A couple of questions

[AlphaNumeric]

If you can't say where that place is, how can you say they actually occupy the same point in space? In physics we deal with measurable systems, represented by Hermitian Matrices. If you can't say where that location is, I doubt you can honestly say that particles at any given moment share well defined point positions.

Then you don't understand the notation. Let's make it simpler, since you obviously don't grasp the general approach Pryzk has given.

Consider the following entangled system, . From this we can see that if particle 1 is in state A then so will particle 2. Similarly if particle 1 is in B. Pryzk just gave the continuous state version of this.

Then why does everyone keep referring to Bose -Einstein condensates, when, if every particle in a Bose-Einstein condensate is said to ''share the same space'' yet, we are talking about a macroscopic system...

...Logically... that is complete rubbish. If it where sharing the same ''point'' in spacetime, then we wouldn't have a macroscopic system, we'd have a point.

BEC may be spread out in space but they illustrate precisely the same concept even then, in that the states etc are now quantum states, such as energy and spin states, perhaps not position. But the concepts are precisely the same. Even if you can't say what state a particular particle is in you know all the particles are in the same state. If the system evolves in time then all the particle states will evolve in the same way. This is the basis of entanglement also, where the particles are separated in space. The formalism and results are identical in their analysis. An analysis you're obviously clueless about.

I am certainly by no means an expert on Condensate matter, but, the statement in itself is folly.

You're obviously not even competent, never mind an expert, in this stuff. Even the most basic of concepts and methods are beyond you. Why you then persist to make assertions about the results, results you don't grasp, I don't know. A rational person would obviously see the dubious nature of their claims in such instances.

Well I think that if a statement is to be true, it better fit observation... which is what quantum mechanics is all about!

Quite clearly the statement that... ''all bosons share the same space'' is patently false and misleading.

No one said bosons all occupy the same space but rather in some systems they can. If you have a multi-particle system with a position space representation of the form then if it's a pair of fermions you'll know for all z, as they cannot be in the same place at the same time, but for bosons if for some z then they CAN be in the same place at the same time. Such formulations and systems exist.

Is everyone just ignoring what I am saying?

Listen to me again. How can the bosons share the same space (a point) and still be a macroscopic object... can someone explain this to me before I really come across as either being

A) thick or
B) simply being ignored

No one is ignoring you, we're correcting your ignorance. The fact you don't want to listen and thus we have to keep repeating it doesn't mean the problem is our end.

If all there was to this, was setting the energies to bosons equal to each other, then I would agree... The more you cool particles down, they will almost certainly reach the same energies. But if someone tells me that they all setting down into the same ''point'' in spacetime, I'd say show me! The answer so far has been Bose Einstein Condensates, however, as has been pointed out, these condensates are actually macroscopic systems i.e. they are not a single point in spacetime. So how can these Bosons occupy a single point...

A BEC doesn't necessarily occupy a single point in space. As pryzk and I have explained several times, the particles could be in lots of places, giving the macroscopic system 'volume' but the particles can all be in the same place. That 'same place' doesn't have to be a single place, it can move around. In fact it MUST move around else you would violate the uncertainty principle. Saying "I don't know where these particles are but I'm certain they are all in the same place" is entirely consistent with the uncertainty principle.

This argument is meaningless until someone can answer my question instead of parroting the usual.

Wow, talk about hypocrisy. You don't understand quantum mechanics yet you're in the pseudo forum spewing out nonsense, cobbling together quantum results you don't understand and just parrot and claiming some result which isn't justified. You're just parroting stuff and in your case you don't understand it. We're telling you basic results but in our case we also understand it.

I am being told that the particles in a Bose Einstein Condensate occupy the same space --- for that to be true, it wouldn't be a macroscopic object I argue, it would be a single point in space, roughly the size of a photon. Obviously they really aren't occupying the same point in space - they must be spread out to constitute a macroscopic object. If same space means, ''they are indistinguishable due to their energies and are closely compact locally'' then I would agree perhaps that this is happening.

Wrong, as I've just explained.

But yeah, I said this to Crunchy as well and I was ignored. If she was talking about the wave form of particles, that's much different than talking about particles and exact locations.

No, it isn't.

Anyway, James hit it on the nail - I was defining myself very well all along, making it clear that I was talking about a ''point'' in space - not a space being point. Obviously my wording has tripped up people and when they tried to justify bosons occupying what I kept calling, ''points in spacetime'', the debates ensued.

Sorry, doesn't wash. You've shown you don't have a clue about this stuff. The problem is you don't understand the formal stuff and all you're doing is trying to cobble together results you don't understand and layperson explanations you've also failed to understand the subtleties of.

I know you're obviously not liking being told this but you don't get it, you're wrong, you're incompetent at quantum mechanics. As the thread of yours over in pseudo shows, you can't do any of the details, all you can do is mess around with coefficients and delude yourself into thinking you're doing proper physics. How many years have you been doing this now Reiku? How many more years are you going to keep doing it? Do you even have a job? I hope so because it pains me to think some of my taxes might be going into your pocket, allowing you to waste your existence doing this nonsense.

[przyk]

To define a position, or attempt to define a position, one would need to make a measurement.

No. In fact very much the opposite of that is true. In order to measure a position, you must first have defined the meaure of position you are using independently of where the particles are located. It is useless to ask where a particle is if you don't first define the notion of position and the axes and units you expect the answer in.

But the act of measuring a particle will begin to define the location and therefore no two particle can really occupy the same point in space.

No, that doesn't follow at all. It may be the case that additional factors, like the way particle states are prepared or interact might make it difficult or even impossible to prepare a state like the one I described in practice. But it is not true that such a state is banned or somehow meaningless in the general framework of quantum physics. Point #2 in your opening post is not correct.

A word on bosons, since they've been mentioned throughout this thread: the defining property of bosons is that systems of multiple identical bosonic particles are always found in states that are symmetric under permutations of the states of the individual particles. The state I gave you in post #11 is obviously symmetric in this way and is thus a perfectly valid bosonic state.

[Crunchy Cat]

Is everyone just ignoring what I am saying?

It's quite the opposite. Everyone is correcting what you are saying.

Listen to me again. How can the bosons share the same space (a point) and still be a macroscopic object... can someone explain this to me before I really come across as either being

A) thick or
B) simply being ignored

Trust me, you have achieved A) over the course of many years. When you cool a boson gas to near absolute zero, the gas condensens into a macroscopic blob. Each boson in the blob is a really big wave that may completely or partially overlap one or more of it's neighbors at any given time.

[Crunchy Cat]

Ok... with that explained better... more so from Pryzk, are you willing to contend there was a unified field at the initial state of big bang...

I think I explained in that pseudoscience thread that there was no point in further discussion. I have not changed my mind.

...and will concede a point on the ... overlapping of photons in one particular positions as waves... ?

Your wording wasn't clear, but do you mean you admit that this does in fact happen in reality? If so, that's good news. It means you learned something.

Either way, it was a debate on something rather pointless, as the initial beginning of the universe began as a point, there were no degrees of freedom to act as waves. Also it's established in the scientific community that there must have been an uncertainty present as you were trying to squeeze these particles to one position.

Like I said in your pseudoscience thread, maybe the crazies will give you an audience.

[AlphaNumeric]

What do you mean... ''it doesn't wash?''

I've been saying point in space, as dimensionless points go in physics, for about several days now! I wasn't talking about particles as waves, though when it was mentioned I said there is a difference.

'It doesn't wash' is 'that isn't a valid argument' or 'that is an insufficient direction to take'. And I note you ignored all of the rest of my post, including the explicit example proving you wrong. That doesn't wash.

You're wrong.

[AlphaNumeric]

So you admit and accept you have been wrong about pretty much everything you've said in this thread, particularly in regards to what pryzk and I have been saying?