[MikeL (OP)]

I have been working on some ideas for a while and have come up with the following which could be useful ontologically in explaining the universe. I have gone to effort to make it simpler than my previous attempt, and to correct any errors I came upon.

We know the universe is expanding at an accelerating rate and the expansion is ubiquitous throughout the universe. We know matter doesn't seem to undergo this same spreading. Such a uniform acceleration of expansion is typical of the forces a wave would exert as its wavelength increased.

Fig 1. In a sine wave both the trough and the crest undergo expansive geometric forces, causing a shift in wavelength as they propagate. The arrows indicate the direction of the forces at that part of the wave.

Fig 2. I would like to ascribe this wave function to the curvature of space-time. Note there is a +1 and -1 reflecting the degree of curvature.

Superimposed onto this wave is the Universal Plane (my word). This is where matter exists. The value of the gravity along this line corresponds to the value of the sine wave at that point. As the wave lengthens, the universal plane is stretched.

Fig 3. If we make the curvature of space where 'gravity' occurs -1, then by convention +1 would become a curvature of space that is 'anti-gravitational'.

In these areas of anti-gravity, matter cannot exist. It will only exist where the gravity is between the value range of 0 and -1. I wish to denote the area of the trough where the gravity is between 0 and -1 as Mike's Gravity (A), to differentiate it from the gravity intrinsic to matter. The crest we can simply call B.

Fig 4. Because matter has its own intrinsic gravity different to Mike's gravity (A), it will act to curve space in this region further. This will cause trough walls in A to close together.

B has not such gravity and does not clump, however the shape is affected by the change in the trough. B would represent areas of no matter. In our universe this would correspond with intergalactic space.

Mikes gravity A, which is separate from the intrinsic gravity of matter could be considered Dark Matter. This is the unaccounted for gravity that I was describing in my Dark Matter OP.

The space in the crests could be argued to display the properties of Dark Energy.

This structure approximates what we see when we look at the Cosmic Web, which shows the relationships between galaxies and intergalactic space (below).

Of course the wave I have described is not an exact duplicate of what we see. For example the wave I have drawn is a 2D representation and the images have a 3D shape. My wave is also simplified in that no attempt at describing interference patterns created by matter with gravity moving independently has occurred.

What are your thoughts?

[Bill S]

Mike, obviously, you have put (are putting) a lot of thought into this, which, in my book, is great.   hope you get some good responses.

My initial question would be: Are you proposing that it is spacetime that is waving; and if so is it waving in a higher dimensional "reality"?

[jeffreyH]

For a photon as wavelength increases then energy decreases so there is less oomph. If a spacetime wave had negative pressure then this decrease in energy would have to be inversely proportional to the strength of this negative pressure.

[MikeL (OP)]

My initial question would be: Are you proposing that it is spacetime that is waving; and if so is it waving in a higher dimensional "reality"?

I hope this answer is well thought out enough that I do not damage my OP.

The idea hinges on the assumption that there are two types of gravity, both exactly the same in every way. We tend to associate gravity with matter, but we know that gravity can also exist independent of matter – namely through the effects of energy.
We know that two gravitational waves in the absence of matter can collide to produce a black hole (theoretically) as theorised by the Max Planck research of Gravitational Physics. http://www.einstein-online.info/spotlights/gravity_of_gravity [nofollow] In another discussion an astronomer confirmed this suggestion.
Yet the first type of gravity, Mike’s Gravity (A) is a much broader curvature of space time than that associated with matter. I am reluctant to suggest it is a gravity wave from the Big Bang as I am not familiar enough with the predicted dynamics of such a wave and do not wish my OP to fail on a technicality – especially as it relates to crests.
Gravity is described as a curvature of space-time, or a change in the energy density of the universe. As such, gravity is an inward curvature of such space-time, causing attraction. For illustrative purposes we can imagine force lines converging. As force lines converge the force of gravity becomes stronger. Following this logic, we can also imagine force lines in two other ways: straight or diverging – after all it would make no sense if all force lines simply converged.
The wave I have illustrated can be thought of as a density distribution of space-time ranging from -1 to +1, or as more geometrically apt, as the curvature of space time ranging from a gravity value between 0 and -1 and an anti-gravity value between 0 and +1.

All that I have described thus far is not the gravity associated with planets, stars or galaxies. Such gravity as these is mobile – as the object of such gravity is mobile. It is an important distinction I wish to stress. Because the gravity of matter is mobile, it will move toward areas of -1 energy value (away from +1). It’s movement, though, while probabilistic (matter will congregate, clump, form black holes etc) is also random due to such influences as gravity slingshots, collisions and other matter related phenomenon.
Because matter itself is sitting inside a larger space-time curvature, we suddenly have a candidate for Dark Matter, a problem where we do not observe enough mass to account for the apparent gravitational effects observed on galaxies.
The crest itself becomes a candidate for Dark Energy. It’s expansive force arising with anti-gravitational properties.
The wave accounts for the seeming ubiquity of expansion of the universe as it redshifts, and accounts for why matter seems impervious to the effects of spatial expansion.
Geometrically speaking also, as the amplitude approaches the 0 point mark, the forces on the wave increase – vectorally they would begin to approximate the direction of the Universal Plane, thus causing an acceleration of expansion.
The Universal Plane is itself a superposition onto this wave. It represents the space that we can observe around us. The curvature of spacetime is only observed through its effects on the physical universe.
I hope that answers your questions. Please feel free to feedback.

[MikeL (OP)]

For a photon as wavelength increases then energy decreases so there is less oomph. If a spacetime wave had negative pressure then this decrease in energy would have to be inversely proportional to the strength of this negative pressure.

It is an interesting question, and one I have just touched upon. As the wavelength increases the density of space-time falls. Gravity lessens. This however, may aid the expansion of the universe - the flattening of the universe, because it is this energy density that is keeping it from laying flat (the flat universe). I think it is also possible to think in terms of the geometric forces of the wave, even in a 3D bubble, if you wanted to invoke that, as aligning more in the direction of expansion of the universe. A high amplitude wave has a lot of its force (vectorally speaking) directed in the vertical plane. As amplitude falls though and wavelength increases the final oomph, as you put it, should be in the horizontal plane and thus increase the rate of expansion.
Does that answers the question sufficiently or clearly enough?

[jeffreyH]

Amplitude is a problematic concept. Does a quantum mechanical wave have amplitude?

[MikeL (OP)]

Amplitude is a problematic concept. Does a quantum mechanical wave have amplitude?

All waves have an amplitude, even if it is just a probability amplitude. Amplitude is often referred to as intensity though, as in the case of the photoelectric effect, so care must be taken not to conflate it with frequency.

In what way do you find it problematic?

[Bill S]

Mike, I’m not going to be asking you for mathematical proof/physical evidence for your ideas, but I will probably pick up on a few points as we go.

As such, gravity is an inward curvature of such space-time,

An “inward curvature” with respect to what? 
Are you visualising spacetime as being curved relative to higher dimensions?

[MikeL (OP)]

An “inward curvature” with respect to what? 
Are you visualising spacetime as being curved relative to higher dimensions?

Hi Bill, the short answer is no I'm not. The slightly longer answer is in previous versions I did.
Space time is curving inward relative to itself. There are a number of ways to picture it. The first most physics based solution is simply with forcelines in 2D drawn across a page. Where they converge toward each other would be an inward curvature. Then they would move back into parallel alignment.

Another way is as energy density. To help with this idea we can envisage an ocean we are moving through. As we move through the ocean the density of the medium changes.

The reason for originally having a reference to another dimension was the shape of the wave itself, which still causes me some angst. In that version the wave I presented here was a physical manifestation/corruption of a perfectly symmetrical energy wave. Even now the degree of curvature of the space-time trough I believe may only be slightly more than the crest, and not as exaggerated as I have made it. Matter will afterall tend to settle at -1. This is seen in the movement of the galaxies toward the Great Attractor ( https://www.businessinsider.com.au/r-new-map-shows-milky-way-lives-in-laniakea-galaxy-complex-2014-9 [nofollow] )

The reason I do not just make the wave symmetric in this version is two fold - the proposed contribution to the expansion of the universe made by dark energy versus ordinary matter and dark matter must be shown in the wave. A larger crest would contribute more toward an expansion.

The other reason is entropy. I don't want to get off topic here, but I suggest that entropy of matter and the rate of expansion of the gravitational portion of the wave are connected. It could be thought of as one drawing the energy of the other out as it expands. This idea, incidentally, also references a higher energy dimension and an inequity of energy due to a masking effect of matter. I have discussed this idea previously (and met with a confirmation that what I said was correct). I don't want to side track the OP with this idea if people disagree, but I am happy to share the post with you here if you like.

Have I answered your question squarely? Thanks for taking an interest.

[jeffreyH]

A change in the amplitude of a wave is the problem. Especially at the elementary particle scale. An ensemble of particles is a different matter. At the moment I am studying Heisenberg's picture of quantum mechanics. I may have more to add.

[Bill S]

Thanks for the detailed answer, Mike.

You might care to comment on the following, from Dr C Baird:

"In everyday language, we use the word "curved" to mean that a bar bends sideways in space away from a straight shape, or a ball traveling through space bends sideways in space away from a straight trajectory as it travels. When we talk about spacetime itself, the word "curved" must mean something else because spacetime itself can't bend sideways in space. A lot of popular writers speak sloppily in this way, but it really makes no sense. Spacetime is not a physical object sitting in spacetime, able to be grabbed and bent like a bar. Spacetime is the underlying universe itself. Anytime a writer says something like this, he is giving you an analogy only. If a spacetime is curved, it means that identical clocks sitting at different points in the spacetime will tick at different rates, even if ever so slightly."

[evan_au]

there are two types of gravity, both exactly the same in every way

If they are the same in every way, why are there two of them?

[MikeL (OP)]

You might care to comment on the following, from Dr C Baird:

Hi Bill,
Sure, I would be more than happy to comment on this after work today. In the meantime, could you provide a reference or link for the statement please?
Thanks.

[Bill S]

Mike, there is no link, I'm afraid; but I'll see if I can find the relevant emails, so I can give you some background.

[MikeL (OP)]

there are two types of gravity, both exactly the same in every way
If they are the same in every way, why are there two of them?

The discreet gravity is associated with matter and as such its effects are local.

[MikeL (OP)]

Spacetime is the underlying universe itself. Anytime a writer says something like this, he is giving you an analogy only. If a spacetime is curved, it means that identical clocks sitting at different points in the spacetime will tick at different rates, even if ever so slightly."

I find the statement curious, which is why I asked for a reference. This doctor suggests that space time can't be curved or else identical clocks sitting at different points will tick at different rates.- This is exactly what happens.

This is a quote from the Ohio state university website on Astronomy 162:

"Further, the satellites are in orbits high above the Earth, where the curvature of spacetime due to the Earth's mass is less than it is at the Earth's surface. A prediction of General Relativity is that clocks closer to a massive object will seem to tick more slowly than those located further away (see the Black Holes lecture). As such, when viewed from the surface of the Earth, the clocks on the satellites appear to be ticking faster than identical clocks on the ground. A calculation using General Relativity predicts that the clocks in each GPS satellite should get ahead of ground-based clocks by 45 microseconds per day.

The combination of these two relativitic effects means that the clocks on-board each satellite should tick faster than identical clocks on the ground by about 38 microseconds per day (45-7=38)! This sounds small, but the high-precision required of the GPS system requires nanosecond accuracy, and 38 microseconds is 38,000 nanoseconds. If these effects were not properly taken into account, a navigational fix based on the GPS constellation would be false after only 2 minutes, and errors in global positions would continue to accumulate at a rate of about 10 kilometers each day! The whole system would be utterly worthless for navigation in a very short time.

The engineers who designed the GPS system included these relativistic effects when they designed and deployed the system. For example, to counteract the General Relativistic effect once on orbit, the onboard clocks were designed to "tick" at a slower frequency than ground reference clocks, so that once they were in their proper orbit stations their clocks would appear to tick at about the correct rate as compared to the reference atomic clocks at the GPS ground stations. Further, each GPS receiver has built into it a microcomputer that, in addition to performing the calculation of position using 3D trilateration, will also compute any additional special relativistic timing calculations required [3], using data provided by the satellites.

Relativity is not just some abstract mathematical theory: understanding it is absolutely essential for our global navigation system to work properly!" http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps.html [nofollow]

[MikeL (OP)]

At the moment I am studying Heisenberg's picture of quantum mechanics. I may have more to add.

I look forward to hearing your take on it.

[Bill S]

“….if a spacetime is curved, it means that identical clocks sitting at different points in the spacetime will tick at different rates, even if ever so slightly."

I see where you get that interpretation, Mike. That’s probably my fault for not posting more of the exchange we had. 
In fact, what he was saying was that gravity is a force, but it is a force that is best described in terms of curvature of spacetime.  However, he suggests not visualising this curvature as spacetime being Bent”.  Another quote may help.

I'll tell you a little trick that helps makes sense of spacetime. Any time spacetime is curved, it makes one direction act differently from the other directions. Put roughly, spacetime curvature makes one direction special. Anytime you have a reference frame where one direction is special, you have spacetime curvature. It is the curvature itself which makes one direction special.

From this, you will see that he uses the term "curvature" as do others, but he adds a "caveat".

[MikeL (OP)]

Any time spacetime is curved, it makes one direction act differently from the other directions.

I think this is true of most things in which there is a variation. As you move into a gravitational field the lines are converging and the force is positive. As you move out of one the lines are diverging and the force is now negative. Such 'density' changes can occur within a structure.

As the universe expands, it flattens, and the uneven density distribution begins to right itself.