Thursday, November 3, 2011

Double Well Potential

So. As many of you might already know (or have heard of), there is a search going on for the moment (and for the past 10 or so years I guess) for something called the 'God Particle' or the Higgs-Boson. This particle supposedly could make up for many holes in the theories of Quantum Gravity and the Unified Field Theory, both of which are not all too solidified. So. At the moment there is a somewhat credible hypothesis circulating on why we can't find the Higgs-Boson or at least where we should generally look.

Let me start with the beginning (a very good place to start, I know). A while ago, a theory was born that the total energy level of the universe could be graphed on a simple x-y plot. It essentially was an even function curve that looked somewhat similar to a 'w' and that had a central origin in the middle spike, with the two sides theoretically stretching into infinity. The idea was that when the universe was born it rested momentarily on the middle spike, at the "ultimate" or "perfect" energy, but soon fell off to either side. Since the minima of the curve seem to suggest that the universal energy level sits at the lowest possible state, that the current 'state of energy' resides at that point (wherever it may be). Now, there is a second large debate over what that 'state of energy' implies, however the current thought is that it relates all relativistic things such as the speed of light, gravity, de Broglie wavelengths, etc. Anyways, whatever it may be, our universe sits at one of the two states of energy. It is completely possible that there is a universe exactly like ours, except on the other side of the peak; or at least this was thought possible until a little thing called the third dimensional well postulate came along.

I cannot remember this name off the top of my head, but soon after the two dimensional well potential arrived, the fairly common outcry was that our universe existed in three dimensions, so shouldn't it be possible that the universe fell in more than just one dimension? The physical and spatial reasoning for this is essentially correct, but the question of the nature of energy really cannot determine this. For example, waves are commonly represented in two-dimensional sinusoidal form. It is usually taught that they don't solely exist in two dimensions, but that the representational figure is much easier to draw in two dimensions. What we do not know is whether the waves are two dimensional or not. Theoretically, under the Heisenberg Uncertainty principle, we may know the shape of the wave relative to wavelength, but since the rotation of the wave is a property related to the shape of the wave relative to the wavelength, both cannot be known at the same time. That does not mean inductively that there is a rotational property and a wavelength property, but it does mean deductively that if they both happened to exist we would never be able to correctly ascertain those properties at the same time. Either way, I digress.

So the theory is that there is a third dimension component of the double well potential. That means if you were to pin the curve down to a point from the top and rotate the function along the y-axis as the primary axis of rotation, you would trace the path of the new curve (just to give you an idea it looks like a bowl with the center pulled up with a smooth [rather than sharp] point in the middle). Now the theory is that after the universe was created from the infinitesimally small point, it fell in some x, y, and z direction down to the bottom of the well and stayed there. Again, spatially it makes some sense but pragmatically it can't be affirmed. So now essentially there is one perfect point and a circular well along which the universe is free to travel. We also should be able to traverse the walls and central point of the curve to some extent, but there is a limit at which the curve holds back the potential total energy.

BUT WAIT THERE'S MORE!

There is one last postulate that was added to explain the seemingly random symmetry of this 'even' function (for those of you who don't know, an even function is one that is symmetrical across the y-axis and rarely occurs with properties in nature). This new postulate is the Offset Postulate, which essentially states that, no, the double well potential is not perfectly the same along the two minima, but that one is actually LOWER than the other (or if you want to be picky that one is higher than the other)! In the two dimensional double well potential this would not make much of a difference in a comparative setting as we in this universe would never know if the other universe or entity or whatever had a higher or lower equilibrium energy point. However, if the three dimensional double well potential (which really at that point can't be called a double well potential, I'd call it a ring well potential) were the one that actually applied and had a lopsided minima circle, then that would explain quite a few things. It would explain why the equilibrium energy remains roughly the same (instead of moving around that ring and changing constantly based on some unforeseen factor) and why when we attempt to disrupt the equilibrium energy in any direction we are always pushed back to the lowest point. With a ring we could change the energy level in the x and z directions (whatever that may imply) easily with no repercussions. As such we have not seen any sign that indicates any condition like that. The final piece of evidence to support a three dimensional lopsided double well (or ring) potential is that it covers all of the other previously hypothesized potentials. A cross section perfectly adjunct to the lopsided axis of symmetry would yield an even function with perfect symmetry in two dimensions. The three dimensional even function ring potential would not need to be accounted for as it would not be supported by the minimum potential theory.

So I just thought that I'd give a minor overview about the nature of our universe (or at least locally) to be able to segue into more broad and global/energy/universal topics.

Thank you for your time.

--J

No comments:

Post a Comment