On 2 Jun 2008 03:17:17 -0400, Warp <war### [at] tagpovrayorg> wrote:

>Stephen <mcavoysAT@aoldotcom> wrote:
>> Do you mean that someone has managed to square the circle?
>
>  The "squaring the circle" problem imposes some restrictions.

Indeed, a straight edge and compass. What more do you need?
-- 

Regards
     Stephen

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> 
>   If there's "no evidence", what do you call the interference pattern?
> "Non-evidence"?

Don't forget: A single electron doesn't make an interference pattern. It 
produces a bright spot on the fluorescence screen saying: Exactly here 
and nowhere else the electron hit the screen.

Only if you observe many many events and add up their positions they 
converge to an interference pattern.

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Darren New <dne### [at] sanrrcom> wrote:
> For example, there's no known mathematical model to indicate where a 
> specific electron is, and indeed if I understand correctly, experiments 
> show there cannot be one.

  That's a bit like being in the middle of the ocean and saying "there's
no mathematical model which says where the water is", speaking as if the
"water" was a point in space and you'd had to locate it at some specific
coordinates.

  Your statement is like that. You are starting from the assumption that
an electron is an extremely small particle with well-defined boundaries,
approximately equal to a mathematical point, and then you ask for a
mathematical model to say where that point is in space. As with the
water example, that's kind of silly.

  What the mathematical model *can* do is to give a distribution function
which tells how the electron is distributed in space (a bit like a
function which tells how the water is distributed, except that with
the electron the "density" of the "water" is not constant).

  These probability functions may not be infinitely accurate (because they
depend, among other things, on finite measurements which are accurate only
to so many decimals), but they can be used for practical calculations.

  It's not like you could shoot an electron to some direction, and then
the electron suddenly hits the other side of the Earth (or the solar
system). It hits a quite accurately calculable place.

-- 
                                                          - Warp

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Stephen <mcavoysAT@aoldotcom> wrote:
> On 2 Jun 2008 03:17:17 -0400, Warp <war### [at] tagpovrayorg> wrote:

> >Stephen <mcavoysAT@aoldotcom> wrote:
> >> Do you mean that someone has managed to square the circle?
> >
> >  The "squaring the circle" problem imposes some restrictions.

> Indeed, a straight edge and compass. What more do you need?

  I assume that dividing the circle into an uncountable set of points.

-- 
                                                          - Warp

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Michael Zier <mic### [at] mirizide> wrote:
> Don't forget: A single electron doesn't make an interference pattern. It 
> produces a bright spot on the fluorescence screen saying: Exactly here 
> and nowhere else the electron hit the screen.

  Wasn't it "impossible" to accurately measure the place and velocity
of a quantum particle? ;)

> Only if you observe many many events and add up their positions they 
> converge to an interference pattern.

  But I believe it can be done by shooting just one electron at a time,
so the electron indeed interferes only with itself, not with other
electrons.

-- 
                                                          - Warp

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Am Mon, 02 Jun 2008 03:41:22 -0400 schrieb Warp:

> Michael Zier <mic### [at] mirizide> wrote:
>> Don't forget: A single electron doesn't make an interference pattern.
>> It produces a bright spot on the fluorescence screen saying: Exactly
>> here and nowhere else the electron hit the screen.
> 
>   Wasn't it "impossible" to accurately measure the place and velocity
> of a quantum particle? ;)

Indeed, and that's what I said: It hit the screen *here* and I have no 
clue how fast and from what direction :P

> 
>> Only if you observe many many events and add up their positions they
>> converge to an interference pattern.
> 
>   But I believe it can be done by shooting just one electron at a time,
> so the electron indeed interferes only with itself, not with other
> electrons.

Yes, I've seen this experiment. *Single* bright spots lighting up 
briefly, no observable pattern if you just look at it. Unless you average 
"all the video frames" (which you can do either with real video frames or 
"simulated" with a photographic film), an interference pattern emerges.

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On 2 Jun 2008 03:38:58 -0400, Warp <war### [at] tagpovrayorg> wrote:

>Stephen <mcavoysAT@aoldotcom> wrote:
>> On 2 Jun 2008 03:17:17 -0400, Warp <war### [at] tagpovrayorg> wrote:
>
>> >Stephen <mcavoysAT@aoldotcom> wrote:
>> >> Do you mean that someone has managed to square the circle?
>> >
>> >  The "squaring the circle" problem imposes some restrictions.
>
>> Indeed, a straight edge and compass. What more do you need?
>
>  I assume that dividing the circle into an uncountable set of points.

Invisible ??? 
:-)
-- 

Regards
     Stephen

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Darren New wrote:
> Warp wrote:
>>   I would say that mathematics can always be used to represent reality
>> when put in the proper context.
> 
> The fascinating thing to wonder about is ... why is this so?
> 
> Most people are so used to it that it's hard to even imagine a world 
> where this isn't true. Even the religious types try to come up with 
> "laws" that would govern the supernatural.
> 
> Of course, maybe that's just anthropogenic. If the universe didn't work 
> consistently, I'd (wild-ass) guess that it's likely that life capable of 
> wondering about it wouldn't have evolved.
> 
> And the thing about QED is there doesn't seem to be math at the bottom 
> level - it's random on an event-by-event basis. (Maybe there's a math 
> for that? I don't know of any. Statistics only deals with multiple events.)

I wouldn't say that it is truly random, but merely that predicting the 
outcome of any interaction requires information that is presently not 
available.

For instance, the decay of unstable particles appears to happen 
randomly, but at what appears to be a predictable rate for aggregate 
amounts of like particles.  What is likely is that the particles decay 
when they encounter certain conditions (such as a gradient in the 
electric or magnetic potential) that is high enough to overcome the weak 
internal cohesiveness of the particle, causing it to come apart.  Since 
the gradient of potential at any place is not (and probably cannot be) 
known with sufficient precision (and is certainly in a state of constant 
change), it appears random.

Regards,
John

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somebody wrote:
> "Darren New" <dne### [at] sanrrcom> wrote in message
> news:484363fb$1@news.povray.org...
>> somebody wrote:
> 
>> For example, there's no known mathematical model to indicate where a
>> specific electron is, and indeed if I understand correctly, experiments
>> show there cannot be one.
> 
> Some syntatically correct questions can be meaningless. What colour is the
> note C#?
> 

It's an octave of blue, if I got the math right. I started from 4435Hz, 
though, instead of a more accurate number, so it's probably off by a bit.

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>> Some syntatically correct questions can be meaningless. What colour is 
>> the note C#?
> 
> It's an octave of blue, if I got the math right. I started from 4435Hz, 
> though, instead of a more accurate number, so it's probably off by a bit.

You see the look on my face right now? This look means that you have 
just BROKEN MY MIND!

http://www.questionablecontent.net/view.php?comic=165

-- 
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*

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