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Gerry Quinn...
Posted: Tue Sep 21, 2010 10:30 am
 
In article <mlevowCMB9kMFwcz at (no spam) charlesfrancis.wanadoo.co.uk>,
NotI at (no spam) charlesfrancis.wanadoo.co.uk says...
[quote]Thus spake Gerry Quinn <gerryq at (no spam) indigo.ie
In article <Wyz0XxAIYAiMFwac at (no spam) charlesfrancis.wanadoo.co.uk>,

This is plainly and utterly in contradiction with your assertion above
that he implicitly proposed the concept of a metric field!

I didn't say he implicitly proposed the concept. I said the concept is
implicitly contained in Euclidean geometry. That is a little different.

The axioms and theorems of Euclidean geometry make no reference to
measurement

The name geometry means literally "world measurement". Geometry can be
described as a mathematical structure which models the behaviour of
physical measurement results. Remember, its origin was in the discovery
of the 3-4-5 right angle triangle which was used to survey flood plane
in Egypt, and then generalised to Pythagoras' theorem
[/quote]
But Euclidean geometry became an axiomatic mathematical system long
before Newton's time.

Now clearly Newton believed that measurements corresponded, or could be
made correspond, to reality. But he did not think of reality as being
constructed by measurements. Nor did he consider any of the main
issues which led physicists in the late nineteenth century to question
previous conceptions of distance and time.

[quote]This is hardly what one may sensibly call an "unempirical constraint".

The parallel postulate is clearly an unempirical constraint (that may be
the simplest way of stating the matter), since it cannot be observed to
be true and since any postulate is a constraint.

We are talking about physics, not geometry.

I don't know any way to do physics without doing measurement. Since
geometry is the rules of measurement, we are talking about geometry.
[/quote]
Geometry is *not* the rules of measurement. That was perhaps a
reasonable definition of gemoetry in 500 BC, but it is not adequate
today. There are numerous geometries (infinitely many in fact) -
Euclidean geometry is just one of these. They are defined as axiomatic
systems.

[quote]The parallel postulate is
an axiom of Euclidean geometry (and thus independent, as all valid
axioms must be). You make a category error when you refer to it as an
unempirical constraint.

Physics is not mathematics. In physics we invent models of how things
might work,

What we should do is observe how things work.
[/quote]
"How things work" is not an observable. We can look at a clockwork
mechanism, but we have to invent models to figure out how the clock
keeps time.

[quote]combined with boundary conditions that should be at least
somewhat realistic, and place these sets of models and boundary
conditions in one-to-one correspondence with axiomatic mathematical
systems, in order that we may easily work out their consequences.

Contrast this with what Einstein and Newton did - abstract mathematical
rules from observation.
[/quote]
I don't think that is a good description of what they did. They did
not observe laws of physics. They invented laws of physics, then they
considered certain examples of how things would behave if these laws
were valid (i.e. they assigned boundary conditions corresponding to the
examples). Then they confirmed that the consequences of laws and
boundary conditions corresponded to observations, and thus validated
the laws.


[quote]flatness is built into the model, whereas in others it tends to be
placed in the boundary conditions (for example, the Schwarzschild
solution is set inside a spacetime that is defined to be asymptotically
flat)

Schwarzschild is an exact solution for an idealised situation, but as
such it can only be an approximation to reality. IOW the idealised
asymptotically flat boundary is not a model of physical reality.
[/quote]
Nevertheless, it is included - why?


[quote]. But since the only useful physical theories consist of both
models and boundary conditions, there is no additional entity being
included in one or the other on this account.

(I would also argue that if all useful solutions - i.e. solutions
corresponding to nature - turn out to involve an assumption of flatness
in one place or the other (i.e. model or boundary conditions) then the
assumption should ultimately be placed in the model.

"If..."? But they don't.
[/quote]
Can you give any example of a solution apparently corresponding to
nature that cannot be interpreted using (macroscopically) flat
spacetime models?

- Gerry Quinn
 
Daryl McCullough...
Posted: Thu Sep 23, 2010 2:24 am
 
Juan R. Gonzŕlez-Ŕlvarez says...
[quote]
Daryl McCullough wrote on Sat, 18 Sep 2010 10:43:02 +0000:

I don't agree. Newton's physics takes place in Galilean spacetime

Nope. The concept of spacetime was introduced in physics by
Poincare, and later by Minkowski and Einstein.
[/quote]
Whether or not the concept of a spacetime manifold was invented
at the time of Newton, his theory can be seen to take place in
such a manifold. It's often the case that a general concept is
not developed until after the specific instance.

The concept of a spacetime manifold encompasses both Einstein's
and Newton's physics, whether or not they were aware of that
fact.

--
Daryl McCullough
Ithaca, NY
 
eric gisse...
Posted: Thu Sep 23, 2010 2:25 am
 
Gerry Quinn wrote:
[...]

[quote]
flatness is built into the model, whereas in others it tends to be
placed in the boundary conditions (for example, the Schwarzschild
solution is set inside a spacetime that is defined to be asymptotically
flat)

Schwarzschild is an exact solution for an idealised situation, but as
such it can only be an approximation to reality. IOW the idealised
asymptotically flat boundary is not a model of physical reality.

Nevertheless, it is included - why?
[/quote]
Because asymptotic flatness is close enough to being true.

There is more to the story than asymptotic flatness, as that boundary
condition alone doesn't fix a solution to the field equations. You need
initial data, like the symmetries of the manifold.

[quote]

. But since the only useful physical theories consist of both
models and boundary conditions, there is no additional entity being
included in one or the other on this account.

(I would also argue that if all useful solutions - i.e. solutions
corresponding to nature - turn out to involve an assumption of flatness
in one place or the other (i.e. model or boundary conditions) then the
assumption should ultimately be placed in the model.

"If..."? But they don't.

Can you give any example of a solution apparently corresponding to
nature that cannot be interpreted using (macroscopically) flat
spacetime models?

- Gerry Quinn
[/quote]
Gravitational wave solutions, FRW manifold.

The second has spatial flatness but not flatness in spacetime, as there are
temporal components to curvature that aren't zero.
 
Juan R." González-Álvarez...
Posted: Fri Oct 01, 2010 7:33 am
 
Gerry Quinn wrote on Wed, 22 Sep 2010 10:25:35 +0200:

[quote]In article <pan.2010.09.20.08.53.47 at (no spam) yahoo.es>,
nowhere at (no spam) canonicalscience.com says...
Daryl McCullough wrote on Sat, 18 Sep 2010 10:43:02 +0000:
Gerry Quinn says...

The axioms and theorems of Euclidean geometry make no reference to
measurement (the same applies to the 'absolute space' postulated by
Newton). Distances in relativity, by contrast, are defined
operationally. Any 'metric field' you purport to find in Newton
has nothing to do with that of general relativity.

I don't agree. Newton's physics takes place in Galilean spacetime

Nope. The concept of spacetime was introduced in physics by
Poincar=C3=A9=, an latter by Minkowski and Einstein. The celebrated
statement by Minkoski was:

"Henceforth space by itself, and time by itself, are doomed to fade
away into mere shadows, and only a kind of union of the two will
preserve an independent reality."

That union is that is named spacetime.

As I put it earlier, prior to the 19th century the dimensional
background of the world was generally thought of as "a flat Euclidean
3-space combined with a single dimension of time". I will grant that
the construction "spacetime" was not yet invented, but in my opinion
it is no more than nitpicking to object to the phrase "Galilean (or
Newtonian) spacetime" to describe such a 3+1 combination. Everybody
understands perfectly well what is meant.
[/quote]
No.

In Newtonian theory, time is not a dimension but an evolution parameter.
The concept of time as dimension was introduced latter

http://en.wikipedia.org/wiki/Relativistic_dynamics#Hypothesis_I

"Galilean spacetime", "Newtonian spacetime", "Leibnizian spacetime",
"Maxwellian Spacetime" and "Neo-Newtonian spacetime" are non-equivalent
spacetimes, none of whom has anything to see with Newtonian ORIGINAL
theory.

(...)

[quote]Newtonian ORIGINAL theory is not a spacetime theory, albeit there is
a generalized misunderstanding in some 20th century references [*].

That's probably because these references are about contrasting
physical theories, not about the history of scientific philosophy.
[/quote]
No. You sniped the true reason and the references given. I reproduce
again the reason:

"some references give a rigorous treatment of Newton theory"



--
http://www.canonicalscience.org/

BLOG:
http://www.canonicalscience.org/publications/canonicalsciencetoday/canonicalsciencetoday.html
 
Juan R." González-Álvarez...
Posted: Fri Oct 01, 2010 7:33 am
 
Daryl McCullough wrote on Thu, 23 Sep 2010 13:24:41 +0100:

[quote]Juan R. GonzĂ lez-Ă€lvarez says...

Daryl McCullough wrote on Sat, 18 Sep 2010 10:43:02 +0000:

I don't agree. Newton's physics takes place in Galilean spacetime

Nope. The concept of spacetime was introduced in physics by Poincare,
and later by Minkowski and Einstein.

Whether or not the concept of a spacetime manifold was invented at
the time of Newton, his theory can be seen to take place in such a
manifold. It's often the case that a general concept is not developed
until after the specific instance.

The concept of a spacetime manifold encompasses both Einstein's and
Newton's physics, whether or not they were aware of that fact.
[/quote]
No. You continue confounding Newton ORIGINAL theory with a metric
theory over spacetime. Fortunately, we can still find experts who are
able to differentiate both (see quotes below for instance).

The theories are not equivalent. This is a fact showed in the textbooks
and papers given in the part of my message but that you have
conveniently snipped.


Joy Christian:

the fact that it is the Newton-Cartan theory of gravity, and not the
original Newton's theory of gravity, that is the true
Galilean-relativistic limit form of Einstein's theory of gravity.

Miguel Alcubierre Moya:

Strictly speaking, Newton's theory is not contained in GR, and there
is no reason why it should be. One is a metric theory, the other is
not.


--
http://www.canonicalscience.org/

BLOG:
http://www.canonicalscience.org/publications/canonicalsciencetoday/canonicalsciencetoday.html
 
Gerry Quinn...
Posted: Wed Oct 06, 2010 9:07 am
 
In article <i7f4j2$4i7$1 at (no spam) news.eternal-september.org>,
jowr.pi.nospam at (no spam) gmail.com says...
[quote]Gerry Quinn wrote:

Can you give any example of a solution apparently corresponding to
nature that cannot be interpreted using (macroscopically) flat
spacetime models?

Gravitational wave solutions, FRW manifold.

The second has spatial flatness but not flatness in spacetime, as there are
temporal components to curvature that aren't zero.
[/quote]
The question was whether they could be interpreted on the basis of a
flat background spacetime, along the lines discussed earlier in the
thread.

In the case of gravitational wave solutions, this is obviously the
case; arguably they are *easier* to interpret in terms of a
gravitational 'force' field than in terms of spacetime curvature.

The cosmological models are more complex, but again there seems no
reason - as far as I am aware - to suppose that there is any problem
with interpretations involving gravity as a spin-2 field on a flat
background spacetime.

To see how this might be so, it may be helpful to look at the Milne
universe.

The FRW solution with zero density (and no cosmological constant) is
the Milne universe, and its spacetime is exactly flat. Choosing
comoving coordinates - i.e. selecting a coordinate system in which the
galaxies, which are flying apart, are considered to have unchanging
coordinates - in the Milne universe yields an expanding space of
negative spatial curvature, compensated if you like by temporal
curvature, since spacetime curvature is zero.

In the Milne universe gravity is of course irrelevant because the
density is zero; it is thus easily possible to describe everything in
the Milne universe using only special relativity. When we describe the
Milne universe in terms of special relativity, we can no longer use
comoving coordinates, and instead we say that the galaxies are flying
apart. In this description space is not expanding, and the
cosmological redshift associated with distant galaxies are interpreted
as ordinary Doppler shifts. But the universe being so described is
exactly the same as in the expanding space secsription.

Now we can increase the density of the Milne universe to the critical
density, in order to get something a bit more like the universe we live
in. Since the universe has positive density, the gravitational
attraction of its contents must be taken into account. In GR terms,
this adds positive curvature which cancels out the negative spatial
curvature of the Milne universe. But - this is what we have been
discussing - we don't *need* to interpret gravity in GR terms. We can
take our special relativistic model of the Milne universe and add
gravity as a 'force' which not just pulls particles together but
affects clocke etc., just as we have been discussing previously in the
thread.

The Milne universe as originally formulated has obvious issues with
isotropy, in essence because, as its special relativistic
interpretation makes clear, it explicitly begins in some sort of point
explosion. This may suggest to some that any sort of alternative
interpretations of the metric expansion of space in our universe are
untenable; a large number of internet sources seem to assert this. But
surely the concept of inflation, generally considered as solving the
flatness problem in currently conventional cosmologies, can equally
well be invoked to solve the isotropy problem of a (densified) Milne
universe? Instead of a point, the post-inflation source may have been
an extended homogeneous region, only a small portion of which has
expanded into the currently observable universe.

This may be an unusual way of looking at the universe, but I think it
illustrates well enough that we can indeed look at realistic
cosmological models in terms of a flat background spacetime if we
choose to. The cosmological evidence does not force us to interpret
gravity in terms of curvature, any more than does the observational
evidence from black holes.

- Gerry Quinn
 
Tom Roberts...
Posted: Wed Oct 06, 2010 3:06 pm
 
Gerry Quinn wrote:
[quote]Gerry Quinn wrote:
Can you give any example of a solution apparently corresponding to
nature that cannot be interpreted using (macroscopically) flat
spacetime models?
The question was whether they could be interpreted on the basis of a
flat background spacetime, along the lines discussed earlier in the
thread.
[/quote]
The example for that is the FRW manifold with positive spatial curvature. It has
topology S^3xR, which is topologically incompatible with a flat spacetime.


Tom Roberts
 
Juan R." González-Álvarez...
Posted: Thu Oct 07, 2010 12:42 am
 
Tom Roberts wrote on Wed, 06 Oct 2010 21:06:46 -0400:

[quote]Gerry Quinn wrote:
Gerry Quinn wrote:
Can you give any example of a solution apparently corresponding to
nature that cannot be interpreted using (macroscopically) flat
spacetime models?
The question was whether they could be interpreted on the basis of a
flat background spacetime, along the lines discussed earlier in the
thread.

The example for that is the FRW manifold with positive spatial
curvature. It has topology S^3xR, which is topologically incompatible
with a flat spacetime.
[/quote]
That was not the question...

The question was if a metric theory can explain *physical* phenomena
that cannot be explained using a flat spacetime theory (e.g. field
theory of gravity).

The references that I gave in this same thread show that flat spacetime
theory works better than a curved spacetime theory (at least for some
tests).

Next I cite another reference that can give an overall idea of what a
flat spacetime theory can do at cosmological scales

"Some Remarks on a Nongeometrical Interpretation of Gravity and the
Flatness Problem" Gen. Rel. and Grav. 31(Cool, 1211-1217. Nikolic,
Hrvoje.

http://arxiv.org/abs/gr-qc/9901057


--
http://www.canonicalscience.org/

BLOG:
http://www.canonicalscience.org/publications/canonicalsciencetoday/canonicalsciencetoday.html
 
 
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