[size=+1]The solution to the flatness problem[/size]
The flatness, horizon, and dark energy problems are major unsolved problems of physics, of cosmology in particular. I’m not going to describe them here, since they’re easily searched for on the web. The physicist in my dream told me solutions to these problems, and more. I’ve already given one, on page 2 for the flatness problem, which is a prerequisite to the others and so I repeat it here:
He told me that space itself is not expanding, as cosmologists think. (Think of the rising raisin loaf example.) That was a false assumption based on Hubble's result, he said. He gave me a thought experiment to show that space need not expand to explain Hubble's result:
In an infinitely large universe whose space neither expands nor contracts, sprinkle an infinity of galaxies. Within some section of this universe let all of the galaxies approach one another. This is possible in principle. The size of the section is arbitrary; make it the size of the universe. Now all of the galaxies in the universe approach one another, yet there is no cosmic center or edge. Now play the film backwards, so to speak, to find that all of the galaxies in the universe can recede from one another, with no cosmic center or edge.
If you look at the history of cosmology, you’ll see that shortly after Hubble’s result, cosmologists assumed that space itself is expanding to explain that result. They felt that if space itself doesn’t expand, then the universe must have a center and an edge. Such center or edge doesn’t satisfy the cosmological principle they had also generally accepted (for good reason). When it is thought that space itself is expanding, an explanation is needed as to why the galaxies and smaller objects don’t expand as well. The explanation cosmologists give today is that each galaxy’s gravity keeps it bound together, maintaining the size it has despite the expanding space. Also, when space itself is expanding SR works to only a limited extent, even in deep space between the galaxies, as the rocket site notes with “For distances bigger than about a thousand million light years, the formulas given here are inadequate because the universe is expanding.”
The thought experiment the physicist gave me shows that the notion of expanding space wasn’t necessary to explain Hubble’s result. It was a bad assumption that has led cosmologists astray ever since.
Removing the notion of expanding space solves the flatness problem, he said, for then space can be flat by default. An infinitely large universe can become sparser or denser without need for space itself to expand or contract. Galaxies and other matter need only move relative to each other. He said there are other implications of this too, for example the observable universe becomes the entire universe.
Another implication of space being flat by default is that SR works to any distance in intergalactic regions, which in turn has many interesting implications.
[size=+1]The solution to the dark energy problem[/size]
Dark energy is an ad hoc solution to the observations that high-redshift (i.e. fast receding) supernovae are accelerating away from us. I’ve shown that SR predicts that a projectile launched directly upward from Earth at a speed close to the speed of light accelerates away initially, as measured by an observer on the ground. The physicist in my dream showed me that the similarity of these findings is no coincidence. The supernovae finding follows from the SR result, after applying an additional bit of logic and without using SR beyond its scope of applicability.
First, we accept that space in our universe neither expands nor contracts, as per the solution above to the flatness problem. Next we consider GR. Let there be an observer who remains at rest with respect to the Earth, at the location of one of the high-redshift supernovae as it passes close by at a speed close to c. For simplicity replace the supernova with a small object whose gravitational attraction is negligible; let’s call it a rock. Remove other matter from the universe, keeping just the Earth, the rock, an observer on the ground on Earth (the “Earth observer”) and the observer past whom the rock moves (the “distant observer”). The distant observer is in a rocket, burning some fuel to remain at rest with respect to the Earth (i.e. hover) instead of falling toward it. These simplifications are fine in a thought experiment.
The distant observer’s clock runs faster than the Earth observer’s clock does, according to GR; that’s gravitational time dilation. In GR it is valid for the distant observer to measure something, and to let an Earth observer convert that measurement using the gamma factor, the difference in the rate of their clocks; the converted values match what the Earth observer would measure. For example, if the distant observer’s clock runs x% faster than the Earth observer’s clock runs, then an event that is local to the distant observer that takes 1 second to occur on that observer’s clock (an explosion, say) will take 1/(1+x) seconds to occur as the Earth observer measures while looking through a telescope. (For every second that elapses on the distant observer’s clock, the Earth observer’s clock elapses
less than 1 second.)
In GR as in SR, a single positive gamma factor adjusts measurements of both space and time, which are always two sides of the same coin in relativity (hence spacetime, one word). A gamma factor that adjusts for gravitational time dilation also adjusts for gravitational length contraction. The distant observer will measure the rock that passes by to accelerate away initially, my equations above show. Let the Earth observer convert this measurement using the gamma factor between these two observers. The Earth observer would also measure acceleration away for the rock, because the same gamma factor adjusts both distance and time measurements. (Try multiplying D and T on the charts above by the same positive factor, or its reciprocal in any combination, to see if you can change the finding of acceleration away. It can’t be done!) This is the solution to the dark energy problem. High-redshift supernovae accelerate away from us due to gravity alone. No new energy is required to explain those observations.
[size=+1]The solution to the horizon problem[/size]
In principle, the SR equations above show, an average recession rate can increase exponentially for any given value for g. The solution to the dark energy problem shows (again in principle) that such an exponentially increasing average recession rate applies as well to objects at any distance, regardless of the curvature of spacetime between the ground observer and the receding object. In other words, cosmic expansion can be arbitrarily fast as measured by an accelerating observer, where “cosmic expansion” is simply objects moving away from one another, rather than space itself expanding. Extremely rapid (exponential) cosmic expansion is what the inflation theory proposes as the solution to the horizon and flatness problems, albeit that theory employs ad hoc energy to fuel such expansion (which is why these problems, along with the dark energy problem, are considered to be unsolved by reasonable cosmologists). I’ve shown—thanks to the physicist in my dream—that gravity alone solves the horizon problem, with no new energy required. Furthermore, in a universe in which space itself neither expands nor contracts, all of the galaxies and other objects in the universe can always be in causal contact with one another, even when that universe is infinitely large.
