(Phys.org)—A pair of mathematicians—one from Indiana University and the other from Sichuan University in China—have proposed a unified theory of dark matter and dark energy that alters Einstein's equations describing the fundamentals of gravity.

Shouhong Wang, a professor in the IU College of Arts and Sciences' Department of Mathematics, and Tian Ma, a professor at Sichuan University, suggest the law of energy and momentum conservation in spacetime is valid only when normal matter, dark matter and dark energy are all taken into account. For normal matter alone, energy and momentum are no longer conserved, they argue.

While still employing the metric of curved spacetime that Einstein used in his field equations, the researchers argue the presence of dark matter and dark energy—which scientists believe accounts for at least 95 percent of the universe—requires a new set of gravitational field equations that take into account a new type of energy caused by the non-uniform distribution of matter in the universe. This new energy can be both positive and negative, and the total over spacetime is conserved, Wang said.

It is curved spacetime, along with a new scalar potential field representing the new energy density, and the interactions between the two that form the foundation for the new gravitational field equations.

"Many people have come up with different theories for dark energy," Wang said. "Unfortunately, the mystery remains, and in fact, the nature of dark energy is now perhaps the most profound mystery in cosmology and astrophysics. It is considered the most outstanding problem in theoretical physics.

"The other great mystery concerning our universe is that it contains much more matter than can be accounted for in our visible stars. The missing mass is termed as dark matter, and despite many attempts at detecting dark matter, the mystery remains and even deepens."

The researchers postulate that the energy-momentum tensor of normal matter is no longer conserved and that new gravitational field equations follow from Einstein's principles of equivalence and general relativity, and the principle of Lagrangian dynamics, just as Einstein derived his field equations. Wang said the new equations were the unique outcome of the non-conservation of the energy-momentum tensor of normal matter.

When Einstein developed his theory, dark energy and dark matter had not yet been discovered, so it was natural for him to start his theory using the conservation law of energy and momentum of normal matter, Wang added.

"The difference between the new field equations and Einstein's equations is the addition of a second-order covariant derivative of a scalar potential field," he said. "Gravity theory is fundamentally changed and is now described by the metric of the curved spacetime, the new scalar potential field and their interactions."

Tensors provide a concise framework for solving general relativity problems and the energy-momentum tensor quantifies the density and current of energy and momentum in spacetime. The second-order covariant derivative would be the geometric analog of a second order derivative in calculus which measures how the rate of change of a quantity is itself changing.

Associated with the scalar field is a scalar potential energy density consisting of positive and negative energies and representing a new type of energy caused by the non-uniform distribution of matter in the universe. The scalar potential energy density varies as the galaxies move and matter redistributes, affecting every part of the universe as a field.

Wang said negative energy produces attraction while the positive energy produces a repelling force fundamentally different from the four forces—gravity, electromagnetism, the weak interaction and the strong interaction—recognized in physics today.

"Most importantly, this new energy and the new field equations offer a unified theory for both dark energy and dark matter, which until now have been considered as two totally different beasts sharing only 'dark' in name," he said. "Both dark matter and dark energy can now be represented by the sum of the new scalar potential energy density and the coupling energy between the energy-momentum tensor and the scalar potential field."

The negative part of this sum represents the dark matter, which produces attraction, and the positive part represents the dark energy, which drives the acceleration of expanding galaxies, he said.

"In a nutshell, we believe that new gravity theory will change our view on energy, gravitational interactions, and the structure and formation of our universe," Wang said.

Kevin Zumbrun, chair of the Department of Mathematics at IU Bloomington, said the new unified theory looked sound in principle.

"It is speculative at the cosmological level, since one must match with experiment, but the math is solid," he said. "It's a new and elegant angle on things, and if this does match experiment, it is a huge discovery. Quite exciting!"

Wang said the new field equations also lead to a modified Newtonian gravitational force formula, which shows that dark matter plays a more important role in a galactic scale at about 1,000 to 100,000 light years, but is less important in the larger scale, where dark energy will be significant (more than 10 million light years).

"This unified theory is consistent with general characterizations of dark energy and dark matter, and further tests of the theory up to measured precisions of cosmic observations are certainly crucial for an eventual validation of the theory," Wang added.

The full research paper, "Gravitational Field Equations and Theory of Dark Energy and Dark Matter," is available at the open access online preprint archive arXiv.

**Explore further:**
Dark matter could provide heat for starless planets

## Benni

THEY STILL HAVE NOT BEEN DISCOVERED, they are still only proposed. Astrophysicists are trying to account for all the gravity that cannot be explained by "visible stars". Einstein could not propose the concept because in 1916 we were only beginning to develop telescopes that could view more than a couple million light years distance.

## Expiorer

## El_Nose

Dark energy is the force driving universal expansion We know what it is we have measured it. We just don't know where it comes from- thats why its dark.

Dark matter has been mapped, it has been measured, we just don't know what it is made of, cause we haven't held it.

we also have not seen the core of the earth, but we believe it to be molten based on measurements. We only have measurement to indicate that quasars are black holes but we have never been there... we use measurements.

You can choose not to believe in DM and DE and you can join others like you at the flat earth society.

## Ophelia

## Ophelia

Isn't it more accurate to state that an effect has been mapped and measured but the cause is yet to be determined?

## PPihkala

## Giovanni L_ B_

Einstein's ones were all linear... thats why we can talk about a cosmological constant in his equations in the first place.

## rubberman

Careful EN, it's effect has been measured, it's location inferred based on stellar/galactic motion. My understanding is that holding "it" would be impossible as it only interracts with normal matter gravitationally. Physicists trying to pinpoint the source is like an oceanographer swimming in the ocean at night and entering a section of water that is 10 degrees C warmer, but for no apparent reason. It doesn't just happen, something caused it but none of the "usual suspects" are present (sun, vents, life). So here you have this effect, with no detectable cause, just theories of varying legitemacy on the cause.

## rubberman

## casualjoe

## cory_saurus

## Scryer

Now, if only we could harness Dark Energy, something that may eventually happen once we learn more about it.

Free energy? Not likely, however, the way technology advances we may just end up reducing power consumption to near nothing, while at the same time harvesting all the energy from the local environment that we could ever need.

## axemaster

## ccr5Delta32

Now I'm going to read the article

## hemitite

That being the case, wouldn't the energy from the "dark matter", or negative manifestation of this new field lead to a runaway increase in the mass, and therefore the gravitational potential of galaxies and galactic clusters just as the "dark energy" aspect is accelerating the expansion of the universe on a larger scale?

If so the result may be a bunch of monstrous black holes being blasted away from each other.

## Tangent2

Is this right?

## Urgelt

There are an awful lot of assumptions in this approach.

I guess the proof will be whether the new equations can make predictions, and I don't mean predictions identical to those the equations were shaped to fit.

I don't think any experiment has demonstrated that conservation of energy and momentum do not apply to normal matter. That would be a step towards proving these new equations. But it sounds like a long shot to my ears.

## Benni

These two guys have gone over the edge. I don't for a minute doubt there are energy fields & undetected matter out there producing a lot of unaccounted for gravity, but for these two guys to say it is "proven" & they know the source of this gravity is "dark energy & matter" is palpably foolish.

OK you two guys in China, send us a picture of all this "dark matter" you've proven to exist! Also tell us what the wavelength of the proven "dark energy" is!

## antonima

## Torbjorn_Larsson_OM

You know they are headed for the cliff when they claim that GR doesn't include DE, which it does in the Lambda-CDM standard cosmology - _that is the point_.

This is so 80's, and so wrong.

## Benni

And Mister, you live on the same plane along with the rest of "flat universe bunch" who believe in things they can't prove exists in a finite quasi-Euclidean universe. Sounds more like you have eschatological ambitions about God in making statements concerning things never having "proven" to exist.

## dtyarbrough

## ValeriaT

## ValeriaT

## Oysteroid

But this is pretty much what he says. We have observed, measured and mapped the effect. We know something must be causing it but no known candidates fit. So we call that something "dark matter/energy" and now are trying to determine what it might be first (what those two guys suggest) and what it actually is (what they propose to test).

Now for the test which may or may not check with their theory.

## Oysteroid

Are you calling 1000 to 100,000 light years scale microscopic?

## Shinichi D_

We already can. It's called Casimir effect.

## johanfprins

## Benni

This is "pseudo-science speak" at its epitome. You understand practically nothing about Einstein's General Relativity evidenced by your choice of words anytime you use the word "infinity" or any of its' derivative forms. "Infinity" does not exist in the spherical quasi-Euclidean universe upon which Einstein bases his GR, but you don't know that because you theorists living in a "flat universe" can't do the math to follow the concept of Conservation of Energy, the laws of Thermodynamics, etc.

## Bernd

Hermann Weyl

If Hermann Weyl is correct, how can we build the physical universe from a concept of elementary particles.

## ValeriaT

## ValeriaT

## ValeriaT

## ValeriaT

## johanfprins

## ValeriaT

## ValeriaT

## Tausch

Cartography for cosmology.

Mathematicians' contributions as well as any source wanting to contribute to an understanding and account for effects.

Acceptance or rejection does not motivate to contribute.

A most fortunate aspect of humans.

## cantdrive85

"...the relativity theory, by the way, is much older than its present proponents. It was advanced over 200 years ago by my illustrious countryman Boskovic, the great philospher, who, not withstanding other and multifold obligations, wrote a thousand volumes of excellent literature on a vast variety of subjects. Boskovic dealt with relativity, including the so-called time-space continuum..."

Tesla also was not impressed with Relativity,

"...magnificent mathematical garb which fascinates, dazzles and makes people blind to the underlying errors. The theory is like a beggar clothed in purple whom ignorant people take for a king ... its exponents are brilliant men but they are metaphysicists, not scientists..." New York Times, July 11, 1935, p23, c8

## cantdrive85

"Today's scientists have substituted mathematics for experiments, and they wander off through equation after equation, and eventually build a structure which has no relation to reality." Nikola Tesla

"We have to learn again that science without contact with experiments is an enterprise which is likely to go completely astray into imaginary conjecture." Hannes Alfvén

## johanfprins

## johanfprins

## johanfprins

Absolutely correct, and the biggest culprit was Paul Dirac who, with his irrelevant and wrong relativistic equation for the electron led the theoretical physicists into Alice's Wonderland where they are spending billions of dollars hunting non-existing Higgs bosons. Don't just smile Cheshire cat rather LOL!

## ValeriaT

## vacuum-mechanics

Yes, but how about its physical view, may be this paper could help to understand it.

http://www.vacuum...14〈=en

## Benni

It isn't my intention to embarrass you guy, but would you kindly tell us what you do for a living? I have six years of engineering school education if it's of any interest to you.

## ValeriaT

## johanfprins

I suspect that Valeria is breaking the rule by being an idiot without any qualifications.

## johanfprins

## Bogey

Its magnatism Jim, but not as we know it.

53 years of really bad spelling, but luckily I can read.

ps, It makes a refreshing change not to have to read "tard" 10.000

times in one of these posts.

## Benni

About the kind of response I expect from someone who has never had a course in calculus that would enable him to follow Einstein's field equations in GR. You see Val, if you can't follow the math there's no hope that you can make an intellectually competent critique of the subject matter. This is not to say you cannnot understand the subject matter unless you can also do the math, you can, but you become a follower not a leader in such a case, but you want to jump to the front of the line & declare yourself a leader with no credentials, which starts with the math.

## Benni

Absolutely correct. This is the reason Einstein revised his 1916 paper & came out with the revised edition in 1924, to account for Hubble's discovery with new telescopes & new spectroscopy capability to accurately detect redshift.

## TheGhostofOtto1923

This is like saying that Kant somehow intrinsically knew something about relativity. Because he was THAT smart i guess. What Rubbish.

## Benni

So what the dark stuff advocates have now done is move the origin of the stuff to some magical distance from our sun to a point where our Earth/orbit bound instrumentation can make no meaningful measurements, then spoonfeed us arguments that this is where the dark stuff begins, you know, somewhere beyond our solar system, & this must be the location of the "glue" that holds the baryonic matter of galaxies together. Well to the ashbin of stardust for that theory too, because we know the central bulge of all galaxies in fact do orbit galactic cores faster than stars in the spiral arms.

## Bernd

If a physical theory is formulated, at some point of the theory calculus is used and I don´t think a theory of relativity can formulated without calculus. At this point Euclidean geometry sneaks in on an infinitesimal local level – which can be proved. Of course a local Euclidean geometry can be used to describe any geometry (Riemann Geometry) on a macro scale. Thus I think ValeriaT did not understand my comments.

This Quote from Albert Einstein probably applies to ValeriaT: Do not worry about your difficulties in Mathematics. I can assure you mine are still greater.

Another Quote from Albert Einstein: ... Any man who reads too much and uses his own brain too little falls into lazy habits of thinking.

## Noumenon

I suspect it's a matter of density, with the space occupied by our immediate surroundings infinitesimal in comparison to galactic scales. Is this not more reasonable than supposing it was placed in a place safe from disproof?

## Lumberjack

## Benni

I'll be perfectly honest with you, this sounds like a better argument than the silly claims made in a previous post in this series. And the reason it sounds almost reasonable is the point I made two posts above, that it is now known for a fact that the stars which populate the central bulge of spiral galaxies orbit the black hole core more frequently than those in the spiral arms, it is no longer presumed there is some kind of baryonic glue that causing everything inside a galaxy to rotate in unison. Time lapse photos reveal stars near our galactic core exhibit dynamics totally out of sync with anything involving "dark stuff", & these dynamics are now believed to extend to the edge of the "bulge".

## ValeriaT

## Shinichi D_

I think Lumberjack described the galaxy clusters like atomic structures. The clusters in his model are surrounded by negativ particles, like the electrons in the case of atoms. In this analogy the dark energy would act in a similar way to PEP.

The problem is with this, that according to our knowledge this would result in a short distance force, and DE seems to be a very long distance interaction.

## Erik

contra-wise: hmm, isn't "any place" at least a few million light-years of some observer, so wouldn't dark energy & repulsion dominate everywhere?

## Deathclock

No... the nearest star to our own is 4.2 light years... so there are trillions upon trillions of stars which are not "within a few light years" from us.

## Lex Talonis

I say this as a world leading scientist, that this is based on the science of faith, without which God and the Universe would not exist.

## Shinichi D_

The other side of this is gravity and Dark Matter. Gravity is the vacuum pressure 'empty' space exerts onto 'solid' objects. Solid – compared to vacuum - can be a star or a gas giant planet, even an interstellar cloud. Direction of gravity is pointing from the densest vacuum – deep space – towards the least vacuumy regions – massive objects.

Particles, that we describe gravitationally interacting, are pushed together by the vacuum pressure. The same goes with planets. Take earth-moon system for example. Earth is surrounded by the vacuum of space. The gravity we experience is however somewhat smaller in one direction. The moon.

cont.

## Shinichi D_

One would argue, that moon is gravitationally interacting with earth, and everything that side on the planet is pulled towards it slightly. For example the tidal waves on the oceans.

But we could say, that from the direction of the moon, there is less vacuum pressure exerted toward earth. Between the two objects, there is a low pressure region, compared to other directions. They shield vacuum field between themselves. They not pulling each other in, they are pressed towards each other.

And here comes Dark Matter in the game. Vaccum pressure is not only exerted onto the two massive objects, but also onto the low(er) pressure region between them. That is Dark Matter. You can't find it around earth, can't find it around moon, but if you look at the system of the two, ther sould be a small ammount of DM present.

cont.

## Shinichi D_

And the deep space surrounding the globular cluster, since it has higher vacuum density, exerts pressure onto the entire cluster, like it would have an extra gravitational field, stronger, than the visible stars would justify. This is the phenomena we call Dark Matter. It's not made up by some mysterious particle, and it's not to be found in a given place. The phenomena is generated by the vacuum density difference within a cluster and the deep space surrounding it.

## Shinichi D_

## Noumenon

I doubt you've read Kant's 'Critique of Pure Reason' yet, so I'll make your argument for you, then defeat it.

Kant's transcendental deduction, that a-priori cognitive faculties determine the form of experience, and so the conditions of science, ...does not imply that Cosmological Space must be Euclidean in form.

His transcendental deduction wrt space and time, is based on 'a-priori synthetic propositions', which means axioms not logically necessary, but logically synthetic, that is, geometric axioms can be denied without contradiction. This actually implies that non-Euclidean geometries are possible, just not intuitively comprehendible.

We don't locally experience a semi-Riemannian inner product space with a torsion free Levi-Civita connection. In the limit of this Riemannian space, locally, the tangent and cotangent spaces, are Euclidean, and so compatible with intuitive understanding.

## Tausch

Conforming that of which you are apart of makes sense.

## Fleetfoot

General relativity explains gravity and other phenomena by treating spacetime using non-Euclidean geometry, specifically that invented by Reimann in 1854. Since Boskovic died in 1787, this is patently untrue.

Merely philosophising about "spacetime" without any actual theory (equations) of practical use is not physics. No matter how smart Boskovic was, without Reimann geometry, the tools weren't there for him to produce relativity.

## johanfprins

Curved space-time, and thus gravity has NOTHING to do with relativity. It follows directly from the wave-nature of matter. What is called the "tunnelling tails" of a matter-wave is the space-time curvature around the mass of such a wave.

The mass itself can be modelled by a stationary Maxwell-wave; within which the electric field-energy is the mass-energy. Lorentz had the right idea except that the electric-field energy is NOT in space surrounding the electron BUT within the wave-intensity which IS the electron.

## ValeriaT

## johanfprins

I just gave you another theory, but as you have proved time and again on these forums you are far tooo much of a closed-minded bigot to consider alternatives in an objective manner.

BTW: I did not say that the tails are those of Maxwell-waves: The tails are the curvature in space-time that traps the light-energy, which can be modelled by Maxwell's wave equation, to become stationary mass-enegy.

## ValeriaT

## johanfprins

## Osiris1

## johanfprins

Just to add: When a rod passes by, it becomes longer and the time "within" the rod as obseved from outside goes from "past" at the tail, to "future" at the nose.

So what is this time-change observed "within" the passing rod? It represents the change in phase-angle of the rod which moves like a coherent matter-wave.

Thus, without realising it, Einstein could have predicted the wave nature of matter about 20 years before de Broglie formulated his postulate for a moving electron. But Einstein decided incorrectly on "rod-contraction". It should be noted that de Broglie's postulate is only valid for a moving electron-wave.

An atomic electron wave-"orbital" is a stationary wave and thus has NO momentum. If it had actual orbital-momentum it would radiate away its kinetic.

BTW: Clocks attached to the rod, and stationary clocks "through" which the rod passes, ALL keep time in sync.

## ChemE

I have just published a new paper on my blog. I have just figured out that dark matter is triggering many of the seismic events and intense low pressure systems on earth. I have posted a technical write-up on my blog:

darkmattersalot "." com

## johanfprins

If you succeed to convince the Orwellian swine in control of modern theoretical physics, and I cannot see why not since your ideas are just as absurd as Dirac's relativistic equation for the electron, you might even win the 2012 Nobel Prize!! Good luck! So many has won it with equally absurd physics, that you deserve it!