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Offline JRowe

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On Stuff
« on: February 25, 2019, 03:38:01 PM »
Matter and energy exist, though there are different forms of each.

For matter, this is simple. Obviously you have different states of matter, different elements, but if you break it all down at the end of the day it's just stuff, whether you want to talk about atoms or baryons or quarks. There is of course the interesting quantum question, of whether these end up just being waves if you look at them closely, but given that waves are typically free to dissipate there is plainly something non-wavelike about matter. All of which is a drastic oversimplification of quantum theory, but it merited acknowledgement.
At a basic level we can break all matter down into this stuff. There are interactions with energy that help distinguish it all, but this provides a simple visualisation. On a macro scale it is even easier to see; you can have a solid cube that you drop into water, say, and it cannot occupy the same location as the water. However if the cube is porous, you end up finding that the water and cube essentially may indeed occupy the same location, the water running through the cube, or the cube running through the water, whichever way you want to visualize it.

Energy, now, is where it gets interesting. There are many types of energy. Heat energy, which manifests essentially as the vibration of molecules (also as a form of radiation, that is waves). Sound energy, which really is just an illusion born of human perception, it is again just vibrations that go through matter, but when those vibrations reach our eardrums it is interpreted a specific way by the brain. Again, just vibration. Kinetic energy, obviously, is just the movement of matter. Electrical energy is manifested by the movement of specific types of matter, and this is when we get onto concepts such as chemical energy, potential energy stored that one day could manifest as another type of energy. At a basic level energy and movement are equivalent.
And then we get to light. Though it is modelled as a wave, and it can indeed impart other forms of energy, it does not seem to be as simple as a vibration carried by matter. The trivial resolution to this is the photon, positing that the photon is the particle which carries the wave of light and thus vibrates in such a fashion, but this is unsatisfactory. It does not allow for wavelike behaviour. What does, however, is ironically simple: multiple particles.

Think now of the famous double slit experiment, only instead of photons, we use water. Water waves interfere with each other, create similar patterns to light, but if you then constrain what happens to a single molecule of water going through at a time, you no longer observe the interference pattern. Understanding the double slit experiment, really, is trivially simple. If you limit things so that you can observe a single basic particle, it no longer has anything to interfere with. Only when things are unlimited, when there is no equipment getting in the way to allow you to observe, can the interference occur.
Light, then, is similar. The notion of an 'aether' that carries light must indeed be accurate, it just wasn't as it used to be posited. The light waves themselves are carried by multiple fundamental particles, photons, that only behave the way they do when they are carrying lightwaves. One might say they are synonymous with light, but at the end of the day the two statements are equivalent; energy cannot be created or destroyed, the emission of a photon simply creates the photon by converting it from some other non-photon potential. Something is done that transforms it into a photon, the addition of 'light' if you will. It then carries this light, and we observe all we do.
The only thing special about light, in this case, is its speed limit. As I hope we all know, anything with mass that approaches the speed of light in vacuum ends up warping spacetime around itself.

So far I'm just expressing what is already known, albeit with a couple of odd bits of focus.
My proposal is thus: there are two building blocks to everything. Movement, and stuff. Movement gives us energy, this 'stuff' gives us matter, though precisely what type of matter depends on energy. There is no more and no less than this. Light is a massless particle with a 'charge' of energy, creating a photon.
This is in line with all we know. The extension is where this gets interesting.

I glossed over photons just now. They are converted from a potential, yes, but what is this? Are lightbulbs haemorrhaging matter without losing mass? We're treading on the toes of thermodynamics with that thought experiment, but it is an illustration. Perhaps it is raw energy converted into matter, we know this is possible, living things do it all the time. The quantum understanding of matter makes this easy; what sets apart a wave of energy and a quantum wave of a fundamental particle of matter is perhaps most simply thought of as some kind of binding that keeps it in place on a macro scale. So long as that can be generated, energy becomes matter.
The third option, though, is the aether response. Instead of a medium which carries a wave, it is a medium composed of stuff already, and the introduction of a light-charge simply shifts a particle of this into a photon, in the same way a colour-charge defines a quark. If there is such a medium it must be universal. If you want to imagine it as a sea of molecules, a light-charge essentially transforms one molecule of substance A into substance B with wholly different properties, such as a velocity.
And thus, we reach the conclusion of this. I propose that the medium of light is spacetime itself, that spacetime is composed of another fundamental form of matter. This isn't an alien idea, John Wheeler hypothesised a type of quantum foam, this is simply a generalisation of that.
Location, then, is much like the porous cube mentioned above. You occupy the same space as this primarily non-interacting matter. In a similar fashion, this also means that the speed of light in vacuum is not a property of light, but rather it is the limit to the movement of the fundamental components of spacetime. If a mass is moving at high speeds, it moves faster than the space it occupies can keep up with, of course that is impossible. Relativity begins to make intuitive sense.

I could take this to more speculative ground, analyze why the postulates of relativity are what they are, rather than merely stating it. One could suppose that the particles composing spacetime are locally uniform, thus any force that keeps them together, limiting movement and causing the speed limit, will be constant. In this way, the assumption of the homogeneity of spacetime and the speed of light in vacuum being constant are equivalent. It also tells us the situations in which relativity will break down, and why, taking us a step closed to a unified model.

This is just a lot of theoretical underpinning to the concept of spacetime possessing some form of building block, and by extension the potential for varying concentrations, but I hope it begins to demonstrate the ramifications for even understood science. A lot of topics are treated as big mysteries, or "This is just the way it is," but there are answers to the why as well.
My DE model explained here.
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Offline QED

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Re: On Stuff
« Reply #1 on: March 09, 2019, 05:27:00 PM »
Hi JRowe,

A very nice exposition! I like your idea of a quantum foam. Quantum Field Theory supports this hypothesis, with the idea of quantum virtual pair particles being created and annihilated all the time. This results in an average background energy density which is non-zero, and hence can be interpreted as a medium. Thus, there really is no vacuum on the quantum level. This immediately raises the question in my mind: how does light propagate through this medium? Does it interact with these virtual pairs? QFT says that it should. But I think it would be difficult to try to describe how on a large scale.

If you have a moment, please check out my post on FE Theory. I need your help!

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Re: On Stuff
« Reply #2 on: March 09, 2019, 07:34:43 PM »
This immediately raises the question in my mind: how does light propagate through this medium? Does it interact with these virtual pairs? QFT says that it should. But I think it would be difficult to try to describe how on a large scale.
Propagation through the medium is the easy part. At a basic level the medium of space time simply acts as a coordinate space, the building blocks being those coordinates. Propagation is just a matter of where a photon exists relative to thsoe coordinates.
The transformation is the interesting topic. Photons would be near unique in this regard, existing and being absorbed instantaneously from its perspective, and given that virtual particles are made/destroyed at the same rate then only something with that property could be made from them.
My DE model explained here.
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Re: On Stuff
« Reply #3 on: March 10, 2019, 02:54:20 AM »
I must confess I am struggling a bit to fully understand that. If a virtual particle interacts with light then (according to QFT now) then couldn’t the particle re-emit it while conserving momentum? If so, then light would not seem to need the same property as the virtual particle. I think maybe that I’m just not getting what you mean though.

Another thought I just had: if a virtual particle interacts in elastic ally with a photon, then it would become on-shell, and manifest as real. So we could observe it! I imagine it would look like a cascade that follows the photon’s trajectory.

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Re: On Stuff
« Reply #4 on: March 10, 2019, 05:34:11 PM »
I must confess I am struggling a bit to fully understand that. If a virtual particle interacts with light then (according to QFT now) then couldn’t the particle re-emit it while conserving momentum? If so, then light would not seem to need the same property as the virtual particle. I think maybe that I’m just not getting what you mean though.

Another thought I just had: if a virtual particle interacts in elastic ally with a photon, then it would become on-shell, and manifest as real. So we could observe it! I imagine it would look like a cascade that follows the photon’s trajectory.
Light isn't something that the medium interacts with, it is a property that some of it can possess, thus 'creating' a photon.
My DE model explained here.
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Re: On Stuff
« Reply #5 on: March 13, 2019, 02:52:02 PM »
I must confess I am struggling a bit to fully understand that. If a virtual particle interacts with light then (according to QFT now) then couldn’t the particle re-emit it while conserving momentum? If so, then light would not seem to need the same property as the virtual particle. I think maybe that I’m just not getting what you mean though.

Another thought I just had: if a virtual particle interacts in elastic ally with a photon, then it would become on-shell, and manifest as real. So we could observe it! I imagine it would look like a cascade that follows the photon’s trajectory.
Light isn't something that the medium interacts with, it is a property that some of it can possess, thus 'creating' a photon.

Hmmm, not sure I’ve ever heard of light being a property of a system before. In QFT, light is represented as a quantum electromagnetic field, which then interacts with the quantum field of a system. The photon that propagates is a local excitation of that field which results from the interaction.

I wonder how one would describe light as a property? Light HAS properties...

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Re: On Stuff
« Reply #6 on: March 13, 2019, 03:14:30 PM »
Hmmm, not sure I’ve ever heard of light being a property of a system before. In QFT, light is represented as a quantum electromagnetic field, which then interacts with the quantum field of a system. The photon that propagates is a local excitation of that field which results from the interaction.

I wonder how one would describe light as a property? Light HAS properties...
It's a slight abuse of terminology, but it's a useful one to help explain things. Nothing gets created or destroyed, merely converted; before light is emitted, everything that is required for a photon already exists in its vicinity, it just has not been 'converted' to a photon. Thus, light can be viewed as a property, and through possessing that property part of the medium becomes what we call a photon, with all the properties that entails. That's the gist at least.
My DE model explained here.
Open to questions, but if you're curious start there rather than expecting me to explain it all from scratch every time.

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Re: On Stuff
« Reply #7 on: March 13, 2019, 04:52:27 PM »
Hmmm, not sure I’ve ever heard of light being a property of a system before. In QFT, light is represented as a quantum electromagnetic field, which then interacts with the quantum field of a system. The photon that propagates is a local excitation of that field which results from the interaction.

I wonder how one would describe light as a property? Light HAS properties...
It's a slight abuse of terminology, but it's a useful one to help explain things. Nothing gets created or destroyed, merely converted; before light is emitted, everything that is required for a photon already exists in its vicinity, it just has not been 'converted' to a photon. Thus, light can be viewed as a property, and through possessing that property part of the medium becomes what we call a photon, with all the properties that entails. That's the gist at least.

I see, that helps. Since nothing is created/destroyed, but only converted from something else, then in principle isn’t everything is a property? If so, what do we identify that it is a property of?

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Re: On Stuff
« Reply #8 on: March 13, 2019, 05:02:09 PM »
Hmmm, not sure I’ve ever heard of light being a property of a system before. In QFT, light is represented as a quantum electromagnetic field, which then interacts with the quantum field of a system. The photon that propagates is a local excitation of that field which results from the interaction.

I wonder how one would describe light as a property? Light HAS properties...
It's a slight abuse of terminology, but it's a useful one to help explain things. Nothing gets created or destroyed, merely converted; before light is emitted, everything that is required for a photon already exists in its vicinity, it just has not been 'converted' to a photon. Thus, light can be viewed as a property, and through possessing that property part of the medium becomes what we call a photon, with all the properties that entails. That's the gist at least.

I see, that helps. Since nothing is created/destroyed, but only converted from something else, then in principle isn’t everything is a property? If so, what do we identify that it is a property of?
To an extent, but that aspect was little more than awkward terminology to demonstrate the bigger point; the concept of spacetime as composed of an actual building block.
At a basic level though, everything is just going to be a function of the two things mentioned in the original post. This 'stuff' as the most fundamental type of matter, devoid of charge and mass and anything, and movement which thus gives means to differentiate via the presence of energy. (Though if you want to get even more basic, at a quantum level matter is just energy bound by something so that binding would be the other fundamental in place of matter).
My DE model explained here.
Open to questions, but if you're curious start there rather than expecting me to explain it all from scratch every time.

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Re: On Stuff
« Reply #9 on: March 13, 2019, 11:03:59 PM »
Hmmm, not sure I’ve ever heard of light being a property of a system before. In QFT, light is represented as a quantum electromagnetic field, which then interacts with the quantum field of a system. The photon that propagates is a local excitation of that field which results from the interaction.

I wonder how one would describe light as a property? Light HAS properties...
It's a slight abuse of terminology, but it's a useful one to help explain things. Nothing gets created or destroyed, merely converted; before light is emitted, everything that is required for a photon already exists in its vicinity, it just has not been 'converted' to a photon. Thus, light can be viewed as a property, and through possessing that property part of the medium becomes what we call a photon, with all the properties that entails. That's the gist at least.

I see, that helps. Since nothing is created/destroyed, but only converted from something else, then in principle isn’t everything is a property? If so, what do we identify that it is a property of?
To an extent, but that aspect was little more than awkward terminology to demonstrate the bigger point; the concept of spacetime as composed of an actual building block.
At a basic level though, everything is just going to be a function of the two things mentioned in the original post. This 'stuff' as the most fundamental type of matter, devoid of charge and mass and anything, and movement which thus gives means to differentiate via the presence of energy. (Though if you want to get even more basic, at a quantum level matter is just energy bound by something so that binding would be the other fundamental in place of matter).

So like, are there any descriptions of this “stuff” that is the building blocks of spacetime? I mean is anything known about it, or is it just postulated as an assumption of your model?

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Re: On Stuff
« Reply #10 on: March 14, 2019, 02:13:06 AM »
So like, are there any descriptions of this “stuff” that is the building blocks of spacetime? I mean is anything known about it, or is it just postulated as an assumption of your model?
Concluded would be a more accurate word than postulated, for the reasons gone into.
All that's used is that it exists, that spacetime is not mere vector. The logical extension from this is to extrapolate a notion of concentration, that coordinate points can be sparser relative to other zones.
My DE model explained here.
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Re: On Stuff
« Reply #11 on: March 15, 2019, 02:39:11 PM »
So like, are there any descriptions of this “stuff” that is the building blocks of spacetime? I mean is anything known about it, or is it just postulated as an assumption of your model?
Concluded would be a more accurate word than postulated, for the reasons gone into.
All that's used is that it exists, that spacetime is not mere vector. The logical extension from this is to extrapolate a notion of concentration, that coordinate points can be sparser relative to other zones.

Do you have any advice on how I would then formalise spacetime? Usually, when describing properties distinguishable by location, one either uses scalar fields or vector fields. I don’t really know of a third option. Since you’ve explained that space time is not a vector (field?), and I assume it isn’t a scalar field either - since you seemed to imply it was something more involved or fundamental than a vector field, while scalar field is more elementary, how do we model it?

So basically, I’m asking for help pinning down the specifics, so that it can be formalised into FE theory.

Any help you can offer would be greatly appreciated.

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Re: On Stuff
« Reply #12 on: March 16, 2019, 09:31:54 AM »
Do you have any advice on how I would then formalise spacetime? Usually, when describing properties distinguishable by location, one either uses scalar fields or vector fields. I don’t really know of a third option. Since you’ve explained that space time is not a vector (field?), and I assume it isn’t a scalar field either - since you seemed to imply it was something more involved or fundamental than a vector field, while scalar field is more elementary, how do we model it?

So basically, I’m asking for help pinning down the specifics, so that it can be formalised into FE theory.

Any help you can offer would be greatly appreciated.
it would still be a vector field, especially over uniform stretches. Non-uniform stretches still function basically the same way, but it isn't as though curved spacetime hasn't been modelled, you just need to allow for the possibility for, say, the distance between two parallel straight lines to not always be constant. Just because spacetime has properties beyond just being a direction doesn't prevent it from being modelled, you just have to  account for those properties too. That's done with relativity, you just need to use tensors to calculate distance instead so you account for more. This situation's a little more involved, and most of the time you could approximate but at the end of the day all you really need is dt, know the rate of change of the concentration at any location. if it's predictable, and it seems reasonable to me that it would be (the only cause that's worth considering, that is without assuming whole new entities, would be the concentration of nearby locations) then in theory there's no problem.
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Re: On Stuff
« Reply #13 on: March 16, 2019, 11:01:17 AM »
Oh! This is just general relativity that you are describing. The object that allows one to transform vectors on curved manifolds is called a covariant derivative, and the object used to help transform the tensors is called a Cristoffel symbol. Using these, it is possible to show that parallel lines stay that way on flat geometries, meet on closed geometries, and diverge on open geometries - this is a common problem that we assign our graduate students.

The paths taken by light through these geometries are called geodesics, and require a complicated mix of the dt’s you were talking about. The concentration you reference is the stress-energy tensor in the field equations.

Sorry, I thought your intention was to describe a theory for FE that competes with general relativity. Perhaps this was a clumsy assumption on my part. FE theory cannot survive alongside GR, because GR is consistent with (and predicts) a RE perspective.

Finally, I just want to point out that you described GR in a very intuitive fashion. Have you studied it before? If not, then I’d invite you to take a look. It’s uncommon to see that kind of intuition about such a complicated topic - the mathematics is so involved that extracting intuition is laborious. You may be a natural :)

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Re: On Stuff
« Reply #14 on: March 16, 2019, 12:22:21 PM »
Sorry, I thought your intention was to describe a theory for FE that competes with general relativity. Perhaps this was a clumsy assumption on my part. FE theory cannot survive alongside GR, because GR is consistent with (and predicts) a RE perspective.
Not just relativity, relativity is not concerned with concentration. This is a generalization without the homogeneity/uniformity of spacetime needing to be assumed. I'm plenty familiar with relativity, that was why it was mentioned, but this goes further than that. As far as relativity is concerned, the concentration referred to above is constant and the distance between parallel straight lines would always be constant, that is the only variation in spacetime would develop from an object's acceleration.
The dt GR uses is dependent on the object, not the local behaviour of spacetime.

GR's greatest flaw is that it isn't concerned with why things happen, only that they do. Assumptions are made because the math requires it, and it's in line with experimental data, but there's no understanding as to where those assumptions originate. That, and it's already accepted that GR is not complete, science never is, and in the same way that Einstein extended Newton, by giving a single formula that, when certain values are small, is identical to Newton, GR can, should and will be extended similarly in such a fashion that, while in certain situations the current math holds, when other variables change so too will the effect. For example, if the concentration of spacetime is included as a factor, one could theoretically encompass QFT as occurring when the sizes of objects nears that of the distance between the 'coordinate points' composing spacetime, for an easy example.

Concentration and curvature are not the same.
My DE model explained here.
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Re: On Stuff
« Reply #15 on: March 16, 2019, 03:09:20 PM »
Sorry, I thought your intention was to describe a theory for FE that competes with general relativity. Perhaps this was a clumsy assumption on my part. FE theory cannot survive alongside GR, because GR is consistent with (and predicts) a RE perspective.
Not just relativity, relativity is not concerned with concentration. This is a generalization without the homogeneity/uniformity of spacetime needing to be assumed. I'm plenty familiar with relativity, that was why it was mentioned, but this goes further than that. As far as relativity is concerned, the concentration referred to above is constant and the distance between parallel straight lines would always be constant, that is the only variation in spacetime would develop from an object's acceleration.
The dt GR uses is dependent on the object, not the local behaviour of spacetime.

GR's greatest flaw is that it isn't concerned with why things happen, only that they do. Assumptions are made because the math requires it, and it's in line with experimental data, but there's no understanding as to where those assumptions originate. That, and it's already accepted that GR is not complete, science never is, and in the same way that Einstein extended Newton, by giving a single formula that, when certain values are small, is identical to Newton, GR can, should and will be extended similarly in such a fashion that, while in certain situations the current math holds, when other variables change so too will the effect. For example, if the concentration of spacetime is included as a factor, one could theoretically encompass QFT as occurring when the sizes of objects nears that of the distance between the 'coordinate points' composing spacetime, for an easy example.

Concentration and curvature are not the same.

That is not my understanding of relativity, though. Uniformity/homogeneity is not an assumption of GR, and in fact is a consequence of taking the weak field limit. GR is not only geometry, but also provides the explanation for it. This is the right side of the field equations. Solving them explains how energy density - the concentrations - create the geometry. The dt in GR is a description of the changing geometry of space itself - not the object. What one has to do is find the geometry first, and THEN compute the trajectories of the objects through them. The reason why this is so hard is because the process is coupled. Objects (having concentrations) can distort the geometry they are moving through too!

The only assumptions of GR is that 1) the laws do not suddenly change if you shift your coordinate system, and b) there isn’t some second kind of mass that characterizes objects. These assumptions originate from occam’s razor, and form a minimum set one would need. All FE conjectures I have seen have them implicitly.

But you propose a different theory, yes?

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Re: On Stuff
« Reply #16 on: March 16, 2019, 11:16:40 PM »
But you propose a different theory, yes?
No more different than Einstein was to Newton, it works as an extension, not replacement. The geometry of spacetime as RET posits is exclusively curvature, when it talks about length and time altering it isn't a variation on the concentration of any coordinate points, at least not directly. All that changes is the curve, not the dispersal; this does have a connection, but not in any formalized way, and it is the only time GR comes close. When I talk about uniformity of spacetime, it's things like this; if you're in an inertial reference frame then there is no vehicle by which spacetime might alter. it allows for no alteration beyond acceleration or mass, and as much as there might be issues with the mass side of it, that's more practical than theoretical. Focusing on this, GR is limited in the situations it can apply.
GR posits that the geometry of spacetime can be calculated exclusively by the behavior of the masses within it. This is unjustified and, in my view, simply false. Rather my view is that the behavior of the local region of spacetime must also be taken into account, which has a concentration that might vary independently of the behaviour of matter and energy within it. That is what my post means when it talks about the dt of spacetime.

GR is not wrong, so much as it is incomplete. it cannot tell you why the speed of light is an absolute limit, only that it is. it cannot tell you why it is not yet unified with other theories, only that it doesn't yet work there.
My DE model explained here.
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Re: On Stuff
« Reply #17 on: March 17, 2019, 02:55:16 AM »
But you propose a different theory, yes?
No more different than Einstein was to Newton, it works as an extension, not replacement. The geometry of spacetime as RET posits is exclusively curvature, when it talks about length and time altering it isn't a variation on the concentration of any coordinate points, at least not directly. All that changes is the curve, not the dispersal; this does have a connection, but not in any formalized way, and it is the only time GR comes close. When I talk about uniformity of spacetime, it's things like this; if you're in an inertial reference frame then there is no vehicle by which spacetime might alter. it allows for no alteration beyond acceleration or mass, and as much as there might be issues with the mass side of it, that's more practical than theoretical. Focusing on this, GR is limited in the situations it can apply.
GR posits that the geometry of spacetime can be calculated exclusively by the behavior of the masses within it. This is unjustified and, in my view, simply false. Rather my view is that the behavior of the local region of spacetime must also be taken into account, which has a concentration that might vary independently of the behaviour of matter and energy within it. That is what my post means when it talks about the dt of spacetime.

GR is not wrong, so much as it is incomplete. it cannot tell you why the speed of light is an absolute limit, only that it is. it cannot tell you why it is not yet unified with other theories, only that it doesn't yet work there.

It is not just mass...it is energy in any form. This is what the stress energy tensor means.

As for inertial frames, GR explains precisely how spacetime would alter - it would be affected by energy densities elsewhere. For example, an inertial frame could encounter a gravitational wave. To say it allows for no alteration beyond acceleration or mass just isn’t true, if I am understanding your statement correctly. There does not need to be mass anywhere, and there will still be a curved geometry.

But I think I am starting to get a feel for your theory. What you want to do is this (please correct me where I’m mistaken):

1: you acknowledge GR as an accurate theory but with limited applicability.

2: you propose to introduce an additional parameterization that measures the “concentration” of spacetime.

3: you propose to demonstrate that this parameter couples with the stress energy tensor to provide a wider predictive landscape for JGR (JRowe’s GR).

So, this is interesting. I have many questions.

a. What is concentrated, exactly. When there is a higher concentration of spacetime, what is there more of? You see, spacetime is a coordinate system. How do you concentrate that? Is there a susbstance that exists? This requires a rigorous definition in order to formally add it to GR.

b. Would the coupling to the stress energy tensor be linear?

c. If yes to b, then it should be easier to add it in. You could even demonstrate that in the weak concentration limit, JGR reduces to GR. That would get scientists’ attention, BTW.

I await with anticipation for your thoughts. It is not easy to find someone here willing to dive in, so I encourage your continued efforts. Kick-ass so far, man.

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Re: On Stuff
« Reply #18 on: March 17, 2019, 10:16:49 AM »
As for inertial frames, GR explains precisely how spacetime would alter - it would be affected by energy densities elsewhere. For example, an inertial frame could encounter a gravitational wave. To say it allows for no alteration beyond acceleration or mass just isn’t true, if I am understanding your statement correctly. There does not need to be mass anywhere, and there will still be a curved geometry.
The energy side effect went unmentioned purely because as far as I'm aware, it's  purely theoretical, the amount of energy it would take is a huge question mark, and ditto for its properties. Either way though, GR posits that spacetime only changes because of the behavior of things within it.

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a. What is concentrated, exactly. When there is a higher concentration of spacetime, what is there more of? You see, spacetime is a coordinate system. How do you concentrate that? Is there a susbstance that exists? This requires a rigorous definition in order to formally add it to GR.
This was the topic of the rest of the thread. The concentration is of, well, those coordinate points; if you want to take Wheeler's hypothesis, more of the building blocks of spacetime. in some places the coordinates are more densely packed, in others more sparsely.

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b. Would the coupling to the stress energy tensor be linear?

c. If yes to b, then it should be easier to add it in. You could even demonstrate that in the weak concentration limit, JGR reduces to GR. That would get scientists’ attention, BTW.
It's not weak concentration limit, just if the rate of change of the concentration over the space examined is zero, then you'd get typical GR. That much probably indicates the issues with adding it; you'd have to account for the difference in concentration between the start and end of the motion, and while that would be infinitesimal at any instant in time, it necessitates a separate PDE where the location of whatever's being examined is incorporated, and the relative concentration is calculated via that, and that is probably the tricky part (and it's not like the rest is easy) because while the solution of that PDE could be included directly into GR, to my knowledge it's not even known if there would be a unique solution.
What would need to be added to the formula would basically be in terms of that solution with the partial derivative in terms of time, and the partial derivative in terms of the axis of the direction of motion (so, t and x basically with a suitable coordinate system). Near the Earth's surface I think that'd be mostly negligible, and that certainly matches up with observations, but more accurate analysis of celestial phenomenon is where it becomes important.
My DE model explained here.
Open to questions, but if you're curious start there rather than expecting me to explain it all from scratch every time.

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Re: On Stuff
« Reply #19 on: March 17, 2019, 02:24:28 PM »
As for inertial frames, GR explains precisely how spacetime would alter - it would be affected by energy densities elsewhere. For example, an inertial frame could encounter a gravitational wave. To say it allows for no alteration beyond acceleration or mass just isn’t true, if I am understanding your statement correctly. There does not need to be mass anywhere, and there will still be a curved geometry.
The energy side effect went unmentioned purely because as far as I'm aware, it's  purely theoretical, the amount of energy it would take is a huge question mark, and ditto for its properties. Either way though, GR posits that spacetime only changes because of the behavior of things within it.

Quote
a. What is concentrated, exactly. When there is a higher concentration of spacetime, what is there more of? You see, spacetime is a coordinate system. How do you concentrate that? Is there a susbstance that exists? This requires a rigorous definition in order to formally add it to GR.
This was the topic of the rest of the thread. The concentration is of, well, those coordinate points; if you want to take Wheeler's hypothesis, more of the building blocks of spacetime. in some places the coordinates are more densely packed, in others more sparsely.

Quote
b. Would the coupling to the stress energy tensor be linear?

c. If yes to b, then it should be easier to add it in. You could even demonstrate that in the weak concentration limit, JGR reduces to GR. That would get scientists’ attention, BTW.
It's not weak concentration limit, just if the rate of change of the concentration over the space examined is zero, then you'd get typical GR. That much probably indicates the issues with adding it; you'd have to account for the difference in concentration between the start and end of the motion, and while that would be infinitesimal at any instant in time, it necessitates a separate PDE where the location of whatever's being examined is incorporated, and the relative concentration is calculated via that, and that is probably the tricky part (and it's not like the rest is easy) because while the solution of that PDE could be included directly into GR, to my knowledge it's not even known if there would be a unique solution.
What would need to be added to the formula would basically be in terms of that solution with the partial derivative in terms of time, and the partial derivative in terms of the axis of the direction of motion (so, t and x basically with a suitable coordinate system). Near the Earth's surface I think that'd be mostly negligible, and that certainly matches up with observations, but more accurate analysis of celestial phenomenon is where it becomes important.

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.

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.

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.