Only two bits of math are necessary to work out and understand much of the past three articles.† One is the formula for the surface of a sphere: four pi times the square of the radius.† This is helpful to see why the effects of gravity and charge fall off as the square of the distance from the center of a spherical field.†† The other is the Pythagorean Theorem: the sum of the squares of the sides of a right triangle equals the square of the hypotenuse.† As we have seen, this is useful in calculating the relationship of the speed of light, C (the hypotenuse), and the relative velocity (one of the sides of the triangle), to get a ratio for the length contraction or time dilation observed in special relativity.
Keep in mind that the theory weíve been building is grounded in Euclidian geometry.† Contained within that geometry is the notion of motion on a surface and the non-Euclidian geometry of geodesics.† For example, think of the standing waves generated by a Bose-Einstein condensate.† Find a suitable wavelength of photon that can pass through this condensate, and imagine it riding up and down on the surface of a folded ribbon of standing waves.† To get through what looks to us like a very short distance from one side of the condensate to the other, the photon travels a surface that is a billion times farther.† No wonder the apparent speed of light in such a medium can appear to be less than ten miles an hour!
There are also no hidden variables or probability clouds in this theory, just observations we are too limited to make.† Thus, if a photon is capable of passing through either of two slits, it may simply pass through both of them partially with the same interference effect as would be noted if a whole barrage of photons passed through at the same time.† This theory is grounded in the fact that a photon is distributed over a volume of space, but it should come as no surprise that an interaction occurs in a very small region of space (where push actually comes to shove), that is, where the forces that transmit the changes of momentum are actually channeled.
Itís probably worth thinking a bit more at this point about the shape of a photon.† Unless we do, the results of the double slit experiment wonít be very intuitive.† The double slit experiment is the observation that when light is passed through two slits, an interference pattern is observed on the other side.† Light was originally thought to be a particle like phenomenon, but this experiment proved that conjecture wrong.† If photons pass through a single slit, they disperse pretty much as particles might disperse.† Interference only occurs if there are two slits.† Howeveróand hereís the punch lineóit doesnít matter if lots of photons are passing through the slits, interfering with each other, or if they pass through one at a time.† The very presence of the second slit gives an interference pattern, even though a single photon must choose one slit or the other to pass through.† Or must it?
A photon exists in a volume of space proportional to its wavelength.† When it interacts, it interacts at what appears to be a point.† Again, the point of interaction is a function of the shape of the photon and the tension of the space around it.† You might think that the amplitude of a photon would have something to do with its volume, but this does not appear to be the case.† The way I see it, itís something like hardness that increases with increasing energy (and decreasing wavelength).† The envelope of a high energy photon is small and hard, and that of a low energy photon is large and soft.
Now consider a photon trying to pass through an opaque surface with a couple of slits in it.† If the size of the photonís envelope is large with respect to the spacing between the slits, then the photon essentially passes through both slits to some degree.† The undulating envelope of the photon simply passes through choppy water.† It will either be completely absorbed by the surface, or it will impart some momentum to it, and be deflected to one side or the other.† The interference pattern is produced because of the ďsoftnessĒ of the photon that allows it to appear to divide and rejoin as it passes through the slits.
The notion of hardness also extends to the tensions in space that transmit changes of momentum in basic interactions (those not involving intermediate photons).† I have said they occur at a point, but this is not perfectly true.† The volume of space involved is inversely related to hardness.
The notion of hardness also relates to the phenomena of coherence, and probably to the weak and strong nuclear forces that physicists have long observed.† In the model I describe, there is no fundamental wave function (although I do not deny the convenience of the description), there are only the deterministic results of interactions between (albeit) somewhat soft and squishy objects.† The fundamental attractions and repulsions of charge, operating over very short distances, especially within particles, can become very large.† Even when large, soft objects are involved, they prefer to nudge each other into coherence rather than have a significant interaction.† The electrons, and especially the sub-nuclear particles, of an atom are pretty hard objects in these terms.† All the rules for their behavior show that they demand coherence quite strongly.† My contention is that the simple properties of photons are sufficient, as a basis, to derive all the other forces we observe in particles and larger combinations of matter.
I canít offhand think of any of the accepted formulae of modern physics that disagree with this theory, but many can be given new interpretations.† Some new conclusions may be developed.† For example, absolute rest can be distinguished from absolute motion.† An accelerating frame can be distinguished from a gravitational frame.† And, the universe is not expanding, nor did the Big Bang ever happen.
How might you determine a state of absolute rest?† Just check your clock.† The clock that runs the fastest is the one in the lowest density of space and the most at rest with respect to absolute space.† How can you tell a gravitational frame from an accelerated frame?† You canít if your laboratory occupies only a point, but if you have any latitude at all, you might be able to discover that separate vectors of acceleration are all perfectly parallel if you are in an accelerated frame, and not quite so, in a gravitational frame.† In the latter frame, the vectors all point back to a single point called the center of gravity.
Finally, how do we know the universe is not expanding and there was no Big Bang?† By finding a more simple explanation of the observations.† When a photon travels for billions and billions of miles, it does so by passing by quite a lot of other quanta.† Every slight deviation of its path transfers a tiny bit of its momentum to the surrounding quanta.† As its energy is bled away, its wavelength becomes longer, and it becomes red shifted.† Call this entropy on a cosmological scale, if you like.† With no recession of distant matter to be accounted for, there need have been no Big Bang.† There certainly needs to be no inflation of space itself.† Assuming that matter and energy are distributed throughout space, as the volume of space approaches infinity the critical density of space approaches zero.† Our universe is therefore closed.† Its volume is finite.† Its energy is finite.† And, none of its fundamental constants need depend on either of these facts.† One truly fundamental constant is the speed of light.† Other values relate to this in such formulae as: Energy equals mass times the square of the speed of light.
I hope itís clear that distance and time are scalar values that depend upon the observerís point of view.† Time is nothing more than a clock-like phenomenon.† Clocks and measurements of distance can be related very reliably (sometimes with minor corrections) across many frames of reference.† Such instruments are the fundamental tools of the physicist.† The concept of going back in time is literally like the concept of a negative distance or a negative speed.† If you are going ten miles an hour, you canít slow down by twenty miles an hour, and itís not the same to turn around and go ten miles an hour in the other direction, so donít even think about it.
Then, what about cosmology?† What happens in the long run?† Thanks to gravity things eventually come together.† As potential energy changes to kinetic energy, things heat up.† Entropy increases, and so does density.† Our universe becomes smaller.† Pieces of it are left behind as we spiral into successively smaller black holes.† Within our own universe, the amount of material contained in black holes of various sizes increases.† By themselves, black holes are eternal objects.† Despite what some have said, nothing special happens at the surface of a black hole, because it has no surface.† To an outside observer itís a point.† It has no volume.† Its clock has stopped, and itís in a condition of absolute stasis.
However, something can always go wrong. Consider an electron and a positron.† Both exist as charged black holes.† They are strongly attracted together, and they annihilate one another when they meet.† This is an example of how a black hole can be cracked from the outside.† Perhaps other black-hole-on-black-hole crackings are possible.† Perhaps a black hole could also be cracked from the inside.† However, not in our universeís lifetime.† This could occur if sufficient annihilations, perhaps a chain reaction of them, ever began to take place.† If sufficient mass were converted to energy, the density of the black hole could be driven down.† Its volume would increase.† It might erupt.† But what it would erupt into, I donít know.
Incidentally, how would you know you were in a black hole?† Assuming a very large black hole and a fairly gradual change of density (so that you could live through it), you would observe that light coming from great distances is blue shifted, or perhaps insufficiently red shifted.† The fact that we see red shifted light in our universe is good news.† We donít appear to be in danger of immanent collapse.
It seems plausible that big bangs, or bangs of any size, could happen.† These types of bang would deposit matter and energy back into an outer universe from a black hole.† The deposit would be in the form of an expanding sphere.† Motion would not exceed the speed of light.† The size of the outer universe would probably be unaffected (unless it were primed for its own eruption).† And, in fact, the likely long term scenario for the Cosmos is a continual cycle of larger and smaller bangs.† Each bang restores a condition of low entropy to the matter and energy of a region.† Thus, would our universe recycle itself.† It could have begun in a Big Bang, but it would have taken place a very long time ago, and there is no way for us to tell.