Science > Physics > Discrete physical space and the mesure problem of QM
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Science > Physics |
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"" |
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10 May 2007 11:01:03 AM |
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Discrete physical space and the mesure problem of QM |
The most important theoretical achievement of natural sciences is the
old idea of atom. The matter can not be divided endlessly into still
smaller parts. The idea of atom hints that in the world exists a
special spatial scale. It is the scale of atom. Today the physicists
generally belive that all phenomena in the nature will appear from the
effects of quantum level. All phenomena appear from the level of one
scale. The scale is always connected to the space.
What is the empty room or space? What kind of structure and properties
does the empty space have? Does the shortest indivisible length exist?
The existence of one special scale refers to grainy space or cell-
structured space. In that case the space can be described with unit
vectors, which generate the cells. This kind of space is absolute, but
it is not the same as Newton's absolute space. It is not possible to
observe the empty space directly, but it is possible to examine its
structure theoretically. When the used space model is cell-structured,
several strange quantum effects can be understood or interpreted in a
new way.
D-theory is a new interpretation of quantum mechanics. It is based on
the hypothesis, which defines the structure of space. It can be proved
that the so called "local hidden variable theories" are possible, if
they use this hypothesis. The cell-structured space of D-theory is
absolute and will produce the Lorentz transformations. The Theory of
Relativity is based on them. How do the phenomena of classical world
appear from the quantum effects of absolute space? The space model
will give answer to this question, too.
When the mathematics is suitable to describe the effects of nature,
must the exhaustive physical theory be able to describe also the
basics of mathematics such as the origin of sets of numbers. The space
is also a mathematical concept and the space combines the physical
world to the basics of mathematics.
The physicists have tried to interpret the quantum mechanics over 70
years and no satisfactory interpretation is found. Observer's
consciousness seems to be a part of the measurement process and a lot
of useless text is witten about it. The model of cell-structured space
gives a new point of view on the role of consciousness in quantum
mechanics. Also another issue in interpretation, the non-locality, is
cleared up with help of the space model and violation of Bell's
inequality. The non-locality is a strong validity evidence of the used
model. The third issue in interpretation is the wave function of a
particle. It is a mathematical abstraction. It has in D-theory a
direct connection to absolute space, which is not unique for a
macroscopic observer because of its structure. Thus for example the
place of an undetected free particle is not unique, too. A measurement
however gives to the particle its place in the linear and unique
observer's space and the wave function of the particle "collapses" .
Different kind of rotations in symmetry spaces are fundamental in
Standard model of quantum mechanics, as well so called gauge
principle. The rotations and gauge principle have direct connections
to the properties of absolute space.
Finally stays left a modest question "What is everything?". D-theory
shows that it is impossible to get answer to this question. One
abstraction stays always left in the model. But only one.
Comments please?
The files:
http://koti.mbnet.fi/mpelt/tekstit/dtheory_1.ppt
http://koti.mbnet.fi/mpelt/tekstit/dtheory_2.ppt
http://koti.mbnet.fi/mpelt/tekstit/dtheory_3.ppt
or
http://koti.mbnet.fi/mpelt/tekstit/dtheory_1.pdf
http://koti.mbnet.fi/mpelt/tekstit/dtheory_2.pdf
http://koti.mbnet.fi/mpelt/tekstit/dtheory_3.pdf
Pekka Virtanen
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| User: "" |
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| Title: Re: Discrete physical space and the mesure problem of QM |
10 May 2007 11:31:29 AM |
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On May 10, 6:01 pm, wrote:
The most important theoretical achievement of natural sciences is the
old idea of atom. The matter can not be divided endlessly into still
smaller parts. The idea of atom hints that in the world exists a
special spatial scale. It is the scale of atom. Today the physicists
generally belive that all phenomena in the nature will appear from the
effects of quantum level. All phenomena appear from the level of one
scale. The scale is always connected to the space.
It is by no means clear if there is a true "uncuttable" or atom. The
chemical atom is of course a misnomer in an etymological sense as it
is indeed cuttable and reducable to smaller parts. Even the electron
must not be uncuttable and eternal as it will evaporate in a burst of
gammas when appropriately collided with its antimatter counterpart.
Will the constituents of space-time itself be found to also be
composed of the sum of their parts? It is likely that the heirarchy
will continue as far as we will be able to observe it, as objects
being made of the sum of their parts seems to be part of the basic
laws governing human thought.
What is the empty room or space? What kind of structure and properties
does the empty space have? Does the shortest indivisible length exist?
The existence of one special scale refers to grainy space or cell-
structured space. In that case the space can be described with unit
vectors, which generate the cells. [...]
Thanks for your post. You might also be interested in this paper on
the atom of space-time in the context of general relativity:
http://arxiv.org/abs/gr-qc/0405132
Sorry I couldn't get that far into your long essays but I found one
thing to disagree with:
"The set of complex numbers is the widest possible set of numbers"
And one to agree with:
"All the dimensions of the world are found in jazz".
Ciao -
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| User: "" |
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| Title: Re: Discrete physical space and the mesure problem of QM |
12 May 2007 06:04:43 AM |
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On 10 touko, 19:31, wrote:
Sorry I couldn't get that far into your long essays but I found one
thing to disagree with:
"The set of complex numbers is the widest possible set of numbers"
Why so? I discussed about this with 2 mathematicists and they agreed.
Note that this has an addition " which includes certain algebraic
basic features (commutativity, associativity, distributive law,
neutral element, negative and inverse element)."
Pekka
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| User: "The_Man" |
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| Title: Re: Discrete physical space and the mesure problem of QM |
12 May 2007 09:33:46 AM |
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On May 12, 7:04 am, wrote:
On 10 touko, 19:31, wrote:
Sorry I couldn't get that far into your long essays but I found one
thing to disagree with:
"The set of complex numbers is the widest possible set of numbers"
What does "widest possible set of numbers" actually mean?
The complex plane has exactly the same number of numbers (pun
intended) as R^2, ordinary Riemann 2-space. Of course, the properties
of the two are quite different, particularly as regards
differentiation.
You can extend the complex plane with a point at infinity, but I don't
know if that is what you are referring to.
Certainly, there are more points in R^3 than in the complex plane.....
Why so? I discussed about this with 2 mathematicists and they agreed.
Note that this has an addition " which includes certain algebraic
basic features (commutativity, associativity, distributive law,
neutral element, negative and inverse element)."
Pekka
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| User: "" |
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| Title: Re: Discrete physical space and the mesure problem of QM |
14 May 2007 03:53:42 PM |
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On May 12, 4:33 pm, The_Man <me_so_hornee...@yahoo.com> wrote:
On May 12, 7:04 am, wrote:
On 10 touko, 19:31, wrote:
Sorry I couldn't get that far into your long essays but I found one
thing to disagree with:
"The set of complex numbers is the widest possible set of numbers"
What does "widest possible set of numbers" actually mean?
The complex plane has exactly the same number of numbers (pun
intended) as R^2, ordinary Riemann 2-space. Of course, the properties
of the two are quite different, particularly as regards
differentiation.
You can extend the complex plane with a point at infinity, but I don't
know if that is what you are referring to.
Certainly, there are more points in R^3 than in the complex plane.....
Is this true?
The set of (x,y) with x,y rational numbers has a one-to-one
correspondance
with the integers and is countable, there are just as many points in
Q^2 as in Q^1.
Why more in R^3 than R^2?
Thanks-
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| User: "Rock Brentwood" |
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| Title: Re: Discrete physical space and the mesure problem of QM |
18 May 2007 02:54:05 PM |
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On May 14, 3:53 pm, wrote:
Certainly, there are more points in R^3 than in the complex plane.....
Is this true?
No, of course not.
there are just as many points in Q^2 as in Q^1.
There are just as many points in Q^n as in Q^1 for all finite
countable dimension n.
There are as many point in Q^w as in R^n for all infinite countable w,
and finite *or* infinite countable dimension n. That is, n-dimensional
spaces have only as many points as a line, even if the number of
dimensions n is (countably) infinite.
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| User: "The_Man" |
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| Title: Re: Discrete physical space and the mesure problem of QM |
14 May 2007 07:47:27 PM |
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On May 14, 4:53 pm, wrote:
On May 12, 4:33 pm, The_Man <me_so_hornee...@yahoo.com> wrote:
On May 12, 7:04 am, wrote:
On 10 touko, 19:31, wrote:
Sorry I couldn't get that far into your long essays but I found one
thing to disagree with:
"The set of complex numbers is the widest possible set of numbers"
What does "widest possible set of numbers" actually mean?
The complex plane has exactly the same number of numbers (pun
intended) as R^2, ordinary Riemann 2-space. Of course, the properties
of the two are quite different, particularly as regards
differentiation.
You can extend the complex plane with a point at infinity, but I don't
know if that is what you are referring to.
Certainly, there are more points in R^3 than in the complex plane.....
Is this true?
The set of (x,y) with x,y rational numbers has a one-to-one
correspondance
with the integers and is countable, there are just as many points in
Q^2 as in Q^1.
Why more in R^3 than R^2?
Maybe I am making a silly mistake (not being a mathematician).
For every point (x, y) in R^2, there are inifinitely many points (x,
y, z) in R^3. Why only allow x, y to be rational, rather than real?
Thanks-- Hide quoted text -
- Show quoted text -
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| User: "" |
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| Title: Re: Discrete physical space and the mesure problem of QM |
15 May 2007 08:40:49 AM |
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On May 15, 2:47 am, The_Man <me_so_hornee...@yahoo.com> wrote:
On May 14, 4:53 pm, wrote:
On May 12, 4:33 pm, The_Man <me_so_hornee...@yahoo.com> wrote:
On May 12, 7:04 am, wrote:
On 10 touko, 19:31, wrote:
Sorry I couldn't get that far into your long essays but I found one
thing to disagree with:
"The set of complex numbers is the widest possible set of numbers"
What does "widest possible set of numbers" actually mean?
The complex plane has exactly the same number of numbers (pun
intended) as R^2, ordinary Riemann 2-space. Of course, the properties
of the two are quite different, particularly as regards
differentiation.
You can extend the complex plane with a point at infinity, but I don't
know if that is what you are referring to.
Certainly, there are more points in R^3 than in the complex plane.....
Is this true?
The set of (x,y) with x,y rational numbers has a one-to-one
correspondance
with the integers and is countable, there are just as many points in
Q^2 as in Q^1.
Why more in R^3 than R^2?
Maybe I am making a silly mistake (not being a mathematician).
For every point (x, y) in R^2, there are inifinitely many points (x,
y, z) in R^3. Why only allow x, y to be rational, rather than real?
It's also true that there are infinitely many rational numbers between
every integer.. and yet these two sets have a one-to-one
correspondence and so are considered the same "size".
I'm not a mathematician either but I see references that Cantor proved
that R^n has the same number of points as R^1. See e.g.
http://en.wikipedia.org/wiki/Space-filling_curve
Cheers -
.
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| User: "The_Man" |
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| Title: Re: Discrete physical space and the mesure problem of QM |
15 May 2007 08:55:10 AM |
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On May 15, 9:40 am, wrote:
On May 15, 2:47 am, The_Man <me_so_hornee...@yahoo.com> wrote:
On May 14, 4:53 pm, wrote:
On May 12, 4:33 pm, The_Man <me_so_hornee...@yahoo.com> wrote:
On May 12, 7:04 am, wrote:
On 10 touko, 19:31, wrote:
Sorry I couldn't get that far into your long essays but I found one
thing to disagree with:
"The set of complex numbers is the widest possible set of numbers"
What does "widest possible set of numbers" actually mean?
The complex plane has exactly the same number of numbers (pun
intended) as R^2, ordinary Riemann 2-space. Of course, the properties
of the two are quite different, particularly as regards
differentiation.
You can extend the complex plane with a point at infinity, but I don't
know if that is what you are referring to.
Certainly, there are more points in R^3 than in the complex plane.....
Is this true?
The set of (x,y) with x,y rational numbers has a one-to-one
correspondance
with the integers and is countable, there are just as many points in
Q^2 as in Q^1.
Why more in R^3 than R^2?
Maybe I am making a silly mistake (not being a mathematician).
For every point (x, y) in R^2, there are inifinitely many points (x,
y, z) in R^3. Why only allow x, y to be rational, rather than real?
It's also true that there are infinitely many rational numbers between
every integer.. and yet these two sets have a one-to-one
correspondence and so are considered the same "size".
I'm not a mathematician either but I see references that Cantor proved
that R^n has the same number of points as R^1. See e.g.http://en.wikipedia.org/wiki/Space-filling_curve
I stand corrected - thanks. :-)
Cheers -- Hide quoted text -
- Show quoted text -
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