What is the radius of a superposition

1. Jan 23, 2014

batmanandjoker

Does superposition have a radius or a space covered distance which cuts off at a certian point based on the size or coherance of the object. I understand it is a statistical distribution like a blanket of qm possibility as to where the object or particle can collapse. But is there a cut off point or does superposition cover the entire known universe and its just a matter of probabilitys as to where the particle or macro object will be, collapse into. Im confused because I know macro objects like myself have a wave function which is extremely small compared to the size of the macroscopic world. My personal wave function is much smaller than any currently measurable sizes. But is there a statistical cut off which renders the probabiliity insignificant or is there always a probability I could be in china at this very moment.

Im sorry for all the qm macro questions the help is much appreciated.

2. Jan 23, 2014

Staff: Mentor

I presume you mean Bell type entanglement.

As far as is known today they is no limit to how far they are apart - they remain entangled.

Thanks
Bill

3. Jan 23, 2014

Maui

The popular vote here is that it's meaningless to speak of size of superpositions, even in extradidinary conditions where effects only attributable to superpositions of states are observed. Clasically, superpositions of states are undefined and meaningless so they have a point but a minority(that includes me) believes there is some reality to states in superposition probed in the right kind of way.

4. Jan 23, 2014

batmanandjoker

thats not what i meant, I meant how big is the range of superposition of micro and macro objects in time and space I mean can an electron in a superposition state be in mars while at the same time be right next to you. Is there a statistical probability range of where the object is,could be in time and space and how does it apply to macro objects as opposed to micro objects.

5. Jan 23, 2014

ZapperZ

Staff Emeritus
That is really not a well-defined question. It's like asking what is the amount of money someone makes in a year. If you answer "well, it depends on the job, how good that person is, where in the world he is working, etc...etc...", then you get the idea on why your question has the same type of answer.

It can be as small as the separation between two electrons in a quantum well, to as large as several kilometers in a superconducting wire! And I'm sure it can be even larger than that if one can maintain the coherence.

Zz.

6. Jan 23, 2014

Staff: Mentor

Now I think I now know what you mean.

Its often said from the principle of superposition an object that can be in a state that is position A and one where its in position B can be in a superposition of those two states - which is true.

Unless its being observed, in which case it will be in either one or the other, then it doesn't have the property of position and cant be said to be anywhere. Its easy to fall into the trap, and I did in the past, to think of superposition as being literal ie it is literally in those two places. From posting on this forum I quickly had my misunderstanding corrected - and I had read a LOT of QM books - it doesn't have a property until its observed to have that property. You cant say anything about position until its observed to have it - in particular if its in a superposition of position you cant say its in a number of different positions at the same time.

I suspect the reason some people fall into this trap, and its true in my case, is Dirac's famous book explains the principle of superposition in a way that suggests its like that - if you read it carefully you can see that's not really what he is saying - but a cursory read does suggest it.

I am now of the view that the principle of superposition, as an actual principle, rather than simply a byproduct of the vector space structure of QM, is probably not the best way to look at it.

So yes - you can in principle have an object in a superposition of states any distance apart - but that doesn't mean its literally in those positions simultaneously - or even that the concept of position is appropriate in such a situation.

Thanks
Bill

7. Jan 24, 2014

batmanandjoker

Thank you for the reply, but this would suggest that in fact the classical world is in fact for the most part(with the exeption of the double slit experiment) collapsed because we perceive finite positions in classical physics. In the classical world unless isolated from the enviorment or put in a vaccum objects collapse on their own like the atoms of my tv are interacting with each other causing the thermodynamic mark in space time as well as interacting with the enviorment and it self collapses. We dont live in a world where everything is in superposition is this correct.

8. Jan 24, 2014

Staff: Mentor

Well yes the classical world emerges from interaction with the environment - and its insidious isolating it from the environment so this doesn't happen.

For example, a few stray photons from the CBMR is enough to decohere a dust particle and give it a definite position.

Thanks
Bill

9. Jan 24, 2014

StevieTNZ

You make it sound like the measurement problem is solved, when it isn't.

Remember in another thread you admitted to us not knowing where collapse actually occurs, but with a statement you posted you make it sound like we know where collapse occurs.

10. Jan 24, 2014

batmanandjoker

At some point you have to draw a line in the sand and recognize statistical insignificance nothing in this world is 100 percent known for certain but we live in a world of probabilitys and that like it or not is good enouph, its all we have.

11. Jan 24, 2014

Staff: Mentor

I think you are reading more into what I say than is intended.

I have said it before, and will say it again. APPARENT collapse is solved - actual collapse, and even if collapse occurs at all (its very interpretation dependent) isn't.

There are tons of threads on this forum for anyone to delve into the detail.

I said in modern times many place it immediately after decoherence. Wigner and Von-Neumann were worried about the Von-Neumann regress and since no place was different placed it in consciousness. We now know a place that is different - immediately after decoherence.

Thanks
Bill

12. Jan 24, 2014

Staff: Mentor

His point s a bit different to that.

It's a subtle point of QM involving the difference between whats called apparent collapse and actual collapse.

Here is a paper that explains the difference:
http://philsci-archive.pitt.edu/5439/1/Decoherence_Essay_arXiv_version.pdf

Its crux is the difference between improper mixed states and proper mixed states. Decoherence transforms a superposition into an improper mixed state which is observationally exactly the same as a proper mixed state. However it is only for proper mixed states the collapse issue is solved. But since there is no way to tell the difference decoceherence has APPARENTLY solved the collapse issue - but not in actuality.

It has been discussed many times on this forum and in many threads - you can do a search and go through them and post with any queries.

I wont discuss it here because such discussions tend to get rather heated.

I also will not hide that the validity of tracing over the environment, which converts superpositions to mixed states, depends on the Born Rule, so cant be used as a proxy for that. Bringing it all together so see how it solves the the collapse issue (again APPARENTLY) requires a bit of care.

Thanks
Bill

Last edited: Jan 24, 2014
13. Jan 24, 2014

StevieTNZ

I stand by my statement that you've made it sound like the measurement problem has been solved, especially by saying a dust particle is given a definite position by the decoherence mechanism (and not including the word 'apparent').

Not everyone has time or know where to look for your posts to see where you say decoherence shows apparent collapse. You should make the distinction each time you endorse the decoherence approach.