Spatial Convexity: a Possible Explanation for Dark Matter and Dark Energy

Disclaimer: In trying to understand how the universe works, and especially in trying to make the subjective part consistent with the objective part, I feel a compelling need to understand physics. I also feel a need to expand on what is “known” with some occasional speculation about what might be found out “someday.”

From time to time, I'll post some of my speculations here. If physics isn't your “bag,” I'm sorry. It seems important to me, but I realize a lot of what interests me is, to put it mildly, unusual. Please feel free to skip over my physics-related posts; it's just speculation, anyway. I don't claim expertise.

There's an awful lot of just plain BS out there calling itself physics, though. I may be guilty of adding to that, and it bothers me. To the extent I am guilty, I apologize in advance.

Most of what I write here is subjective, and about things that are subjective. My views are worth as much as anyone's. Physics is just about the only area where there actually is a right and wrong. Physics either works or it doesn't. As best I can, I apply that same criteria to my subjective stuff: does it work to increase sanity or not? Testing the subjective isn't easy, though, and unlike physics, even the results are subjective and vulnerable to misinterpretation..

When I do write about physics, I can only tell you that I'm sincere, that I check and re-check against “accepted” physics, and wherever possible I ask “real” (professional) physicists for their opinions and criticisms. I have learned a lot doing that! I have come up with some really wacky ideas along the way, most of which have been proven wrong. Meanwhile, I'm a lot more careful these days, and I hope you'll find my ideas worth reading and considering.

On the off-chance that any “real” physicist should read here, I'd welcome your comments and criticisms! Really! Meanwhile, I hope that someday, at least some of my ideas lead the “real” physicists to a valuable finding or two. I hope they'll help my other readers, too.
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Spatial Convexity: a Possible Explanation for Dark Matter and Dark Energy

(Update:  The "rainbow effect" described here is almost certainly wrong.  See comments.  The rest still stands, though.)

One reason theoretical physics is unpopular is that it's hard to understand. While it's easy to grasp that when I jump, I come down again -- every time -- it's not at all obvious that when I run fast enough in a straight line, I can actually escape Earth's gravity, and orbit in space. I don't even have to jump up! Yet it's proven to be true every time we launch a satellite.

In recent years, one of the more incomprehensible ideas physicists have offered is that of “dark matter” and “dark energy.” Very briefly speaking, as we have developed new and more accurate measuring tools and methods, anomalies have been discovered that bring into question our previously-accepted view of how gravity works, and of how space expands as a result.

After several years of effort trying to grasp the problem and to imagine how we could have been so wrong 'til now, I believe I've come up with a relatively simple and obvious solution. Ironically, it's about how we subjectively interpret the data we see. In other words, I don't think any of the observations are incorrect. However, by re-interpreting the meaning of the “facts,” I think I've come up with a way to incorporate the new data with our old view of things.

In a sentence, I think I've eliminated the need for “dark matter” and I've explained “dark energy” as something we've been seeing all along. In other words, our old view of how things worked wasn't really far off. The interpretation just needs a bit of tweaking.

The tweaking necessary requires three assumptions:

1) Space is not nothing. It is not a “thing” in the sense that you can't pick it up; it can't be separated into parts (except in our minds); it has no weight; etc. But it exists, and it makes a difference in everything we see and do.

2) Space does have one characteristic that affects matter and thus can be indirectly measured; it has shape.

3) The force we call gravity affects the shape of space. Gravity does not attract matter, per se. It changes the shape of space so that matter “falls” into the depression/concavity it causes.

We have known number 3 above since Einstein worked out the theory of General Relativity (GR). Yet, for reasons hard to fathom, we have persisted in assuming that gravity is a force that affects matter. (*see note)

In any case, all of Einstein's calculations, and all of everyone else's calculations are based on how gravity affects matter. The idea that this effect is indirect; must have gotten lost in the shuffle. It's indirect because gravity actually affects the shape of space, and that, in turn, affects the matter within the space.

So, what happens to the shape of space when there's no gravity to make it concave? Up 'til now, it's been assumed that space without matter (gravity) to distort it is effectively flat. In other words, space has been considered not to matter unless there's matter to shape it with gravity. I find it ironic that we say it doesn't matter, and than we prove that it matters after all.

In explaining that the universe is expanding, it's as if we've been saying that new space is magically appearing out of nowhere. Everyone agrees that the amount of matter in the universe is not growing. Matter is not appearing out of nowhere. Why should space be different?

Yet space is expanding. Areas of space where there is little or no matter, expand. In a sense, space “pushes” the matter of one galaxy (cluster of galaxies) apart from the next one. Well, what is the shape of expansion in all directions? Convexity. It's like a balloon blowing up. It gets bigger, and more convex. And that, I think, explains “dark energy.” The numbers need to be checked. It needs to be proven that areas in the universe which show greater red-shift (faster expansion) are, in fact, more devoid of matter than other areas. It should be verifiable.

Spatial convexity, as I'm describing it, is synonymous with spatial expansion.

Then why do more distant galaxies appear to be expanding faster than nearer ones? The answer, I think, is that we are seeing them through more convexities. Which brings me to lensing, and the rainbow effect.

Astronomers measure the speed of spatial expansion using something called the red-shift. Essentially, red-shift is thought to be due to a kind of Doppler effect, where light, from a source moving away from us, is less energetic than light from a source that's standing still or moving toward us. Red light is less energetic than blue light. Since light travels at light speed in any case, this motion of recession doesn't slow the light down, it just gets redder instead. Compare it to sound from an object traveling away from us; the sound seems to go down in pitch as it recedes, and the faster it recedes, the lower the pitch.

That is no doubt correct as far as it goes. But convex lensing, I think, can also produce the same effect.

First, let me point out that we see concave lensing affect (distort) light when we see light from distant galaxies distorted as it passes through the gravity of nearer galaxies. It's called gravitational lensing, which means that the concavity of space caused by the nearer galaxy is causing the distortion. In other words, it is a recognized fact that the shape of space does affect light.

In fact, GR was first proved to be correct by observing light from distant stars as it was gravitationally lensed (distorted) by passing through the sun's gravitational field (concavity) during an eclipse.

So, lensing caused by convex space should also affect light. Looking through a convex glass lens spreads light out. Objects seen through such a lens on Earth, appear larger (and get blurry) as a result. Convex spatial lensing is different, though. Convex spatial lensing is essentially spherical, whereas the glass lenses we normally use are only partial spheres. In a spherical convex lens, the light is spread out as it enters, but gets re-focused as it exits out the other side of the lens.

However, one other important thing happens: as the light gets spread, the colors of that light get separated as in a rainbow. That's because light is not a single thing; it's composed from different colors, or wavelengths, and each one has its own degree of energy. In visible light, the least energetic wavelengths are red, and the most energetic are blue.

Each wavelength of light is bent by the convex lens according to its wavelength, with the least energetic red light bending the most. To put it another way, the path traveled by the red light, as it passes through the lens, is longer (bent more; more curved). Even though it exits the lens at the same time as the other colors, the fact that it has traveled a longer distance makes it appear more separated (redder) from the other colors. Each color is affected, too, it's just affected less. As each color separates from the others, we see a rainbow.

Thus, as light travels through the convex lenses of space, it appears to redden. The different colors, in fact, lose energy at different rates. Even though the light is re-focused upon exiting the lens, it retains some of this rainbow effect, and the red light (and the other colors to a lesser extent) appears redder. The more lenses the light traverses on its way to us, the redder it gets. Thus, more distant galaxies have a greater red-shift.

Doppler-caused red-shift (speed of recession) is real, too, I think. After all, as convexity increases, it increases the straight-line distance as well as the curving between here and "there."  But if there are two causes of red-shift, as I am suggesting, then our view of spatial expansion is distorted. It's not all due to Doppler, it's a combination of Doppler and convex lensing. Determining how much is attributable to each cause is going to be a ticklish process, I think. Nonetheless, it might be possible as I'll describe in a minute.

On another front, astronomers measure the speed at which stars rotate around the center of galaxies by using the Doppler effect of red-shift, too. And it's that measurement that suggests most of the stars in the galaxies we measure are rotating too fast to account for the gravity we think they have (they have to be seen edge-on, or nearly so to measure them). Because of that, astronomers have proposed “dark matter” to make up for the deficiency in gravity.

However, if spatial convex lensing, and the rainbow effect, is taken into account, I think we can eliminate the need for this mysterious “dark matter.” In other words, those stars are probably not rotating as fast as we thought they were.

Testing for the rainbow effect might be possible by comparing visible light spectrographs with X-ray spectrographs. X-rays are even more energetic than visible light. They should therefor be distorted less by lensing than visible light. On the other hand, the red-shift effect of recessional speed should be the same, or nearly so for both bands.

I suggest that we use these effects to compare equivalent spectrographs in the different bands. Red-shift due mostly to recession speed should be measured according to the X-ray graphs, and any additional effects caused by lensing should be measured according to visible light graphs. Subtracting one from the other should give an indication of how much the rainbow effect is distorting our view of things. Note that lensing will still affect the X-ray graph, and recession speed will still affect the visible light graph, but lensing should affect one more than the other. I have to leave the math to the experts.

The fact is that it's darned hard to picture space as a not-nothing that affects matter, but it's a lot easier to picture that, and assume we've been nearly correct all along, than it is to picture mysterious, spooky, and invisible “dark matter” and “dark energy.”


One other thing while I'm here: Physicists have been working to create a “Grand Unified Theory” (GUT) that explains all the forces in the universe in relation to each other. To grossly simplify, they want to make the “story” of how the universe works into a single, relatively simple, one-page story.


The story originally had four pages (the four forces). One page for the electro-magnetic force, one for the strong atomic force, one for the weak atomic force, and a final one for gravity. So far, the first three forces have, in fact, been consolidated into a single page.


Gravity seems completely incompatible, though.


I think that's because the force of gravity is an interaction between matter and space, while the other forces are interactions between matter and other matter. In other words, E=mc2 is only true for the three matter-matter forces. Gravity (and spatial convexity) are completely different things. They aren't really forces at all in the usual sense of that word. They are shape-shifters.


And, by the way, gravity doesn't come in waves, either.

That's my story, and I'm sticking with it until I'm proven wrong. Thanks for reading! Comments and criticisms welcomed.

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*Note: I can only guess that Einstein, himself, got confused when it was discovered that GR needed a “cosmological constant” to make the universe static and “forever.” When Edmund Hubble later discovered that the universe was, in fact, expanding, Einstein felt so embarrassed about the cosmological constant error, that he called it his biggest mistake. I am saying here that Einstein's cosmological constant should have been a variable that mathematically describes spatial convexity. Then GR would have fit perfectly with an expanding universe. In other words, I'm sort of saying “Einstein was right.” (Again! --  He was an amazing guy.)