Symmetry

Interesting Symmetries

By: John K. Harms

Abstract:

This text is designed to be a somewhat less-serious adventure into the world of physics-related symmetries. Thirteen opposite pairs are exhibited as well as three equations containing many of the ideas combined together. The relationship of these thirteen opposite pairs to many of the other texts is discussed. These symmetries (or patterns) have led to many of the author's subsequent insights. Your comments are welcome.

Introduction

It is very interesting how the Universe is filled with opposites. Something + its opposite and these two items when combined are equal to zero--they can cancel-out. The interesting aspect of this takes place when comparisons are performed between two or more of these sets of opposites. These comparisons can reveal some very interesting symmetries that may take place in nature.

By Richard Feynman's definition of mathematics i.e., that mathematics is "looking for patterns", this text essentially looks for patterns in a somewhat unique fashion (Feynman, 1999). This is accomplished primarily by the comparison of mirror image opposites with each other. Using this type methodology, the author has uncovered primarily thirteen sets of physics-related opposites (or patterns) worthy of note.

Thirteen Interesting Symmetries--Plus Three Equations

Here are thirteen sets of canceling symmetries, can you (the reader) think of any other such sets that do not appear on this list?

Let's begin with gravity. The author pictures gravity as a negative radiation pressure effect and antigravity as similar to ordinary radiation pressure. See the author's published gravity text for more information about these concepts. See this link also below for more information. This can be written (in # 1 and # 2) as:

1) Positive Radiation Pressure + Negative Radiation Pressure = 0

2) Antigravity + Gravity = 0

Note that in # 1 and #2 that the right sides and the left sides are equivalent. Let's add a third (also equivalent) canceling symmetry:

3) A Photon + A Photon Hole (The Absence Of A Photon) = 0

Photon holes are essentially negative radiation pressure, the absence of photons. This is what the author pictures as matter as well as the space surrounding matter. The imbalance of photon holes is gravity, the curvature of space and time. Hence, matter automatically has gravity. See the "Matter As Photon Holes" or "Space" texts for further descriptions. One can, therefore, see the next symmetry as:

4) A Background Photon (Of The Proper Energy) + A Matter Particle = 0

Colors and particle decay can be understood as photons falling-into photon holes (in # 3) or equivalently as photons canceling matter in # 4. This is similar somewhat to P. Dirac's electron model--electron holes. Again, note that all items on the right (in # 1, # 2, # 3 and # 4) match as do items on the left.

S. W. Hawking suggests an additional (and important) opposite cancellation pair (Hawking, 1996):

5) Gravitational Potential + Matter = 0

This important pair (Gravity and matter) are discussed in detail also in the gravity text. This is also related to the beginning of the Universe, where the matter (and energy) in the Universe is financed by energy taken from gravitation.

Another opposite might be:

6) A Photon + A Time-Reversed Photon = 0

A time-reversed photon can be understood as equivalent to a photon hole as well as (surprisingly enough) matter.

In equation A below, it can be understood that photons can travel backwards in time. Recent experiments appear to verify that this is the case. These are the so-called faster-than-light photons. Hence, there are two types of photons, a forward-in-time and backward-in-time variety. The backward-in-time photon can be viewed as equivalent to matter. This idea is elaborated upon in greater detail in the "Photon Emission" text at the link below.

An additional related opposite to time-reversed is:

7) Antimatter + Matter = 0

Matter/antimatter is similar to forward-in-time/backward-in-time. These were the insights of John Wheeler and Richard Feynman.

One might ask the question: if antimatter + matter = 0 and matter + photons = 0, what is the relationship between antimatter and photons? One might picture this relationship as: Antimatter <----> Matter <----> Photons. Thus, it may be no surprise that matter/antimatter annihilation produces as a byproduct; photons. There is an intimate "three-way" relationship here. Or, could it be that antimatter is composed of photons? This idea is explored in the "Antimatter" text at the link below.

It is known that electrons of the same charge can interfere with each other as in Thomas Young's (quite famous) two-slit experiment. When particles have opposite charges, they can completely cancel-out (or dampen) leaving, because of energy conservation, only photons of radiation. Hence, matter/antimatter annihilation may be the dampening of matter and antimatter. See equation A, B and C below.

Antimatter can be pictured as a time-reversed entity. This was Richard Feynman's conclusion about positrons (positive electrons); that positrons were electrons traveling backward-in-time. This was Feynman's model to replace Dirac's electron holes--the Dirac sea. Electrons in time-reverse can be essentially an opposite and out-of-phase distortion of space-time from that of an ordinary electron. See "decay" text. Link provided below.

Hence, a cancellation occurs when an electron meets a positron. When a proton meets an antiproton, matter and antimatter cancel each other and the resulting energy (from energy conservation) adds to a high energy photon.

In the context of waves, gravity (which can be also explained by the wave viewpoint) might be pictured as:

8) A Wave "Inphase" + A Wave Exactly "Out-Of-Phase" = 0

Indeed, photon holes as matter may be pictured as inphase waves meeting out-of-phase waves. When identical wavelengths meet that are precisely out-of-phase with each other, they may cancel or dampen each other. This observation has wide-reaching consequences for much of the author's work. For example, gravity may be pictured as a wave exactly "out-of-phase" with an "inphase" matter wave, and the basic premise of the author's ideas about "color" also.

An equivalent picture is that of particle spin, here seen as:

9) A Right-Handed Spin Particle + A Left-Handed Spin Particle = 0

This is similar to conservation of angular momentum. The total spin (angular momentum) of the Universe is always zero. One can substitute, in most all cases, spin for the wave quality known as phase i.e., inphase and out-of-phase, as will be seen shortly in equations B and C.

Einstein's work suggests this model:

10) A Positive Space-Time Distortion + A Negative Space-Time Distortion = 0

If both matter and radiation are pictured as distortions of space-time, one can see how they might (as proposed earlier) cancel-out. This is how radiation and matter/antimatter are pictured dampening each other in equations A, B and C below. The particle quality known as spin might be pictured as a type of space-time distortion.

Another symmetry is:

11) Positive Matter/Energy + Negative Matter/Energy = 0

Photon holes (or out-of-phase waves) can be pictured as negative matter/energy, which might be viewed mathematically as: - E = - mc^2. Matter as photon holes is essentially negative mass and energy. Photon holes as matter has gravity automatically! See the "Matter As Photon Holes" text below for further details.

One can understand this relationship with the following logic:

From # 3 above: Photons + Photon Holes (Matter) = 0

Or similarly (in # 11 above) as: Positive Matter/Energy + Negative Matter/Energy = 0

Hence, matter as negative energy photon holes, can be understood (same as above) as: - E = - mc^2, or equivalently in (B) as: - E + mc^2 = 0.

Photons, which are positive energy, can be viewed as: E = mc^2, or also equivalently in (C) as: E - mc^2 = 0.

Therefore, one can construct an equation from the logic of A above that:

equation C above + equation B above = 0, or by substitution that:

E - mc^2 + - E + mc^2 = 0

Which reduces after cancellations to:

0 = 0

Most physicists do not like negative matter or energy, however, in this author's opinion, all matter is negative mass/energy! Gravity is also widely viewed as a type of negative energy (and this is subsequently mentioned by Hawking also). A false-vacuum, the driving force of cosmic inflation, is also pictured as being driven by negative energy. Space as being photon holes have this same inflationary effect upon the Universe if space is on the large scale relatively uniform.

If one compares all left-side items above, one might conclude that antimatter is negative matter/energy, a wave out-of-phase with ordinary inphase matter. Matter and antimatter have opposite spins. Antimatter is also a negative space-time distortion and matter/antimatter cancellation always results in radiation (line # 12 below). Perhaps, antimatter has ordinary gravity (and never antigravity as some have proposed) and this explains line # 5 above.--this is not a certainty, however. Most importantly, antimatter can be pictured as time-reversed matter. Richard Feynman and John Wheeler both came to this conclusion also.

It is concluded, therefore, in the "Color", "Gravity" and "Decay" texts that an important pair must be:

12) Electromagnetic Radiation Waves + Matter Waves = 0

When compared to # 4 ( background photons and space), we see in # 12 that matter is closely related to space. This is because matter and space occur together, they are similar negative radiation pressures that do attract each other. Thus, space quanta "clump" close to matter and are responsible for gravitational effects. See the "Space" or "GTR" links below for further details.

In addition, in # 3 (a photon and a photon hole), a theory of matter can constructed that matter is actually a high density of photon holes. If photons + photon holes = 0 (which must be true), then this suggests (from # 12) that matter waves (or matter) is equivalent to an aggregate structure of photon holes. Gravity can then be understood in this context. See the "GTR" text at the link below for more about this.

Finally, if one combines a photon and a photon hole, forward-in-time and backward-in-time, positive energy and negative energy and assumes that the experience of darkness is caused by massless photon holes at speed c, one derives:

13) All Darkness (as photon holes) In The Universe + All Radiation (at all frequencies) In The Universe = 0.

This was concluded in the "Photon Emission" and "Space-Grid" texts and resulted in the writing of this darkness/blackness model; "The Photon Hole Darkness Model"--see the link below for more about this idea.

Equations A, B and C--Combining Symmetries

By combining several of these symmetries (# 6, # 8 and # 9 to be precise), one might arrive at these important equations to describe reality:

Equation--A:

Radiation (inphase, backward-in-time) -- note that this may be darkness radiation.

+ Matter (inphase, forward-in-time)

+ Antimatter (out-of-phase, backward-in-time)

+ Radiation (out-of-phase, forward-in-time)

= 0

Hence, a piece of antimatter may be a negative out-of-phase distortion (similar to an out-of-phase photon) because it travels backward-in-time. A photon may not travel backward-in-time, unless it travels faster-than-light. This may or may not be precisely true, however, because photon holes in the electromagnetic field may travel at c. Current experiments demonstrate, under controlled conditions, that ordinary photons can now travel faster-than-light. Photons that travel backward-in-time are, like ordinary matter, an inphase wave of space-time. The ordinary out-of-phase photon has an antiparticle with which to annihilate; it is a photon that is inphase. An inphase photon traveling backward-in-time may be equivalent to a piece of antimatter, matter traveling backward-in-time. A photon, since there are two types; inphase and out-of-phase, is out-of-phase with its partner yielding cancellation as in Young's (photon) two-slit experiment.

Equation B substitutes spin in the particle viewpoint for phase in the wave picture. This yields:

Equation--B:

Radiation (right-handed spin, backward-in-time) --may be darkness radiation

+ Matter (right-handed spin, forward-in-time)

+ Antimatter (left-handed spin, backward-in-time)

+ Radiation (left-handed spin, forward-in-time)

= 0

One can see that matter and antimatter have opposite spins and that two photons are predicted with opposite spins. Gravity, color, particle decay and matter/antimatter annihilation and pair creation may all pictured as the differences in spin of particles. In the early Universe, antimatter and backward-in-time- right-handed spin polarized photons may have all canceled-out. The only antimatter now seen is in cosmic-ray showers and particle accelerators. The two-slit experiment is the interaction of right-handed and left-handed photons yielding cancellation (zero).

To describe both the particle and wave picture, the two equations (A and B) can also be combined (a sum of A and B) to yield:

Equation--C:

Radiation (right-handed spin, inphase, backward-in-time) --darkness radiation

+ Matter (right-handed spin, inphase, forward-in-time)

+ Antimatter (left-handed spin, out-of-phase, backward-in-time)

+ Radiation (left-handed spin, out-of-phase, forward-in-time)

= 0

It can be understood that: Radiation (right-handed spin, inphase, backward-in-time) may be equal to darkness. Darkness may be equivalent to massless matter--a structure of photon holes i.e., - E = - mc^2.

It is seen from statement # 9 above that: right-handed spin + left-handed spin = 0, is equivalent to statement # 8 above: inphase + exactly out-of-phase = 0. Spin is the particle picture and phase the wave approach. The relationship of spin and phase can be deduced and understood by comparing these symmetries in Equations A, B and C above.

These eleven symmetries (plus equation--A, B and C above) offer more opportunities for speculation, here are a few:

A photon "hole" form the elements of space and matter (as shown in # 4). If it's massless, a photon hole may be a particle of darkness in the electromagnetic field. This all depends upon the frequencies of the Higgs mechanism giving mass to the particles.

An imbalance of quantum space is what causes gravity in the author's text on gravity. The void which drives gravity is a photon hole, or the absence of photons. A photon is electromagnetic radiation and can be pictured as a negative space-time distortion, a wave exactly out-of-phase with a matter wave or a difference in spin of matter and radiation particles. Antigravity could occur where ordinary matter did interact with radiation of right-handed spin, inphase and traveling backward-in-time, but there must be relatively little of this type of radiation around today. Perhaps, the majority of it has been dampened in the early Universe by antimatter. Perhaps, however, antimatter is present, but is not visible. See the "Antimatter" text for more information about this idea.

When a comparison is made between line # 8 and line # 12, are matter waves equivalent to out-of-phase photons? Thus, matter may be a distortion of space-time, the same as a out-of-phase photon--a photon hole. Photon holes come in massive and massless varieties. Massive holes compose matter, while massless photon holes are viewed as creating darkness perception in the electromagnetic field.

Furthermore, whether they be massive or massless, are space, matter and darkness all time-reversed photons? This might be another conclusion from comparing # 4, # 6 and # 13.

Photons of radiation are pictured as the quanta of the curvature of space-time, the role usually given to gravitons. A graviton may be a photon hole, perhaps, also a particle of darkness--darkness photon. This is why photon holes might be ideal for gravitation as seen in the gravity text. Moreover, this suggests that gravity waves are identical to ordinary radiation--a disturbance of quantum space. This viewpoint is held in the "Black Hole" text. See link below.

Conclusion

This has been a less-serious exploration of conceptual logic. A frolic with some interesting yet notable patterns. It was an absolute delight to play with these pairs of opposites and perhaps uncover, through comparisons, new underlying symmetrical patterns. Many of the author's works were generated by utilizing very similar methods of symmetrical reasoning. The author has enjoyed this adventure into these physics-related harmonies. Hopefully, the reader has also.