General Relativity Proves HV Lifters' Create Significant Space-Time Curvature

waitedavid137

Honorable
Yeah everybody loves to say that. But since there's no accurate translation in the english language for the concepts of metric tensor calculus, we'll have to get by with the metaphorical approximations of the english language ...
We? I speak tensor calculus fine.
...Are there any published papers which discuss this model or is this your own unpublished idea...
Someone already referenced a couple of them early in this thread.
…Sure, but the positive and negative gravitational poles are arranged front-to-back...
No, that's not even close to what that image is about. That image isn't even about acceleration of the ship. Even if the ship is at constant warp speed, it doesn't change that image which is NOT about a gravity dipole. Its a proposed way to imagine the geometry of a spacelike hypersurface through the ship for constant warp speed.
... both of which involve the negative gravitational pole and the positive gravitational pole...
No.

 
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waitedavid137

Honorable
I am going through actual papers from places like Harvard and they are telling me about rapid expansion and black hole binary systems but no actual observations of Dark Energy yet. If i do find one with observations then i will retract my statements but as of now there is no direct Observations, Also how TF does the cosmological constant equal ratios of dark energy and dark matter when we have no actual clue what dark matter and dark energy is... Some of this is going a past Theoretical into hypothetical...
Or instead of confirmation bias, you could look at the references at the bottom of the link as I suggested.
 

waitedavid137

Honorable
Consider for the moment the following warp drive in cylindrical coordinates appropriate for a remote observer with respect to which the ship is at rest when β is zero,
ds² = dct² - (dZ-βfdct)² - dZ² - r²dφ²
just so that you can compare to what you can look up.
I find it more helpful working with warp drive to express things in coordinates more appropriate for the perspective of ship frame observers. After all, you want it to be the ship forming the stress energy tensor to engage the warp drive. So do the transformation
z=Z - ∫βdct
where β is a function of time that you are doing an anti derivative with respect to.
Also define a new function g of
g = 1-f
The new coordinate expression for warp drive appropriate for the perspective of on board observers becomes
ds² = dct² - (dz+βgdct)² - dz² - r²dφ²
Now you can take β to be any function of time that is zero when the ship isn't at warp and g is any function of (z,r) that has boundary conditions that
g → 0 as z²+r² → 0
and
g → 1 as z²+r² → ∞ .
Define ρ
ρ² = z²+r²
You can now calculate the Einstein tensor to get the ship frame energy density and find it is
T⁰⁰ = - β²(c⁴/32ⲡG)(dg/dρ)²(r/ρ)²
This describes the energy density according to the ship frame throughout ALL space. Notice that there is no energy dipole. No positive energy on one side of the ship with negative on the other. No gravity dipole. And since this is valid for any function of time for β, it remains that case even when it is "accelerating". The negative energy density for Alcubierre's warp drive is ringed around its sides. What determines the direction that it goes into warp toward is actually the T¹⁰ , T⁰¹ terms, at its sides.
 

Dejan Corovic

As above, so bellow
Discussion is getting interesting.

Real question and the simple answer, in a plain English of course, is would that lifter distort gravitational field enough to self-move when out there in the outer space, surroiunded just with vacuum of space?
 
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We? I speak tensor calculus fine.
Someone already referenced a couple of them early in this thread.
No, that's not even close to what that image is about. That image isn't even about acceleration of the ship. Even if the ship is at constant warp speed, it doesn't change that image which is NOT about a gravity dipole. Its a proposed way to imagine the geometry of a spacelike hypersurface through the ship for constant warp speed.

No.

Consider for the moment the following warp drive in cylindrical coordinates appropriate for a remote observer with respect to which the ship is at rest when β is zero,
ds² = dct² - (dZ-βfdct)² - dZ² - r²dφ²
just so that you can compare to what you can look up.
I find it more helpful working with warp drive to express things in coordinates more appropriate for the perspective of ship frame observers. After all, you want it to be the ship forming the stress energy tensor to engage the warp drive. So do the transformation
z=Z - ∫βdct
where β is a function of time that you are doing an anti derivative with respect to.
Also define a new function g of
g = 1-f
The new coordinate expression for warp drive appropriate for the perspective of on board observers becomes
ds² = dct² - (dz+βgdct)² - dz² - r²dφ²
Now you can take β to be any function of time that is zero when the ship isn't at warp and g is any function of (z,r) that has boundary conditions that
g → 0 as z²+r² → 0
and
g → 1 as z²+r² → ∞ .
Define ρ
ρ² = z²+r²
You can now calculate the Einstein tensor to get the ship frame energy density and find it is
T⁰⁰ = - β²(c⁴/32ⲡG)(dg/dρ)²(r/ρ)²
This describes the energy density according to the ship frame throughout ALL space. Notice that there is no energy dipole. No positive energy on one side of the ship with negative on the other. No gravity dipole. And since this is valid for any function of time for β, it remains that case even when it is "accelerating". The negative energy density for Alcubierre's warp drive is ringed around its sides. What determines the direction that it goes into warp toward is actually the T¹⁰ , T⁰¹ terms, at its sides.
On the one hand, it’s cool that you’re posting here in a thread that's about your own work. Everyone here would like to understand it more clearly.

But on the other hand you’re not really making an effort to be understood. And the abstracts of these two papers from 1947 and 1948 that Dejan cited earlier in this thread make no mention of anything discernibly applicable to the gravitational field propulsion principle that you’re describing:

Papapetrou, A. (1948): "A static solution of the equations of the gravitational field for an arbitrary charge distribution", Proc. Roy. Irish Acad. A 51 191.

"ABSTRACT: A stationary axially symmetric exterior electrovacuum solution of the Einstein-Maxwell field equations was obtained. An interior solution for rotating charged dust with vanishing Lorentz force was also obtained. The two spacetimes are separated by a boundary which is a surface layer with surface stress-energy tensor and surface electric 4-current. The layer is the spherical surface bounding the charged matter. It was further shown, that all the exterior physical quantities vanished at the asymptotic spatial infinity where spacetime was shown to be flat. There are two different sets of junction conditions: the electromagnetic junction conditions, which were expressed in the traditional 3-dimensional form of classical electromagnetic theory; and the considerably more complicated gravitational junction conditions. It was shown that both—the electromagnetic and gravitational junction conditions—were satisfied. The mass, charge and angular momentum were determined from the metric. Exact analytical formulae for the dipole moment and gyromagnetic ratio were also derived. The conditions, under which the latter formulae gave Blackett’s empirical result for rotating stars, were investigated."
A. Papapetrou, “A Static Solution of the Equations of the Gravitational Field for an Arbitrary Charge-Distribution,” Proceedings of the Royal Irish Academy, Vol. 51, 1945-1948, p. 191. - Open Access Library

And:

Majumdar, S D (1947). "A Class of Exact Solutions of Einstein's Field Equations". Physical Review. 72 (5): 390–398.

ScreenHunter_2013 Apr. 12 06.24.jpg
Phys. Rev. 72, 390 (1947) - A Class of Exact Solutions of Einstein's Field Equations

And then you go out of your way to argue that the spatial contraction at the front of an Alcubierre warp bubble, and the spatial expansion at the rear of the bubble, don't constitute a gravitational dipole. But the primary source material suggests otherwise.

For example, when we look at Alubierre’s paper:

Alcubierre Abstract.1994.jpg

He employs the same kind of isometric diagram that we saw in Dr. Harold White’s paper – here we see that Alcubierre labeled Fig. 1 “Expansion of the normal volume elements” where the volume elements are contracted in the front of the craft and expanded behind the craft:

Alcubierre.Paper diagram contracting and expanding volume elements.1994.jpg

And in this section (below) he even explicitly describes how “the spacecraft will be pushed away from the Earth and pulled towards a distant star by spacetime itself.” That certainly sounds like an antigravitational field behind the craft akin to the dark energy effect, and a gravitational field ahead of the craft:

Alcubierre.Paper quote.1994.jpg

And in White's paper he explicitly labels the diagram with “Space Contraction” in front of the ship and “Space Expansion” at the rear of the ship...strange that didn't label them as "spacelike hypersurfaces":

warp field orientation.jpg

So how is that not equivalent to an antigravitational field at the rear of the bubble...and a positive gravitational field at the forward side of the warp bubble? It's the presence of an antigravitational field throughout the cosmos that expands the space between the galaxy clusters, and the presence of a positive gravitational field that contracts the space between more proximal bodies, so the spacetime regions on opposite sides of the warp bubble sure look like positive and negative poles of gravitation to me. Frankly I'm bewildered that anyone doesn't see it that way.

These regions also correspond to the York time so White labels the same diagram in this way, with an explanation right above it: “The region directly in front of the spacecraft experiences the most contraction of space, while the region directly behind the spacecraft experiences the most expansion of space.”

ScreenHunter_2009 Apr. 12 01.09.jpg

The expansion of space between two bodies is antigravity, aka negative gravity, by definition. That's why the dark energy field is regarded as an antigravity field and is associated with a gravitational blueshift (time contraction), whereas the contraction of space between two bodies describes a positive gravitational field between them and is associated with a gravitational redshift (time dilation).

Sure, the nomenclature isn’t steeped in the rigorous formal vernacular of the tensor calculus equations of GR – but it was good enough for Alcubierre, and Dr. White the Advanced Propulsion Team Lead for the NASA Engineering Directorate, and Dr. Hal Puthoff.

So yes – this is clearly a gravitational dipole, and it makes zero sense to argue that it’s not: all of these diagrams depict the spacetime distortions that represent positive and negative gravitational fields. The same diagram can be seen in this paper published by Dr. Puthoff with the warp metric clearly depicted as positive and negative regions of the gravitational field, alongside his discussion of Alcubierre's concept in terms of "gravity/antigravity propulsion":

ScreenHunter_2012 Apr. 12 05.42.jpg

So although Robert Forward’s concept of a self-accelerating gravitational dipole is produced in a much simpler manner than the Alcubierre metric - Forward's notion simply places a body with gravitational field in front of a body with negative gravitational (antigravity) field and off they go:

Negative Matter Propulsion.Robert L. Forward.1990.jpg

...whereas with the Alcubierre metric the negative mass-energy region surrounds the spacecraft in a toroidal ring perpendicular to the direction of acceleration...the core motive principle at work appears to be identical in nature: a positive and a negative gravitational pole self-accelerating in the direction of the positive pole, dragging everything in-between right along with them.

Unfortunately none of this pertains to the topic of this thread: your gravitational field propulsion concept that’s based on the electric field. If you actually want anyone to understand your proposal, then you’ve failed to do that. I would be thrilled if you explained it in a manner that the rest of us here could understand, but I’m not convinced that you have any interest in doing that because you've made no effort to do so.

And that’s a shame, because I’m only aware of three viable theories of gravitational field propulsion: the proposals of Robert L. Forward (negative matter propulsion), Miguel Alcubierre (the Alcubierre metric), and Jack Wisdom ("swimming in spacetime," which depends on a gravitational field gradient in the vicinity of the device but not produced by the device...which limits its utility to regions immediately surrounding highly massive astronomical bodies).

I've always wanted to add a fourth viable gravitational field propulsion concept to that very short list, but none of us here can do that because you haven't bothered to explain it in a manner that the rest of us here can comprehend. You've obviously spent years performing post-grad-level derivations of general relativity; nobody else here has that level of experience. And you know that. So I'm unconvinced that you're correct, because the discovery of a gravitational field propulsion concept that doesn't require either very substantial negative mass-energies, or the context of an intense external gravitational field, would make headlines all around the world. Maybe even win you the Nobel Prize in physics. If it was actually viable.

I ran into similar obfuscation and intransigence last year when I asked Dr. Jack Sarfatti about his unpublished (and therefore not peer-reviewed) low-power warp drive concept, so I'm inclined to disbelieve both claims of a reasonably accessible approach to gravitational field propulsion. Because if I were to someday come up with a potentially world-changing breakthrough in the theoretical physics of gravitational field propulsion, I'd be delighted to get the gist of the idea across to anyone who was interested.

But aside from posting a couple of links to well-trodden electrical field equations, you still haven't made any effort to explain your revolutionary breakthrough gravitational field propulsion concept at all. Why is that?
 

waitedavid137

Honorable
...But on the other hand you’re not really making an effort to be understood...But aside from posting a couple of links to well-trodden electrical field equations, you still haven't made any effort to explain your revolutionary breakthrough gravitational field propulsion concept at all. Why is that?
How so? Writing the exact solutions and being absolutely precise in description is the best anyone can do to be correctly understood.
...And the abstracts of these two papers from 1947 and 1948 that Dejan cited earlier in this thread make no mention of anything discernibly applicable to the gravitational field propulsion principle that you’re describing...
They shouldn't have to. The metric solution itself is the GR corresponding thing to the Newtonian gravitational potential. That is commonly understood among anyone with one single course on the subject behind them and in fact the Newtonian potential can be easily read off at a glance from the very first term from just a first order Taylor expansion easily done in ones head.
...And then you go out of your way to argue that the spatial contraction at the front of an Alcubierre warp bubble, and the spatial expansion at the rear of the bubble, don't constitute a gravitational dipole. But the primary source material suggests otherwise...

It doesn't matter if your favorite god says otherwise as I just explicitly proved it wrong.
...I ran into similar obfuscation and intransigence last year when I asked Dr. Jack Sarfatti about his unpublished (and therefore not peer-reviewed) low-power warp drive concept, so I'm inclined to disbelieve both claims of a reasonably accessible approach to gravitational field propulsion. Because if I were to someday come up with a potentially world-changing breakthrough in the theoretical physics of gravitational field propulsion, I'd be delighted to get the gist of the idea across to anyone who was interested.

But aside from posting a couple of links to well-trodden electrical field equations, you still haven't made any effort to explain your revolutionary breakthrough gravitational field propulsion concept at all. Why is that?
I find it far more likely that you haven't done the work necessary to understand what is being said and in your own pride assume that your opinion is of value anyway.
 

waitedavid137

Honorable
Look here is how you read it off. In the paper you sighted it reads
...
(ds)² = - (e^-ω)[(dx¹)²+(dx²)²+(dx³)²] + (e^ω)(dt)²
...
ω = -2log(1 + v)…
He is using a semi rare convention at least to layman that the base of log is e, not 10 so
ω = -2ln(1 + v)
So it can be written
(ds)² = - (e^2ln(1 + v))[(dx¹)²+(dx²)²+(dx³)²] + (e^-2ln(1 + v))(dt)²
I drop a lot of parenthesis as they are commonly understood there and used
dσ² = (dx¹)²+(dx²)²+(dx³)²
, so
ds² = - (e^2ln(1 + v))dσ² + (e^-2ln(1 + v))dt²
I also don't bother to use c = 1 everywhere and use a convention x⁰ = ct
So in my notation this is
ds² = (e^-2ln(1 + v))dct² - (e^2ln(1 + v))dσ²
Now
e^2ln(1 + v) = [e^ln(1 + v)]² = (1 + v)²
resulting in
ds² = dct²/(1 + v)² - (1 + v)²dσ²
For the uniform electric field case I was referring to,
v = -αz/c²
So
ds² = dct²/(1-αz/c²)² - (1-αz/c²)²dσ²
which was my expression in post #60 of this thread.
Now g₀₀ using my 0 through 3 notation instead of his 1 through 4 is
g₀₀ = 1/(1-αz/c²)²
The first order taylor expantion of which is a no brainer
1+2αz/c²
The Newtonian gravitational potential is therefor
Φ = αz
The gravitational acceleration field is then minus the gradient of that potential,

along the z direction.
 
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Dejan Corovic

As above, so bellow
The Newtonian graviotational potential is therefor
Φ = αz
The gravitational acceleration field is then minus the gradient of that potential,

in the z direction.

Should I dare to ask to translate that to English, for us lowly earthlings. Will that be self-driven, in vacuum of space, gravitational propulsion? Something UFO style ...
 
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nivek

As Above So Below
 

waitedavid137

Honorable
Should I dare to ask to translate that to English, for us lowly earthlings. Will that be self-driven, in vacuum of space, gravitational propulsion? Something UFO style ...
Lol, I thought I had. So for an example case of that I was saying there. If you have a uniform electric field, and you drop a neutral test mass into that field, it will accelerate gravitationally anyway as if there was a uniform gravitational field there. The effect is comparable to earths surface gravity when the electric field strength is about 114 billion V/m.
 

Shadowprophet

Truthiness
Look here is how you read it off. In the paper you sighted it reads

He is using a semi rare convention at least to layman that the base of log is e, not 10 so
ω = -2ln(1 + v)
So it can be written
(ds)² = - (e^2ln(1 + v))[(dx¹)²+(dx²)²+(dx³)²] + (e^-2ln(1 + v))(dt)²
I drop a lot of parenthesis as they are commonly understood there and used
dσ² = (dx¹)²+(dx²)²+(dx³)²
, so
ds² = - (e^2ln(1 + v))dσ² + (e^-2ln(1 + v))dt²
I also don't bother to use c = 1 everywhere and use a convention x⁰ = ct
So in my notation this is
ds² = (e^-2ln(1 + v))dct² - (e^2ln(1 + v))dσ²
Now
e^2ln(1 + v) = [e^ln(1 + v)]² = (1 + v)²
resulting in
ds² = dct²/(1 + v)² - (1 + v)²dσ²
For the uniform electric field case I was referring to,
v = -αz/c²
So
ds² = dct²/(1-αz/c²)² - (1-αz/c²)²dσ²
which was my expression in post #60 of this thread.
Now g₀₀ using my 0 through 3 notation instead of his 1 through 4 is
g₀₀ = 1/(1-αz/c²)²
The first order taylor expantion of which is a no brainer
1+2αz/c²
The Newtonian gravitational potential is therefor
Φ = αz
The gravitational acceleration field is then minus the gradient of that potential,

along the z direction.

Now when I say this, Know That this is a Question, Not an accusation, I assume no role of leadership in this discussion, You seem to be applying a lot of Newtonian physics in here, Now here is the question part, Hasn't a lot of the understanding of the function of gravity changed since this information was considered accurate?
 

Dejan Corovic

As above, so bellow
Lol, I thought I had. So for an example case of that I was saying there. If you have a uniform electric field, and you drop a neutral test mass into that field, it will accelerate gravitationally anyway as if there was a uniform gravitational field there. The effect is comparable to earths surface gravity when the electric field strength is about 144 billion V/m.

WOW, man! Thank you so much.

OK, so purely electrically neutral test mass will be gravitational accelerated, say, towards the wire or towards the foil. But we can't make make a spaceship that way? What about wire/foil combo pushing itself against the vacuum and moving in a similar way to warp drive will?

Somewhere, back in this thread ( actually post #18 ), I've shown come humble calculations of mine trying to turn that electric field strength into voltage, so that practicality can be checked. Unfortunately the result was that the 20 cm long AWG40 wire ( diameter: 0.0031" or 0.0050 mm ) would need to charged to 38.792 MV, which is a way above any voltage that was so far humanely feasible.
 
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Look here is how you read it off. In the paper you sighted it reads

He is using a semi rare convention at least to layman that the base of log is e, not 10 so
ω = -2ln(1 + v)
So it can be written
(ds)² = - (e^2ln(1 + v))[(dx¹)²+(dx²)²+(dx³)²] + (e^-2ln(1 + v))(dt)²
I drop a lot of parenthesis as they are commonly understood there and used
dσ² = (dx¹)²+(dx²)²+(dx³)²
, so
ds² = - (e^2ln(1 + v))dσ² + (e^-2ln(1 + v))dt²
I also don't bother to use c = 1 everywhere and use a convention x⁰ = ct
So in my notation this is
ds² = (e^-2ln(1 + v))dct² - (e^2ln(1 + v))dσ²
Now
e^2ln(1 + v) = [e^ln(1 + v)]² = (1 + v)²
resulting in
ds² = dct²/(1 + v)² - (1 + v)²dσ²
For the uniform electric field case I was referring to,
v = -αz/c²
So
ds² = dct²/(1-αz/c²)² - (1-αz/c²)²dσ²
which was my expression in post #60 of this thread.
Now g₀₀ using my 0 through 3 notation instead of his 1 through 4 is
g₀₀ = 1/(1-αz/c²)²
The first order taylor expantion of which is a no brainer
1+2αz/c²
The Newtonian gravitational potential is therefor
Φ = αz
The gravitational acceleration field is then minus the gradient of that potential,

along the z direction.
Okay, thank you - that's all I was was asking for; to be walked through it. I need to think this through for awhile; I had no idea that an electric field of any configuration could yield a directional gravitational acceleration. Even the Gertsenshtein effect doesn't touch on this possibility afaik.

Nivek - is there any way to get a LaTeX/MathJax add-on for the forum so we can see equations in a clearer format? I could pony up some dough if there's an extra charge for it. This formatting is workable, but it would be really nice to see it in the proper format. Grazie.

Now when I say this, Know That this is a Question, Not an accusation, I assume no role of leadership in this discussion, You seem to be applying a lot of Newtonian physics in here, Now here is the question part, Hasn't a lot of the understanding of the function of gravity changed since this information was considered accurate?
He's giving us GR derivations here. I haven't drawn the lines between the Newtonian model and these metric tensor equations yet, but this is definitely GR. Remember that Newtonian gravitation is the weak-field limit of GR, so Newtonian gravitation doesn't invalidate anything; it's just a special case. Oliver Heaviside expanded Newtonian gravitation with Maxwell's equations to discover gravitoelectromagnetism about 20 years before GR, and those principles are an intrinsic feature of GR but his values are only correct in the weak-field limit because GR is nonlinear.
 

waitedavid137

Honorable
Now when I say this, Know That this is a Question, Not an accusation, I assume no role of leadership in this discussion, You seem to be applying a lot of Newtonian physics in here, Now here is the question part, Hasn't a lot of the understanding of the function of gravity changed since this information was considered accurate?
I'm just showing the Newtonian limit hoping that it will be better understood here. The exact calculation of geodesic motion for the solution of a more arbitrary static electric field configuration is 7.1.20abc at
Electromagnetism
 

waitedavid137

Honorable
WOW, man! Thank you so much.

OK, so purely electrically neutral test mass will be gravitational accelerated, say, towards the wire or towards the foil. But we can't make make a spaceship that way? What about wire/foil combo pushing itself against the vacuum and moving in a similar way to warp drive will?

Somewhere, back in this thread ( actually post #18 ), I've shown come humble calculations of mine trying to turn that electric field strength into voltage, so that practicality can be checked. Unfortunately the result was that the 20 cm long AWG40 wire ( diameter: 0.0031" or 0.0050 mm ) would need to charged to 38.792 MV, which is a way above any voltage that was so far humanely feasible.
The voltage is a potential. Its direct value actually isn't interesting as it can be arbitrarily changed by guage. Essentially in Coulomb guage you can add or subtract any constant to it and get the same physical results. Its how the voltage changes from place to place, or the field that matters.
 

Shadowprophet

Truthiness
I'm just showing the Newtonian limit hoping that it will be better understood here. The exact calculation of geodesic motion for the solution of a more arbitrary static electric field configuration is 7.1.20abc at
Electromagnetism

No worries, This is the reasons people stop an question me a lot, I'm not fully on board with General relativity. I feel It's incomplete, People assume I disregard Gr. I just feel Relativity makes bold assumptions. I'm not saying the Quantum model is the way to go, I just feel relativity has Uhh.. "Plot Holes"

But yeah, It will take me a few minutes on the Ricci Calculus, I'm not swift with it. I can "Decipher it" But I'm no authority,
 

Shadowprophet

Truthiness
Though it may yield acceleration, its not like a warp drive. It won't go faster than light, but also requires no negative energy matter, nothing exotic.

Again Keep in mind, I have a broad understanding of physics, but I haven't committed to a model.
Would this method produce time dilation in its gravitational field? yes, I am hinting at time travel.

Or at least the dilation of time, to decrease the time necessary to get from a to b?
 
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