I have recently read "The trouble with physics" by Lee Smolin. An excellent book for the un-initiated. And an excellent book for the initiated but non practitioner.
I have a PhD in theoretical physics. Although I must admit my PhD was mostly bullshit. My masters, however, was a deep training in all things modern in theoretical physics. I spent a year studying field theory, string theory, the standard model and particle physics. I must admit, I didn't get it. I could do the math in string theory, it was actually quite easy, that was not the problem. The problem was that I could not understand what I was doing, the "meaning" of it all completely escaped me. I was and remain a 19th century type physicist, I was quite at ease with classical mechanics and electro-magnetism.
That EM waves would propagate through vacuum was to me such an absurdity that I never really believed it. Yes I could model particles with "fields" but fields of what, through what. That a mathematical model tells me that particles emerge from the wiggling of strings, is fine, but strings of what? It seemed philosophically imperative that there be a medium in which the waves propagate.
I first imagined spring based medias in college to account for gravity and light propagation, and my professor quickly educated me on so called "Ether" theories. These theories were in vogue in the late 19th century and dispelled by the Michelson-Morley experiments that showed that the speed of light was the same in any direction measured. If there is an ether, we should detect our movement through it.
Get the book, or ANY scientific american that talks about cosmology and you will get an earful about what is troubling physics these days: dark energy and dark matter. Observation of the movement of distant galaxies is explained with a new kind of matter and a new kind of energy that amounts to "negative gravity". Nothing in the standard model or general relativity explains this. Physics is in a profound state of flux as they are now positing gravity that pushes back and does not attract. Funny.
The standard model and general relativity explain the visible matter and that matter accounts for 20% of what makes up the universe. The rest we just don't know.
Conflict is good
This is all a good thing as it means observation is once again leading theory.
A new toy model: the universe as an elastic medium
I recently revisited those ideas, mostly for fun but it tickles my fancy as it actually plays into a lot of the current issues.
Imagine that the universe is a huge elastic ball. A spring in 3 dimensions. Touch the spring slightly and it will start an harmonic oscillator. Light could be the basic vibrations of this elastic "ball".
Baryons and Tachyons
Clumps of "compressed springs" are matter. Vibrations are light waves. mmkay?
See the generalized Tensor expression of Hooke's law . The tensor representing elasticity has 21 free dimensions, enough to recreate most of the standard model. String theory needs 11 spatial dimensions. That is disturbing we only observe 3.
Matter is Energy
The Einsteinian insight is trivially rebuilt here at an intuitive level. Matter is a compressed ball. It takes energy to compress the ball and the compressed ball has a higher density and is measured as "mass". So energy is mass. The calculation in one dimension is obviously false but yields interesting insights from a dimensional analysis. Energy of a 1D spring = kX^2. Velocity of a wave c = sqrt(k/density). So k is related to the square of c and while completely false, you can see Energy = mass x velocity of light squared terms appearing. I tried a more detailed calculation yesterday in 1D and it all falls apart, which is not surprising but again, E=mc2 could appear as is in higher dimensional springs.
2D spring theory is link to string theory
If you compress the medium in 2 direction you end up with "tiny strings" that will start vibrating. In essence and in theory, you could then recreate string theory. These theories have accounted for most of visible physics (minus dark energy and matter) and should therefore be recreated.
WIMPS and dark matter
if matter is 2D compression then 1D "lasers" (as a stable non-dissipating waveform) and stable 3D will create "matter" of an different nature. The model will include new "particles".
If you compress the ball you stretch the outside of it. In essence a wave propagating through that stretched medium, will feel an acceleration towards the compressed part (mass). I think I can work the math out in 1D (since v=sqrt(k/dens) and dens is computable). I have no idea how to work the math in 2D and 3D. Each dimension will yield different results due to geometric concerns. One will hit the 1/r2 nature of EM and gravity. Gravity is the geometry of the stretched and compressed ball. Velocity of vibrations depends on density it would be interesting to carry the calculation of a longitudinal wave through a asymetrical spring and show an acceleration of the wave. Would be a good training.
Assuming a compression is balanced by a stretch and that the stretch is in "matter" form (i.e. stable waveform) then that stretch also has energy (the same as the real matter). It is anti-matter.
Big bang and dark energy
Compress the spring to its maximum. Assume the springs have a compression quanta, beyond which you lose elasticity, you cannot go. These ideas are very close to "quantum loop theory" where the fabric of the universe is "matter balls" as unit quantas. Here we do not focus on matter but rather the spring nature of the fabric. Compress the fabric and release it. It is charged with energy and will expand rapidly. Eventually it will reach a point where it will compress back, it is an harmonic oscillator in 3D.
The speed of light
Light is vibrations INSIDE the expanding ball. The smallest vibration. So nothing can go faster than it inside the ball (bigger vibration have smaller speed). I am struggling massively with the ether syndrome. If one needs to account for the speed of light. It seems that the notions of time and speed need to be taken in their relativistic sense. In other words, a "unit" of time is the time it takes for light to travel, as a wave, through the medium in a "unit" spring. Velocity of light is a constant no matter what the length of the spring is because our perception of time stretches with the underlying. Or rather, we UNDERSTAND a unit time as the "time it takes" for light to travel along a unit of length, a tautological definition that starts from the notion of speed as a constant. We base all time measurements on the fastest movement in the medium.
Faster than light expansion
The universe is a spring ball that is still expanding. Light travels INSIDE the ball. The expansion of the ball is un-correlated to light and not subject to the speed limit of light. It is the expansion of the springs themselves. Light travels at constant speed (remember that time is what is defined from it) and the expansion of the ball can be anything.
Also in this model, it is trivial to see that the outer part of the ball expands exponentially faster than the inner parts. This is observed and in contradiction with general relativity.
If the universe seems fairly uniform in density, it may mean that we exist in the "middle" expansion in time. Take spring, compress, it will become an harmonic oscillator, we may be at the most relaxed part of the expansion (the middle of the oscillation) where the springs are "at rest". They will start stretching next, creating a "positive gravity" that will add to the gravity we know from general relativity.
I assume the regime we are in is elastic. Meaning f=kx. There are no reason for this, just ease of use. It could be anything.
Unfortunately I am hampered in the math department, not as nimble as when I was young. I could carry the 1D calculation (to their non-sensical results) about energy and mass and the speed of light, modeling the compression of the spring. It did not require integration. I will continue doing this for 2D and 3D, which should be a lot more complicated and I couldn't find ready made results for the "energy of a compressed 3D elastic medium" although I am sure they exist.
Good clean intellectual fun.