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Is there any Einsteinian spacetime bending near an infinite plate?
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Is there any Einsteinian spacetime bending near an infinite plate?
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mad aetherist
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Is there any Einsteinian spacetime bending near an infinite plate?
«
on:
22/12/2018 23:30:57 »
The Newtonian equation
for the gravity force on an object (M kg) near an infinite plate (density D kg/sqm) is
F=2 π G D M.
Here F is uniform, it doesn’t change with distance from the plate. Hencely g (m/s/s) is uniform too (g=F/M).
The Einsteinian equation
doesn’t exist, because GR & SR are useless here. The field equations of GR cant be used. And SR says that the gravity force & g are nearly infinite everywhere outside an infinite plate. For some unknown reason Einsteinians ditch SR & adopt the Newtonian equation (hey everybody, look over there, it’s a blackhole).
Strangely it seems that Einsteinians can use GR & SR to calculate F near an
infinite spherical shell
, here F is double the Newtonian value for an infinite plate (ie F for an infinite spherical shell = 4 π G D M). Praps this suggests to Einsteinians that for an infinite plate the Newtonian F=2 G D M is more likely than the SR value of F= ∞ π G D M. I might have this reasoning etc all wrong.
Not important, but can there be any such thing as an infinite sphere? An infinite plate is impossible (but possible in mathland), but an infinite sphere seems to me to be impossible even in mathland.
The Aetherist equation
is very simple, F & g are zero everywhere inside & outside an
infinite plate
.
The streamlines of the aether inflow into the plate are all at 90 deg to the plate, ie parallel, hencely there is zero acceleration of aether, hencely zero force on an object near the plate & not near.
The streamlines for inflow to an
infinite wire
converge in two dimensions hencely F varies per 1/R (R is distance to object)(from center of wire i think)(not sure).
The streamlines for inflow to a
point-mass or sphere
converge in three dimensions hencely F varies per 1/RR.
Einsteinian thinking intrigues me.
I can see their silly spacetime bending in three dimensions around a point-mass or sphere. And bending in two dimensions around a long wire or cylinder. But for a large or infinite plate i cant see how spacetime can bend. The horizontal components of bending (parallel to the plate) for
each elementary particle
would all cancel, leaving the vertical components only, which would be additive (for particles exactly on that vertical line only). So, u get a large vertical component of spacetime bending. How is such a thing possible? How can one dimension bend?
Or think of the plate being made of lots of wires
, each having a two dimensional bending associated with it. The horizontal components of the bendings for each elementary particle in an individual wire all cancel in the axial direction. After combining all of the wires to form a plate the transverse horizontal components of the bendings for individual wires must now cancel, so now u have zero bending in any horizontal direction. So once again u are left with some sort of faux-pseudo-phantom vertical bending, in one dimension.
So, there can be no nett Einsteinian spacetime bending associated with an infinite plate.
So the Einsteinian equation for gravity is if u like...... F=0 π G D M, ie..... F=0.
So, according to my logic, Einsteinians & Aetherists should agree (or is it Einsteinists & Aetherians).
One thing for sure, the Newtonian equation F=2 π G D M is false.
For a large but not infinite plate the value of F & g on the surface will be nearly zero, but F & g will increase as the height above the surface increases reaching a max when the height equals the width say, & thereafter F & g will decrease as height increases to infinity.
Arthur C Clarke's book
2010: Odyssey Two
includes some Newtonian theory used to measure the mass of a 2000 m by 889 m by 222 m slab (made by aliens & called Big Brother) orbiting Jupiter. D G Simpson likes the Newtonian theory but points out some minor errors & says that the mass was more like 94,200,000 tons rather than Clarke's 950,000 tons.
http://www.pgccphy.net/ref/gravity-clarke.pdf
However Simpson didnt account for the fact that the measurement involved timing the shuttle Nina falling from 100 m to the surface of the slab, ie Nina started its fall when 322 m from the bottom of the slab & 444.5 m from the nearer sides of the slab & 1000 m from the farthest sides. And when it hit the surface (after 3000 sec of fall) Nina was 222 m from the bottom of the slab. Hencely the situation had only a little resemblance to an infinite slab. My naïve calculations show that the average Newtonian g on Nina during its fall was 76.55% of the g due to an infinite slab with that same density per sqm. Therefore the Newtonian mass was 123,050,797 tons.
However the Aetherian g on Nina during its fall would have been on average less than that, as the contribution to g from some of the slab would have been nearly zero when Nina got close, & my naive calculations suggest that g was 23.45% of the Newtonian, hencely Simpson's 94,200,000 tons must be upped to 401,706,000 tons.
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Last Edit: 23/12/2018 05:37:48 by
mad aetherist
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mad aetherist
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Re: Is there any Einsteinian spacetime bending near an infinite plate?
«
Reply #1 on:
24/12/2018 06:27:35 »
That Nina-X might be problematic.
If Nina takes 3000 sec to fall 100 m to the slab, then that is an average of
33.3 mm/s
.
I calculate that two identical side by side orbits of Jupiter if starting 100 m apart will twice per orbit approach each other at
60 mm/s
, ie as a natural part of orbiting-falling. And likewise twice per orbit will recede at
60 mm/s
. And twice per orbit will more or less stay 100 m apart for a while, say for 1/8th of an orbit, which is say 1,312 sec (an orbit is at minimum say 10,500 sec).
Hencely the 3000 sec of falling to the slab needs to be corrected for orbit.
And there are say three or more possible orientations of slab, ie xx & yy & zz, or a combination, with Nina on one side or the other side.
If the 100 m is in line with a common orbit of slab & Nina then Nina will gradually
enter a higher orbit or a lower orbit
as it gets closer.
Is the slab rotating
such that it faces Jupiter at all times? Or something else.
This is an interesting detour from our main topic re gravity for an infinite plate.
«
Last Edit: 24/12/2018 06:37:29 by
mad aetherist
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