resonance states of the neutron

[d.086@hotmail.com]

Hi,

The neutron is believed to have some sort of internal structure. I'm
not up on current quark theory. The free neutron decays with a half
life of ~15 min according to:

n -> p + e + 1.29 MeV, (ignore neutrinos)

That's a lot of energy per unit mass. Fortunately the relatively long
decay time provides some kind of "get away from danger grace time".

However, in the event of a relatively high energy inelastic nuclear
collision, internal resonance states of the neutron might be excited
that might enhance the rate of decay. That would make high kinetic
energy neutrons more dangerous than might be expected from the value
of the kinetic energy alone. I'm thinking of processes that might take
place in less than a millisecond.

My questionis to any quark experts out there: Are internal resonance
states of the neutron known that might effectively 'catalyze' more
rapid release of neutron energy?

[Uncle Al]

d.086@hotmail.com wrote:
>
> Hi,
>
> The neutron is believed to have some sort of internal structure. I'm
> not up on current quark theory. The free neutron decays with a half
> life of ~15 min according to:
>
> n -> p + e + 1.29 MeV, (ignore neutrinos)

> That's a lot of energy per unit mass. Fortunately the relatively long
> decay time provides some kind of "get away from danger grace time".

What does that mean? Look up the mean velocity of a thermal neutron.
Can you run supersonic? Compare rads with rems for beta-rays and fast
neutrons.

> However, in the event of a relatively high energy inelastic nuclear
> collision, internal resonance states of the neutron might be excited
> that might enhance the rate of decay. That would make high kinetic
> energy neutrons more dangerous than might be expected from the value
> of the kinetic energy alone. I'm thinking of processes that might take
> place in less than a millisecond.

High energy neutrons decay with *longer* externally observed
half-lives - Special Relativity.

> My questionis to any quark experts out there: Are internal resonance
> states of the neutron known that might effectively 'catalyze' more
> rapid release of neutron energy?

H-bomb secondaries propagate without any exotic corrections for fast
(2.45 MeV for D+D, 14.1 Mev for D+T) neutron decay.

--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/lajos.htm#a2

[d.086@hotmail.com]

On Apr 28, 6:11 pm, Uncle Al <Uncle...@hate.spam.net> wrote:

> What does that mean?

Metaphorical language.

>
> High energy neutrons decay with *longer* externally observed
> half-lives - Special Relativity.
>
> > My questionis to any quark experts out there: Are internal resonance
> > states of the neutron known that might effectively 'catalyze' more
> > rapid release of neutron energy?
>
> H-bomb secondaries propagate without any exotic corrections for fast
> (2.45 MeV for D+D, 14.1 Mev for D+T) neutron decay.

We know all that. But you haven't answered the question

Let's use the device of metaphor to illuminate the question better.
Let's say you have a chemical substance that is unstable and decays
with a half life of 15 minutes at a specific temperature. At that
temperature, energy is distributed among internal degrees of freedom
and Boltzman statistics and kinetic factors controls the rate at which
molecules surmount the energy barrier and decay to product(s). When
you raise the temperature, there is a greater amount of energy
distributed amoung the internal degrees of freedom and molecules
surmount the kinetic energy barrier at a faster rate.

Now the neutron is said to have internal structure and weak force
mediated beta decay. I don't know all the details. My question is
whether it is known whether internal degrees of freedom can be excited
within the neutron by inelastic collision and increase the rate of
beta decay. This is unrelated to relativistic effects. Is there a
known quantum mechanical energy level diagram for the neutron? If so
then Boltzman statistics and kinetic theory would allow prediction of
enhanced decay rate. The nucleus is held together by the strong force
and it does have higher energy states. These higher energy states can
be accessed by inelastic collision with neutrons or charged particles,
by neutron absorbtion, by high energy EM excitation all to enhance the
rate of nuclear reactions, typically fission energy release.

Do I make myself clear? The neutron is said to have internal
structure. If so then there ought to be some expectations about its
behavior. BTW this may be controversial but there are plenty of
nuclear rate processes whose rate changes at temperatures near
ambient. There are isotopes whose rate of beta decay or electron
capture decay depend on crystal field (chemical) effects. To put my
question in the most simple terms, is the rate of neutron beta decay
temperature dependent?

[Uncle Al]

d.086@hotmail.com wrote:
>
> On Apr 28, 6:11 pm, Uncle Al <Uncle...@hate.spam.net> wrote:
>
> > What does that mean?
>
> Metaphorical language.
>
> >
> > High energy neutrons decay with *longer* externally observed
> > half-lives - Special Relativity.
> >
> > > My questionis to any quark experts out there: Are internal resonance
> > > states of the neutron known that might effectively 'catalyze' more
> > > rapid release of neutron energy?
> >
> > H-bomb secondaries propagate without any exotic corrections for fast
> > (2.45 MeV for D+D, 14.1 Mev for D+T) neutron decay.
>
> We know all that. But you haven't answered the question
>
> Let's use the device of metaphor to illuminate the question better.
> Let's say you have a chemical substance that is unstable and decays
> with a half life of 15 minutes at a specific temperature. At that
> temperature, energy is distributed among internal degrees of freedom
> and Boltzman statistics and kinetic factors controls the rate at which
> molecules surmount the energy barrier and decay to product(s). When
> you raise the temperature, there is a greater amount of energy
> distributed amoung the internal degrees of freedom and molecules
> surmount the kinetic energy barrier at a faster rate.
>
> Now the neutron is said to have internal structure and weak force
> mediated beta decay. I don't know all the details. My question is
> whether it is known whether internal degrees of freedom can be excited
> within the neutron by inelastic collision and increase the rate of
> beta decay. This is unrelated to relativistic effects. Is there a
> known quantum mechanical energy level diagram for the neutron? If so
> then Boltzman statistics and kinetic theory would allow prediction of
> enhanced decay rate. The nucleus is held together by the strong force
> and it does have higher energy states. These higher energy states can
> be accessed by inelastic collision with neutrons or charged particles,
> by neutron absorbtion, by high energy EM excitation all to enhance the
> rate of nuclear reactions, typically fission energy release.
>
> Do I make myself clear? The neutron is said to have internal
> structure. If so then there ought to be some expectations about its
> behavior. BTW this may be controversial but there are plenty of
> nuclear rate processes whose rate changes at temperatures near
> ambient. There are isotopes whose rate of beta decay or electron
> capture decay depend on crystal field (chemical) effects. To put my
> question in the most simple terms, is the rate of neutron beta decay
> temperature dependent?

Given substructure, where is the neutron's electric dipole moment?
Its electric quadrupole moment?

<http://minoserv.maps.susx.ac.uk/~nedm/method1.htm>
|d| < 3.0 10^(-26) e-cm

Why would fractional eV externals affect MeV nuclear chemistry?
(Except for electron capture inverse beta-decay where the kinetics are
not nuclear)

Newton was wrong. Get over it. Quantum mechanics is the proper
model.

--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/lajos.htm#a2

[d.086@hotmail.com]

> H-bomb secondaries propagate without any exotic corrections for fast
> (2.45 MeV for D+D, 14.1 Mev for D+T) neutron decay.

H-bomb secondaries undergo disassembly within nanoseconds so any
second order correction for neutron decay rate is insignificant (at
that time scale).

[d.086@hotmail.com]

On Apr 29, 4:06 pm, d....@hotmail.com wrote:

> To put my
> question in the most simple terms, is the rate of neutron beta decay
> temperature dependent?

I don't seem to be making any progress in probing the minds of quark
experts so I'll use the metaphorical device again to rephrase the
question.

The neutron is a spin 1/2 particle and so neutron magnetic resonance
spectroscopy exists and at a field strength of 14.7 Tesla the
resonance frequency of the neutron is around 30 MHz, (IIRC). It is
known that at very low temperatures, the neutron undergoes total
reflection from the walls of many materials. So, it is possible to do
long time neutron magnetic resonance studies, except for the
complication that the neutron decays. I have no knowledge of the
magnetic resonance of unstable nuclei (it is too dangerous) so I
cannot use that for constructing another metaphor. But I do have
knowledge of electron spin resonance. In ESR one selects an electron
spin label that is long lived and one generally studies spin labeled
molecules that are long lived. However, if one's molecule or one's
spin label decays in a time of about 15 minutes then one would expect
that decay to be reflected in ESR line shape or in the time dependent
signal decay. If only one decay mechanism pertains then one would see
only monoexponential decay. If more than one decay mechanism pertains
then one would expect to observe biexponential or multiexponential
signal decay. Now the mathematical analysis of noisy multiexponential
decay is almost intractable so such analysis is almost on the
forefront of mathematics, AFAIK.

However, my rephrased metaphorical question is directed at experts in
neutron magnetic resonance. Has any multiexponential signal decay
analysis of free neutron magnetic resonance been derived? If so that
would shed some light on the question of whether neutron beta decay is
temperature dependent and on the existence of resonance states of the
neutron. That should provide some kind of validation for the quark
experts. I'm an experimentalist. So far I have not seen sufficient
experimental validation to justify me putting sufficient effort into
the mastery of quark theory.

[J. J. Lodder]

<d.086@hotmail.com> wrote:

> Do I make myself clear? The neutron is said to have internal
> structure. If so then there ought to be some expectations about its
> behavior. BTW this may be controversial but there are plenty of
> nuclear rate processes whose rate changes at temperatures near
> ambient. There are isotopes whose rate of beta decay or electron
> capture decay depend on crystal field (chemical) effects.

That is an electron density effect, not a temperature effect.
(except indirectly)

> To put my
> question in the most simple terms, is the rate of neutron beta decay
> temperature dependent?

To make dent in the neutron decay rate
you need -huge- electron densities.
Think white dwarf/neutron star,

Jan

[Uncle Al]

d.086@hotmail.com wrote:
>
> > H-bomb secondaries propagate without any exotic corrections for fast
> > (2.45 MeV for D+D, 14.1 Mev for D+T) neutron decay.
>
> H-bomb secondaries undergo disassembly within nanoseconds so any
> second order correction for neutron decay rate is insignificant (at
> that time scale).

Room temp is 0.025 eV; neutron half-life is 613.9 sec at 4 kelvins
(3.45x10^(-4) eV). Assume it is unchanged at room temp. What follows
is therefore *very* conservative.

<http://www.ornl.gov/info/ornlreview/v37_1_04/article_17.shtml>

Kinetics is exponential with temp via the Arrhenius equation

k = Ae^[-E_a/RT]

Boosting the absolute temp by a factor of 98 million (0.025 eV to 2.45
MeV) will decrease the half-life by a factor of e^(98 million) or
10^(42,560,859). Tell Uncle Al how nanoseconds are large compared
with

(613.9 seconds)/10^(42.56 million)

Uncle Al grants you a slop factor of 10^(42 million). Tell Uncle Al
how nanoseconds are large compared with

(613.9 seconds)/10^(560,859)

Still too pessimistic for possibly changing decay mechanisms? Allow a
slop factor of 10^(42.5608 million)

(613.9 seconds)/10^(59)

That is 47 orders of magnitude smaller than nanoseconds. H-bombs and
nuclear reactors (1 MeV fission neutrons must travel to repeatedly
bounce off moderator atoms) would not work by a huge margin if neutron
half-life were inversely temperature dependent. The Original Poster
is a simpleton.

--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/lajos.htm#a2

[John Park]

(d.086@hotmail.com) writes:
> On Apr 29, 4:06=A0pm, d....@hotmail.com wrote:
>
>> To put my
>> question in the most simple terms, is the rate of neutron beta decay
>> temperature dependent?
>
> I don't seem to be making any progress in probing the minds of quark
> experts so I'll use the metaphorical device again to rephrase the
> question.
>
> The neutron is a spin 1/2 particle and so neutron magnetic resonance
> spectroscopy exists and at a field strength of 14.7 Tesla the
> resonance frequency of the neutron is around 30 MHz, (IIRC). It is
> known that at very low temperatures, the neutron undergoes total
> reflection from the walls of many materials. So, it is possible to do
> long time neutron magnetic resonance studies, except for the
> complication that the neutron decays. I have no knowledge of the
> magnetic resonance of unstable nuclei (it is too dangerous) so I
> cannot use that for constructing another metaphor. But I do have
> knowledge of electron spin resonance. In ESR one selects an electron
> spin label that is long lived and one generally studies spin labeled
> molecules that are long lived. However, if one's molecule or one's
> spin label decays in a time of about 15 minutes then one would expect
> that decay to be reflected in ESR line shape or in the time dependent
> signal decay. If only one decay mechanism pertains then one would see
> only monoexponential decay. If more than one decay mechanism pertains
> then one would expect to observe biexponential or multiexponential
> signal decay. Now the mathematical analysis of noisy multiexponential
> decay is almost intractable so such analysis is almost on the
> forefront of mathematics, AFAIK.

I'm not sure how far you're taking the metaphor. To materially alter the ESR
lineshape, any decay process would have to have lifetme of the order of
nanoseconds (or maybe a large fraction of a microsecond). To follow neutron
decay by MR one would need to measure linwidths to sub-millihertz accuracy
or monitor signal intensity for an hour or so.

I haven't done neutron MR but used to work with ESR; my guess is that the
required measurements are difficult

[...]

--John Park

[Gerry Quinn]

In article <481B397F.4D4CA39B@hate.spam.net>, UncleAl0@hate.spam.net
says...

> Kinetics is exponential with temp via the Arrhenius equation
>
> k = Ae^[-E_a/RT]
>
> Boosting the absolute temp by a factor of 98 million (0.025 eV to 2.45
> MeV) will decrease the half-life by a factor of e^(98 million) or
> 10^(42,560,859). Tell Uncle Al how nanoseconds are large compared
> with

Does this argument apply also to the decay of, say, Uranium or Radium?
Their nuclei, after all, are certainly capable of entering high energy
vibrational states. If not, perhaps you would care to explain why it
must apply to the decay of the neutron.

> That is 47 orders of magnitude smaller than nanoseconds. H-bombs and
> nuclear reactors (1 MeV fission neutrons must travel to repeatedly
> bounce off moderator atoms) would not work by a huge margin if neutron
> half-life were inversely temperature dependent. The Original Poster
> is a simpleton.

The OP never asserted that the decay rate would be inversely dependent
on temperature - he peoposed, rather, that resonant states might be
thermally induced, and would result in an increased decay rate. I agree
that his speculation of a millisecond decay rate is implausible - even
if neutrons have accessible low energy vibrational states, which seems a
bit implausible. But you say nothing here that eliminates the
possibility of some such effect.

- Gerry Quinn

[d.086@hotmail.com]

On May 3, 2:20 pm, Uncle Al <Uncle...@hate.spam.net> wrote:
> d....@hotmail.com wrote:
>
> > > H-bomb secondaries propagate without any exotic corrections for fast
> > > (2.45 MeV for D+D, 14.1 Mev for D+T) neutron decay.
>
> > H-bomb secondaries undergo disassembly within nanoseconds so any
> > second order correction for neutron decay rate is insignificant (at
> > that time scale).
>
> Room temp is 0.025 eV; neutron half-life is 613.9 sec at 4 kelvins
> (3.45x10^(-4) eV).  Assume it is unchanged at room temp.  What follows
> is therefore *very* conservative.
>
> <http://www.ornl.gov/info/ornlreview/v37_1_04/article_17.shtml>
>
> Kinetics is exponential with temp via the Arrhenius equation
>
> k = Ae^[-E_a/RT]

You cannot use reductio ad absurdum to prove that the Arrhenius
equation does not apply to neutron decay. At first blush there are two
unknowns, A, the transmission factor and E_a the activation energy. So
you cannot make approximations from the equation in any meaningful
manner, unless you make assumptions about their values. At second
blush, you need to have a more sophisticated appreciation of kinetic
theory to understand the Arrhenius equation. Only over small
temperatures is it correct to approximate the transmission factor A as
a constant. One can derive a functional form for the transmission
factor from assumptions but that is not good science when you try to
apply the Arrhenius equation outside its normal domain of application.
A good scientist would try to find the functional form for the
temperature dependance of the transmission factor by fitting
experimental data to candidate functional forms. After that he might
to try to make conclusions about mechanics.

Another problem is whether the Arrhenius equation is thought to be
derived from classical or quantum statistical assumption and if the
activation energy E_a should be treated as temperature dependendent.
Avtivation energies vary with environmental factors. That is what
catalysis is all about. That is why it is meaningful to ask if a
inelastic collision can catalyze an enhanced rate of neutron decay.

Given all these unknowns, the only conclusion that can be obtained
from the Arrhenius equation is that the rate of decay will be faster
at a high temperature. How much is unknown. I don't think anyone will
disagree with that conclusion.

On the other hand if we had some idea about resonance states of the
neutron we would have some feeling for temperature dependence of
neutron decay and we would have some feeling for enhancement of decay
by inelastic collision. The problem is that the decay mechanism that
we were all taught in grade school is highly simplistic. Hence we end
up asking stupid questions and getting stupid answers in reply.

[Uncle Al]

Gerry Quinn wrote:
>
> In article <481B397F.4D4CA39B@hate.spam.net>, UncleAl0@hate.spam.net
> says...
>
> > Kinetics is exponential with temp via the Arrhenius equation
> >
> > k = Ae^[-E_a/RT]
> >
> > Boosting the absolute temp by a factor of 98 million (0.025 eV to 2.45
> > MeV) will decrease the half-life by a factor of e^(98 million) or
> > 10^(42,560,859). Tell Uncle Al how nanoseconds are large compared
> > with
>
> Does this argument apply also to the decay of, say, Uranium or Radium?
> Their nuclei, after all, are certainly capable of entering high energy
> vibrational states. If not, perhaps you would care to explain why it
> must apply to the decay of the neutron.
>
> > That is 47 orders of magnitude smaller than nanoseconds. H-bombs and
> > nuclear reactors (1 MeV fission neutrons must travel to repeatedly
> > bounce off moderator atoms) would not work by a huge margin if neutron
> > half-life were inversely temperature dependent. The Original Poster
> > is a simpleton.
>
> The OP never asserted that the decay rate would be inversely dependent
> on temperature - he peoposed, rather, that resonant states might be
> thermally induced, and would result in an increased decay rate. I agree
> that his speculation of a millisecond decay rate is implausible - even
> if neutrons have accessible low energy vibrational states, which seems a
> bit implausible. But you say nothing here that eliminates the
> possibility of some such effect.
>
> - Gerry Quinn

Gee Gerry - Uncle Al awarded you a factor of 10^40 slop in the gears
and it still wasn't enough! Why don't you engage the same enthusiasm
for volunteering a temperature-coupled mechanism for neutron half-life
decay alteration? Goodness, there are none?

No proposed pathway for stellar element synthesis couples isotope
decay half-lives to ambient temp. Temperature-dependent *reaction*
cross-sections are highly temperature dependent - collision energy.
Nuclear decay and especially neutron decay are insensitive to ambient
temperature. A pack of neutrons toodling about at 50 m/s or zipping
about at 10% of lightspeed, relative to the observer, don't change
their internals. H-bomb secondaries pop as predicted, ditto fission
of their depleted uranium casings by fast neutron capture. Reactions
proceed as modeled.

That isn't true for a pack of molecules. There are rotational,
vibrational, and electronic transitions that strongly couple to
temperature by well studied mechanisms. Neutron spherical symmetry
makes such couplings moot. Tell us what the symmetry-allowed
corresponding mechanisms are for neutrons short of particle
accelerator chemistry.

The singular exception is electron capture decay - because it is
mediated by s-electron antinode density at the nucleus. Mere
oxidation state can change decay rate by percentages. A fully ionized
nucleus would be indefinitely stable.

--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/lajos.htm#a2

[Ulf Torkelsson]

d.086@hotmail.com skrev:

[some text snipped]

> Now the neutron is said to have internal structure and weak force
> mediated beta decay. I don't know all the details.

The neutron consists of one up-quark (u) and two down-quarks (d).

> My question is
> whether it is known whether internal degrees of freedom can be excited
> within the neutron by inelastic collision and increase the rate of
> beta decay. This is unrelated to relativistic effects. Is there a
> known quantum mechanical energy level diagram for the neutron?

There is a partially known diagram of the energies of the different
states that udd can exist in. Each one of these levels are usually
considered to be their own kind of elementary particle or resonance.
The energy differences between these different levels are typically 100s
of GeV. For instance the neutron, which is a spin 1/2 particle, has a
mass of 940 GeV, and the spin 3/2 udd particle is Delta-0, which has an
energy of 1232 GeV. The lifetime of Delta-0 is 1e-23 s.

[ Mod. note: That would be MeV instead of GeV. -ik ]

> If so
> then Boltzman statistics and kinetic theory would allow prediction of
> enhanced decay rate.

In theory yes, but the energy gaps between the different particles
are so huge that there will not be any effect at any temperature that
can be achieved in the laboratory.

Ulf Torkelsson

[Richard Saam]

Ulf Torkelsson wrote:
> d.086@hotmail.com skrev:
>
> [some text snipped]
>
>> Now the neutron is said to have internal structure and weak force
>> mediated beta decay. I don't know all the details.
>
> The neutron consists of one up-quark (u) and two down-quarks (d).
>
>> My question is
>> whether it is known whether internal degrees of freedom can be excited
>> within the neutron by inelastic collision and increase the rate of
>> beta decay. This is unrelated to relativistic effects. Is there a
>> known quantum mechanical energy level diagram for the neutron?
>
> There is a partially known diagram of the energies of the different
> states that udd can exist in. Each one of these levels are usually
> considered to be their own kind of elementary particle or resonance. The
> energy differences between these different levels are typically 100s of
> GeV. For instance the neutron, which is a spin 1/2 particle, has a mass
> of 940 GeV, and the spin 3/2 udd particle is Delta-0, which has an
> energy of 1232 GeV. The lifetime of Delta-0 is 1e-23 s.
>
> [ Mod. note: That would be MeV instead of GeV. -ik ]

Back of the envelop calculation:
Assuming that the lifetime of Delta-0 1E-23 sec is a reflection of a
nuclear frequency 1/1E-23 or 1e23 /sec, then
nuclear energy quantum = h * 1E23 ~400 Mev
(close to above neutron mass 940 MeV)
nuclear wave length ~ c/1e23 ~3E-13 cm
(approximately the observed nuclear proton diameter 1.7E-13 cm)
nuclear temperature ~ h * 1E23/boltzmann = 5E12 K

It is remarkable that these extreme energies
reside (and do not normally express themselves) in our 310 K bodies.

Richard Saam

>
>> If so
>> then Boltzman statistics and kinetic theory would allow prediction of
>> enhanced decay rate.
>
> In theory yes, but the energy gaps between the different particles are
> so huge that there will not be any effect at any temperature that can be
> achieved in the laboratory.
>
> Ulf Torkelsson
>

[Tom Roberts]

Richard Saam wrote:
> nuclear temperature ~ h * 1E23/boltzmann = 5E12 K
> It is remarkable that these extreme [temperatures]
> reside (and do not normally express themselves) in our 310 K bodies.

It's not really very remarkable, because it's due to the very same
mechanism that makes atoms stable: quantum mechanics. As these systems
(nuclei and atoms) are in their ground state, they cannot radiate. Their
internal structure prevents them from absorbing thermal radiation from
their surroundings (its energy is inadequate to excite their internal
degrees of freedom). So they cannot exchange energy with their
surroundings, and thus cannot come into thermal equilibrium with them.

While there's nothing wrong with discussing the temperature of nuclei,
in most cases people consider them as point particles to which an
internal temperature cannot be assigned. Indeed in many cases this is
done for atoms as well. This is valid when their enforced isolation and
great difference in energy scales applies; it fails when either the
isolation or scale difference doesn't apply (e.g. in flames and He-Ne
lasers for atoms, thermonuclear weapons for nuclei, etc.).

Tom Roberts

[Jonathan Thornburg [remove -animal to reply]]

In sci.physics.research Tom Roberts <tjroberts137@sbcglobal.net> wrote:
> As these systems
> (nuclei and atoms) are in their ground state, they cannot radiate. Their
> internal structure prevents them from absorbing thermal radiation from
> their surroundings (its energy is inadequate to excite their internal
> degrees of freedom). So they cannot exchange energy with their
> surroundings, and thus cannot come into thermal equilibrium with them.
>
> While there's nothing wrong with discussing the temperature of nuclei,
> in most cases people consider them as point particles to which an
> internal temperature cannot be assigned. Indeed in many cases this is
> done for atoms as well. This is valid when their enforced isolation and
> great difference in energy scales applies; it fails when either the
> isolation or scale difference doesn't apply (e.g. in flames and He-Ne
> lasers for atoms, thermonuclear weapons for nuclei, etc.).

As another example of a system with components having wildly different
"temperatures" which don't seem to equilibriate, consider the stars in
our galaxy as "gas" particles. In the solar neighborhood typical stellar
random velocities might be a few 10s of km/second. Equating the kinetic
energy of a typical star moving at 15 km/second with 3/2 k T gives a
truly "astronomical" temperature (around 10^61 Kelvin if my arithmetic
is right). Fortunately for our continued existence, there's no easy way
for that kinetic energy to equilibriate with (say) the ~300K kinetic
temperature of the Earth's biosphere.

--
-- From: "Jonathan Thornburg [remove -animal to reply]" <J.Thornburg@soton.ac-zebra.uk>
School of Mathematics, U of Southampton, England
"If cattle and horses, or lions, had hands, or were able to draw with
their feet and produce the works which men do, horses would draw the
forms of gods like horses, and cattle like cattle, and they would make
their gods' bodies the same shape as their own." -- Xenophanes, c.500 BCE

[Richard Saam]

Tom Roberts wrote:
> Richard Saam wrote:
>> nuclear temperature ~ h * 1E23/boltzmann = 5E12 K
>> It is remarkable that these extreme [temperatures]
>> reside (and do not normally express themselves) in our 310 K bodies.
>
> It's not really very remarkable, because it's due to the very same
> mechanism that makes atoms stable: quantum mechanics. As these systems
> (nuclei and atoms) are in their ground state, they cannot radiate. Their
> internal structure prevents them from absorbing thermal radiation from
> their surroundings (its energy is inadequate to excite their internal
> degrees of freedom). So they cannot exchange energy with their
> surroundings, and thus cannot come into thermal equilibrium with them.

This is of course true, but it is still remarkable that such large
energy differences exist in close proximity

> While there's nothing wrong with discussing the temperature of nuclei,
> in most cases people consider them as point particles to which an
> internal temperature cannot be assigned.
But is this an oversimplification?
As previously posted there is an approximated relationship between
nuclear dimensions (lambda), frequency (nu), speed of light (c), plancks
constant (h), nuclear mass (m), boltzmann constant (k) and absolute
temperature (T).

Energy = h * c / lambda = h * nu = m * c^2 = k * T

The vibrating nuclear entity of dimension lambda
expresses itself a mass m = Energy/c^2

> Indeed in many cases this is
> done for atoms as well. This is valid when their enforced isolation and
> great difference in energy scales applies; it fails when either the
> isolation or scale difference doesn't apply (e.g. in flames and He-Ne
> lasers for atoms, thermonuclear weapons for nuclei, etc.).
>
> Tom Roberts
>
Would these concepts (at a much different energy condition)
be applicable to 'dark matter'?

The argument is routinely made that any 'dark matter'
should be in thermal equilibrium with the CMBR at 2.7 K
and this equilibrium surely would occur within 13.7 billion years
after the Big Bang.

What if the 'dark matter' had the properties as you describe
by paraphrasing your above:

> (dark matter) is in its ground state, and cannot radiate. Its
> internal structure prevents it from absorbing thermal radiation from
> its surroundings (its energy is inadequate to excite its internal
> degrees of freedom). So the dark matter cannot exchange energy
> with its surroundings, and thus cannot come into
> thermal equilibrium with them.

A dark matter in the form of a
Bose Einstein Condensate (BEC) may fit this description.

So the concept would be that
extremely cold (~1E9K) chunks of hydrogen BEC
adiabatically created after Big Bang primordial nucleosynthesis
would still partially be with us (<<< 2.7 K)
(gravitationally affecting galactic rotation)
but not electromagnetically observed.

It is understood that the hydrogen nuclei in a BEC
are at ~5E12 K.

Richard D. Saam

[Nicolaas Vroom]

I have a problem in understanding the difference between
deterministic verus non-deterministic as axplained in the following url:
http://en.wikipedia.org/wiki/Deterministic_system_%28philosophy%29

Are the following examples deterministic yes or no:
1. The movement of a round rubber ball with a certain weight,
dropped 1 meter above the centre of a round table.
After a couple of bounces the ball will come to rest at the centre
of the round table.
2. The same as #1 but the ball (same weight) has the same of an
american football.
The ball will not come to rest at the center of the table.
3. The same as #2 but the ball has the shape of a dice
4. The same as #1 but the ball (same weight) is made from glass.
The ball will come to rest, but not at the centre of the table.
5. The movement of the comet Schumacher Levy from just
before its break up into its 20 fragments, until each of those
fragments collided with the planet Jupiter.

IMO non of those examples is deterministic, but that opinion
is in conflict with the information in Wikipedia.

Nicolaas Vroom
http://users.pandora.be/nicvroom/

[guille2306]

On Jun 10, 1:52 pm, "Nicolaas Vroom" <nicolaas.vr...@pandora.be>
wrote:
> I have a problem in understanding the difference between
> deterministic verus non-deterministic as axplained in the following url:http://en.wikipedia.org/wiki/Deterministic_system_%28philosophy%29
>
> Are the following examples deterministic yes or no:
> 1. The movement of a round rubber ball with a certain weight,
> dropped 1 meter above the centre of a round table.
> After a couple of bounces the ball will come to rest at the centre
> of the round table.
> 2. The same as #1 but the ball (same weight) has the same of an
> american football.
> The ball will not come to rest at the center of the table.
> 3. The same as #2 but the ball has the shape of a dice
> 4. The same as #1 but the ball (same weight) is made from glass.
> The ball will come to rest, but not at the centre of the table.
> 5. The movement of the comet Schumacher Levy from just
> before its break up into its 20 fragments, until each of those
> fragments collided with the planet Jupiter.
>
> IMO non of those examples is deterministic, but that opinion
> is in conflict with the information in Wikipedia.
>
> Nicolaas Vroomhttp://users.pandora.be/nicvroom/

Any classical system (i.e., where quantum mechanics plays no role) is
deterministic. Given the equations of evolution and the exact initial
conditions, you can predict exactly the evolution of the system. Of
course there will be problems: maybe you don't know the exact
equations or it is not possible to solve them in a reasonable time
(because of their complexity), and most probably you only have an
approximation of the initial conditions (which is specially bad in
chaotic systems). All of your examples (taken only as classical
systems and forgetting about QM) fall in one of those categories: for
example, even for a perfectly rigid "dice ball" on a perfectly rigid
flat surface, the rest position will depend strongly of the angle
between the first corner to hit the surface and the surface itself.
But, if you repeat the experiment with exactly the same initial
conditions, the ball will do exactly the same. It is, as stated in the
Wikipedia article, a matter of philosophy: you can't predict the
result for practical reasons, but it is predictable in theory.

When quantum mechanics enters the picture things change completely.
Even in theory, if you know the exact initial condition, the most you
can do is predict probabilities for the different results. But here I
have my own question to anyone: we can (in theory) predict the exact
evolution of the wave function of the system, does that means that
system is deterministic, or we should only apply the word
"deterministic" to systems where we can predict the result of the
measurement? I think that the second is the most correct approach, but
I would like to know if there is any consensus about this.

Guillermo

[Nicolaas Vroom]

"guille2306" <guille2306@gmail.com> schreef in bericht
news:f86f6f7d-8ad5-47fa-b474-ef58f1354a10@k13g2000hse.googlegroups.com...
> On Jun 10, 1:52 pm, "Nicolaas Vroom" <nicolaas.vr...@pandora.be>
> wrote:
>> I have a problem in understanding the difference between
>> deterministic verus non-deterministic as explained in the following
url:
http://en.wikipedia.org/wiki/Deterministic_system_%28philosophy%29
>>
>> Are the following examples deterministic yes or no:
>> 5. The movement of the comet Schumacher Levy from just
>> before its break up into its 20 fragments, until each of those
>> fragments collided with the planet Jupiter.
>>
>> IMO non of those examples is deterministic, but that opinion
>> is in conflict with the information in Wikipedia.
>
> Any classical system (i.e., where quantum mechanics plays no role) is
> deterministic. Given the equations of evolution and the exact initial
> conditions, you can predict exactly the evolution of the system. Of
> course there will be problems: maybe you don't know the exact
> equations
In many cases you only know them approximate or nothing at all.

For example fluids through pipes at different speeds.
For example eartquakes
All systems in which human beings are involved.
All systems in which animals are involved.
The beating of my hart.

Do you consider all those systems deterministic ?

> or it is not possible to solve them in a reasonable time
> (because of their complexity), and most probably you only have an
> approximation of the initial conditions (which is specially bad in
> chaotic systems). All of your examples (taken only as classical
> systems and forgetting about QM) fall in one of those categories: for
> example, even for a perfectly rigid "dice ball" on a perfectly rigid
> flat surface, the rest position will depend strongly of the angle
> between the first corner to hit the surface and the surface itself.
Correct
Do you call that determistic ?

> But, if you repeat the experiment with exactly the same initial
> conditions, the ball will do exactly the same.
Only with a computer

> It is, as stated in the
> Wikipedia article, a matter of philosophy: you can't predict the
> result for practical reasons, but it is predictable in theory.

> When quantum mechanics enters the picture things change completely.
> Even in theory, if you know the exact initial condition, the most you
> can do is predict probabilities for the different results.
Because you do not know the internal processes.
The same for all the five examples above.

Calculate probabilities is all what you can do with a "rigid dice"
or a round ball made from glass.
For a round ball from glass: the higher you drop the ball the futher
away (on average) the ball will stop from the point of impact.

> But here I
> have my own question to anyone: we can (in theory) predict the exact
> evolution of the wave function of the system,
Of any system ? How ?

> does that means that
> system is deterministic, or we should only apply the word
> "deterministic" to systems where we can predict the result of the
> measurement? I think that the second is the most correct approach, but
> I would like to know if there is any consensus about this.
>
> Guillermo
>

Anyway the word combination determistic mathematics is a misnomer.
All forms of mathematics is determistic as far as I can see.
For the physical world that is different.
The problem is where do you draw the line
between deterministic and non-deterministic.

Nicolaas Vroom http://users.pandora.be/nicvroom/

[Lou Pecora]

In article <_pf3k.21435$X6.13023@newsfe30.ams2>,
"Nicolaas Vroom" <nicolaas.vroom@pandora.be> wrote:

> I have a problem in understanding the difference between
> deterministic verus non-deterministic as axplained in the following url:
> http://en.wikipedia.org/wiki/Deterministic_system_%28philosophy%29
>
> Are the following examples deterministic yes or no:
> 1. The movement of a round rubber ball with a certain weight,
> dropped 1 meter above the centre of a round table.
> After a couple of bounces the ball will come to rest at the centre
> of the round table.
> 2. The same as #1 but the ball (same weight) has the same of an
> american football.
> The ball will not come to rest at the center of the table.
> 3. The same as #2 but the ball has the shape of a dice
> 4. The same as #1 but the ball (same weight) is made from glass.
> The ball will come to rest, but not at the centre of the table.
> 5. The movement of the comet Schumacher Levy from just
> before its break up into its 20 fragments, until each of those
> fragments collided with the planet Jupiter.
>
> IMO non of those examples is deterministic, but that opinion
> is in conflict with the information in Wikipedia.
>
> Nicolaas Vroom
> http://users.pandora.be/nicvroom/
>

If you have no other assumptions and I am reading this correctly, they
are all deterministic. Where the system ends up (as a trajectory or an
equibrilium point because of friction) only depends on the starting
point in phase space (sometimes called state space). You start the each
case with the same initial conditions (position, velocity, etc.) and it
will end up in exactly the same place. That's determinism. I'm of
course, ignoring quantum effects and noise (as a stochastic forcing)
which make the system not classically deterministic.

--
-- Lou Pecora

[Lou Pecora]

In article <t884k.118888$%B6.71022@newsfe13.ams2>,
Nicolaas Vroom <nicolaas.vroom@pandora.be> wrote:

> > Any classical system (i.e., where quantum mechanics plays no role) is
> > deterministic. Given the equations of evolution and the exact initial
> > conditions, you can predict exactly the evolution of the system. Of
> > course there will be problems: maybe you don't know the exact
> > equations
> In many cases you only know them approximate or nothing at all.
>
> For example fluids through pipes at different speeds.
> For example eartquakes
> All systems in which human beings are involved.
> All systems in which animals are involved.
> The beating of my hart.
>
> Do you consider all those systems deterministic ?

Sure. All evidence so far points to all non-quantum systems as
deterministic. I am ignoring noise here although that is often thought
of as forces from other deterministic systems. Not knowing the
equations is not the point. Gravitational forces are deterministic and
were so before Newton formulated the equations.


> > or it is not possible to solve them in a reasonable time
> > (because of their complexity), and most probably you only have an
> > approximation of the initial conditions (which is specially bad in
> > chaotic systems). All of your examples (taken only as classical
> > systems and forgetting about QM) fall in one of those categories: for
> > example, even for a perfectly rigid "dice ball" on a perfectly rigid
> > flat surface, the rest position will depend strongly of the angle
> > between the first corner to hit the surface and the surface itself.
> Correct
> Do you call that determistic ?

Yes.

> > But, if you repeat the experiment with exactly the same initial
> > conditions, the ball will do exactly the same.
> Only with a computer

?? No, evidence is that it will do the same thing as long as the initial
conditions are the same. You can argue about the ability to set the
initial conditions the same each time, but that is not the same thing as
being deterministic.

--
-- Lou Pecora

[Phil scadden]

> Do you consider all those systems deterministic ?

Just dont confuse "deterministic" with "predictable"
--
Phil Scadden
GNS Science Ltd
764 Cumberland St, Private Bag 1930, Dunedin, New Zealand
Ph +64 3 4799663, fax +64 3 477 5232

[Ian Parker]

On 12 Jun, 20:00, Lou Pecora <pec...@anvil.nrl.navy.mil> wrote:
> In article <t884k.118888$%B6.71...@newsfe13.ams2>,
>  Nicolaas Vroom <nicolaas.vr...@pandora.be> wrote:
>
> > > Any classical system (i.e., where quantum mechanics plays no role) is
> > > deterministic. Given the equations of evolution and the exact initial
> > > conditions, you can predict exactly the evolution of the system. Of
> > > course there will be problems: maybe you don't know the exact
> > > equations
> > In many cases you only know them approximate or nothing at all.
>
> > For example fluids through pipes at different speeds.
> > For example eartquakes
> > All systems in which human beings are involved.
> > All systems in which animals are involved.
> > The beating of my hart.
>
> > Do you consider all those systems deterministic ?
>
> Sure.  All evidence so far points to all non-quantum systems as
> deterministic.  I am ignoring noise here although that is often thought
> of as forces from other deterministic systems.  Not knowing the
> equations is not the point.  Gravitational forces are deterministic and
> were so before Newton formulated the equations.
>
Do you regard chaos as being deterministic? Perhaps it is a
philosophical point. If I take a chaotic sytem in its simplest form,
if I balance a pencil on its point, is that deterministic? Now I can
make the point I am balancing the pencil on as close as possible to
the vertical though the CG. I can do it to 6 figures, 12 10^100
figures but eventually it will fall unpredictably. Clearly the more
figures I have the longer a system stays deterministic.

Chaos is sometimes looked at in topological terms. The pencil balanced
on a point has the simplest topology. If I take a dynamical system and
construct eigenvalues. (We can view this as a kind of homotopy). Some
of these eigenvalues will be pencil points, others will be stable.
Topology, the Hausdorff set gives us a map of instability. With simple
unstable systems we get attractors etc.

The point I must return to again and again is that the dynamics, the
Hamiltonian matrix is unpredictable.

> > > or it is not possible to solve them in a reasonable time
> > > (because of their complexity), and most probably you only have an
> > > approximation of the initial conditions (which is specially bad in
> > > chaotic systems). All of your examples (taken only as classical
> > > systems and forgetting about QM) fall in one of those categories: for
> > > example, even for a perfectly rigid "dice ball" on a perfectly rigid
> > > flat surface, the rest position will depend strongly of the angle
> > > between the first corner to hit the surface and the surface itself.
> > Correct
> > Do you call that determistic ?
>
> Yes.
>
> > > But, if you repeat the experiment with exactly the same initial
> > > conditions, the ball will do exactly the same.
> > Only with a computer
>
> ?? No, evidence is that it will do the same thing as long as the initial
> conditions are the same.  You can argue about the ability to set the
> initial conditions the same each time, but that is not the same thing as
> being deterministic.
>
This is philosopy again, suppose we vary it by 1 part in 10^100, the
end result will be different. Is this determinism? Suppose we move
Pluto 1km and wait a billion yrs. The difference in position will now
be half an orbit.

With a computer results depend on out word length, this has been
proved. If I change (in C) "float" to "double" the results will be
completely different.


- Ian Parker

PS I have not used the Q word anywhere.

[Arnold Neumaier]

guille2306 wrote:

> Any classical system (i.e., where quantum mechanics plays no role) is
> deterministic.

This is far from the truth.

There are plenty of classical systems described by stochastic
differential equations, the simplest being Brownian motion.

Deterministic classical systems are only a convenient approximation
to the more realistic stochastic case.

For example, a deterministic damped harmonic oscillator is obtained
from a stochstic damped harmonic oscillator by completely ignoring
the damping mechanism.


Arnold Neumaier

[Lou Pecora]

In article
<fd9d8c86-f59a-4cea-b798-c699a78c4be7@f36g2000hsa.googlegroups.com>,
Ian Parker <ianparker2@gmail.com> wrote:

> Do you regard chaos as being deterministic? Perhaps it is a
> philosophical point. If I take a chaotic sytem in its simplest form,
> if I balance a pencil on its point, is that deterministic? Now I can
> make the point I am balancing the pencil on as close as possible to
> the vertical though the CG. I can do it to 6 figures, 12 10^100
> figures but eventually it will fall unpredictably. Clearly the more
> figures I have the longer a system stays deterministic.
>
> Chaos is sometimes looked at in topological terms. The pencil balanced
> on a point has the simplest topology. If I take a dynamical system and
> construct eigenvalues. (We can view this as a kind of homotopy). Some
> of these eigenvalues will be pencil points, others will be stable.
> Topology, the Hausdorff set gives us a map of instability. With simple
> unstable systems we get attractors etc.
>
> The point I must return to again and again is that the dynamics, the
> Hamiltonian matrix is unpredictable.

Don't confuse difficulty in prediction, which is what you are saying,
with determinism. Chaotic systems are deterministic. Many can be
modeled well with differential equations which are deterministic.

A pencil balanced on its point is not a chaotic system, although it is a
deterministic system.

> >
> This is philosopy again, suppose we vary it by 1 part in 10^100, the
> end result will be different. Is this determinism? Suppose we move
> Pluto 1km and wait a billion yrs. The difference in position will now
> be half an orbit.

Not philosophy. You are just saying what I said. If you change the
initial conditions, then the outcome changes. That's a tacit admission
that if you do not change the initial conditions, the outcome is the
same.

> With a computer results depend on out word length, this has been
> proved. If I change (in C) "float" to "double" the results will be
> completely different.

Is a computer deterministic? Why? You have remarked a few times that
things are only deterministic on a computer. But a computer is a
physical system. Is it deterministic?

Think that through.

--
-- Lou Pecora

[guille2306]

First of all: as Phil Scadden said before, do not confuse
"deterministic" with "predictable". All your concerns about my answer
can be traced to that problem. One system is deterministic if there is
a mathematical expression that relates the initial physical state and
the final physical state. It doesn't mater if you don't know which is
that mathematical expression or you don't know the initial state with
infinite precision, being deterministic is a property of the system
and not of your capabilities to describe what's going on. Obviously
any deterministic system can be unpredictable (actually, all of them
are at a certain level of precision).

Now my answers:

On Jun 12, 10:52 am, Nicolaas Vroom <nicolaas.vr...@pandora.be> wrote:
> >> I have a problem in understanding the difference between
> >> deterministic verus non-deterministic as explained in the following
>
> url:http://en.wikipedia.org/wiki/Deterministic_system_%28philosophy%29
>
> >> Are the following examples deterministic yes or no:
> >> 5. The movement of the comet Schumacher Levy from just
> >> before its break up into its 20 fragments, until each of those
> >> fragments collided with the planet Jupiter.
>
> >> IMO non of those examples is deterministic, but that opinion
> >> is in conflict with the information in Wikipedia.
>
> > Any classical system (i.e., where quantum mechanics plays no role) is
> > deterministic. Given the equations of evolution and the exact initial
> > conditions, you can predict exactly the evolution of the system. Of
> > course there will be problems: maybe you don't know the exact
> > equations
>
> In many cases you only know them approximate or nothing at all.
>
> For example fluids through pipes at different speeds.
> For example eartquakes
> All systems in which human beings are involved.
> All systems in which animals are involved.
> The beating of my hart.
>
> Do you consider all those systems deterministic ?

The first two are most probably deterministic. The next two involve
too much quantum mechanics to be sure (see below). The last one is in
between of the other two groups.

> > or it is not possible to solve them in a reasonable time
> > (because of their complexity), and most probably you only have an
> > approximation of the initial conditions (which is specially bad in
> > chaotic systems). All of your examples (taken only as classical
> > systems and forgetting about QM) fall in one of those categories: for
> > example, even for a perfectly rigid "dice ball" on a perfectly rigid
> > flat surface, the rest position will depend strongly of the angle
> > between the first corner to hit the surface and the surface itself.
>
> Correct
> Do you call that determistic ?

Yes, see next

> > But, if you repeat the experiment with exactly the same initial
> > conditions, the ball will do exactly the same.
>
> Only with a computer

Not, in the real world. Exactly the same initial conditions will give
exactly the same result. It doesn't mater if you can't really put the
system in that initial state again, in theory it is true (that's why
there is a big IF in the sentence).

> > It is, as stated in the
> > Wikipedia article, a matter of philosophy: you can't predict the
> > result for practical reasons, but it is predictable in theory.
> > When quantum mechanics enters the picture things change completely.
> > Even in theory, if you know the exact initial condition, the most you
> > can do is predict probabilities for the different results.
>
> Because you do not know the internal processes.
> The same for all the five examples above.

Yes and not, see below

> Calculate probabilities is all what you can do with a "rigid dice"
> or a round ball made from glass.
> For a round ball from glass: the higher you drop the ball the futher
> away (on average) the ball will stop from the point of impact.

Not, a classical mechanical system is a huge set of equations, highly
non linear and extremely hard to solve, but that gives only one answer
for one input (again, in theory and if you where able to do the maths
with infinite precision).

> > But here I
> > have my own question to anyone: we can (in theory) predict the exact
> > evolution of the wave function of the system,
>
> Of any system ? How ?

It is figure of speech (that's way it says "in theory"). Again, it
doesn't mater if you know the equation as long as the equation is
there.

> > does that means that
> > system is deterministic, or we should only apply the word
> > "deterministic" to systems where we can predict the result of the
> > measurement? I think that the second is the most correct approach, but
> > I would like to know if there is any consensus about this.
>
> Anyway the word combination determistic mathematics is a misnomer.
> All forms of mathematics is determistic as far as I can see.
> For the physical world that is different.
> The problem is where do you draw the line
> between deterministic and non-deterministic.
>
> Nicolaas Vroomhttp://users.pandora.be/nicvroom/

Well, you're making my point. Any theory in physics IS mathematics, so
any theory in physics IS deterministic.
Now, the difference between classical mechanics and quantum mechanics
is that in the classical world the theory deals with observables, so
there is a mathematical and deterministic path between the position
now (or any other observable) and the position before. In the quantum
world, on the other hand, the theory deals with wave functions, that
are not observables, so there is a mathematical and deterministic path
between the wave function now and the wave function before, but not
anymore between the position now and the position before. In that
sense, one can say that any system in which QM can't be neglected
won't be deterministic, as we can't predict, even in theory, which
will be it's position in the future.

Of course, one can be a purist and say that QM is everywhere, so that
at the end all the world is non-deterministic. But, on the other hand,
one can say that all the wave-function stuff in QM comes from our
inability to describe some underlaying processes (hidden variables?),
and then all the world would be deterministic, even the human mind
(but still, absolutely unpredictable).

Guillermo

[guille2306]

On Jun 12, 9:04 pm, Ian Parker <ianpark...@gmail.com> wrote:

> Do you regard chaos as being deterministic? Perhaps it is a
> philosophical point. If I take a chaotic sytem in its simplest form,
> if I balance a pencil on its point, is that deterministic? Now I can
> make the point I am balancing the pencil on as close as possible to
> the vertical though the CG. I can do it to 6 figures, 12 10^100
> figures but eventually it will fall unpredictably. Clearly the more
> figures I have the longer a system stays deterministic.
>
> Chaos is sometimes looked at in topological terms. The pencil balanced
> on a point has the simplest topology. If I take a dynamical system and
> construct eigenvalues. (We can view this as a kind of homotopy). Some
> of these eigenvalues will be pencil points, others will be stable.
> Topology, the Hausdorff set gives us a map of instability. With simple
> unstable systems we get attractors etc.
>
> The point I must return to again and again is that the dynamics, the
> Hamiltonian matrix is unpredictable.

I fully agree with you on that: chaotic systems are totally
unpredictable. But that doesn't means that they aren't deterministic.
You can find chaos in really simple equations, but they still are
mathematical (and hence deterministic) equations. You raise a valid
point here: which is the definition of deterministic? I'm taking a
system as deterministic when there is a mathematical equation below
that relates the initial and final states. If we can't measure the
initial state with enough precision is our problem, not the system's
one. That's a different issue of being predictable or not (see my
other post).

> This is philosopy again, suppose we vary it by 1 part in 10^100, the
> end result will be different. Is this determinism? Suppose we move
> Pluto 1km and wait a billion yrs. The difference in position will now
> be half an orbit.

Yes, but, if you do the maths with the new position (and infinite
precision) you will get the right answer again.

> With a computer results depend on out word length, this has been
> proved. If I change (in C) "float" to "double" the results will be
> completely different.

And that has to do with the system being unpredictable, but not with
it being deterministic or not (actually, by writing the equation you
are assuming at some point that it is deterministic, at least without
QM)

> - Ian Parker
>
> PS I have not used the Q word anywhere.

Guillermo

[Arnold Neumaier]

Lou Pecora wrote:

> Don't confuse difficulty in prediction, which is what you are saying,
> with determinism. Chaotic systems are deterministic. Many can be
> modeled well with differential equations which are deterministic.

Not many, but all.

By definition, a chaotic system is a system governed by an ordinary
differential equation which exhibits a specific form of sensitive
dependence on initial conditions. Such systems are therefore always
deterministic.


> A pencil balanced on its point is not a chaotic system, although it is a
> deterministic system.

A pencil balanced on its point is not a deterministic system,
although one can consider deterministic approximate models for it.
In that case it is chaotic, once you include forces on its point,
which are always present for a real pencil.

However, there is always some modeling error, which is not just
uncertainty in a constant, but uncertainties changing unpredictably
at each instant of time. Thus it must be modelled by a stochastic
term.

Of course, the uncertainty ultimately stems from quantum mechanics,
since a pencil balanced on its point is of course nothing but a
large quantum system.


Arnold Neumaier

[Chris H. Fleming]

On Jun 11, 12:22 pm, guille2306 <guille2...@gmail.com> wrote:
> On Jun 10, 1:52 pm, "Nicolaas Vroom" <nicolaas.vr...@pandora.be>
> wrote:
>
>
>
> > I have a problem in understanding the difference between
> > deterministic verus non-deterministic as axplained in the following url:http://en.wikipedia.org/wiki/Deterministic_system_%28philosophy%29
>
> > Are the following examples deterministic yes or no:
> > 1. The movement of a round rubber ball with a certain weight,
> > dropped 1 meter above the centre of a round table.
> > After a couple of bounces the ball will come to rest at the centre
> > of the round table.
> > 2. The same as #1 but the ball (same weight) has the same of an
> > american football.
> > The ball will not come to rest at the center of the table.
> > 3. The same as #2 but the ball has the shape of a dice
> > 4. The same as #1 but the ball (same weight) is made from glass.
> > The ball will come to rest, but not at the centre of the table.
> > 5. The movement of the comet Schumacher Levy from just
> > before its break up into its 20 fragments, until each of those
> > fragments collided with the planet Jupiter.
>
> > IMO non of those examples is deterministic, but that opinion
> > is in conflict with the information in Wikipedia.
>
> > Nicolaas Vroomhttp://users.pandora.be/nicvroom/
>
> Any classical system (i.e., where quantum mechanics plays no role) is
> deterministic. Given the equations of evolution and the exact initial
> conditions, you can predict exactly the evolution of the system. Of
> course there will be problems: maybe you don't know the exact
> equations or it is not possible to solve them in a reasonable time
> (because of their complexity), and most probably you only have an
> approximation of the initial conditions (which is specially bad in
> chaotic systems). All of your examples (taken only as classical
> systems and forgetting about QM) fall in one of those categories: for
> example, even for a perfectly rigid "dice ball" on a perfectly rigid
> flat surface, the rest position will depend strongly of the angle
> between the first corner to hit the surface and the surface itself.
> But, if you repeat the experiment with exactly the same initial
> conditions, the ball will do exactly the same. It is, as stated in the
> Wikipedia article, a matter of philosophy: you can't predict the
> result for practical reasons, but it is predictable in theory.
>
> When quantum mechanics enters the picture things change completely.
> Even in theory, if you know the exact initial condition, the most you
> can do is predict probabilities for the different results. But here I
> have my own question to anyone: we can (in theory) predict the exact
> evolution of the wave function of the system, does that means that
> system is deterministic, or we should only apply the word
> "deterministic" to systems where we can predict the result of the
> measurement? I think that the second is the most correct approach, but
> I would like to know if there is any consensus about this.
>
> Guillermo

Given a Hamiltonian, the evolution of the wavefunction is
deterministic. The question is, is it appropriate to model the
universe as a wavefunction evolving in accord with a Hamiltonian, e.g.
the Wheeler-DeWitt equation. In which case, the statistical
interpretation of the wavefunction must arise perhaps as a kind of
open-system approximation.

I do not believe there is any consensus on this matter, nor should
there be given a lack of empirical evidence one way or the other.
Quantum noise is as random as can be measured and I do not think that
a deterministic open-system model could predict anything measurably
different given that Avogadro's number is so overwhelmingly large.

[Chris H. Fleming]

On Jun 12, 8:04 pm, Ian Parker <ianpark...@gmail.com> wrote:
> On 12 Jun, 20:00, Lou Pecora <pec...@anvil.nrl.navy.mil> wrote:
>
> > In article <t884k.118888$%B6.71...@newsfe13.ams2>,
> > Nicolaas Vroom <nicolaas.vr...@pandora.be> wrote:
>
> > > > Any classical system (i.e., where quantum mechanics plays no role) is
> > > > deterministic. Given the equations of evolution and the exact initial
> > > > conditions, you can predict exactly the evolution of the system. Of
> > > > course there will be problems: maybe you don't know the exact
> > > > equations
> > > In many cases you only know them approximate or nothing at all.
>
> > > For example fluids through pipes at different speeds.
> > > For example eartquakes
> > > All systems in which human beings are involved.
> > > All systems in which animals are involved.
> > > The beating of my hart.
>
> > > Do you consider all those systems deterministic ?
>
> > Sure. All evidence so far points to all non-quantum systems as
> > deterministic. I am ignoring noise here although that is often thought
> > of as forces from other deterministic systems. Not knowing the
> > equations is not the point. Gravitational forces are deterministic and
> > were so before Newton formulated the equations.
>
> Do you regard chaos as being deterministic? Perhaps it is a
> philosophical point. If I take a chaotic sytem in its simplest form,
> if I balance a pencil on its point, is that deterministic? Now I can
> make the point I am balancing the pencil on as close as possible to
> the vertical though the CG. I can do it to 6 figures, 12 10^100
> figures but eventually it will fall unpredictably. Clearly the more
> figures I have the longer a system stays deterministic.

There are chaotic model systems which are also solvable. They (as well
as many non-solvable systems) are deterministic as given a single-
valued solution that maps initial data to final data, then that
necessarily implies that the final data is _determined_ by the initial
data.

Determinism has to do with what the fates allow and not with what mere
humans can readily measure and predict. So yes, it is a philosophical
point. Really, a semantic point.

> Chaos is sometimes looked at in topological terms. The pencil balanced
> on a point has the simplest topology. If I take a dynamical system and
> construct eigenvalues. (We can view this as a kind of homotopy). Some
> of these eigenvalues will be pencil points, others will be stable.
> Topology, the Hausdorff set gives us a map of instability. With simple
> unstable systems we get attractors etc.
>
> The point I must return to again and again is that the dynamics, the
> Hamiltonian matrix is unpredictable.
>
>
>
> > > > or it is not possible to solve them in a reasonable time
> > > > (because of their complexity), and most probably you only have an
> > > > approximation of the initial conditions (which is specially bad in
> > > > chaotic systems). All of your examples (taken only as classical
> > > > systems and forgetting about QM) fall in one of those categories: for
> > > > example, even for a perfectly rigid "dice ball" on a perfectly rigid
> > > > flat surface, the rest position will depend strongly of the angle
> > > > between the first corner to hit the surface and the surface itself.
> > > Correct
> > > Do you call that determistic ?
>
> > Yes.
>
> > > > But, if you repeat the experiment with exactly the same initial
> > > > conditions, the ball will do exactly the same.
> > > Only with a computer
>
> > ?? No, evidence is that it will do the same thing as long as the initial
> > conditions are the same. You can argue about the ability to set the
> > initial conditions the same each time, but that is not the same thing as
> > being deterministic.
>
> This is philosopy again, suppose we vary it by 1 part in 10^100, the
> end result will be different. Is this determinism? Suppose we move
> Pluto 1km and wait a billion yrs. The difference in position will now
> be half an orbit.
>
> With a computer results depend on out word length, this has been
> proved. If I change (in C) "float" to "double" the results will be
> completely different.
>
> - Ian Parker
>
> PS I have not used the Q word anywhere.

[Lou Pecora]

In article <485245A0.5000007@univie.ac.at>,
Arnold Neumaier <Arnold.Neumaier@univie.ac.at> wrote:

> guille2306 wrote:
>
> > Any classical system (i.e., where quantum mechanics plays no role) is
> > deterministic.
>
> This is far from the truth.
>
> There are plenty of classical systems described by stochastic
> differential equations, the simplest being Brownian motion.
>
> Deterministic classical systems are only a convenient approximation
> to the more realistic stochastic case.
>
> For example, a deterministic damped harmonic oscillator is obtained
> from a stochstic damped harmonic oscillator by completely ignoring
> the damping mechanism.
>
>
> Arnold Neumaier

This will get you into the argument about what is "noise". Signals from
other, deterministic systems? Is the overall system, including the
noise sources, then deterministic? The idea of noise is a convenient,
modeling approach to dealing with complex external forcing. The usual
view of non-quantum physics is that when you put it all together the
whole system is deterministic, energy-conserving, etc.

--
-- Lou Pecora

[Ian Parker]

On 13 Jun, 19:40, Arnold Neumaier <Arnold.Neuma...@univie.ac.at>
wrote:
> Lou Pecora wrote:
> > Don't confuse difficulty in prediction, which is what you are saying,
> > with determinism.  Chaotic systems are deterministic.  Many can be
> > modeled well with differential equations which are deterministic.
>
> Not many, but all.
>
> By definition, a chaotic system is a system governed by an ordinary
> differential equation which exhibits a specific form of sensitive
> dependence on initial conditions. Such systems are therefore always
> deterministic.
>
> > A pencil balanced on its point is not a chaotic system, although it is a
> > deterministic system.
>
> A pencil balanced on its point is not a deterministic system,
> although one can consider deterministic approximate models for it.
> In that case it is chaotic, once you include forces on its point,
> which are always present for a real pencil.
>
> However, there is always some modeling error, which is not just
> uncertainty in a constant, but uncertainties changing unpredictably
> at each instant of time. Thus it must be modelled by a stochastic
> term.
>
> Of course, the uncertainty ultimately stems from quantum mechanics,
> since a pencil balanced on its point is of course nothing but a
> large quantum system.
>
I think I can say something a little bit more. We can tie in
determinism to entropy and information theory. Let us for the sake of
argument start at a point š aray from somewhere. Now let me take, let
me see 200 decimal places (not exactly š) and make a prediction. It
will be as if I had š exactly for a finite length of time. If I take
200 more my prediction will last longer.

Do you all see what is happenning? I am trading prediction time for
decimal places. I can state the entropy of š as being the number of
decimal places I have. Hence although my system obeys deterministic
equations, it is indeterminate and the actions of stating š to the
required number of decimal places and the actions of "tweaking" the
system when it is running involve the same information content. This
is what I mean by indeterminate.

Of course quantum theory puts a strict limit on the accuracy of any
measurement, but I still think it is important to look at the
behaviour of dynamical systems without the Q word.


- Ian Parker

[Nicolaas Vroom]

"Arnold Neumaier" <Arnold.Neumaier@univie.ac.at> schreef in bericht
news:4852AB71.8020203@univie.ac.at...
> Lou Pecora wrote:
>
>> Don't confuse difficulty in prediction, which is what you are saying,
>> with determinism. Chaotic systems are deterministic. Many can be
>> modeled well with differential equations which are deterministic.
>
> Not many, but all.
>
> By definition, a chaotic system is a system governed by an ordinary
> differential equation which exhibits a specific form of sensitive
> dependence on initial conditions. Such systems are therefore always
> deterministic.

There are differential equations which show chaotic behaviour.
Such equations you can call/could determistic.
The question is are there systems which are correctly described
by those equations. IMO only by approximation.
It is not only that the equation is not perfect, a different problem
is the parameter values. Also those are only known by approximation.
As such does it make sense to call those systems deterministic ?

What make sense is to find the equations, the parameters
and the boundary conditions that better describe these systems.

In many cases many systems are unique.
They are there only once.
Huricanes, Tornados, Earthquakes, Tsunamies
Do we know the equations that describe those systems ?
Only by approximation.
Do we no the parameters of the equations ?
Only by approximation.
Does it makes sense to call these systems/process deterministic ?

>> A pencil balanced on its point is not a chaotic system, although it is a
>> deterministic system.
>
> A pencil balanced on its point is not a deterministic system,
> although one can consider deterministic approximate models for it.
> In that case it is chaotic, once you include forces on its point,
> which are always present for a real pencil.

If you place a pencil on its point it will always fall down.
(except etc)
To which side is completely random.
If that is what you mean I agree it is not deterministic.

> However, there is always some modeling error, which is not just
> uncertainty in a constant, but uncertainties changing unpredictably
> at each instant of time.

That is correct.
IMO that is the case with each process.
Specific with Huricanes, Tornados, Earthquakes, Tsunamies
IMO that makes each non-deterministic
I prefer the term unpredictable.

> Thus it must be modelled by a stochastic term.

Can you give an example.

> Of course, the uncertainty ultimately stems from quantum mechanics,
> since a pencil balanced on its point is of course nothing but a
> large quantum system.

The uncertainty in eartquakes comes because we do not know
what happens internally in our earth at almost any scale.
(The same with the sun spots on the sun)

> Arnold Neumaier

Nicolaas Vroom
http://users.pandora.be/nicvroom/

[Tom Roberts]

guille2306 wrote:
> [...]

I essentially agree with all you said, but I advocate a different
terminology. I think the basic problem is a category error in the words
used, starting with the subject of this thread: "Deterministic systems".
AFAIK there is no system in the world we inhabit that is deterministic
(meaning EXACTLY deterministic). Indeed, I doubt very much that the
adjective "deterministic" can sensibly apply to any real system.

Including even such simple systems as a pool cue for which
that end moves when I push on this end -- there is a minuscule
but nonzero chance that a thunderbolt out of the blue will
split the cue between push and movement. This is obviously an
artificial example to illustrate the basic point: in the real
world you NEVER know enough about the initial conditions to
obtain true determinism.

But "deterministic" does apply to our MODELS of many systems. Classical
mechanics is a theory that provides a framework for constructing
deterministic models of many systems of interest. Such models are always
deterministic IN PRINCIPLE, but applying the model to a real system
invariably reduces that to an approximation. For pulleys and inclined
planes that approximation is excellent, but in the case of chaotic
systems the approximation of determinism might be valid only for an
extremely short time interval.

So, for instance, a classical model of a pencil standing on its point is
deterministic. Ditto for a classical model of thrown dice. But upon
examination one finds that such classical models are inadequate to
predict the actual outcomes of real pencils or dice, because QM
inherently poses limits on the specification of the initial conditions
that are large enough to spoil the approximation of determinism for the
time scales on which we typically observe such systems (but for a few
microseconds that approximation is quite good :-)).

In short: it is important to not confuse the model with the system being
modeled. The former can be deterministic, but the latter cannot.

Tom Roberts

[Chris H. Fleming]

On Jun 13, 10:28 am, Arnold Neumaier <Arnold.Neuma...@univie.ac.at>
wrote:
> guille2306 wrote:
> > Any classical system (i.e., where quantum mechanics plays no role) is
> > deterministic.
>
> This is far from the truth.
>
> There are plenty of classical systems described by stochastic
> differential equations, the simplest being Brownian motion.
>
> Deterministic classical systems are only a convenient approximation
> to the more realistic stochastic case.
>
> For example, a deterministic damped harmonic oscillator is obtained
> from a stochstic damped harmonic oscillator by completely ignoring
> the damping mechanism.
>
> Arnold Neumaier

You are correct in that there are classical models which are
stochastic and not deterministic.

But I can go one further. The damped harmonic oscillator with noise is
obtained by considering the the deterministic dynamics of the system &
environment and then averaging out the environmental degrees of
freedom. In quantum mechanics, the result is the HPZ master equation
(for a environment which also consists of oscillators).

So it can be said that the stochastic damped harmonic oscillator is
yet another idealization which ignores the atomic (and very well
deterministic) causes of its dissipation and fluctuations.

The brilliance of Einstein's derivation of the classical diffusion
relation was that it implied atomic causes to Brownian motion. This
was before atomic theory was as accepted as it is now. Einstein
provided a prediction that could be validated by experiment. This was
a small part of the determination of Avogadro's number.

[Nicolaas Vroom]

"Phil scadden" <p.scadden@_no_spam_gns.cri.nz> schreef in bericht
news:g2s8hv$uhs$1@lust.ihug.co.nz...
>> Do you consider all those systems deterministic ?
>
> Just dont confuse "deterministic" with "predictable"
> --
The question is what does each mean.

IMO predictability of a system comes as a value between 0 and 1
with 1 meaning that the system (outcome) is highly predictable
and 0 that the system (outcome) is unpredictable
Highly predictable means that you can predict with great precision
the future behaviour of a system.
That means that the difference between actual behaviour
and calculated behaviour at a future moment tf is small.
For an unpredictable system this difference is large.
In order to calculate the future of a system you need
1. A mathematical model of the system
2. Time series of the measurements of the variables of the system
starting at t0 until tn
3. A computer program.

This mathematical model includes
1. A set of differential equations as a function of the variables.
2. Parameters
3. Constraints.

The computer program consists of two parts:
First you calculate the parameters and initial conditions at t0
(based on the measurements)
Secondly you calculate the variables starting from t0 until tf.
Finally you compare the calculate values at tf with the measured
values at tf.
That means you calculate an overall error:
Abs(Measured Value-Calculated Value)/Measured Value

When the error is zero your system is highly predictable.
When the error is one your system is highly unpredictable.

The most obvious way to improve your prediction
is to modify the differential equations.

In the case of our solar system
the variables are the positions of the Sun and the planets.
the parameters are the masses of the Sun and the planets.
the equations are either Newton's Law or GR

Deterministic if I follow the most used opinion
comes only in two flavours:
A system is either determistic or not.
Determistic are all non-quantum systems.
Not Determistic are all quantum systems.

Even writing this e-mail is considered deterministic.

IMO this opinion is highly related to what is called
Laplace's Demon. See:
http://en.wikipedia.org/wiki/Laplace's_demon

General speaking this theory states:
That if you know all forces and positions of all
items you can calculate the future of all items.
In casu all is deterministic.
With all meaning the whole universe.
With items meaning each star and each atom
With calculate meaning Newton's Law.

IMO this is only a theory
it can never be proved
and it is not practical.

Nicolaas Vroom
http://users.pandora.be/nicvroom/

[Lou Pecora]

In article <4852AB71.8020203@univie.ac.at>,
Arnold Neumaier <Arnold.Neumaier@univie.ac.at> wrote:

> Lou Pecora wrote:
>
> > Don't confuse difficulty in prediction, which is what you are saying,
> > with determinism. Chaotic systems are deterministic. Many can be
> > modeled well with differential equations which are deterministic.
>
> Not many, but all.
>
> By definition, a chaotic system is a system governed by an ordinary
> differential equation which exhibits a specific form of sensitive
> dependence on initial conditions. Such systems are therefore always
> deterministic.

Not quite right. A chaotic system is a dynamical system in which at
least one Lyapunov exponent is positive. That opens it up to ODEs, PDEs,
Delay DEs, maps, and perhaps more. It's not limited to ODEs.

>
> > A pencil balanced on its point is not a chaotic system, although it is a
> > deterministic system.
>
> A pencil balanced on its point is not a deterministic system,
> although one can consider deterministic approximate models for it.
> In that case it is chaotic, once you include forces on its point,
> which are always present for a real pencil.

Too vague. A classical model of a pencil balance on point under the
influence of gravity is an ODE system. Without friction it may be
chaotic if you allow bouncing from the table supporting it. With
friction it will probably be a fixed point attractor. Not chaotic. It
depends on how you are modeling it. Including other forces then opens
it up to being anything. That's too vague. I was assuming classical
models with no other things added. That's deterministic.
>
> However, there is always some modeling error, which is not just
> uncertainty in a constant, but uncertainties changing unpredictably
> at each instant of time. Thus it must be modelled by a stochastic
> term.

Or a deterministic term that takes into account *all* the other systems
interacting with the pencil. But this is not the point of this
discussion. You can always add other forces to change the system.
>
> Of course, the uncertainty ultimately stems from quantum mechanics,
> since a pencil balanced on its point is of course nothing but a
> large quantum system.

I think everyone agrees with that, but that's not the point of the
discussion. That' another issue.

--
-- Lou Pecora

[Nicolaas Vroom]

"Lou Pecora" <pecora@anvil.nrl.navy.mil> schreef in bericht
news:pecora-89F83B.10195713062008@ra.nrl.navy.mil...

> Is a computer deterministic?

Yes

> Why?

Only in the sense that on the same computer every time when
you run the same program the same answer appears,
assuming that as part of program execution no human being is involved.

When you play the game of Golf on a computer, the program
becomes non-deterministic in the sense that every time
when you play the same game you get a different result.

> You have remarked a few times that
> things are only deterministic on a computer. But a computer is a
> physical system. Is it deterministic?

When you consider a computer as a physical system
at electron level as soon as you turn the machine different
electrons are involved. You can call that non-deterministic
but it has no practical value.

A much more interesting question is if a Q computer
is a determistic system in the sense that every time
when you run the same program you get the same
result.
If I am correct the answer is NO.
If that is correct than the question becomes how often
do you have to run the same program in order to be sure
(99% confidence) that you have the correct answer.

May be this also depends about the type of problem
to be solved.

> Think that through.

Nicolaas Vroom
http://users.pandora.be/nicvroom/

[Nicolaas Vroom]

"Tom Roberts" <tjroberts137@sbcglobal.net> schreef in bericht
news:_4H4k.13867$co7.6919@nlpi066.nbdc.sbc.com...
> guille2306 wrote:
>> [...]
>
> I essentially agree with all you said, but I advocate a different
> terminology. I think the basic problem is a category error in the words
> used, starting with the subject of this thread: "Deterministic systems".
> AFAIK there is no system in the world we inhabit that is deterministic
> (meaning EXACTLY deterministic). Indeed, I doubt very much that the
> adjective "deterministic" can sensibly apply to any real system.

Accordingly to Webster deterministic means: relating to or implying
determinism
Determinism means: (1b) the theory that all occurences in nature
are determined by antecedent causes or take place in accordance
with natural laws - called also cosmological determinism.

> Including even such simple systems as a pool cue for which
> that end moves when I push on this end -- there is a minuscule
> but nonzero chance that a thunderbolt out of the blue will
> split the cue between push and movement. This is obviously an
> artificial example to illustrate the basic point: in the real
> world you NEVER know enough about the initial conditions to
> obtain true determinism.

Initial conditions is only one part of the problem.
For a small set of problems they are not important.
If you draw a ball in a bolar hat, it comes always at rest at the bottom.

> But "deterministic" does apply to our MODELS of many systems. Classical
> mechanics is a theory that provides a framework for constructing
> deterministic models of many systems of interest. Such models are always
> deterministic IN PRINCIPLE,
Models = mathematical equations are deterministic by definition ?
> but applying the model to a real system
> invariably reduces that to an approximation.
That is correct. This is the second part of the problem.

But there are more:
The parameters of your equations.
The boundary conditions.
The measurements of the variables.

The measurements in the past are important to calculate the parameters
and initial conditions as accurate as possible.
In effect this is an iterative process dependent about your model
and best estimates of the parameters and initial conditions.

(If you change from Newton to GR you have to start all over in
calculating the masses of the objects involved)

> For pulleys and inclined
> planes that approximation is excellent, but in the case of chaotic
> systems the approximation of determinism might be valid only for an
> extremely short time interval.
>
> So, for instance, a classical model of a pencil standing on its point is
> deterministic. Ditto for a classical model of thrown dice. But upon
> examination one finds that such classical models are inadequate to
> predict the actual outcomes of real pencils or dice, because QM
> inherently poses limits on the specification of the initial conditions
> that are large enough to spoil the approximation of determinism for the
> time scales on which we typically observe such systems (but for a few
> microseconds that approximation is quite good :-)).

IMO in general at a scale much larger than atoms and molecules
you have a problem of predicting the outcome of an experiment
or (natural) process with a certain accuracy.

> In short: it is important to not confuse the model with the system being
> modeled. The former can be deterministic, but the latter cannot.
>
> Tom Roberts
>

Nicolaas Vroom
http://users.pandora.be/nicvroom/

[Lou Pecora]

In article <TB75k.77674$yb3.5535@newsfe18.ams2>,
"Nicolaas Vroom" <nicolaas.vroom@pandora.be> wrote:

> "Lou Pecora" <pecora@anvil.nrl.navy.mil> schreef in bericht
> news:pecora-89F83B.10195713062008@ra.nrl.navy.mil...
>
> > Is a computer deterministic?
>
> Yes
>
> > Why?
>
> Only in the sense that on the same computer every time when
> you run the same program the same answer appears,
> assuming that as part of program execution no human being is involved.
>
> When you play the game of Golf on a computer, the program
> becomes non-deterministic in the sense that every time
> when you play the same game you get a different result.

On the same computer the same program will generate the same answer
almost every time. I think the OP has opened up the very interesting
question about how we label a physical system according to the the model
of the system we choose. That's at the heart of this discussion. You
call the computer deterministic because the model of the system is
deterministic. Indeed, the engineering of a computer is carefully done
to make sure the machine states are reproducible given the same initial
conditions (programs, memeory, etc.). This is so successful that we
assume the computer is the ultimate deterministic systems sometimes.
But we are really thinking more of the model than the system. I think
that mixing of the physical system and model accounts for most of the
posts in this thread. And most of the misunderstanding of the OP.

It all leaves me thinking a bit more about how we categorize things by
their model's behavior.

--
-- Lou Pecora

[Nicolaas Vroom]

[Moderator's note: Lines reformatted to make them shorter. Although 80
is a maximum to enable nice display on almost all terminals, it's better
to keep your own, original, unquoted text in posts at 72 characters per
line or less, to enable it to be quoted a couple of times and still keep
things at less than 80 characters per line total. Also, don't use more
than 2 characters (including space) for a quote symbol. -P.H.]

"Lou Pecora" <pecora@anvil.nrl.navy.mil> schreef in bericht
news:pecora-FE644D.11182716062008@ra.nrl.navy.mil...

> On the same computer the same program will generate the same answer
> almost every time. I think the OP has opened up the very interesting
> question about how we label a physical system according to the the model
> of the system we choose. That's at the heart of this discussion.

The heart of the discussion is if you can describe the total physical
univerese in all its complexities, stuctures and beauties in a
mathematical language by mathematical equations accurately. IMO this is
not possible in principle nor in practice. Computers have nothing to do
with this issue. You could also raise a similar question: Is it possible
to describe the total universe by physical laws and or by laws of
nature. IMO the answer is NO.

What we can do is to describe a certain number of phenomena in
mathematical language under certain conditions. Newton's Law works well
for the movement of sperical objects with constant mass. As soon this is
not the case you have a problem. Our earth is not spherical and what
makes it even more difficult is that its mass distribution is not
constant i.e. the tides. You have to take that into account. All the
planets have a different composition. There are no laws which describe
those. Our earth is part solid part fluid, which constituents influence
each other. Also here there are no laws which describe this evolution
nor for example when earthquakes arise and their strength

The surface of the earth is of specific complexity and beauty. Here we
have plants, flowers and life. What we can do is to describe those
different life forms, how they looked and when they first appeared and
disappeared. We can also describe how they evolved one out of the other
and why during the different era, but there is no way to actual predict
this evolution starting some where in the past nor to predict what will
happen in the future given the current situation. The reason is simple:
we do not know enough (and we will never do)

> You call the computer deterministic because the model of the system is
> deterministic.

To call the "model" of the system determistic is a misnomer. The same if
you call the mathemics in order to describe the behaviour:
deterministic. The word determistic has no added value in those
circumstances.

Anyway this is not the issue. The issue is can we describe all systems
(the evolution of the total world) by mathematical equations
accuratelly. The answer is no

Pierre Simon Laplace was very much involved with the movement of the
planets. He confirmed that this motion could very well be calculated by
applying Newton's Law. In his view there is order in the planets and in
the total Universe. As such the Universe is determistic.

But is this reasoning correct if you consider all the complexities at
different scales finally going down to the level of electrons and
protons ? IMO the answer is no. You cannot describe all the details of
the Universe including the behaviour of humans by applying Newton's Law,
even stronger you cannot describe it by any form of mathematics.

Nicolaas Vroom
http://users.pandora.be/nicvroom/

[guille2306]

On Jun 25, 3:07 am, "Nicolaas Vroom" <nicolaas.vr...@pandora.be>
wrote:

> Anyway this is not the issue. The issue is can we describe all systems
> (the evolution of the total world) by mathematical equations
> accuratelly. The answer is no
>
> Pierre Simon Laplace was very much involved with the movement of the
> planets. He confirmed that this motion could very well be calculated by
> applying Newton's Law. In his view there is order in the planets and in
> the total Universe. As such the Universe is determistic.
>
> But is this reasoning correct if you consider all the complexities at
> different scales finally going down to the level of electrons and
> protons ? IMO the answer is no. You cannot describe all the details of
> the Universe including the behaviour of humans by applying Newton's Law,
> even stronger you cannot describe it by any form of mathematics.
>
> Nicolaas Vroomhttp://users.pandora.be/nicvroom/

OK, now I'm getting what you meant. Your first question ("Are these
system deterministic?") was too general. Now you have reformulated it
into "Can we totally describe the Universe through deterministic
models?" IMHO, those two question are different and that's why you got
two distinct group of answers here. For the second, I agree with you: in
practice there is no way that we could describe all the details of the
Universe, symply because there are too much details...

But, the "in principle" part implied in the first question is another
matter. Is a matter of faith: I believe that, in principle, the
equations are there and we only can try to make better aproximations
each time, but at the end the Universe is deterministic (except for my
discussion on QM in a previous post). You believe the contrary. It's
fine: there is no way that we can probe one or the other, as both agree
that "in practice" it's impossible to write the correct equations...

Guillermo

[Nicolaas Vroom]

"guille2306" <guille2306@gmail.com> schreef in bericht
news:85f55a01-e03d-4e6b-8a23-dc8594e284b4@b1g2000hsg.googlegroups.com...
> On Jun 25, 3:07 am, "Nicolaas Vroom" <nicolaas.vr...@pandora.be>
> wrote:
>
>> Anyway this is not the issue. The issue is can we describe all
>> systems (the evolution of the total world) by mathematical
>> equations accuratelly. The answer is no
>>
>> Pierre Simon Laplace was very much involved with the
>> movement of the planets. He confirmed that this motion
>> could very well be calculated by applying Newton's Law.
>> In his view there is order in the planets and in
>> the total Universe. As such the Universe is determistic.
>>
>> But is this reasoning correct if you consider all the complexities
>> at different scales finally going down to the level of electrons and
>> protons ? IMO the answer is no.
>> You cannot describe all the details of the Universe including
>> the behaviour of humans by applying Newton's Law,
>> even stronger you cannot describe it by any form of mathematics.
>>
>
> OK, now I'm getting what you meant. Your first question ("Are these
> system deterministic?") was too general. Now you have reformulated it
> into "Can we totally describe the Universe through deterministic
> models?" IMHO, those two question are different and that's why you got
> two distinct group of answers here. For the second, I agree with you: in
> practice there is no way that we could describe all the details of the
> Universe, symply because there are too much details...
>
In the document
http://math.ucr.edu/home/baez/physics/Relativity/SR/mass.html
under discussion in the thread
"New version of"Does mass increase with speed?" FAQ"

we read: "The very fact that we can describe Nature using
mathematics is a deep and mysterious thing."
The problem is we cannot.
We can only describe parts of Nature by mathematics
with a limitted accuracy.
(As such "you" can remove the words deep and mysterious)
Certain parts better: the movement of the planets.
Certain parts poorly: the falling of a leaf.
You can call the movement of the planets deterministic
but IMO this is not appropiate in the case of leaves.
Not in practice nor in principle.

The reason "quatum mechanics" is too simple.
To say that we cannot predict the stock market
because of quatum mechanics is IMO wrong.

Nicolaas Vroom http://users.pandora.be/nicvroom/