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NNTP-Posting-Date: Sun, 17 Nov 2024 18:05:11 +0000
Subject: Re: Is Curved Space An Improvement Over The Use of the Concept of
 Forces?
Newsgroups: sci.physics.relativity
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From: Ross Finlayson <ross.a.finlayson@gmail.com>
Date: Sun, 17 Nov 2024 10:05:08 -0800
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On 11/17/2024 09:52 AM, Ross Finlayson wrote:
> On 11/16/2024 11:50 PM, ProkaryoticCaspaseHomolog wrote:
>> On Sat, 16 Nov 2024 23:48:09 +0000, LaurenceClarkCrossen wrote:
>>
>>> Is Curved Space An Improvement Over The Use of the Concept of Forces?
>>
>> [SNIP]
>>
>> The following text has been edited very little from the version that
>> I added to Wikipedia in April 2018.
>> https://en.wikipedia.org/wiki/Spacetime#Is_spacetime_really_curved?
>>
>> Is spacetime really curved?
>>
>> In Poincaré's conventionalist views, the essential criteria according
>> to which one should select a Euclidean versus non-Euclidean geometry
>> would be economy and simplicity. A realist would say that Einstein
>> discovered spacetime to be non-Euclidean. A conventionalist would say
>> that Einstein merely found it more convenient to use non-Euclidean
>> geometry. The conventionalist would maintain that Einstein's analysis
>> said nothing about what the geometry of spacetime really is.
>>
>> Such being said,
>>   1) Is it possible to represent general relativity in terms of flat
>>      spacetime?
>>   2) Are there any situations where a flat spacetime interpretation
>>      of general relativity may be more convenient than the usual
>>      curved spacetime interpretation?
>>
>> In response to the first question, a number of authors including
>> Deser, Grishchuk, Rosen, Weinberg, etc. have provided various
>> formulations of gravitation as a field in a flat manifold. Those
>> theories are variously called "bimetric gravity", the "field-
>> theoretical approach to general relativity", and so forth. Kip
>> Thorne has provided a popular review of these theories.
>>
>> The flat spacetime paradigm posits that matter creates a gravitational
>> field that causes rulers to shrink when they are turned from
>> circumferential orientation to radial, and that causes the ticking
>> rates of clocks to dilate. The flat spacetime paradigm is fully
>> equivalent to the curved spacetime paradigm in that they both
>> represent the same physical phenomena. However, their mathematical
>> formulations are entirely different. Working physicists routinely
>> switch between using curved and flat spacetime techniques depending on
>> the requirements of the problem. The flat spacetime paradigm is
>> convenient when performing approximate calculations in weak fields.
>> Hence, flat spacetime techniques tend be used when solving
>> gravitational wave problems, while curved spacetime techniques tend be
>> used in the analysis of black holes.
>
> The space-time curvature is a mere mental model
> to effect to reflect a milieu of "gravity" in a theory
> with massy bodies and a universal law of gravitation.
>
> So, all it is, is, a "geodesy", that has all these level or
> plane curves according to integral analysis, that
> accordingly, a "test-mass", which is an arbitrarily
> small amount of mass, that the test-mass in this
> field of potentials, follows in the geodesy, its
> "world-line", that is merely the gradient descent,
> that the test-mass follows its world-line.
>
> Then, the theory has a "mass-energy equivalency"
> combined with an L-principle, and indeed two L
> principles, that "relativistic mass" reflects inertially
> resistance to acceleration, yet as well, tendency
> to fall faster in the world-line.
>
> So, there's an L-principle that light's speed is a
> constant, and that light, though mass-less,
> behaves as a test-mass in the geodesy, that's
> what it's said to do. Then also there's that
> the energy according to arbitrarily referenced
> velocity, has that this "c" is effectively infinity
> in this theory, that to reach it requires infinite
> energy because a given massy body accumulates
> or radiates any, "relativistic mass".
>
> Then, in this "potential well", of gravity, this geodesy,
> it's always evaluated instantaneously with regards
> to all massy-bodies everywhere all the time constantly.
> This is usually left out yet otherwise has that nothing
> would ever happen or move.
>
> So, most usually it's considered with regards to
> the gravity well of Earth the terrestrial, that
> humans are so small as to be like test-masses,
> and any "curvature" of space-time, is no different
> than Newton's universal law of gravitation,
> according to Earth's mass and Galileo's what
> results the constancy there, of gravity, is yet
> only because the 2-body system has it so negligeable,
> what's otherwise the mutually proportional product,
> inverse the distance square.
>
>
> Then it results that the gradient descent the
> world-line, is merely "down", that it's "down"
> in the gravity well, that of course there's an
> implicit tendency of massy bodies to accelerate
> according to gradient descent and a tautochrone,
> that's also usually left out as it was already given
> back to the universal law of gravitation, and
> Galileo's simplifications of what's otherwise
> inter-actions.
>
> "Down, Einstein?" "Yeah, straight down."
>
>
> So, the frames are the containers as it were
> of mass, and relativistic mass, and live in a space.
>
> Thusly you can notice that a variety of things
> are left under-defined, for example how a
> photon can be mass-less and travel at c,
> versus being a test-mass and follow a world-line.
>
>
> Similarly there's that a given frame _has space in it_,
> that a frame has spaces in it and a space has frames
> in it, space-frames and frame-spaces, that usually
> the theory is nested frames, and space is just a
> great outside local "flat" section, whatever is
> the nearest center gravitationally.
>
> It doesn't have to be that way, and in the same theory,
> that there are implicits and "un-stated" assumptions
> in the theory, that are always givens, while yet it's
> always world-lines the geodesy and a flat locality
> where things go straight down, as down the ramp,
> the ramp, of the gradient descent, of "space-time",
> keeping up the tauto-chronous like that, as after
> a most sort of machine in operation, the inclined
> plane, or ramp.
>
>
> Then, in a sense, it's always _of_ and "flat space-time",
> what's down, and always in a "flat space-time",
> what's around.
>
> Then, as with regards to what defines the ramp
> the gradient descent, it's classical universal law
> of gravitation what makes a geodesy, considering
> relativistic mass, and, classical motion down a ramp
> in classical linear downward gravitation, about
> all of classical mechanics.
>
>
> So, these are as well under-defined, and also,
> classical mechanics is even under-defined, as
> with regards to whatever's more than a
> space-time where everything orbits or falls,
> apart from each other, and nothing ever meets.
> That's all given to "classical mechanics".
>
> So, anyways, "curved space-time", is a mental model
> about the universal law of gravitation and
> a classical model of classical mechanics, of it,
> and then also "and photons follow world-lines
> like test-masses".
>
> That's all there is to it, yet, there's another
> theory, that has all the same actions, where
> space is a frame and a frame is also space,
> and objects in motion and massy-bodies are,
> ..., mostly space, and their space goes along
> with them. This then is in a space, a great
> altogether flat, as empty, with potential
> about orbits the geodesy, that the model
> of space-time as, "curved", is, dispensable.
>
> Then there's the cosmological constant
> "vanishing, yet, non-zero: an infinitesimal"
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