CONSERVATION AND SYMMETRY
By Roland Watson
In the last article, I examined the understanding - and confusion - that has been revealed by quantum mechanics, which is one of the fundamental forms of universal order. In this article, I will review another deep level of order that has been observed, beginning with what are known as conservation laws.
As the physicist Richard Feynman noted in his book The Character of Physical Law, "Conservation just means that it does not change." For example, the amount of matter-energy is always conserved. No matter what happens, whatever subatomic particle interactions take place, matter-energy is conserved. Matter may be converted to energy, or energy to matter, but nothing is ever lost or eliminated in the process.
Indeed, this is the basis for the idea that the universe is self-contained. Whatever exists has always been here. Nothing is being introduced from, or lost to, the "outside."
I can add, this is a significant argument against the existence of miracles.
There are many conservation laws, including for matter-energy, for force charges, for spin, and even for quantum-mechanical probability. In addition, the center of gravity of mass is conserved, which implies - to me at least - that the universe has a center.
An associated level of order, on which all the forces, principles and conservation laws are predicated, involves an even greater degree of abstraction. At this level, we find what are known as the universal "symmetries." According to Hermann Wehl, which quote was included in Feynman's book. "A thing is symmetrical if there is something that you can do to it, so that after you have finished doing it, it looks the same as before."
From this we can see that symmetry comes first. The various forces are, quoting Brian Greene, "required in order that the universe embody particular symmetries."
So, in practical terms, what is symmetry? A simple example is what is known as left and right symmetry. This occurs if you draw a line through the middle of an object, and the two sides are the same. It obviously holds with geometric objects, such as circles and squares, but what about for other things, particularly for the actual systems and forms that exist throughout the universe? For instance, humans are left and right symmetrical, although this is only on the surface, and it also is imperfect.
As another example, it has been discovered that the molecules in the cells of all life forms - at least on our planet - have a characteristic spin or thread to the left. They are not symmetrical.
Similarly, electrons that are released in radioactive disintegration also have a characteristic spin to the left. Quoting Feynman again: "Therefore it is possible to tell right from left, and thus the law that the world is symmetrical for left and right has collapsed."
Universal symmetry is a demanding test. Because of this, physicists talk of partial and near symmetries, and also of symmetry breaking.
Another symmetry is that space and time are "homogenous." In other words, if you conduct an experiment here and now, the basic result will be the same as if you do it somewhere else and tomorrow. This symmetry actually has two parts. The first is called translation in space, and for it to work, according to Feynman, you "must take into account everything that might affect the situation, so that when you move the thing - he's referring to an experiment here - you move everything."
The second part of homogenous space and time is called delay in time. Again, the condition holds that everything else must remain constant.
These are imperfect or partial symmetries as well. For translation in space, the basic result of the experiment will be the same, but the specific result, which will reflect the element of chance that is described by the uncertainty principle, may well be different. For delay in time, the idea that nothing changes is inconsistent with the fact that time does have a boundary into the past. Conducting an experiment at or just following the Big Bang, for which period physical law is poorly understood, could well have different results. In effect, translation in space and delay in time assume certainty; an infinite universe in all directions - including in time; and also a universe that is not undergoing any structural changes, in its governing forces, laws, principles, and constants.
Even more, I believe another type of symmetry is revealed by this, by quantum uncertainty, which is the symmetry between chaos theory and quantum mechanics. In chaos theory - one - a system is energized and enters a phase transition; two - the turbulence leads to a chance outcome; but - three - the outcome is not solely the product of chance, not purely random, because of underlying strange attractors.
In quantum mechanics, one - a wave function of all particle potentials exists; two - the actual particle that results is a chance outcome; but - three - is this really the case - is it truly random? The accepted view, according to Feynman, is that "nature does not even know herself which way the electron is going to go," meaning, it is random.
On the other hand, if the universe, and everything in it, is alive, the question should be asked: Are subatomic particles free to choose. Can they in some unexplained way manifest will?
The symmetry of relativity
A different type of symmetry, the symmetry of relativity theory, quoting Feynman again, is that "the laws of physics are not affected by motion." The laws do not change when a system is in motion, even when the velocity of its motion is itself changing - when it is accelerating or decelerating. Furthermore, relativity also means that between a system in motion and one that appears to be at rest, it is impossible to say that the first is the one that is actually moving. However, an exception to this again exists, with angular momentum, or rotation in space. Not all motion is relative. From Feynman: "If you are spinning at a uniform angular speed in a space ship, it is not true to say that you cannot tell if you are going around."
I can further add that the symmetry of relativity itself has two components. The Principle of Relativity, which is also known as special relativity, applies only to constant-velocity motion. Physical law does not change if the motion of the system to which it applies is constant. Einstein extended special relativity to general relativity, though, through the Principle of Equivalence. Through this he demonstrated, quoting Greene, that "the laws of physics are actually identical for all observers, even if they are undergoing complicated accelerated motion."
A similar idea is called "conformal invariance," or, quoting Peat, "the property of being unchanged under changes of scale." There are numerous instances where such a symmetry does not hold, yet it appears to apply to the universe as a whole. The universe is expanding, growing in scale, but its laws and principles remain unchanged.
The final examples of symmetry that I will consider are the symmetries of particles. For example, particles can be substituted. One electron is the same as another, and one atom of gold identical with every other. In addition, these symmetries can extend across different types of particles, although imperfectly. Regarding the strong force, protons can be substituted with neutrons, but this does not hold with the electromagnetic force, since protons have electrical charge and neutrons do not.
A further symmetry with particles, which develops from this, is that they display certain similarities and affinities, such that they have been grouped into a set of classes and families known as the Standard Model. In addition, under what is known as gauge symmetry, these classes and families are linked to the various forces. Each force exists in a "gauge field," which is associated with the exchange of the force particles and also what is called the "shifting" in value of their force charges. However, the Standard Model also is imperfect. Among other things, the actual particle groupings that have been observed are not consistent with the underlying mathematics that predicts them. Physicists have concluded that the symmetries must have been broken. Perhaps if we could observe the particles at sufficiently high energies, this would not be the case.
In conclusion, all of this begs the question, is the universe asymmetrical? Right and left are not identical. They can be distinguished. Our categorization of particles is in some ways arbitrary. And time, which we believe had a beginning, has no end in sight. Our search for symmetry has yielded not a confirmation of a consistent underlying order, but rather a universe filled with exceptions and curiosities. In our search for an understanding of order, then, where do we go from here?
In the next article, I will examine a level of universal order that is seemingly even deeper than quantum mechanics, conservation and symmetry. I will discuss certain implicit assumptions that we make in our discussions about reality.
© Roland Watson 2015