Hi, this is my first posting, about a question I have been pondering for a long time.
I graduated in physics (Honors degree) back in 1992 but wasn’t apparently good enough to pursue a career as a theoretical physicist, so I did a second degree in biology (as I wanted to have a broad view of all aspects of nature, from the most elementary particles to the most elaborate things like living beings) before finally studying to become the translator I am now. I did manage to take a few more classes in physics after getting my degree, most notably a graduate course in quantum field theory, and read a lot of textbooks on field theory, general relativity, etc. Understanding attempts made toward a unified field theory has remained an important goal for me.
So, right now, I am reading the excellent book by B. Zwieback, A first course in string theory (before I found it I had lost hope of ever finding anything accessible at the undergraduate level on the subject). It got me thinking again about a question that has been puzzling me for a long time and for which it seems physics has not yet given an answer. Basically, it goes like this :
1) There is a finite velocity that cannot be exceeded in our universe and it happens to be the speed of light given by Maxwell’s equations.
2) There is a quantum of action (Planck’s constant) and it limits the accuracy with which we can measure the position and momentum of a particle (uncertainty principle).
3) But when c goes to infinity and h goes to zero, the physics becomes Newtonian mechanics. Moreover, because of time dilation, if we could travel at the speed of light, it would feel like traveling at infinite speed.
Question : Why is that?
For me at least, it cannot be just a coincidence : there must be some deeper meaning to the fact that no information can exceed the speed of light (just like the equality between gravitational mass and the mass of inertia was seen as a coincidence until Einstein and the principle of equivalence).
From what I understand (and please correct me here if I’m wrong), string theory does not explain or justify special relativity or quantum mechanics; it just use them to obtain the particle states on vibrating strings. So, even if string theory is the correct unified description of all the interactions and particles, it seems to me that it leaves the biggest question unanswered (as an analogy, we can explain the periodic table in terms of atoms of increasing atomic number and layers of electrons without digging at the level of elementary particles and their fundamental interactions).
So I went back to where it all began by reading the first few chapters of my old quantum mechanics textbook. I get the feeling that the explanation might be there, hidden in the most elementary notions : the behavior of particles is described in terms of probability waves and those waves are combined in wave packets. And then it appears : the width of the wave packet multiplied by the width of the Fourier transform of the wave (in terms of k, the wave number, related to the impulse by Planck’s constant) cannot be smaller than a finite number. We have an uncertainty principle!
Nothing new here. But wave packets have a phase velocity and a group velocity. The group velocity can never exceed that of light (for instance, EM waves in a wave guide), but the phase velocity can be much higher.
So, here is my idea : couldn’t the description of phenomena in terms of waves of probability explain special relativity in the following way :
1) We can only observe the group velocity, despite the fact that individual waves may have velocities as high as we want.
2) Somehow, the speed of light c and Planck’s constant h should be related as a single parameter, so that both theories could be derived from a single explanation and thus unified. This parameter could be a characteristic of the medium of the waves (which could be real waves in a vibrating medium).
In summary, the picture (perhaps vague and naive) that comes to my mind from the pieces of the puzzle I see here is as follows :
1) Reality is a medium that can vibrate. The simplest choice for this medium might be spacetime itself, with some number of dimensions D (I also think this geometry should explain why there is only one time dimension that can only be traveled in one direction, toward the future), so that the psi wave of Schrodinger’s equation would be like a gravitational wave, although it may differ from it, for instance by not affecting the same dimensions, etc.
2) The velocity of the wave is not limited. But being made of particles (waves) ourselves (this would be true of any observer in general, of anything that interacts with anything else, be it a proton or a human being) we can only observe the world through interactions between waves (interference) and so can only measure the group velocity of wave packets. This velocity is limited by a parameter of the medium which also gives rise to the constant in the uncertainty principle.
3) We thus have a distinction between a Real world and an Observable world (back when I was a teenager I read a great book by Jean Charon where this distinction plays an important role). The Real world obeys classical, Newtonian mechanics and this is why Newtonian physics appears as a limit case. But we can only measure things in the observable world and this is where quantum and relativistic effects appear.
4) And why are there strings? Could strings be one-dimensional quanta of the psi wave field (just like particles are point-like – zero-dimensional – quanta in quantum field theory)? It makes sense to me. And their vibrations would give rise to the interactions and particles we know.
In this description, the wave-particle duality is easy to understand (no real particles, just wave packets) and the universe (the Real world) truly does not play dice (Einstein would have loved this idea!)
This of course may sound like an interpretation of quantum mechanics and I know some consider this as more philosophy than science. I don’t think we can be sure of that. What if a unified description of special relativity and quantum mechanics gave rise to new predictions, for instance that SP and QM themselves are approximations or that they break down in some extreme circumstances?
It would remains to do what I am not qualified to do : to develop a mathematically precise geometrical model of this Real world, find the correct relationship between c and h, and look into the idea of one-dimensional quanta for strings.
But like Einstein once said, sometimes the most difficult thing is not finding the answer, but finding the question.
Any thoughts or suggested reading on the subject are greatly appreciated.
























