Illustration of Antimatter/Matter Annihilation. (NASA/CXC/M. Weiss)

## Antigravity Could Replace Dark Energy as Cause of Universe’s Expansion

18 Apr , 2011 by

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Since the late 20th century, astronomers have been aware of data that suggest the universe is not only expanding, but expanding at an accelerating rate. According to the currently accepted model, this accelerated expansion is due to dark energy, a mysterious repulsive force that makes up about 73% of the energy density of the universe. Now, a new study reveals an alternative theory: that the expansion of the universe is actually due to the relationship between matter and antimatter. According to this study, matter and antimatter gravitationally repel each other and create a kind of “antigravity” that could do away with the need for dark energy in the universe.

Massimo Villata, a scientist from the Observatory of Turin in Italy, began the study with two major assumptions. First, he posited that both matter and antimatter have positive mass and energy density. Traditionally, the gravitational influence of a particle is determined solely by its mass. A positive mass value indicates that the particle will attract other particles gravitationally. Under Villata’s assumption, this applies to antiparticles as well. So under the influence of gravity, particles attract other particles and antiparticles attract other antiparticles. But what kind of force occurs between particles and antiparticles?

To resolve this question, Villata needed to institute the second assumption – that general relativity is CPT invariant. This means that the laws governing an ordinary matter particle in an ordinary field in spacetime can be applied equally well to scenarios in which charge (electric charge and internal quantum numbers), parity (spatial coordinates) and time are reversed, as they are for antimatter. When you reverse the equations of general relativity in charge, parity and time for either the particle or the field the particle is traveling in, the result is a change of sign in the gravity term, making it negative instead of positive and implying so-called antigravity between the two.

Villata cited the quaint example of an apple falling on Isaac Newton’s head. If an anti-apple falls on an anti-Earth, the two will attract and the anti-apple will hit anti-Newton on the head; however, an anti-apple cannot “fall” on regular old Earth, which is made of regular old matter. Instead, the anti-apple will fly away from Earth because of gravity’s change in sign. In other words, if general relativity is, in fact, CPT invariant, antigravity would cause particles and antiparticles to mutually repel. On a much larger scale, Villata claims that the universe is expanding because of this powerful repulsion between matter and antimatter.

What about the fact that matter and antimatter are known to annihilate each other? Villata resolved this paradox by placing antimatter far away from matter, in the enormous voids between galaxy clusters. These voids are believed to have stemmed from tiny negative fluctuations in the primordial density field and do seem to possess a kind of antigravity, repelling all matter away from them. Of course, the reason astronomers don’t actually observe any antimatter in the voids is still up in the air. In Villata’s words, “There is more than one possible answer, which will be investigated elsewhere.” The research appears in this month’s edition of Europhysics Letters.

By  -
Vanessa earned her bachelor's degree in Astronomy and Physics in 2009 from Wheaton College in Massachusetts. Her credits in astronomy include observing and analyzing eclipsing binary star systems and taking a walk on the theory side as a NSF intern, investigating the expansion of the Universe by analyzing its traces in observations of type 1a supernovae. In her spare time she enjoys writing about astrophysics, cosmology, environmental science, biology, and medicine, making delicious vegetarian meals, taking adventures with her husband and/or Nikon D50, and saving the world. Vanessa is currently a science writer at Brown University.

### 76 Responses

1. BLACK HOLES, EXPANSION, AND DARK ENERGY

In the continuum of space and time, exists the dichotomy of matter and energy. All things exist as both matter and energy, but are experienced as one or the other.
As energy, all things exist as wave patterns. Most wave patterns are interferences of simpler wave patterns. The simplest wave forms are those that do not interfere with other waves. These simplest wave forms hold their shape as they propagate. There are three such wave forms.

The rest of this comment has been deleted as it is in violation of Universe Today’s comment policy.

• Hon. Salacious B. Crumb says:

Consider the torus as a universe.

No. The universe is unlikely to be a torus.

• Lawrence B. Crowell says:

The universe is not a torus, or at least not likely to be. Of course this does touch a bit on the problem of negative energy, for multiply connected spacetimes such as a torus has a stress-energy T^{00} which is negative. Also such a universe is a type of time machine with closed timelike curves. This is of course a problem with the whole idea of negative energy, it tends to give spacetimes which have pathological causal conditions.

LC

• TonyTrenton says:

L.C. Is it reasonable to think of the Universe as a globule of electromagnetic energy?

• Lawrence B. Crowell says:

No, but it may have emerged from some gauge field vacuum which tunnelled out of another cosmology. Electromagnetism is the simplest case of a YM gauge field.

LC

• Olaf says:

Is it me? Or is this a lot of scientific sounding words mixed together that sounds impressive but in reality means nothing.

• Manu says:

This is spamming or I’ve never seen any.

All things exist as both matter and energy,

That is an open question, as I understand it.

Fields are made up of particles, but according to string theory not everything needs to approximate fields. There have been research into “particle less sectors” of string theory, fairly decently accepted by that community I believe.

As for the wave function, it is complicated. Particle wavelets in QM aren’t simple when they travel without interaction (free as opposed to confined); all types of persistent solitons are more complicated still (because they _do_ interact with the environment).

2. Lawrence B. Crowell says:

Something is not right here. I looked at the paper and will try to read this to see what is wrong. There is a germ of something here though.

Here is the problem. I just use Newton’s second law of motion F = ma and consider the force as Newtonian gravity F = -Gmm’/r^2. We let m be mass and m’ be anti-mass. Let us consider the motion of the anti-mass m’ a = -Gm/r^2,

where it turns out the sign of m’ is irrelevant to the acceleration of m’. The means the anti-mass is attracted to the mass. Now consider the acceleration of the mass m,

ma = -Gmm’/r^2 – -> a = -Gm’/r^2,

and since m’ a = -Gm’/r^2,

where the sign of the anti-mass considered is irrelevant, but the other antimass flips the sign of the gravity acceleration. Consequently two anti-masses would accelerate apart from each other.

To think about general relativity with respect to anti-mass, consider Hawking radiation from a black hole. A black hole has this event horizon, and for a modest black hole the horizon may have sufficient curvature that a little bit of wave scattering by curvature occurs. Consider the case where the wave scattered is the Dirac field. The Dirac field is the “square root” of the momentum interval in special relativity E^2 – p^2 = m^2 in quantized form. This means the spinor fields have positive and negative energy solutions. The energy-momentum of the field upon scatter changes its root value. This is the Dirac sea, and the curvature of spacetime is perturbing the Dirac sea of negative energy states and the particle states of positive energy. This means that Dirac particles of negative energy can be scattered out of the Dirac sea by the spacetime curvature into a real particle state, which is Hawking radiation

Negative energy in this Dirac sea, which is a form of the quantum vacuum, enters a black hole and cancels a unit of mass in the black hole where this mass appears outside the black hole. This is standard Dirac sea logic, where a quanta of anti-energy E + mc^2 (both negative) interact with some positive mass E to generate a positive mass particle with mass m and some kinetic energy. Due to other quantum numbers, such as charge, which are conserved the input energy has to be sufficient to generate a particle plus anti-matter particle. The negative mass particle has opposite values of other quantum numbers, where only the anti-mass is flipped to mass.

Now let us consider the Dirac vacuum as a set of occupation states (all filled) with negative energy (anit-mass). The above analysis with Newtonian gravity indicates that this vacuum is self-repelling. Now the Dirac vacuum has particles with mass m existing within a momentum light cone with energy E = E’ + m < 0 which is arbitrarily large. So there is something which cancels this out. It is the supersymmetric partner with these fermionic particles. When the quantum numbers are computed (which has not been done completely) the vacuum energy might indeed be negative. Or maybe better put, it has some negative aspect to it. This is a part of the “sign problem” with understanding the Fermi-Dirac field. One might then say that this over all negative component of the vacuum state is self-repelling and this is maybe then an aspect of why the universe accelerates away.

LC

• Lawrence B. Crowell says:

I reposted this. Unfortunately this has a problem with carot signs, which means less than symbols have the effect of killing off parts of things. I have encountered this before elsewhere, which is extremely annoying.

Something is not right here. I looked at the paper and will try to read this to see what is wrong. There is a germ of something here though.

Here is the problem. I just use Newton’s second law of motion F = ma and consider the force as Newtonian gravity F = -Gmm’/r^2. We let m be mass and m’ be anti-mass. Let us consider the motion of the anti-mass 0 > m’

m’a = -Gmm’/r^2 – -> a = -Gm/r^2,

where it turns out the sign of m’ is irrelevant to the acceleration of m’. The means the anti-mass is attracted to the mass. Now consider the acceleration of the mass m,

ma = -Gmm’/r^2 – -> a = -Gm’/r^2,

and since 0 > m’ the sign of the acceleration is changed. This means the mass accelerates away from the anti-mass. This means that if the mass m and the anti-mass m’ have the same magnitude, so the total mass m + m’ = 0, then the mass and the anti-mass will accelerate away in the same direction. This is a funny situation, but since the total mass is zero this amounts to the acceleration away of nothing in total.

What happen if both m and m’ are anti-masses? Well the second law of motion is

ma = -Gmm’/r^2 – -> a = -Gm’/r^2,

where the sign of the anti-mass considered is irrelevant, but the other antimass flips the sign of the gravity acceleration. Consequently two anti-masses would accelerate apart from each other.

To think about general relativity with respect to anti-mass, consider Hawking radiation from a black hole. A black hole has this event horizon, and for a modest black hole the horizon may have sufficient curvature that a little bit of wave scattering by curvature occurs. Consider the case where the wave scattered is the Dirac field. The Dirac field is the “square root” of the momentum interval in special relativity E^2 – p^2 = m^2 in quantized form. This means the spinor fields have positive and negative energy solutions. The energy-momentum of the field upon scatter changes its root value. This is the Dirac sea, and the curvature of spacetime is perturbing the Dirac sea of negative energy states and the particle states of positive energy. This means that Dirac particles of negative energy can be scattered out of the Dirac sea by the spacetime curvature into a real particle state, which is Hawking radiation

Negative energy in this Dirac sea, which is a form of the quantum vacuum, enters a black hole and cancels a unit of mass in the black hole where this mass appears outside the black hole. This is standard Dirac sea logic, where a quanta of anti-energy E + mc^2 (both negative) interact with some positive mass E to generate a positive mass particle with mass m and some kinetic energy. Due to other quantum numbers, such as charge, which are conserved the input energy has to be sufficient to generate a particle plus anti-matter particle. The negative mass particle has opposite values of other quantum numbers, where only the anti-mass is flipped to mass.

Now let us consider the Dirac vacuum as a set of occupation states (all filled) with negative energy (anit-mass). The above analysis with Newtonian gravity indicates that this vacuum is self-repelling. Now the Dirac vacuum has particles with mass m existing within a momentum light cone with energy 0 > E = E’ + m which is arbitrarily large. So there is something which cancels this out. It is the supersymmetric partner with these fermionic particles. When the quantum numbers are computed (which has not been done completely) the vacuum energy might indeed be negative. Or maybe better put, it has some negative aspect to it. This is a part of the “sign problem” with understanding the Fermi-Dirac field. One might then say that this over all negative component of the vacuum state is self-repelling and this is maybe then an aspect of why the universe accelerates away.

LC

Wasn’t the Dirac sea abandoned because it is an awfully finetuned model introducing infinite energies (having infinite positive energy making up for the infinite negative sea)?

I peeked into Wikipedia, and what do you know: they mention that, and also reminded me/pointed out that
– The Dirac sea was based on fermions for state separation. We don’t have that here, I think, as the graviton is a force mediating boson. I’m not sure it helps that gravity is coupled to vacuum energy density, if the balance is based on the net of graviton states. (But maybe it isn’t and I just can’t see how.)

If we don’t have a sea, particles would be shedding energy indefinitely. Anti-particles would try to shoot out of any containment trying to get away from gravity fields ASAP (thus achieving even higher negative energy, unless I’m mistaken)! That isn’t observed.

– You can always find new particles that can be inserted into the sea. The concept may not be self-consistent. “Captin, I think we have a wee bit of a problem here.”

I guess my question, aside from any technical difficulties, is if a Dirac sea can be reintroduced for one type of particle alone? That doesn’t seem to be a likely outcome.

3. Hon. Salacious B. Crumb says:

No. Unlikely.
(Is that comment short enough for you, Nancy?).

4. Jaysus says:

5. Dudok22 says:

huh? antigravity?

6. ScottieD says:

Could it be both?

7. interI0per says:

so: an aggregated mass of antimatter will cause either a positive or negative “gravometric” field.
(gravity or antigravity)

if antigravity: then the remaining antimatter from the big bang is causing expansion.
if gravity: then the antimatter is expanding with all the rest of the matter.

third posit: the entire universe is expanding into a larger region of lesser “gravometric” density. the asymmetric production of matter and antimatter was resolved by initial annihilation- the result being the current intermix. the universe is not so much being driven to expand from within as being pulled apart from without.

this points to the universe having been the result of a hypermassive collision in a much
larger (infinite) void of near zero “gravometric” density.
the vector sum of the collision being in the direction of the “great attractor.”

what we need here is enough antimatter to see if it flies away!

8. bugz says:

novice here, but aspects of the idea sound more ‘logical’ and comprehensible to me than some of the convoluted explanations of how the mysterious dark matter works, or multiple dimensions intersecting, etc.

9. Olaf says:

The word “gravity” is used, so I expect some nutjobs here.
The word “anti-gravity” is used so I expect even more nutjobs than the nutjobs that claim gravity does not exist.

10. Olaf says:

WOW!
According to this study, matter and antimatter gravitationally repel each other

Repell?
What evidence is there that they repel.

Also I think that if they repel each other and form dense locations of only anti-matter, then these regions should be visible the same way as normal matter regions. They have the same properties as normal matter with one small exception, so you would have normal planets and stars out there.

• Olaf says:

I really miss some editing feature here, put the closing italics at the wrong place.

• Manu says:

Just experimenting…

• Trippy says:

D’oh. Let’s see if this works.

• Trippy says:

Apprently not Maybe one of the admin can fix it.

• Split_Infinity says:

That would make some pretty cool science fiction eh, they were from two worlds, two parts of the universe …one matter, one anti-matter …they could never meet …but their love would bring them together …lol, or some really bad space soap opera!

11. Olaf says:

Matter repelling anti-matter, is something the smells funny.

But I am wondering if matter has the property to attract other matter.
And anti-matter could have the property to repel other anti-matter.
No scientific claim here, just loud thinking.

12. Well you wait just one doggone minute here…

I thought it was the universe (space-time) that is expanding, and specifically not merely just the bits of matter (and anti-matter) moving away from each other…

— Yosemite Sam…

13. DrFlimmer says:

Oh, Olaf screwed the layout 😀

We need Ivan3man, the master of the italics, immediately. 😉

I am neither an expert on GR nor on particle physics (had some courses on it, though). However, matter and anti-matter repelling each other sounds strange to me.
Matter and anti-matter annihilates (btw: why is that?). If we put an electron and a positron close together, they will attract each other.
Since the attraction is orders of magnitude stronger than the repulsion, they wikk destroy each other in the end. (Ok, this does not contradict the idea.)
So, the repulsion could only be at work, if we have neutral particles, like atoms. An Atom and an anti-atom should repel each other according to the idea.
However, in the first 300.000 years after the Big Bang there were only charged particles and no atoms. This is quite enough time to annihilate due to the much stronger attraction.
As it seems, this would only work if the universe was cold right after its “creation”. Sounds a bit like the ideas of Alfvèn, about an infinite universe where matter is put in “one place” and anti-matter in “another”.

These are my thoughts at the moment….

• Olaf says:

Oops did I do this?

14. Greg says:

I will make a much simpler argument as to why this other attractive argument is likely inaccurate. There no evidence of anti-matter structures which would be generating the necessary anti-gravity proportedly causing these voids to expand. Such structures should be colossal in size and in fact quite visible. Unless you want to go down the path that the source of anti-gravity in the voids is dark anti-matter or enormous anti-black holes. If this is the case than perhaps the sparse galaxies we see in these voids are anti-matter galaxies. I don’t think that the physics of this will pan out considering there is just no evidence for anything in these voids that would be providing anti-gravity.

15. Lawrence B. Crowell says:

I believe I have figured out what the problem is. Before charging into that, there is a simple argument which illustrates how this is flawed without going into gravity. Suppose you have an electron and a positron. These are carefully brought together so there is not much energy involved with the conditions leading up to their interaction. This is how positronium is made, which is a hydrogen atom-like system of a +/- positron/electron system. This decays and produces gamma ray photons which have a total energy equal to 2mc^2, for m the mass of the electron and positron. This is an experiment done long ago and consistently works. Now suppose the positron has a negative mass. This means the net mass-energy is (m – m)c^2 = 0 and there should be no photons created. Matter and anti-matter would annihilate each other by producing nothing. This is not observed in nature

Here is the flaw in the author’s paper. The author uses the geodesic equation

d^2x^a/ds^2 + Gam^a_{bc)U^bU^c = 0

to make his case. Let us concentrate on the second term. In the PT reversal Gam^a_{bc}, which is the connection term, transforms into its negative. In a weak gravity field Gam^a_{00} = -GMx^a/r^2, which is a Newtonian force in the vector direction x^a. The PT operation will reverse M – -> -M. So far so good. The spacetime velocities U^b = dx^b/ds are reversed by x^b – -> -x^b and s – -> -s, so these remain the same. Everything is fine up to this point. However, the author then performs the same with the first term with x^a – -> -x^a and s^2 – -> s^2 and gets a sign reversal there as well.

It is with this second part that things go wrong. CPT operations act on fields. For some field f = f(q, x, t) one performs the operation CPT*f(q, x, t) = f(-q, -x, -t). So if I have an equation F = ma, the first part of this “F” is a dynamical field effect, as is F/m. The mass m is a scalar quantity. The acceleration is a geometric quantity and is the unknown part of the equation. So if I have an unknown on one side of an equation and I want to know how it transforms under a symmetry operation on the other side, I perform that operation and see how the unknown transforms. I don’t transform both sides, and CPT operations are preformed on fields.

In the case of the geodesic equation the fundamental thing which is transformed is the covariant derivative of the metric. A metric term g_{00} = 1 – 2GM/rc^2 under a derivative gives the Gam^a_{00} = -GM/r^2. This is the field that is transformed by CPT. From there you compute what the dynamics are. As a result, the argument I made with just Newton’s laws holds. Anti-mass particles would repel each other, mass particles attract and mass + anti-mass system runs away.

Negative energy is a horrible thing really. In what I wrote about the Dirac equation it has some applicability to the Boulware vacuum across black hole horizons. But a general negative energy in the universe, in particular negative mass particles, results in catastrophes.

Ah yes, another paper demolished! Sorry for the long posts on this, but when I see something like this I know there is a “bug in the program” and I have to find out what it is.

LC

• Lawrence B. Crowell says:

I made a mistake in my argument above. I wrote Gam^a_{00} = -GMx^a/r^2, which should be

Gam^a_{00} = -GMx^a/r^3

LC

• IVAN3MAN_AT_LARGE says:

It’s all Greek to me! 😉

• Olaf says:

That is what I like, peer review

• Tim McDaniel says:

“Now suppose the positron has a negative mass.” A reply above has “Let us consider the motion of the anti-mass 0 > m’”.

The article summary above says “First, he posited that both matter and antimatter have positive mass and energy density.”

Mind you, I would guess that his claim is bollocks. I don’t have anywhere near the physics or math backgrounds to follow the rest of the arguments made. I just wanted to point out that the rebuttals don’t seem to address the claims as summarized here.

The details of his claim I don’t know. Maybe he would posit a new multiplicand in the equation F = G*m1*m2/r^2, or rather the relativistic replacement? Or maybe he would throw in the absolute value of the mass in other equations where needed?

• Lawrence B. Crowell says:

The article basically invokes negative mass in the way the CPT is applied. On page 5 there is a statement to this effect. In that way there is a funny apparent inconsistency here. The PT operation on the geodesic equation changes the sign of the connection term, but all this ends up saying is that the geodesic is examined in a time reversed manner. So the dynamics of gravity repulsion between two anti-masses is the same as the time reversed viewing of the attraction between two masses.

LC

• jaymantra says:

Hi LC

Unfortunately I can’t speak about this at such a high level of mathematical understanding, but would the fact that the observed direction of time runs backwards for anti-matter be a problem? A reversal in polarity of every property of matter could include the effects it has on the space-time surrounding it.

Even if anti-matter does produce an anti-gravity effect, I’m not quite sure why or how any expansion might be explained by this guys theory anyway, as any possible distribution of matter/anti-matter throughout the universe would result in something quite different from what we are seeing! But I am glad people are looking for alternatives to dark energy and dark matter, as pretty as it sounds. I think there are explanations of our observed ‘expansion’ to do with other factors, involving shifting densities of space-time, in and around dense pockets of matter (like a galaxy for instance), and that the concepts of dark matter and dark energy are not required for this.

J

• jaymantra says:

Oops, ok I just realised anti-matter is supposed to repel anti-matter too…

• TonyTrenton says:

According to Stephen Hawking +ve matter is attractive and will form Universes.
-ve matter is repulsive and will disperse and not form Universes.

• Lawrence B. Crowell says:

If I understand what +ve and –ve means then this reference to Stephen Hawking is correct, which is seen in my simple calculations on the previous page to this blog post. Of course we have to separate out our meaning of antimatter and anti-mass. Antimatter is well understood, antiprotons are produced in the LHC to generate hadron collisions with zero net quantum number, such as charge, baryon number etc. The generation of anti-hydrogen has been used to determine if antimatter has anti-mass, and if I remember right the test indicated it has positive mass.

A world of negative mass would be very strange. Freeman Dyson wrote a little paper where he asked what would happen if electric charge were imaginary, e – -> ie for i = sqrt{-1}. The electric potential U = -ke*e’/r would not be negative, but positive due to i^2 = -1. The result would be the vacuum filled with electron and positron pairs would produce them with enormous abandon. Rather than attracting each other they repel and the vacuum is unstable. In effect a world with anti-mass is similar to this. For m a mass and m’ an antimass (less than zero) then m*m’ is less than zero. This is equivalent to Dyson’s transformation to imaginary charge, but here we just say that both m and m’ are imaginary. So this has a certain relationship to the tachyon state. Tachyons are fields which are cancelled on the vacuum in string theory, which is a long story there I can’t go into here. The runaway situation of a mass and anti-mass is a funny situation which is similar to a tachyon, where the tachyon is not cancelled on the vacuum state.

LC

• fractal says:

Congratiolations for demolishing the paper! You should send your bulldozer to Europhysics Letters.

In your first post you say:
“if the mass m and the anti-mass m’ have the same magnitude, so the total mass m + m’ = 0, then the mass and the anti-mass will accelerate away in the same direction”
If m’ is larger than m though, then the mass and the anti-mass will accelerate apart from each other if I understand it correctly, because -Gm’/r^2 > -Gm/r^2.
Villata places antimatter far away from matter, in the voids between galaxy clusters. If we assume that that is true, then is there a problem with the newtondynamic aspect of Villata’s theory in case there would be more antimatter in the voids than matter in the galaxy clusters? (Not considering relativity.) Matter-matter pulls together, antimatter-antimatter repel, and in this case antimatter-matter would repel as well.

• Lawrence B. Crowell says:

If this anti-matter existed in these voids there should then be gravitational lensing of more distant objects.

LC

• fractal says:

The antimatter would be diffusely spread across the voids, it wouldn’t coagulate because of its self-repelling character. Therefore gravitational lensing could be not very distinct.
I am sure you demolished Villata’s theory correctly. I’m just wondering if there is a problem with newtondynamics if the voids between clusters would contain antimatter, in similar or larger amounts than the amount of matter in the clusters. (Not considering relativity or any issues other than newtondynamics.) Could that model match the expansion of the universe the way it is observed?

16. IVAN3MAN_AT_LARGE says:

Attempting italic fix…
i {font-style: normal}

• Olaf says:

Test test. Is this none-itallic?

• IVAN3MAN_AT_LARGE says:

Scheiße!

• IVAN3MAN_AT_LARGE says:

The bloody HTML filter won’t let me use the appropriate tags to fix the italics!

• DrFlimmer says:

Scheiße!

Nice try to surround the swear-word filter — just use another language!

😀

17. Olaf says:

Wow the itallics are gone!

18. Todd Coolen says:

I solved this in May 2007 by adding a third body to the equation to be the negative gravitational force. Say where there is no negative gravitational force or zero, Newton’s second law is not compromised.

So, F=(G(m1*m2/r^2))+(-G(m1*m3/r^2))

where -G is the negative gravitational force and m3 is the mass of the antimatter body (antimatter will have negative mass).. Also please read about Mr. Forward:

Mr. Robert L. Forward in a link
called “Exotic Matter” by wikipedia:
“Ever since Newton first formulated his theory of gravity, there have been at least three conceptually distinct quantities called mass. However, these
three—inertial mass, active gravitational mass, and passive gravitational mass—have so far always been found to be equivalent. When considering
hypothetical particles with negative mass, it is important to consider which of these concepts of mass are negative. From Newton’s law:

F=m(sub i)a

Thus it can be seen that an object with negative inertial mass would be expected to accelerate in the opposite direction to that in which it was pushed, which is arguably a strange concept. If one were to treat inertial mass m(sub i), passive gravitational mass m(sub p), and active gravitational mass m(sub a)
distinctly, then Newton’s law of universal gravitation would take the form

F=(-G(m(sub p)m(sub a)/r^2))

Thus objects with negative gravitational mass (both passive and active), but with positive inertial mass, would be expected to be repelled by positive
active masses, and attracted to negative active masses. If all such negative matter were like this, then gravity would work similarly to the electric force except that like masses would attract and unlike masses would repel.” endquote

I use the example of the Pioneer Anomaly. Say this is being affected by antigravity in a system that has a large gravity body and a large antigravity body. Call this a mirror system that has a balance between being affected by either body. But for my example, the Pioneer has found itself affected by the antigravity body “a little”.

Use the formula:

F=(G(m1*m2/r^2))+(-G(m1*-m3/r^2))

where the mass of the Pioneer 10 is affected by the antimatter monopole as it approached the mirror system. The second term becomes positive (from the two negatives) and the force becomes increasingly stronger against the Pioneer 10 as it traverses the mirror system toward the antigravity body. This in turn causes a deceleration as it approaches the antigravity body..

Now let’s assume that the Pioneer 10 was an antimatter body traversing our solar system. The equation calculates to a negative force being a repulsive force:

-F=(G(-m1*m2/r^2))+(-G(-m1*-m3/r^2))

so these formulae allow for no violation of Newton’s Law and at the same time, allow for variances and if we were privy to an antigravitational system, this variance would be more prolific.

I do believe that dark energy is a negative gravitational force and we cannot observe it directly due to the scattering of light against the antimatter body. In our observeable universe, we see what is not obscured by the affects of antimatter. Take two magnets opposite poles and image one of those as a light ray and the other antimatter. Unless the light ray is repulsed back directly into our observeable universe, we would not see it. Any reflected light we do see would be from an object that is not an antimatter body. Ergo, we would not “see” the dark energy or antimatter body directly and may not even know it’s there.

I just wanted to say my 2 cents and am glad to see that Universe Today is more open-minded now.

Okay I’ll go back to just observing again.

Todd Coolen

• Lawrence B. Crowell says:

The behavior of a negative mass is indeed to be repelled by any gravity field, whether from positive or negative mass. The author of this paper has clearly made a mistake in concluding anti-mass would attract anti-mass.

The inflationary pressure is due to positive energy. The gravity field is due to the quantum vacuum, and this defines an effective stress-energy tensor T^{ab} with components T^{00} = const*e, for e and energy density 0 = time coordinate index, and T^{ij} = const*pu^iu^j, for i and j running over spatial coordinates u^i velocity and p a pressure density. For the de Sitter spacetime the energy density and pressure satisfies a state p = w*e where w = -1. So the pressure in effect is what is stretching out space and frame dragging galaxies with it. There is no need for a negative energy density or exotic matter.

Negative energy density or negative mass fields have serious pathologies. Principally since they are due to quantum mechanics the negative eigen-energy states have no lower bound. This then means the vacuum for these fields is unstable and would descend to ever lower energy levels and produce a vast amount of quanta or radiation. I don’t believe this happens.

As for Pioneer 10 fogettaboudit. I think it likely this is due to some sort of leaking pressure tank, sublimation of frost, or …, more or less prosaic processes.

LC

The Pioneer anomaly is now predicted from first principles of thermal radiation, so it is an “anomaly” (read: “‘E’s off the twig! ‘E’s kicked the bucket”).

Unless the research is wrong, but that risk is slim to none: earlier work removed 1/3 of the initial anomaly.

Oops, sorry: just to be clear, I didn’t mean to evaluate the rest of the comment. It was a fact of the context (that recently circulated).

19. Aqua says:

No way… that’s far too easy a solution! Matter/anti matter annihilation creating all those humongous magnetic fields and particles and herding all that matter into neutrally charged accretion disks around galaxies and stars… no way.

• Aqua says:

Here I feel I must note the recently detected gamma ray fountains at either pole of the Milky Way…

20. theghostoutside says:

ok, now you’ll all have to excuse my lack of university degree (i’m in the process 😉 ), but it is not strange for the microscopic and the macroscopic species of our universe to behave alike, so why would it be wrong to hypothesize a migration of mass, comparable to osmosis in gas particles, with respect to space-time itself. It would thin out, desiring a less dense region of.. well.. emptiness to occupy ?? feel free to disprove, but spare me some dignity.

Antigravity Could Replace Dark Energy as Cause of Universe’s Expansion

No. [Hey, shorter than HSBC!]

– There is no mechanism in GR for antigravity (but for negative pressure and/or diminishing what spacetime curvature there is). I don’t think Villata has managed to change GR. Conveniently for me I’m short on time and LC has studied GR anyway, so I can defer this for now. 😉

– Gravitational mass = inertial mass in GR, and that has been tested many times over. And tests put antiproton inertial mass = proton inertial mass to 10 significant digits or so.

– Large scale structures. I agree on what has been said above, and I think it is the most damning prediction that this idea fails.

22. interI0per says:

seems to me that gravity is charge agnostic.
if it is then antimatter stellar systems could possibly form.
they would not radiate antiphotons but be indistinguishable from normal stars.

or not…

23. FleetFoot says:

Picking up on Todd’s point regarding the three types of mass, it seems qualitatively straightforward:

As far as any mass is concerned, it simply moves into its future following the GR equivalent of a straight line which is a geodesic as long as there is no force acting on it. This follows from symmetry since, without an external force, there is nothing to identify a preferred direction in which the particle would deviate from the geodesic. This means that anti-matter should follow the same path as matter under the influence only of the gravitational effect of other ordinary matter. “Passive gravitational mass” is really a pseudo-effect created by coordinate rotation and thus must be positive.

Inertial mass can be determined from the action of an electric or magnetic field on an anti-particle. We know it is accelerated in the oppposite direction from ordinary matter and tis could be attributed either to the particle having the opposite charge polarity or having negative inertial mass. If total charge is to be conserved, the polarities must be opposite hence the inertial mass must be positive.

That leaves the active gravitational mass. If that were negative, it would cause geodesics to curve away from anti-matter rather than towards, but as has been said above, both matter and anti-matter must follow those geodesics thus either anti-matter has positive active gravitational mass like ordinary matter or it must repel anti-matter as well as matter.

In conclusion, the idea that anti-matter could form galaxies which would repel normal matter galaxies doesn’t appear feasible either way, either anti-matter flies apart or it attracts matter.

On more general note, surely if say 1% of the universe were some form of exotic mass which generated “repulsive gravity”, surely that would only reduced the net expansion by 2% at all times. For the effect to grow with time, it needs to be stronger at long range and weaker at short, or evolving in time in some way.

• Lawrence B. Crowell says:

Your conclusion is similar to mine. Antimatter does not have anti-mass. Besides all the anti-mass states in the Dirac theory compose the vacuum state as the so called Dirac sea.

LC

• Hon. Salacious B. Crumb says:

I haven’t commented here, but I agree.
The only thing really special about antimatter, is that the nucleus has a negative charge (anti-protons) and positive electrons (positrons). They are essentially the same particles but or reverse in their polarity.
The other problem is if there were pockets or regions of antimatter still existing in the universe, the boundaries between matter and antimatter regions would be a blaze with energy and gamma rays; but there does not seem to be an astrophysical phenomena that would support that view.
Another issue would be with magnetic fields and jets whose positrons colliding with electrons along the field lines could easily travel significant distances and trigger astrophysical observable phenomena (which we do not see.) Also, if there was any repulsion, we would see either the matter jets antimatter jets travelling in a straight line, then at the boundary of the matter and antimatter a ultra bright gamma ray ‘star’ where the annihilations would occur. (Again not seen in nature.)
Finally, if the Big Bang is correct, I though that the energy seen in the universe was created by matter and antimatter, and hat the reason why the universe is one kind of matter, is that there was a slight excess of one for over another. This net energy drives and continues the expansion.
If the force was repulsive, wouldn’t the universe after all this time be like little clumps of matter and antimatter regions scattered everywhere? Instead we see galaxies distributed along surfaces akin to many many lathered soap bubbles. Also, would not the ‘centres’ of these bubbles (void) there should be anti-matter galaxies? f so, you would expect something to be observed there. (as far as I’ve read, there is no observational evidence to support this view!

• Lawrence B. Crowell says:

As I showed yesterday, anti-mass (antimatter with negative mass) repels itself. I think in general we would be living in a different sort of world than the one we observe.

LC

• Hon. Salacious B. Crumb says:

Lawrence
I am not as clued up with this subject as I should be. While I was surprised with this story popping up, I came across (admittedly from investigating our mutual ‘friend’s’; Hunter, J.H. Jr., “On the cosmology of Alfvén and Klein”, MNRAS, 137, 271 (1967).

This has some interesting ideas and discussion on matter / antimatter issues (pg.271) and the kinds of astrophysical objects that might be expected. Whilst the conclusions may have now been mostly rejected by astrophysics, this referenced article in this story has some quite interesting parallels.

After reading this article, it seems just another different way of trying to bring antimatter into the cosmos equation.

As for you saying; “I think in general we would be living in a different sort of world than the one we observe.” is truly the point. I.e.

“We are the way we are because the Universe is the way that it is… and no vice-versa.”

• Lawrence B. Crowell says:

Antimatter clearly plays a role in the universe. The high energy universe is likely CP invariant. This means given a wave function Y_q(x) that CP Y_q(x) = Y_{-q}(-x) and CP invariance means this returns the same wave function. CP discrete symmetry is broken at lost energy and this gave rise to an excess of matter over anti-matter in the colder low energy universe. Antimatter states are due to the occurrence of sufficient positive mass-energy on the Dirac negative momentum-energy states which are filled up and define the Fermi-Dirac vacuum. This means that a negative mass virtual particle state with quantum number opposite those of the positive mass-energy particles now exist with positive energy.

The Dirac equation is the spinorial form of the square root of the Klein-Gordon equation. The KG equation is a quantized form of the special relativistic momentum interval

(mc^2)^2 = E^2 – (pc)^2.

Going into the spinor mathematics of the Dirac equation is a bit beyond the scope of UT, and further requires some graphic math-tools not available here. So looking this up, even on wikipedia, is advised. However, the square root of an equation has two roots, and just as y = x^2 has positive and negative x’s (and recall the binomial equation) the same happens with the Dirac equation.

The physics of CP violations is a big issue, and Fermilab has been looking hard at CP violations with the T-quark, which follows the Desy results on the B-quark factory results. The T and B quarks are in the highest mass doublet of QCD.

LC

• Hon. Salacious B. Crumb says:

Funny you mention the CP violations. I read today on the New Scientist website “Lonely, spun-out proton reveals magnetic secret”, which talks about the g-factor.
According to this, there is a possible experiment to verify if the g-factor has the same value between protons and antiprotons.
In this story, if the fields of either are of different strengths, then it would pose an additional problem for astrophysical phenomena and even nucleosynthesis / stellar evolution. (This linked article has the arXiv paper attached with it.) Again, this is a possible broken symmetry.

• Lawrence B. Crowell says:

I would be surprised if the Lande g-factors differed between matter and antimatter. The factor is g = 2.0023318416 for

mu = -geS/2m

for the magnetic moment. The straight forwards calcuation gives g = 2. It requires QED to get g – 2, where physics related to the Lamb shift give the departure. There are expected departures for the muon g factor, where there can be a virtual transition to the neutralino state.

LC

{Violation of comment policy: text deleted. There is a thread on this topic in BAUT’s Against the Mainstream section.}

• FleetFoot says:

“For example, the electron and the positron have the plus mass, although the positron is an antiparticle in relation to the electron. However, this is a very large problem, which is outside the framework of this chapter.”

Why quote the chapter then? The suggestion that the positron (for example) would have negative active gravitational mass is the topic being discussed. You wouldn’t be trying to publicise your book, would you?

• Olaf says:

I think we have a copyright issue here with such a big excerpt that clearly is a copy and paste of a book.

25. interI0per says:

here is a tidbit of some salience:

http://www.bbc.co.uk/news/science-environment-13097370

where are the antineutrons?

• FleetFoot says:

Anti-neutrons are produced in anti-proton factories but last I heard they had no way to slow them down. You can’t use a moderator (e.g. graphite) of ordinary matter obviously and techniques like laser slowing only work well (if at all) on charged particles.

• Lawrence B. Crowell says:

A high energy event with particles can generate a proton plus anti-neutron plus a positron and an antineutrino.

LC

• Lawrence B. Crowell says:

Oops, sorry I wrote too fast. I meant an anti-neutron plus proton plus and electron and neutrino.

LC

26. Olaf says:

Recently I started to realize that a lot of people have a big wrong concept of what gravity is.
I think that a lot of conspiracy theorists think that gravity is a surface effect only. For example the moon pulls up the surface and thus cause tension inside the interior.

Reality is that gravity acts on every atom and in the complete Earth pulling all in the same direction. This includes the back side, the inner side, the left and right side and the front side. The resulting vectors is basically near zero in gravitational difference between the backside and the front-side. Earth does not get stretched like a big balloon but moves in the orbit as one whole thing.

27. wjwbudro says:

The “effect” of gravity is canceled (zero G) at the center of a mass which is located at the bottom of the space/time well it itself created. This center will be offset in the direction of the centers of other nearby masses (n-body physics).
This is what I came away with the many times this subject was tackled here on UT.

28. VIGNESHRAJU says:

I’m 10 std student,i cant able to understand all.But i know it is very difficult to explore the universe when expands