wavefunction collapse is odd, but it's a much more literal interpretation of the mathematics than many worlds or pilot waves.
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No - we cannot answer this question. It is this lack that allows the many different interpretations of quantum mechanics. Whilst the interpretations are very interesting and sooner or later someone will find a way to experimentally test and disprove some of them - we do not need the interpretations to use quantum mechanics as the maths works fine without the more metaphysical side question of "what is really going on"
I am absolutely not interested in the metaphysical, science should come up with the answer at some point, so why can't we on this scientific forum propose our own scientific ideas on the topic
Alan
Alan further to JP's comments. You might have interpreted my "we cannot answer" as "can never answer" - this was sloppy wording on my point; at present there is no way we can answer, but that situation may change. IMHO - in order to propose your own scientific ideas on the topic you need a solid grounding in the subject and for Quantum mechanics that's a tall order; JP and Pete could further elaborate on the difficulty in getting to grips with QM, but remember they both have postgrad physics experience in research and academia. It is hubris to believe that one can make a significant contribution to an area without a thorough and easy knowledge of the mathematical basis, the theory, and the current work. That said - feel free to speculate :-)
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At a very basic level, "measuring a particle makes its wave-function collapse" because conservation of energy demands it.
A subatomic particle in flight has many potential values for position and momentum, each with a certain probability. This probability density is represented by the wavefunction.
However, when the particle interacts with a detector (eg striking a silver nitrate molecule on a photographic plate, or a silicon atom in a CCD detector, for example), there is an actual position and actual momentum which acts on the detector (eg to decompose the silver nitrate molecule, or kick an electron into the conduction band, in this example). This interaction uses the energy represented by the wavefunction.
You cannot have both the actual energy dissipated in the detector, and retain the potential energy represented by the wavefunction - which could then strike a different part of the detector and cause changes there too. Conservation of energy forbids it.
Therefore, interaction of the wavefunction with an observer/detector causes the wavefunction to collapse.
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At a very basic level, "measuring a particle makes its wave-function collapse" because conservation of energy demands it.
A subatomic particle in flight has many potential values for position and momentum, each with a certain probability. This probability density is represented by the wavefunction.
However, when the particle interacts with a detector (eg striking a silver nitrate molecule on a photographic plate, or a silicon atom in a CCD detector, for example), there is an actual position and actual momentum which acts on the detector (eg to decompose the silver nitrate molecule, or kick an electron into the conduction band, in this example). This interaction uses the energy represented by the wavefunction.
You cannot have both the actual energy dissipated in the detector, and retain the potential energy represented by the wavefunction - which could then strike a different part of the detector and cause changes there too. Conservation of energy forbids it.
Therefore, interaction of the wavefunction with an observer/detector causes the wavefunction to collapse.
Good post,you gave a good account of how to cause a quantum particle to collapse into its wavefuction.
However, we are still left with the question "as to why" a quantum particle collapses into its wave function, when observed or measures?
Alan
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All physical theories leave open a "why" question because none is a theory of everything. Quantum mechanics is no different. It's an open question (and one of philosophy at this point) of whether or not the scientific method can even find an ultimate theory.
And as Matthew pointed out earlier, wavefunction collapse isn't the only way to interpret the mathematics of quantum mechanics. For example, Bohmian mechanics or the many-worlds interpretation offer alternative explanations of the math that don't use collapsing wavefunctions--which is a reason why their proponents like them.
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Schrödinger pointed out that the wave function is just a metaphor based on the general form of the QM equation's form. It's too bad that metaphysics is not respected by physicists because it is the tool for analyzing fundamental questions like this. Physics today excels in math but sucks at logic and physical models and thought experiments are painfully sloppy.
There is exactly one category of model that is consistent with both relativity and QM observations: multiverse. It enables us to eliminate non-causal things like randomness and impossibilities like simultaneity (action at a distance). It makes all physics local. Observation doesn't alter the observed, it alters the observer.
The observable justifications for a multiverse include Bell's Inequality.
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I'd argue that physics in general excels at physical models because that's the whole point of physics, but doesn't address fundamental questions of reality because that's not the point of physics (some branches do try to reach towards that, though). I don't think most physicists look down on metaphysics, but they understand that it isn't a science and can't be relied on to provide physical models that can be used to make predictions with the same robustness as science. It's a different tool for a different job.
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Unfortunately, contemporary physics doesn't excel at providing physical models. For example, Stephen Hawking's physical model for determining the thermodynamics of event horizons ignores the distance between the box full of light he lowers toward the event horizon and the event horizon. Unfortunately, this distance is infinite for all observers. Einstein (an absolute genius at physical models) recognized this problem which is why he always insisted that event horizons cannot form.
Another example would be the extra space dimensions posited for some models. It's simple to show that causality only works in systems of 3 space dimensions and 1 time.
I don't know how many times I've heard physicists say that something (like the fact that nothing can fall to an event horizon in finite time, including the matter that would initially create it) is "just the way the world looks", as though any other factor could determine the nature of reality. Another absurdity is the "co-moving frame" which many cosmologists confuse themselves with.
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Unfortunately, contemporary physics doesn't excel at providing physical models.
Sure it does. The standard model of particle physics is the most accurate of any model we have in any field of science. Untested models are of course not to be trusted, but a major job of physics is to create testable models for nature that can then be validated or rejected. Even the bad models tend to be useful, since they make testable predictions.
I don't know enough general relativity and cosmology to comment on your examples in any depth, but it sounds like many of them haven't yet been tested. The many dimension models sound like those of string theory (though as far as I understand, their extra dimensions don't necessarily behave in the same way as space does). Many physicists (myself included) dislike string theory precisely because it hasn't yet made testable predictions.
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Assuming that a arrow disappear at Planck scale makes a lot of things more complicated for me. The only thing I can see there is probabilities, and wave functions. And a wave function use a arrow, doesn't it? Or could I define it as existing in a 'separate space' all by itself, obeying some form of causality? Obeying, as we must assume that for a outcome to exist we will need a arrow in where it can express itself. In a space without a arrow, using wave functions, you either assume that they all are 'co-existing' or that they have some 'hidden variable' defining them. A way out of this is to assume a symmetry between our definition of a 'arrow of time' and that space in where we only find wave functions, not 'expressed'. doing so you will find statistics measuring. Crazy, isn't it :)
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And if you want to take this reasoning a step further, you might assume that all wave functions, ignoring 'hidden variables' for this, must express themselves, somewhere. With a hidden variable though, you might assume that only those fitting that hidden definition of a 'allowed reality' can exist. If you do that though, you also will need to define what this hidden variable is. Both expressions can be reconciled using the idea of a symmetry though, as I think for now :) Take it or leave it.
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Included in a 'arrow of time' we then also must include all positional evidence, temporal as well as spatial, including you observing. and that is the main thing missing as I think. The realization that when we measure, we are involved in creating a outcome. That doesn't state that the universe disappear without a observer, as long as we define everything measuring on each other as 'observers', live or dead matter etc..
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There are at least two ways to observe, one is passive, for example astronomic evidence, you observing incoming light. The other I see now is the one in where you 'probe' something, for example using light. Maybe there are some other way you can do it too, at least theoretically.
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But maybe we need a 'hidden variable' defining a wave function, I actually think we do, If we define it to the symmetry between the universe we know, relative that 'space' belonging to wave functions, we find constants defining that 'hidden variable' for us, don't we?
So, why is there constants?
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Constants must be the way to define what 'reality' we perceive. although maybe a 'symmetry' is good enough in itself? I don't know. the problem is that I doubt we ever will be happy with defining a symmetry, without searching for a reason for it to come to be.
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The wave function is not an actual property of an actual particle. It is a description of where we might find a particle.
You don't know where your keys are, but you have some idea of where you are likely to have left them, so you search in increasingly improbable places until you find them. Or you could say that the wavefunction of your keys collapses at the point of interaction with your hand. That is a more general statement because it describes the keys equally well regardless of how many hands you have (though very few octopi care much about keys).
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Those I described are all definitions, and you can use several. The idea of a wave function as being a 'reality' in itself, is a recent development in a theorem, still discussed as I saw. but it doesn't matter for me really, my definitions of a arrow ends at Planck scale :) 'under it' there is no arrow as I see it. but you still have probabilities and 'wave functions'. If we use the idea of waves then a wave function exist. It is a description of the possibility of something, based on statistics.
I expect you to need something beyond a arrow, or you will find that everything you define must have it to make sense to us. Entanglements doesn't use a arrow, 'communicating' for example.
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It doesn't matter to me defining what improbability of a 'time' it needs 'communicating' here btw, if one now wanted to find a time FTL. I define a arrow to 'c' and doing so anything 'faster' than that will pass into improbability for my definitions :)
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To me our universe goes back to constants, the most important, and so far inexplainable , being 'c', locally defined. Statistics is histories to me, defining a logic. You can define 'c' two ways as I think. As a strictly 'local constant', or as a strictly local constant, measured over frames of reference. Locally that becomes a difference because imagining one single frame of reference 'c' disappear in the second definition. The theory of relativity discuss measurements over frames of reference, in my thoughts I use it because it's such a clear description, but I want to discuss what 'locality' might mean from it. Locality becomes scales, scales becomes quantum logic.
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But using the second definition you still will find that as soon as you introduce another frame of reference in this universe, you must find 'c' measuring (for simplicity 'as inertially defined') And 'one frame of reference' is, to me, referable to Planck scale. And that is at the limit of quantum logic I think? Passing beyond that we have loops and strings, maybe?
But using my definitions of a arrow, strings can't 'vibrate', although maybe it is possible to define a static 'tension'? That as the arrow 'disappeared' for me, meeting Planck scale, which also becomes that 'single frame of reference' I wonder about. As always it is the words we use, and how we define them. And even though our definition of 'c' as a 'speed', as well as my (equivalent) arrow, disappear at that scale, this 'origin' of a 'frame of reference' still must contain the properties, allowing 'c' to be measured over frames of reference. So even though 'c' can't be measured in it, it contain properties.
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Assuming wave functions to exist we might be able to 'split them' into probabilities, even when not realized as a outcome? That one is seriously weird though :) as it somehow assume that what lies under Planck scale, be it a string or a loop, to 'vibrate' through having probabilities of existing? As I said, I don't know how to define that one at all, as I can't use a arrow for it. But that may on the other side be the point of describing something under Planck scale?
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The idea that observation alters the thing observed is an outdated concept that has stifled quantum mechanics for decades. Observation doesn't alter the observed. Observation alters the observer. Once the state of the observer is changed, ONLY observations physically consistent (obeying all conservation symmetries) are possible. That's a basic rule of QM... if a system (i.e. an observer or object described by an eigenmatrix) interacts with anything (makes an observation, described by an eigenvector) that is inconsistent (even one quantum, or eigenvalue mismatch between the vector and the matrix) will leave the system (object/observer) in an impossible state (non-Hermitian state matrix). Schrödinger described such a situation as unobservable.
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A professional journal to which I subscribe did a special edition on quantum communication. I am still trying to get my head around:
- Transmitting quantum states called "qubits", which are a superposition of 0 & 1, but when measured, collapse into an actual 0 or 1.
- And if you "entangle" two qubits, both are a superposition of 0 & 1, but they share a quantum state (wavefunction?), potentially across a distance of many kilometers; measuring one of them causes it to collapse, and this is correlated with the state of other one, no matter how far away it is
A network generating and distributing entangled qubits seems a likely outcome, once the technology matures. Perhaps if/when it becomes a mainstream technology, some of these quantum oddities may become more intuitive to us.
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A wave function is the probability (density) of something before a measurement. You don't need a matrix for defining this. Matrices are overall questionable if the universe is observer dependent, as your matrix only can be mine, agreeing on a measurement and position in space and time, when us being at absolute rest with each other, (or) equivalent in all circumstances and respects. If there is a matrix to the universe, it will not be a measurable one, only theoretical. Doesn't mean it can't exist, but I don't think we will be able to measure it from where we are.
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what I might be able to argue is that as we find some principles to be common 'laws', no matter what we measure relative each other, 'locality' should be the most objective description of what a measurement, and the universe, is. And as locality has a direct coupling to scaling, and as QM also is a question of at what scale you are measuring? Then again, to assume some 'objectively possible' common to us all matrix to exist at a very small plane, should crave you to create a split between macroscopic observer dependencies and this 'objective microscopic reality'. Either we can magnify and shrink, using scales, and smoothly so, a universe. Or we will need 'emergences' taking place, a little like black body radiation coming in discrete energies 'photons', as well as creating discrete 'orbitals'.
It makes sense to me, assuming that scaling takes us closer to some 'commonly shared universe', as it is converging on what 'locality' should mean, practically. But it is also a view in where you should define what is common from what a repeatable experiment tells you, locally measured. Then again, all of this is assuming that there is a logic existing, and that our ideas and mathematics are able to describe it.
Also, defining it from 'locality' is not necessarily the same as what we have used to think of as our 'common universe', as proved by 'repeatable experiments'. What locality demands, as I think or hope :), Is that there is a way to define our 'common' universe macroscopically as coming from some simple principles, constants, valid locally. If you define it this way, the universe we see is a 'mental construct' we agree on, although finding observer dependencies measuring, the 'reality' being those constants becoming a property of all frames of reference, even when not measurable 'locally'. Relativity uses two frames, at least, and comparisons, but what I'm wondering about is one frame, and what you might define it as consisting of.
(One more thing, by 'locality' I'm not defining it as of actions and reactions, as some linear processes, proceeding from some center. What I mean by it is that all experiments done are local, any measurements created done from your 'frame', relative some other. That's relativity. It's not a statement of a frozen geometry on that small scale, just think of entanglements. And if you look at relativity you will find that it can't be a frozen geometry relativistically either. Using 'locality' as a description of particles interacting only from adjoining positions in space and time is wrong, in my thoughts. There are too many experiments questioning that.
Instead I lean to the idea of 'gestalts' as in configurations where you are inseparable from your experiment (Copenhagen definition), and in a wider context also Mach's ideas of everything being connected. What makes us differ it, is the arrow we perceive.
But it is definitely local, the arrow you find, as well as everything else, and the question should be how to minimize what 'local' should mean. That's why one frame of reference is interesting, and if it is possible to relate such a frame to some mathematical object, constants, or 'quantum grain' if you like.)
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How and why does measuring a particle make its wave-function collapse,
producing the concrete reality that we perceive to exist? The issue, known as
the measurement problem, may seem mysterious, but understanding of what
reality is, or if it exists at all, hinges upon the answer.
Thus can physics answer this question yet?
Alan
"How?" and "Why?" questions are answered by specifying the mechanism behind what is going on. Quantum mechanics does not have an answer for what that mechanism is as of yet. And it may never have.
Let's talk about what it means for the wave function to collapse. The wave function is defined such that the square of its magnitude is proportional to the probability density of finding the particle in a region of space. So, for instance, when the particle's position is unknown the wave function is not collapsed. Now measure the location of the particle. The location is then determined and the wave function is now changed to be highly peaked in the region where the particle was found. Mathematically we say that the wave function changes to an eigenfunction of position where the eignvalue is the position measured. This is what it means for the wave function to be collapsed.
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No - we cannot answer this question. It is this lack that allows the many different interpretations of quantum mechanics. Whilst the interpretations are very interesting and sooner or later someone will find a way to experimentally test and disprove some of them - we do not need the interpretations to use quantum mechanics as the maths works fine without the more metaphysical side question of "what is really going on"
I don't think I understand the precise nature of the problem that you have with this question. I take it that you don't disagree that the wave function collapse is very well defined in quantum mechanics, right? E.g. before a measurement the system is, in general, in an arbitrary quantum state. When a measurement is made only the eigenvalues of the observable can be measured. The wave function then becomes the eigenfunction of that obserable. This is how the term "wave function collapses" is defined.
I take it that you're referring to the how and why part of the question, yes?
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No - we cannot answer this question. It is this lack that allows the many different interpretations of quantum mechanics. Whilst the interpretations are very interesting and sooner or later someone will find a way to experimentally test and disprove some of them - we do not need the interpretations to use quantum mechanics as the maths works fine without the more metaphysical side question of "what is really going on"
I am absolutely not interested in the metaphysical, science should come up with the answer at some point, so why can't we on this scientific forum propose our own scientific ideas on the topic
Alan
His answer was not metaphysical. It has to do with the philosophy of science. Not doing philosophy means not doing science. How and why are not something science has a handle on yet and may never have.