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Any reality to real numbers?

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Christophe de Dinechin

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Feb 16, 2007, 6:22:46 AM2/16/07
to
There is a common assumption that real numbers are a good way to
represent physics values, for example, space coordinates. Why is this
justified?

For example, consider a distance measurement. Whatever physical
process I choose to use, it will give me countable measurement
results. A pocket ruler will give me a number of tick marks, a clock
will give me a number of seconds based on some cyclic physical
process (e.g. quartz oscillations). So it's all about counting.

Now, I can figure out what 0.5 meter means. If I have a reference
meter rod, I can cut it in half, make sure there are the same number
of atoms in each half, and I have 0.5 meter. But what about pi
meters? Many rational numbers make sense, but irrational numbers? OK,
the smart guy in the back says: if I have a circle with a 1 meter
radius, then I can measure pi meters using its circumference. Well,
after a surprisingly short number of decimals, you end up making
rather foolish assumptions about just how flat spacetime is where you
measure... Bottom line, it might work in some abstract mathematical
space, but not in physical space.

Yet, real numbers are everywhere: in Einstein's "continuum", or in
the axiom of quantum mechanics that observables have real
eigenvalues... So, is there any chance we can get rid of real numbers
in physics?

I've tried to do just that. This leads to some surprising results.
I've tried to write this up at http://cc3d.free.fr/tim.pdf, and I
would very much appreciate your comments. There may be a big logic
flaw in my reasoning, but I just can't see it...


Thanks
Christophe

Oh No

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Feb 16, 2007, 7:29:45 AM2/16/07
to
Thus spake Christophe de Dinechin <chris...@dinechin.org>

>There is a common assumption that real numbers are a good way to
>represent physics values, for example, space coordinates. Why is this
>justified?
>
>For example, consider a distance measurement. Whatever physical
>process I choose to use, it will give me countable measurement
>results. A pocket ruler will give me a number of tick marks, a clock
>will give me a number of seconds based on some cyclic physical process
>(e.g. quartz oscillations). So it's all about counting.

Absolutely.


>
>Now, I can figure out what 0.5 meter means. If I have a reference
>meter rod, I can cut it in half, make sure there are the same number
>of atoms in each half, and I have 0.5 meter. But what about pi meters?
>Many rational numbers make sense, but irrational numbers? OK, the
>smart guy in the back says: if I have a circle with a 1 meter radius,
>then I can measure pi meters using its circumference. Well, after a
>surprisingly short number of decimals, you end up making rather
>foolish assumptions about just how flat spacetime is where you
>measure... Bottom line, it might work in some abstract mathematical
>space, but not in physical space.

Indeed.


>
>Yet, real numbers are everywhere: in Einstein's "continuum", or in the
>axiom of quantum mechanics that observables have real eigenvalues...
>So, is there any chance we can get rid of real numbers in physics?

I think so.


>
>I've tried to do just that. This leads to some surprising results.
>I've tried to write this up at http://cc3d.free.fr/tim.pdf, and I
>would very much appreciate your comments. There may be a big logic
>flaw in my reasoning, but I just can't see it...
>

This is an excellent paper and I commend your clarity of thought. I have
no hesitation in recommending it to all readers interested in
foundational issues in physics. As it stands, it is perhaps more suited
to a philosophy journal than one on physics where the editors don't seem
to recognise the importance of such issues. Have you tried to publish?
What is your background?

I have also been working on these lines for many years. You may be
interested in

gr-qc/0508077
A Relational Quantum Theory Incorporating Gravity

gr-qc/0604047
Does a Teleconnection between Quantum States account for Missing Mass,
Galaxy Ageing, Lensing Anomalies, Supernova Redshift, MOND, and Pioneer
Blueshift?

gr-qc/0605127
A Treatment of Quantum Electrodynamics as a Model of Interactions
between Sizeless Particles in Relational Quantum Gravity

Regards

--
Charles Francis
substitute charles for NotI to email

Christophe de Dinechin

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Feb 17, 2007, 7:48:52 AM2/17/07
to
Oh No <No...@charlesfrancis.wanadoo.co.uk> writes:

On Feb 16, 1:29 pm, Oh No <N...@charlesfrancis.wanadoo.co.uk> wrote:
> This is an excellent paper and I commend your clarity of thought. I have
> no hesitation in recommending it to all readers interested in
> foundational issues in physics.

I appreciate the compliment.


> As it stands, it is perhaps more suited
> to a philosophy journal than one on physics where the editors don't seem
> to recognise the importance of such issues.

Isn't it a bit too technical for a philosophy journal? Or am I underestimating the interest of
philosophy journals for articles containing equations... Regarding editors, one downside of peer
reviews is that it tends to filter out anything that does not look kosher, or too speculative. Glad we
now have a group to discuss this kind of ideas :-)


> Have you tried to publish?

It's still in "draft" form. I requested feedback from a number of physicists, but most are just too busy
to even read the article. Too bad there is such an incentive to publish these days that you no longer
have time to read :-(

Could you recommend good journals where publishing is inexpensive (ideally, free), and that are
actually being read? I don't have an institution to back me up, so I'm not ready to pay hundreds of
dollars to get published. In my primary field of expertise, I'm more used to being paid for articles ;-)


> I have also been working on these lines for many years. You may be

> interested in [references cut for brevity]

Thanks a lot. I did a quick scan, and it looked quite interesting, but I did not go into much detail yet.
It looks like you went quite far in reconstructing a complete mathematical formalism. I must admit
that I'm only accumulating questions at that point. Mind if I send them once I'm positive the answer
is not obvious? ;-)
--
Regards
Christophe

Oh No

unread,
Feb 17, 2007, 8:22:44 AM2/17/07
to
Thus spake Christophe de Dinechin <chris...@dinechin.org>
>Oh No <No...@charlesfrancis.wanadoo.co.uk> writes:
>
>
>> As it stands, it is perhaps more suited
>> to a philosophy journal than one on physics where the editors don't seem
>> to recognise the importance of such issues.
>
>Isn't it a bit too technical for a philosophy journal? Or am I
>underestimating the interest of
>philosophy journals for articles containing equations...

I think you are underestimating them. Many philosophers study
theoretical physics to a quite passable standard these days, since they
respect the fact that theoretical physics is important to philosophy.

>
>Could you recommend good journals where publishing is inexpensive
>(ideally, free), and that are
>actually being read?


The one which springs to mind is Studies in History and Philosophy of
Science Part B:Studies in History and Philosophy of Modern Physics.

http://www.elsevier.com/wps/find/journaldescription.cws_home/30566/descr
iption#description

I have read papers in this journal by the now editor, D. Dieks. I think
you will find that philosophers, if not physicists are quite sympathetic
to the views you express. Whether they feel they have already thought
further on these lines, I can't hazard a guess, though I doubt they
have. It may be as well to try and get a look at a few issues of this
journal before submitting if you can get to an appropriate library.


>
>> I have also been working on these lines for many years. You may be
>> interested in [references cut for brevity]
>
>Thanks a lot. I did a quick scan, and it looked quite interesting, but
>I did not go into much detail yet.
>It looks like you went quite far in reconstructing a complete
>mathematical formalism. I must admit
>that I'm only accumulating questions at that point. Mind if I send them
>once I'm positive the answer
>is not obvious? ;-)

I will be very pleased to discuss any aspect of it on s.p.f.

Thomas Smid

unread,
Feb 17, 2007, 10:02:39 AM2/17/07
to
Christophe de Dinechin <chris...@dinechin.org> writes:

> There is a common assumption that real numbers are a good way to
> represent physics values, for example, space coordinates. Why is this
> justified?
>
> For example, consider a distance measurement. Whatever physical
> process I choose to use, it will give me countable measurement
> results. A pocket ruler will give me a number of tick marks, a clock
> will give me a number of seconds based on some cyclic physical
> process (e.g. quartz oscillations). So it's all about counting.
>
> Now, I can figure out what 0.5 meter means. If I have a reference
> meter rod, I can cut it in half, make sure there are the same number
> of atoms in each half, and I have 0.5 meter. But what about pi
> meters? Many rational numbers make sense, but irrational numbers? OK,
> the smart guy in the back says: if I have a circle with a 1 meter
> radius, then I can measure pi meters using its circumference. Well,
> after a surprisingly short number of decimals, you end up making
> rather foolish assumptions about just how flat spacetime is where you
> measure... Bottom line, it might work in some abstract mathematical
> space, but not in physical space.
>
> Yet, real numbers are everywhere: in Einstein's "continuum", or in
> the axiom of quantum mechanics that observables have real
> eigenvalues... So, is there any chance we can get rid of real numbers
> in physics?

Hi Christophe,

I don't think it would be a good idea if we would restrict ourselves to
rational numbers in physics. You might as well restrict the numbers to a
certain maximum. The point is that you need both a continuous and infinite
number line in order to represent all potentially possible cases.
Of course you can get arbitrarily close to any irrational number using
rational numbers, but the point is that as soon as you specify a particular
one, there is finite difference left which could potentially be relevant.

Thomas

zathra...@yahoo.com

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Feb 17, 2007, 12:46:04 PM2/17/07
to
On Feb 17, 10:02 am, Thomas Smid <thomas.s...@gmail.com> wrote:

> Christophe de Dinechin <christo...@dinechin.org> writes:
>
>
>
> > There is a common assumption that real numbers are a good way to
> > represent physics values, for example, space coordinates. Why is this
> > justified?
>
> > For example, consider a distance measurement. Whatever physical
> > process I choose to use, it will give me countable measurement
> > results. A pocket ruler will give me a number of tick marks, a clock
> > will give me a number of seconds based on some cyclic physical
> > process (e.g. quartz oscillations). So it's all about counting.
>
> > Now, I can figure out what 0.5 meter means. If I have a reference
> > meter rod, I can cut it in half, make sure there are the same number
> > of atoms in each half, and I have 0.5 meter. But what about pi
> > meters? Many rational numbers make sense, but irrational numbers? OK,
> > the smart guy in the back says: if I have a circle with a 1 meter
> > radius, then I can measure pi meters using its circumference. Well,
> > after a surprisingly short number of decimals, you end up making
> > rather foolish assumptions about just how flat spacetime is where you
> > measure... Bottom line, it might work in some abstract mathematical
> > space, but not in physical space.
>
> > Yet, real numbers are everywhere: in Einstein's "continuum", or in
> > the axiom of quantum mechanics that observables have real
> > eigenvalues... So, is there any chance we can get rid of real numbers
> > in physics?
>
> Hi Christophe,
>
> I don't think it would be a good idea if we would restrict ourselves to
> rational numbers in physics. You might as well restrict the numbers to a
> certain maximum. The point is that you need both a continuous and infinite
> number line in order to represent all potentially possible cases.
> Of course you can get arbitrarily close to any irrational number using
> rational numbers, but the point is that as soon as you specify a particular
> one, there is finite difference left which could potentially be relevant.
>
> Thomas

I'm not sure what is meant by "specify" in the context. If you're talking
about an experiment, this type of approximation is done by the equipment.
Furthermore, with any experimental equipment that digitizes data, the
observations will always be rational numbers (you need an infinite number of
bits to express any irrational number).

The biggest problem with restricting reality to the rationals is that
integration becomes much harder to define mathematically. Integration relies
on the fact that the real numbers is a closed set, while the rational numbers
are not. For example, you can create a sequence of rational numbers {1, 1.4,
1.41, 1.414, ...} that converges to an irrational number. With ordinary
integration theory, the "size" (measure) of the rational numbers, so
integration itself would have to be completely redone.

Paul S
.

Oh No

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Feb 17, 2007, 1:48:06 PM2/17/07
to
Thus spake zathra...@yahoo.com
I actually go one stage further. Any physical apparatus is bounded in
both range and resolution. One can therefore represent the results of
measurement by a finite subset of the integers.

In practice I don't think this makes things harder mathematically. I
think it is actually rather important to formulate relativistic quantum
mechanics like this, using finite dimensional Hilbert space. If one uses
finite dimensional Hilbert space, the divergent quantities which have
plagued qed can be avoided. Mostly they are just a matter of taking
limits in the wrong order anyway.

It doesn't stop one using integration and differentiation either. One
formulates the theory using difference equations and then uses the
association between a difference equation and a differential equation.
Although formulating the theory in terms of a particular measurement
apparatus means it is not manifestly covariant, after replacing the
difference equations with a covariant differential equation, one can
then recover the discrete formulation in any other reference frame,
defined by a different apparatus simply by making the appropriate
restriction to discrete coordinates. In this way one formulates the set
of all possible discrete formulations, and shows that this is equivalent
to using the reals, but at the same time avoiding divergences.

Christophe de Dinechin

unread,
Feb 18, 2007, 5:32:16 AM2/18/07
to
Oh No <No...@charlesfrancis.wanadoo.co.uk> writes:

> >On Feb 17, 10:02 am, Thomas Smid <thomas.s...@gmail.com> wrote:
> >> I don't think it would be a good idea if we would restrict ourselves to
> >> rational numbers in physics. You might as well restrict the numbers to a
> >> certain maximum. The point is that you need both a continuous and infinite
> >> number line in order to represent all potentially possible cases.

I am not suggesting restricting ourselves to rational numbers, but to observable values. As long as
we use a measurement apparatus with a finite number of possible results, we actually don't need a
continuous and infinite number line to represent all physically possible cases.

Now, I'm not advocating rational numbers or integers, I'm really advocating symbolic representations
of measurement results. If my measurement apparatus can give me two results, "0 and 1" or "true
and false" or "present and not present" are valid sets. The set of real numbers can be used, but it
introduces difficulties, such as the possibility that a theory using real numbers could predict 0.7 or
-13, which is a physically impossible result, because the measurement apparatus cannot give it.

You find a more subtle variation of this with the relatively frequent statement that, since the
wavefunction in general tends towards zero without ever reaching it, there is a chance that a particle
will be observed, say, on the moon (to take the words of Brian Greene in "The Fabric of the Cosmos").
Well, if I'm using a photographic plate to detect a photon, what point on the plate corresponds to
this prediction that I found it on the moon? As long as the plate is not itself on the moon, I believe
there is none. So I'm suggesting that instead the predictions about the experiement needs to be
rephrased as a prediction about a finite number of locations on the plate, and one additional
location, "not on the plate".

Now, this prediction can be computed using real numbers, for instance some gaussian curve. But the
final physics prediction itself needs to be truncated to observable results. And there is quite some
value in the original gaussian curve. Presumably, if the theory leading to the gaussian curve is
correct, adding one detector on the moon would not change the gaussian curve, but would change
the countable predictions.


> Thus spake zathra...@yahoo.com


> >I'm not sure what is meant by "specify" in the context. If you're talking
> >about an experiment, this type of approximation is done by the equipment.
> >Furthermore, with any experimental equipment that digitizes data, the
> >observations will always be rational numbers (you need an infinite number of
> >bits to express any irrational number).

Not just digitizing equipment. Any mechanical equipment is made of a finite number of atoms, so it
can only give a finite number of results.


> >The biggest problem with restricting reality to the rationals is that
> >integration becomes much harder to define mathematically. Integration relies
> >on the fact that the real numbers is a closed set, while the rational numbers
> >are not. For example, you can create a sequence of rational numbers {1, 1.4,
> >1.41, 1.414, ...} that converges to an irrational number. With ordinary
> >integration theory, the "size" (measure) of the rational numbers, so
> >integration itself would have to be completely redone.

Very interesting point. But if you recall, integration is initially defined as a limit of sums. In the
physical world, we can simply stay with the sum. As long as you don't do an infinite number of steps
in your limit, you remain within rational numbers. Also, as Charles Francis pointed out, in many
cases, the integral diverges. So in reality, you have a closed set only if you include infinities.


> I actually go one stage further. Any physical apparatus is bounded in
> both range and resolution. One can therefore represent the results of
> measurement by a finite subset of the integers.

Yes. But integers are not convenient. The actual set is more something like "0.1m, 0.2m, 0.3m", and
so on. It is a countable set, but integers might not be a good fit. Two measurements are not even
necessarily related by a linear relationship. In my paper, I give the example of two measures of time,
one with cyclic motion of celestial bodies (e.g. number of years), and the other counting a particular
population of atoms (carbon dating). The relationship between the two uses an exponential.

This illustrates where real numbers fit in. An exponential is much easier to define using real
numbers. In general, the theories are best expressed using real functions. On the other hand, both
the number of atoms and the number of years are integral numbers. You can count fractions of
years, of course, but this is not very relevant with respect to carbon dating...


> In practice I don't think this makes things harder mathematically. I
> think it is actually rather important to formulate relativistic quantum
> mechanics like this, using finite dimensional Hilbert space. If one uses
> finite dimensional Hilbert space, the divergent quantities which have
> plagued qed can be avoided. Mostly they are just a matter of taking
> limits in the wrong order anyway.

Yup. That is a primary driver for trying this: getting rid of useless infinities.


> It doesn't stop one using integration and differentiation either. One
> formulates the theory using difference equations and then uses the
> association between a difference equation and a differential equation.
> Although formulating the theory in terms of a particular measurement
> apparatus means it is not manifestly covariant, after replacing the
> difference equations with a covariant differential equation, one can
> then recover the discrete formulation in any other reference frame,
> defined by a different apparatus simply by making the appropriate
> restriction to discrete coordinates.

Though doing that probably involves some real-based mathematics in a large number of cases. For
example, the easiest way to express a rotation remains with a cosine and a sine, which are
unnecessarily harder to define on countable sets of coordinates.


> In this way one formulates the set
> of all possible discrete formulations, and shows that this is equivalent
> to using the reals, but at the same time avoiding divergences.

My point exactly...
--
Regards
Christophe

Oh No

unread,
Feb 18, 2007, 6:13:33 AM2/18/07
to
Thus spake Christophe de Dinechin <chris...@dinechin.org>
>Oh No <No...@charlesfrancis.wanadoo.co.uk> writes:
>
>> >On Feb 17, 10:02 am, Thomas Smid <thomas.s...@gmail.com> wrote:
>> >> I don't think it would be a good idea if we would restrict ourselves to
>> >> rational numbers in physics. You might as well restrict the numbers to a
>> >> certain maximum. The point is that you need both a continuous and infinite
>> >> number line in order to represent all potentially possible cases.
>
>
>Now, I'm not advocating rational numbers or integers, I'm really
>advocating symbolic representations
>of measurement results. If my measurement apparatus can give me two
>results, "0 and 1" or "true
>and false" or "present and not present" are valid sets. The set of real
>numbers can be used, but it
>introduces difficulties, such as the possibility that a theory using
>real numbers could predict 0.7 or
>-13, which is a physically impossible result, because the measurement
>apparatus cannot give it.

I find this is described by using measurement results as a basis for
Hilbert space in quantum theory. One should use a finite basis. The
basis states describe actual results "the particle was found at x", "the
particle was not found at x". This is extended to include probability
amplitudes "the particle would be found at x if a measurement were done"

>
>> I actually go one stage further. Any physical apparatus is bounded in
>> both range and resolution. One can therefore represent the results of
>> measurement by a finite subset of the integers.
>
>Yes. But integers are not convenient. The actual set is more something
>like "0.1m, 0.2m, 0.3m", and
>so on.

Those are just integers expressed in conventional units - the
multiplication by a scale factor is trivial.

>It is a countable set,

finite

> but integers might not be a good fit. Two measurements are not even
>necessarily related by a linear relationship. In my paper, I give the
>example of two measures of time,
>one with cyclic motion of celestial bodies (e.g. number of years), and
>the other counting a particular
>population of atoms (carbon dating). The relationship between the two
>uses an exponential.

That is an inconvenience, but still not fundamentally a problem. One can
for example, define a basis using integers but make the scale factor
much smaller than the resolution of either method. Then the measurement
results are described by subsets of the Hilbert space instead of by
unique states.


>
>> In practice I don't think this makes things harder mathematically. I
>> think it is actually rather important to formulate relativistic quantum
>> mechanics like this, using finite dimensional Hilbert space. If one uses
>> finite dimensional Hilbert space, the divergent quantities which have
>> plagued qed can be avoided. Mostly they are just a matter of taking
>> limits in the wrong order anyway.
>
>Yup. That is a primary driver for trying this: getting rid of useless
>infinities.
>
>
>> It doesn't stop one using integration and differentiation either. One
>> formulates the theory using difference equations and then uses the
>> association between a difference equation and a differential equation.
>> Although formulating the theory in terms of a particular measurement
>> apparatus means it is not manifestly covariant, after replacing the
>> difference equations with a covariant differential equation, one can
>> then recover the discrete formulation in any other reference frame,
>> defined by a different apparatus simply by making the appropriate
>> restriction to discrete coordinates.
>
>Though doing that probably involves some real-based mathematics in a
>large number of cases. For
>example, the easiest way to express a rotation remains with a cosine
>and a sine, which are
>unnecessarily harder to define on countable sets of coordinates.

I don't object to using real-based mathematics any more than I object to
using imaginary numbers in mathematics. The point is to be able to
recover physics at any point from the mathematics. That is done by
restricting the real formulae to a suitable discrete subset, and does
not imply that the reals seen in the formulae are physically real.


>
>
>> In this way one formulates the set
>> of all possible discrete formulations, and shows that this is equivalent
>> to using the reals, but at the same time avoiding divergences.
>
>My point exactly...

Regards

Cl.Massé

unread,
Feb 18, 2007, 12:13:37 PM2/18/07
to
Christophe de Dinechin <chris...@dinechin.org> writes:

>> There is a common assumption that real numbers are a good way to
>> represent physics values, for example, space coordinates. Why is this
>> justified?
>>
>> For example, consider a distance measurement. Whatever physical
>> process I choose to use, it will give me countable measurement
>> results. A pocket ruler will give me a number of tick marks, a clock
>> will give me a number of seconds based on some cyclic physical
>> process (e.g. quartz oscillations). So it's all about counting.
>>
>> Now, I can figure out what 0.5 meter means. If I have a reference
>> meter rod, I can cut it in half, make sure there are the same number
>> of atoms in each half, and I have 0.5 meter. But what about pi
>> meters? Many rational numbers make sense, but irrational numbers? OK,
>> the smart guy in the back says: if I have a circle with a 1 meter
>> radius, then I can measure pi meters using its circumference. Well,
>> after a surprisingly short number of decimals, you end up making
>> rather foolish assumptions about just how flat spacetime is where you
>> measure... Bottom line, it might work in some abstract mathematical
>> space, but not in physical space.
>>
>> Yet, real numbers are everywhere: in Einstein's "continuum", or in
>> the axiom of quantum mechanics that observables have real
>> eigenvalues... So, is there any chance we can get rid of real numbers
>> in physics?

Some people try and construct theories starting only from integers. Some
other think that for example space is quantified at the scale of the Plank
length. Although those ideas are appealing by their simplicity, and yield
some interesting results, they are very far from leading to a full-fledged
theory.

Real numbers are used because, they work. There is no other reason.
Conversely, rational or integer numbers only don't allow to formulate the
current theories, that use square roots and other irrational functions.
Although all the real numbers intervene in principle, in practice only a
very little subset of them are used for expressing the result of
measurements, and that makes no difference at all.

--
~~~~ clmasse on free F-country
Liberty, Equality, Profitability.

Christophe de Dinechin

unread,
Feb 19, 2007, 3:49:53 AM2/19/07
to
"Cl\.Massé" <ret...@contactprospect.com> writes:
> Christophe de Dinechin <chris...@dinechin.org> writes:
> Some people try and construct theories starting only from integers. Some
> other think that for example space is quantified at the scale of the Plank
> length. Although those ideas are appealing by their simplicity, and yield
> some interesting results, they are very far from leading to a full-fledged
> theory.

That is not what I am suggesting. Apparently, I need to explain a bit more about the "incomplete
measurements" theory (http://cc3d.free.fr/tim.pdf) on this thread.

As explained in that article, if you have a measurement apparatus that can return n results
m_1,...,m_n, you can entirely describe the state of a system with respect to that measurement
apparatus as probabilities p_1,...,p_n to get each measurement. The condition that the p_i are
positive and that their sum is 1 can be expressed by writing p_i=u_i^2, and having the vector u be a
unit vector on the unit n-sphere. Any physical operation on the system changes the probabilities of
obtaining m_i, so it can be seen as an operator P on u.

An important point at that stage is that nothing constrains the m_i to be real numbers. Also, the
operator P is not necessarily linear, there are plenty of counter examples. However, under a set of
conditions on the measurement (which includes the measurement m_i being mapped to real
numbers using a "graduation equation", see the article), it is possible to construct a linear operator
that can be shown to have the same properties at the traditional quantum mechanics observable, for
instance with respect to computing the expected value for a measurement where the m_i are real. I'll
refer you to the article to see how all but one quantum mechanics "axioms" are recovered in this
approach.

Therefore, I interpret quantum mechanics as an approximation of the necessary form of "probability
mechanics" under some specific conditions (essentially: linearity and m_i being real). More
importantly, as long as you accept the now demonstrated fact that some measurements cannot be
predicted with more than probabilities, I believe that I have demonstrated that quantum mechanics is
essentially the necessary form for physics. Not just infinitesimal physics, any physics.

The axiom of QM that cannot be reconstructed this way is Schroedinger's equation, so I'm initially
just "stealing it" from quantum mechanics to build a complete theory. But that's only temporary, I
believe I have now found how to reconstruct Schroedinger as well (using a very different angle of
attack based on replacing energy in Schroedinger with entropy, and rebuilding Schroedinger as a
probability equation indicating that the system evolves according to probabilities).

So I'm not trying to build a theory on integers. Instead, I'm trying to build a theory on finite sets that
correspond to what the instrument being used can actually return as a result.

That leads to interesting considerations when you relate two measurements of "the same thing". For
example, what we currently write as "x", a space coordinate, can be measured using multiple physical
devices. Are these equivalent? My answer is that they are only equivalent to the extent that we
calibrate them to measure the same thing. For example, we choose that 3 feet are one meter. But if
you define the meter using light waves and the foot using some antique hero's shoes, you can only
line up the two measurements at short scale. At large scale, they may diverge, because the
corresponding physical processes are not sensitive to the same environment changes. See the article
for a more in-depth discussion of this.

Ultimately, what this means is that there is no "absolute space" x, only various measurements of
space x/i (I use the notation x/i to indicate a dependency on the physical process i, in the article
primarily on the section on scaling). None is better or more absolute than another, even if some are
more precise, because they are generally impacted by different physical phenomena. These various
x/i are related by laws which we often chose to be "linear at least locally" for simplicity. But not
always, cf. time measurements using atom population counts in carbon dating and number of earth
revolutions around the sun, which are related by an exponential law.

So I believe this is pretty far away from "constructing a theory based on integers".


> Real numbers are used because, they work. There is no other reason.

There are cases where they don't work and even get in the way. Here is an example. Interpreting the
wavefunction as the probability to find the particle at position x, the normalization condition for the
wave function indicates that the particle has to be found somewhere in space. So it's written as
"integral of probability over all space", and that is translated into "integral of probability over x
ranging from minus infinity to plus infinity".

So, what does that mean, precisely, "to infinity and beyond" in that case? What do the infitesimal, but
non-zero probabilities at x="on the moon" mean? As interpreted by Brian Greene in "The Fabric of
the Cosmos", this means that there is a chance that I will find the particle on the moon. Problem:
what if, in my experiment, I don't have a detector on the moon? How could I possibly find the particle
on the moon if there is no detector there?

Another more technical issue is that such integrals at infinity very often diverge. So we end up with a
renormalization process where we replace an infinity with the observed value.

These problems essentially go away if you start by limiting yourself to the values you can actually
measure. In other words, if you replace an abstract notion of "absolute space" x with the notion of
"measured space" x/i.

Then, whether you represent x/i as an integer, a real or a binary blob does not matter much, except
when you write equations relating two measurements. For example, if you write F = k / r^2, you
relate measurements of F and measurements of r, and then it matters what graduation equation you
picked for F and r, if only to precisely determine k.

> Conversely, rational or integer numbers only don't allow to formulate the
> current theories, that use square roots and other irrational functions.

Yes, you can still use real functions (or complex functions or whatever) when relating symbolic forms
of measurements. If the symbolic form is real, then you can use real functions. The key insight here
is the "graduation equation", that maps a physical state of the display of your measurement
apparatus to a real number or some other symbolic representation of the state.


> Although all the real numbers intervene in principle, in practice only a
> very little subset of them are used for expressing the result of
> measurements, and that makes no difference at all.

That makes a huge, essential difference. Let me call it "relativity of measurements" to sound big. It
means that if you have x/i that can give you an integral number of feet, and x/j that can give an
integral number of EM wavefronts, both x/i and x/j are equally valid to express laws of physics, BUT
the laws of physics as written using x/i and x/j are not necessarily identical.

Today, most physics textbooks just assume that there is an absolute x and that x/i and x/j are just
two more or less precise measurements of that same absolute x. In doing so, we ignore that the
physical processes differ in more than just precision. They often diverge at large scale, which means
that an integral at infinity over x/i is not necessarily the same thing as an integral at infinity over x/j.

If you have trouble visualizing this, consider a QM guru trying to actually compute their integral at
infinity from measured values. So they pick up the latest and most accurate laser interferometer to
measure the distance to distant stars down to the nanometer. Ah, but wait a minute, there is some
large mass at some point in the universe, and their laser beams cross each other. Crossing laser
beams, as in Ghostbusters, is "bad". It essentially means that your integral at infinity just does not
make sense, because now the "x" in the equation depends on which path light took...
--
Thanks
Christophe

Christophe de Dinechin

unread,
Feb 19, 2007, 3:51:10 AM2/19/07
to
[Moderator: Sorry, this is a reply to the wrong message in the thread, because news.killfile.org will
not let me follow up on the original message, maybe because it's too deep...]

On Feb 18, 12:13 pm, Oh No <N...@charlesfrancis.wanadoo.co.uk> wrote:
> Those are just integers expressed in conventional units - the
> multiplication by a scale factor is trivial.

When two measurements are related by a linear law, I agree that scaling is trivial. However, this is not
a general rule, see my earlier example of carbon dating vs. time counters based on celestial bodies.

Even trivial linear scaling is optimistic from a physical point of view. Consider distance measured by a
laser and distance measured by walking on earth. The two physical processes are related by linear
scaling on a short scale. Yet, they are not impacted by the same environmental changes. Footsteps
are influenced by gravity more than laser measurements, but laser measurements are more sensitive
to air pressure, temperature or humidity changes. So on a large scale, they diverge. It appears to be
the general case more than the exception.


> >It is a countable set,
> finite

You are right that for any specific measurement instrument, the set is finite. However, there are
experiments where the set is potentially infinite, as long as you do not specify the measurement
instrument (or allow it to be "improved" over time). For example: how many seconds does it take for
a ball thrown upwards to fall back on the ground. In theory, I can make the result as big as I want.

But I'll grant you that for any well-defined physical experiements, it's a finite set (and that's what I
wrote it in the article http://cc3d.free.fr/tim.pdf).

> >The relationship between the two
> >uses an exponential.
>
> That is an inconvenience, but still not fundamentally a problem. One can
> for example, define a basis using integers but make the scale factor
> much smaller than the resolution of either method. Then the measurement
> results are described by subsets of the Hilbert space instead of by
> unique states.

If you do that, simple laws lead to non-zero probabilities for the intermediate states, and you are
back to the theory predicting 0.7 for a measurement that can return only 0 or 1. Alternatively, you
need to introduce really complicated artifacts in the theory to force the probabilities to zero except
for measured values. In the end, this is not an improvement over real numbers.

Furthermore, I chose the exponential because it maps fractions to irrational numbers, so scaling will
never quite do it.

In my opinion, what this means is that we must bite the bullet, and accept that an exponential law
relates two finite or countable sets of fractional numbers. This exponential law relates probabilities
of seeing 1 cycle or 2 cycles on the graduation marks of the first measurement to probabilities of
seeing ratios of populations of atoms that are close to K.exp(-1) and K.exp(2), where K is a
calibration constant relating the two measurements so that they "line up".

> >> In practice I don't think this makes things harder mathematically. I
> >> think it is actually rather important to formulate relativistic quantum
> >> mechanics like this, using finite dimensional Hilbert space. If one uses
> >> finite dimensional Hilbert space, the divergent quantities which have
> >> plagued qed can be avoided.

Agreed. In plain physics terms, if you are measuring the position of a particle using 256 detectors
along the x axis, the normalization condition for the wavefunction is a sum on 256 probabilities (257
if you add "not detected") corresponding to the various x_i. Today, we traditionally use an integral on
x ranging from minus infinity to plus infinity, which often happens to diverge at infinity.


> >> Mostly they are just a matter of taking
> >> limits in the wrong order anyway.

Could you elaborate on that?
--
Thanks
Christophe

Thomas Smid

unread,
Feb 19, 2007, 5:47:54 AM2/19/07
to
Christophe de Dinechin <chris...@dinechin.org> writes:

> Oh No <No...@charlesfrancis.wanadoo.co.uk> writes:
>
> > >On Feb 17, 10:02 am, Thomas Smid <thomas.s...@gmail.com> wrote:
> > >> I don't think it would be a good idea if we would restrict ourselves
> to
> > >> rational numbers in physics. You might as well restrict the numbers to
> a
> > >> certain maximum. The point is that you need both a continuous and
> infinite
> > >> number line in order to represent all potentially possible cases.
>
> I am not suggesting restricting ourselves to rational numbers, but to
> observable values. As long as
> we use a measurement apparatus with a finite number of possible results, we
> actually don't need a
> continuous and infinite number line to represent all physically possible
> cases.

Yes, but I am sure you are not suggesting would should model reality after the
insufficiencies and limitations of our measuring devices. The point is that
*in principle* we can make our measurents arbitrarily accurate and extensive,
so we need a continuous and infinite number line to reflect this circumstance.

Thomas

Oh No

unread,
Feb 19, 2007, 5:47:42 AM2/19/07
to
Thus spake Christophe de Dinechin <chris...@dinechin.org>
>[Moderator: Sorry, this is a reply to the wrong message in the thread,
>because news.killfile.org will
>not let me follow up on the original message, maybe because it's too deep...]
>
>On Feb 18, 12:13 pm, Oh No <N...@charlesfrancis.wanadoo.co.uk> wrote:
>> Those are just integers expressed in conventional units - the
>> multiplication by a scale factor is trivial.
>
>When two measurements are related by a linear law, I agree that scaling
>is trivial. However, this is not
>a general rule, see my earlier example of carbon dating vs. time
>counters based on celestial bodies.

Yes, but I answered that too. Further discussion below.

>
>Even trivial linear scaling is optimistic from a physical point of
>view. Consider distance measured by a
>laser and distance measured by walking on earth. The two physical
>processes are related by linear
>scaling on a short scale. Yet, they are not impacted by the same
>environmental changes. Footsteps
>are influenced by gravity more than laser measurements, but laser
>measurements are more sensitive
>to air pressure, temperature or humidity changes. So on a large scale,
>they diverge. It appears to be
>the general case more than the exception.

That is largely a matter of the choice of a fundamental unit, which is
linear by definitional truism, and calibration of other units to it.


>
>
>> >It is a countable set,
>> finite
>
>You are right that for any specific measurement instrument, the set is
>finite. However, there are
>experiments where the set is potentially infinite, as long as you do
>not specify the measurement
>instrument (or allow it to be "improved" over time). For example: how
>many seconds does it take for
>a ball thrown upwards to fall back on the ground. In theory, I can make
>the result as big as I want.

Nonetheless, one is always limited by a particular measurement
instrument. Ultimately one is limited by the size of the universe,
provided of course it is finite. In practice when one follows through
the approach to its logical conclusion one finds that one needs to adopt
the teleconnection to reconcile quantum theory with general relativity.
This leads to a reinterpretation of cosmological redshift and is such
that supernova redshifts do indeed indicate a closed universe.

>But I'll grant you that for any well-defined physical experiements,
>it's a finite set (and that's what I
>wrote it in the article http://cc3d.free.fr/tim.pdf).

Yes. I think we are agreed on the matter of fundamental principle.


>
>> >The relationship between the two
>> >uses an exponential.
>>
>> That is an inconvenience, but still not fundamentally a problem. One can
>> for example, define a basis using integers but make the scale factor
>> much smaller than the resolution of either method. Then the measurement
>> results are described by subsets of the Hilbert space instead of by
>> unique states.
>
>If you do that, simple laws lead to non-zero probabilities for the
>intermediate states, and you are
>back to the theory predicting 0.7 for a measurement that can return
>only 0 or 1. Alternatively, you
>need to introduce really complicated artifacts in the theory to force
>the probabilities to zero except
>for measured values. In the end, this is not an improvement over real numbers.

I am not sure what you are saying here. The result of the measurement is
presumably 1 if the result is within a given subset, and zero if it is
not. Ultimately we do need probabilities which are not 0 or 1 in order
to describe all the states of matter. That is what quantum theory is
largely about.


>
>
>> >> In practice I don't think this makes things harder mathematically. I
>> >> think it is actually rather important to formulate relativistic quantum
>> >> mechanics like this, using finite dimensional Hilbert space. If one uses
>> >> finite dimensional Hilbert space, the divergent quantities which have
>> >> plagued qed can be avoided.
>
>Agreed. In plain physics terms, if you are measuring the position of a
>particle using 256 detectors
>along the x axis, the normalization condition for the wavefunction is a
>sum on 256 probabilities (257
>if you add "not detected") corresponding to the various x_i. Today, we
>traditionally use an integral on
>x ranging from minus infinity to plus infinity, which often happens to
>diverge at infinity.

In practice loop integrals do not diverge at infinity, but rather at
zero.


>
>
>> >> Mostly they are just a matter of taking
>> >> limits in the wrong order anyway.
>
>Could you elaborate on that?

There have been a number of divergence problems in qed. The infrared
divergences were solved fairly early, they are due to the need to
integrate over the possibility of an infinite number of low energy
photons (with finite total energy).

The main problem is the ultraviolet divergence, which is still resolved
in mainstream text books by writing down expressions equivalent to

1 + infinity + infinity^2 + infinity^3+... = 1/(1-infinity) = 0

Physicists say "oh, but it works, so it must be right"! Then they
attempt to "renormalise" the theory, which means they put divergent
quantities into the Hamiltonian, intending them to cancel out from the
results.

Of course all of that is nonsense. Actually the mathematical problem was
resolved in the seventies, in the method of Epstein and Glaser, and the
appearance of the divergence is due to the abuse of Wick's theorem.
Essentially the problem arises because quantum fields cannot be defined
as linear operators on a covariant Hilbert space, the reason being that
the equal point multiplication generates a term <x|x> which is
indefinable in a Hilbert space defined on a continuous basis.

Scharf, in Finite QED, shows how to avoid the equal point multiplication
by using a continuous switching function which vanishes at zero to
approximate the the step function, -1 for x<0, +1 for x>0. When he takes
the limit (in the correct order) the ultraviolet divergence does not
appear.

The problem with that, imv, is that it is physically completely
unmotivated. I use a much simpler, and cruder approach, based on what we
are discussing here, using finite dimensional Hilbert space. That means
I am sacrificing manifest covariance, but I use physical arguments to
say that Hilbert space must always be defined in terms of a particular
measurement apparatus, and I replace manifest covariance with "quantum
covariance" which I think more correctly describes the underlying
principle that the laws of physics are always the same. I also define
Hilbert space at given time, H=H(t), again reflecting physical
properties of measurement. Interactions are then defined as operators
from H(t) to H(t+dt). That way the equal point multiplication does not
arise, and again the ultraviolet divergence is not a problem.

Neither this, nor Scharf, is sufficient to remove divergences
altogether. If you allow the minimum time for an interaction, dt, to go
to zero, then you still have sum an infinite sequence of terms which
diverges at the Landau pole. My resolution for that is to say that
nature is fundamentally discrete and that there is a finite minimum time
between the interactions of an elementary particle.

This idea gets a great deal of support, imv, because if one carries out
a reanalysis of special relativity based on the radar method, but
includes a minimum time for the reflection, then one has to change the
metric. Instead of Minkowski metric, I show that one gets a metric
satisfying Einstein's Field equation. Ultimately then, using an approach
based, in the first instance on the discreteness of measurement results
in practice, but later on an underlying discreteness at a scale much
smaller than anything we will ever be able to measure (c10^-66m iirc)
one finds a formulation of qed which has no divergences and which also
explains gravity.

The teleconnection is another side of this model. It is needed to
discuss the relationship between states in one place and states in
another when there is no physical means to calibrate measurement in the
two places.

Oh No

unread,
Feb 19, 2007, 6:08:23 AM2/19/07
to
Thus spake Thomas Smid <thoma...@gmail.com>

>Christophe de Dinechin <chris...@dinechin.org> writes:
>
>> Oh No <No...@charlesfrancis.wanadoo.co.uk> writes:
>>
>> > >On Feb 17, 10:02 am, Thomas Smid <thomas.s...@gmail.com> wrote:
>> > >> I don't think it would be a good idea if we would restrict ourselves
>> to
>> > >> rational numbers in physics. You might as well restrict the numbers to
>> a
>> > >> certain maximum. The point is that you need both a continuous and
>> infinite
>> > >> number line in order to represent all potentially possible cases.
>>
>> I am not suggesting restricting ourselves to rational numbers, but to
>> observable values. As long as
>> we use a measurement apparatus with a finite number of possible results, we
>> actually don't need a
>> continuous and infinite number line to represent all physically possible
>> cases.
>
>Yes, but I am sure you are not suggesting would should model reality after the
>insufficiencies and limitations of our measuring devices.

The point is that the mathematics should reflect what we can actually do
in measurement. It does not necessarily model the underlying reality.
That is a different issue, but if we correctly model what we can
measure, we will have a better prospect of understanding the underlying
reality too.

> The point is that
>*in principle* we can make our measurents arbitrarily accurate and extensive,

That is a metaphysical assumption which we cannot justify empirically.
One should be very wary of assuming something which we cannot show. In
practice I believe the failure of constructive field theory is caused
largely because this assumption is actually not true in nature.

>so we need a continuous and infinite number line to reflect this circumstance.
>
>Thomas
>

Regards

Christophe de Dinechin

unread,
Feb 20, 2007, 2:41:30 AM2/20/07
to
Oh No <No...@charlesfrancis.wanadoo.co.uk> writes:

> >When two measurements are related by a linear law, I agree that scaling
> >is trivial. However, this is not
> >a general rule, see my earlier example of carbon dating vs. time
> >counters based on celestial bodies.
>
> Yes, but I answered that too.

I understood your answer as "I increase the resolution (and dimension of Hilbert space) and the
problem goes away". I am skeptical, because a change of resolution cannot compensate for
qualitative differences. To take the example of space measurements, if distinct physical
measurements give geometries with distinct curvatures, how can you make them fit one another just
by adjusting the resolution? Locally, they can all be flat and so you can make them fit. But at large
scale?

Note that I'm really eager to understand your "quantum covariance", it might be a better tool than
what I have so far to address that class of problems.

> >Even trivial linear scaling is optimistic from a physical point of

> >view. [...]


> That is largely a matter of the choice of a fundamental unit, which is
> linear by definitional truism, and calibration of other units to it.

Calibrating other units to the reference unit assume that all the units that you might want to consider
have the same properties, or that one can obviously be taken as the "reference" unit. This is the
specific belief I no longer have.

There are two usual ways to select the "reference". The first one is "highest precision", the other one
is "least sensitive to external factors". Now, consider that I want to count objects, and I have two
tools. The first one is a spoon, the other is the naked eye. The first measurement is "I pick objects
up", the other measurement is: "I see how many there are".

Based on resolution, the eye is better. With it, I can for instance count tiny grains of sand (if there
aren't too many), something which is difficult to do reliably with a spoon because I can't pick them
up.

But now look at objects into an aquarium, looking through the corner of the aquarium, and you can
see the same object twice. Yet, you will never be able to pick the duplicates with the spoon... So
based on sensitivity to external influence, the eye loses.

This is a very simple table top experiment. It is a very simple measurement. Yet I can find two
physical processes where there is no obvious "reference unit". What basis do I have, then, to say that
for much more complex things, like space measurements, there is some obvious reference unit, or
that by increasing the resolution I necessarily have found my reference unit?

> I am not sure what you are saying here. The result of the measurement is
> presumably 1 if the result is within a given subset, and zero if it is
> not. Ultimately we do need probabilities which are not 0 or 1 in order
> to describe all the states of matter. That is what quantum theory is
> largely about.

What I was saying is: if you have a measurement instrument that can return exactly two results, 0
and 1, you do not simplify its description by increasing the resolution of the model, i.e. by assuming
that there is some "reality" giving a meaning to measured values (not probabilities) 0.1 or pi/4.

In particular, if there are physical reasons why the measurement can only have two values (e.g. a
binary predicate like "is the particle in the box"), then if you try increasing the number of dimensions
of the Hilbert space, you end up with plenty of "useless" dimensions, and you then have to add
bizarre rules preventing your mathematical model from predicting cats that are half dead and half
alive.

To rephrase the above, prediction about Schroedinger's cat being alive are based on a 2D Hilbert
state. If you add dimensions to the HIlbert space corresponding to "half alive", you have then to
justify why the corresponding probabilities are always zero.

> In practice loop integrals do not diverge at infinity, but rather at
> zero.

Zero is another non-physical limit for a number of measurements, including distance measurements.
But I think it is already hard enough to convince people with reasoning at infinity, despite the fact
that most people intuitively accept that it is impossible to build an infinite ruler :-)

> >Could you elaborate on that?

[Elaboration cut for clarity]

Thanks for the clear explanation. I had also started understanding what you meant after reading
more of your work. "Physically unmotivated" is, I believe, the key phrase :-)
--
Thanks
Christophe

Thomas Smid

unread,
Feb 20, 2007, 5:32:34 AM2/20/07
to
Oh No <No...@charlesfrancis.wanadoo.co.uk> writes:

The continuity of space and time doesn't need to be shown. Space and time
aren't physical objects but cognitive forms, and as such their continuity
(i.e. their lack of structure) is logically self-evident. The mere fact that
between any two points one can *imagine* another point is sufficient for
this.
What one has to realize is that we can actually recognize discreteness only
on the background of continuity, so the latter is always bound to be the
underlying form. As a real-life example, if one has a fishing net and
asks 'Can't we just do with the holes and get rid of the rest of the net?',
the obvious answer is 'No, we can't'.

Thomas

Christophe de Dinechin

unread,
Feb 20, 2007, 7:04:52 AM2/20/07
to
Thomas Smid <thoma...@gmail.com> writes:
> > > The point is that *in principle* we can make our measurents
> > > arbitrarily accurate and extensive,
> > That is a metaphysical assumption which we cannot justify empirically.
> > One should be very wary of assuming something which we cannot show.

> The continuity of space and time doesn't need to be shown.

That's where Charles Francis and myself disagree with you. Your statements
are true of some mathematical representations of space and time.
But you cannot infer logically that such continuity therefore applies
to physically possible measurements of space and time.

Just because I can talk about 10^-123456789 meter does not mean that
it has any sensible physical meaning. I do not agree that we can,
even in principle, make our measurement that accurate. On the contrary,
I believe that quantum mechanics taught us that such a distance is not
just beyond our reach in practice, but physically meaningless.

> Space and time aren't physical objects but cognitive forms,

I can agree with this definition. But in physics, whatever cognitive form we
select is subject to one additional constraint: it is more useful if it
actually matches physical observation.

Unfortunately, the hypothesis that space is continuous is at odds with,
at the very least, our practical and, I believe, theoretical capabilities
to measure distance. So the entire question becomes: can we find
useful cognitive forms that do not make the continuum hypothesis?


> and as such their continuity (i.e. their lack of structure) is
> logically self-evident.

Continuity and lack of structure are not the same thing. There are
many different continuous spaces, if only considering the number
of dimensions.

> The mere fact that between any two points one can *imagine*
> another point is sufficient for this.

...in the mathematical realm, yes. But it is not sufficient to prove that
for any physical distance measurement, you can build another with twice
the resolution.

> What one has to realize is that we can actually recognize discreteness
> only on the background of continuity,

This is mathematically incorrect. Peano and others have shown this.

> As a real-life example, if one has a fishing net and
> asks 'Can't we just do with the holes and get rid of the
> rest of the net?', the obvious answer is 'No, we can't'.

This irrelevant analogy totally failed to convince me :-)

A more relevant fishing net analogy would be: since to catch
smaller fish, I only need to build a smaller net, I should
logically be able to build a fishing net small enough to
catch electrons. Do you believe that this is true?
--
Thanks
Christophe

Oh No

unread,
Feb 20, 2007, 7:35:43 AM2/20/07
to
Thus spake Thomas Smid <thoma...@gmail.com>
>Oh No <No...@charlesfrancis.wanadoo.co.uk> writes:
>
>> The point is that the mathematics should reflect what we can actually do
>> in measurement. It does not necessarily model the underlying reality.
>> That is a different issue, but if we correctly model what we can
>> measure, we will have a better prospect of understanding the underlying
>> reality too.
>>
>> > The point is that
>> >*in principle* we can make our measurents arbitrarily accurate and
>> extensive,
>>
>> That is a metaphysical assumption which we cannot justify empirically.
>> One should be very wary of assuming something which we cannot show.
>
>The continuity of space and time doesn't need to be shown. Space and time
>aren't physical objects but cognitive forms,

true.

>and as such their continuity
>(i.e. their lack of structure) is logically self-evident.

Actually not. Showing that the continuum can be constructed in a
mathematically meaningful way was a big problem a couple of centuries
back, address by Weierstrass, Cauchy et al.

>The mere fact that
>between any two points one can *imagine* another point is sufficient for
>this.

No. That naive approach was refuted because of the logical
inconsistencies to which it led.

>What one has to realize is that we can actually recognize discreteness only
>on the background of continuity, so the latter is always bound to be the
>underlying form.

Actually we start with discreteness and define a continuum only by using
the limit of infinite procedures. These infinite procedures are valid in
thought, but we cannot actually carry them out.

>As a real-life example, if one has a fishing net and
>asks 'Can't we just do with the holes and get rid of the rest of the net?',
>the obvious answer is 'No, we can't'.
>

Actually we can. I often liken Feynman diagrams to a fishing net. The
only aspect of the net which has meaning are the strands. The space
between has no impact on the mathematical formula corresponding to the
diagram. It is a convenience for visualisation only.

Thomas Smid

unread,
Feb 20, 2007, 11:11:01 AM2/20/07
to
On 20 Feb, 12:04, Christophe de Dinechin <christo...@dinechin.org> wrote:

> Thomas Smid <thomas.s...@gmail.com> writes:
>
> > The mere fact that between any two points one can *imagine*
> > another point is sufficient for this.
>
> ...in the mathematical realm, yes. But it is not sufficient to prove that
> for any physical distance measurement, you can build another with twice
> the resolution.

I would say, quite on the contrary: it is only in mathematics that one can
define discrete functions. In physics there are stricty speaking no
discontinuities (not even in atomic physics).
Even if one can mathematically approximate an observable O(x) by a discrete
function, one should note that it is the *value* of the observable that is
discontinuous, not the argument x. In order to define O(x) fully in the first
place, it is obvious that x (which may be for instance a spatial variable)
must be continuous. One can not just leave out the regions where O(x) is zero,
as they are as vital for defining O(x) as the regions where they are different
from zero. Taking out any infinitesimal part from the x-line would change the
function O(x), so x has to be continuous.

Thomas

Cl.Massé

unread,
Feb 20, 2007, 1:16:16 PM2/20/07
to
"Christophe de Dinechin" <chris...@dinechin.org> a écrit dans le message
de news: guest.20070219072814$35...@news.killfile.org

> That is not what I am suggesting.

I thought of Noyes' constructive physics.

> Apparently, I need to explain a bit
> more about the "incomplete measurements" theory
> (http://cc3d.free.fr/tim.pdf) on this thread.

> Therefore, I interpret quantum mechanics as an approximation of the


> necessary form of "probability mechanics" under some specific conditions
> (essentially: linearity and m_i being real). More
> importantly, as long as you accept the now demonstrated fact that some
> measurements cannot be
> predicted with more than probabilities, I believe that I have
> demonstrated that quantum mechanics is essentially the necessary form for
> physics. Not just infinitesimal physics, any physics.
>
> The axiom of QM that cannot be reconstructed this way is Schroedinger's
> equation, so I'm initially
> just "stealing it" from quantum mechanics to build a complete theory.

The Schrödinger equation represents the dynamics. So, without an evolution
equation, you have only set the stage, but nothing happen, just like in
classical mechanics the space and the time are set first. Actually, even
with a linear evolution equation nothing would happen. If on a stage, if
the characters doesn't speak to each other, there is no story. Then, the
interactions are what really gives a physical content. In turn, interaction
means non-linearity.

Cl.Massé

unread,
Feb 20, 2007, 1:15:37 PM2/20/07
to
"Oh No" <No...@charlesfrancis.wanadoo.co.uk> a écrit dans le message de
news: ZHdUkoNH...@charlesfrancis.wanadoo.co.uk

> One should be very wary of assuming something which we cannot show.

But at the same time, what is shown need not to be assumed. What we should
be wary of is not to forget the assumptions we made.

Oh No

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Feb 20, 2007, 2:46:17 PM2/20/07
to
Thus spake Cl.Massé <ret...@contactprospect.com>

>"Oh No" <No...@charlesfrancis.wanadoo.co.uk> a écrit dans le message de
>news: ZHdUkoNH...@charlesfrancis.wanadoo.co.uk
>
>> One should be very wary of assuming something which we cannot show.
>
>But at the same time, what is shown need not to be assumed. What we should
>be wary of is not to forget the assumptions we made.
>
Indeed. I am strongly in favour of a formal approach, especially in
foundational issues. One should proceed from axioms clearly stated and
use deduction only from axioms which have been formally stated. I divide
axioms into two types, those I call postulates which state something
physical, preferably something from observation, and those I call
definitions which merely determine mathematical structure.

zathras...@yahoo.com

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Feb 20, 2007, 2:40:32 PM2/20/07
to
Thomas Smid <thoma...@gmail.com> writes:

. . . .

> Yes, but I am sure you are not suggesting would should model reality after
> the
> insufficiencies and limitations of our measuring devices. The point is that
> *in principle* we can make our measurents arbitrarily accurate and
> extensive,
> so we need a continuous and infinite number line to reflect this
> circumstance.
>
> Thomas
>

Practicing science means being limited by what we can observe. We cannot
observe beyond the limits of instrumentation, by definition. Any extension
beyond is theology, since by definition there is no empirical evidence otherwise.

Oh No

unread,
Feb 20, 2007, 3:29:16 PM2/20/07
to
Thus spake zathras...@yahoo.com
True. But we may be able to deduce beyond the limits of instrumentation,
not from the results of measurement, of course, but from the manner of
doing measurement. That is what Einstein did in special relativity. Von
Neumann did much the same, in quantum logic. From sr and qm, Dirac was
able to deduce the description of the electron. We can have a scientific
description which goes beyond observation.

Christophe de Dinechin

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Feb 20, 2007, 5:47:03 PM2/20/07
to
POST
User-Agent: Xnntp/beta05 (UNIBIN Mac OS 10.4+)

Thomas Smid <thoma...@gmail.com> wrote:
>> ...in the mathematical realm, yes. But it is not sufficient to prove that
>> for any physical distance measurement, you can build another with twice
>> the resolution.
>
> I would say, quite on the contrary: it is only in mathematics that one can
> define discrete functions. In physics there are stricty speaking no
> discontinuities (not even in atomic physics).

Show me tenths of electrons with one tenth the charge, and I'll concede your
point.

> Even if one can mathematically approximate an observable O(x) by a discrete
> function, one should note that it is the *value* of the observable that is
> discontinuous, not the argument x.

Traditionally, observable values are not written as O(x), so I'm not sure if you
mean: the expectation value, an observable that is itself a function of
position, or something else.

> In order to define O(x) fully in the first
> place, it is obvious that x (which may be for instance a spatial variable)
> must be continuous.

Are you saying that it is "obviously" not possible to define a function on the
set of integers? I'm not following you. What about f(n)=n? Or, more subtle, f(z)
=lim(k->infinity) (z^k)...

> One can not just leave out the regions where O(x) is zero,
> as they are as vital for defining O(x) as the regions where they are different
> from zero.

I was talking about zero probability along some dimensions of a Hilbert space.
This is not quite the same thing as O(x) being 0.

> Taking out any infinitesimal part from the x-line would change the
> function O(x), so x has to be continuous.

I do not understand this reasoning, and I suspect it is not even wrong.


Regards
Christophe


--
Thanks
Christophe de Dinechin

Oh No

unread,
Feb 21, 2007, 7:28:11 AM2/21/07
to
Thus spake Christophe de Dinechin <chris...@dinechin.org>
>Oh No <No...@charlesfrancis.wanadoo.co.uk> writes:
>
>> >When two measurements are related by a linear law, I agree that scaling
>> >is trivial. However, this is not
>> >a general rule, see my earlier example of carbon dating vs. time
>> >counters based on celestial bodies.
>>
>> Yes, but I answered that too.
>
>I understood your answer as "I increase the resolution (and dimension
>of Hilbert space) and the
>problem goes away". I am skeptical, because a change of resolution
>cannot compensate for
>qualitative differences. To take the example of space measurements, if
>distinct physical
>measurements give geometries with distinct curvatures, how can you make
>them fit one another just
>by adjusting the resolution? Locally, they can all be flat and so you
>can make them fit. But at large
>scale?

Ultimately I think all measurement of distance is reducible to the
minimum proper time taken for two way photon exchange, as in the radar
method. Although the situation is less clear when this method cannot be
directly applied, in qed photon exchange is the underlying mechanism for
the electromagnetic force which gives rise to all the structures we
observe.


>
>
>Calibrating other units to the reference unit assume that all the units
>that you might want to consider
>have the same properties, or that one can obviously be taken as the
>"reference" unit. This is the
>specific belief I no longer have.

I think we have to take something as a fundamental reference from which
all else is defined. I believe that the maximum speed of information
transfer is the fundamental from which all measurement of distance must
be determined, and that all measurements ultimately boil down to the
measurement of position of something, albeit only the position of a
pointer.

>There are two usual ways to select the "reference". The first one is
>"highest precision", the other one
>is "least sensitive to external factors". Now, consider that I want to
>count objects, and I have two
>tools. The first one is a spoon, the other is the naked eye. The first
>measurement is "I pick objects
>up", the other measurement is: "I see how many there are".

>
>Based on resolution, the eye is better. With it, I can for instance
>count tiny grains of sand (if there
>aren't too many), something which is difficult to do reliably with a
>spoon because I can't pick them
>up.
>
>But now look at objects into an aquarium, looking through the corner of
>the aquarium, and you can
>see the same object twice. Yet, you will never be able to pick the
>duplicates with the spoon... So
>based on sensitivity to external influence, the eye loses.
>
>This is a very simple table top experiment. It is a very simple
>measurement. Yet I can find two
>physical processes where there is no obvious "reference unit". What
>basis do I have, then, to say that
>for much more complex things, like space measurements, there is some
>obvious reference unit, or
>that by increasing the resolution I necessarily have found my reference unit?

Following, I think, Leibniz, I distinguish measurement from a simple
count of objects, and define it to mean a count of units of a measured
quantity, where the definition of the unit of measurement invokes
comparison between some aspect of the subject of measurement and a
property of the reference matter used to define the unit of measurement.

>
>To rephrase the above, prediction about Schroedinger's cat being alive
>are based on a 2D Hilbert
>state. If you add dimensions to the HIlbert space corresponding to
>"half alive", you have then to
>justify why the corresponding probabilities are always zero.

One wouldn't do that anyway. "half alive" is presumably just a
superposition of states in the 2D Hilbert space, and does not increase
the number of dimensions. Another dimension would refer to some
completely independent measurement.#

I probably mistake your meaning. I am very rusty on the technicalities,
but I think you mean that you have a many dimensioned Hilbert space with
a partition into two subspaces, in one the cat is "alive" and in the
other "dead". I see no problem there. These subspaces are the basis for
the 2D Hilbert space. Here there is not particular way of assigning
probabilities to states within the subspaces, but I don't see an issue
here, since only the 2D Hilbert space is meaningful.

Christophe de Dinechin

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Feb 21, 2007, 4:43:57 PM2/21/07
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POST
User-Agent: Xnntp/beta05 (UNIBIN Mac OS 10.4+)

Oh No <No...@charlesfrancis.wanadoo.co.uk> wrote:

> Ultimately I think all measurement of distance is reducible to the
> minimum proper time taken for two way photon exchange, as in the radar
> method.

Interesting. I notice the "two way" part of that definition, I see where it
comes from in your papers. I was not familiar with this approach. Is that your
invention?


> Although the situation is less clear when this method cannot be
> directly applied, in qed photon exchange is the underlying mechanism for
> the electromagnetic force which gives rise to all the structures we
> observe.

Agreed. But what if the photon travels in a medium causing dispersion? Does the
distance depend on the frequency of the photon being used?


> I think we have to take something as a fundamental reference from which
> all else is defined.

I would like to be able to do that, but I have quite some trouble finding a
reference that is without possible discussion more fundamental than the rest..


> I believe that the maximum speed of information
> transfer is the fundamental from which all measurement of distance must
> be determined,

Interesting idea.


> and that all measurements ultimately boil down to the
> measurement of position of something, albeit only the position of a
> pointer.

What about something that turns on or off (but stays in place), like a LED?


> Following, I think, Leibniz, I distinguish measurement from a simple
> count of objects, and define it to mean a count of units of a measured
> quantity, where the definition of the unit of measurement invokes
> comparison between some aspect of the subject of measurement and a
> property of the reference matter used to define the unit of measurement.

Are you saying that a count is not a measurement, or that there are measurements
that are not counts? If the former, I disagree. If the latter, that does not
invalidate my initial observation, which I summarize as:

1/ Even a simple measurement like a count can be performed using multiple
physical methods

2/ Among two methods, one can have higher resolution and the other be more
robust, meaning that choosing the "best one" or "reference" is not obvious.

3/ If for a simple measurement, the choice of the "reference" is not obvious,
that casts doubt on the proposition that there is an obvious reference for a
more complex measurement, like a measurement of distance.


>>To rephrase the above, prediction about Schroedinger's cat being alive
>>are based on a 2D Hilbert
>>state. If you add dimensions to the HIlbert space corresponding to
>>"half alive", you have then to
>>justify why the corresponding probabilities are always zero.
>
> One wouldn't do that anyway. "half alive" is presumably just a
> superposition of states in the 2D Hilbert space, and does not increase
> the number of dimensions. Another dimension would refer to some
> completely independent measurement.

Precisely. Normally, the cat's state often described as "half alive" is a
superposition of kets corresponding to 100% dead, |dead> and 100% alive, |
alive>. These could for example be entangled states along directions |dead> + |
alive> or |dead> - |alive> in the Hilbert space.

In QM, I can associate real eigenvalues to |dead> or |alive>, so if M is the
observable corresponding to "is the cat alive", and if I choose eigenvalues 0
for "dead" and 1 for "alive", I have M |dead> = 0 |dead> and M |alive> = 1 |
alive>. The measurement is quantized, I cannot measure 0.5 because there is no
vector such that M |v> = 0.5 |v>. So far, so good.

One of my early points in this thread is that as long as an actual distance
measurement is quantized physically, with for example possible measurement
results 0, 0.1, 0.2, ... 0.9, 1.0, I can do just as above. If D is the distance
observable, I can use a finite Hilbert space, where D |0> = 0 |0>, D |0.1> = 0.1
|0.1>, and so on. But why would I need |pi> verifying D |pi> = pi |pi> (not to
mention all other real numbers), if pi is not a result that my measurement
apparatus can ever return?

Now, earlier in the discussion, you suggested that the reason for needing that
is that we can increase the resolution as we wish. In other words, the reason I
would need |0.01> is because 0.01 would be more precise than 0.0 or 0.1.

I used the cat example as my counter argument. By the same reasoning of
"increased resolution", I could add a |zombie> state to |dead> and |alive>,
obeying the eigenvalue equation M |zombie> = 0.5 |zombie>. In theory, it's neat,
but the problem is that I will never actually find a zombie cat when measuring,
so now I have to introduce all sorts of cutoffs and special rules so that the
probability for the state |zombie> is zero.

It seems to me like the same is true for space measurements, then. If I can only
measure 0.1 and 0.2 but my measurement apparatus is not precise enough to
measure 0.25, there is no point in having |0.25> in the Hilbert space.

> I probably mistake your meaning.

Did the explanation above clarify?

Oh No

unread,
Feb 21, 2007, 5:57:54 PM2/21/07
to
Thus spake Christophe de Dinechin <chris...@dinechin.org>
>POST
>User-Agent: Xnntp/beta05 (UNIBIN Mac OS 10.4+)
>
>Oh No <No...@charlesfrancis.wanadoo.co.uk> wrote:
>
>> Ultimately I think all measurement of distance is reducible to the
>> minimum proper time taken for two way photon exchange, as in the radar
>> method.
>
>Interesting. I notice the "two way" part of that definition, I see where it
>comes from in your papers. I was not familiar with this approach. Is that your
>invention?

No. I attended a lecture by Hermann Bondi on Relativity and Common Sense
when I was 17. Funnily enough one of the questions at the end of the
lecture was about "what happens if you assume a time delay in the
reflection". Bondi answered, of the cuff, "oh that's the start of
general relativity". I thought he meant it at the time, and it is only
quite recently that I finally convinced myself that actually this was a
pat answer and that no work had ever been done on the idea. In practice
I found I could not make it work without using quantum theory.

>> Although the situation is less clear when this method cannot be
>> directly applied, in qed photon exchange is the underlying mechanism for
>> the electromagnetic force which gives rise to all the structures we
>> observe.
>
>Agreed. But what if the photon travels in a medium causing dispersion?
>Does the
>distance depend on the frequency of the photon being used?

No. the distance depends on the maximum theoretical speed of information
transfer, not on the actual speed of photons. Actually, I think, though
I haven't studied it, that to model photons in a medium in qed you have
to take into account that they are being absorbed and reemitted, and
that this is the reason the classical wave moves more slowly. The
photons themselves still move at c.

>> I think we have to take something as a fundamental reference from which
>> all else is defined.
>
>I would like to be able to do that, but I have quite some trouble finding a
>reference that is without possible discussion more fundamental than the rest..

Either there is a maximum speed of information or not. If there is no
maximum speed of information the laws of physics would be entirely
different from those we observe. Ergo, I think this is a fundamental.
The fact of photons moving at c is convenient, but not essential. One
cannot empirically exclude the possibility that they have an incredibly
small mass. Figures on the max value of this mass have been quoted on
s.p.r. in the past.

>
>> and that all measurements ultimately boil down to the
>> measurement of position of something, albeit only the position of a
>> pointer.
>
>What about something that turns on or off (but stays in place), like a LED?

Its still the position of an excitation.

>> Following, I think, Leibniz, I distinguish measurement from a simple
>> count of objects, and define it to mean a count of units of a measured
>> quantity, where the definition of the unit of measurement invokes
>> comparison between some aspect of the subject of measurement and a
>> property of the reference matter used to define the unit of measurement.
>
>Are you saying that a count is not a measurement, or that there are
>measurements
>that are not counts? If the former, I disagree.

It is a matter of semantics. It is useful to make this distinction. If I
don't define measurement like this, I would have to make some, probably
more obscure, definition.

> If the latter, that does not
>invalidate my initial observation, which I summarize as:

No, I think all measurements are counts.


>
>1/ Even a simple measurement like a count can be performed using multiple
>physical methods
>
>2/ Among two methods, one can have higher resolution and the other be more
>robust, meaning that choosing the "best one" or "reference" is not obvious.
>
>3/ If for a simple measurement, the choice of the "reference" is not obvious,
>that casts doubt on the proposition that there is an obvious reference for a
>more complex measurement, like a measurement of distance.

I think this illustrates why the distinction is valuable. Counting
objects is a separate problem, which here confuses that which needs to
be clear.

Quite.


>
>Now, earlier in the discussion, you suggested that the reason for needing that
>is that we can increase the resolution as we wish. In other words, the
>reason I
>would need |0.01> is because 0.01 would be more precise than 0.0 or 0.1.

Perhaps. But we cannot increase resolution indefinitely. In practice we
just need some bounding resolution more accurate than any measurement we
are able to perform. Then we can express the results of any given
measurement using a partition of Hilbert space.


>
>I used the cat example as my counter argument. By the same reasoning of
>"increased resolution", I could add a |zombie> state to |dead> and |alive>,
>obeying the eigenvalue equation M |zombie> = 0.5 |zombie>. In theory,
>it's neat,
>but the problem is that I will never actually find a zombie cat when
>measuring,
>so now I have to introduce all sorts of cutoffs and special rules so that the
>probability for the state |zombie> is zero.
>
>It seems to me like the same is true for space measurements, then. If I
>can only
>measure 0.1 and 0.2 but my measurement apparatus is not precise enough to
>measure 0.25, there is no point in having |0.25> in the Hilbert space.

I think this is a bit different from the Zombie cat. The reason for
having |0.25> in the Hilbert space is that one wants to be able to
describe things in as simple a way as possible. Suppose the measurement
you are using becomes more accurate near 0, so that 0.05 is possible to
measure, even though 0.25 is not. Then it is convenient to include
states at intervals of 0.05 in the Hilbert space. The actual results of
measurement are then represented as subsets of Hilbert space, with
different numbers of states in each subset, depending on the resolution
in that region. This is a lot simpler to deal with than introducing non-
linearity into the definition of the basis of Hilbert space.

Oz

unread,
Feb 22, 2007, 4:59:50 AM2/22/07
to
Thomas Smid <thoma...@gmail.com> writes

>I would say, quite on the contrary: it is only in mathematics that one can
>define discrete functions. In physics there are stricty speaking no
>discontinuities (not even in atomic physics).

Ultimately a description is digital, this is demanded by information
theory.

There is a finite amount of information in the observable universe.
One thing QM does is limit the amount of information a particle can in
principle 'deliver'.

So one must conclude that, ultimately, a purely digital (ie discrete)
description is as good as you can get.

Whether its sensible to go this far is, of course, quite another matter.
Almost always one uses bulk analog descriptions. Note that in practice
this applies particularly to low energy (ie discrete with small
momentum) qm descriptions.

--
Oz
This post is worth absolutely nothing and is probably fallacious.

Oz

unread,
Feb 22, 2007, 4:59:03 AM2/22/07
to
Christophe de Dinechin <chris...@dinechin.org> writes

>Show me tenths of electrons with one tenth the charge, and I'll concede your
>point.

I'm pretty sure there are qm devices where this is sort-of true.
Ie the electron is in ten energy wells and can be made to behave like
(in some sense) 1/10 e (or more likely 1/2).

Of course its not a 'free' electron. One could crudely argue that an
(appropriate) electron is "as big as a lump of conductive metal".

Oz

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Feb 22, 2007, 5:01:03 AM2/22/07
to
Christophe de Dinechin <chris...@dinechin.org> writes
>Just because I can talk about 10^-123456789 meter does not mean that
>it has any sensible physical meaning. I do not agree that we can,
>even in principle, make our measurement that accurate.

That depends on what you are measuring.

You can do this for (say) an average position of a 'large' object.
You can't for a small, light one.

Its where I disagree with ohno.

The discretised space for the expression of the position of an object is
not infinite since you need particles to define the position and one can
only use these to measure to -+ a wavelength. In general qm-ists cheat
by defining only the starting and ending detectors which are typically
small (atom sized), these require significant unmodelled swept-under-
the-carpet interactions to function as detectors.

Oh No

unread,
Feb 22, 2007, 5:28:31 AM2/22/07
to
Thus spake Oz <O...@farmeroz.port995.com>
You say you disagree with me on this, but I can't see any disagreement.
Oh, maybe I know what you mean. The structure of quantum mechanics is
abstracted from measurement results, and is true irrespective of the
processes involved in producing those measurement results. In that
respect it exists, in its entirity, as a black box theory of
meausurement where all you need to impose is covariance to get the wave
interference effects as well as the superposition. It follows that you
would get the interference effects in any covariant quantum theory
irrespective of underlying processes. The claim that it is necessarily a
theory of sizeless particles requires an additional ingredient, namely
that interactions are also covariant. This leads to the locality
condition in field theory. In the language of quantum logic, the
locality condition is a clear statement that particles are point-like.

Oh No

unread,
Feb 22, 2007, 5:28:17 AM2/22/07
to
Thus spake Oz <O...@farmeroz.port995.com>

>So one must conclude that, ultimately, a purely digital (ie discrete)
>description is as good as you can get.
>
>Whether its sensible to go this far is, of course, quite another
>matter.

I would say so, or there is no rigorous qed. It was a point of
contention with the wizard who said it was impossible to go this far,
because of covariance considerations. An important point, in fact, one
which lead me to review the meaning of covariance.

Oz

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Feb 22, 2007, 8:43:01 AM2/22/07
to
Oh No <No...@charlesfrancis.wanadoo.co.uk> writes

>You say you disagree with me on this, but I can't see any disagreement.
>Oh, maybe I know what you mean. The structure of quantum mechanics is
>abstracted from measurement results, and is true irrespective of the
>processes involved in producing those measurement results. In that
>respect it exists, in its entirity, as a black box theory of
>meausurement where all you need to impose is covariance to get the wave
>interference effects as well as the superposition. It follows that you
>would get the interference effects in any covariant quantum theory
>irrespective of underlying processes. The claim that it is necessarily a
>theory of sizeless particles requires an additional ingredient, namely
>that interactions are also covariant. This leads to the locality
>condition in field theory. In the language of quantum logic, the
>locality condition is a clear statement that particles are point-like.

Er, probably.

But the problem is that by definition they aren't pointlike (they are
waves). The **detectors** (or emitter, by time reversal) are assumed
pointlike which is a fair approximation as long as this is valid.

Its unlikely to be valid in extremis, though.

Oz

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Feb 22, 2007, 8:43:31 AM2/22/07
to
Oh No <No...@charlesfrancis.wanadoo.co.uk> writes

>Thus spake Oz <O...@farmeroz.port995.com>
>>So one must conclude that, ultimately, a purely digital (ie discrete)
>>description is as good as you can get.
>>
>>Whether its sensible to go this far is, of course, quite another
>>matter.
>
>I would say so, or there is no rigorous qed. It was a point of
>contention with the wizard who said it was impossible to go this far,
>because of covariance considerations. An important point, in fact, one
>which lead me to review the meaning of covariance.

There is a problem in that the resolution of distance is momentum-
related. That is you can fit more high (4-)momentum particles into a
space than you can low momentum particles. The implication is that high
momentum implies high information. Unfortunately I can't see how this
can be as it (should) take as much information to describe a high energy
photon than a low energy photon (ie its momentum is a single number).

Unless, of course, there is a finite minumum size (or something
equivalent), or perhaps maximum size.

Gee, I guess I should get banned from spf for random speculation of the
worst kind....

Cl.Massé

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Feb 22, 2007, 12:45:00 PM2/22/07
to
"Christophe de Dinechin" <chris...@dinechin.org> a écrit dans le message
de news: guest.20070219072814$35...@news.killfile.org

> The axiom of QM that cannot be reconstructed this way is Schroedinger's
> equation,

Dirac and Maxwell equations, then. You can't reconstruct them because you
have no geometry. The equations are derived from the metric of space-time,
or in other words, the evolution operator must belong to a representation of
the symmetry group of space-time.

Oh No

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Feb 22, 2007, 2:17:52 PM2/22/07
to
Thus spake Christophe de Dinechin <chris...@dinechin.org>
>The axiom of QM that cannot be reconstructed this way is Schroedinger's
>equation,


I beg to differ. It can be reconstructed, and indeed it follows from
covariance requirements. To reconstruct it one observes that the
solutions in all discrete formulations using difference equations are
all solutions of the same differential equiation.

Christophe de Dinechin

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Feb 22, 2007, 6:24:28 PM2/22/07
to
POST
User-Agent: Xnntp/beta05 (UNIBIN Mac OS 10.4+)

Oh No <No...@charlesfrancis.wanadoo.co.uk> wrote:

> Thus spake Christophe de Dinechin <chris...@dinechin.org>
>>The axiom of QM that cannot be reconstructed this way is Schroedinger's
>>equation,
>
> I beg to differ. It can be reconstructed, and indeed it follows from
> covariance requirements.

Yes, by adding the appropriate covariance requirements (which is fine, but
it's not "this way" in the original context, it's adding a few new
postulates).

More to the point: I recall a few different derivations of Schroedinger's
equation, based on analyzing first order variations in psi which are not
exactly GTR's covariance requirements. So I guess I'm not sure what you
mean with covariance requirements here.


> To reconstruct it one observes that the
> solutions in all discrete formulations using difference equations are
> all solutions of the same differential equiation.

I noticed that you were doing something like that in one of your papers.
But I need to pause until I understand "covariance requirements", sorry...

Thomas Smid

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Feb 23, 2007, 10:52:56 AM2/23/07
to
Christophe de Dinechin <chris...@dinechin.org> writes:

> POST
> User-Agent: Xnntp/beta05 (UNIBIN Mac OS 10.4+)
>
> Thomas Smid <thoma...@gmail.com> wrote:
> >> ...in the mathematical realm, yes. But it is not sufficient to prove
> that
> >> for any physical distance measurement, you can build another with twice
> >> the resolution.
> >
> > I would say, quite on the contrary: it is only in mathematics that one
> can
> > define discrete functions. In physics there are stricty speaking no
> > discontinuities (not even in atomic physics).
>
> Show me tenths of electrons with one tenth the charge, and I'll concede
> your
> point.

Well, show me a physical measuring device that would display a truly
discontinuous change of the measured charge (or any other physical observable
for that matter). There can't be any. It isn't even in principle possible: if
you consider for instance the ionization of an atom, then it will always take
a finite time until the electron has completely escaped from the atom, i.e.
the latter will gradually develop from a neutral one (charge=0) to an ionized
one (charge=+1).

Thomas

Cl.Massé

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Feb 23, 2007, 1:58:50 PM2/23/07
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"Oh No" <No...@charlesfrancis.wanadoo.co.uk> a écrit dans le message de
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> True. But we may be able to deduce beyond the limits of instrumentation,

"Deduce" isn't the right term. Logically, it is rather "induce" or
"infer". Really, the right term is "imagine", and we must then verify,
until falsification.

> not from the results of measurement, of course, but from the manner of
> doing measurement. That is what Einstein did in special relativity. Von
> Neumann did much the same, in quantum logic. From sr and qm, Dirac was
> able to deduce the description of the electron. We can have a scientific
> description which goes beyond observation.

All those example still belongs to standard physics, but what about the
pre Kepler epicycles? There are leaps in nature between the different
refined theories, CM to QM for instance, even though the former can be
derived from the newer. But even that derivation isn't obvious. From QM
other approximate models can be derived.

Oh No

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Feb 23, 2007, 3:30:44 PM2/23/07
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Thus spake Cl.Massé <ret...@contactprospect.com>

>"Oh No" <No...@charlesfrancis.wanadoo.co.uk> a écrit dans le message de
>news: QqB3mTS1...@charlesfrancis.wanadoo.co.uk
>
>> True. But we may be able to deduce beyond the limits of instrumentation,
>
>"Deduce" isn't the right term. Logically, it is rather "induce" or
>"infer". Really, the right term is "imagine", and we must then verify,
>until falsification.

No, I meant deduce. Induce means from the results of observation. I said
from the method of measurement. The method defines the quantity. So long
as the method can be applied the quantity has certain properties which
can be deduced.


>
>> not from the results of measurement, of course, but from the manner of
>> doing measurement. That is what Einstein did in special relativity. Von
>> Neumann did much the same, in quantum logic. From sr and qm, Dirac was
>> able to deduce the description of the electron. We can have a scientific
>> description which goes beyond observation.
>
>All those example still belongs to standard physics, but what about the
>pre Kepler epicycles?

I don't think this could be done before Einstein. Now we can derive the
fundamental properties of relativity from simple principles, much of
quantum theory from similar simple principles. We can put that together
and derive also the Dirac equation, which tells us the actual properties
of matter.

> There are leaps in nature between the different
>refined theories, CM to QM for instance, even though the former can be
>derived from the newer. But even that derivation isn't obvious.

No. None of the derivations are obvious. Even now top physicists
"derive" the classical correspondence using quite false methods, like
letting h, a fundamental constant, go to zero.

Peter

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Feb 25, 2007, 12:50:40 PM2/25/07
to

> > >> ...in the mathematical realm, yes. But it is not sufficient to prove
> > that
> > >> for any physical distance measurement, you can build another with
> twice
> > >> the resolution.

Note that the assumption that something is divisible ad infinitum does *not*
mean that there are infinitesimal parts of it. There are not smallest parts,
but every part is finite.

> > > I would say, quite on the contrary: it is only in mathematics that one
> > can
> > > define discrete functions.

The notion function is a mathematical one ;-)


> > > In physics there are stricty speaking no
> > > discontinuities (not even in atomic physics).
> >
> > Show me tenths of electrons with one tenth the charge, and I'll concede
> > your point.

I would have replied the same.

> Well, show me a physical measuring device that would display a truly
> discontinuous change of the measured charge (or any other physical
> observable for that matter).

Any apparatus that measures the charge stored on the plates of a capacitor
will do. How else would Faraday have discoverd the existence of an elementary
quantum of charge? Analogously for the number of Na atoms in a given quantity
of NaCl.

> There can't be any. It isn't even in principle possible:
> if you consider for instance the ionization of an atom, then it will always
> take
> a finite time until the electron has completely escaped from the atom, i.e.
> the latter will gradually develop from a neutral one (charge=0) to an
> ionized one (charge=+1).

This point has been stressed by Schrödinger (1926), and I agree.
But it is well known in quantum chemistry that there is no unique definition
of the charge of an atom within a molecule. Thus, you cannot measure a
partial ionization, because you cannot define it, at least not in terms of
charge.

Altogether, why do you stick to 'only/always continuous' or 'only/always
discrete'? Why not saying, some things/processes are continuous, while other
are discrete?

Peter

Andreas Most

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Feb 26, 2007, 4:13:10 AM2/26/07
to
Peter wrote:
>> Well, show me a physical measuring device that would display a truly
>> discontinuous change of the measured charge (or any other physical
>> observable for that matter).
>
> Any apparatus that measures the charge stored on the plates of a capacitor
> will do. How else would Faraday have discoverd the existence of an elementary
> quantum of charge?

It was definitely not Faraday but Robert Millikan who discovered the
elementary charge. (see http://en.wikipedia.org/wiki/Robert_Millikan)

Thomas Smid

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Feb 26, 2007, 11:33:34 AM2/26/07
to
Peter <end...@dekasges.de> writes:

But there are no definite discrete values apparent in *any* physical
experiment. One always has a certain distribution of values around some
average. This distribution is continuous if one makes an infinite number of
measurements. In certain cases, like for the 'elementary charge', the strong
concentration of this distribution suggests that it is reasonable to postulate
discrete physical entities, but this is only because you see the continuous
distribution function sharply peak at multiples of a certain value. So
conceptually, the measuring unit of 'charge' has to be continuous in the first
place if you want to be able to detect any 'discrete' properties.

Thomas

Christophe de Dinechin

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Feb 26, 2007, 12:13:26 PM2/26/07
to
On Feb 26, 5:33 pm, Thomas Smid <thomas.s...@gmail.com> wrote:
> But there are no definite discrete values apparent in *any* physical
> experiment. One always has a certain distribution of values around some
> average. This distribution is continuous if one makes an infinite number of
> measurements.

Now I finally understand your point. And my objection is that you have
to write "if one makes an infinite number of measurements", which I
think you would agree is not a physical experiment, but a conceptual
one.

I would say that a distribution around an average is not one
measurement, but a mathematical computation from multiple
measurements, each giving one result. The computation is made with the
belief that, on average, the noise cancels out and the precision
increases. There are other algorithms, like "measure again and again
until the value stabilizes within a preset epsilon", or "collect min
and max, emit an error bar". And so on.


Regards
Christophe

Cl.Massé

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Feb 26, 2007, 1:00:20 PM2/26/07
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"Oh No" <No...@charlesfrancis.wanadoo.co.uk> a écrit dans le message de
news: u4fFePb$503F...@charlesfrancis.wanadoo.co.uk

> Now we can derive the
> fundamental properties of relativity from simple principles, much of
> quantum theory from similar simple principles. We can put that together
> and derive also the Dirac equation, which tells us the actual properties
> of matter.

But where do we get the principles? And if they are false? Practically, we
get the principles through imagination using experimental data. They
include the measurement procedures and the meaning of physical quantities,
which shows they aren't self obvious. The derivation is necessary to have a
logically consistent theory.

For example, the pre Kepler epicycles was a principle that allowed to
describe and predict the motions of planets. But that principle proved
false.

> No. None of the derivations are obvious. Even now top physicists "derive"
> the classical correspondence using quite false methods, like letting h, a
> fundamental constant, go to zero.

Here I agree. Actually, QM can't describe classical phenomena, even with
"shut up and calculate". It's what the Schrödinger's cat shows, and even
decoherence is of no help. Then, the principles of QM and CM aren't the
same. The principles are still to be found from which those of QM and CM
both derive (and GR.) Explicitly, there is still an inconsistency when
h -> 0, and when L -> h.

Oh No

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Feb 28, 2007, 7:35:45 AM2/28/07
to
Thus spake Cl.Massé <ret...@contactprospect.com>

>"Oh No" <No...@charlesfrancis.wanadoo.co.uk> a écrit dans le message de
>news: u4fFePb$503F...@charlesfrancis.wanadoo.co.uk
>
>> Now we can derive the
>> fundamental properties of relativity from simple principles, much of
>> quantum theory from similar simple principles. We can put that together
>> and derive also the Dirac equation, which tells us the actual properties
>> of matter.
>
>But where do we get the principles?

>From the manner in which we define measured quantities.

> And if they are false?

Definitions cannot be false. They can break down and become
inapplicable, which we see in the quantum domain when measurement of
position becomes impossible in principle, but so long the definition can
be applied, both it and its consequences are truism.

>Practically, we
>get the principles through imagination using experimental data.

No. What I am saying is that, since Einstein, Von Neumann and Dirac, we
no longer need to induce from data as the basis of scientific law.

> They
>include the measurement procedures and the meaning of physical quantities,
>which shows they aren't self obvious. The derivation is necessary to have a
>logically consistent theory.
>
>For example, the pre Kepler epicycles was a principle that allowed to
>describe and predict the motions of planets. But that principle proved
>false.

But then, later still, the principle proved true, and we use it all the
time in Fourier analysis. Not in this instance of course; it would be
far too complicated. But the underlying principle holds.

>> No. None of the derivations are obvious. Even now top physicists "derive"
>> the classical correspondence using quite false methods, like letting h, a
>> fundamental constant, go to zero.
>
>Here I agree. Actually, QM can't describe classical phenomena, even with
>"shut up and calculate".

It can if one correctly derives classical phenomena as the expectation
of large numbers of quantum phenomena.

>It's what the Schrödinger's cat shows, and even
>decoherence is of no help.

Schrodinger's cat is a misapplication. A cat is always a large number of
quantum particles, so always classical. The mixed states only appear in
a mathematical description and say no more than "I don't know whether
the cat is alive or dead".

> Then, the principles of QM and CM aren't the
>same. The principles are still to be found from which those of QM and CM
>both derive (and GR.) Explicitly, there is still an inconsistency when
>h -> 0, and when L -> h.
>

One cannot let h->0. One has h/N -> 0, when N -> oo.

Peter

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Mar 1, 2007, 6:23:09 AM3/1/07
to
> > But where do we get the principles?
>
> From the manner in which we define measured quantities.
>
> > And if they are false?
>
> Definitions cannot be false. They can break down and become
> inapplicable, which we see in the quantum domain when measurement of
> position becomes impossible in principle, but so long the definition can
> be applied, both it and its consequences are truism.
>
> > Practically, we
> > get the principles through imagination using experimental data.
>
> No. What I am saying is that, since Einstein, Von Neumann and Dirac, we
> no longer need to induce from data as the basis of scientific law.

I would also say that the principles are abstractions from experience. In
classical mechanics, we have got a ground under our foots we can trust. When
proceeding step by step without loosing the contact to this ground, we can
hope to have it still under us when moving in quantum and gravity land.

> > For example, the pre Kepler epicycles was a principle that allowed to
> > describe and predict the motions of planets. But that principle proved
> > false.

> But then, later still, the principle proved true, and we use it all the
> time in Fourier analysis. Not in this instance of course; it would be
> far too complicated. But the underlying principle holds.

I disagree. The underlying principle was the metaphysical superiority of
circular motion. The new principle is to realize that the single effect
(earth's orbit) can exhibit a lower symmetry than its cause (force field of
sun) (after Zee, Fearful Symmetry, paperback, p.12, this is due to Newton).
The set of all possible planetary orbits at given total energy exhibits
spherical symmetry.

BTW, when I asked Klauder few years ago about the comparison of the epicycles
and the current particle zoo, he replied that particle physics is waiting for
its Kepler.

> > Then, the principles of QM and CM aren't the
> > same. The principles are still to be found from which those of QM and CM
> > both derive (and GR.)

You can deduce Schrödinger's equation from classical mechanics
*axiomatically*, ie, without assuming h, wave-particle dualism and the like,
see Enders & Suisky, Int. J. Theor. Phys. 2005 (I can email a copy at
request). The clue is to start not with Newton's, but with Euler's axiomatics.

> Explicitly, there is still an inconsistency when
> >h -> 0, and when L -> h.

> One cannot let h->0. One has h/N -> 0, when N -> oo.

More exactly, because h is dimensionful,

h/characteristic_action -> 0

Best wishes,
Peter

Oh No

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Mar 1, 2007, 7:21:20 AM3/1/07
to
Thus spake Peter <end...@dekasges.de>

>> > But where do we get the principles?
>>
>> From the manner in which we define measured quantities.
>>
>> > And if they are false?
>>
>> Definitions cannot be false. They can break down and become
>> inapplicable, which we see in the quantum domain when measurement of
>> position becomes impossible in principle, but so long the definition can
>> be applied, both it and its consequences are truism.
>>
>> > Practically, we
>> > get the principles through imagination using experimental data.
>>
>> No. What I am saying is that, since Einstein, Von Neumann and Dirac, we
>> no longer need to induce from data as the basis of scientific law.


>I would also say that the principles are abstractions from experience. In
>classical mechanics, we have got a ground under our foots we can trust. When
>proceeding step by step without loosing the contact to this ground, we can
>hope to have it still under us when moving in quantum and gravity land.

We have to lose that ground, because we have to lose the notion of a
background space. If we think sufficiently clearly about how we measure
things, that is more solid ground.

>> > For example, the pre Kepler epicycles was a principle that allowed to
>> > describe and predict the motions of planets. But that principle proved
>> > false.
>
>> But then, later still, the principle proved true, and we use it all the
>> time in Fourier analysis. Not in this instance of course; it would be
>> far too complicated. But the underlying principle holds.
>
>I disagree. The underlying principle was the metaphysical superiority of
>circular motion.

I do not allude to metaphysical superiority, merely mathematical
trickery. I say it can be done, not that it is superior. Clearly it is
not superior.

>
>BTW, when I asked Klauder few years ago about the comparison of the epicycles
>and the current particle zoo, he replied that particle physics is waiting for
>its Kepler.

I am not sure how many years ago that was, but Murray Gell-Mann
undoubtedly filled that position in the 1950's and 60's, so I think
Klauder may have been a bit behind the times.


>
>> > Then, the principles of QM and CM aren't the
>> > same. The principles are still to be found from which those of QM and CM
>> > both derive (and GR.)
>
>You can deduce Schrödinger's equation from classical mechanics
>*axiomatically*, ie, without assuming h, wave-particle dualism and the like,
>see Enders & Suisky, Int. J. Theor. Phys. 2005 (I can email a copy at
>request). The clue is to start not with Newton's, but with Euler's axiomatics.
>

I don't think one even needs those axioms, and I find the notion of
deducing quantum motions from classical somewhat odd. I would rather
start with postulates drawn from studying measurement processes, in the
manner of Einstein and Von Neumann.

Regards

--
Charles Francis
moderator sci.physics.foundations.

Peter

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Mar 1, 2007, 9:36:25 AM3/1/07
to
> >I would also say that the principles are abstractions from experience. In
> >classical mechanics, we have got a ground under our foots we can trust.
> When
> >proceeding step by step without loosing the contact to this ground, we can
> >hope to have it still under us when moving in quantum and gravity land.
>
> We have to lose that ground, because we have to lose the notion of a
> background space.

We have not. Classical mechanics can incorporate the picture that the space
is spanned by the bodies. Sciama's model of Mach's principle (any change in
the velocity vector of a body is opposed by the gravitation field of all
other bodies) yields even a nice picture for the reason of inertia (for
Newton and Euler, this is a general property of bodies).

> If we think sufficiently clearly about how we measure
> things, that is more solid ground.

I don't think so, because this presupposes many notions and imaginations (cf.
below).



> >> > For example, the pre Kepler epicycles was a principle that allowed to
> >> > describe and predict the motions of planets. But that principle
> proved
> >> > false.

> >> But then, later still, the principle proved true, and we use it all the
> >> time in Fourier analysis. Not in this instance of course; it would be
> >> far too complicated. But the underlying principle holds.

> >I disagree. The underlying principle was the metaphysical superiority of
> >circular motion.

> I do not allude to metaphysical superiority, merely mathematical
> trickery. I say it can be done, not that it is superior. Clearly it is
> not superior.

I was just referring to the historical development.

> >BTW, when I asked Klauder few years ago about the comparison of the
> epicycles
> >and the current particle zoo, he replied that particle physics is waiting
> for
> >its Kepler.
>
> I am not sure how many years ago that was, but Murray Gell-Mann
> undoubtedly filled that position in the 1950's and 60's, so I think
> Klauder may have been a bit behind the times.

It was in October 2004. None of us denied the great progress done in the
systematization of elementary particles. IMHO, it are still too many.
Moreover, I hesitate to trust a theory with such anthropomorphisms as certain
names of some quantum numbers.

> >You can deduce Schrödinger's equation from classical mechanics
> >*axiomatically*, ie, without assuming h, wave-particle dualism and the
> like,
> >see Enders & Suisky, Int. J. Theor. Phys. 2005 (I can email a copy at
> >request). The clue is to start not with Newton's, but with Euler's
> axiomatics.
> >
> I don't think one even needs those axioms, and I find the notion of
> deducing quantum motions from classical somewhat odd.

Why?
I guess, because you are familiar only with Lagrange's and Hamilton's
mechanics. Then you face the same problems that Bohr, Heisenberg and
Schrödinger have found unsurmountable, of course.

> I would rather
> start with postulates drawn from studying measurement processes, in the
> manner of Einstein and Von Neumann.

They didn't find a satisfactory result. You can do better, but you must first
define ALL notions used independently of classical physics. You will convince
me when having achieved the latter :-)

These statements do not wish to contradict my positive reaction to the use of
Hilbert spaces for describing the statistics of certain measurements
(measurements of quantum objects by classical equipments - thus, first
describe what is a *classical* apparatus ;-).

Good luck :-)
Peter

Oh No

unread,
Mar 1, 2007, 10:34:07 AM3/1/07
to
Thus spake Peter <end...@dekasges.de>

>> >I would also say that the principles are abstractions from experience. In
>> >classical mechanics, we have got a ground under our foots we can trust.
>> When
>> >proceeding step by step without loosing the contact to this ground, we can
>> >hope to have it still under us when moving in quantum and gravity land.
>>
>> We have to lose that ground, because we have to lose the notion of a
>> background space.
>
>We have not. Classical mechanics can incorporate the picture that the space
>is spanned by the bodies. Sciama's model of Mach's principle (any change in
>the velocity vector of a body is opposed by the gravitation field of all
>other bodies) yields even a nice picture for the reason of inertia (for
>Newton and Euler, this is a general property of bodies).

If you do that you have already lost the classical notion of background
space and the theory is not classical.

>> If we think sufficiently clearly about how we measure
>> things, that is more solid ground.
>
>I don't think so, because this presupposes many notions and imaginations (cf.
>below).

There is nothing left to the imagination about the empirical definitions
of measured quantities.

>
>> >BTW, when I asked Klauder few years ago about the comparison of the
>> epicycles
>> >and the current particle zoo, he replied that particle physics is waiting
>> for
>> >its Kepler.
>>
>> I am not sure how many years ago that was, but Murray Gell-Mann
>> undoubtedly filled that position in the 1950's and 60's, so I think
>> Klauder may have been a bit behind the times.
>
>It was in October 2004. None of us denied the great progress done in the
>systematization of elementary particles. IMHO, it are still too many.

Only because of the Higgs and the gluons, for which the evidence appears
to me scanty and inconsistent.

>Moreover, I hesitate to trust a theory with such anthropomorphisms as certain
>names of some quantum numbers.

Naming is hardly a matter of scientific evidence.

>> >You can deduce Schrödinger's equation from classical mechanics
>> >*axiomatically*, ie, without assuming h, wave-particle dualism and the
>> like,
>> >see Enders & Suisky, Int. J. Theor. Phys. 2005 (I can email a copy at
>> >request). The clue is to start not with Newton's, but with Euler's
>> axiomatics.
>> >
>> I don't think one even needs those axioms, and I find the notion of
>> deducing quantum motions from classical somewhat odd.
>
>Why?
>I guess, because you are familiar only with Lagrange's and Hamilton's
>mechanics.

Because you plainly cannot derive an indeterminist theory from a
determinist one. If you think you have a way to do so, by reducing
quantum indeterminacy to classical probabilities of unknown quantities,
then you have not understood the mathematical structure of quantum
theory.

>> I would rather
>> start with postulates drawn from studying measurement processes, in the
>> manner of Einstein and Von Neumann.
>
>They didn't find a satisfactory result.

They found very satisfactory results for the time in which they were
working. There is nothing so silly as the way this argument gets trotted
out as a reason for not continuing their work. One hardly needs to look
further than this to realise why so little theoretical progress has been
made since their time.


> You can do better, but you must first
>define ALL notions used independently of classical physics. You will convince
>me when having achieved the latter :-)

Then you will need to cite where you think I have not done so.

>These statements do not wish to contradict my positive reaction to the use of
>Hilbert spaces for describing the statistics of certain measurements
>(measurements of quantum objects by classical equipments - thus, first
>describe what is a *classical* apparatus ;-).

An apparatus is something from which we can read a value. I do not care
to describe its workings, nor do I need to assume they are classical.
Actually I assume its workings obey the same fundamental behaviour as
any other matter in the universe.

Peter

unread,
Mar 1, 2007, 12:19:39 PM3/1/07
to
Andreas Most <Andrea...@nospam.de> writes:

I was referring to Faradays electro-chemical Laws. IMHO, they are equivalent
to the existence of an elementary quantum of charge. They are not mentioned
in the article you have referred to.

This is by no means intending to diminuish the great work by Robert Millikan
who was obviously the first to have done sufficiently accurate measurements
of e.

Thank you for your addendum,
Peter

Peter

unread,
Mar 1, 2007, 4:18:55 PM3/1/07
to

Oh No schrieb:

> Thus spake Peter <end...@dekasges.de>
> >> >I would also say that the principles are abstractions from experience. In
> >> >classical mechanics, we have got a ground under our foots we can trust.
> >> When
> >> >proceeding step by step without loosing the contact to this ground, we can
> >> >hope to have it still under us when moving in quantum and gravity land.
> >>
> >> We have to lose that ground, because we have to lose the notion of a
> >> background space.
> >
> >We have not. Classical mechanics can incorporate the picture that the space
> >is spanned by the bodies. Sciama's model of Mach's principle (any change in
> >the velocity vector of a body is opposed by the gravitation field of all
> >other bodies) yields even a nice picture for the reason of inertia (for
> >Newton and Euler, this is a general property of bodies).
>
> If you do that you have already lost the classical notion of background
> space and the theory is not classical.

I had in mind that CM can be extended by the picture that the space is
spanned by the bodies *without* touching its dynamical axioms.

> >> If we think sufficiently clearly about how we measure
> >> things, that is more solid ground.
> >
> >I don't think so, because this presupposes many notions and imaginations (cf.
> >below).
>
> There is nothing left to the imagination about the empirical definitions
> of measured quantities.

I don't understand this sentence, I'm afraid.

> >... None of us denied the great progress done in the


> >systematization of elementary particles. IMHO, it are still too many.
>
> Only because of the Higgs and the gluons, for which the evidence appears
> to me scanty and inconsistent.

:-)

> >Moreover, I hesitate to trust a theory with such anthropomorphisms as certain
> >names of some quantum numbers.

> Naming is hardly a matter of scientific evidence.

Yes, of course not, if seen isolated.
I add the cultural environment of over-pragmatism that had converted
Heisenberg's uncertainty relations (a mathematical property of the
Schrödinger equation) into Heisenberg's uncertainty *principle* (an
almost ideology).

> >...I guess, because you are familiar only with Lagrange's and Hamilton's mechanics.

> Because you plainly cannot derive an indeterminist theory from a
> determinist one.

I derive Schrödinger's wave mechanics, ie, a deterministic theory from
a deterministic one.

> If you think you have a way to do so, by reducing
> quantum indeterminacy to classical probabilities of unknown quantities,
> then you have not understood the mathematical structure of quantum
> theory.

Let's keep to be polite :-)

> >> I would rather
> >> start with postulates drawn from studying measurement processes, in the
> >> manner of Einstein and Von Neumann.

> >They didn't find a satisfactory result.

> They found very satisfactory results for the time in which they were
> working. There is nothing so silly as the way this argument gets trotted
> out as a reason for not continuing their work. One hardly needs to look
> further than this to realise why so little theoretical progress has been
> made since their time.

Ok, I don't know to what exactly you are referring to, but I admit
that I may not know that.
To be definite, do they obey Schrödinger's (1926) requirements to
(any) quantization?

> > You can do better, but you must first
> >define ALL notions used independently of classical physics. You will convince
> >me when having achieved the latter :-)

> Then you will need to cite where you think I have not done so.

Will look at :-)

> >These statements do not wish to contradict my positive reaction to the use of
> >Hilbert spaces for describing the statistics of certain measurements
> >(measurements of quantum objects by classical equipments - thus, first
> >describe what is a *classical* apparatus ;-).

> An apparatus is something from which we can read a value. I do not care
> to describe its workings, nor do I need to assume they are classical.
> Actually I assume its workings obey the same fundamental behaviour as
> any other matter in the universe.

Will try to refine my requirement


Thank you for your patience,
Peter

Oh No

unread,
Mar 1, 2007, 9:17:39 PM3/1/07
to
Thus spake Peter <end...@dekasges.de>

>
>Oh No schrieb:
>
>> Thus spake Peter <end...@dekasges.de>
>> >
>> >We have not. Classical mechanics can incorporate the picture that the space
>> >is spanned by the bodies. Sciama's model of Mach's principle (any change in
>> >the velocity vector of a body is opposed by the gravitation field of all
>> >other bodies) yields even a nice picture for the reason of inertia (for
>> >Newton and Euler, this is a general property of bodies).
>>
>> If you do that you have already lost the classical notion of background
>> space and the theory is not classical.
>
>I had in mind that CM can be extended by the picture that the space is
>spanned by the bodies *without* touching its dynamical axioms.

But then, how would you preserve conservation of momentum? Or rather, if
momentum is to be conserved, how do you stop space itself from shifting
about, and not only that, shifting differently depending on which bodies
you use to define it?

>> >> If we think sufficiently clearly about how we measure
>> >> things, that is more solid ground.
>> >
>> >I don't think so, because this presupposes many notions and
>> >imaginations (cf.
>> >below).
>>
>> There is nothing left to the imagination about the empirical definitions
>> of measured quantities.
>
>I don't understand this sentence, I'm afraid.

The formal definition of a measured quantity is not a matter of
imagination.

>> >Moreover, I hesitate to trust a theory with such anthropomorphisms
>> >as certain
>> >names of some quantum numbers.
>
>> Naming is hardly a matter of scientific evidence.
>
>Yes, of course not, if seen isolated.
>I add the cultural environment of over-pragmatism that had converted
>Heisenberg's uncertainty relations (a mathematical property of the
>Schrödinger equation) into Heisenberg's uncertainty *principle* (an
>almost ideology).

I understand that the inequality known as the uncertainty relation was
not even proved by Heisenberg, but by Kennard in 1927. I am not sure
that Heisenberg even gave a clear statement. There is a discussion in
quant-ph/9803046. However, I am not sure what that has to do with the
"eight-fold way". My main objection to the theory is that, after calling
the octuplet "the eight-fold way" after the advice of the Buddha, Gell-
Man did not then call the decuplet "the ten commandments". Definite
signs of religious prejudice, I fear.

>> >...I guess, because you are familiar only with Lagrange's and
>> >Hamilton's mechanics.
>
>> Because you plainly cannot derive an indeterminist theory from a
>> determinist one.
>
>I derive Schrödinger's wave mechanics, ie, a deterministic theory from
>a deterministic one.

But quantum theory is not deterministic. All we can say is that motion
is equivalent to wave theory + collapse, not one taken on its own.

>> If you think you have a way to do so, by reducing
>> quantum indeterminacy to classical probabilities of unknown quantities,
>> then you have not understood the mathematical structure of quantum
>> theory.
>
>Let's keep to be polite :-)

I apologise, but the problem remains. If you derive wave mechanics you
have to account for collapse and avoid the no-go theorems.

>> >> I would rather
>> >> start with postulates drawn from studying measurement processes, in the
>> >> manner of Einstein and Von Neumann.
>
>> >They didn't find a satisfactory result.
>
>> They found very satisfactory results for the time in which they were
>> working. There is nothing so silly as the way this argument gets trotted
>> out as a reason for not continuing their work. One hardly needs to look
>> further than this to realise why so little theoretical progress has been
>> made since their time.
>
>Ok, I don't know to what exactly you are referring to,

The first time I came up against the argument, it was from the external
examiner for my PhD, when I asked him to comment on a part of the
thesis.

> but I admit
>that I may not know that.
>To be definite, do they obey Schrödinger's (1926) requirements to
>(any) quantization?

I am not directly familiar with Schrodinger's work. I was taught by a
student of Dirac. We went very quickly to ket notation, and were simply
told of the Heisenberg and Schrodinger approaches and that they were
equivalent. Von Neumann formalised the axioms of quantum theory in 1936,
and with Birkhoff, related them to many valued logic.

Peter

unread,
Mar 2, 2007, 2:34:56 AM3/2/07
to
> >I had in mind that CM can be extended by the picture that the space is
> >spanned by the bodies *without* touching its dynamical axioms.
>
> But then, how would you preserve conservation of momentum? Or rather, if
> momentum is to be conserved, how do you stop space itself from shifting
> about, and not only that, shifting differently depending on which bodies
> you use to define it?

If space is spanned by all bodies, no such problems arise.

> >> >Moreover, I hesitate to trust a theory with such anthropomorphisms
> >> >as certain
> >> >names of some quantum numbers.
> >
> >> Naming is hardly a matter of scientific evidence.
> >
> >Yes, of course not, if seen isolated.
> >I add the cultural environment of over-pragmatism that had converted
> >Heisenberg's uncertainty relations (a mathematical property of the
> >Schrödinger equation) into Heisenberg's uncertainty *principle* (an
> >almost ideology).
>
> I understand that the inequality known as the uncertainty relation was
> not even proved by Heisenberg, but by Kennard in 1927. I am not sure
> that Heisenberg even gave a clear statement. There is a discussion in
> quant-ph/9803046. However, I am not sure what that has to do with the
> "eight-fold way". My main objection to the theory is that, after calling
> the octuplet "the eight-fold way" after the advice of the Buddha, Gell-
> Man did not then call the decuplet "the ten commandments". Definite
> signs of religious prejudice, I fear.

Now you understand how these things are interrelated :-)

"language which writes for you and thinks for you" (Friedrich Schiller)



> >> >...I guess, because you are familiar only with Lagrange's and
> >> >Hamilton's mechanics.
> >
> >> Because you plainly cannot derive an indeterminist theory from a
> >> determinist one.
> >
> >I derive Schrödinger's wave mechanics, ie, a deterministic theory from
> >a deterministic one.
>
> But quantum theory is not deterministic. All we can say is that motion
> is equivalent to wave theory + collapse, not one taken on its own.

'Schrödinger's wave mechanics' means the theory of the Schrödinger equation.
Wave function collaps occurs when you destroy the system under consideration.
This is not part of this theory, correct, this may be a limitation. But few
theories contain the destruction of their subjects, don't they?

> ... If you derive wave mechanics you


> have to account for collapse and avoid the no-go theorems.

I have not, see above.

> >To be definite, do they obey Schrödinger's (1926) requirements to
> >(any) quantization?

> I am not directly familiar with Schrodinger's work. I was taught by a
> student of Dirac. We went very quickly to ket notation, and were simply
> told of the Heisenberg and Schrodinger approaches and that they were
> equivalent.

This explains a lot ;-)
During the last 8 years I have read Schrödinger's 1926 papers again and again.
Wave mechanics and matrix mechanics are *mathematically* equivalent, but not
physically. For example, how can one describe the continuity of quantum
transitions within matrix mechanics?

> Von Neumann formalised the axioms of quantum theory in 1936,
> and with Birkhoff, related them to many valued logic.

This is great work and complies with Schrödinger's requirements to use maths
appropriate to the nature of quantum systems (while the maths of eigenvalue
problems does not). Moreover, oneshould justify the use of the classical
expressions for kinetic and potential energy, IMHO, this cannot be done by
logical means.


Thank you and best wishes,
Peter

Oh No

unread,
Mar 2, 2007, 3:32:14 AM3/2/07
to
Thus spake Peter <end...@dekasges.de>

>> >I had in mind that CM can be extended by the picture that the space is
>> >spanned by the bodies *without* touching its dynamical axioms.
>>
>> But then, how would you preserve conservation of momentum? Or rather, if
>> momentum is to be conserved, how do you stop space itself from shifting
>> about, and not only that, shifting differently depending on which bodies
>> you use to define it?
>
>If space is spanned by all bodies, no such problems arise.

But we have no way of defining space with respect to all bodies. In
practice we have to choose reference matter and define space relative to
that. This was acknowledged even by Newton in the Principia, and was the
central point of Leibniz disagreement with the concept of absolute
space. This point has never been resolved since - merely ignored because
no one has developed the mathematical theory to describe it. The central
idea in my papers is to show that when one does develop a mathematical
theory of physics correctly taking this into account one inevitably
finds quantum theory, complete with Schrodinger's equation and collapse,
though these are features of the mathematical apparatus, not the
physical description. One finds general relativity also.


>
>> >> >Moreover, I hesitate to trust a theory with such anthropomorphisms
>> >> >as certain
>> >> >names of some quantum numbers.
>> >
>> >> Naming is hardly a matter of scientific evidence.
>> >
>> >Yes, of course not, if seen isolated.
>> >I add the cultural environment of over-pragmatism that had converted
>> >Heisenberg's uncertainty relations (a mathematical property of the
>> >Schrödinger equation) into Heisenberg's uncertainty *principle* (an
>> >almost ideology).
>>
>> I understand that the inequality known as the uncertainty relation was
>> not even proved by Heisenberg, but by Kennard in 1927. I am not sure
>> that Heisenberg even gave a clear statement. There is a discussion in
>> quant-ph/9803046. However, I am not sure what that has to do with the
>> "eight-fold way". My main objection to the theory is that, after calling
>> the octuplet "the eight-fold way" after the advice of the Buddha, Gell-
>> Man did not then call the decuplet "the ten commandments". Definite
>> signs of religious prejudice, I fear.
>
>Now you understand how these things are interrelated :-)
>
>"language which writes for you and thinks for you" (Friedrich Schiller)

Still, whatever the quirks in terminology, the basic structure, three
generations of two leptons and two quarks, together with the photon, the
W and the Z, seems as solid to me as the periodic table. Moreover, we
know, (or we should know, because string theorists et al do not seem to
realise this) that these particles are fundamental because they obey the
only equations possible for fundamental particles. I am not sure what
further simplification you require. The only issues seems to be, why are
the masses as they are, and why are the charges as they are. I see no
real prospect of addressing those questions properly until existing
scientific knowledge is given the proper foundation of a rigorous
mathematical theory. Doing that should have been the task of
mathematical physicists for the last 50-70 yrs, but in fact mathematics
has been divorced from physics and anyone who even attempts the job is
marginalised by the community. Still, some good may come of it. This is
why we have sci.physics.foundations.

>> >> >...I guess, because you are familiar only with Lagrange's and
>> >> >Hamilton's mechanics.
>> >
>> >> Because you plainly cannot derive an indeterminist theory from a
>> >> determinist one.
>> >
>> >I derive Schrödinger's wave mechanics, ie, a deterministic theory from
>> >a deterministic one.
>>
>> But quantum theory is not deterministic. All we can say is that motion
>> is equivalent to wave theory + collapse, not one taken on its own.
>
>'Schrödinger's wave mechanics' means the theory of the Schrödinger equation.
>Wave function collaps occurs when you destroy the system under consideration.
>This is not part of this theory, correct, this may be a limitation. But few
>theories contain the destruction of their subjects, don't they?

It seems like a fundamental limitation, because without it one is not
describing the observed behaviour of matter.

>> >To be definite, do they obey Schrödinger's (1926) requirements to
>> >(any) quantization?
>
>> I am not directly familiar with Schrodinger's work. I was taught by a
>> student of Dirac. We went very quickly to ket notation, and were simply
>> told of the Heisenberg and Schrodinger approaches and that they were
>> equivalent.
>
>This explains a lot ;-)
>During the last 8 years I have read Schrödinger's 1926 papers again and again.
>Wave mechanics and matrix mechanics are *mathematically* equivalent, but not
>physically. For example, how can one describe the continuity of quantum
>transitions within matrix mechanics?

I don't understand the question. It is very straightforward, given the
Hilbert space of kets together with a law of time evolution U(t,to) to
write down, for any state |f> at time to, the wave function as a matrix
product, i.e.

<x|U(t,to)|f>

That is continuous. From that one gets a probability. Transitions in
probability theory are not continuous. The change abrubtly when new
information is known.

>> Von Neumann formalised the axioms of quantum theory in 1936,
>> and with Birkhoff, related them to many valued logic.
>
>This is great work and complies with Schrödinger's requirements to use maths
>appropriate to the nature of quantum systems (while the maths of eigenvalue
>problems does not).

It seems quite appropriate to me, and not different from what I have
written.

>Moreover, oneshould justify the use of the classical
>expressions for kinetic and potential energy, IMHO, this cannot be done by
>logical means.

Again, I don't know what you mean. If one requires that U(t,t0) has a
relativistic form then the expressions for energy follow in the same
manner as E=mc^2.

Cl.Massé

unread,
Mar 2, 2007, 12:39:15 PM3/2/07
to
> Thus spake Peter <end...@dekasges.de>

>> You can deduce Schrödinger's equation from classical mechanics
>> *axiomatically*, ie, without assuming h, wave-particle dualism and the
>> like, see Enders & Suisky, Int. J. Theor. Phys. 2005 (I can email a copy
>> at request). The clue is to start not with Newton's, but with Euler's
>> axiomatics.

First of all, I don't see what *axiomatically* has special. Indeed, the
least action principle already contains *wave mechanics*. But QM can't be
true without experimental evidence saying so, what will never spring from a
sheet of paper full of symbols.

That said, Schrödinger equation isn't QM, it can model classical systems as
well. We have to add the projection postulate, and above all to know what
to do with the infinity of states that this generalization of CM brings with
itself. What is a dead and alive cat? Does it exist? Can it be observed?
Clearly, even with some equations in common, we are in presence of two
fundamentally different theories, and the measurement problem is its
illustration, being at their junction. Classical objects must have very
special states, which doesn't evolve into each other through the Schrödinger
equation, even if decoherence is taken into account.

Cl.Massé

unread,
Mar 2, 2007, 12:39:40 PM3/2/07
to
"Oh No" <No...@charlesfrancis.wanadoo.co.uk> a écrit dans le message de
news: cYD5ZCFX...@charlesfrancis.wanadoo.co.uk

> I am not sure how many years ago that was, but Murray Gell-Mann
> undoubtedly filled that position in the 1950's and 60's, so I think
> Klauder may have been a bit behind the times.

Making the nucleons made up of other particles is more similar to the
epicycles. The true challenge is to describe all particles, including
leptons, through a unique and simple motion.

Oh No

unread,
Mar 2, 2007, 1:22:44 PM3/2/07
to
Thus spake Cl.Massé <ret...@contactprospect.com>

>"Oh No" <No...@charlesfrancis.wanadoo.co.uk> a écrit dans le message de
>news: cYD5ZCFX...@charlesfrancis.wanadoo.co.uk
>
>> I am not sure how many years ago that was, but Murray Gell-Mann
>> undoubtedly filled that position in the 1950's and 60's, so I think
>> Klauder may have been a bit behind the times.
>
>Making the nucleons made up of other particles is more similar to the
>epicycles. The true challenge is to describe all particles, including
>leptons, through a unique and simple motion.
>
They are. Fermions are described by the Dirac equation.

Peter

unread,
Mar 2, 2007, 4:06:35 PM3/2/07
to
"Cl\.Massé" <ret...@contactprospect.com> writes:

> > Thus spake Peter <end...@dekasges.de>
>
> >> You can deduce Schrödinger's equation from classical mechanics
> >> *axiomatically*, ie, without assuming h, wave-particle dualism and the
> >> like, see Enders & Suisky, Int. J. Theor. Phys. 2005 (I can email a copy
> >> at request). The clue is to start not with Newton's, but with Euler's
> >> axiomatics.
>
> First of all, I don't see what *axiomatically* has special.

It has special that you don't first puts into the theory what later comes
out. For instance, when you presupposes that there is a quantum of action, it
will be in you theory. Such jumps have led to the difficulties to interpret
the new formalisms invented by Heisenberg and Schrödinger.

The clou is to start from a theory that is sufficient flexible and to go step
by step without making new axiomatic assumptions. In the way mentioned above,
it is possible to fulfill 4 requirements Schrödinger has posed for any
quantization.

> Indeed, the
> least action principle already contains *wave mechanics*.

It does as much and as less as the Chapman-Kolmogorov equation 'contains'.
The latter 'contains' also Maxwell's microscopic equations. But you will
neither of them obtain from it without specifying the Green's function. In
other words, without specifying the Lagrange function, you don't get any
physics out of the least action principle.


> But QM can't be
> true without experimental evidence saying so, what will never spring from a
> sheet of paper full of symbols.

Why being aggressive? Of course, like Newton's Laws, the axioms or basic
equations and their consequences, resp., have to be tested experimentally.



> That said, Schrödinger equation isn't QM...

I agree, Schrödinger's equation is only a part of quantum mechanics. But you
must differenciate between the equation and its interpretation. There is one
equation, but many interpretations.

As a matter of fact, an axiomatic deduction of an equation provides one with
valuable hints of its interpretation.

For instance, Schrödinger (1826, 4th Communication) has interpreted |psi(x)|
^2 as a "weight function" for the configuration 'x'. A similar interpretation
emerges during the derivation cited above.

As a consequence, the wave functions of a free quantum (Schrödinger) particle
are normalizable (unfortunately, I have realized this only after that paper
and my book were printed). The approaches you have in mind yield the 'ugly',
unphysical result they aren't; at least is this stated in all textbooks I
know. (Actually, I have learned it from Eugene Stefanovich's book
'Relativistic Quantum Dynamics', arXiv.)

> , it can model classical systems as
> well.

How? :-o

> We have to add the projection postulate, and above all to know what
> to do with the infinity of states that this generalization of CM brings
> with itself.

What exactly do you have in mind?

> What is a dead and alive cat? Does it exist? Can it be observed?

IMHO, the cat problem is one of the contradictions that arise when trying to
introduce too much classical viewpoints into the theory.

If one just compare the Schrödinger equation with Newton's equation of
motion, one faces two problems at once: Different states and different
motions. Additionally, most think in terms of Laplace's notion of state
(Laplace's deamon), while at least the stationary quantum states are much
closer to Newton's notion of state (the state of a body is described by its
momentum): the stationary quantum states of a single electron is - despite of
spin - described by 3 quantum numbers (like 3 components of momentum).


> Clearly, even with some equations in common, we are in presence of two

> fundamentally different theories,...

Many difficulties in the understanding of quantum theory stem from stressing
the differences to classical physics. It helps a lot to study also the common
parts, eg, the existence of conservation laws, of minimum principles, of
states etc.


> ... and the measurement problem is its


> illustration, being at their junction.

It is one of several junctions

> Classical objects must have very
> special states, which doesn't evolve into each other through the
> Schrödinger equation, even if decoherence is taken into account.

Rather the opposite is true:
For [oscillating] ions ... the set of stationary states is less than for the
bodies of our experience. (Einstein, 'Planck's theory of radiation and the
theory of specific heat, 1907, p.184)

BTW, in this paper, Einstein uses Newton's notion of state and shows that the
difference between classical and quantum statistics has nothing to do with
the indistinguishability of quantum particles (equal bodies in equal
Newtonian states are indistinguishable as well). Furthermore, Einstein's
approach avoids Gibbs' paradox, but this is another story of 'good
axiomatics'.


Best wishes,
Peter


microscopic Maxwell equations and the Lorentz force exhibit exactly this
form, in order that charged bodies move according to the laws of common
Hamiltonian mechanics :-)

Cl.Massé

unread,
Mar 3, 2007, 1:08:02 PM3/3/07
to
>>>> But where do we get the principles?

"Oh No" <No...@charlesfrancis.wanadoo.co.uk> a écrit dans le message de
news: cYD5ZCFX...@charlesfrancis.wanadoo.co.uk

>>> From the manner in which we define measured quantities.

There are many manner we have to choose from, including the manner we still
haven't imagined. For instance, the manner Einstein use to define distance
isn't directly given, that's what stalled the other physicists, although
they had definitions too. And there are quantities that aren't or wasn't
necessarily known, for example heat quantity, mole number, or magnetic field
strength.

>>>> And if they are false?

>>> Definitions cannot be false.

By definition, a definition isn't knowledge, that's why they can't be false.
But they may be useless if there is no knowledge to express with them.

>>>> Practically, we
>>>> get the principles through imagination using experimental data.

>>> No. What I am saying is that, since Einstein, Von Neumann and Dirac, we
>>> no longer need to induce from data as the basis of scientific law.

And not inducing from data, physics no longer advances fundamentally. Von
Neumann discouraged even the search of other principles, by implying that
reality should be investigated through the theories we already have. There
are the copycats of Einstein who attempt to find The Group, from SU(5) to
supersymmetry, without any interesting result. The scientific community is
entered in a state of self satisfaction that is its worst enemy. The very
existence of this group is the testimony that today, it is forbidden to
think. Just define and listen to the experts.

>>> But then, later still, the principle proved true, and we use it all the
>>> time in Fourier analysis. Not in this instance of course; it would be
>>> far too complicated. But the underlying principle holds.

No, for a simple reason: it was in the frame of the geocentric system and of
absolute space, the principles didn't include the laws of dynamics. It
isn't a mere transformation like Fourier since that implies that the motion
of the earth is known, which was impossible unless the stars are postulated
to be fixed. It didn't captured reality in its simplicity, and that is what
is expected from a physical theory.

Kepler thought that the orbit should be simple and symmetric, including the
one of earth around the sun, and from that postulated his three laws, which
don't follow directly from the experimental data. He introduced the first
dynamical notions.

Oh No

unread,
Mar 3, 2007, 4:30:52 PM3/3/07
to
Thus spake Cl.Massé <ret...@contactprospect.com>

>>>>> But where do we get the principles?
>
>"Oh No" <No...@charlesfrancis.wanadoo.co.uk> a écrit dans le message de
>news: cYD5ZCFX...@charlesfrancis.wanadoo.co.uk
>
>>>> From the manner in which we define measured quantities.
>
>There are many manner we have to choose from, including the manner we still
>haven't imagined.

The only fundamental one's we have to define are the measurement of time
and position. Everything else is defined in terms of these.

> For instance, the manner Einstein use to define distance
>isn't directly given, that's what stalled the other physicists, although
>they had definitions too.

Indeed, but Bondi used the radar method as the basis of special
relativity, and measured time and distance in a single process.

>
>
>>>> No. What I am saying is that, since Einstein, Von Neumann and Dirac, we
>>>> no longer need to induce from data as the basis of scientific law.
>
>And not inducing from data, physics no longer advances fundamentally. Von
>Neumann discouraged even the search of other principles, by implying that
>reality should be investigated through the theories we already have.

Indeed it should. A great deal can be deduced just by putting together
quantum theory and relativity. That has lead to quantum electrodynamics,
and if science had been pursued like this it would have lead much
further.

>There
>are the copycats of Einstein who attempt to find The Group, from SU(5) to
>supersymmetry, without any interesting result.

These are not copycats of Einstein. These are people who haven't begun
to understand Einstein's approach to science. They postulate stuff from
thin air, and it is not surprising they get no results.

> The scientific community is
>entered in a state of self satisfaction that is its worst enemy. The very
>existence of this group is the testimony that today, it is forbidden to
>think. Just define and listen to the experts.

It would be better to listen to the true experts, like Einstein, Dirac
Von Neumann and Feynman.


>
>
>Kepler thought that the orbit should be simple and symmetric, including the
>one of earth around the sun, and from that postulated his three laws, which
>don't follow directly from the experimental data. He introduced the first
>dynamical notions.
>

Actually, on a point of history, Kepler did no such thing. He worked
exclusively from empirical data, the measurements of Tycho de Brahe. He
expected it to be complicated and was held up for years because he
didn't seriously consider to try the ellipse. He did not introduce
dynamical notions, but expressed three kinematic laws. The dynamical
notions came from Galileo principally I believe. I am not sure he was
first to express them, but he got close to a coherent expression. The
main credit goes to Newton of course, who picked up on the correct
notions, in among a huge amount of dross floating around at the time,
and built the mathematical apparatus for dealing with it.

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