andyandy
anthropomorphic ape
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ok so to clarify....
so a sub-atomic particle has a non-zero probability of being observed anywhere, until we actually observe it - and then the whole probability wave is collapsed? And then, when we have observed say its position, we are unable to observe its momentum.....?
right, a couple of probably silly questions......
if a sub-atomic particle's position has been observed, then for how long can we know its position? will the probability wave ever be re-established? Is there a separate probability wave to describe its momentum?
does measurement constitute observation, or does observation require consciousness of the measurement?
*ok, i don't expect any definitive answers to that last one
edit.
I've just had another think about this.....if one can only know either the position or the momentum, then one can only know the position whilst it is under observation - ie. as soon as the observation is finished, you have to use the probability field again to describe where it could now be observed.....
i was hoping to edit my post on the sly before anyone else posted, but too late
so a sub-atomic particle has a non-zero probability of being observed anywhere, until we actually observe it - and then the whole probability wave is collapsed? And then, when we have observed say its position, we are unable to observe its momentum.....?
right, a couple of probably silly questions......
if a sub-atomic particle's position has been observed, then for how long can we know its position? will the probability wave ever be re-established? Is there a separate probability wave to describe its momentum?
does measurement constitute observation, or does observation require consciousness of the measurement?
*ok, i don't expect any definitive answers to that last one
edit.
I've just had another think about this.....if one can only know either the position or the momentum, then one can only know the position whilst it is under observation - ie. as soon as the observation is finished, you have to use the probability field again to describe where it could now be observed.....
i was hoping to edit my post on the sly before anyone else posted, but too late
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Jimbo07
Illuminator
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There is just the wave function which evolves in time. Mathematically, things like momentum and position are operators (something that does something) that are applied. To find the particle's position for a given wave function and boundary conditions, you mathematically 'hit it' with the position operator.
After that, left to its own devices, the wavefunction will continue to evolve in time.
Don't know. I asked a question here about measurement once and got smacked down.
...
From the engineer's vantage point, I'd just like to say about QM: QM works. Whatever sort of metaphysical 'truths' people try to glean from it, they do at their own peril. What they seem to forget (or whistfully think is not true), is that for the vast majority of us in the vast majority of everyday experience... classical physics and mechanics works.
UndercoverElephant
Pachyderm of a Thousand Faces
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[interlude]
Given the title of this thread, I couldn't resist the temptation to make a post on Gorgias
(Greek, 483-375 BC).
A detailed explanation of his ultra-nihilism is here:
http://www.iep.utm.edu/g/gorgias.htm
A summary runs as follows:
1) nothing exists.
2) if anything does exist, it cannot be known.
3) if anything does exist and can be known, it cannot be communicated.
The amazing thing is that this was considered meaningful enough to have been preserved by history for us to read.
[/interlude]
Given the title of this thread, I couldn't resist the temptation to make a post on Gorgias
(Greek, 483-375 BC).
A detailed explanation of his ultra-nihilism is here:
http://www.iep.utm.edu/g/gorgias.htm
A summary runs as follows:
1) nothing exists.
2) if anything does exist, it cannot be known.
3) if anything does exist and can be known, it cannot be communicated.
The amazing thing is that this was considered meaningful enough to have been preserved by history for us to read.
[/interlude]
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DanishDynamite
Penultimate Amazing
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Not as amazing as the thought that some current sprouts of philosophy, who are also spouting gibberish, think their thoughts mights also be worthy of serious contemplation, not just today, but perhaps even several years in the future.
andyandy
anthropomorphic ape
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[interlude]
Given the title of this thread, I couldn't resist the temptation to make a post on Gorgias
(Greek, 483-375 BC).
A detailed explanation of his ultra-nihilism is here:
http://www.iep.utm.edu/g/gorgias.htm
A summary runs as follows:
1) nothing exists.
2) if anything does exist, it cannot be known.
3) if anything does exist and can be known, it cannot be communicated.
The amazing thing is that this was considered meaningful enough to have been preserved by history for us to read.
[/interlude]
some nice verbal gymnastics there....the last part of his argument (3) seems to have some merit.....
i'm not so sure about (1) or (2) though
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andyandy
anthropomorphic ape
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more thinking.....
the standard model for chemistry A-level at school was the rather simplistic concentric circles to represent shells where electrons circulated the atomic nucleus....
the first shell can only hold 2 electrons, the second shell 8 etc.....
and so a Hydrogen atom with an outer shell containing only 1 electron could "share" its electron with an atom with an electron deficiency on its outer layer.....
So an Oxygen atom which was two electrons short on the second shell, would share 2 electrons from 2 hydrogen atoms....and this of course leads to the molecule H(2)O
so, would it be right to actually regard the shells as probability areas in which the electrons are most likely to be observed?
But once an electron is shared within a molecule, is it still described by the same probability wave - or is it in some way "tied" to a specific position?
to extend that further, being as i am a collection of molecules made up of sub atomic particles, are these in some way bounded, or are they still described by probability waves? Is there a non-zero chance of one of my electrons being observed elsewhere?
the standard model for chemistry A-level at school was the rather simplistic concentric circles to represent shells where electrons circulated the atomic nucleus....
the first shell can only hold 2 electrons, the second shell 8 etc.....
and so a Hydrogen atom with an outer shell containing only 1 electron could "share" its electron with an atom with an electron deficiency on its outer layer.....
So an Oxygen atom which was two electrons short on the second shell, would share 2 electrons from 2 hydrogen atoms....and this of course leads to the molecule H(2)O
so, would it be right to actually regard the shells as probability areas in which the electrons are most likely to be observed?
But once an electron is shared within a molecule, is it still described by the same probability wave - or is it in some way "tied" to a specific position?
to extend that further, being as i am a collection of molecules made up of sub atomic particles, are these in some way bounded, or are they still described by probability waves? Is there a non-zero chance of one of my electrons being observed elsewhere?
Stimpson J. Cat
Graduate Poster
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Soapy Sam,
First of all, you cannot really think of the photon as something which pops into existence at some point in time (not in this context). The photon is the quanta of the electromagnetic field, and the electromagnetic field is already everywhere at all times.
When an event occurs locally, such as an electron in an atom dropping to a lower state and emmiting a photon, this is actually a wave in the electromagnetic field which propogates out from the source of the event. So the probability of detecting a photon with a given energy at a specific time, becomes much larger in the region of space where we classically think of the photon as being. But remember, the field is everywhere all the time. And because of the uncertainty principle, the probability of detecting a photon with a given energy at any given place or time, is non-zero. So in that sense, yes, you could detect the photon outside of the light cone. But when you look at things on this level (field theory), it is no longer really meaningful to talk about the photon you detected as having been emitted by the atom at some previous time and place. Instead, we are just talking about fields evolving in time according to a set of equations, and the probabilities of making various observations being given by those fields.
jmercer,
andyandy,
At that point, you can talk about the probability distribution of where it will be observed in the future. To do this, you also need to have an idea of its momentum. This is where the uncertainty principle comes in. If you try to measure both position and momentum, then both are measured with some uncertainty. You then have a probability distribution of where it will be observed the next time you look, which evolves over time according to Schroedinger's equation.
Geometrically, you can think of it this way. Imagine that position is just along one dimension. Then you can think of momentum as a dimension perpendicular to it. Measuring its position and momentum then amounts to locating a point on that plane. But because of the uncertainty principle, no observation can actually narrow it down to a single point on the plane. Instead, you find it in some area. You can make that area very broad in one direction, and very narrow in the other, but you can't make the area smaller than a certain amount.
Unfortunately, the standard model of QM has no answer for this question. On one hand, the math clearly does indicate that a complex system (like a human being) will only ever observe one outcome. This comes from the fact that it is truly a linear superposition of possibilities. In a complex macroscopic system, these difference possibilities do not interact with each other.
The easiest way to visualize this is the Many Worlds hypothesis of QM. In this interpretation, every possible outcome happens, but from the point of view of any complex (approximately classical) system, this amounts to a branching of the wave-function, where every outcome is represented by a different branch, and they do not interact with each other. From the classical point of view, each branch is a different world, in which one specific outcome happened.
This also deals with the apperant indeterminacy of QM. The overal wave-function is completely deterministic, but the vast majority of the branches will appear to be completely random at the quantum level, simply due to statistics.
The obvious question this raises, though, is whether or not these other branches "really exist". That is a metaphysical question, though, and cannot be answered.
Dr. Stupid
As Zombified said, such things require field theory to address, which is much more complicated, but I will try to explain it in a way that is clear.
First of all, you cannot really think of the photon as something which pops into existence at some point in time (not in this context). The photon is the quanta of the electromagnetic field, and the electromagnetic field is already everywhere at all times.
When an event occurs locally, such as an electron in an atom dropping to a lower state and emmiting a photon, this is actually a wave in the electromagnetic field which propogates out from the source of the event. So the probability of detecting a photon with a given energy at a specific time, becomes much larger in the region of space where we classically think of the photon as being. But remember, the field is everywhere all the time. And because of the uncertainty principle, the probability of detecting a photon with a given energy at any given place or time, is non-zero. So in that sense, yes, you could detect the photon outside of the light cone. But when you look at things on this level (field theory), it is no longer really meaningful to talk about the photon you detected as having been emitted by the atom at some previous time and place. Instead, we are just talking about fields evolving in time according to a set of equations, and the probabilities of making various observations being given by those fields.
jmercer,
That kind of depends on your definition of God. Remember that even in the multiverse theory, there are some serious constraints on what can and can not exist. And most conceptions of God require that God be the creator of the universe, which makes it somewhat difficult to talk about it existing in that universe.
andyandy,
Not exactly. Once we have observed it, it is no longer to talk about the probability of having observed it at that position, because the event has already occured. In that sense, the probability distribution collapses to a single point in the same sense that the probability distribution of how a coin will land collapses to a single result when it lands.
At that point, you can talk about the probability distribution of where it will be observed in the future. To do this, you also need to have an idea of its momentum. This is where the uncertainty principle comes in. If you try to measure both position and momentum, then both are measured with some uncertainty. You then have a probability distribution of where it will be observed the next time you look, which evolves over time according to Schroedinger's equation.
For zero time. You know only where it was when you observed it.
Yes, immediately.
There is one wave function which describes both. This is actually the mathematical source of the uncertainty principle. The wave doesn't actually tell you the probability of measuring a specific position or momentum. It tells you the probability of measuring them both within some ranges. The narrower one range is, the wider the other is.
Geometrically, you can think of it this way. Imagine that position is just along one dimension. Then you can think of momentum as a dimension perpendicular to it. Measuring its position and momentum then amounts to locating a point on that plane. But because of the uncertainty principle, no observation can actually narrow it down to a single point on the plane. Instead, you find it in some area. You can make that area very broad in one direction, and very narrow in the other, but you can't make the area smaller than a certain amount.
Yes, measurement constitutes observation. The rather confusing issue of consciousness does not come from the so-called "wave collapse", which happens any time a quantum partical interacts with a complex system (which is the QM definition of 'measurement'). It comes from the fact that this collapse (called decoherence) does not collapse to a single result, but rather to a superposition of all possible results. This leads to the whole "dead cat/live cat" problem. But we only ever observe one result. The obvious question is: "why"?
Unfortunately, the standard model of QM has no answer for this question. On one hand, the math clearly does indicate that a complex system (like a human being) will only ever observe one outcome. This comes from the fact that it is truly a linear superposition of possibilities. In a complex macroscopic system, these difference possibilities do not interact with each other.
The easiest way to visualize this is the Many Worlds hypothesis of QM. In this interpretation, every possible outcome happens, but from the point of view of any complex (approximately classical) system, this amounts to a branching of the wave-function, where every outcome is represented by a different branch, and they do not interact with each other. From the classical point of view, each branch is a different world, in which one specific outcome happened.
This also deals with the apperant indeterminacy of QM. The overal wave-function is completely deterministic, but the vast majority of the branches will appear to be completely random at the quantum level, simply due to statistics.
The obvious question this raises, though, is whether or not these other branches "really exist". That is a metaphysical question, though, and cannot be answered.
Dr. Stupid
Dr Richard
Thinker
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- Mar 15, 2006
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You could try The Road to Reality by Rogen Penrose. The maths gets pretty darn scary but if you have undergrad maths then you may find it easier than I did. It is cartainly MUCH harder than Emperor's New Mind and Shadows of the Mind, which I really liked.
Just browsing in Waterstones the other week and I saw this: Quantum Mechanics Demystified.
It has plenty of maths in it but at the same time it seems to be pitched as an introductory book.
Yes, the shells are just the probability of the electron being found in that area. As far as the electron is concerned there is no difference between an atom and a molecule. All it knows is that there are one or more positive things attracting it, and the wave function is distributed around them according to the laws of electro-magnetism. This makes much more complex "shells" than with a single atom, but the concept is still exactly the same.
to extend that further, being as i am a collection of molecules made up of sub atomic particles, are these in some way bounded, or are they still described by probability waves? Is there a non-zero chance of one of my electrons being observed elsewhere?
All particles are always described by their wavefunction, whether they are floating around by themselves or part of some molecule. At the sub-atomic scale they are always governed by probability. If you look at an indivisual electron there will always be a non-zero chance of it being found anywhere within its wavefunction, which is technically everywhere. However, the chance is so small that it will be observed anywhere other than within its molecule that it usually makes no sense to even talk about it being possible.
As a simple example, assume the rest of the universe doesn't exist. The electron in a hydrogen atom has a non-zero chance of being found at any distance from the nulceus. This chance decreases extremely rapidly with distance, so it can effectively be descibed as bounded and the size of the atom can sensibly talked about. Although there is a chance that it will suddenly by observed outside this size, the chance is so small that we can confidently say it will never happen, and can do calculations assuming this. If this is scaled up to your body, there are now quite a lot of electrons, all of which have this very small chance. So there may now be a chance (still incredibly small) that one of them will be observed outside its accepted orbital. However, since there are so many particle, the unlikely behaviour of one of them has no effect on your body as a whole, and so even if there is a real chance of one of the particles behaving non-classically, your body as a whole behaves as if quantuim mechanics didn't exist.
As to the question of are particles really particles or a probablity function, that question is actually meaningless. A quantum wavefunction represents all the knowledge of a particle that is available to the outside world, whether it is us measuring it or another particle interacting with it. This means that whatever the "true nature" particles, if they even have one, is essentially unknowable. This is much the same problem as faces the many worlds vs. other theories behind quantum mechanics - if they all predict the same behaviour then we can never sy which, if any, is reality and so the question of which one is real becomes irrelevant.
That was much longer than it was supposed to be.
Regarding "shells": in quantum mechanics, everything is represented by a single state vector, which is another name for wave function. States with definite values of energy, angular momentum, etc, have specific vectors associated with them, and the actual state of an atom is represented as a linear combination of these vectors (they form a basis, in linear algebra terms). The probability of something being in a particular state is related to how much of that state's basis vector is mixed into the overall state.
The orbital shells are just the wave functions associated with fixed energies and angular momentums. If an electron is in one of those states, you can only measure one possible energy and one possible angular momentum.
Atoms are often found these way because atoms with extra energy are unstable and emit photons to go to lower energy states. Because you can only have one electron per state, though, the states fill up.
The orbital shells are just the wave functions associated with fixed energies and angular momentums. If an electron is in one of those states, you can only measure one possible energy and one possible angular momentum.
Atoms are often found these way because atoms with extra energy are unstable and emit photons to go to lower energy states. Because you can only have one electron per state, though, the states fill up.
I think this is an unanswerable question. How would you ever know if measurement alone were enough? At some point a human being would have to observe the results of the experiment. It could be that the outcome was undecided, existing as a godawfully huge macroscopic superposition, right up to the moment where a conscious observer saw the results.
I have a pretty good suspicion what Occam would have to say about such a thing, though.
andyandy
anthropomorphic ape
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split from another thread, I posted the following
to which piggy replied
I read up a little more and posted
Piggy replied to my (first) question as to what Feynman would say with
so i have taken this to the science forum.....if anyone could expand upon piggy's comments i would be grateful
to which piggy replied
I read up a little more and posted
Piggy replied to my (first) question as to what Feynman would say with
so i have taken this to the science forum.....if anyone could expand upon piggy's comments i would be grateful
andyandy
anthropomorphic ape
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This is stimpson's explanation from earlier in the thread.....
andyandy - keep this snippet from Dr Stupid in mind at all times when discussing this subject:
As I said in this thread's originating thread English does not have the grammar nor vocabulary to accurately discuss or even accurately represent the concepts required to discuss this subject.
As I said in this thread's originating thread English does not have the grammar nor vocabulary to accurately discuss or even accurately represent the concepts required to discuss this subject.
andyandy
anthropomorphic ape
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it's nice to be out of the rather emotive hard-atheism thread, and sure, i appreciate your point
However, i'm not sure i agree that such subjects can not be discussed with reference to QM - or more accurately, that even though it may be difficult to express mathematical concepts with English language, we should not be at least willing to try . I would certainly recommend Brian Greene's Fabric of the Cosmos* (far more so that Hawking's A brief History ) as a book which does attempt to do just that.
*maybe i should start collecting a commision from Penguin for the number of times i mention it on JREF....
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