First, a quote from the Wiki page on Fractals (http://en.wikipedia.org/wiki/Fractal):

A fractal is generally "a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole," a property called self-similarity. The term was coined by Benoît Mandelbrot in 1975 and was derived from the Latin fractus meaning "broken" or "fractured."

A fractal often has the following features:
It has a fine structure at arbitrarily small scales.
It is too irregular to be easily described in traditional Euclidean geometric language.
It is self-similar (at least approximately or stochastically).
It has a Hausdorff dimension which is greater than its topological dimension (although this requirement is not met by space-filling curves such as the Hilbert curve).
It has a simple and recursive definition.

And an example:

http://upload.wikimedia.org/wikipedia/commons/thumb/2/21/Mandel_zoom_00_mandelbrot_set.jpg/300px-Mandel_zoom_00_mandelbrot_set.jpg
The Mandelbrot set is a famous example of a fractal.

http://upload.wikimedia.org/wikipedia/en/thumb/d/d4/Mandelpart2_red.png/300px-Mandelpart2_red.png
A closer view of the Mandelbrot set.

Now, imagine a 3D version of a fractal created by an oscillating disturbance at its centre. The oscillation means that the orientation of the fractal (into its mirror image) changes with a certain frequency and that the speed at which the newly created fractal moves away from its source is governed by the medium of propegation it finds itself in. The shape, size and type of the fractal is determined by the particular shape, size and type of the disturbance. It is possible for the shape of two fractals to be equal in every way except for the orientation being in the opposite direction (i.e. it points outward instead of inward).

My question is: Is it possible for the interaction between these two fractals, equal except for orientation, to exert an attractive force on each other? Would two of the exact same fractals then exert a repulsive force on each other?

No takers?

Does a pair of "2"s generate a force?
Attractive or repulsive?
What you're seeing is a mathematical construct...

From the Wiki page on Fractals:

"Approximate fractals are easily found in nature. These objects display self-similar structure over an extended, but finite, scale range. Examples include clouds, snow flakes, crystals, mountain ranges, lightning, river networks, cauliflower or broccoli, and systems of blood vessels and pulmonary vessels. Coastlines may be loosely considered fractal in nature."

The images in the OP was only to get a casual reader an idea of what a fractal is.

I was thinking of fractals in the form of self-similar reducing eddies in a medium, that is, reducing as the energy is dissipated with distance by forming multitudes of smaller and similar eddies (if that makes sense). This hypothetical medium would have no internal friction as one would expect from water, say.
By oscillating I mean that they form mirror images of each other along an axis running through the source, roughly in the same manner a sine-wave would.

So assuming that nature can not be infinitely reduced (the space-time fabic for instance), I guess this fractal would have to terminate after a certain number of instances. Maybe even straight down to the planck length.

For simplification, think of a wave-form being emitted around an axis of symmetry, similar to a sine wave, but instead of the regular positive and negative curves, you have (alternating between each side of the axis) spirals/eddies curling in the direction of the disturbance. This single arm comes into contact with the arm of another disturbance. The direction of rotation of the spirals/eddies will clash head-on with the spirals/eddies of the other arm. Now extrapolate this to a 3D situation with large numbers of arms from the two disturbances interacting with each other. The disturbances should be attracted to each other, no?

Just to be clear: I am not making any claims, just doing a mind experiment.

The images in the OP was only to get a casual reader an idea of what a fractal is.
And "casual reader" is what you come across as.
A "fractal" as a fractal is not a physical thing, it's a dimensionality, a shape.
As for your "experiment" - flow in liquids and gases is fractal and chaotic at particular levels, which is one reason why aero and hydrodynamicists don't do exact calculations....
If you punch two holes in the bottom of a barrel full of water will the two holes move closer together as the flow occurs?
The holes (generators) won't move but there may be instances when the flows interact destructively or in support of each other.
Without specifying exactly what the paterns are there's no way of knowing (and very probably even if you did specify - see above comment abou aer0/hydrodynamics) what would happen.

Big whorls have little whorls
That feed on their velocity,
And little whorls have lesser whorls
And so on to viscosity.
-- Lewis Fry Richardson

And "casual reader" is what you come across as.And I guess it would also be accurate. I am not a scientist, as you rightly point out and this fact is evidentially obvious from my post.

A "fractal" as a fractal is not a physical thing, it's a dimensionality, a shape.I did gather as much from my casual reading, but is it theoretically impossible for a 3D manifold type fractal to exist in the hypothetical medium as I described, i.e. with zero internal friction etc?

You see, I am trying to think of a mechanism whereby attraction/repulsion between two disturbances in the medium as described might happen. The disturbance, in this hypothetical, is itself part of the medium.

An analogy for the disturbances: if you take a sheet of rubber, took a pair of pliers and gripped and twisted the rubber and then released. The rubber has zero internal resistance, so the twist will uncurl and then re-twist in the opposite direction as a result of the momentum. Since there is no internal resistance, the rubber will oscillate as the energy of the initial twist does not dissipate. If you imagine twisting the rubber, there should be some spiral arms in the rubber emanating from the source twist (maybe a piece of cloth would have been a better analogy for this part).

In this hypothetical, the disturbances are in a 3D medium and the disturbances themselves are far more complex. Now imagine two of these disturbances approaching each other and you have the premise of this thread.;)

It is with these spiral arms where I am thinking of the possibility of them consisting of self-similar fractals that reduce in size, both upon magnification at a certain spot on the arm and as you move further out to the tip, as a possible way for the disturbances to attract/repel each other.

I do not know the precise nature/shape of these fractals, but am interested if fractals of some type could conceivable produce the effects of repulsion/attraction with the parameters of the hypothetical as given?

I did gather as much from my casual reading, but is it theoretically impossible for a 3D manifold type fractal to exist in the hypothetical medium as I described, i.e. with zero internal friction etc?
Short answer: no.
No more than it's possible for a square to exist anywhere.
It's got to be a sqaure (or fractal) something...

You see, I am trying to think of a mechanism whereby attraction/repulsion between two disturbances in the medium as described might happen. The disturbance, in this hypothetical, is itself part of the medium./quote]
If you're talking about disturbances then look no further than fluid dynamics.

[quote]An analogy for the disturbances: if you take a sheet of rubber, took a pair of pliers and gripped -excision- complex. Now imagine two of these disturbances approaching each other and you have the premise of this thread.;)
Yup, fluid flow, hydro/ aero dynamics.

It is with these spiral arms where I am thinking of the possibility of them -excision again- could conceivable produce the effects of repulsion/attraction with the parameters of the hypothetical as given?
Entirely possible. But it comes down to the exact nature of the medium (your hypothetical one is probably Unobtanium :) ) and the disturbances themselves - some will interfere and destroy each other, some reinforce, etc.
Whirlwinds, for example.... they can do that, but what any given pair WILL do is not known (and posibly not knowable with current levels of knowledge).

Ok, thanks. I guess it is time to let the cat out of the bag now, if you had not guessed it by now.

What I am trying to do is basically start from scratch and see if I might be able to explain observable phenomena and experimental results in a way that could at least potentially allow for it to be quantifiably described and verified by both Einsteinian Relativity and QM. Now I know all too well that every second schmuck thinks he can come up with his own little "theory" and more often than not professes him/herself to be the author of THE TOE/GUT. This is also almost always accompanied with wild claims, unsubstantiated assumptions and shoddy or no math. I am trying to do nothing of the sort. I first want to run with this hypothetical to see if it could at least qualitatively provide a logically consistent framework for current physics theory to exist in. If some insurmountable problem arises, I’ll abandon it as I am not interested in nonsense half baked “theories”. I am genuinely interested in the truth.

I did post my initial thoughts on this forum HERE (http://www.sciforums.com/showthread.php?t=76357) if you’d care to read it. If not I’d be happy to expand if you are interested (morbidly amused would also do ;) ).
Some of them has evolved somewhat while still keeping with the initial premise, which is the possibility that all of the universe (matter and forces) are geometric distortions of an infinite medium. I am thinking that if a qualitative framework could be erected, that some testable predictions might be possible with the addition of the appropriate math and that it could ultimately bridge the gap between QM and Relativity. Of course, it has to WORK first and that is where you come in.

I think how this thread relates to my “hypothesis” is obvious by now?

If nothing else, this is an interesting and stimulating mind experiment (at least for me) and I highly appreciate any input you can provide, whether it be suggestions, criticism or suggested further reading. You might deem this thread suitable for the pseudoscience section, by I don't think it is as I am not making claims as such, only "whatif's".

So there you have it.:o

Can I mention that chaotic motion or behaviour is fractal?

There's some fairly recent (last 2 decades) work on Chaos Theory, which has had spin-offs in communications.

“It is with these spiral arms where I am thinking of the possibility of them -excision again- could conceivable produce the effects of repulsion/attraction with the parameters of the hypothetical as given? ”

Entirely possible. But it comes down to the exact nature of the medium (your hypothetical one is probably Unobtanium ) and the disturbances themselves - some will interfere and destroy each other, some reinforce, etc.I was provided with a link to Einsteins View (http://www.tu-harburg.de/rzt/rzt/it/Ether.html) on the compatibility of an aether with relativity on another site. It has made me think a bit further on the nature of the proposed aether. Einstein says that for the aether to be consistent with Relativity it can not be thought of as existing of individual particles in relation to which motion can be measured. But then how can it have the needed properties for electromagnetic radiation and gravity to exist? Logic dictates that everything is infinitely devisable, for when you choose to stop dividing after any number of divisions you could still in principle divide to yet another level. So if you take it to the limit (pun intended) mathematically, you will be left with a particle with dimensions that tend toward zero. An infinite number of these particles together? And you have a possible aether! What do you think?

So first Kalster let me applaud your attempt to think it out for yourself. As I am not a physicist, it is not clear to me what exactly it is you are trying to do.

Let me say this though: the criticism that your "fractal theory" is wrong because fractals are simply mathematical geometric constructions is also wrong. After all, Riemannian geometry is just that - geometry - and yet it wonderfully describes the universe we inhabit. It's called spacetime.

Now, by your definition, a fractal has, among other properties, that of self-similarity. Roughly speaking, this means it looks the same at any level of magnification, as your pictures show.

So. The problem that seems to have scuppered all attempts at a unified theory so far is that the universe is not self- similar - that is the laws that describe the large scale, principally gravity, and those that describe the small scale, say quantum mechanics, are incompatible (or so I read).

So, if your assertion is that, if a unified theory can ever be found (apparently some doubt it), then it must endow our universe with the property of self-similarity, then this is close to being a tautology!

Whether this theory will endow our universe with the other properties of fractals, I have no idea (and I doubt anyone has).

But keep thinking!

First off, thanks for the encouragement!

After all, Riemannian geometry is just that - geometry - and yet it wonderfully describes the universe we inhabit. It's called spacetime.Its funny you should mension this. Can Riemannian Geometry describe the nature of a fractal of sorts? The fractals need not be infinitely devisable.

I was reading through the wiki article on Superfluidity (http://en.wikipedia.org/wiki/Superfluidity) and came across this gob-smacking passage:

"A more fundamental property than the disappearance of viscosity becomes visible if superfluid is placed in a rotating container. Instead of rotating uniformly with the container, the rotating state consists of quantized vortices. That is, when the container is rotated at speed below the first critical velocity (related to the quantum numbers for the element in question) the liquid remains perfectly stationary. Once the first critical velocity is reached, the superfluid will very quickly begin spinning at the critical speed. The speed is quantized - i.e. it can only spin at certain speeds."

This is exactly the type of stuff I was thinking and wondering about! Could the medium I am considering produce such vortices? Can vortices have a fractal nature, even if only stochastically? Could an oscillating source create the kind of vortices I am looking for?

Is there some kind of simulation engine where I can feed it variables and see what happens anywhere available?

You know about the zeta?A particularly tantalising aspect of the chaotic scattering process is that it may connect the mysteries of quantum chaos with the mysteries of number theory. The calculation of the time delay leads straight into what is probably the most enigmatic object in mathematics, Reimann's zeta function.
...
the prime numbers play the same role as the classical closed orbits of the Hydrogen atom in a magnetic field: the primes indicate some of the hidden correlations among the zeros of the zeta function.
In the scattering problem the zeros ...give the values of the momentum where the time delay changes strongly. The chaos of the Riemann zeta function is particularly apparent in a theorem that has only recently been proved: the zeta function fits locally any smooth function.
...
The theorem suggests that the [zeta] function may describe all the chaotic behaviour a quantum system can exhibit.--Martin C. Gutzwiller
Scientific American Jan. 1992

Hi Kalster, and welcome.

In post 8 you give a link (to a post 53 elsewhere) where I found you explaning inertia as a front-to-back differential rate of "streching of space," or in your exact words (as I may have missunderstood):

"... when acceleration occurs, the amount of space stretched is always more than the amount being released so a net resistance is resultant. This resistance would increase with the level of acceleration achieved as the gradient between the rate of stretch and release becomes more pronounced. This ties up with observation. ..."

But that seems to me to be in contradiction with the facts (Does not "ties up with observation") for two reasons:
(1)When the object is traveling essentially at the speed of light, it still exhibits inertia yet it is not significantly accelerating, it is just becoming more massive. You seem to be predicting that inertial is more related to the volume of the object than its mass! I.e.
(2)If I understand you, you are saying that golf ball and pin-pong ball have essentially the same inertia.

Comments?

Guys, Thanks for your input!

You know about the zeta?I have heard of it before, but my mathematics is limited to high school level. What they are saying about that it theoretically "may describe all the chaotic behaviour a quantum system can exhibit" does highlight it's apparent importance. ;)

But that seems to me to be in contradiction with the facts (Does not "ties up with observation") for two reasons:
(1)When the object is travelling essentially at the speed of light, it still exhibits inertia yet it is not significantly accelerating, it is just becoming more massive. You seem to be predicting that inertial is more related to the volume of the object than its mass! I.e.
(2)If I understand you, you are saying that golf ball and ping-pong ball have essentially the same inertia.
(1)My idea of what a particle might be is a complex wave-bundle of sorts. That means it is made of stretched and configured space-time fabric. The particle stretches space-time, bigger particles stretching it more. So the larger the volume, the more space-time has to be stretched during movement. Imagine you are making large bubbles with a coat hanger. The faster you spin, the bigger the bubble becomes. If the bubble were not easily popped, you would expect the total drag created to increase with the size of the bubble. The same is happening in my mind experiment. The faster the particle moves, the bigger it's volume(mass) becomes and the more space-time has to be stretched per unit time, which also increases as the speed increases.

(2)With the above explanation, this question is answered also. (I was dealing with particles)

Did that clear it up? Please don't hesitate to ask, I know my analogies fall short sometimes.

...
(1)My idea of what a particle might be is a complex wave-bundle of sorts. That means it is made of stretched and configured space-time fabric. The particle stretches space-time, bigger particles stretching it more. So the larger the volume, the more space-time has to be stretched during movement. Imagine you are making large bubbles with a coat hanger. The faster you spin, the bigger the bubble becomes. If the bubble were not easily popped, you would expect the total drag created to increase with the size of the bubble. The same is happening in my mind experiment. The faster the particle moves, the bigger it's volume(mass) becomes and the more space-time has to be stretched.

(2)With the above explanation, this question is answered also. (I was dealing with particles)

Did that clear it up? Please don't hesitate to ask, I know my analogies fall short sometimes.Not at all! You seem to think analogies are explainatory.

Golf ball and ping-pong balls are just collections of particles interacting with same volume of space* yet vastly different inertia. You seem to be confirming my fear that, in your POV, inertia is related to volume instead of mass.

Also the near speed of light particle still has inertia but no acclearation problem is not addressed - the front of it and the rear of it are stressing and releasing stress equally. That was your POV for case when slow particle travels with no accleartion explaining why no force is require to continue the motion. Why is a force increasing the mass in the near speed of light case but not he slower moving particle in your "it all space" POV.
--------------

*If difference is fact only one is hollow, then take case of two solid spheres of same number of atoms and same radius but different metals (say lead and copper) with different lattice sturctures and / or temperatures so this is possible. Would these different mass not have the same inertia in your "ïts the volume of space streached" model? - a clear contradiciton of the observed fact that ineritia is linear in mass, not volume.

Golf ball and ping-pong balls are just collections of particles interacting with same volume of space* Yes, and the number of particles is where the difference is. Each particle (proton, electron, etc) would resist acceleration with a certain amount. The ball of lead contains vast numbers of each compared to the ping-pong ball, hence more inertia. As particles in this hypothetical are essentially 3D waves, it would follow that the inside of the ping-pong ball does not pose a problem, the medium would move through it just the same. With the lead and copper balls their mass is made up of the accumulated mass of the constituent particles, lead has more than copper -> more inertia.

Why is a force increasing the mass in the near speed of light case but not he slower moving particle in your "it all space" POV.It does. You apply a force, it accelerates, it gains mass, you release force, it moves perpetually with new increased mass. The bigger the mass, the more resistance to acceleration (inertia) as the net amount of space-time that needs to be stretched is more proportionately with the mass increase.

To Kalster:
Yes, and the number of particles is where the difference is. Each particle (proton, electron, etc) would resist acceleration with a certain amount. ...
OK. I admit that two spheres with the same number of atoms and same radius but different masses, possible because they are made of different elements with different crystal lattices spacing and structure (and “fine tunned” by having different temperature for exact equality of size and atom counts) does not destroy your model. You defended it by stating that it is not the atoms that stress the space in front of them as they accelerate but the individual protons, neutrons and electrons of the atom that stress the space to give inertia (resistance to the acceleration so force is required).

What do you say then to explain the mass (and inertial)* difference (compared to the ground state of the same atom) in the case of nuclear isomers? (Not to be confused with nuclear isotopes that have only the proton counts the same.) In this case, the number of protons, neutrons and electrons are exactly the same for both, yet the excited state has more inertia than the ground state. (It will not do you any good the try the same trick again – i.e. to step down to the quark level as the isomer has exactly the same number of up and same number of down quarks as the ground state.) For example, excited hafnium, (Hf-178m2) which has the unusually long half life (for a nuclear isomer) of 31 years has more inertia than the ground state (Hf-178) So much more mass that ONE GRAM of Hf-178m2 contains 1330 mega Joules of energy or the same energy as 700 pounds of TNT releases! (DARPA has considered trying to make nuclear bombs of it that do not violate the arms limitation treaties!)

For more details, see: http://en.wikipedia.org/wiki/Nuclear_isomer

*One “escape” still open to save your model is to claim that the extra mass of nuclear isomers does not have any inertia associated with it, but that will get you into even greater conflict with the facts. Inertial mass and gravitation mass/energy need not be equal in principle, but are known to be with very high precision and I think all sorts of bad things happen if they are not. Earth spiral into sun perhaps?


PS my wife had a para-thyroid tumor removed after isomer Tc-99m (with a half-life of 6.01 hours) or more probably Tc-95m (with a half-life of 61 days) was injected into her to confirmed the tumor. Para-thyriod is normally size of grain of rice and finding it in neck or chest is difficult without this radiological aid. Hers was like a large raisin when removed.

Thanks for sticking with this! My model is far from being completed and it is probing questions like these that test it and provides an opportunity for it to develop. I read up about Nuclear isomers and I think I may have a possible explanation.

Ok, here goes.
I gather that atoms in excited states also exhibit increased inertia and mass? This thread started with an idea I had for how to explain the fundamental forces (excluding gravity) by suggesting that the space-time medium is a superfluid. Particles are wave-bundle configurations in this medium. I then proposed the mechanism in the OP of this thread; fractals. By the (admittedly vague, but plausible) mechanism proposed in the op, fractals can have resultant repulsive/attractive effects on other fractals depending on the orientation and type of the interacting fractal. I am also thinking that the fractals can be sufficiently complex for them to simultaneously exhibit both attractive and repulsive properties toward opposing fractals with an equilibrium distance between particles resulting. I envisage the fractals as being part of the mass of the particle, as the fractals themselves are eddies of sorts and so also adds to the total density differential of the particle.

Photons are the fundamental waves in the medium that can travel at the maximum speed possible. [Analogy: Steel cable. Shaking one end up and down creates transverse waves (particles) and tapping it with a hammer produces longitudinal wave (light)]

Superfluids create quantized vortices under certain conditions and I am thinking of the same type of thing for particles and their fractals. When a light wave interacts with a particle it can elevate the fractals/particle to a higher state if its energy is equal to or more than the energy difference between possible levels of quantization. Nuclear isomers are when one or more nucleon is in an excited state. The stability of the isomer depends on the chance of the nucleon/s to revert to its ground state, determined by the orientation of the Strong-force fractals of the excited nucleons relative to those of the surrounding nucleons. When the Strong-Force fractals are elevated to a new quantized state, the equilibrium point shifts and the nucleons re-orientate themselves to an island of stability. Depending on the conditions in the atomic nucleus of the various elements, the island of stability can vary.

Anyway, the point is that the potential energy of excited particles is stored in the associated fractals and so adds to the total mass of the system. Well that was long winded!:o

PS: I hope your wife is ok.

To Kalster:

I have only looked at your starting concepts. You can keep modifying them but they are getting progressively more vague and resemble very more the sort of hand waving you said you would try to avoid with math etc.

I also point out another problem with your "inertia results from differential streching of space" when object (or even just an electon) is accelertating model:

Consider a heavy atom, say U238. Its neutrons and protons of the nuclus are densly packed in very nearly a sphere. (many are in the interor in contact with those on the leading side of the acceleration. Your model requires that the space behind one on the surface of this sphere on the advancing edge be giving up the stretch that is occuring on the front side of that Leading outter surface nucleon; yet that very same space is the front side of the interor nucleon contacting that front surface nucleon's back side. How can the same space be both being streched (by the advancing interior nucleon) and also be "un streching" behind the back side of the leading outer nucleon? You want to have your cake and eat it too - I.e. model is internally inconsistent. - the worst possible defect a model can have. Even hand waving will not cure self contradiction.

Hope you understand my point. Not that an analogy proves any thing, but one may help you understand my point. It is sort of like one truck closely following another the second truck is partially shielded fromn the wind. The second interior neutron, in contact with the back side of the leading outer surface neutron is entering the same space that the leading one is leaving. Is that space streching from undistrubed distant space or relaxing back to the unstressed state behind the leading outer nucleon?

It ias nice to try to find a mechanism explaining inertia, but I think you need one that explains BOTH inertia and mass. I.e. not one built on something that only happens to object when accelerating, but also to one sitting stationary on the bathroom scales. I.e. I think this is the fundamental flaw in your model.

While we're on the subject of fractals and topological defects:
Hypothetical fields, called Higgs fields ... follow equations of motion similar to those of electric and magnetic fields. Just like those fields, the Higgs fields tend to minimise their energy by assuming a uniform strength throughout space.

Unlike other fields, ...a Higgs field does not drop to zero in its lowest energy state. Instead it takes on a particular non-zero strength throughout the universe. [This] breaks the symmetry between the forces and particles that couple to it.
...
One of the main goals for the next generation of particle accelerators is to search for the Higgs particle, which should be associated with the electroweak Higgs field. ...For example, the direction of the electroweak Higgs field breaks the symmetry of electron/neutrino "space".
The "direction" in which it points acquires mass [(like the way a compass needle acquires an orientation because of the direction of the Earth's magnetic field)] and becomes the electron.
--Scientific American March 1992 pp 40-41

[T]he Higgs field can support four kinds of deformations, [or topological defects]. Such defects are created during a phase transition, when a Higgs field breaks symmetry.

When a discrete symmetry is broken, domain walls separate regions within which the Higgs field takes on different values (for example +1 or -1).

Cosmic strings form when ... the Higgs field can point in any direction in a two-dimensional space. As one travels around a cosmic string, the Higgs field rotates through all these values.

Monopoles appear when the Higgs field can point in any direction in a three-dimensional space. At the center of these defects, the Higgs field strength is zero.

Textures form when the Higgs field can choose any direction in a four-dimensional space. ...[Vectors of] field orientation around the texture are parallel. As a result, the texture can unwind, permitting the surrounding field to reconnect smoothly.--Scientific American March 1992 p 38

The second interior neutron, in contact with the back side of the leading outer surface neutron is entering the same space that the leading one is leaving. Is that space streching from undistrubed distant space or relaxing back to the unstressed state behind the leading outer nucleon? How can the same space be both being streched (by the advancing interior nucleon) and also be "un streching" behind the back side of the leading outer nucleon? I am sorry, but I don't see a problem here. It is not like two vacuum-packed metal cubes, with the plastic representing space. The particles-waves themselves are part and of the medium. Consider a MacDonald’s M type graph, the two peaks representing the adjoining particles. If you make a reference dot and had the M travel through it, the dot would have no choice but rise and fall with the curve.

It is nice to try to find a mechanism explaining inertia, but I think you need one that explains BOTH inertia and mass.I thought I had? When a particle is formed, it stretches the surrounding space, similar to taking pliers and twisting the centre of a rubber sheet. Twisting the rubber locally unavoidably causes the stretching of the surrounding rubber, the tension starting at a maximum locally and growing less with distance. This tension in the space-time fabric is what gravity is in this model. More particles together mean more gravity. Mass and energy is equivalent, the applied energy twisting the space-time fabric (creating the particle), with gravity (tension in surrounding space) and inertia (resistance to acceleration) as the direct result. The more energy applied, the more the space-time fabric is stretched (mass), the more tension in surrounding space (gravity), the bigger the differential will be between the front and back of the particle per unit acceleration.

You can keep modifying them but they are getting progressively more vague and resemble very more the sort of hand waving you said you would try to avoid with math etc. My aim is to stay with what can be possible with the premise given: The space-time fabric is a continuous medium exhibiting superfluid qualities. When I am presented with a problem, I confine myself to what (in my mind) can be possible with this given. If I produce an explanation or a solution to a problem that cannot follow from the possible dynamics of such a system, that is where I need help. It HAS to make sense, or it is worthless. If anything is too vague I’d be happy to explain my thoughts again. I have seen from your profile that you were a physics professor for 30 years! That is why I value your input so much. It is obvious that I, a non-scientist, have much less credibility than you’d have, not to mention the theoretical background needed to be able to know of all sorts of experimental results, established theories and predicted phenomena that this hypothetical of mine would need to satisfy. So I may be waving my hand around, but I do my best to stick with what is possible with this hypothetical.

...When a particle is formed, it stretches the surrounding space, similar to taking pliers and twisting the centre of a rubber sheet. Twisting the rubber locally unavoidably causes the stretching of the surrounding rubber, the tension starting at a maximum locally and growing less with distance. This tension in the space-time fabric is what gravity is in this model. More particles together mean more gravity. Mass and energy is equivalent, the applied energy twisting the space-time fabric (creating the particle), with gravity (tension in surrounding space) and inertia (resistance to acceleration) as the direct result. The more energy applied, the more the space-time fabric is stretched (mass), the more tension in surrounding space (gravity), the bigger the differential will be between the front and back of the particle per unit acceleration. ...I am not much with the math of general relativity, GR, (or to be honest, not even with special relativity anymore) but your words above seem to me to be as exact a discription of GR as is possible in words. Perhaps you are just "reinventing the wheel" and only lacking the math to express it as Einstein et. al. did?

PS
Your words helped me better understand why my rule:
"Energy that is the same in all inertial frames makes mass and gravity but other energy does not."
works. Example kinetic energy is just energy - makes no mass, but thermal energy makes mass and gravity.

Billy T, I have to thank you for your comments. My intension from the beginning was to provide an intuitive framework wherein Einsteinian relativity could exist, to provide an explanation for why it works and in doing so maybe open the door to reconciling Relativity with QM. It is still quite far from doing that in its entirety, but your comments and contributions has really made my personal process worthwhile! I am now more motivated than ever to take this as far as it will go.

I would still welcome any contributions from you or anyone else following this thread, be it scalding criticism, advice or challenges.;)

Any more questions or refutations?

it sounds like you are touching on string theory
the fractals then are the different "notes" on the string
the greater potential energy the higher the "tension" in the string
on a musical instrument the points of harmonic resonance are arrayed in a fractal pattern.

it sounds like you are touching on string theory
the fractals then are the different "notes" on the string
the greater potential energy the higher the "tension" in the string
on a musical instrument the points of harmonic resonance are arrayed in a fractal pattern.I am not sure about the exact nature of the medium yet, but by coincidence my ideas about fractals representing forces and the medium being a superfluid seam to be confirmed on a very shaky level by the fact that superfluids do present defined quantized vortices (which should have a defined fractal nature in a "string soup" medium, I am thinking) under excitation. One problem though is that how would gain energy be expressed in such a setup. The fractals are quantized and as such should have clearly defined energy/quantization levels with not intermediary levels, like electron orbitals. This makes me think that the gained energy would translate into higher vibration modes for the "string soup" which would enlarge the fractals without actually needing more strings to come into the fray and so providing intermediary energy levels. Once the excited "string soup" reaches a new available quantization energy the fractals could stabilize with the acquisition of more fractals per unit area. This probably sounds like complete nonsense, and it probably is. I am just thinking out loud.;)