On Friday, December 8, 2023 at 6:29:13 PM UTC-6, RichD wrote:
> On December 2, Prokaryotic Capase Homolog wrote:
> >> >>> Note the center of mass of a collection of masses is not necessarily the
> >> >>> point with the lowest Newtonian gravitational potential. >
> >
> >> >> Isn't that a contradiction, if the center of mass doesn't coincide
> >> >> with zero potential?
> >
> >>> Eh, zero potential is out at infinity.
> >
> >> That's an arbitrary number, no objective significance.
> >> Potential refers to energy. Place a test mass at a point, release,
> >> watch it fly.
> >> The point where it remains motionless is the lowest potential.
> >
> > Leaving aside for the moment your continued confusion
> > about gravitational potential:
>
> You put your reading disability on display. Again.
>
> Potential is defined on a field, as the energy difference between
> a point and a reference point. Place a test mass at a point,
> observe the kinetic energy gain as it flies to the reference.
>
> Normally, at the reference, we see no acceleration, no
> energy gain. The fixed point theorem guarantees the existence
> of such a point. By definition, that's the lowest potential.
>
> You're welcome.
>
> Now a chance to display your thinking (dis)ability. You dig a shaft
> straight through the center of the earth, 10 meters diameter.
> You aim a camera, with an arc lamp powerful enough to light the entire shaft.
>
> Standing on the rim, you drop a ball over the lip, such that it rolls down
> the wall. Ignore rolling and air resistance. (thought experiments are
> always frictionless)
>
> You observe: the ball slowly follows a counterclockwise trajectory as
> it rolls down, a spiral pattern. Eventually it makes a 1/4 turn, then falls
> straight through.
>
> Explain.

You haven't answered my question. You had previously asserted,
in the form of a question, that zero potential should coincide with
the center of mass. You wrote, "Isn't that a contradiction, if the
center of mass doesn't coincide with zero potential?" Several
people, including Lodder, Roberts and myself, have attempted to
correct your misconceptions about gravitational potential.

To repeat:
Consider two unequal point masses. Call the lighter one A
and the more massive one B.
1) How do you compute the center of mass of this system?
2) Place a test particle at the computed center of mass.
Is the test particle closer to A or to B?
3) Will this test particle remain motionless?

You snipped this, so I presume you were afraid to admit
that you had made a stupid mistake.

Now, as to your challenge: The Earth rotates. Your time estimate,
however, appears to be *WAY* off, but then, your problem is
rather poorly framed so maybe I have misunderstood it.

On Saturday, December 9, 2023 at 9:32:37 AM UTC-8, Prokaryotic Capase Homolog wrote:
> On Friday, December 8, 2023 at 6:29:13 PM UTC-6, RichD wrote:
> > On December 2, Prokaryotic Capase Homolog wrote:
> > >> >>> Note the center of mass of a collection of masses is not necessarily the
> > >> >>> point with the lowest Newtonian gravitational potential. >
> > >
> > >> >> Isn't that a contradiction, if the center of mass doesn't coincide
> > >> >> with zero potential?
> > >
> > >>> Eh, zero potential is out at infinity.
> > >
> > >> That's an arbitrary number, no objective significance.
> > >> Potential refers to energy. Place a test mass at a point, release,
> > >> watch it fly.
> > >> The point where it remains motionless is the lowest potential.
> > >
> > > Leaving aside for the moment your continued confusion
> > > about gravitational potential:
> >
> > You put your reading disability on display. Again.
> >
> > Potential is defined on a field, as the energy difference between
> > a point and a reference point. Place a test mass at a point,
> > observe the kinetic energy gain as it flies to the reference.
> >
> > Normally, at the reference, we see no acceleration, no
> > energy gain. The fixed point theorem guarantees the existence
> > of such a point. By definition, that's the lowest potential.
> >
> > You're welcome.
> >
> > Now a chance to display your thinking (dis)ability. You dig a shaft
> > straight through the center of the earth, 10 meters diameter.
> > You aim a camera, with an arc lamp powerful enough to light the entire shaft.
> >
> > Standing on the rim, you drop a ball over the lip, such that it rolls down
> > the wall. Ignore rolling and air resistance. (thought experiments are
> > always frictionless)
> >
> > You observe: the ball slowly follows a counterclockwise trajectory as
> > it rolls down, a spiral pattern. Eventually it makes a 1/4 turn, then falls
> > straight through.
> >
> > Explain.
> You haven't answered my question. You had previously asserted,
> in the form of a question, that zero potential should coincide with
> the center of mass. You wrote, "Isn't that a contradiction, if the
> center of mass doesn't coincide with zero potential?" Several
> people, including Lodder, Roberts and myself, have attempted to
> correct your misconceptions about gravitational potential.
>
> To repeat:
> Consider two unequal point masses. Call the lighter one A
> and the more massive one B.
> 1) How do you compute the center of mass of this system?
> 2) Place a test particle at the computed center of mass.
> Is the test particle closer to A or to B?
> 3) Will this test particle remain motionless?
>
> You snipped this, so I presume you were afraid to admit
> that you had made a stupid mistake.
>
> Now, as to your challenge: The Earth rotates. Your time estimate,
> however, appears to be *WAY* off, but then, your problem is
> rather poorly framed so maybe I have misunderstood it.

It's sort of a "centroid", of mass, ....

Ever heard of, "matroids"?

If you keep finding words that already exist instead of
being stuck with ones that don't quite suffice, ....

On December 2, J. J. Lodder wrote:
>> >> >> The geoid is defined a set of points at the same potential?
>
>> >>> To a physicist, the geoid is the locus of all points on earth that have
>> >>> the same metric (considering just the earth). For all practical purposes
>> >>> this is the same as having the same Newtonian gravitational potential.
>
>>>> How is the metric measured? How does one determine empirically if
>>>> two separated points share the same metric? That is, without measuring
>>>> any clock rate, which is the subject under discussion.
>
>> Observe the test mass acceleration, and use the Lorentz
>> momentum formula. Calculate the g force, assuming Newton's
> > model. The Newtonian potential follows directly, if you know
> > the distribution of mass.
>
> That is not the claim.
> It is that relative rates of clocks at different points
> depend on the potential difference between those points.
>
>> The claim is that in general relativity, clock rate depends only on
>> potential, not on local g. We want to verify this. How to measure
>> potential, locally, independently of g?
>
> Easily verified, on the geoid clocks run at the same rate,
> while the local g on the geoid varies a lot,

step 1: Identify two distant points on the same geoid surface.
step 2: Observe their clock rates.
step 3: Are they identical?

How to perform step 1, without recourse to clocks (which would
be circular), and ignoring local g, which supposedly varies relative
to the potential?

--
Rich

RichD <r_delaney2001@yahoo.com> wrote:

> On December 2, J. J. Lodder wrote:
> >> >> >> The geoid is defined a set of points at the same potential?
> >
> >> >>> To a physicist, the geoid is the locus of all points on earth that have
> >> >>> the same metric (considering just the earth). For all practical
> >> >>> thpurposes is is the same as having the same Newtonian
> >> >>> thgravitational potential.
> >
> >>>> How is the metric measured? How does one determine empirically if
> >>>> two separated points share the same metric? That is, without measuring
> >>>> any clock rate, which is the subject under discussion.
> >
> >> Observe the test mass acceleration, and use the Lorentz
> >> momentum formula. Calculate the g force, assuming Newton's
> > > model. The Newtonian potential follows directly, if you know
> > > the distribution of mass.
> >
> > That is not the claim.
> > It is that relative rates of clocks at different points
> > depend on the potential difference between those points.
> >
> >> The claim is that in general relativity, clock rate depends only on
> >> potential, not on local g. We want to verify this. How to measure
> >> potential, locally, independently of g?
> >
> > Easily verified, on the geoid clocks run at the same rate,
> > while the local g on the geoid varies a lot,
>
> step 1: Identify two distant points on the same geoid surface.
> step 2: Observe their clock rates.
> step 3: Are they identical?
>
> How to perform step 1, without recourse to clocks (which would
> be circular), and ignoring local g, which supposedly varies relative
> to the potential?

By the process called levelling.
This is what geometers have been doing for hundreds of years.
Find the local level, or plumb line, and use your theodolite
to find the relative altitude of neighbouring points.
In its simplest form, take a flexible tube, fill with water,
and find points at the same potential.
(yes, I know it is more complicated than that in practice,
if you want to go beyond building a level house)
For points far away use the mean sea level as the reference.
(with the necessary corrections)
To find vertical potential differences calculate \int dz g(z),
going straight up.
There are limits to what can be achieved this way.
In practice a few cm is often the best that can be done.
(which is still good enough, given the limitations of cesium clocks)

In the near future we will have to pass on to 'chronometric levelling',
using clocks to establish level. And no, nothing circular about it.
The two mwthods will still have to agree with each other,
to the realisable accuracy of course.

And yes, clock rates are identical on the (rotating) geoid,
to the accuracy to which they can be measured.
This is a basic fact on which all of physics, and much of modern
technology, depends. Whe couldn't have accurate TAI, and TUC without it.

It is backed up by over 50 years of experience with hundreds atomic
clocks in standards laboratories all over the world.

Jan

On Sunday, December 10, 2023 at 1:49:07 AM UTC-8, J. J. Lodder wrote:
> RichD <r_dela...@yahoo.com> wrote:
>
> > On December 2, J. J. Lodder wrote:
> > >> >> >> The geoid is defined a set of points at the same potential?
> > >
> > >> >>> To a physicist, the geoid is the locus of all points on earth that have
> > >> >>> the same metric (considering just the earth). For all practical
> > >> >>> thpurposes is is the same as having the same Newtonian
> > >> >>> thgravitational potential.
> > >
> > >>>> How is the metric measured? How does one determine empirically if
> > >>>> two separated points share the same metric? That is, without measuring
> > >>>> any clock rate, which is the subject under discussion.
> > >
> > >> Observe the test mass acceleration, and use the Lorentz
> > >> momentum formula. Calculate the g force, assuming Newton's
> > > > model. The Newtonian potential follows directly, if you know
> > > > the distribution of mass.
> > >
> > > That is not the claim.
> > > It is that relative rates of clocks at different points
> > > depend on the potential difference between those points.
> > >
> > >> The claim is that in general relativity, clock rate depends only on
> > >> potential, not on local g. We want to verify this. How to measure
> > >> potential, locally, independently of g?
> > >
> > > Easily verified, on the geoid clocks run at the same rate,
> > > while the local g on the geoid varies a lot,
> >
> > step 1: Identify two distant points on the same geoid surface.
> > step 2: Observe their clock rates.
> > step 3: Are they identical?
> >
> > How to perform step 1, without recourse to clocks (which would
> > be circular), and ignoring local g, which supposedly varies relative
> > to the potential?
> By the process called levelling.
> This is what geometers have been doing for hundreds of years.
> Find the local level, or plumb line, and use your theodolite
> to find the relative altitude of neighbouring points.
> In its simplest form, take a flexible tube, fill with water,
> and find points at the same potential.
> (yes, I know it is more complicated than that in practice,
> if you want to go beyond building a level house)
> For points far away use the mean sea level as the reference.
> (with the necessary corrections)
> To find vertical potential differences calculate \int dz g(z),
> going straight up.
> There are limits to what can be achieved this way.
> In practice a few cm is often the best that can be done.
> (which is still good enough, given the limitations of cesium clocks)
>
> In the near future we will have to pass on to 'chronometric levelling',
> using clocks to establish level. And no, nothing circular about it.
> The two mwthods will still have to agree with each other,
> to the realisable accuracy of course.
>
> And yes, clock rates are identical on the (rotating) geoid,
> to the accuracy to which they can be measured.
> This is a basic fact on which all of physics, and much of modern
> technology, depends. Whe couldn't have accurate TAI, and TUC without it.
>
> It is backed up by over 50 years of experience with hundreds atomic
> clocks in standards laboratories all over the world.
>
> Jan

Yeah the atomic clock lattices are pretty great,
you just wave your hand past them and the space-contraction
results a read-out.

You seem to be pooh-poohing 'it's acceleration' which
is gravity's here on Earth, in the current theories or
according to the metric that "is whatever it is".

I.e. it seems here to be effects as about the Earth's, the "geoid"'s,
rotating frame.

Weber bars detect gravitational waves since when.

Don't forget Allais!