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Observing Particles
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In quantum mechanics, particles do not have a definite state unless they're being observed.
Explanation please?
Explanation please?
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That's a big question and I'm trying to decide how to answer it.
A lot depends, basically, on how literally you take the mathematics of Quantum Mechanics. The idea is that if a particle could, in principle, be in any state, then it makes sense to start by writing down the sum over possible states. If the possible states are 1, 2, 3 etc then the sum would be
current state = a*1 + b*2 + c*3 + ...
where the numbers a, b and c are weightings representing that it may be more likely for a particle to be in one state than another. The measurement will then pick out one of these states.
At this point is where the interpretations kick in. Is this sum physically real, or is it a mathematical trick?
If real, then the sum instantly implies that a particle is in multiple states simultaneously, until measured, when it will pick out one particular state with a certain probability (e.g. state 1 with probability a^2).
Since the states can also be positions, this also implies that a particle is free to be in several places at once until observed in one particular place, which is kind of freaky. Again, though, this depends on the "reality" of the current state. Since the numbers a, b, c can themselves not be "real" (often they include complex numbers, ie the square root of -1), then it's probably better to interpret the whole "current state" thing as "the square root of reality". Whatever the hell that means.
These are complicated things, anyway, and you can explain it in multiple ways. In the long run the most succinct answer is that "it just works", but you can have a lot of thing discussing the philosophy behind why it does.
A lot depends, basically, on how literally you take the mathematics of Quantum Mechanics. The idea is that if a particle could, in principle, be in any state, then it makes sense to start by writing down the sum over possible states. If the possible states are 1, 2, 3 etc then the sum would be
current state = a*1 + b*2 + c*3 + ...
where the numbers a, b and c are weightings representing that it may be more likely for a particle to be in one state than another. The measurement will then pick out one of these states.
At this point is where the interpretations kick in. Is this sum physically real, or is it a mathematical trick?
If real, then the sum instantly implies that a particle is in multiple states simultaneously, until measured, when it will pick out one particular state with a certain probability (e.g. state 1 with probability a^2).
Since the states can also be positions, this also implies that a particle is free to be in several places at once until observed in one particular place, which is kind of freaky. Again, though, this depends on the "reality" of the current state. Since the numbers a, b, c can themselves not be "real" (often they include complex numbers, ie the square root of -1), then it's probably better to interpret the whole "current state" thing as "the square root of reality". Whatever the hell that means.
These are complicated things, anyway, and you can explain it in multiple ways. In the long run the most succinct answer is that "it just works", but you can have a lot of thing discussing the philosophy behind why it does.
Well it knows in the sense that the interaction has changed the system.
Two watchers could see different things in principle, depending on how the particle is behaving. In certain cases one measurement fixes the behaviour of the particle for all time; in others, it sets the particle to a single state but it then reverts to a sum over all possible states (time-dependent quantum mechanics).
It's weird once you try to put it in words; at the level of mathematics the behaviour is rather less weird.
Two watchers could see different things in principle, depending on how the particle is behaving. In certain cases one measurement fixes the behaviour of the particle for all time; in others, it sets the particle to a single state but it then reverts to a sum over all possible states (time-dependent quantum mechanics).
It's weird once you try to put it in words; at the level of mathematics the behaviour is rather less weird.
BBC4 showed a 3 part series Chemistry - A volatile history a few weeks ago.
In part 3 he does get into the whole subject of the elements and he tried to show how they behave when being "watched".
I found the whole series interesting, and I understood most of part 1 and 2 of the series, but much of part 3 lost me, but if you have an understanding of the subject you may be able to follow it.
The whole of part 3 is on YouTube (part 1 and 2 are as well I think)
In part 3 he does get into the whole subject of the elements and he tried to show how they behave when being "watched".
I found the whole series interesting, and I understood most of part 1 and 2 of the series, but much of part 3 lost me, but if you have an understanding of the subject you may be able to follow it.
The whole of part 3 is on YouTube (part 1 and 2 are as well I think)
My view/understanding, which I accept may be flawed.
The thing is that we find it intellectually difficult to accept something is both particle and wave at the same time. We use analogies to understand things, and it seems logical that it could only be one thing or another. But it appears that, that common sense approach fails us when digging deeper into whatever "reality" is. It seems everything is both wave and particle, but shove enough together and a divergence emerges so at our size we tend to see them as separate.
So everything is effectively everywhere at once, as a probability at the very least. And to find out what state we see it in we have to sum all the possibilities together and come up with an area where the highest possibility is. And chances are we see it in a particular state there.
As for the observer having noted a definite state, well I think that is more to do with the observer. Maybe the wave/particle is still everywhere, and it is just we looking at it that has frozen it in one place for our own personal experience.
As for mathematical tricks, I'm not sure I believe in them. If the result fits then I suspect the maths is mimicking something "out there" that really occurs. How accurate your maths mimic is though, is another matter. What is within acceptable experimental error at one time, becomes a genuine calculation error that needs a tweak to the understanding/explanation/maths at a later date.
The thing is that we find it intellectually difficult to accept something is both particle and wave at the same time. We use analogies to understand things, and it seems logical that it could only be one thing or another. But it appears that, that common sense approach fails us when digging deeper into whatever "reality" is. It seems everything is both wave and particle, but shove enough together and a divergence emerges so at our size we tend to see them as separate.
So everything is effectively everywhere at once, as a probability at the very least. And to find out what state we see it in we have to sum all the possibilities together and come up with an area where the highest possibility is. And chances are we see it in a particular state there.
As for the observer having noted a definite state, well I think that is more to do with the observer. Maybe the wave/particle is still everywhere, and it is just we looking at it that has frozen it in one place for our own personal experience.
As for mathematical tricks, I'm not sure I believe in them. If the result fits then I suspect the maths is mimicking something "out there" that really occurs. How accurate your maths mimic is though, is another matter. What is within acceptable experimental error at one time, becomes a genuine calculation error that needs a tweak to the understanding/explanation/maths at a later date.
"How accurate your maths mimic is though, is another matter. "
I guess to some extent this is what I'm saying. It's possibly risky to ascribe too much truth to the reality of what the mathematics appears to be telling you. That it works suggests that it cannot be far off the truth, to be sure (and I'm not talking about a "hidden variables" theory either). On the other hand, how you interpret that in words is somewhat personal. I tend to think of things not as being both particles and wave, but as never being particles in the first place. The particle model is then only an approximation in the limit that you can't see the wave-nature, or at least that the wave-nature doesn't matter. But it's a personal view that is probably no more true than talking of things as if one instant they are particles and the next waves.
And finally it is important that some of these things cannot be exactly measured. Some of my work, and a lot of the work done in offices on my corridor, considers the construction and evaluation of what are known simply as "amplitudes". Very complex objects, all sorts of weird stuff going on, plenty of trickery needed to evaluate them in particular cases. But then to get to something you can actually measure you square the amplitudes anyway, having summed them first, and then an infinite set of other contributions has been neglected as too small to care about, and you might normalise to account for other effects, and deal with infinities emerging in the sum, and so on...
The physical meaning of the amplitude, then, is somewhat up for debate. You can never see it, only its square. It's then safer not to get too bogged down in what the amplitude actually is, as it can never be observed.
I guess to some extent this is what I'm saying. It's possibly risky to ascribe too much truth to the reality of what the mathematics appears to be telling you. That it works suggests that it cannot be far off the truth, to be sure (and I'm not talking about a "hidden variables" theory either). On the other hand, how you interpret that in words is somewhat personal. I tend to think of things not as being both particles and wave, but as never being particles in the first place. The particle model is then only an approximation in the limit that you can't see the wave-nature, or at least that the wave-nature doesn't matter. But it's a personal view that is probably no more true than talking of things as if one instant they are particles and the next waves.
And finally it is important that some of these things cannot be exactly measured. Some of my work, and a lot of the work done in offices on my corridor, considers the construction and evaluation of what are known simply as "amplitudes". Very complex objects, all sorts of weird stuff going on, plenty of trickery needed to evaluate them in particular cases. But then to get to something you can actually measure you square the amplitudes anyway, having summed them first, and then an infinite set of other contributions has been neglected as too small to care about, and you might normalise to account for other effects, and deal with infinities emerging in the sum, and so on...
The physical meaning of the amplitude, then, is somewhat up for debate. You can never see it, only its square. It's then safer not to get too bogged down in what the amplitude actually is, as it can never be observed.
If you're meaning my post at 16:12 on Wednesday then I suppose the reason you can't understand it is because I was somewhat deliberately engaging in technobabble. The point I'm trying to make, I suppose, is that I think a lot of people when writing about or interpreting quantum mechanics look at the equations (which they almost invariably never show you), and then interpret them as if these equations are real objects when they are not (probably).
Pretty much everyone struggles to put these equations into words. It's very difficult to and I'm going to be little better at it than anyone else, and probably worse, given that so far in this thread I'm not even sure I've tried.
I've stared at this text box for several minutes and I'm not really sure how to continue. I'll try to come back with something more useful later.
Pretty much everyone struggles to put these equations into words. It's very difficult to and I'm going to be little better at it than anyone else, and probably worse, given that so far in this thread I'm not even sure I've tried.
I've stared at this text box for several minutes and I'm not really sure how to continue. I'll try to come back with something more useful later.
You were staring into something that was formed by a particle that didn't have a solid state? It can't be explained. You know it deep down I am sure. You are not what you think and neither am I.
Look at your hands. Where does your hand stop? At your tip of fingers. Where does your nerve endings reach your brain? We know this. But we don't know the slightest bit about our conciousness. Where does that stop? If it did stop we would already know the limitations. People like to think of death as a limitation to our conciousness as it's their way of dealing with what we are. The state of an illusionary particle should be the least of our worries
Look at your hands. Where does your hand stop? At your tip of fingers. Where does your nerve endings reach your brain? We know this. But we don't know the slightest bit about our conciousness. Where does that stop? If it did stop we would already know the limitations. People like to think of death as a limitation to our conciousness as it's their way of dealing with what we are. The state of an illusionary particle should be the least of our worries
That wasn't exactly what I meant. Something closer to "I sort of know what I want to say but I can't quite figure out how to put it into words".
There is a deep link between quantum mechanics and probability, for example. So if you understand what probability is telling you then you can understand quantum mechanics a lot clearer and avoid some of this fuzziness. As an example, take a coin toss. On the assumption that it is essentially fair, then there's a 50/50 chance of getting heads or tails. You can regard tossing the coin as a measurement, in some sense. Then you get heads or tails each time you take a measurement. Taking many hundreds of such measurements and you can expect the results to tend towards half heads, half tails overall. Does the coin "know" to do this? Of course not. But the laws of probability are such that this is what is going to happen with overwhelming likelihood.
In essence, it is the same with quantum mechanics, which would be essentially equivalent to normal probability if you didn't have a square root of -1 shoved in at various points. In principle, though, both can be written in the same language. In normal probability it's an un-necessary abstraction, which is why no-one does it -- but they could, if they wanted to.
Incidentally, this: "The only way we could have interaction with something by looking at it would mean we are somehow in some kind of generated world and we are not who we think we are..." is not true.
An interaction means that the particle you are looking at has emitted or absorbed a photon, or hit a particle in some detector, or what have you, and is therefore a clear physical event. There is no need to throw in "[computer-]generated world" as an explanation. Or consciousness, for that matter, as some people are prone to doing.
Also Dark matter is rather less vague than your posts. We know a great deal about what it isn't, and that in itself is no small achievement.
It is perhaps good practice to understand something first, before criticising it.
There is a deep link between quantum mechanics and probability, for example. So if you understand what probability is telling you then you can understand quantum mechanics a lot clearer and avoid some of this fuzziness. As an example, take a coin toss. On the assumption that it is essentially fair, then there's a 50/50 chance of getting heads or tails. You can regard tossing the coin as a measurement, in some sense. Then you get heads or tails each time you take a measurement. Taking many hundreds of such measurements and you can expect the results to tend towards half heads, half tails overall. Does the coin "know" to do this? Of course not. But the laws of probability are such that this is what is going to happen with overwhelming likelihood.
In essence, it is the same with quantum mechanics, which would be essentially equivalent to normal probability if you didn't have a square root of -1 shoved in at various points. In principle, though, both can be written in the same language. In normal probability it's an un-necessary abstraction, which is why no-one does it -- but they could, if they wanted to.
Incidentally, this: "The only way we could have interaction with something by looking at it would mean we are somehow in some kind of generated world and we are not who we think we are..." is not true.
An interaction means that the particle you are looking at has emitted or absorbed a photon, or hit a particle in some detector, or what have you, and is therefore a clear physical event. There is no need to throw in "[computer-]generated world" as an explanation. Or consciousness, for that matter, as some people are prone to doing.
Also Dark matter is rather less vague than your posts. We know a great deal about what it isn't, and that in itself is no small achievement.
It is perhaps good practice to understand something first, before criticising it.
Oh sorry I always thought that dark matter covered the anomalies that describe rotation. You know when 0 article physics doesn't match Einstein?
Anyway I look at someone and they look at me we are interacting on a non physical basis. If we interact on a non physical basis with particles then what else can it be than non physical,? Don't worry Jim there are lots of tubes and mirrors at work as we speak.
Anyway I look at someone and they look at me we are interacting on a non physical basis. If we interact on a non physical basis with particles then what else can it be than non physical,? Don't worry Jim there are lots of tubes and mirrors at work as we speak.
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