A missed unification?, Unifying relativity and quantum physics

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.

The "mystery" of light speed is not a mystery if you throw away your assumptions of Euclidean space time and Galilean relativity and ask which concept of relativity makes the most sense for our physical universe. (See section 10.8 of this textbook and the Appendices, especially I). Given that it's reasonable to assume a upper speed limit to the universe, you have to ask is it finite or infinite, and if it is finite what is it? If it is finite, then it has to be SOMETHING (and that something numerically depends on your choice of units) and its reasonable that massless particles would only be observed traveling at that speed, which is the limit of very light particles with some sort of push applied. As light is modeled as a massless particle, it's speed in vacuum (where, by definition, there's nothing to interact with) is c.

Particle physicists and gravity experts almost exclusively use units where c = 1.

http://www.courses.fas.harvard.edu/~phys16/Textbook/ch10.pdf

http://www.courses.fas.harvard.edu/~phys16..._appendices.pdf

Math is never going to tell you "why" something is. Why is 22/7 close to pi? A nearly meaningless question. pi has to be close to SOME rational approximation.

A physics model, like Minkowski space or pseudo-Riemannian manifolds is not going to tell you "why" the model is a good approximation of reality, but only that it's arbitrarily close to the correct math of the universe.

As the child's game goes, "why" forms an infinite regress:

• Why is the sky blue?
• Why is Rayleigh scattering right?
• Why are atoms stable?
• Why is QED correct?
• Why is the universe the way it is?
• Why is there a universe?

Eventually, why runs past what physics can tell us. If what we now believe about the universe is true, Man will never be able to have direct evidence of what happened before the first seconds of the universe. If the Brane World model is correct, we could all be wiped out by a collision we are powerless to anticipate or influence. So we do the best we can with what we have, and we ask "how" and "by how much" when our attempts to answer "why" go unanswered.

Light speed seems a misnoemer, or alternately the context has changed over time and has little to do with either light or speed.

Consider that some delays must exist in interactions between objects otherwise time wouldn't exist and the entire timeline of the universe would occur simultaneously without any chronologic order or any way to segment time and compare rates etc.

So some delays must exist. We often measure rates of one type of occurance versus another and call these ratios times, but if there's truly an underlying analog equivalent to all this, then quantizing rates isn't as accurate as measuring delays. If these interactions are discrete, then we can't measure inside a unit of time, but if there is an underlying analog approximation, we can do better than simply add up number of occurances of one thing and compare them to other occurances. For one thing, by simply summing these up over time, we ignore any variations in rate and assume the rate is constant, but you can actually determine rates faster by working with delays rather than counting number of occurances.

If you have a runner going around a 1 mile track and you want to measure the speed, you don't have him run around for an hour and then count how many laps he completed. This inherently quantizes the value (in this case to integer MPH values) simply because of the manner in which it was measured. Instead you'd simply have him run a lap and measure the delay (of course this ignores variations within this lap but it's still better).

If you had a timer tick off seconds and a second event occuring at some rate, if you wanted to measure how faster the secondary rate was occuring relative to 10 seconds, you might simply begin counting at some one second tick and then stop 10 seconds later and come up with an integer ratio down to 10ths of a second, but if you make the assumption that these rates are spaced evenly through time you can do better by actually recording the chronology of the ticks (even ignoring any way to measure within, or more accurately than a second).

Just to show you the general technique, imagine these results were recorded (though you can estimate rates much more accurately when you're comparing multiple events simultneously)

1st second, 2 ticks on secondary source
2nd second, 3 ticks on secondary source
3rd second, 3 ticks on secondary source
4th second, 2 ticks on secondary source
5th second, 3 ticks on secondary source
6th second, 2 ticks on secondary source
7th second, 3 ticks on secondary source
8th second, 2 ticks on secondary source
9th second, 3 ticks on secondary source
10th second, 2 ticks on secondary source

We would normally sum these up and say the secondary source runs between 2.4Hz and 2.6Hz but by using apriori assumptions that these are constant rates, we include phase relationships between ticks and limit the number of possible rates that could generate this (it comes out to 2.5 to ~2.572Hz is the maximum range that can generate this pattern).

I think when you dig down far enough time is a chronology of events. The problem with looking at lightspeed is likely that the analog space we perceive is simply an approximation of things and that meters and seconds are loose mental constructs that don't have a direct correlation to spacetime.

It might be that if we can fix our ruler for time, we'll find a better metric for space also.

P.S. By comparing multiple references for rates simultaneously, you can improve the results for measurements of time even better (a dramatic improvement could be gained in the above example by using 2 clocks, one at one second and another at some relatively prime ratio ... of course the faster, the better), of course this only works to the extent that these rates actually do have the equivalent of analog phase components, with a complex position that can be implicitly detected.

(Oh and this thread is a great example of why I hate intellectual property laws ... if this technique isn't already patented then sooner or later it probably will be, but it makes it so few people want to share information and when you do share information it quickly becomes useless as it gets claimed. You can't steal ideas like physical property, you can only copy them and consider that the only need for property laws is because we can't infinitely replicate tangible things in the same way as ideas, but if we could copy physical property in the same manner dang we'd all be wealthy ...)

This post has been edited by StevenA on Jul 19 2006, 11:17 PM

The speed of light, as the upper limit of speed, makes sense. It is not the only fixed state of reality in the universe that is a finite number. Absolute zero is another one. Neither are mathematical constants needed to make equations/correlations work but measurable constants in reality. They appear to have something in common. For example, at absolute zero, matter is at the lowest energy level. This would be the lowest energy quanta.

I brought the next point up in another discussion but it doesn't yet strike a chord in anyone. Because energy is moving at C, and because it is massless, it is still a moving phenomena that uses special relativity, but only in distance and time. As such, the speed of light energy reference should only exhibit the energy quanta associated with absolute zero due to infinite gamma in distance and time.

Yet in our reference energy displays finite distance contraction and time dilation, as finite wavelength and frequency, associated with something going velocities less than C, even though we know it is traveling at C. Everything in the universe above absolute zero has this space-time inversion due to the finite distance and times aspect of energy.

It is subtle. If a spaceship moved near C, it would display a certain distance contraction and time affect in our reference connected to its velocity. If it displayed a distance contraction and time dilation, in our reference that was different than its velocity, we would say that something was wrong with one of the two measurements. But energy does exactly this, it travels at C yet can show output associated with a wide range of relativistic velocities less than C.

This bears on several recent posts..

IMHO opinion 'c' appears to be the amount time changes with distance. This isn't a theory it is an observation put together from trying to work out 'why relativity?'. It may well be so far from the truth that it isn't even wrong. I don't know.

-C2.

Edit .. actually 1/c .. but this is just one number instead of another .. the principle remains unchanged.

This post has been edited by Confused2 on Aug 24 2006, 08:43 PM

B******s! I think I might have posted this on the wrong thread.

Hi Ladara7, Confused2, MDT, StevenA, rpenner et al,

A man after my own heart, someone who is actually thinking about this issue. You will see that my posts over the last couple of years are littered with references to these points especially the Fourier Transform paradigm of "matter waves". I also think that the connection between dimensions is not linear, as in extremely compact dimensions below the Planck length. I am convinced the connection is harmonic in dealing with these extra dimensions and these additional dimensions are on a greater manifold related to ours through "reciprocal space"... a "T-dual" resulting in the quantum near-field of "shells" in Quantum Electrodynamics representing "shadows" of bosonic sparticles on our "spacetime" derived from the hybridization of nuclear sub-atomic fermions but in those higher dimensions and "inflated" on demand by spin energy.

You sound like a smart person I am sure that much of this will already be understood by you when you recognize that wave-particle duality are two sides of the one "classical" coin and represent the frequency and the time domains respectively of the extra spatial dimensions that host the unseen quanta... there are "locally" at least six of these and together with out three spatial dimensions and time form a totally background independent 10 dimensional basis which may be embedded holographically into other similar 10 dimensional spaces connected by at least one more dimension... as you have intimated... a minimum of a one dimensional "matter-string".

As to quantum mechanics... in order to squeeze the known universe into our current three dimensions plus time, a number of operational projections in quantum theory were necessary to arrive at our current theory of particles. This has resulted in quantum theory with all of its necessary assumptions none of which have been justified as pure physics and the results are interpreted now as pure statistical behavior. It has had a great success but it has also reached the end of a long road and it is time to continue the path into the woods. There is dissent and one way to proceed was to go down the path of further "particleization". This has a resulted in a number of corpses littered through the history of science, most notably quantum gravity in all of its incarnations. The square peg will not fit in the round hole. Too bad ... so sad. It is time to attempt the problem anew from a totally different perspective, from the other logical end, of classicised quantum theory by adding dimensions and removing the quantum assumptions by replacing it with the so called hidden parameters as real spatial dimensions plus physics. This is exactly the way Einstein may have proceeded if he were alive today and if he understood the present direction of research.

You are on the ball with Zwiebach's book but the dominant role of "string theory" is far too ambitious in trying to solve "strings" taken from below the level of the Planck's Length then working up (assuming there is a realm below the Planck Length... I disagree for very good science reasons). Then a few seconds of thought in that direction would lead all sane "Physicists" to dismiss this approach. This is a realm about which we have no direct knowledge and from which we cannot obtain any direct proof. Nothing into nothing gives "infinity", as many of them as you want... he he he! Einstein was right.. work on down from the known working with what we know right now. As Leonard Susskind once said "If anything is strings, everything are strings"... that includes the photon and its "minions".

I will not bore you with this unless you "agree" at least look into it. Get back to me or look at my previous posts if you like by logging in and clicking on my name (Good Elf) then on that page under my name check out some of the things I have been saying along your lines. You are not "Robinson Crusoe". The unfortunate thing about all this is it is far too big a job as dissenting 'amateurs" vs honored icons to overthrow nearly a hundred years of established paradigm. I am not interested in a complete revision but you eventually must deal with the practical aspects of higher dimensions some time even if that hundred years of work, as laudable as it was, all needs reworking throughout if we are to get new answers to old questions.

Cheers

PS: I will be adding a post to the "speed of light" here very soon...
speed of light

This post has been edited by Good Elf on Aug 26 2006, 02:36 AM

Hi Ladara7,

Missed this point. This is simply because as we experience less of the "passage" of time in any "trip". Due to the scalar "Relativistic Transverse Doppler" as the result of acceleration, our measured velocity appears as distance divided by time... any distance divided by a zero (or close to zero) is "infinite". Travel the length of the galaxy and return in an "instant" of your experience of time but our star may have died in that elapsed "instant". Still... look at the reference above when I finally add something here.

Cheers

This post has been edited by Good Elf on Aug 26 2006, 02:57 AM

Have a quick look here...
Double Slit Experiment
See if this appeals or not.

Here is Yquantum's Leonard Susskind's tilt on strings...
Proposed String Theory Test

Cheers

This post has been edited by Good Elf on Aug 26 2006, 04:19 AM

Ladara7 and Good Elf

I think I have a site or two that may interest you two.

I stumbled across a site while doing other research, but came back to it. The site was devoted to the work of a physicist, Dr. Milo Wolf and his theory called W.S.M. or the Wave Structure of Matter. http://www.spaceandmotion.com/

Milo Wolfs paper on the electron that started this theory can be found at. http://www.quantummatter.com/body_point.html

My humble model of the atom based on his paper can be found at. http://forums.hypography.com/science-paper...m-expanded.html

Please let me know what you think. His theory has attracted more philosophers than physicists, though the science seems sound. I agree the three points Ladara7 made in her post, but it took me some time to reach those conclusions. Good Elf, I would also like to thank you for your posts and links.

Good Elf, Ladara & Aireal etc,

Firstly, more excellence from G'E'...I just love your posts!

Ladara/Aireal, I offer you this....my model of things:

Spacial Vacuoles

First of all, welcome to the forums Ladara7! Let me congratulate you on making your first post an excellent post IMO. All of the points you mention in your post, I agree with and they are in fact included in an entire unified model that I've built over the past 3 years.

Some info about me: I'm from Pakistan, 19 years old, and 2 more years before I complete a BSc. in CompSci. I have an intense curiousity about theoretical physics, as I love to just sit or lay down and ponder and think for hours about these mysteries...even trying to picture 4-dimensional pictures in my head. These kind of tendencies sort of reached a watershed right before my 16th birthday...and thats when the flood gates opened and I started working on my own model of a unified physics theory. There were many "aha" moments (for example, when I derived the time-dilation factor of special relativity from only the assumption that velocity is 4-dimensional and its magnitude is constant). From that day onwards, I was hooked...

Anyways, here's what I've come up with so far. I completely agree that the best way to model our universe is to consider particles/waves to be waves (and other types of disturbances) which exist in a medium. In my model, the medium is 4-dimensional. I've been able to derive gravity, electromagnetism, and both of the nuclear forces from these concepts. It also explains some other mysteries like why there is more matter in the universe than antimatter, as well as the truly bizarre like quantum delayed eraser experiments.

The geometric model used in my model is 4-dimensional Euclidean. It's like Minkowskian spacetime, but the time-coordinate is multiplied by "i", resulting in what Hawking terms as "imaginary time", but I like to think that that time is the real time, and the time we use is the imaginary time. The difference between the two is that the first time is invariant, but the second time is attached to individual observers, resulting in time dilation and those kind of things. The basic idea is that the universes started out as a dense ball of 4-dimensional fluid. This fluid expanded at an enormous rate into a surrounding void (the "true vacuum"). The expansion rate was faster than speed of disturbances in the medium (which, of course, varies with density), and this resulting in the medium "bubbling" and condensing, kind of like superheated water erupting when disturbed. The process is called spontaneous symmetry breaking in current physics. The outward flow of the fluid creates an aetheric wind around everything. The direction of this wind is always outwards from the hypercenter of the universe, which means it's more or less aligned with the time axes of individual observers. As this wind came across knots, bubbles, and other types of density pockets in the medium, brought on by the spontaneous symmetry breaking, it refracted around. Many of these density pockets formed into stable self-refracting 4-dimensional waves, with a 3-dimensional "spin" (the spin of the Earth or that of a top, in comparison, is 2-dimensional). This 3-d spin results in electromagnetism. The outwards wind of the expanding universe results in a bias on all interactions...creating the weak force. This is most strongly seen in the CP-violation between matter and antimatter, because antimatter is oppositely aligned with this wind. The strength of the weak force was much stronger in the early universe, due to rapid expansion, and this resulted in an enormous bias towards matter being created rather than antimatter. Today, the value of the CP-violation factor is much weaker. The structure of quarks and the strong force is also simple to explain here. In a proton, for instance, we have 3 quarks forming a stable union. The whole of the stable union results in a big, stable self-refracting wave pattern. The individual quarks are then distinct subsets of the wave, so to speak. They can't exist by themselves because they do not consitute an entire wave. On a more grander scale, as huge quantities of stable wave patterns travel around in the medium, they also carry their density pockets with them...meaning that energy density = medium density. This causes things to refract towards each other, resulting in gravity.

Let me know what you think of that

What a great thread, and a good collection of sensible theories. The present ΛCDM standard cosmology based on General Relativity (GR) where ’Λ’ (Lambda) refers to the dark energy, or the cosmological constant, and ’CDM’ to the cold dark matter that are believed to pervade the universe. Is being given a shake by several other theories that appear to solve some anomolies better than the current model, but I favour the time variation models. One on which I have done some research proposes that even C is relative bearing in mind that our definition of speed is time dependent (V=d/t). If time varies then C is relative to our position in the time continuum.

There is a link between gravity and time, so an earlier denser universe would have had a greater gravitational field and therefore time would have passed more slowly. The full concept is obviously too lengthy for a forum post but if anyone wants to follow that concept further I will dig up some more detail.

So you can even consider the AWT, a very primitive & negligible theory, consisting just from two equations...
There's nearly no point to dwell with this..

This post has been edited by Zephir on Aug 26 2006, 03:56 PM

Hi Ladara7, Confused2, MDT, StevenA, rpenner et al,

Not much action on this thread at the moment so I will respond. These relationships are important...

Here we can see where de Broglie and Einstein "come together". The next set are interesting too...

The second equation I will not fully justify because of the source but it comes from..

You will see why the derivations are not quite right for many of his proposals but I just got to hand it to him for his ingenuity and this does work. The first equation is no surprise and comes from de Broglie's famous 1923 Comptes Rendues Note. Together we are able to derive an easy equation for frequency independent of h but dependent on R, the radius of the particle.

This quote, modified and abridged from Louis de Broglie says it all..

The special case for light is not quite as suspected by Louis de Broglie, the temporal nature of light just does not occur unless it is in the region of the emitting or absorbing particle's evanescent region. The statement is correct for all sub-light particles with mass. Only there are the photon's properties of momentum and energy able to be transferred in "dynamics" where the particle is subjected to the property of "time". I will repeat that... no time... no dynamics. The equation of mass indicates clearly that the mass of a particle is inversely proportional to it's radius. This is not just for photons but applies "universally". This is not actually the "rest mass" but depends on its locality... and I think "locality" is most important as v -> 0. In the special case of photons they spread latitudinally but not longitudinally. This varies rapidly and greatly for any photon, so much so that within a vanishingly small distance from the source, the property of mass for any photon would quickly vanish.... and stay that way until it reached the point it was finally absorbed... this may be galaxies away and along that trip it was expanding on the surface of a wavefront of light (frequency remaining constant). Along the way the only phenomena that affect it are simple diffraction, tunneling and interference effects such as near thin edges. Also time dilation within the rest frame of the photon quickly reaches infinity from the point of view of any external observer frame of reference. It is very clear to me that all kinematic process where momentum and energy are being transferred require time so no such process can occur in the quantum state.

The next point I would like to reiterate is the one I made previously... that de Broglie Hypothesis and Einsteins Special Relativity form a "continuum" and are a winding on the brane of our particle universe in "quantum space". People are familiar with with my views on the electron and the topological interpretation imbedded in higher "stringy" dimensions. This mass derivation above of Dr. Albrecht Giese is consistent with the interpretation of Williamson and Van der Mark of a "photon trapped in a topological trap" but adds considerably to it.
http://members.chello.nl/~n.benschop/electron.pdf
These derivations are "background independent" so would be "helpful" in any unified "string theories" and I will have more to say about this later.

Comments welcome... Missed unification indeed!

Cheers

PS: I am still intending to report a bit more extensively on some aspects of time and light propagation soon in another thread.

This post has been edited by Good Elf on Aug 27 2006, 04:16 PM