[David Cooper (OP)]

What does it actually mean to say that something can be in two different places at the same time? Imagine a set of scales with an object on one side and a second object of equal mass on the other side - the scales will balance. Now introduce a second set of scales with a third object of the same mass as the other two on one side and nothing on the other side - these scales do not balance. Now introduce some quantum magic and make one of the objects from the first set of scales occupy two places at the same time, one of those places being it's original location and the other location being the previously-vacant location on the second set of scales. What will happen now? Will both sets of scales balance out level, or will the object which is in two locations at the same time now display only half its original mass in each location?

[Soul Surfer]

If you consider that individual particles and composite assemblages of them can always be expressed in terms of momentum probability waves. It becomes completely logical that like an interference or a diffraction pattern these waves can have multiple peaks of probability depending on how they have interacted with some other object. The important thing to remember is that these probability functions always integrate to unity.  That is the probability of finding the a particle somewhere in the entire universe is 100% and if there are three peaks (that is the particle can be in three places) the individual probabilities will always be less than 100% and add up to it for example the three peaks may be say 50% 40% and 10%.

As an extension to this when particles are entangled their wave functions are connected and have a phase ambiguity between the two peaks which show where each of the particles are moving.  When this ambiguity is resolved at one point because phase shifts can propagate faster than the velocity of light and even with infinite velocity (an easily and demonstrable truth not often talked about) the state of the other particle is simultaneously resolved.  This phase propagation however cannot carry information and therefore does not break any of the rules that say information cannot be transmitted faster than light.

[David Cooper (OP)]

It sounds as if you're implying that the mass of the particle will indeed be halved at each location, though you haven't directly said so.

When this ambiguity is resolved at one point because phase shifts can propagate faster than the velocity of light and even with infinite velocity (an easily and demonstrable truth not often talked about) the state of the other particle is simultaneously resolved.

This leads on to another question I've been wondering about for a long time. If the state of the other particle is simultaneously resolved at a great distance, doesn't that blow apart the idea in relativity that there is no such thing as simultaneous events separated in space?

[yor_on]

What you ask seems to be what rules there is to QM, and if they will make the same sense as our macroscopic?

I would say that JP is the guy that works with them, but I'll give it a try all the same. Hubris my middle name.

First of all there is a wave particle duality. That's important to understand, and also hinge on your choice of experiment to give it one value or the other. In fact I expect that one to be complementary, meaning that both is constantly there. Another definition is about matter being 'waves', but of quantized values. That one speaks about a electron as a form of 'standing wave' around a atom, able to have a defined quantized 'energy'. This site is one of the nicest I've seen, defining QM concepts. 

And when it comes to the duality we see in QM we have a new way, called weak measurements, that some see as 'the way' forward. The problem with such an idea being that as it assume that the possibility and probability of inferring something exists as a real thing, it also leads us to a presumption stating that because we can, it also must be.  Quantum mechanics rule 'bent' in classic experiment. (particle/wave duality)

And electrons being in two 'places' do exist, as defined by probability, but somehow that and the wave/particle duality seems very similar to me. Take a look at this experiment and compare it to the one above. First quantum effects seen in visible object. You can read it as the measurements done always will give you one 'state', including superpositions. It's also called collapsing the wave function.

There's a lot more to it of course
But it's a beginning.

[simplified]

If we don't  know something, then we must have duality of opinion.

[JP]

This is one of the very confusing points about quantum mechanics.  We're used to thinking about particles and waves as different things in everyday life.  A particle is classically a physical object that has a specific position.  It can't be in two places at once.  We're used to waves from water, sound or light.  We're familiar with the fact that any of these kinds of waves can spread out over a region of space and therefore be in many places at once.

What quantum mechanics says is that a particle has some properties of waves.  Specifically, there is a wave that tells you the probability of seeing a particle at different positions when you measure it.  If the particle wave is on both ends of the scale, you can rightly say that the particle is in two places at once, and you won't know where it is until you measure it.

You might ask why we know there is a wave instead of just not knowing which side of the scale the particle is on.  After all, if you flip a coin, it is either heads or tails, even if you haven't shown me yet.  We know it's a wave because we can cause it to interfere with itself or with other things in ways that the coin flip can't.  The classic example of this is the two slit experiment, in which case you get a wavelike ripple pattern in the probabilities of where an electron can land after it's wave passes through two slits.  The only explanation for this ripple is that the wave passed through both slits simultaneously, since the sum of waves from each slit independently doesn't show this effect.   A particle's wave is therefore physically in multiple places at once, and so we say the same about where a particle can be: http://en.wikipedia.org/wiki/Double-slit_experiment#Overview

I think the other posts addressed the question of why this doesn't violate special relativity better than I can.

[yor_on]

SR doesn't break down. It is defined from a constant, being 'c' and that one holds. I guess you're thinking of entanglements there? What they do is to beget a value 'instantaneously' as you measure one of them, the distance between particles notwithstanding, as far as we know that is, the furthest we have tested this was in optic fibers, some kilometers? As far as I remember.

If you could assume that there would be a applicable communication, making sense, then the idea of 'c' defining a limit for the 'speed' of communication would be wrong, but 'c' would still be a constant. And that's what makes 'time dilations' and Lorentz contractions possible between 'frames of reference'. Same will be the point if we find that mass (neutrinos) is faster than light SR will still hold, although we now will find a very weird world where 'light runs as syrup.' and rods speeds away, like, ah, hot rods?
==

There is the definition of mass getting growing infinitely, as it speed up to lights speed though. But as the basic fact remains, and have been tested for a hundred years, namely 'c'. Then whatever those neutrinos does can't be 'speeding' in the usual description. If it is correct, which I still doubt, then 'tunnelings' etc seems more reasonable.

[Pmb]

This doesn't sound right. If the same particle appeared in two different places then energy won't be conserved.

[yor_on]

I don't know Peter?

After all, you only should get one value in your final measurement as I think of it. if we really could catch an interaction where we saw the kinetic energy doubled though? Now that would be interesting. Makes me think of Hotta and 'zero point energy' though.

But yes, the conservation laws would be questioned.

[David Cooper (OP)]

What you ask seems to be what rules there is to QM, and if they will make the same sense as our macroscopic?

QM isn't a subject I know much about, as no doubt you can tell. I keep hearing claims about QM that don't appear to make full sense, but that's most likely just a failing of language. I want to know what it actually means to say that something is in two places at once. It now sounds as if everything is in some sense everywhere at the same time, and clearly everything isn't fully everywhere at the same time, so there must be some kind of spreading out of things which dilutes the degree to which they occupy any specific location, until someone tries to measure them, at which point the whole item presumably has to decide on one location to appear in - the scales I mentioned earlier would be measuring the item in question, so it would have to decide which set of scales it was on rather than being on both - it would only be in one place. Alternatively, each set of scales would have to be in two states at the same time: one state in which they're level and another in which they're tilted.

That one speaks about a electron as a form of 'standing wave' around a atom, able to have a defined quantized 'energy'. This site is one of the nicest I've seen, defining QM concepts.

Good interactive diagram in that.

And when it comes to the duality we see in QM we have a new way, called weak measurements, that some see as 'the way' forward. The problem with such an idea being that as it assume that the possibility and probability of inferring something exists as a real thing, it also leads us to a presumption stating that because we can, it also must be.  Quantum mechanics rule 'bent' in classic experiment. (particle/wave duality)

I missed that news story somehow - thanks to pointing me towards it.

[Soul Surfer]

david (and others) when I say the probability in the wave function is a multiple locations with a particular probability it is only like that until you measure this and find it at one of the three locations and then it is clearly 100% at that location.  However if you perform exactly the same experiment a large number of times the locations found would display the probabilities indicated.  As with the original numbers I suggested   50%, 40%, 10%, within the normal probabilities of deviation of statistical experiments based on the total number of times the experiment was carried out.

This is the way particle physicists measure the results of their experiments.

[David Cooper (OP)]

SR doesn't break down. It is defined from a constant, being 'c' and that one holds. I guess you're thinking of entanglements there? What they do is to beget a value 'instantaneously' as you measure one of them, the distance between particles notwithstanding, as far as we know that is, the furthest we have tested this was in optic fibers, some kilometers? As far as I remember.

Yes, it's when you force one particle to take on a specific state by measuring it, the other at a distance is said to be forced to take on a specific state instantly. What interests me here is the bit about instantaneous action over a distance, because if it isn't limited to the speed of light, it sounds as if you ought to be able to identify a preferred frame of reference by synchronising clocks at a distance.

If you could assume that there would be a applicable communication, making sense, then the idea of 'c' defining a limit for the 'speed' of communication would be wrong, but 'c' would still be a constant.

This suggests that you can't synchronise clocks at a distance using this method, and I assume that's because the second particle doesn't announce the moment at which it's been forced to take up a specific state, in which case, how do you know that the transmission is instantaneous and not simply limited to the speed of light? When you examine the first particle to see what state it's in, it looks as if you can't know if the other particle has taken up a specific state until you've examined it as well, and that means you aren't going to know if it took up that specific state before you examined it or because you examined it.

[David Cooper (OP)]

david (and others) when I say the probability in the wave function is a multiple locations with a particular probability it is only like that until you measure this and find it at one of the three locations and then it is clearly 100% at that location.  However if you perform exactly the same experiment a large number of times the locations found would display the probabilities indicated.  As with the original numbers I suggested   50%, 40%, 10%, within the normal probabilities of deviation of statistical experiments based on the total number of times the experiment was carried out.

This is the way particle physicists measure the results of their experiments.

Yes, my original thought experiment was faulty - I was trying to have one part of it in two states at one time while another part of it was in one state, and that second part would automatically collapse the wave function of the first.

[Bill S]

If the particle wave is on both ends of the scale, you can rightly say that the particle is in two places at once, and you won't know where it is until you measure it.

Would it not be more in the spirit of QM to replace "you won't know where it is until you measure it" with "it won't be in one specific place until you measure it"?

[Bill S]

As usual there are some interesting responses.  It looks as though we are getting nearer to answering  David’s original question but it is still not entirely answered.  Perhaps there is no answer.  Perhaps the concepts of classical physics are so far removed from those of quantum physics that this sort of answer is not possible.

Regular posters will be well aware of the fact that I am not a scientist, however, I cherish the thought that someone looking in from outside might, at least, be able to ask a question that an insider might not think to ask because the answer seems so obvious; or perhaps the “hitch-hiker might put a different slant on something.

Let’s start with the wave/particle duality.  My understanding is that QM is consistent with the idea that particles may not actually exist as physical entities.  The more precisely one can locate a wave, the more it resembles a particle.  (See JP’s post with the wave diagrams, above).  This might lead to the conclusion that a particle is nothing more than a precisely located wave.

The next step is to consider that the wave, in its own frame of reference, is still an expanded wave, going to infinity and occupying the entire Universe.  Only in the frame of reference of an observer might the wave be considered as a particle, having location and mass.

The idea that every wave occupies the entire Universe, and might continue to do so, even if an observer perceives it as being localised, may be counter-intuitive, but that certainly does not necessarily mean it cannot be the case.  QM tells us that our reality is non-local, although this is not what we perceive.  Instantaneous actions between entangled particles can (probably) occur over boundless distances.  Something links these particles.  Would it be totally illogical to suggest that they are linked by their wave nature, and that this wave nature is their normal and permanent state?  If this were the case, it might be only our restricted 4D view of reality that obliges us to interpret their state as particulate under certain conditions.

[yor_on]

David "Experimental results have demonstrated that effects due to entanglement travel at least thousands of times faster than the speed of light.[22][23] In another experiment, the measurements of the entangled particles were made in moving, relativistic reference frames in which each respective measurement occurred before the other, and the measurement results remained correlated.[24][25]" From Quantum_entanglement 

Just follow the numbers in parenthesis to find the experiments. If we had a Big Bang it would be reasonable to assume that everything was entangled at that point, as it primary is about 'sharing' a wave function, or expressed otherwise, in some way gaining a exact same 'property' that links two particles together. But Einsteins relativity also questions distance, although differently through the Lorentz contractions.

And speaking of waves, the particle waves are quantized, which make them real weird from a normal classical 'wave definition'. You don't see water waves getting quantized as far as I know? And the way we describe waves we do not quantize them normally. Those waves are 'discrete' in some strange manner as I see it.

[JP]

Let’s start with the wave/particle duality.  My understanding is that QM is consistent with the idea that particles may not actually exist as physical entities.  The more precisely one can locate a wave, the more it resembles a particle.  (See JP’s post with the wave diagrams, above).  This might lead to the conclusion that a particle is nothing more than a precisely located wave.

Well put.  I'd just add to this that as far as we can tell, the localized wave of a particle can be as small as we'd like--there's no lower limit that we know of on its size.  (Though we haven't tested this as the Planck volume, where our theories will have issues).  For most cases, when doing calculations, we treat the particle as a single infinitely small point.  Whether or not that's correct or not, it seems to be very accurate within the limits of our theories.

[Bill S]

we treat the particle as a single infinitely small point

This may seem like nit-picking, but it isn't intended as such, I just have this "thing" about infinity. (I bet that surprised you!  ). 

Would I be right in thinking that "infinitely small" must refer to a mathematical infinity?  Otherwise, how would you distinguish between "infinitely small" and "non-existent"?

[imatfaal]

we treat the particle as a single infinitely small point

This may seem like nit-picking, but it isn't intended as such, I just have this "thing" about infinity. (I bet that surprised you!  ). 

Would I be right in thinking that "infinitely small" must refer to a mathematical infinity?  Otherwise, how would you distinguish between "infinitely small" and "non-existent"?

It's zero dimensional - dunno if that helps or causes more confusion.  They have position but no extension

[Bill S]

It's zero dimensional - dunno if that helps or causes more confusion

The concept of the zero dimensionality has never helped before; it would need more than a bald statement to alter that.   

They have position but no extension

How do you locate a position that has no extension?
What occupies the position?