What is the true source of the 10 m/s/s "force" of gravity

I asked a good friend what is the source of the 10 meters/second/second
force we feel and attribute to "gravity", and his response was, verbatim:

The Lorentz transformation defines the difference between the clock at your
head and the clock at your feet. For the gravitational time dilation, that
is sqrt(1-(2*G*m/R*c*c)), where G is the gravitational constant, and R is
the distance to the center of the earth, and m is the mass of the earth.
That comes out to 0.00003731 at your feet. At your head, you need to add
your height to the radius of the earth. Neither Wolfram Alpha nor Google
Calculator has enough digits to show the difference, but you can do the
arithmetic yourself by hand. Acceleration is per second per second, so you
have to use that tiny value twice in your division. Use your mass and the
distance to the center of the earth to get the force you see on the
bathroom scale.

Where his email had linked the math to the following two links.
https://www.wolframalpha.com/input?i=sqrt%282+*+G+*+%28mass+of+the+earth%29+%2F%284000+kilometers+*+c+*+c%29%29
https://www.wolframalpha.com/input?i=sqrt%282+*+G+*+%28mass+of+the+earth%29+%2F%28%286371+kilometers+%2B+2+meters%29*+c+*+c%29%29

My fundamental question here is whether this seems worthy of approaching
the understanding of the problem this way, given I'm no physicist.

I'm a layman with just calculus as the highest math so far.
Is this approach worthy of further exploration in your opinion?

At some point I'll have to tackle the constants, such as G,
where just knowing what they are isn't satisfying to me in
terms of understanding why they are what they are; but for
now, all I want to do is calculate the "forces" correctly
knowing that Kip Thorne is on record saying time is far
more fundamental to gravity than anything else, which is why
the focus above from my friend started with the time dilation.

On 3/18/23 1:39 AM, rdb wrote:
> I asked a good friend what is the source of the 10
> meters/second/second force we feel and attribute to "gravity", and
> his response was, verbatim: The Lorentz transformation defines the
> difference between the clock at your head and the clock at your
> feet. [...]

You need more knowledgeable friends. This is flat-out wrong -- the
Lorentz transform does no such thing.

To understand physics requires study. The best introduction I know to
the modern theory of gravity is:
Geroch, _General_Relativity_from_A_to_B_. This is a
non-mathematical introduction to the ideas and
concepts of GR.

Tom Roberts

On Saturday, 18 March 2023 at 17:47:53 UTC+1, Tom Roberts wrote:
> On 3/18/23 1:39 AM, rdb wrote:
> > I asked a good friend what is the source of the 10
> > meters/second/second force we feel and attribute to "gravity", and
> > his response was, verbatim: The Lorentz transformation defines the
> > difference between the clock at your head and the clock at your
> > feet. [...]
>
> You need more knowledgeable friends.

Knowledgeable, that we're FORCED!!!
And that THE BEST WAY!!!!!!!

> Geroch, _General_Relativity_from_A_to_B_. This is a
> non-mathematical introduction to the ideas and
> concepts of GR.

And in the meantime in the real world, forbidden
by relativistic idiots improper clocks keep
measuring t'=t in improper seconds.

rdb <rdb@usa.usa> wrote:

> What is the true source of the 10 m/s/s "force" of gravity
>
> I asked a good friend what is the source of the 10 meters/second/second
> force we feel and attribute to "gravity", and his response was, verbatim:
>
> The Lorentz transformation defines the difference between the clock at your
> head and the clock at your feet.

Nonsense.

> For the gravitational time dilation, that
> is sqrt(1-(2*G*m/R*c*c)), where G is the gravitational constant, and R is
> the distance to the center of the earth, and m is the mass of the earth.
> That comes out to 0.00003731 at your feet. At your head, you need to add
> your height to the radius of the earth. Neither Wolfram Alpha nor Google
> Calculator has enough digits to show the difference, but you can do the
> arithmetic yourself by hand. Acceleration is per second per second, so you
> have to use that tiny value twice in your division. Use your mass and the
> distance to the center of the earth to get the force you see on the
> bathroom scale.

Incompetent computation. The answer is gh/c^2,
with g the local acceleration of gravity.
Remember that h << R, and gh << c^2, and that g ~ constant.

> My fundamental question here is whether this seems worthy of approaching
> the understanding of the problem this way, given I'm no physicist.

This is simply correct, and with modern optical clocks
the rate difference over 2 meter can easily be measured.

> I'm a layman with just calculus as the highest math so far.
> Is this approach worthy of further exploration in your opinion?

It is rapidly becoming routine technology.

> At some point I'll have to tackle the constants, such as G,
> where just knowing what they are isn't satisfying to me in
> terms of understanding why they are what they are; but for
> now, all I want to do is calculate the "forces" correctly
> knowing that Kip Thorne is on record saying time is far
> more fundamental to gravity than anything else, which is why
> the focus above from my friend started with the time dilation.

Fine, as long as you understand
that all this will not teach you anything
about 'the true source of gravity',

Jan