Toward a better theory of “gravity” - Bubbles

As indicated in a previous study, the "gravity" hoax is founded in the arbitrary definition of "mass" as its source and thereby also "density" as not defining the closeness of the atoms but the summarized "mass" of the atoms per volume. In order to ever find a better theory for what "gravity" really is and how it operates, we have to get out of this dead-end "mass"-inertia paradigm. We do this by returning to the basics of forces in materials and makes sure, we stay away from those inventions.

Atoms/molecules in a medium/material are drawn to each other or bound by some form of binding force (dipole-binding, electron-binding, covalent binding etc.). This is the fundamental force holding all substances together. This attractive force is small to none and even negative (repelling) in a gas whereas it in a fluid is conclusively positive while being large to extremely large in solid materials.
Considering a fluid as example, inside the medium, one atom/molecule experiences a zero net force of movements from being equally pulled in all directions or pushed equally from all directions. The forces are however there, keeping the substance together.
The molecules at the surface, on the other hand, do not have neighboring molecules above the surface and will therefore be drawn towards the solution overall as well as experience a lumping effect on the surface, resulting in a raise in density on the surface. The increased binding and force adds to the internal pressure inside the substance (which comes from the stickiness of the atoms in general). It also makes the surface of the material strive to become minimal.
The minimum surface-to-volume ratio is obtained when the volume forms a sphere (soap bubbles, balloons,…) and this relationship is described by the Laplace equation. As a step toward a new formulation of “gravity” outside of the Newtonian (“mass”, “density”, “gravity”) paradigm, let's derive the  equation and examine the consequences.

Note that in the case of a balloon or soap bubble, the surface is made up of some other, more sticky or stretchy material than the enclosed volume substance. For instance rubber. This allows for the volume substance to even be a gas that might otherwise fly apart as the cohesive force of rubber is likely more then 100 times stronger than that of water.

Let's consider the case of a soap bubble (with air inside). The mathematics is interesting not only because it shows the fundamental steady state of this simpler bubble configuration that then we will likely see take part in other cases. The soap being a liquid shell, will also provide understanding that could be extrapolated to liquid-only scenarios. It also gives an interesting case of where a less dense material is trapped and compressed by a more dense one. Another example of this would otherwise be the rising CO₂ bubble rising in a glass of beer or the rise of a hot-air or helium-mix balloon in the atmosphere. These cases are all physically similar (or exactly the same) and and they all ultimately come from the same kind of driving-forces.

If we look at the energy (E) of the situation, a molecule in contact with a neighboring molecule has a lower energy than if isolated. The reason is that a molecule (or atom) in the bulk of a solution has as many neighboring atoms/molecules and on average is fitted in with them in a static structure and so, has less/no energy difference relative these (the rest of the substance). A molecule set apart or significantly stretched away from the rest has an energy difference relative to the amount of that stretching. So, being at rest under larger forces, the molecules at the surface lack neighbors and are harder tied to the remaining ones and will therefore have a higher energy relative to the internal atoms/molecules of the solution overall since any movement on the surface will then require and/or release more energy. Consequently, for the solution to totally minimize its energy, the number of surface molecules (i.e. the surface area) needs to be minimized.

The SI-units of surface tension are N/m or J/m², representing two possible understandings of surface tension:
1. As the force, F, required to stretch out a film of a substance a tiny distance, dx, i.e. (force/length) in N/m.
2. The free energy (or surface energy), dE, required to enlarge a surface area, dA, of a substance i.e. energy/area (J/m²).
Looking at item (2.), at equilibrium, this change in free energy is equal to the increase in surface energy, E, such that

dE = γ · dA

(Eq.1)

where the energy-stretching coefficient, γ = dE/dA, the proportionality constant that express how much energy is stored per unit surface area, and is needed or released when changing the area one unit.

A conceptual experiment : A soap film residing on a wire frame is stretched one-dimensionally a tiny length dx by a force F. By this action, the free energy, dE, generated/added to the soap film is

dE = F · dx

(Eq.2)

In this case  the differential dA of the area A is

dA = 2 · L · dx

(Eq.3)

where the “2” comes from that fact that the film in this case has two surfaces, one facing towards the reader and one facing away from the reader. Double surfaces is indeed the case when we look at soap-bubbles but in general this need not be so. One such different case is for solid bubbles of fluids (like water) in zero “gravity”. Another is fluid-filled balloons, where there is no fluid surface and the rubber instead pose as the surface and the main opposition to the water that might otherwise disperse. The internal stickiness of water is very low relative to that of the rubber, but it is there of course also in that case.

Note also that within the fluid film of our soap bubble, we are assuming that the inner volume fluid requires molecules/atoms are very easy-flowing compared to the atoms in the two surfaces, so that the force, F, required is (approximately) only attributable to the stretching of the surface(s). Moving on, by putting together Eqs.1,2 & 3, we get

F·dx = dE = γ dA = γ 2 L · dx

From this, we see that for this case

F = 2γL
γ = F/(2L)	(Eq.4)

It is interesting to reflect on the meaning and source of γ as it is clearly determined by the stress-energy and stress-force relationship of the substance in the film. It is not a force dependent on the “mass” nor the volume of the substance. As we can see in our initial model pictures of the bonding forces between the molecules/atoms of the substance, it is clear that γ is a combined macro-level kind-of spring-constant of the surfaces but it is not a force-spring but an energy-spring, valid only as a first linear approximation related to very small stretching of the film, dx. It is also a first concept to expand into a 2-dimensional stretching of the surfaces of a soap-film making up a soap-bubble at/near equilibrium.

If we turn from the force-perspective to the thermodynamic or energy-perspective and consider the situation for a bubble that undergoes a tiny change in size i.e. a tiny change in radius, dr, we note the basic area, volume and derivatives of those for a sphere are:

The energy equation of this tiny change will look something like this:

dE = dA γ + ΔW

(Eq.5)

Here, the reduction of energy in the soap film covering the bubble is due to change of area, dA and this is opposed by mechanical work, ΔW, inside the bubble and relative to the surroundings. As we can see in the picture above, dA= -8πr·dr is already clear as we are considering a shrinking sphere (dr is negative). We also know how to obtain, γ for the substance by the previous experiment. And of course, since it is a stress-force relationship that is physically defined material property, we can likely find it out from tables of physical data. ΔW is a bit trickier but considering that this work will mainly (only) come from an increased pressure, ΔP, inside the bubble, it can be expressed as

ΔW = - ΔP·dV = - ΔP·A·dr = - ΔP·4πr2dr

(Eq.6)

Here, we assume that higher-order terms of dr (like dr² and dr³) are negligible. Note that because the surface is bent, such higher-order terms will appear. Putting dA, (Eq. 5) and (Eq. 6) together, we now get the expression for dE for the energy as:

dE = γ (-8πr·dr) + ΔP·4πr2dr

which at equilibrium (dE=0 & dE/dr=0) gives

0 =	γ (-8πr·dr) + ΔP·4πr2dr
γ8πr =	ΔP·4πr2

And this gives us the Laplace equation for a soap bubble

ΔP = 2γ/r

(Eq.7)

This equation means that the pressure inside a soap-bubble (or a material) is greater than the ambient (outside) pressure and that the pressure difference is a function of to the radius and the surface tension of the soap film. It also means that for a fixed radius, the pressure inside the bubble cannot be allowed to grow larger than the ambient pressure by a factor more than 2γ/r because this is the limit of the tension that the soap surface can hold. Any larger pressure difference and the bubble bursts. This especially becomes a factor when the surrounding pressure drops. One example of this is the bursting of helium balloons at high enough altitudes. Alike there will not be enough soap to cover and hold an ever expanding soap-bubble, the fabric surrounding the helium balloons is ripped apart. Note also that a smaller bubble will have a larger pressure difference i.e. measured in the same ambient pressure, the pressure inside a small bubble is greater than in a larger bubble.

Notice also how all forces here are material forces. No "gravity".

So, what does it mean?

This mathematics regarding one soap-film coated bubble, could be simply integrated to model the forces holding together a homogeneous material bubble in zero-“gravity” (like a fluid). The math show how the inherent material stickiness and especially surface tension plays a role in how internal pressure is set up inside ALL materials with positive stickiness γ (gas, liquid as well as solid). Clearly defining this stickiness is a key to modelling every case.

This case also proves that NASA's pictures showing how an air bubble is "stuck" in a zero-gravity water-bubble on some "space-station", is very likely a fake. NASA claims that the bubble is stuck inside the water because there is no “gravity” forcing it out, which, given what we know, is complete nonsense. They probably decided to “prove” that “gravity” is what sets up the pressure gradients in materials on Earth, like the pressure of the water of the oceans. All fake of course but they will say and anything to keep the masses oblivious. In their “experiment” they likely used a transparent gel to mimic the water-bubble or some photo trickery. The air bubble is also stationed in the center of the "water", meaning that it should experience little or no net pressure force towards any part of the "water" surface anyway since it is equally far from all parts of it.  

From the math of this simple study, it is clear that ALL material pressures are naturally (normally) built up by the materials internal stickiness, not by some external made-up fairly-tale force called "gravity". - So, for instance, the pressure of the water on the bottom of the sea, is created by the sea water alone sticking to itself(!) Just like the soap film of our bubble in our mathematical experiment, squeezes the air inside the bubble to a higher pressure, the sea water squeezes the bottom of the ocean and similarly any point inside it. -Plus the atmospheric pressure.

Extrapolating the math, we also understand how bubbles of relatively lower “density” will be forced to the surface of a “denser” fluid (for instance beer), not because the surface pulls the bubble to it, but because the “denser” material (the beer) by means of the pressure-gradient inside it (built up by itself!), pushes the squeezed less dense (air-bubble) or material towards the lower pressure (the surface or adjacent air bubbles). But, again, "density" (as we have been taught to think about it), is not the driver of the force. "Mass"-density is a made-up variable equivalent of the “mass” that the entire “gravity” hoax is based on and should not be considered real. – But they are sure a very clever deception(!)

The unifying or expelling force is basically due to the unwillingness of the atoms to move over and relinquish room to something else (the unwillingness comes from the stickiness between them). It is NOT from the atoms being relatively "heavy" inside an external "gravity" field.

Interestingly, you can fake natural stickiness by forcibly increasing denseness (form instance by compressing the air of the atmosphere inside a pressure  chamber). This represents an external force that on the atomic level make the atoms behave as if they were tied together harder, and you will find results of movement through such a compressed air to be more similar to that kind of fluid scenario, but in that case, it is NOT due to there being any higher stickiness between the atoms/molecules of the air. This proves that, final denseness of a material is set up by (a function of) the (summarized) total internal stickiness plus/minus other contracting or repelling forces (surface-tension, heat-motion, ambient pressure etc) adding to or diminishing to its appearance. Note the difference between the denseness (closeness of atoms) and the phony "mass" “density”, which is “mass” ("heaviness") per volume (as manifested in "gravity").

If we switch to and interpret another case (Newtons apple!), then based on this understanding, it is NOT the (extremely low) inherent stickiness-forces of a less dense fluid/gas/mix (the atmospheric air) that forces a “denser” material (an apple) to “fall” through it (the atmosphere) and join with a material of the same or even more dense nature (the Earth). BUT it is the same kind of force that is at play in this scenario, however the viewpoint on the effects is different. If we disregard the breaking of the “falling” apple by the air (consider a vacuum) then the driving force has to be found by thinking upside-down of the apple as the air-bubble in the beer-glass (rising downwards) and something much more sticky than the matter of the apple, must represent the beer. But what would that be? What is the ultimate “material” that exists everywhere and is more sticky than any material (including that of the apple)? The very possible answer is the room/”space”, which is clearly stickier than any material, as proven by the extremely high speed of light. This would then also mean that the room is a factor in all applications/cases.

In conclusion, it is clear that "gravity" is a mirage that is fully attributable to material buoyancy (no news there ...).
From the previous study, we also know that there exists no "gravity" driven by any "mass"-related "density", setting up any acceleration "field" outside of itself. Instead, consistent with reality and verifiable, non circularly reasoning science, this study shows that the appearance of forces between materials is due to the stickiness (or internal stress-force tensor) on the surface of- and inside all coherent materials, in combination with the second law of thermodynamics forcing energy inside and between materials into stable configurations or to "zero". (helium balloons, "falling" apples, bubbles in beer etc etc).

Another insight from this study is that the stickiness represents a more explicit theory where all kinds of forces can affect, add to and reduce the natural "stickiness" of the material and how large it appears to be. Gone is the all-encompassing magic variable and covering curtain called "mass" and "inertia" around which all ideas of mechanical forces have been centered. "Mass" likely represents one of the greater deceptions and intellectual dead-ends ever intentionally invented. It is interesting to look into a mathematical physics handbook and note how the integrals for calculation of buoyancy are quickly reformulated from stress-tensor form into "mass"/"density" form and how the stress-tensor is completely forgotten and from there, everything is all about "mass", "density" and "inertia".

Note:
More examples and scenarios need to be examined and the math expanded by integrations to verify above logical extrapolations from the soap-film math of this study. Someone could also look more into the stress-tenor form of  buoyancy integrals and figure out the transformation between this and the "mass" paradigm. etc. Curious about "inertia" also.

Thank you for your work fleshing this out. I'll have to study your argument to completely understand the math (math is not my subject). Some grammar corrections could be made in the transcript, would you mind if I made the corrections and sent it back to you for your approval (Please don't take this as a criticism, I'm just trying to help.)? I would like to send this to my heliocentric brother-in-law for him to consider (Math is his subject.). My email is JohnWillert@Hotmail.com if you're interested.