Science > Physics > How to determine whether a system is open or closed
| Topic: |
Science > Physics |
| User: |
"PD" |
| Date: |
19 Oct 2005 11:03:43 AM |
| Object: |
How to determine whether a system is open or closed |
Y. Porat got me thinking about something and it's bothering me enough
that I'm bringing it to the group. I hope that enough physicists will
pay attention to one of my posts to offer some insight.
The question has to do with conserved quantities and closed systems,
about which there is a known element of circularity. We know a quantity
is conserved when it comes out to be the same in a closed system,
regardless of internal interactions; we know a system is closed by
noting that the usual quantities pertaining to the system are
conserved.
We're successful in doing this with energy and momentum, with mass,
with various charges. We even are able to do this successfully though
we can't always ascribe the conserved quantity to be a property of
particular objects in the initial or final state; the invariant mass of
a pair of back-to-back photons comes to mind.
Here's the question: How do we know this doesn't apply to another
quantity, not yet assigned this way? To make it concrete, let's
consider "matter" as a quantity, and for the sake of argument I'll take
that quantity to be the scalar sum of the invariant masses of
individual particles in the system. We know that in our current
thinking, matter is not conserved (this is what we in fact call
matter-energy conversion), but a counterargument would be that our
system is not closed after all, and that there is some component with
matter that is not included in the system, and that if we *did* include
that other component of matter we would not only have a closed system
again but a new conservation law.
I'll briefly go over what I would consider to be poor arguments against
this:
1. "If there were something missing, it would show up as imbalances in
the other conservation laws." That's plausible, but not mandatory. It's
certainly possible, for example, to miss some energy in the final state
of a system and have the momentum of the system still remain conserved.
I only present this as a proof-of-principle that decoupling could
occur.
2. "An open system would imply a net interaction with the system, which
we should see." This again presumes that the only interactions are
those that we know about. Making a system that we once thought closed,
now open, would of course suggest the presence of a new interaction.
So I guess my question is this: How do we know that a closed system is
really closed, and that a non-conserved quantity is not really a
conserved quantity in some larger-scope system that is *really* the
closed system?
PD
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| User: "Gregory L. Hansen" |
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| Title: Re: How to determine whether a system is open or closed |
20 Oct 2005 09:04:14 AM |
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In article <1129737823.722416.254570@g44g2000cwa.googlegroups.com>,
PD <TheDraperFamily@gmail.com> wrote:
So I guess my question is this: How do we know that a closed system is
really closed, and that a non-conserved quantity is not really a
conserved quantity in some larger-scope system that is *really* the
closed system?
This is a philosophical question, and gets at the nature of science. The
answer is we don't know a system is really closed to everything, and we
don't know that there's some unknown quantity that is really conserved.
Or rather, we don't know that we can't make an internally and
experimentally consistent theory with those properties. There's always
the possibility of not-yet-discovered things, like the neutrinos that were
proposed just to conserve energy in beta decays.
On the other hand, why should we create such a theory? There's no
experimental need, and the theory we have now is aesthetically pleasing.
A theory is a set of postulates, and probably any given postulate can be
inserted into a theory as long as the others are chosen or rewritten
to preserve internal and external consistency. Lorentz had his aether
that acted like it wasn't there. There's no reason you can't include
massinos that account for non-conservation of mass but otherwise act like
they're not there, if you can think of a good reason for it.
My random sig selector picked a good one.
--
"We need to remember that when we are faced with an unstructured problem
it is we who create the model in the form of a quantitative metaphor;
there is no correct model waiting in the wings for us to call onstage." --
Thomas L. Saaty, "Mathematical Methods of Operations Research" (1988)
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| User: "tadchem" |
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| Title: Re: How to determine whether a system is open or closed |
20 Oct 2005 09:41:38 AM |
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'Quantitative metaphor' - I like that phrase.
Tom Davidson
Richmond, VA
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| User: "Andy Resnick" |
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| Title: Re: How to determine whether a system is open or closed |
19 Oct 2005 02:02:25 PM |
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PD wrote:
<snip>
So I guess my question is this: How do we know that a closed system is
really closed, and that a non-conserved quantity is not really a
conserved quantity in some larger-scope system that is *really* the
closed system?
Start by assuming the system is open. Then, by the Reynolds Transport
Theorem, you can write down the time-rate of change of any physical
quantity in your region of interest, whether the region itself changes
in time or not. Now, measure the physical property of interest within
your region of interest over some time interval. Then you will know if
there is a flux across the boundary or not, and you will know what the
jump condition is across the boundary as well. The boundary need not be
a physical boundary, nor need it be static.
--
Andrew Resnick, Ph.D.
Department of Physiology and Biophysics
Case Western Reserve University
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| User: "FrediFizzx" |
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| Title: Re: How to determine whether a system is open or closed |
19 Oct 2005 07:14:30 PM |
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"Andy Resnick" <andy.resnick@op.case.edu> wrote in message
news:dj65bq$9m2$1@eeyore.INS.cwru.edu...
| PD wrote:
| <snip>
| > So I guess my question is this: How do we know that a closed system
is
| > really closed, and that a non-conserved quantity is not really a
| > conserved quantity in some larger-scope system that is *really* the
| > closed system?
|
| Start by assuming the system is open. Then, by the Reynolds Transport
| Theorem, you can write down the time-rate of change of any physical
| quantity in your region of interest, whether the region itself changes
| in time or not. Now, measure the physical property of interest within
| your region of interest over some time interval. Then you will know
if
| there is a flux across the boundary or not, and you will know what the
| jump condition is across the boundary as well. The boundary need not
be
| a physical boundary, nor need it be static.
What exactly would a "non-physical" boundary be? Example?
FrediFizzx
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| User: "" |
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| Title: Re: How to determine whether a system is open or closed |
19 Oct 2005 08:15:49 PM |
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http://pespmc1.vub.ac.be/ASC/OPEN_SYSTE.html
A system with input, an entity that changes its behavior in response to
conditions outside its boundaries. Systems are rarely ever either open
or closed but open to some and closed to other influences (see
channel). Because of their need to combat decay within, food intake
makes biological organisms and societies open to matter/ENERGY from
their environment. But this property says nothing about openness to
information. adaptation, learning and all manifestations of
intelligence require some openness to information. Unlike biological
organisms, computers and social institutions exemplify openness to
organization which indicates that structural changes are determined
from the outside. Whether or not a system has outputs does not enter
the distinction between open and closed systems. Systems without output
are non-knowable by an external observer, e.g., black holes in the
visible universe (see ether). Systems without inputs are not
controllable (see control, closed system). (Krippendorff)
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| User: "Al Zenner" |
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| Title: Re: How to determine whether a system is open or closed |
19 Oct 2005 11:49:41 PM |
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wrote in news:1129770949.209066.60150@g43g2000cwa.googlegroups.com:
snip
Systems are rarely ever either open
or closed but open to some and closed to other influences (see
channel).
Try getting into this.
<http://www.physics.arizona.edu/~cronin/Research/Lab/some%20decoherence%20refs/JOO99.pdf>
snip
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| User: "Andy Resnick" |
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| Title: Re: How to determine whether a system is open or closed |
20 Oct 2005 02:12:43 PM |
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FrediFizzx wrote:
"Andy Resnick" <andy.resnick@op.case.edu> wrote in message
news:dj65bq$9m2$1@eeyore.INS.cwru.edu...
| PD wrote:
| <snip>
| > So I guess my question is this: How do we know that a closed system
is
| > really closed, and that a non-conserved quantity is not really a
| > conserved quantity in some larger-scope system that is *really* the
| > closed system?
|
| Start by assuming the system is open. Then, by the Reynolds Transport
| Theorem, you can write down the time-rate of change of any physical
| quantity in your region of interest, whether the region itself changes
| in time or not. Now, measure the physical property of interest within
| your region of interest over some time interval. Then you will know
if
| there is a flux across the boundary or not, and you will know what the
| jump condition is across the boundary as well. The boundary need not
be
| a physical boundary, nor need it be static.
What exactly would a "non-physical" boundary be? Example?
A boundary is nothing more than a dividing surface. In general, we like
to pick boundaries corresponding to physical discontinuities (material
interfaces, shocks, etc), but it not *need* be, and that is the
important concept. I may consider the airflow in my office, and
construct a boundary surface across the room. This surface has no
physical existence, but a perfectly well-defined mathematical one.
--
Andrew Resnick, Ph.D.
Department of Physiology and Biophysics
Case Western Reserve University
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| User: "Puppet_Sock" |
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| Title: Re: How to determine whether a system is open or closed |
20 Oct 2005 12:54:46 PM |
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FrediFizzx wrote:
[snip]
What exactly would a "non-physical" boundary be? Example?
A conceptual boundary. Such as "those particles on the
left and those on the right."
A procedural boundary. Such as "those particles moving
to the left and those to the right." Or "those that have
come from the bailer and those that have come from the
coffee machine."
A political boundary. Such as "the air mass over Canada
and the air mass over the USA."
Socks
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| User: "FrediFizzx" |
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| Title: Re: How to determine whether a system is open or closed |
20 Oct 2005 01:49:59 PM |
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"Puppet_Sock" <puppet_sock@hotmail.com> wrote in message
news:1129830886.753504.275190@g43g2000cwa.googlegroups.com...
| FrediFizzx wrote:
| [snip]
| > What exactly would a "non-physical" boundary be? Example?
|
| A conceptual boundary. Such as "those particles on the
| left and those on the right."
|
| A procedural boundary. Such as "those particles moving
| to the left and those to the right." Or "those that have
| come from the bailer and those that have come from the
| coffee machine."
|
| A political boundary. Such as "the air mass over Canada
| and the air mass over the USA."
| Socks
Hmm... Those boundaries all seem to have physical attributes that can
be associated with them.
FrediFizzx
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| User: "PD" |
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| Title: Re: How to determine whether a system is open or closed |
25 Oct 2005 11:16:50 AM |
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Andy Resnick wrote:
PD wrote:
<snip>
So I guess my question is this: How do we know that a closed system is
really closed, and that a non-conserved quantity is not really a
conserved quantity in some larger-scope system that is *really* the
closed system?
Start by assuming the system is open. Then, by the Reynolds Transport
Theorem, you can write down the time-rate of change of any physical
quantity in your region of interest, whether the region itself changes
in time or not. Now, measure the physical property of interest within
your region of interest over some time interval. Then you will know if
there is a flux across the boundary or not, and you will know what the
jump condition is across the boundary as well. The boundary need not be
a physical boundary, nor need it be static.
--
Andrew Resnick, Ph.D.
Thanks, all, for your responses. This reply resonated most in my mind.
I have to think about how this applies in the case that provoked the
original post. Matter (defined to be the scalar sum of rest masses of
bodies in a system) is known to be a quantity that is not in general
conserved, though invariant mass does seem to be. The question is
whether this is something to be comfortable with, or whether there is a
redefinition of system boundaries such that matter IS conserved. In
applying the Reynolds Transport Theorem, one quickly runs into a
condition that at least is indicative (though not obvious) of E=mc^2
equivalence -- namely, that there is good reason why mass is expected
to be a conserved quantity but matter is not. I was hoping for a clear
round-trip indicator -- something that says "no, this is not a
conserved quantity in ANY definition of a system, but *that* is
instead."
PD
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| User: "Gregory L. Hansen" |
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| Title: Re: How to determine whether a system is open or closed |
26 Oct 2005 01:05:17 PM |
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In article <1130257010.898396.228790@g14g2000cwa.googlegroups.com>,
PD <TheDraperFamily@gmail.com> wrote:
Andy Resnick wrote:
PD wrote:
<snip>
So I guess my question is this: How do we know that a closed system is
really closed, and that a non-conserved quantity is not really a
conserved quantity in some larger-scope system that is *really* the
closed system?
Start by assuming the system is open. Then, by the Reynolds Transport
Theorem, you can write down the time-rate of change of any physical
quantity in your region of interest, whether the region itself changes
in time or not. Now, measure the physical property of interest within
your region of interest over some time interval. Then you will know if
there is a flux across the boundary or not, and you will know what the
jump condition is across the boundary as well. The boundary need not be
a physical boundary, nor need it be static.
--
Andrew Resnick, Ph.D.
Thanks, all, for your responses. This reply resonated most in my mind.
I have to think about how this applies in the case that provoked the
original post. Matter (defined to be the scalar sum of rest masses of
bodies in a system) is known to be a quantity that is not in general
conserved, though invariant mass does seem to be. The question is
whether this is something to be comfortable with, or whether there is a
redefinition of system boundaries such that matter IS conserved. In
applying the Reynolds Transport Theorem, one quickly runs into a
condition that at least is indicative (though not obvious) of E=mc^2
equivalence -- namely, that there is good reason why mass is expected
to be a conserved quantity but matter is not. I was hoping for a clear
round-trip indicator -- something that says "no, this is not a
conserved quantity in ANY definition of a system, but *that* is
instead."
PD
What Resnick described is what you would do many times in an undergrad
engineering thermodynamics course. A jet engine, for instance, is not a
closed system. But the jet engine plus the rest of the universe is-- if
it's not in the engine then it's in the rest of the universe. Draw
meaningful boundaries (like at the inlet, after the compressor, after the
combustion chamber, etc.) and do the accounting for mass flow in and mass
flow out, momentum in and momentum out, energy in and energy out, entropy
in and entropy out.
But that doesn't say anything about the specific physics. We declare the
conservation of energy and say the energy in the engine plus the energy in
the rest of the universe is a constant. All we can say about entropy is
that the entropy in the engine plus the entropy in the rest of the
universe is non-decreasing, and we need to insert additional assumptions
to analyze the engine, like maybe adiabatic compression. The engineering
assumption is that the mass in the engine plus the mass in the rest of the
universe is constant, but if mass is created or destroyed in the engine
you would need to provide additional assumptions concerning that process.
--
"In any case, don't stress too much--cortisol inhibits muscular
hypertrophy. " -- Eric Dodd
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| User: "" |
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| Title: Re: How to determine whether a system is open or closed |
19 Oct 2005 12:40:30 PM |
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PD wrote:
Y. Porat got me thinking about something and it's bothering me
enough that I'm bringing it to the group. I hope that enough
physicists will pay attention to one of my posts to offer some
insight.
The question has to do with conserved quantities and closed
systems, about which there is a known element of circularity.
We know a quantity is conserved when it comes out to be the
same in a closed system, regardless of internal interactions;
we know a system is closed by noting that the usual quantities
pertaining to the system are conserved.
We're successful in doing this with energy and momentum, with
mass, with various charges. We even are able to do this
successfully though we can't always ascribe the conserved
quantity to be a property of particular objects in the initial
or final state; the invariant mass of a pair of back-to-back
photons comes to mind.
Here's the question: How do we know this doesn't apply to
another quantity, not yet assigned this way?
[..]
One answer is Noether's theorem
[ http://math.ucr.edu/home/baez/noether.html ]
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| User: "Puppet_Sock" |
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| Title: Re: How to determine whether a system is open or closed |
19 Oct 2005 12:19:42 PM |
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PD wrote:
[snip]
So I guess my question is this: How do we know that a closed system is
really closed, and that a non-conserved quantity is not really a
conserved quantity in some larger-scope system that is *really* the
closed system?
You are asking an epistemology question. How do we know
what we know? For answers to what is *really* going on
(really really) you will need to look elsewhere.
For starters, refer to R. Decartes, and the "evil genius"
problem. How do we ever *really* know anything? Once you've
exhausted the amusement in that question (and it should
only take a couple minutes) then come back.
We have good reason to believe things in science. We don't
know what is "*really*" going on, only what seems to match
up with all our experience and theories. So, we don't think
a particular thing is happening, because we have a theory that
works for a wide range of diverse experience, and that thing
does not happen within that theory.
How do you know *really* that New York City is still there
when you are not looking directly at it? Well, to doubt that
would be to doubt your entire life experience. Sure, it's
possible in a remote theoretic sense. You *could* be in a
_Matrix_ type of environment, being fed sensory data by an
evil genius. But if that's true, then you can't accomplish
anything, as you have no contact with reality. We accept that
we have contact with reality, not because we *really* know
that, but because it's the only game in town.
Science comes along and says:
- I saw this stuff happen.
- I have this theory that it happens this way.
Cycle B: Repeat forever:
Cycle A: Repeat till failure.
- Work with the theory to try to find it's predictions.
- The theory predicts X, Y, and Z.
- Look for X, Y, and Z. If I don't see them then
Cycle A failure. Otherwise, go back and do more A.
- Fix up the theory so it matches what was seen. Go back
and start Cycle A again.
Note that this is endless. We keep looking. The expectation
is that each time Cycle A fails, we learn something. Of course,
the evil genius theory can't fit in this, as it can't make
predictions. There is no way for the evil genius theory to
fail Cycle A.
So too the implied notion of your question about what "*really*"
happens. Science can't ask those questions, as it has no way
of contacting absolutes. All it can do is access sensory experience.
But note that the loop *is* endless. And this is quite nice
for scientists. Because the expectation is, we will not run
out of the requirement for them. It's job security.
But, how do we get things done? How do we manage to build
bridges and laundry hampers and things, if we never get
to what is *really* going on? Well, that gets us to the
notion of "range of validity." We know, for example, that
if you want to build a city and make a map of that city,
and you don't mind inaccuracies in your map of a meter,
then you don't need to worry about the non-flatness of
the surface of the Earth out to some kilometers. So, a
"flat Earth theory" is wrong, but still applicable over
a distance of about 10 km, if you tolerate an error of
as much as 1 meter. So, for this application, you don't
need to know what is *really* going on. You don't need
to know the *actual* shape of the Earth in order to
build a city. Nor to draw a map that lets you find the
corner store and get home again. Nor even a map that
lets the bridge builders decide where on the river to
put that new bridge.
So too the notions of conserved quantities we use just
now. They work for the tasks we have to date, and so far
have not failed. There is no promise that they will
never fail. But they work for the range of experience
we have had so far. So far, the application has not
noticed that the Earth is anything other than flat.
Socks
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