- #71
Simon Phoenix
Science Advisor
Gold Member
- 291
- 224
I thought it might be useful for some to see one situation where 'wave-particle' duality arises. I think it's useful to remind ourselves why the idea ever arose in the first place. I'm going to imagine a world in which we can perform perfect experiments and I'm going to be a little bit cavalier with language in an attempt to get the basic ideas across. For this I hope I can be forgiven.
We're going to imagine that we have something we're going to call a 'single-photon source' that spits out these (hypothetical) photons at the rate of 1 every second. We've done experiments on this source and, sure enough, if we put a detector at the output we see that we get a 'click' every second. Furthermore, we don't seem to ever be able to generate 'half a click'. So we feel justified in thinking that we have some source that is producing little blobs of energy that can't be divided.
Now it's perfectly possible to construct a theory in which the supposed photons are just classical fields and the discrete clicks occur because of quantum 'stuff' in the atoms of the photodetector. Whilst this works OK for a source feeding directly into the detector, it's not really all that good when we put beamsplitters in there. Classical fields behave in a certain way at beamsplitters - for a 50:50 splitter, half of the field goes one way and half the other way. So let's see why we might think we actually have 'particles' we call photons.
Let's look at experiment 1 here. We fire our single photons into the BS (we assume 50:50). We find that one of the detectors, at random, clicks every second, but never both. That's very hard to explain if we had a classical EM field going in there - we'd get 'half' of the field going to detector A and half going to detector B. If 'half' of a field is sufficient to fire a detection event, why do we never see both detectors fire? Furthermore, we find that all of the energy ends up at one detector - so if something was going on both paths the energy only arrives at one place or t'other. Echoes of non-locality here.
But there is a neat explanation for experiment 1. Suppose we really did have these indivisible blobs we call particles - then if the particle goes one way or the other, at random, at the beamsplitter we'd get exactly the observed behaviour. So at this point we feel fairly confident, armed with such a neat and simple explanation, that we have particles.
But now we do experiment 2. We bring the outputs from the first BS and feed them into a second BS. Based on our interpretation of experiment 1 we'd expect that we're going to get exactly the same behaviour at detectors C and D - one or other will fire at random, but never both.
But suppose we put a phase modulator in the output arms from the first BS. Now what do we find? We find that we can find settings such that detector C fires every second, or detector D fires every second - in other words we have a switch. This depends on the ##relative## setting of the modulators. How can this be? Haven't we already established that we have something going one way, and nothing the other? So one modulator acts on something, but what is the other modulator acting on? So clearly ##something## must be going on both paths. This is just the interference we'd expect from classical waves so problem solved! It's a classical wave after all.
But hang on - now we can't explain the properties of experiment 1. So we're left with a dilemma. Particles explain experiment 1 very nicely, but fail at explaining experiment 2. Waves explain experiment 2 very nicely, but can't explain experiment 1. Therein lies our problem. Do we have 'waves' or 'particles'?
There's nothing paradoxical about nature, of course, the problem, or apparent paradox, here is generated by our attempt to explain things in terms of particles and waves. It just doesn't work. So what do we conclude? That nature is somehow schizophrenic - or that there's something wrong with the way we're trying to explain things? Obviously it has to be the latter
So we see in this really simple couple of experiments why there's an issue at all - the correct conclusion to draw isn't that wave-particle duality exists, it's that there's something wrong with our interpretation of what's going on. I'm sorry if I'm just teaching my grandmother to suck eggs here* - but I hope some find it useful.
*this is a bizarre UK phrase which means "stating the bleedin' obvious"
We're going to imagine that we have something we're going to call a 'single-photon source' that spits out these (hypothetical) photons at the rate of 1 every second. We've done experiments on this source and, sure enough, if we put a detector at the output we see that we get a 'click' every second. Furthermore, we don't seem to ever be able to generate 'half a click'. So we feel justified in thinking that we have some source that is producing little blobs of energy that can't be divided.
Now it's perfectly possible to construct a theory in which the supposed photons are just classical fields and the discrete clicks occur because of quantum 'stuff' in the atoms of the photodetector. Whilst this works OK for a source feeding directly into the detector, it's not really all that good when we put beamsplitters in there. Classical fields behave in a certain way at beamsplitters - for a 50:50 splitter, half of the field goes one way and half the other way. So let's see why we might think we actually have 'particles' we call photons.
Let's look at experiment 1 here. We fire our single photons into the BS (we assume 50:50). We find that one of the detectors, at random, clicks every second, but never both. That's very hard to explain if we had a classical EM field going in there - we'd get 'half' of the field going to detector A and half going to detector B. If 'half' of a field is sufficient to fire a detection event, why do we never see both detectors fire? Furthermore, we find that all of the energy ends up at one detector - so if something was going on both paths the energy only arrives at one place or t'other. Echoes of non-locality here.
But there is a neat explanation for experiment 1. Suppose we really did have these indivisible blobs we call particles - then if the particle goes one way or the other, at random, at the beamsplitter we'd get exactly the observed behaviour. So at this point we feel fairly confident, armed with such a neat and simple explanation, that we have particles.
But now we do experiment 2. We bring the outputs from the first BS and feed them into a second BS. Based on our interpretation of experiment 1 we'd expect that we're going to get exactly the same behaviour at detectors C and D - one or other will fire at random, but never both.
But suppose we put a phase modulator in the output arms from the first BS. Now what do we find? We find that we can find settings such that detector C fires every second, or detector D fires every second - in other words we have a switch. This depends on the ##relative## setting of the modulators. How can this be? Haven't we already established that we have something going one way, and nothing the other? So one modulator acts on something, but what is the other modulator acting on? So clearly ##something## must be going on both paths. This is just the interference we'd expect from classical waves so problem solved! It's a classical wave after all.
But hang on - now we can't explain the properties of experiment 1. So we're left with a dilemma. Particles explain experiment 1 very nicely, but fail at explaining experiment 2. Waves explain experiment 2 very nicely, but can't explain experiment 1. Therein lies our problem. Do we have 'waves' or 'particles'?
There's nothing paradoxical about nature, of course, the problem, or apparent paradox, here is generated by our attempt to explain things in terms of particles and waves. It just doesn't work. So what do we conclude? That nature is somehow schizophrenic - or that there's something wrong with the way we're trying to explain things? Obviously it has to be the latter
So we see in this really simple couple of experiments why there's an issue at all - the correct conclusion to draw isn't that wave-particle duality exists, it's that there's something wrong with our interpretation of what's going on. I'm sorry if I'm just teaching my grandmother to suck eggs here* - but I hope some find it useful.
*this is a bizarre UK phrase which means "stating the bleedin' obvious"