OK, so I couldn’t leave this for the next issue. There will be a lot less math, and a lot more of a thought project. But there will be a bit of math. The problem presented here is only loosely tied to the problem outlined in Physice 202. This problem comes from my uncertanty about Hubble’s Law interpretation of the red shifts of galaxies. That is, that it is caused by a doppler shift resulting from their rapid motion away from us, providing evidence for an expanding universe and the big bang. With no direct experiences with light’s behavior over long distances, it has always seemed that this was not the only possibility. There are reasons for light to red shift that have nothing to do with the speed of recession of the source.
Consider the fact that two beams of light traveling paralell to each other, are known to bend from their straight path toward each other. While photons have no rest mass they have energy, and E = M C2 shows us the relationship between energy and mass. The bending of the beams shows us that this energy creates a gravitational distortion. The beams both creates gravitational attraction from their effective mass, and are also effected by the gravitational attraction.
Now concider an empty point in space. One second there is nothing there, next there is a photon there, and soon it is gone. Before it was there, there was no mass or energy to create a gravitational field at that point, when the photon appears, its mass energy equivalence creates a gravitational field. There is no reason to believe that this energy field radiates at anything other than the speed of light. So, when the photon moves on, so does the gravitational potiential it created in its last location. As the photon moves it creates gravitational potentials that follow it as it travels, so it accumulates the gravitational potentials from all its past locations as it travels through space. Thus, a photon in an empty universe with no motion involved would slowly loose energy, redshifing over time. In a local laboratory, this effect can not be measured. It would only be seen over inter-galactic distances. The Hubble Constant could just as easily be an effect of light on itself, rather than an effect caused by an expanding universe
Here is the problem: Each bit of potential generated in the photon’s past, is attenuated with distance by the inverse square law. When you try to set up integrals to compute all the potentials along the phonton’s back path, if you consider space to be continuous, then this integral must be done from zero to the currnt position. The problem is that such integrals are unbounded. They produce infinite results. This would mean that if space is continuous a photon could never overcome its own gravitaitonal potential. It would never be able to move away from its origins because all its energy would be removed by this unbounded potential. This obviously isn’t the case. Photons move. If we consider the results from Physics 202, and also consider that this universe may be a simulation, then only time need be discontinuous for the math to work. Space acts discontinuous because of the connection between the plank length and the plank time, defining the descreet distance light can travel in a plank time period. Discussing the photon’s behavior in these discreet time periods is more in line with looking at something like light, and the math should be easier.
I have not yet worked out the math. The first order solution is off because it assumes the photon has the same energy it started with at each point, sums over each point reducing the potential from each point by the inverse square of that point’s distance. This ignores the fact that the photon lossed energy, and therefore effective mass as it travels, so at each point in its travels it is a bit more red shifed and less energeic than the last point. I am still working on how best to set up this sum, but plank time seems to be the correct ruler for getting at least some portion of the Hubble Constant from the gravitaional self redshift.
Our understanding of Physics may not be as settled as we think. Theories supported by experimental evidence are always subject to revision when new evidence is obtained. This issue with self redshifting photons may put a different light on how things work. The 4 degree Kelvin background radiation may may just be all the old light still hanging out in the universe. Dark matter could just be the gravitational energy created by all this old light. The universe could be completely static, or doing any number of complex motions. I think we still need more evidence. New observations are being made all the time, like the most recent discovery that cosmic rays may not be coming from all over, but from a specific location in a distant galaxy. How this may change our cosmological perspectives is not yet clear, but the world is clearly still a more interesting place that we currently understand.