[ethigSmimbine]

Mathematicians offer unified theory of dark matter, dark energy, altering Einstein field equations
September 7, 2012



(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.
http://arxiv.org/pdf/1206.5078v2.pdf
Provided by Indiana University



http://phys.org/news/2012-09-mathema...-einstein.html

[gagagaridze]

Here we go Bogs. It was the wrong thread. I hereby transfer my comment 'At last an explanation that doesn't involve mystery matter/energy', to this thread.

[sarasaraseda]

Here we go Bogs. It was the wrong thread. I hereby transfer my comment 'At last an explanation that doesn't involve mystery matter/energy', to this thread.

And reiterate the question 'How long till this is reviewed'?

[naturaherbal]

Mathematicians offer unified theory of dark matter, dark energy, altering Einstein field equations
September 7, 2012

......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.

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.

Thanks for the info BC. A well written article. It makes sense to me. The equation adds things to the GR mix to better represent the current state of cosmology accounting for the non-uniform distribution of matter throughout the universe by the addition of a new field that incorporates DE and DM into the universal density.

IMO the equation goes the next step for GR and hopefully, if validated, provides some new angles of insight.

If energy and momentum is conserved when holistically dealing with DE, DM and normal matter but no longer conserved when dealing with normal matter alone, what could the implications be? I would assume there would be some experimental setup that could demonstrate if this may be correct. I wonder how we could test this?

[Clielldub]

Thanks for the info BC. A well written article. It makes sense to me. The equation adds things to the GR mix to better represent the current state of cosmology accounting for the non-uniform distribution of matter throughout the universe by the addition of a new field that incorporates DE and DM into the universal density.

IMO the equation goes the next step for GR and hopefully, if validated, provides some new angles of insight.

If energy and momentum is conserved when holistically dealing with DE, DM and normal matter but no longer conserved when dealing with normal matter alone, what could the implications be? I would assume there would be some experimental setup that could demonstrate if this may be correct. I wonder how we could test this?

It also begs the question, what happens to the cosmological constant in this new equation if DE is taken into account elsewhere in the equation. :-))

[N9u9ie4p]

It's not clear to me that there is anything fundamentally new here. Modifications to the Einstein equation are really about distinguishing observable energy-momentum from unobservable energy-momentum. It should be noted that whether or not a particular form of energy-momentum is observable is deducible from the symmetry of the energy-momentum. The cosmological constant does have the symmetry to be unobservable as energy-momentum, and also allows the observable energy-momentum to be conserved. On the other hand, there is energy-momentum with the symmetry to make it unobservable, but isn't a cosmological constant. In this case, neither forms of energy-momentum are separately conserved, though the total is conserved.

It would be interesting to provide the most general form of the Einstein equation where the observable and unobservable forms of energy-momentum are clearly distinguished. I wonder if that is what the authors were trying to achieve and whether they succeeded.

[Nopayof]

It would be interesting to provide the most general form of the Einstein equation where the observable and unobservable forms of energy-momentum are clearly distinguished. I wonder if that is what the authors were trying to achieve and whether they succeeded.

I thought that was what it was driving at. Is there anything else that really needs clarification?

[limpoporanique]

Dark matter is a myth a fiction of grammar

you seem to think because there is a word ie matter there must be something thing in the universe corresponding to it
like there is a word unicorn so you then believe there must an existent unicorn

take this myth
http://www.abcforums.com/showthread....d-Field-Theory
(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. All this talk of dark matter is ridiculous as no one know what matter is

http://en.wikipedia.org/wiki/Matter

Typically, matter includes atoms and other particles that have mass, but this definition confuses mass and matter, which are not the same.[4] Different fields use the term in different and sometimes incompatible ways; there is no single agreed scientific meaning of the word "matter," even though the term "mass" is better-defined The term "matter" is used throughout physics in a bewildering variety of contexts: for example, one refers to "condensed matter physics",[89] "elementary matter",[90] "partonic" matter, "dark" matter, "anti"-matter, "strange" matter, and "nuclear" matter. In discussions of matter and antimatter, normal matter has been referred to by Alfvén as koinomatter.[91] It is fair to say that in physics, there is no broad consensus as to a general definition of matter, and the term "matter" usually is used in conjunction with a specifying modifier.

[realnilkless]

DM/E is a set of observations that as yet has not been understood. It has been termed DM and DE due to the various natures of the observations. No one has yet asserted that there is other than yet to be interpreted observations.

[feeshyLew]

DM/E is a set of observations you are talking nonsense
as

It is fair to say that in physics, there is no broad consensus as to a general definition of matter, Different fields use the term in different and sometimes incompatible ways

[KeettyGlots]

I thought that was what it was driving at. Is there anything else that really needs clarification?

The article focused on dark energy and dark matter. The question that I'm asking is about whether or not the term added to the Einstein equation satisfies the symmetry of the vacuum.

[SHaEFU0i]

The article focused on dark energy and dark matter. The question that I'm asking is about whether or not the term added to the Einstein equation satisfies the symmetry of the vacuum. you cant talk about DM as no one knows what matter is
It is fair to say that in physics, there is no broad consensus as to a general definition of matter, and when scientist do disscus it they contradict each other

Different fields use the term in different and sometimes incompatible ways you are in search of science myths
science version of the unicorn myth

[ANCETPYNCTEXT]

Dark matter is a myth a fiction of grammar

you seem to think because there is a word ie matter there must be something thing in the universe corresponding to it
like there is a word unicorn so you then believe there must an existent unicorn

Well, no. The observations are telling us that there is something that we cannot see that is affecting the gravitation of galaxies. What words we choose to describe this is irrelevant to the observations that require explanation.

[Seesspoxy]

you cant talk about DM as no one knows what matter is so? we don't know what gravity is either or photons or....if we reduce everything to this level then why talk about anything?

[Pjayjukr]

so? we don't know what gravity is either or photons or....if we reduce everything to this level then why talk about anything?

hehehehehe :-))

[toreesi]

What words we choose to describe this is irrelevant to the observations that require explanation. all you have are words
you use the word DM
scientist use the word matter
these are myths
when scientist talk about it they contradict themselves
Different fields use the term in different and sometimes incompatible ways you seem to think because there is a word ie matter there must be something thing in the universe corresponding to it
like there is a word unicorn so you then believe there must an existent unicorn

[Stasher11]

all you have are words

Well that's certainly not true. We also have mathematics.

[embefuri]

Well that's certainly not true. We also have mathematics.

....and the aqueduct :-))

[verybigf]

you'll have to do a bit more than repeat yourself gzasky if you want to convince us.

specially if you only have words....

*breaks into song*

Smile an everlasting smile
A smile could bring you near to me
Don't ever let me find you gone
'Cause that would bring a tear to me
This world has lost it's glory
Let's start a brand new story
Now my love right now there'll be
No other time and I can show you
How my love
Talk in everlasting words
And dedicate them all to me
And I will give you all my life
I'm here if you should call to me
You think that I don't even mean
A single word I say
It's only words, and words are all
I have to take your heart away
You think that I don't even mean
A single word I say
It's only words, and words are all
I have to take your heart away
It's only words, and words are all
I have to take your heart away

Words
Bee Gees

http://www.lyricsdepot.com/the-bee-gees/words.html

[FuXA8nQM]

Well that's certainly not true. We also have mathematics. but DM is a word
and your word ends in nonsense
Different fields use the term in different and sometimes incompatible ways