The Bakhos Theory of Dark Energy and Matter

I propose that gravity reverses and becomes repulsive at approximately 1.5 million light years. It becomes more and more strongly repulsive, reaches a peak, and then decreases trailing off to zero.

This does away both with dark matter and also dark energy. It would explain why most galaxies are accelerating away from each other – leaving no need for cosmological expansion or dark energy.

It also explains gravitational rotational rates without the need of dark matter. Galaxies are pushing dust and gas into the interstitial space between galaxies. This dust and gas means that each galaxy or small galaxy cluster is surrounded by a womb of material at a distance that repulsive gravity operates. This repulsive womb, along with the pressure from other galaxies, holds outer stars in place, explaining higher than expected rotation.
You may read the justification for this theory here, along with responses to objections at the bottom:

I think that General Relativity can be adjusted such that we keep time dilation, BUT ditch curved or dilated space. I.e. we should work with flat, 3D , Euclidean space + time dilation. I explain about this in the notes at the bottom of the article.


@physicists, what do you think of @Joe_Bakhos idea?

This may be an amateur question, as my area is Biophysics and not Cosmology, but what do you have to say about the Andromeda Galaxy which is at 2.5 million light years away and is moving towards us at about 70 miles per second? If gravity is repulsive beyond 1.5 million light years then how should we think about our closest major neighbor galaxy moving toward us? You may have addressed this somewhere but I don’t have time at the moment to go through your thoughtful post on reddit.

I would add though that this quote of yours from one of your replies on the Reddit thread struck me as interesting:

Someone please test this equation to see if slight adjustment of the constants will account for galactic motion or not. If it does, then proceed to the rest of the theory.

I can’t necessarily blame you that you want or perhaps need in this case for someone to test an equation for you and if so, then test the entire rest of your idea vs. all of the thousands of observations that could be tested. That’s a tall order for anyone to fill and is one of the challenges to theories of modified gravity - that is the large amount of success that General Relativity has along with many predictions of future data that we have indeed found/measured the most impressive being gravitational waves.

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It appears he is proposing a type of MOND. I’d be surprised if it hasn’t been tested Imlicitely or explicitly in the literature yet. Do you know where @PdotdQ?

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Not to anticipate his own reply, but as @PdotdQ brought up insightfully several months ago regarding MOND:

In other words, there’s a complex web of evidence that needs to be navigated, and it is hard for one theory to fully resolve all the major, contradictory problems we currently have. At face value, @Joe_Bakhos’s theory seems to be a modification of Newtonian physics, or a version of MOND, so it wouldn’t be surprising if it can be tweaked to explain galaxy dynamics well. But that’s not enough to satisfy astronomers and cosmologists. I think no satisfactory cosmological model has ever been constructed assuming MOND.


@Joe_Bakhos I am glad that a layperson such as yourself are engaged enough with science to the point of making pointed inquiries about our current understanding. This is commendable and you should be proud of yourself!

However, it seems that you are trying to run before learning how to walk. I read through the posts you linked from reddit, and you have many misconceptions and errors in your understanding with regards to mainstream science. Before making modifications to mainstream science (which by the way, is done by mainstream scientists everyday), it is important to understand what mainstream science actually says.

This is important, especially as your theory might have overarching consequences that you might not want. For example, it seems that you reject space contraction while accepting time dilation. This will cause electromagnetism to stop working. Are you ready to pit your theory against the electromagnetic theory (which has passed many tests for hundreds of years)?

Once you understood mainstream science, you can clean up your theory and turn it into a form that can be theoretically compared with our current understanding of the Universe. As it stands, your theory is not a complete theory, but rather a data fitting, which one can always do trivially with enough number of parameters.

For example, you propose that we modify Newton’s gravity:

\vec{F}=\frac{G M_1 M_2}{r^2} \hat{r} into F = - k \frac{M_1 M_2}{r^2} \cos\Theta . (Note: the equation for \Theta you provided is wrong, i.e. it is not the angle between M_1, M_2, and C.)

However, \vec{F}=\frac{G M_1 M_2}{r^2} \hat{r} is not really Newton’s gravity, but rather an approximation that is valid only for point particles (it is never valid in the real world). The true Newton’s equation of gravity is the Poisson’s equation: \vec{\nabla} \cdot \vec{g} = 4 \pi G \rho, where \rho is the mass density.

What you did was modify an approximation of Newton’s gravity instead of modifying Newton’s gravity. If one is to modify Newton’s gravity, one has to modify it at least at the level of \vec{\nabla} \cdot \vec{g} = 4 \pi G \rho.

This is not even going to general relativity (which by the way, predicts repulsive gravity even for non-negative masses).

Once you have a complete theory, we can start talking about all the fun consequences of your theory. Before that, all you have is a data fit, which again, can be done trivially with enough number of parameters.

That said, let us see how good your data fit is. I would like to also hear the answer to this:

Before you claim that this is just matter far away pushing them together, realize that this behavior is not restricted to Milky Way and Andromeda. Galaxies and clusters orbit each other in very complex patterns (for example, in a Galaxy Cluster). The only way this can be replicated by repulsive matter far away is if these matter are:

  1. Very massive
  2. Moves very quickly
  3. Moves in an arbitrary pattern in such a way to make orbits that look like an attractive force is doing the job

Finally, you should not be discouraged if it turns out that your theory is wrong. This is just your first foray into the field. No professional physicist expects their first theory to be correct. You should be proud of yourself that you engaged in the sciences as a layperson.


While MOND stands for Modified Newtonian Dynamics, it actually refer to a very particular modification to Newtonian dynamics. This theory, while modifies Newtonian dynamics, is not THE modification to Newtonian dynamics that is MOND.


Now that I’ve had the time to read through some of your Reddit posts. @PdotdQ has already provided strong criticisms about the theory itself. I’d like to add that if the implications of your theory creates more problems than it solves, then it is just not a good theory. You list 17 implications. One of them, for example:

There is no “anti-matter.” There are only positrons and electrons.

doesn’t even make sense to me. An antimatter particle is a partner particle of an ordinary particle that has the same mass but opposite charge. By this definition, positrons are the antimatter partners of electrons. So what do you mean by saying that antimatter doesn’t exist? Even by your own standards your statements are contradictory.

There are people worldwide whose job is to trap and study antimatter. How do you explain the fact that they are able to do this if antimatter doesn’t exist?

Later in the thread, you admit:

My point is this: Either I have stumbled onto a genuine insight that requires a re-working of all known physics, or I have not.

If your theory is genuinely true, then even its ability to explain dark matter and dark energy would be inconsequential compared to the necessity of reworking all of known physics. You would basically have to explain away previous decades of experimental results about antimatter, general relativity, etc. as wrong or massively misinterpreted. What are the odds do you think this to be likely?


Related to this: MOND certainly seems more sophisticated and thought through than Bakhos’ theory. However, as far as I can tell MOND simply posits that gravity behaves differently at very low accelerations, as expressed by an interpolating function. There does not seem to be a deeper explanation for why gravity behaves this way; the interpolating function and its parameters seem to be picked primarily to get the best fit to the galaxy rotation curve data. So fundamentally, am I right in saying that MOND is just a sophisticated version of data fitting, just like Bakhos’ theory?


No: It started as a phenomenological model, i.e. data fitting, exactly like Bakhos’ theory. However, it has grown far beyond that. These days when people say “MOND”, they actually mean the family of relativistic MONDian theories such as TeVeS or AQUAL.

Indeed, the phenomenological MOND model did not even respect Newton’s third law or momentum conservation.


@pevaquark I will try to reply to each of the questions raised. First as regards the Andromeda galaxy:

Simple motion is not enough — the motion of the galaxies is not just dependent upon local galactic gravitation.

Andromeda’s motion towards us must also be described using its initial velocity, which I don’t know.

We would have to do a very detailed analysis of the change in velocity over time — not such an easy task when talking about a galaxy.

Also my initial guess of 1.5 million light-years as the zero-gravity-point is just that: An initial guess. I arrived at this number by just taking the approximate radius of the largest known galaxy; I figured that this would approximate the upper limit.

However, your observation immediately suggests a good way that my idea might be falsified. I am not an astrophysicist, so I have no idea if our measuring apparatus is sensitive enough to do this or not, BUT

If my idea is correct, then Andromeda should be decelerating, or at least its acceleration should deviate from what is expected. Its velocity would still be coming towards us (because of its initial velocity); it would still be blue-shifted to show this.

But the question is not whether it is coming towards us. The question is this: Is it speeding up, slowing down, deviating from what we expect? Or does its acceleration match what current theory would predict?

Current theory modelling galactic motion factors in the effects of cosmological expansion using hubble’s constant; So in my previous comments, where I asked whether the acceleration of Andromeda matches up with what we’re “expecting”, I mean what we’re expecting WITHOUT factoring in expansion — since the idea that I’m positing does away with spacial expansion altogether.

I stumbled upon this idea while working on something else: A geometric proof that continuous space can only have 3 dimensions. If you read through the reddit article, it will explain how this work led me to posit my ideas on dark matter and dark energy.
I am only educated to little past the high school level in Physics. Most of what you’ve said is beyond me. I do understand that correlation does not imply causation – I agree with you that right now if we can simultaneously model both galactic rotation rates and also cosmological expansion using the paradigm that I am expressing, this does not prove that my idea is correct. It is, as you say, data fitting.

But often in science a correlation like this raises a red flag. It notifies one that there may be an avenue worth exploring here. My idea does not rise to the level of a theory; I am aware of that. At this point it is merely the crude, rough initial speculations leading to a hypothesis.

I am intrigued by your statement that electromagnetic theory will not work without space dilation. I suspect, without being able to prove, that you might be mistaken – and that it might be possible to re-work electro-magnetic theory while keeping time dilation and getting rid of space dilation. Might you elaborate more upon that?

As far as the angle I am talking about: Imagine two bodies. Draw a line between them. Find the midpoint. From this midpoint travel out perpendicular to the line about 1.5 million light years, and then stand there. Then use your arms, each one pointing at one of the objects. The angle I’m talking about is the angle between your two arms.
About the correct expressions for gravity; I acknowledge what you’re saying, but my approximations are a layman’s crutch. They are only meant to get my idea across. An expert would express my idea in a more advanced way.

About the behavior of galaxies you are mistaken. Either galaxies in a cluster are relatively close together, like let’s say closer than 1.5 million light years – in which case they may be gravitationally bound and can orbit each other like you are saying, OR they are further apart – in which case even current theory has them subject to cosmological expansion. Even under current theory, galaxies very far apart cannot behave in the way you’re describing.

@ Daniel Ang:

Now about anti-matter; I did not mention quarks because I am not versed in chromodynamics. I will explain my reasoning.

I speculated that IF gravity reverses, maybe the other forces do too? Maybe some of the observed effects of the other forces might be due to this reversal rather than a model that assumes anti-matter.

So I thought to myself that maybe the strong force attracts electrons IF they are close enough, and otherwise repels them.

So what if, for example, in an atom of hydrogen, the standard orbital distance from the nucleus for the electron is the distance where repulsion from the strong force exactly balances the attraction from the electro-magnetic force?

If this is so, then perhaps when Dirac predicted the positron, he was NOT predicting the existence of “anti-matter”, instead he was predicting something that was always there.

Perhaps a neutron is actually some sort of sub-neutron that has both a positron and also an electron bound to it. In this model, a proton is merely a neutron that has lost an electron but retained its positron.

According to this model, electron and positrons have mirroring electromagnetic charge, BUT they react differently to the strong force. I.e. the point of reversal for a positron – where it would be repelled by the strong force rather than attracted- would be much further out than it is for an electron.

SO in other words, there is no such thing as “antimatter” – it is just different arrangements of positrons and electrons.

Now all of this aspect of my work is both highly speculative and also in an area entirely outside my expertise – so I am much less confident about it.

I am pretty sure that I am correct about dark energy and dark matter.

About this subatomic stuff I have no idea if I’m making good guesses or not.

Electromagnetism is Lorentz covariant. Unfortunately it is difficult to explain this concept to a layperson without at least 1 hour with a whiteboard together. Suffice it to say that the whole idea of length contraction and time dilation is baked into the very core of eletromagnetism. Indeed, this is the way relativity is first introduced to students in many universities.

Galaxy clusters can have a diameter of ~10 Mpc. Galaxies in galaxy clusters orbit each other as if a central force is doing the job. Some might argue that there is a MONDian correction to motions in galaxy clusters, but they do not expand away from each other. For example, check out this image:

This is a supercluster instead of a cluster, but the idea is the same. The grey blobs are the position of these galaxies now, while the black lines denote their motion in the past. All of them are moving towards each other. Further, notice that some of them curve. This curving motion is a signature of an attractive force.

Another thing that I thought you should be aware of: in your reddit posts, you mentioned how your theory might deal with gravitational lensing. However, there is no gravitational lensing effect in your theory! Plug in m=0 in the equation of your theory, and it is clear then that photons (which are massless) are not affected by gravity.

Here’s the thing, and do not take this the wrong way. Like I said, I am glad that a layperson is interested enough in physics to even ask these questions. You are trying to run before you know how to walk. You cannot posit your theory (which include a reworking of almost all of physics), but then only rely on a “layman’s crutch”. Give us a full theory, and we can compare whether your theory is better or worst than the current one.


First about photons:

One of the obvious consequences of my idea is that gravity must act upon light; so lensing would still occur.

Again about galactic motion: It is obvious that the travel lines showing the galaxies moving could not possibly have been observed; they would have to be extrapolated based on current velocities and modelled by current theory. What you are showing me is a picture of how current theory would predict and depict their past motion – which does not at all prove what you’re saying.

About “clusters”: This is a vague term that we use to describe a group of galaxies; because of the time scales the individual motion of each galaxy in the cluster must be modelled, it cannot be observed. All we have right now is their current velocities; we obviously do not have access to their observed velocities for the past several billion years.

The real proof that you are mistaken on this specific point is that if my model for galactic motion could not in any way be fitted to galactic data, then neither could Dr. Farnes’ model.

Since he, unlike me, IS an expert familiar with everything you’re saying, I assume that he would be able to answer your objections about modelling this motion with reverse gravity.

Why is this obvious? The force equation you showed clearly gives F=0 if m=0.

Correct. However, the velocity vectors point towards the galaxies converging. Furthermore, a lot of galaxies posses stellar streams, which are stars that are stripped out of galaxies as it travels. These streams give footprints of where the galaxies were in the past.

Dr. Farnes’ model is very different from yours! His model still has attractive gravity beyond 1.5 million lightyears, he just have positive matter and negative matter in a nice mixture. On the other hand, in your model every single matter is repulsive beyond 1.5 million lightyears! Notice that Dr. Farnes do not need to rely on the repulsive effect of faraway matter to explain e.g. Andromeda and Milky Way coming together.

Further, he is modelling dark matter and dark energy. I think you have a misconception here. Dark energy does not cause the expansion of space! It causes the acceleration of the expansion of space. Dr. Farnes’ model still possess the expansion of space from standard cosmology.

It is obvious that gravity must act upon light because IF I am right about space being 3D, flat, Euclidean, then it logically follows that the curvature of the path of light near a gravity source is not caused by the warping of space, ergo gravity must act upon light. You are correct to observe that if light has a mass of zero, and if gravity acts only upon mass, this creates a contradiction. Therefore a logical consequence of what I’m saying is that either light has mass or else gravity acts upon things other than mass as well.

I had not heard of stellar streams before. I clicked upon your link. All of the listed lengths of the streams are less than a million light years, so at face value they are irrelevant to what we’re talking about. They certainly do not provide the implied track of billions of galaxies over the course of billions of years.

In my view, our discussion of this point is still leaving out the major issue: Cosmological expansion. I am saying that cosmological expansion can be modelled with reverse gravity. The points that you are trying to make seem to be saying that we should ignore the issue of cosmological expansion.

To put the issue plainly:

Let us assume that two galaxies are completely at rest with respect to each other. We both agree that if they are close enough together, gravity will beat expansion and they will move closer. We both agree that if they are far enough apart, expansion will beat gravity and they will move further apart.

The distance where I’m claiming gravity reverses is the balance point, where both these effects cancel each other. So for a moment I ask you to consider this thought experiment and to answer my question: At what distance would gravity and expansion exactly cancel each other if both galaxies were perfectly at rest?

Good, so now you have to come up with a theory in which light is massive or come up with a better formulation of your theory that takes into account that gravity acts on things other than mass. Certainly this cannot be your F=… equation. This is what I meant by you needing to put in more into the theory than modifying that particular approximation of Newton’s gravitational equation.

Let’s take the stellar stream of MW. Its orbits takes it above the MW at a distance that is far larger than the MW is wide, which is of course, still under the 1.5 million light years. However, If your theory does not change the behavior of stellar streams, then your theory also cannot explain the flat rotation curve of MW! This is the main reason dark matter is introduced! If this is the case, your theory cannot explain dark matter.

No, you misunderstood me. The point is that dark energy does not cause cosmological expansion, but the acceleration of its expansion.

Cosmological expansion is not a force. Close by, it looks more like extra velocity. Comparing gravity (which in both the Newtonian case and in your model is a force, ergo an acceleration if you divide by mass) with cosmological expansion is erroneous, as you can’t compare velocities with accelerations.

@Joe_Bakhos, would you mind either clicking reply on my post or tagging me like so: @PdotdQ in your post? I do not get a notification that you have replied otherwise.

@PdotdQ I did not insist that light has mass. I said that IF my idea is correct, then EITHER light has mass, OR else gravity acts on other things as well as mass.

Now how about this logical exercise: 1. Assume (as Einstein did) that mass and energy are equivalent. Further assume that light is a form of energy. THEN light can in some sense be said to have mass. As I noted up above, I am not insisting upon this; I am just saying it is a possibility.

Again about the stellar streams: You have now switched to a new topic. We were talking about stellar streams as potentially tracking the long term motion of galaxies through the universe. Now you are shifting them to the question of galactic rotation rates. You are correct to note that my idea would need to line up both with the behavior of the outer stars in a galaxy and also correctly model the behavior of the stellar streams. So, the question is, how does current dark matter theory model their behavior, and, if you know this, why or how is it different from how my idea would model it? Current theory would model it as being pulled by the dark matter halo of our galaxy, whereas my idea would model it as being pushed by the womb of dust, gas, and other galaxies surrounding our own. Because my idea necessitates a complex curve of changing gravitational force including change of direction …. I think that this would be a very difficult model to construct. You are implying that in a matter of minutes you can deduce all the consequences – I am skeptical.

As for your statements about cosmological expansion: I’ve seen scholarly papers saying its less than expected, more than expected. I’ve seen papers that say it is uniform throughout the universe and other papers that say local expansion rates seem to be different than each other. Debating whether it is a force or not, or exactly what it is, is rather moot – because no one knows what it is. No one knows what “dark energy” is or how it works. All we observe is the following:

  1. Most galaxies seem to be accelerating away from each other. Current theory models this with cosmological expansion.

  2. Galaxies that are close enough to be gravitationally bound, don’t do this.

My thought-experiment question to you is pretty straight forward: At what distance, according to current theory, would two galaxies at rest with respect to each other, NOT be gravitationally bound because of cosmological expansion?

@Joe_Bakhos I have to be brief this time, and this would be my last post for a bit, as I have other commitments I have to run to.

Correct! this was my point.

Not all the consequences, but some of its most important ones (such as the fact that the womb has to move arbitrarily and react very quickly, if such a model can even be constructed). Don’t take it the wrong way, but I am a physicist, and have been in physics for a decade. Of course I would be able to figure out the consequences of physical models faster than you could.

Again, this is false. Current theory models this with dark energy, which again, causes the acceleration of cosmological expansion, not the cosmological expansion itself.

Again, cosmological expansion is not a force. Close by it is akin to velocity. Its effect do not subtract from the effect of gravitational acceleration in the way you are thinking of!

@Joe_Bakhos Again, I have something I have to go to now. Unfortunately I do not have the time to fully engage with all of your points. I would enjoy discussing with you some other time. Perhaps we can chat via voice if you are comfortable with it. If you don’t mind, please do not post any of my messages in your reddit thread. I am very internet-shy and prefer to leave little trace on the internet.