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The general expression for gravitational potential energy arises from the law of gravity and is equal to the work done against gravity to bring a mass to a given point in space. Because of the inverse square nature of the gravity force, the force approaches zero for large distances, and it makes sense to choose the zero of gravitational potential energy at an infinite distance away. The gravitational potential energy near a planet is then negative, since gravity does positive work as the mass approaches.
Gravitational Potential Energy
Why choose a convention where gravitational energy is negative?
As with all potential energies, only differences in gravitational potential energy matter for most physical purposes, and the choice of zero point is arbitrary. Given that there is no reasonable criterion for preferring one particular finite r over another, there seem to be only two reasonable choices for the distance at which U becomes zero: r=0 and r=∞. The choice of U=0 at infinity may seem peculiar, and the consequence that gravitational energy is always negative may seem counterintuitive, but this choice allows gravitational potential energy values to be finite, albeit negative.
Gravitational potential energy
Although no particles are known to have negative mass, physicists (primarily Hermann Bondi in 1957,[3] William B. Bonnor in 1989,[9] then Robert L. Forward[10]) have been able to describe some of the anticipated properties such particles may have. Assuming that all three concepts of mass are equivalent the gravitational interactions between masses of arbitrary sign can be explored, based on the Einstein field equations:
* Positive mass attracts both other positive masses and negative masses.
* Negative mass repels both other negative masses and positive masses.
Negative Mass
In 1970, Jean-Marie Souriau demonstrated, through the complete Poincaré group of dynamic group theory, that reversing the energy of a particle (hence its mass, if the particle has one) is equal to reversing its arrow of time.[12][13]
The universe according to general relativity is a Riemannian manifold associated to a metric tensor solution of Einstein’s field equations. In such a framework, the runaway motion prevents the existence of negative matter.[3][9]
Some bimetric theories of the universe propose that two parallel universes instead of one may exist with an opposite arrow of time, linked together by the Big Bang and interacting only through gravitation.[14][15][16] The universe is then described as a manifold associated to two Riemannian metrics (one with positive mass matter and the other with negative mass matter). According to group theory, the matter of the conjugated metric would appear to the matter of the other metric as having opposite mass and arrow of time (though its proper time would remain positive). The coupled metrics have their own geodesics and are solutions of two coupled field equations: [equations removed to reduce snippet size]
The Newtonian approximation then provides the following interaction laws:
* Positive mass attracts positive mass.
* Negative mass attracts negative mass.
* Positive mass and negative mass repel each other.
Those laws are different to the laws described by Bondi and Bonnor, and solve the runaway paradox. The negative matter of the coupled metric, interacting with the matter of the other metric via gravity, could be an alternative candidate for the explanation of dark matter, dark energy, cosmic inflation and accelerating universe.[17][18]
Nobody knows whether negative mass can exist but there have nevertheless been plenty of analyses to determine its properties. In particular, physicists have investigated whether negative mass would violate various laws of the universe, such as the conservation of energy or momentum and therefore cannot exist. These analyses suggest that although the interaction of positive and negative mass produces counterintuitive behaviour, it does not violate these conservation laws.
Cosmologists have also examined the effect that negative mass would have on the structure of space-time and their conclusions have been more serious. They generally conclude that negative matter cannot exist because it breaks one of the essential assumptions behind Einstein’s theory of general relativity.
Today, Saoussen Mbarek and Manu Paranjape at the Université de Montréal in Canada say they’ve found a solution to Einstein’s theory of general relativity that allows negative mass without breaking any essential assumptions. Their approach means that negative mass can exist in our universe provided there is a reasonable mechanism for producing it, perhaps in pairs of positive and negative mass particles in the early universe.
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The crucial breakthrough by Mbarek and Paranjape is to show that negative mass can produce a reasonable Schwarzschild solution without violating the energy condition. Their approach is to think of negative mass not as a solid object, but as a perfect fluid, an otherwise common approach in relativity.
And when they solve the equations for a perfect fluid, it turns out that the energy condition is satisfied everywhere, just as in all other solutions of general relativity that support reasonable universes.
Cosmologists Prove Negative Mass Can Exist In Our Universe
From that low-complexity state, the system of particles then expands outward in both temporal directions, creating two distinct, symmetric and opposite arrows of time. Along each of the two temporal paths, gravity then pulls the particles into larger, more ordered and complex structures—the model’s equivalent of galaxy clusters, stars and planetary systems. From there, the standard thermodynamic passage of time can manifest and unfold on each of the two divergent paths. In other words, the model has one past but two futures. As hinted by the time-indifferent laws of physics, time’s arrow may in a sense move in two directions, although any observer can only see and experience one. “It is the nature of gravity to pull the universe out of its primordial chaos and create structure, order and complexity,” Mercati says. “All the solutions break into two epochs, which go on forever in the two time directions, divided by this central state which has very characteristic properties.”
Although the model is crude, and does not incorporate either quantum mechanics or general relativity, its potential implications are vast. If it holds true for our actual universe, then the big bang could no longer be considered a cosmic beginning but rather only a phase in an effectively timeless and eternal universe. More prosaically, a two-branched arrow of time would lead to curious incongruities for observers on opposite sides. “This two-futures situation would exhibit a single, chaotic past in both directions, meaning that there would be essentially two universes, one on either side of this central state,” Barbour says. “If they were complicated enough, both sides could sustain observers who would perceive time going in opposite directions. Any intelligent beings there would define their arrow of time as moving away from this central state. They would think we now live in their deepest past.”
2 Futures Can Explain Time's Mysterious Past
originally posted by: solve
a reply to: ChaoticOrder
have you seen the zero theorem?
Physics-X is a one of a kind course taught at Michigan Technological University, for credit. The course is aimed at upper level undergraduate students in Physics, however the concepts involved in the course are easily accessible to everyone.
The course deals with some of the most extraordinary concepts in physics, most of which try to provide the Physics background behind some cool phenomena and theories like Time Travel, Special Relativity, Worm Holes and Black Holes, Quantum Mechanics, Parallel Universes, etc.
The matter of the twin fold forms big stable clumps, which repel the matter of our fold of the universe, this last taking place in the remnant space. By opposition to the pancake model numerical simulations, this pattern is fairly non-linear. After its formation, corresponding to the Jeans time of the high density system (2.10 9 years) , there is no significant evolution of the general pattern over a time comparable to the age of the Universe so that this model could be a good candidate to explain the observed spongy aspect of our fold of the Universe, at large scale.
The basic idea is that positive matter clumps together and forms galaxies with structure whereas the negative energy remains in a fluid/plasma state and doesn't form any large structures. Since the negative matter/fluid is gravitationally repelled from the positive matter you end up with cavities in the negative matter/fluid where the positive galaxies are located. This creates the inverse gravitational lensing effect we normally attribute to dark matter and can also explain the expansion of space
The matter of the twin fold forms big stable clumps, which repel the matter of our fold of the universe, this last taking place in the remnant space.
This is what I was mixed up with but I now understand. So no large structures form in this negative fluid and cavities is a far better description than "strands" but I think were mainly on the same page once you explained how the cavities relate to the inverse gravitational lensing effect.
remnant space=cavities correct? This is where we find "our fold of the universe". So "our fold" is constantly being pushed against by the negative void surrounding it.
The problem of the gravitational lensing must be reconsidered. As suggested in the previous paper [1], in the present model the confinement of the galaxies is mainly due to the action of the surrounding antipodal matter, located in the twin fold, to be consistent to the strong missing mass effect. Numerical simulations provided some description of a galaxy, surrounded by halos of antipodal matter [1]. See figure 7:
originally posted by: AthlonSavage
a reply to: ChaoticOrder
Do you know a way of deriving a formula which combines the energy mass equation with the inverse law of gravity?
As an object in the galaxy moves further away from the galactic core it gets closer to the halo edge and experiences an increasingly stronger force trying to push it back towards the core.
I am currently reading through the rest of the text, but I just want to ask a question before I continue: What matter has negative mass? It cannot be antimatter, because antimatter has positive energy.
Now, if I get your theory correctly, you are saying that negative energy can only be achieved by object traveling back in time, which would make them carry a negative mass for obvious reasons.
I suggest reading the rest of my post because I explain all of this fairly well.
if we assume that negative energy must exist in order to produce a zero-energy universe, we can use the mass-energy equivalence principle to calculate that negative energy should possess a negative mass. And if an object were to have a negative mass, the math tells us that it should be traveling backwards through time. Therefore if we model the Big Bang as an instantaneous creation of an equal amount of positive and negative energy, the two forms of energy will travel in opposite directions through time and cause the universe to split into two parallel universes which can only interact through the force of gravity.
originally posted by: swanne
a reply to: ChaoticOrder
Now we know that some galaxies have no rotational curve anomaly - can your theory support such events?
So could the new analysis be faulty? "One really needs excellent data to pull this off," says Stacy McGaugh of the University of Maryland in College Park, US, an expert in galaxy formation and evolution. "I'm afraid my grumpy first impression is that I just don't buy it."
McGaugh points out that other galaxies have shown declining rotation curves, but later observations have always shown that beyond a certain distance, they flatten out, which can't be explained by ordinary gravity from visible stars and gas. "If we believe this decline, it seems like the exception and not the rule," he says.