[JP]

From a mathematics standpoint, a point with no extension is easy to imagine.  If I choose some point in space, that point doesn't have to have volume at all.  For example, if I draw a perfect sphere, the exact center of it is a point with no extension.  A point on a number line is also a point with no extension.

Physics is a science, though, and it deals with using mathematics to describe reality and testing that mathematics with experiments.  When we say that fundamental particles have no spatial extent, what we're really saying is that our mathematical model assumes they can be perfect mathematical points.  We then test this model by measuring the sizes of the fundamental particles.  So far, no matter how well we measure, we haven't found any evidence that particles do have a finite spatial extent.

Now, this doesn't mean that they are perfect points.  All our experiments have some finite resolution, and if a particle is smaller than that resolution, we can't tell the difference between that particle and a perfect point.  So when we call them point particles, it just means that they're smaller than the resolution limits of our best experiments.  Its likely that when we push things down to the Planck length, a lot of interesting new physics will be discovered, and this idea of point particles will need to be revisited, but so far the theory works fine.

[David Cooper (OP)]

"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

I can't access the details of the experiments without handing over a lot of money, so I can't see how they're actually doing them. I also can't see how anyone knows that both the particles haven't taken up specific states before one of them is examined, so I really need to find simple, clear explanations of the basics of all this. Unfortunately I don't have a lot of time to put into hunting information down because I'm tied up in an A.I. project which gives me virtually no time off. If there's no easy way in, I'll just have to put all this quantum stuff back on the shelf for now and look into it later.

[yor_on]

Hmm, didn't check for if it was paysites, sorry. "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? " Now that seems very true to me, and as far as I've seen you will need a communication at light speed to tell you what and when that spin means. Try this for a nice Signal Travels Farther and Faster Than Light. introduction, one thing though, Einstein didn't 'sneer' at all, as I know? Entanglements was actually his creation, as I understands it, although he expected the idea to prove the opposite to what it actually did.  EPR paradox.

[David Cooper (OP)]

Try this for a nice Signal Travels Farther and Faster Than Light. introduction, one thing though, Einstein didn't 'sneer' at all, as I know? Entanglements was actually his creation, as I understands it, although he expected the idea to prove the opposite to what it actually did.  EPR paradox.

Thanks for those links - I'm finding really interesting things in them. I'll think about all this for a while before asking any further questions. In the meantime, thanks to everyone who's commented in this thread - I haven't responded to everything that's been said, but all of you have added to my knowledge and I appreciate that greatly.

[Bill S]

From a mathematics standpoint, a point with no extension is easy to imagine

Mathematically, I agree; but then I try to apply this to the "real" world and say something like: if I put 100 of these points side by side, would they still occupy no space, because 0 x 100 = 0.

[cover it]

If you stand in front of a mirror, theoretically you are now in two places at one time 

[David Cooper (OP)]

I think I might be getting somewhere. Please tell me where I've gone wrong with this:-

You start out with an electron positron pair in a spin singlet quantum state, then you move them far apart before examining them. You want to examine them both at the same time, so I imagine that means repeating the experiment many times with different delays between both measurements to cover the possibility that the whole experiment is moving relative to a possible preferred frame of reference. No matter how you do the experiment you always find that you can only successfully measure the x-spin of both particles or the z-spin of both particles, but you can never measure the x-spin of one and the z-spin of the other without finding one or other of them to be uncertain.

Now, I must have got part of that wrong, because if you manage to measure the x-spin of one particle and fail to get a certain answer when trying to measure the z-spin of the other, that would indicate that the former measurement really did occur before the latter, and that would allow you to identify a preferred frame of reference by pinning down simultaneous events separated in space.

[imatfaal]

From a mathematics standpoint, a point with no extension is easy to imagine

Mathematically, I agree; but then I try to apply this to the "real" world and say something like: if I put 100 of these points side by side, would they still occupy no space, because 0 x 100 = 0.

Possibly so - but in reality various forces mean that a point particle can have a range of influence - ie stop you putting them "side by side".

On a more philosophical note - if the maths and the theory works, then why does it matter that we puny humans cannot get our head around a concept.  QM, GR, and Particle Physics are strange stuff - and all require an acceptance that not everything is readily (or even possibly) visualisable (is this a word - my spell-check says no).  The nub of the matter is that modern science is the creation of models that accurately predict experimental/observational outcomes - not about some inner hidden truth.  Even a Grand Unified Theory would be really just be set of equations and conditions that allowed precise predictions to be made - and not a description of an final truth.