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Re: On Stuff
« Reply #20 on: March 17, 2019, 04:07:37 PM »
I do not think it is a huge question mark, because you can run the equation both ways. You can take a certain manifold and then solve for exactly the energy density needed to produce it. As for physical sources, one might find such energies during supernova events or in the early Universe.
Again, in theory, solving any tensor equation is far from easy and we've not observed any in nearly enough detail to comment, as far as I know.

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So the coordinates themselves contract. Interesting. What you are describing is similar to Lorentz contraction, except the claim is that you can boost this into a stationary frame.
The principle is different to curvature, it'd effect space more than it would time. There are no timelike curves, no distortion, it's just a matter of how far it is A to B. No matter how long the distance is, it wouldn't impact the rate at which you progress through time. Thinking about it as any kind of analogue to curvature won't help. Curvature, in this model, is essentially how long it takes you to get from one coordinate point to another; in flat spacetime, there'd be no difference, and the concentration of spacetime purely measures the distance from A to B, and the distance from one coordinate to the next stays constant.

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So there’s is a dynamic application here and a geometric one. Have you begun developing the equations? You seem to have thought through the structures, maybe it’s time to begin writing it down?

I’d love to see what you have so far, and am happy to do some of the mule work of checking limiting cases, locality, conservation properties, etc. These things would need to be checked anyway, and are usually considered by theorists to be a pain. Since I’ve done it many times for my own, I could probably whip through it and send you the calculations for your further development.
Did start a while ago, but would need to track it down. Modelling spacetime with a concept akin to diffusion, the logical behaviour of varying concentration, with a lack of viscosity (or at least negligible, though would be capped by the speed of light, but want to get it working in everyday situations before extending it that far) you get a PDE, and observations of the world get us boundary conditions. That was as far as my work got then, and it seemed like there were oversights with the BCs, but discussion ended up impossible with trolls derailing it, and the basic tools like separation of variables were insufficient. Might try tracking it down.
Honest it's never been a priority, as much as it gets brought up, it's never felt like math is going to help make my case, particularly anything advanced. Most people use it more to distract that discuss, if it gets provided they don't talk about it, if it doesn't they crow about it, and either way it tends more to get in the way of talking about principles. My goal's always been more to get interest and consideration, as much as scientists might be interested, the boundary conditions are based on my model of a FE and there's no way to justify any of that in a paper without ensuring no scientist will ever read further. Before it could ever be incorporated into GR I'll lose them.
I don't expect to be the next Einstein or anything, I know when something's beyond my skillset.
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Re: On Stuff
« Reply #21 on: March 17, 2019, 11:43:57 PM »
If your model’s curvature is how long it would take along a trajectory, then I am confused how it is space-like and not time-like. It seems to be to be a definition of curvature based on time.

Also, how can it not impact the rate you move through time of the rate is what you’re using to describe the geometry?

Yeah, separation of variables is likely not going to work in this regime. I encourage you to track it down and present it. Forget the trolls, we can work on it. It is critical to establishing the idea and checking to see if it will work.

And to be honest, scientists publish theories all the time that are based on models which they don’t think are correct. It is the exploration and open-mindedness that defines science. Heck, I’ve published 1D models for 3D phenomena! You’d be surprised how often it can lead to insights otherwise missed. So I disagree that you’d lose their attention.

Science is free, anything goes. Folks research all sorts of bizarre shit, from teleportation to warp drives to 2D spacetime...

Actual science is not what a lot of folks on this forum say it is.
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Re: On Stuff
« Reply #22 on: March 18, 2019, 12:36:07 AM »
If your model’s curvature is how long it would take along a trajectory, then I am confused how it is space-like and not time-like. It seems to be to be a definition of curvature based on time.

Also, how can it not impact the rate you move through time of the rate is what you’re using to describe the geometry?
They're describing different things. There are no curves, timelike or spacelike. Taking graph paper with irregularly spaced squares as an analogue for spacetime, if you curve it into a n shape then the dispersal of those squares doesn't change, but climbing up the curved surface does take a little longer. Ok, that's only because of gravity, but it's the principle.
The situation described in previous posts focuses on the dispersal of coordinate points, assuming that two adjacent points always take the same time to go between. The properties there are exclusively of those coordinate points.
GR doesn't even need the coordinates to exist, it'd lack some explanatory power but it could function with an arbitrary plane described by vector and devoid of building block, and it is focused on the journey from A to B. Assuming fixed distance between coordinate points, it is the journey that becomes harder. The cliche description of relativity is a bowling ball dropped in a blanket, but that kind of curvature only exists by pulling in more of the surroundings, but there's no flow of space caused by acceleration, you don't get drawn towards Concorde or any such thing, when, say, length dilation fundamentally takes the form of there seeming to be more distance to cross, if that was because of coordinates then those coordinate points would need to come from somewhere. That is, those distances can only seem to increase if distances elsewhere decrease, and that doesn't happen. it cannot be the same principle at play. Curvature as a term doesn't really cross over to this extension particularly well, it's more a measure of how difficult it is to move through spacetime. A kind of spatial friction if you will; when you near the speed of light you struggle to progress forward through time so things would seem to take longer, and you wouldn't seem  to progress as far as you should be through space (from an external reference point, of course).
Ties back to what the first post mentioned about photons, and the speed of light as a limit being an intrinsic property of spacetime.

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Yeah, separation of variables is likely not going to work in this regime. I encourage you to track it down and present it. Forget the trolls, we can work on it. It is critical to establishing the idea and checking to see if it will work.
Will try. Tempted to glance over but go from scratch, the underlying thought process was simple enough, don't want to make the ame mistakes. Should have time in a couple of days.
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Re: On Stuff
« Reply #23 on: March 18, 2019, 03:13:00 AM »
Oh, I see what your doing now. I didn’t understand that your model keeps the time between two points as invariant. Now it makes sense what you mean. Yes, this is quite different than GR; you are proposing an inherent coordinate system for the Universe as being fundamental, and then working forward.

You lose me with some of the discussion regarding application and GR comparison, but I think that’s just a function of attempting to describe it over a forum, an also me being used to talking about it non-colloquially.

It will be much clearer when we can reference the mathematics as the common language.

I look forward to it :)
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Re: On Stuff
« Reply #24 on: March 18, 2019, 11:28:35 AM »
It will be much clearer when we can reference the mathematics as the common language.

I look forward to it :)

That can't necessarily be promised, in my experience math helps with prediction more than understanding, and even then not always, particularly on topics like this. Like, my last notes were:

Mt + c1 M Mx + c2 M My + c3 M Mz = 0

And it's been a while so can't tell you all the details of how that was settled on, know it came from analyzing a number of wave equations used to model similar behaviour and this being the most accurate for inviscid flows, M modelling the concentration at any point, derivatives therefore how that concentration is varying/flowing in one direction, or over time, what's missing is the initial conditions but wanted to go through those again to double check, and that'll give more of a view of my model in general rather than the details of how this works. Like, Mx(0,0,0,t) = My(0,0,0,t)=Mz(0,0,0,t)=Mt(0,0,0,t)=0, but that's a subset of a separate boundary condition so... (Will properly define origin etc too with the rest, short version under the central pole, z as altitude).
Equally, Mz(0,0,z,t)=-gz-2
First steps at least.
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Re: On Stuff
« Reply #25 on: March 18, 2019, 11:50:28 AM »
It will be much clearer when we can reference the mathematics as the common language.

I look forward to it :)

That can't necessarily be promised, in my experience math helps with prediction more than understanding, and even then not always, particularly on topics like this. Like, my last notes were:

Mt + c1 M Mx + c2 M My + c3 M Mz = 0

And it's been a while so can't tell you all the details of how that was settled on, know it came from analyzing a number of wave equations used to model similar behaviour and this being the most accurate for inviscid flows, M modelling the concentration at any point, derivatives therefore how that concentration is varying/flowing in one direction, or over time, what's missing is the initial conditions but wanted to go through those again to double check, and that'll give more of a view of my model in general rather than the details of how this works. Like, Mx(0,0,0,t) = My(0,0,0,t)=Mz(0,0,0,t)=Mt(0,0,0,t)=0, but that's a subset of a separate boundary condition so... (Will properly define origin etc too with the rest, short version under the central pole, z as altitude).
Equally, Mz(0,0,z,t)=-gz-2
First steps at least.

Don’t worry, I won’t hold you to any promise. Let’s just explore :)

Thanks for the initial equation. What would help the discussion in the future is exposition like the following example:

The horizontal position of an object undergoing projectile motion is modelled as:

x(t)=x0+v0*t

Where x(t) is the x position as a function of time, x0 is the initial x position (the position at time=zero), v0 is the initial x speed, and t is the independent time variable.

In this fashion, every term is detailed for the reader, and it is clear how the equation is used.
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Re: On Stuff
« Reply #26 on: March 18, 2019, 04:42:06 PM »
Mt + c1 M Mx + c2 M My + c3 M Mz = 0 (not certain on this without finding my earlier reasoning, will say, meant to essentially function as a diffusion wave equation with Turing patterns and I can't find anything resembling this in a bit of hasty research I've done now)

Where M=M(x,y,z,t).
(x,y,z)=(0,0,0) is essentially the centre of the Earth, a point under the central pole, and each c is a constant to be determined by experimentation.
x,y are between -R and R, where R is the radius of the Earth. z between -h and h where h is... complicated to explain quickly, but basically the ellipsoid region formed by this (x,y,z) marks the point up to a significant discontinuity (which are after all pretty common when it comes to flows). t>0 signifies time, naturally.
M is essentially the amount of spacetime at a coordinate. The tricky part of this is that we're kind of inventing a coordinate system underlying spacetime, as we can't measure it with itself, but it is strictly mathematical. Mx My Mz are the rate of change in that direction, basically the flow. Mt is the rate of change in one location over time.

With boundary conditions:

M(x,y,z,t)=M(-x,-y,-z,t)
Mx(x,y,z,t)=Mx(-x,-y,-z,t)
My(x,y,z,t)=My(-x,-y,-z,t)
Mz(x,y,z,t)=Mz(-x,-y,-z,t)
Mx(x,y,0,t)= ek1(x+y)cos(x*n*pi)
My(x,y,0,t)= ek2(x+y)sin(y*m*pi)
Mz(0,0,z,t)=-g(h-z)-2
M(x,y,z,t)=M(x,y,z,t+P)

Each k, m, n are also constants to be found by experimentation.

(Beyond this region, M will be constant. Equally, M integrated over the region (x,y,z) to determine the net 'amount' within will also be constant and not depend on t).
So, basically there's a kind of reflective symmetry over the disk, rotational motion that forms shrinking inwards circular, spiralling motion at z=0, and a straight downwards force following the inverse square law over the centre, with z=9.8 approx. Also M is periodic over time. Though they tie more to my FE model than to GR.

The ideal situation would be some kind of solution, and the c values would determine things like whether M got larger or smaller towards the edge of the boundary, and that they could be approximately determines to give a gauge for the behaviour of spacetime. To be honest I don't expect that to happen, but wanted to give some indication as to the potential long term goals.
M itself admittedly is of less use due to its mathematical construction, but its derivatives give us a more constant rate of change that would have observable results relative to the Earth.

I think that's right at least, some of that's just copying things I noted down years back and I haven't yet tracked down where I got them from so there could be mistakes.
« Last Edit: March 19, 2019, 09:41:26 PM by JRowe »
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Re: On Stuff
« Reply #27 on: March 19, 2019, 12:15:59 AM »
Great! That was fast. My initial thoughts:

1. How can M be a flow rate if the units are not the units of a rate?

2. The boundary conditions have different dimensions in z direction vs x and y.

3. How does one interpret the cosine of a coordinate? What is the cosine of a meter? Is that physical?

4. Your constants c must have units of 1/M.

5. Cosine is an even function, so Mx(x,y*,*)=Mx(-x,-y,*,*) is possible to satisfy, but sine is an odd function, so I don’t see how one can simultaneously conserve parity while maintaining periodic boundary conditions.

6. By gauge for spacetime, do you mean a measure, or do you mean an extra degree of freedom (e.g., like choosing the Coulomb gauge in electrodynamics)?

Lastly, just want to express how bad-ass it is that you’re bringing these ideas to the forums. It’s not easy putting oneself out there like that. Takes balls and poise. I really appreciate your efforts and am enjoying the discussion.
« Last Edit: March 19, 2019, 12:18:45 AM by QED »
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Re: On Stuff
« Reply #28 on: March 19, 2019, 10:02:25 AM »
1. How can M be a flow rate if the units are not the units of a rate?

2. The boundary conditions have different dimensions in z direction vs x and y.

3. How does one interpret the cosine of a coordinate? What is the cosine of a meter? Is that physical?

4. Your constants c must have units of 1/M.

5. Cosine is an even function, so Mx(x,y*,*)=Mx(-x,-y,*,*) is possible to satisfy, but sine is an odd function, so I don’t see how one can simultaneously conserve parity while maintaining periodic boundary conditions.

6. By gauge for spacetime, do you mean a measure, or do you mean an extra degree of freedom (e.g., like choosing the Coulomb gauge in electrodynamics)?

Lastly, just want to express how bad-ass it is that you’re bringing these ideas to the forums. It’s not easy putting oneself out there like that. Takes balls and poise. I really appreciate your efforts and am enjoying the discussion.
1. M isn't the flow rate, its derivatives are. M is just the raw amount of of concentration. 
2. Yep, the region isn't meant to be a sphere.
3. Coordinate times pi, as far as I remember that's the standard way of creating a circle in polar coordinates, using radians.
4. They're dimensionless. M is a function.
5. The presence of z and t would presumably answer that, but looking back I'm not sure those sine/cosine boundary conditions work, they were one of the bits I copied and the x-2 factor I don't think quite has the effect I wanted. WIll go back and tweak.
6. Gauge as in measure. I try to avoid using technical terms where possible for accessibility's sake.
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Re: On Stuff
« Reply #29 on: March 19, 2019, 10:50:19 AM »
1. Okay

2. No, I mean the units aren’t the same. Look at Mx and compare to Mz, they have different units.

3. Yes you can do this with radians, but not a length. It’s unphysical to to take the cosine of a length ( or exponentiate it.

4. Look at the equation for a moment. How can you add Mt to c1MMx? The only way is if they have the same units. Just like how you can’t add 5 seconds to 3 meters. So assuming all M’s have the same unit, then c1 must have units of 1/M, otherwise the equation is dimensionally invalid.

5. Got it.

6.  Cool.
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Re: On Stuff
« Reply #30 on: March 19, 2019, 11:40:29 AM »
Coordinates aren't in units. Even if you create a graph where each coordinate is 1m apart, that doesn't change the point (1,1) to (1m,1m). Take the heat equation:

u denotes temperature, but there's no attempt to balance the two, particularly given alpha is often set to one. Differentiate it once with respect to time, and you have the same dimension has it being differentiated twice with respect to space; none. Same for taking the cosine, it's not the cosine of 1m*pi, just 1*pi, say.
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Re: On Stuff
« Reply #31 on: March 19, 2019, 04:13:27 PM »
Coordinates aren't in units. Even if you create a graph where each coordinate is 1m apart, that doesn't change the point (1,1) to (1m,1m). Take the heat equation:

u denotes temperature, but there's no attempt to balance the two, particularly given alpha is often set to one. Differentiate it once with respect to time, and you have the same dimension has it being differentiated twice with respect to space; none. Same for taking the cosine, it's not the cosine of 1m*pi, just 1*pi, say.

The heat equation absolutely agrees dimensionally. Alpha is the thermal diffusivity, and has a dimension. It is set to unity when you are solving the problem in units of alpha. But this does not somehow erase the dimensions from the final answer. U has units of kelvin. It’s independent variables are x,y,z. So when you plug in those coordinates - which are physical coordinates of distance - and evaluate the function, you get units of temperature.

Your Mx equation doesn’t give you units of flow when you input the x coordinate. Dimensionally it just doesn’t yield what you want it to.

And there does not exist any equation that evaluates the cosine of a dimensional quantity. A radian is a ratio of lengths, and is hence dimensionless.

Hope this helps!
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Re: On Stuff
« Reply #32 on: March 19, 2019, 09:40:48 PM »
The heat equation absolutely agrees dimensionally. Alpha is the thermal diffusivity, and has a dimension. It is set to unity when you are solving the problem in units of alpha. But this does not somehow erase the dimensions from the final answer. U has units of kelvin. It’s independent variables are x,y,z. So when you plug in those coordinates - which are physical coordinates of distance - and evaluate the function, you get units of temperature.

Your Mx equation doesn’t give you units of flow when you input the x coordinate. Dimensionally it just doesn’t yield what you want it to.

And there does not exist any equation that evaluates the cosine of a dimensional quantity. A radian is a ratio of lengths, and is hence dimensionless.

Hope this helps!
It's hard to comment on this. Universally everything I saw when studying equations like this made zero mention of units at any stage, for constants and for each term, my conclusion was that they were used simply as coordinates and it was only when all was said and done that it was applied directly to the physical phenomenon as is.

On the units present, M is basically dimensionless in of itself. It's essentially the amount of space in a certain space; that's L/L. Equally, I'll admit when I used the word 'flow' it was inaccurate, that's just how I tend to visualize it; at a basic level a flow is just the description of how something changes, and the derivative is by definition rate of change. Either way you wouldn't get the units for a flow of a fluid.
As far as radians go, can fix that with relative ease without changing the formula.
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Re: On Stuff
« Reply #33 on: March 20, 2019, 03:37:48 AM »
The heat equation absolutely agrees dimensionally. Alpha is the thermal diffusivity, and has a dimension. It is set to unity when you are solving the problem in units of alpha. But this does not somehow erase the dimensions from the final answer. U has units of kelvin. It’s independent variables are x,y,z. So when you plug in those coordinates - which are physical coordinates of distance - and evaluate the function, you get units of temperature.

Your Mx equation doesn’t give you units of flow when you input the x coordinate. Dimensionally it just doesn’t yield what you want it to.

And there does not exist any equation that evaluates the cosine of a dimensional quantity. A radian is a ratio of lengths, and is hence dimensionless.

Hope this helps!
It's hard to comment on this. Universally everything I saw when studying equations like this made zero mention of units at any stage, for constants and for each term, my conclusion was that they were used simply as coordinates and it was only when all was said and done that it was applied directly to the physical phenomenon as is.

On the units present, M is basically dimensionless in of itself. It's essentially the amount of space in a certain space; that's L/L. Equally, I'll admit when I used the word 'flow' it was inaccurate, that's just how I tend to visualize it; at a basic level a flow is just the description of how something changes, and the derivative is by definition rate of change. Either way you wouldn't get the units for a flow of a fluid.
As far as radians go, can fix that with relative ease without changing the formula.

Hmmm, that is a surprise to me. One of the first things we teach our physics students is something called dimensional analysis, which trains them to always assure that the units balance. Any equation that does not do this is by definition unphysical (and is the worst mistake a student can make on their problem sets). But they are trained for this, of course, and I do not intend criticism of you, only to convey assurance that this is indeed true.

The conceptual difficulty here is that describing the amount of space in a space requires the space to exist in something. It makes no sense to talk about the space volume, i.e., the amount of space in a given volume, or the space density if you prefer, because the space DEFINES the volume. We really need space to exist in something for this to work. In other words, at some point we’ll need to either define some kind of substrate that space exists within, or resort to a geometrical definition of concentration. Either option may be viable, but you should be the one to make the call.
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Re: On Stuff
« Reply #34 on: March 20, 2019, 01:30:36 PM »
Hmmm, that is a surprise to me. One of the first things we teach our physics students is something called dimensional analysis, which trains them to always assure that the units balance. Any equation that does not do this is by definition unphysical (and is the worst mistake a student can make on their problem sets). But they are trained for this, of course, and I do not intend criticism of you, only to convey assurance that this is indeed true.

The conceptual difficulty here is that describing the amount of space in a space requires the space to exist in something. It makes no sense to talk about the space volume, i.e., the amount of space in a given volume, or the space density if you prefer, because the space DEFINES the volume. We really need space to exist in something for this to work. In other words, at some point we’ll need to either define some kind of substrate that space exists within, or resort to a geometrical definition of concentration. Either option may be viable, but you should be the one to make the call.
I approached on more mathematical grounds, that might be all. I'm familiar with dimensional analysis, just never in applying it to PDEs.
Mathematically it is being modelled with reference to an underlying dimension, just because that's the easiest way to model it. In practise it's essentially geometrical, the same as curvature; it's not like space curves through another dimension, it's just how we refer to it because we're talking in a language invented to point out which tree had the nice fruit up it rather than outline the fundamentals of reality. If we have two identical objects, we can put one in location A, then if the other appears larger at location B and smaller at location C than the original (from the perspective from location A), then B would be defined to have a lower concentration and C to have a higher. Equally, if you were at location B then both would seem smaller, and at C both would seem larger.
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Re: On Stuff
« Reply #35 on: March 20, 2019, 10:54:22 PM »
Hmmm, that is a surprise to me. One of the first things we teach our physics students is something called dimensional analysis, which trains them to always assure that the units balance. Any equation that does not do this is by definition unphysical (and is the worst mistake a student can make on their problem sets). But they are trained for this, of course, and I do not intend criticism of you, only to convey assurance that this is indeed true.

The conceptual difficulty here is that describing the amount of space in a space requires the space to exist in something. It makes no sense to talk about the space volume, i.e., the amount of space in a given volume, or the space density if you prefer, because the space DEFINES the volume. We really need space to exist in something for this to work. In other words, at some point we’ll need to either define some kind of substrate that space exists within, or resort to a geometrical definition of concentration. Either option may be viable, but you should be the one to make the call.
I approached on more mathematical grounds, that might be all. I'm familiar with dimensional analysis, just never in applying it to PDEs.
Mathematically it is being modelled with reference to an underlying dimension, just because that's the easiest way to model it. In practise it's essentially geometrical, the same as curvature; it's not like space curves through another dimension, it's just how we refer to it because we're talking in a language invented to point out which tree had the nice fruit up it rather than outline the fundamentals of reality. If we have two identical objects, we can put one in location A, then if the other appears larger at location B and smaller at location C than the original (from the perspective from location A), then B would be defined to have a lower concentration and C to have a higher. Equally, if you were at location B then both would seem smaller, and at C both would seem larger.

Okay, so geometrical it is.

Now, the question is how to formalize it in a way that is consistent and testable.

Your idea is quite similar to special relativity, which already accounts for the distortion of objects sizes (Lorentz contraction), and only assumes the speed of light to be constant - a very bare bones set of assumptions.

To adapt this to geometry is the key, and we cannot use the trick of special relativity since you want the time intervals to be concentration independent (the time it takes to travel is adjacent coordinates is invariant). Hence, what then must change are the speeds. This means, for two observers in the same reference frame, they will measure the same object moving at different speeds and having a different size, but will agree on the travel time.

This should be testable. The question is how much concentration do we need to notice a measurable difference in the speed, and can we produce that on Earth?

Any ideas?
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Offline JRowe

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Re: On Stuff
« Reply #36 on: March 21, 2019, 02:10:35 AM »
To adapt this to geometry is the key, and we cannot use the trick of special relativity since you want the time intervals to be concentration independent (the time it takes to travel is adjacent coordinates is invariant). Hence, what then must change are the speeds. This means, for two observers in the same reference frame, they will measure the same object moving at different speeds and having a different size, but will agree on the travel time.

This should be testable. The question is how much concentration do we need to notice a measurable difference in the speed, and can we produce that on Earth?

Any ideas?
Speed probably would be the best way to directly measure this aspect, yes. Producing's something of a question mark, a way for matter to directly influence is not something I have more than speculation on, but as far as using pre-existing concentrations go that might be doable. The question mark would be, like you say, how much of a variation would be needed to observe a difference in speed. That much is what the equation is meant to answer, shoulder it be solved, so precise figures are currently not feasible.
But, so the theory goes, concentrations do increase at higher altitudes. That would be the most practical example of this issue. The biggest problem I see there would be measuring the speed from the more distant observer.
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Re: On Stuff
« Reply #37 on: March 21, 2019, 03:03:19 PM »
Your altitude boundary condition, Mz=-g(h-z)^2, has units of s^(-2)m^(-1). So this means that it is not time invariant. That is, it will not permit the time interval to be the same between adjacent spacetime coordinates.

I recommend using speed in your equations, since that is what must change depending on the observer. Somehow, the resulting speed must change depending on the observer’s position in that Reference frame, and must do so without any time dependence. Something like this:

Mz=-R_abcd*g^(ab)*[v^(c)]^2/[(h-z)*g]

Where R_abcd is the curvature tensor, g^(ab) is your curvature metric, v^(c) is your four-velocity vector, and g is local gravity.

The curvature tensor contracts across two spacetime coordinates with the metric to give you the area curvature, and then this contracts with your four velocity to give proper velocity along one axis (z). The proper velocity will be modified by the height (z) above some scale factor (h) and depends on local gravity there.

Try tinkering with this a while. The next stage is to discover transformation equations so that the proper velocity appears different to observers depending on their coordinates in that frame.
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Re: On Stuff
« Reply #38 on: March 21, 2019, 03:20:46 PM »
Your altitude boundary condition, Mz=-g(h-z)^2, has units of s^(-2)m^(-1). So this means that it is not time invariant. That is, it will not permit the time interval to be the same between adjacent spacetime coordinates.
It's g the mathematical constant, not the acceleration.

Quote
Try tinkering with this a while. The next stage is to discover transformation equations so that the proper velocity appears different to observers depending on their coordinates in that frame.
Will try to unpack it in a sec.
My DE model explained here.
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Offline QED

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Re: On Stuff
« Reply #39 on: March 22, 2019, 03:45:08 AM »
Your altitude boundary condition, Mz=-g(h-z)^2, has units of s^(-2)m^(-1). So this means that it is not time invariant. That is, it will not permit the time interval to be the same between adjacent spacetime coordinates.
It's g the mathematical constant, not the acceleration.

Quote
Try tinkering with this a while. The next stage is to discover transformation equations so that the proper velocity appears different to observers depending on their coordinates in that frame.
Will try to unpack it in a sec.

Do you mean Newton’s constant? That’s G=6.7*10^(-11) m^3 kg^(-1) s^(-2).

In this case, Mz has units of m*kg^(-1)*s^(-2) and is still not time invariant.

Cool, let me know how it strikes you. 
The fact.that it's an old equation without good.demonstration of the underlying mechamism behind it makes.it more invalid, not more valid!

- Tom Bishop

We try to represent FET in a model-agnostic way

- Pete Svarrior