Wednesday, February 23, 2005

Millenium Math Problem; Existence of Mass Gap in Yang Mills Theory

The problem of existence of mass gap in the Yang Mills Theory is one of the 7 Millenium Math Problems of the Cray Institute.

My research has solved the mass gap problem! The answer, surprisingly, is that the mass gap does NOT exist in Yang-Mills theory. Not only I have proved positively that in mathematics, Yang-Mills theory does not yield a definite mass gap, I have also proved that even if Yang Mills Theory does yield a definite mass gap mathematically, it still does NOT result in the physical mass gap we see in the real world.

My conclusion is that the mass gap DOES EXIST in the physical world. But also that the physical mass gap does NOT come from Yang Mills Theory, which is a theory based on infinite spacetime.

The real physical mass gap arises from the FINITENESS of spacetime, i.e., it is only because our universe is finite and enclosed, that we observe a mass gap, and strong and weak interactions therefore has a limited range.

The proof that mass gap does not exist in Yang Mills theory is actually extremely simple. All you need to do is a little bit scale transformation. i.e., try to like say scale space coordinates X into beta*X, you will find that the beta can lump into a separable coefficient and be removed, so you result in exactly the same Yang Mills Theory. But the original Yang Mills theory would lead to a mass gap of Delta, and the new form of Yang Mills Theory will lead to (Delta/beta), with everything else equal. So Delta = Delta/beta for arbitrary beta, therefore Delta === 0.

The insight of why Yang Mills, or for that purpose ANY existing theory, does NOT yield a mass gap, is that all of these theories lack of an essential constant without which it is impossible to lead to a definite calculation of the value of a mass gap, therefore they can not possibly lead to a definite and none-zero mass gap.

Yang Mills and all existing quantum theory takes these two constants as input: light speed C, and Planck constant hbar. It is very easy to show that using just these two constants, there is NO way you can put up a formula which combines these two constants and calculates a value of the unit of mass, or energy.

You need a further input into the theory, a characteristic mass, or a characteristic length scale, to be able to arrive at a definite mass gap value. GUITAR is the only theory capable of doing it.



Anonymous Anonymous said...

Dear Professor Quantoken,
I regret to inform you that, after the latest adjustments to the beam pipe at Tevatron, and collating with the data stream from the first run of LIGO, we have found conclusive evidence that the predictions of the GUITAR theory are completely wrong. See hep-ph/0502355 for details.

7:09 AM

Blogger Quantoken said...

This is off topic, but I am just archiving a message that I expect Lubos to erase on his BLOG, an event that can not be measured very accurately in time.

Lubos said:
"Even according to quantum mechanics, it is possible to construct ARBITRARILY accurate clocks that will measure the amount of elapsed time with ARBITRARILY good accuracy you want. You must produce the clocks using a right technology, and they must be sufficiently "large" so that certain probabilistic, fluctuating effects of quantum mechanics are suppressed, and so on."

See here is how Lubos making low level mistakes again. There is no absolute space or time. The time is ALWAYS associated with events that happen on time. You can not talk about time measurements unless you are talking about time associated with certain events you are trying to measure.

Therefore, the theoretical possible accuracy of time measurement is ALWAYS dependent on what events you are talking about.

How accurate your time measurement can be really depend on how well defined the events are in terms of time. For example, the exact time when Lubos will wake up this morning will not be well defined and so no matter what technology you use you can not determine that time to better than a fraction of second accuracy. And possible up to 10 minutes inaccurate if Lubos is a lazy sleeper.

In quantum mechanics limit, the theoretical time accuracy really depend on the scale of energy involved in events. It's the Heisenberg uncertainty principle. For example, the exact time a photon of frequency 1x10^14Hz really can not be determined any better than 1x10^-14 seconds accuracy. If the photon emitted has higher energy, you may be able to determine the time more accurately, but still there is a limit.

Further there is an absolute limit of the best time accuracy you could achieve, based on all accepted science today. That is the Planck Time, which corresponds to a mass/energy of one planck mass. You can involve a higher energy scale than Planck mass but it does not help you, because then you have a mini-blackhole and you can not determine the position better than the radius of the mini-blackhole, which is one planck length. Again space and time are really the same thing in relativity, so any inaccuracy in position measurement also translates into inaccuracy of time measurements. Worse, near the event horizen of the mini blackhole, time actually freezes and so it's not even meaningful any more.

And finally, according to special relativity, no matter how accurate a time measurement you think you have achieved, I can always watch your measurements from a spaceship that flys at almost the light speed, and I see you are doing your measurements in a terribly slow pace and your measurements are not precise at all in terms of time accuracy. The more closer to light speed I am, the more inaccurate I find your measurement to be.

So it's a complete nonsense claiming that theoretically you can achieve any arbitrary precision of time measurement. The total quantum information of the universe is a fixed amount and that puts an ultimate limit of accuracy of any physical measurements.

12:20 AM


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