meaning of the Einstein equation
Edward Green
with respect to each other, the rate at which it begins to shrink is
proportional to its volume times: the energy density at the center of
the ball plus three times the pressure at that point."
http://math.ucr.edu/home/baez/einstein/node3.html
I have a problem with that. If the test particles are at rest with
respect to each other, then the pressure associated with them is
zero. Of course, that doesn't falsify the result, but it does make
the second term on the rhs redundant. Or are we to think of the
pressure as due to some finer particles than the test particles
buzzing around?
dlzc
On Aug 23, 9:43 am, Edward Green <spamspamsp...@netzero.com> wrote:
> "Given a small ball of freely falling test
> particles initially at rest with respect to
> each other, the rate at which it begins to
> shrink is proportional to its volume times:
> the energy density at the center of the ball
> plus three times the pressure at that point."
>
> http://math.ucr.edu/home/baez/einstein/node3.html
>
> I have a problem with that. If the test
> particles are at rest with respect to each
> other, then the pressure associated with them
> is zero.
There is such a ball at your feet. They are at rest wrt to each
other, yet their pressure is sufficient to launch lava thosuands of
feet into teh air.
> Of course, that doesn't falsify the result,
> but it does make the second term on the rhs
> redundant.
No, it doesn't. It describes how the system evolves over time, as the
"uniform" separation starts to decrease to allow dust-to-dust contact.
> Or are we to think of the pressure as due to
> some finer particles than the test particles
> buzzing around?
No LeSage particles, or virtual exchange gravitons, no.
David A. Smith
Tom Roberts
> "Given a small ball of freely falling test particles initially at rest
> with respect to each other, the rate at which it begins to shrink is
> proportional to its volume times: the energy density at the center of
> the ball plus three times the pressure at that point."
> http://math.ucr.edu/home/baez/einstein/node3.html
>
> I have a problem with that. If the test particles are at rest with
> respect to each other, then the pressure associated with them is
> zero.
These are test particles, in that they have negligible mass, negligible
interactions, and only respond to the geometry. In particular, they pass right
through any other matter without interactions. The "pressure" mentioned above is
for other matter, not the test particles; ditto for the energy density.
Tom Roberts
mpc755
Dark matter and matter are different states of the same material.
Dark matter and matter have mass.
Dark matter is displaced by matter.
Dark matter is not at rest when displaced.
Dark matter displaced by matter exerts pressure towards the matter.
Pressure exerted by displaced dark matter towards matter is gravity.
The plates in the Casimir Effect displace dark matter. Each plate
displaces the dark matter past the other plate. Dark matter is not at
rest when displaced. Dark matter displaced by matter exerts pressure
towards the matter. Since the dark matter displaced by each plate
extends past the other plate and the displaced dark matter is exerting
pressure towards the plates, the plates are forced together. Pressure
exerted by displaced dark matter towards matter is gravity. The
Casimir Effect is caused by gravity.
mpc755
The Casimir Effect is not always an attractive force.
http://en.wikipedia.org/wiki/Casimir_effect#Repulsive_forces
"Repulsive forces
There are few instances wherein the Casimir effect can give rise to
repulsive forces between uncharged objects. In a seminal paper, Evgeny
Lifshitz showed (theoretically) that in certain circumstances (most
commonly involving liquids), repulsive forces can arise. This has
sparked interest in applications of the Casimir effect toward the
development of levitating devices. Other scientists have also
suggested the use of gain media to achieve a similar levitation
effect,though this is controversial[citation needed] because these
materials seem to violate fundamental causality constraints and the
requirement of thermodynamic equilibrium. An experimental
demonstration of the Casimir-based levitation was recently carried out
by the Capasso group at Harvard through experiments involving a gold-
coated particle and silica thin film immersed in bromobenzene."
The cumulative displaced dark matter between the objects exceeds the
displaced dark matter outside the objects. The dark matter displaced
by the objects is not at rest. The force associated with the dark
matter attempting to return to its previous state causes the
levitation.
Daryl McCullough
>
>Dear Edward Green:
>> Or are we to think of the pressure as due to
>> some finer particles than the test particles
>> buzzing around?
>
>No LeSage particles, or virtual exchange gravitons, no.
Ed is right in this case. The pressure is *not* due to
the test particles. As Tom Roberts points out, the "test
particles" for this thought experiment should be particles
that have no non-gravitational interactions. Otherwise, the
equation isn't true. For example, a little ball of electrons
will not shrink, because the electrons will repel one another.
--
Daryl McCullough
Ithaca, NY
mpc755
wrote:
The pressure is due to the dark matter displaced by the test
particles. Dark matter and matter are different states of the same
material. Dark matter is displaced by matter. Dark matter is not at
rest when displaced. Dark matter displaced by matter exerts pressure
towards the matter. Pressure exerted by displaced dark matter towards
matter is gravity. The small ball consisting of freely falling test
particles shrinks due to the pressure exerted by the displaced dark
matter towards the test particles.
dlzc
On Aug 24, 5:28 am, mpc755 <mpc...@gmail.com> wrote:
> On Aug 24, 7:30 am, stevendaryl3...@yahoo.com (Daryl McCullough)
> wrote:
>
> > dlzc says...
>
> > >Dear Edward Green:
> > >> Or are we to think of the pressure as due to
> > >> some finer particles than the test particles
> > >> buzzing around?
>
> > >No LeSage particles, or virtual exchange
> > >gravitons, no.
>
> > Ed is right in this case. The pressure is *not*
> > due to the test particles. As Tom Roberts points
> > out, the "test particles" for this thought
> > experiment should be particles that have no
> > non-gravitational interactions. Otherwise, the
> > equation isn't true. For example, a little ball
> > of electrons will not shrink, because the
> > electrons will repel one another.
>
> The pressure is due to the dark matter displaced
> by the test particles.
Dark Matter does not interact with itself, or anything else, except
via gravitation. Same for the test particles. No ability to develop
pressure for either.
You are worse than BURT for chiming in with the silliest drivel.
David A. Smith
mpc755
Dark matter is, or behaves as, a frictionless superfluid.
Dark matter and matter are different states of the same material.
Dark matter and matter have mass.
Dark matter is displaced by matter.
Dark matter is not at rest when displaced.
Dark matter displaced by matter exerts pressure towards the matter.
Pressure exerted by displaced dark matter towards matter is gravity.
The plates in the Casimir Effect displace dark matter. Each plate
displaces the dark matter past the other plate. Dark matter is not at
rest when displaced. Dark matter displaced by matter exerts pressure
towards the matter. Since the dark matter displaced by each plate
extends past the other plate and the displaced dark matter is exerting
pressure towards the plates, the plates are forced together. Pressure
exerted by displaced dark matter towards matter is gravity. The
Casimir Effect is caused by gravity.
The pressure associated with displaced dark matter is gravity.
The fact that you think dark matter interacts via gravitation and are
too conceptually deficient to understand pressure exerted by displaced
dark matter towards matter is gravity shows how ignorant you are.
dlzc
On Aug 24, 4:30 am, stevendaryl3...@yahoo.com (Daryl McCullough)
wrote:
> dlzc says...
...
> >> Or are we to think of the pressure as due to
> >> some finer particles than the test particles
> >> buzzing around?
>
> >No LeSage particles, or virtual exchange
> >gravitons, no.
>
> Ed is right in this case. The pressure is *not*
> due to the test particles.
Then Ed is NOT right in this case, depending on the definition of
"fine".
> As Tom Roberts points out, the "test particles"
> for this thought experiment should be particles
> that have no non-gravitational interactions.
"Finer" particles would have no interaction at all, either
gravitational or the ability to resist via pressure. As test
particles have had "charge" and "size" already shaved off them...
> Otherwise, the equation isn't true. For
> example, a little ball of electrons
> will not shrink, because the electrons will
> repel one another.
No, I understand where I was wrong, that's OK. A system of equations
developed for Dark Matter (as that is what "test particles" are), ends
up producing a constraint that applies to particles that interact via
photons (of various flavors) too.
David A. Smith
mpc755
The test particles are not dark matter. The original post consists of
"a small ball of freely falling test particles". The original post
then goes on to ask, "Or are we to think of the pressure as due to
some finer particles than the test particles buzzing around?"
What the original poster mistakes is the concept of dark matter
consisting of particles.
Spacetime = ether = dark matter.
Einstein states the ether should not be thought of as consisting of
particles which can be separately tracked through time.
'Ether and the Theory of Relativity by Albert Einstein'
http://www-groups.dcs.st-and.ac.uk/~history/Extras/Einstein_ether.html
"But this ether may not be thought of as endowed with the quality
characteristic of ponderable media, as consisting of parts which may
be tracked through time. The idea of motion may not be applied to it."
"Think of waves on the surface of water. Here we can describe two
entirely different things. Either we may observe how the undulatory
surface forming the boundary between water and air alters in the
course of time; or else-with the help of small floats, for instance -
we can observe how the position of the separate particles of water
alters in the course of time. If the existence of such floats for
tracking the motion of the particles of a fluid were a fundamental
impossibility in physics - if, in fact nothing else whatever were
observable than the shape of the space occupied by the water as it
varies in time, we should have no ground for the assumption that water
consists of movable particles. But all the same we could characterise
it as a medium."
"[There may be supposed to be extended physical objects which] may not
be thought of as consisting of particles which allow themselves to be
separately tracked through time."
"The special theory of relativity forbids us to assume the ether to
consist of particles observable through time, but the hypothesis of
ether in itself is not in conflict with the special theory of
relativity."
Dark matter is, or behaves as, a frictionless superfluid one-
something.
The test particles, which have mass, displaced dark matter, which has
mass. Dark matter is not at rest when displaced and exerts pressure
towards the test particles. The small ball shrinks due to the pressure
exerted by the displaced dark matter towards the particles.
dlzc
On Aug 24, 6:52 am, mpc755 <mpc...@gmail.com> wrote:
...
> Dark matter is, or behaves as, a frictionless
> superfluid.
Dark Matter is what the model of General Relativity is based on. It
is no wonder that it comes out as a "necessary solution". Normal
matter is much more difficult to deal with.
You see Dark Matter through glasses of your choosing. Rest of your
post deleted unread (and I'm sure you don't care).
David A. Smith
mpc755
> Dear mpc755:
>
> On Aug 24, 6:52 am, mpc755 <mpc...@gmail.com> wrote:
> ...
>
> > Dark matter is, or behaves as, a frictionless
> > superfluid.
>
> Dark Matter is what the model of General Relativity is based on.
Correct. Spacetime = ether = dark matter.
'Ether and the Theory of Relativity - Albert Einstein'
http://www.tu-harburg.de/rzt/rzt/it/Ether.html
"According to the general theory of relativity space without ether is
unthinkable"
"the state of the [ether] is at every place determined by connections
with the matter and the state of the ether in neighbouring places, ...
disregarding the causes which condition its state."
Ether and matter are different states of the same material.
Ether has mass.
Ether is dark matter.
Dark matter is Ether.
Spacetime is ether is dark matter.
The state of the dark matter is at every place determined by
connections with the matter and the state of the dark matter in
neighboring places. Displacement by matter is the cause which
conditions its state.
Since you are able to understand "Dark Matter is what the model of
General Relativity is based on" you should be able to understand
gravity is pressure exerted towards matter by dark matter displaced by
the matter.
Tom Roberts
> Dark Matter does not interact with itself, or anything else, except
> via gravitation.
We don't know that. Essentially all we know about dark matter is that it does
not interact electromagnetically.
At present the leading guesses for the constituents of dark matter are WIMPs --
weakly interacting massive particles. WIMPs certainly do interact with each
other, but via the short-range weak force (range << 1 fm). The range of this
interaction is so short it is not important on atomic scales, much less on
astronomical scales.
Tom Roberts
mpc755
Spacetime = ether = dark matter.
Einstein states the ether should not be thought of as consisting of
particles which can be separately tracked through time.
'Ether and the Theory of Relativity by Albert Einstein'
http://www-groups.dcs.st-and.ac.uk/~history/Extras/Einstein_ether.html
"But this ether may not be thought of as endowed with the quality
characteristic of ponderable media, as consisting of parts which may
be tracked through time. The idea of motion may not be applied to it."
"if, in fact nothing else whatever were observable than the shape of
the space occupied by the water as it varies in time, we should have
no ground for the assumption that water consists of movable particles.
But all the same we could characterise it as a medium."
"[There may be supposed to be extended physical objects which] may not
be thought of as consisting of particles which allow themselves to be
separately tracked through time."
"The special theory of relativity forbids us to assume the ether to
consist of particles observable through time, but the hypothesis of
ether in itself is not in conflict with the special theory of
relativity."
Dark matter is, or behaves as, a frictionless superfluid one-
something.
The test particles, which have mass, displaced dark matter, which has
mass. Dark matter is not at rest when displaced and exerts pressure
towards the test particles. The small ball shrinks due to the pressure
exerted by the displaced dark matter towards the particles.
dlzc
GR is based on Dark Matter (or "dust"), that interacts (self- or
otherwise) only by gravitation at all scales. So it is no surprise
that descriptions of Nature by GR *must* arrive at some Dark Matter
observed. Dark Matter is intended to be a non-physical mathematical
tool.
Whether Nature has something like that, like you say, remains to be
seen. But it will not be called Dark Matter (except in popular
press), but something else. Maybe I'm wrong...
David A. Smith
mpc755
Dark Matter is not 'dust' and GR is not based on such a concept.
You are completely misinterpreting everything Einstein stated about GR
and ether (which is dark matter).
Everything Einstein states about GR and ether is the ether does not
consist of particles which can be separately tracked through time.
Einstein's concept of GR and ether is the opposite of 'dust'.
'Ether and the Theory of Relativity by Albert Einstein'
http://www-groups.dcs.st-and.ac.uk/~history/Extras/Einstein_ether.html
"But this ether may not be thought of as endowed with the quality
characteristic of ponderable media, as consisting of parts which may
be tracked through time. The idea of motion may not be applied to it."
"if, in fact nothing else whatever were observable than the shape of
the space occupied by the water as it varies in time, we should have
no ground for the assumption that water consists of movable particles.
But all the same we could characterise it as a medium."
"[There may be supposed to be extended physical objects which] may not
be thought of as consisting of particles which allow themselves to be
separately tracked through time."
"The special theory of relativity forbids us to assume the ether to
consist of particles observable through time, but the hypothesis of
ether in itself is not in conflict with the special theory of
relativity."
Dark matter (i.e. spacetime/ether) is, or behaves as, a frictionless
superfluid one-something.
mpc755
And it has been seen:
'Hubble Finds Ghostly Ring of Dark Matter'
http://www.nasa.gov/mission_pages/hubble/news/dark_matter_ring_feature.html
Tom Roberts
> GR is based on Dark Matter (or "dust"), that interacts (self- or
> otherwise) only by gravitation at all scales.
GR itself has no such basis at all. But the FRW manifolds that are the basis of
cosmological models do include such dust.
> So it is no surprise
> that descriptions of Nature by GR *must* arrive at some Dark Matter
> observed. Dark Matter is intended to be a non-physical mathematical
> tool.
Nobody else considers it that way. To everyone else, dark matter is just matter
that does not interact electromagnetically, and is thus invisible to our telescopes.
> Whether Nature has something like that, like you say, remains to be
> seen. But it will not be called Dark Matter (except in popular
> press), but something else.
Sure, once we know more about what constitutes dark matter we will have better
notions of what to call it.
Tom Roberts
mpc755
Call it spacetime. Call it ether. Call it aether. Call it
quintessence. It doesn't matter what you call it. What matter is
understanding its physical behaviors.
Dark matter is matter in its base state. Dark matter may not consist
of particles which can be separately tracked through time.
Dark matter is displaced by matter.
Dark matter and matter has mass.
Dark matter is not at rest when displaced.
Dark matter displaced by matter exerts pressure towards the matter.
Pressure exerted by displaced dark matter towards matter is gravity.
A moving particle has an associated dark matter displacement wave. In
a double slit experiment the particle enters and exits a single slit.
The associated dark matter displacement wave enters and exits multiple
slits and creates interference after exiting the slits. The direction
the particle travels is altered by the interference. Detecting the
particle causes decoherence of the associated dark matter displacement
wave (i.e. turns the wave into chop) and there is no interference.
DOES THE INERTIA OF A BODY DEPEND UPON ITS ENERGY-CONTENT?' A.
EINSTEIN
http://www.fourmilab.ch/etexts/einstein/E_mc2/e_mc2.pdf
"If a body gives off the energy L in the form of radiation, its mass
diminishes by L/c2."
The mass of the body does diminish, but the matter which no longer
exists as part of the body has not vanished. It still exists, as dark
matter. As matter converts to dark matter it expands in three
dimensional space. The physical effects this transition has on the
neighboring dark matter and matter is energy. Mass is conserved.
dlzc
On Aug 24, 4:25 pm, Tom Roberts <tjroberts...@sbcglobal.net> wrote:
> dlzc wrote:
> > GR is based on Dark Matter (or "dust"), that
> > interacts (self- or otherwise) only by
> > gravitation at all scales.
>
> GR itself has no such basis at all. But the FRW
> manifolds that are the basis of cosmological
> models do include such dust.
GR is based on infinitely differentiable volumes of mass (meaning
continuous mass "density"), that interact via only gravitation. True
or false?
> > So it is no surprise that descriptions of
> > Nature by GR *must* arrive at some Dark Matter
> > observed. Dark Matter is intended to be a
> > non-physical mathematical tool.
>
> Nobody else considers it that way. To everyone
> else, dark matter is just matter that does not
> interact electromagnetically, and is thus
> invisible to our telescopes.
Not mutually exclusive.
> > Whether Nature has something like that, like
> > you say, remains to be seen. But it will not
> > be called Dark Matter (except in popular
> > press), but something else.
>
> Sure, once we know more about what constitutes
> dark matter we will have better notions of what
> to call it.
Thank you.
David A. Smith
mpc755
> Dear Tom Roberts:
>
> On Aug 24, 4:25 pm, Tom Roberts <tjroberts...@sbcglobal.net> wrote:
>
> > dlzc wrote:
> > > GR is based on Dark Matter (or "dust"), that
> > > interacts (self- or otherwise) only by
> > > gravitation at all scales.
>
> > GR itself has no such basis at all. But the FRW
> > manifolds that are the basis of cosmological
> > models do include such dust.
>
> GR is based on infinitely differentiable volumes of mass (meaning
> continuous mass "density"), that interact via only gravitation. True
> or false?
>
> > > So it is no surprise that descriptions of
> > > Nature by GR *must* arrive at some Dark Matter
> > > observed. Dark Matter is intended to be a
> > > non-physical mathematical tool.
>
> > Nobody else considers it that way. To everyone
> > else, dark matter is just matter that does not
> > interact electromagnetically, and is thus
> > invisible to our telescopes.
>
> Not mutually exclusive.
>
Dark matter physically exists and has mass. This is mutually exclusive
to it being a non-physical mathematical tool.
Tom Roberts
> On Aug 24, 4:25 pm, Tom Roberts <tjroberts...@sbcglobal.net> wrote:
>> dlzc wrote:
>>> GR is based on Dark Matter (or "dust"), that
>>> interacts (self- or otherwise) only by
>>> gravitation at all scales.
>> GR itself has no such basis at all. But the FRW
>> manifolds that are the basis of cosmological
>> models do include such dust.
>
> GR is based on infinitely differentiable volumes of mass (meaning
> continuous mass "density"), that interact via only gravitation. True
> or false?
False. GR can accommodate any types of interactions among the particles and
matter, as long as they can be described by the energy-momentum tensor. Among
other things, this requires that all such interactions be local (i.e. they
depend only on the fields at each point and their derivatives).
>>> So it is no surprise that descriptions of
>>> Nature by GR *must* arrive at some Dark Matter
>>> observed. Dark Matter is intended to be a
>>> non-physical mathematical tool.
>> Nobody else considers it that way. To everyone
>> else, dark matter is just matter that does not
>> interact electromagnetically, and is thus
>> invisible to our telescopes.
>
> Not mutually exclusive.
Most physicists consider dark matter to be a physical substance of as-yet
unknown composition. Not a "non-physical mathematical tool".
Dark energy, on the other hand, is much more mysterious, and
it is not clear that either "physical" or "substance" apply....
Tom Roberts
dlzc
On Aug 25, 1:43 pm, Tom Roberts <tjrob...@sbcglobal.net> wrote:
> dlzc wrote:
> > On Aug 24, 4:25 pm, Tom Roberts <tjroberts...@sbcglobal.net> wrote:
> >>dlzc wrote:
> >>> GR is based on Dark Matter (or "dust"), that
> >>> interacts (self- or otherwise) only by
> >>> gravitation at all scales.
> >> GR itself has no such basis at all. But the FRW
> >> manifolds that are the basis of cosmological
> >> models do include such dust.
>
> > GR is based on infinitely differentiable volumes
> > of mass (meaning continuous mass "density"), that
> > interact via only gravitation. True or false?
>
> False. GR can accommodate any types of interactions
> among the particles and matter, as long as they can
> be described by the energy-momentum tensor. Among
> other things, this requires that all such
> interactions be local (i.e. they depend only on the
> fields at each point and their derivatives).
And be infinitely differentiable themselves, at least in
approximation, and some means of describing how it changes when the
bits come shoudler-to-shoulder. Making it scale dependent in this
Universe. Which cannot be done as you describe. So your answer is,
by not neglecting the problem in a different term, "sort of True, just
not about the mass term". Please feel free to correct me here too...
> >>> So it is no surprise that descriptions of
> >>> Nature by GR *must* arrive at some Dark Matter
> >>> observed. Dark Matter is intended to be a
> >>> non-physical mathematical tool.
> >> Nobody else considers it that way. To everyone
> >> else, dark matter is just matter that does not
> >> interact electromagnetically, and is thus
> >> invisible to our telescopes.
>
> > Not mutually exclusive.
>
> Most physicists consider dark matter to be a
> physical substance of as-yet unknown composition.
> Not a "non-physical mathematical tool".
Macht nichts (aka. Mox nix). Different intentions maybe, but the same
characteristics. Dark Matter written in, get Dark Matter out.
> Dark energy, on the other hand, is much
> more mysterious, and it is not clear that
> either "physical" or "substance" apply....
Is Dark Energy and the cosmological constant *potentially* the same
thing? As "substance" it could have arbitrary spatial distribution.
As a parameter, it has to have a single value everywhere for a given
time.
David A. Smith
mpc755
Einstein clearly did not consider ether to consist of particles which
can be separately tracked through time.
Spacetime = ether = dark matter.
> Dark energy, on the other hand, is much more mysterious, and
> it is not clear that either "physical" or "substance" apply....
>
> Tom Roberts
Dark energy is a change in state of dark matter, just like energy is a
change in state of matter.
eric gisse
> "Given a small ball of freely falling test particles initially at rest
> with respect to each other, the rate at which it begins to shrink is
> proportional to its volume times: the energy density at the center of
> the ball plus three times the pressure at that point."
>
> http://math.ucr.edu/home/baez/einstein/node3.html
>
> I have a problem with that. If the test particles are at rest with
> respect to each other, then the pressure associated with them is
> zero. Of course, that doesn't falsify the result, but it does make
> the second term on the rhs redundant. Or are we to think of the
> pressure as due to some finer particles than the test particles
> buzzing around?
Read the paragraph more carefully. Energy density *PLUS* pressure.