Where is Tomorrow?

Copyright © March, 1996 by Tienzen (Jeh-Tween) Gong

I am writing this topic "Where is Tomorrow?" now. You will read it in a later time than now. But, this topic was clearly thought though in my mind 20 years ago. Thus, I do know that there are past, present and future. Should we still wait for an experimental proof from physicist before we believe that tomorrow is really a reality. Or, we simply prefer to play the word game to classify tomorrow as a potentiality, not a reality and thus to shelf the question. Physicists are able to calculate the potential of any physical field and to obtain a value for it. Is that value not a physical reality? Is potentiality not a physical reality?

However, there is no need to argue over these points. "Where tomorrow is" can be clearly described in terms of physics. You can judge it yourself after you have read all the following arguments.

I: A brief history on the concept of time

In order to know how tomorow becomes today in terms of physics, we need first to revisit the historical thoughts on space and time.

In Newtonian physics, both space and time are viewed as absolute at least in four aspects.

The space and time in Einstein's special relativity differ from Newtonian concepts completely.

The phenomenon of special relativity is a fact in nature; thus it is not wrong. Only the interpretation of that fact by Einstein and other physicists are inadequate. They do not know that the relativeness is the foundation of absoluteness. Perhaps, Einstein did recognize that there is a major problem in his special relativity theory. In fact, he did change his opinion about space and time in his general relativity.

In General Relativity, there is an absolute time. Time can no longer defined arbitrarily at any reference frame as the Special Relativity has suggested. Time is defined by a geometrical structure caused by mass. Nonetheless, this absolute frame of time cannot be known by physicists because General Relativity does not know the geometry of universe.

Not only the three views about time above contradict one another but they do not truly give a metaphysical definition about "what is time?" They only described a partial characteristics of time, especially from the operational point of view.

Besides this relativeness and absoluteness issue, there is another issue about time --- the directionality of time. Today, most physicists recognize three arrows of time.

But, this three arrows are, in fact, effects, not causes.
  1. What is the direction of time when and if the universe contracts? So far, no experiment or theoretical works show that the direction of time will be reversed when the universe contracts.
  2. Life creates order and reduces entropy inside its skin although the global entropy still obeys thermodynamics. So, the arrow of entropy and the arrow of life (before its death) are running in opposite directions.
  3. The brain creates intellectual knowledge and is the best order creation (entropy reduction) machine. So, the arrow of intellectual and the arrow of physiological of brain are also running in opposite directions. Why shall one direction (physiological) be more prestige than the other (intellectual) in terms of time?

Furthermore, not only life reduces entropy but is the result of increasing entropy. The life on earth is supported by the energy of the Sun. The temperature on the surface of Sun is 6,000 degrees kelvin. The temperature of empty space that surrounds earth is 3 degrees kelvin. This huge thermal imbalance accelerates the entropy increasing processe. If this imbalance is reduced, say, if the temperature on the surface of Sun drops 1,000 degrees, then all lives on earth will be frozen to death. In fact, the change does not need to be this big, say, if the background temperature of the empty space increases 100 degrees, then Earth surface will be unable to cool below 150 degrees Celsius, that is, all lives on Earth will be baked to death. In short, life is feed on and supported by this increasing entropy. Only with this increasing entropy process, the reduction entropy of lie can survive.

Nonetheless, we do know that time had a direction. No one (except a few in Hollywood) will confuse tomorrow with yesterday. The directionality of time must be explained by a new physics.

In short, in order to know "Where is tomorrow?" we must answer the following questions.

  1. What is time?
  2. Why is there time?
  3. How does the direction of time arise?

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II: Intrinsic Spin and Supersymmetry

In quantum physics, there are two types of particles -- fermion and boson. They differ in their intrinsic spin. Fermion endows a fraction number of spin unit (1/2), boson the even number. All leptons are fermions. Although hadrons can be either fermions or bosons, their constituents the quarks are fermions. Only photon and graviton differ from either quarks or leptons in being fundamental bosons. The photon has spin 1, the graviton 2.

The intrinsic spin of quantum particles gives rise to a strange geometrical properties. If an ordinary (non-quantum) spinning body is rotated in space through 360 degrees, it returns to its original configuration. A quantum particle with spin 1/2, however, will not do this. It is necessary to rotate it 720 degrees (two revolutions) for a spin 1/2 particle to come back to its starting state. It is as though a spin 1/2 particle somehow sees two identical copies of universe, one for each 360 degrees of rotation. On the other hand, a spin 1 quantum particle, such as photon, sees only one copy of universe, and it returns to its original configuration after only 360 degrees of rotation. A spin 2 quantum particle, such as graviton, sees only half the universe, and it returns to its original configuration after only 180 degrees rotation.

In 1970s, this geometrical oddity of intrinsic spin was suggested to be a new kind of geometrical symmetry, the supersymmetry. It is possible to represent supersymmetry operation mathematically by attaching to the four dimensions of ordinary spacetime another four dimensions, forming something known as Superspace. Although fermions and bosons are radically different in terms of geometrical symmetry operations, supersymmetry provides fermions and bosons a common geometrical description. In short, the difference between fermions and bosons is because the supersymmetry is broken. Therefore, both fermion and boson must have a symmetry partner while supersymmetry was not broken. The superpartner of a photon is called the photino, the graviton the gravitino. Then there are the bosonic superpartners for the fermions, squarks and sleptons.

The supersymmetric geometry could also be used as the basis of a geometrical theory of gravity -- the supergravity. Further supersymmetry operations produce many more exotic particles. In the favored supergravity theory, called N=8 on account of the fact that there are eight gravitons, the total assemblage of superpartners to the graviton is 172. The reason, it is said, why nobody has yet detected any of those exotic (fictitious) particles is because they only interact very weakly with ordinary matter and so would not have been readily observed in a detector. Furthermore, their masses could be much higher than the current accelerators could produce. In short, both supersymmetry and supergravity remained a mere speculation. They did not make contact with physics.

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III: Superstring theory

In the Standard Model, all forces are transmitted through force carriers. There are two types of force -- attractive and repulsive. When two persons are passing a ball between them in the skating rink, they will be pushed away from each other. So, the repulsive force carrier can be a ball. On the other hand, passing a ball between two particles cannot attract them closer together, but a rubber string between them can do it. The idea of rubber string as the attractive force carrier not only provides an attractive force between two particles but gives rise to the asymptotic freedom for particles when this rubber string is at a relaxed state. So, a string theory was initially developed as a model for nuclear strong (attractive) force in 1970s, but it was abandoned after quantum Chromodynamics was accepted as the standard model of the nuclear strong force.

Both supersymmetry and supergravity theories faced another dismal failure. They both give a meaningless answer (divergent expressions) when they try to calculate the gravitation with the requirements of quantum theory. This failure has three possible root causes.

Without the ability to address the issues of self-entanglement and of quantum vacuum energy, many physicists rushed to tackle the point-particle issue. They stretched the mathematical point into a geometrical string. The old abandoned strong force string theory was modified to become a new supersymmetrical string theory, more colloquially called superstring theory.
Superstring is a very simple theory, and it consists of only three parts.
This simple superstring theory indeed produced some good results.
Besides these two half-achievements, superstring theory raises more questions than it gives answers.
Those comments were from superstring physicists themselves. They were saying that superstring theories lack guiding principles from above and cannot make contact with physics below. Note: Dr. Csaba Balazs (Department of Physics, Michigan State University, East Lansing, MI) just informed me (on 3-20-1999) that the above statement is not true anymore. A new string phenomenology can connect the fundamental string with the real world.

I am not an opponent of superstring theories. In fact, the reason that I spent quite a few pages to describe them is not for superstring bashing but because they are the very important link between a new physics and the Standard Model. I need to use their wonderful successes and dismal failures as a checklist when I discuss this new physics in the following sections.

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IV: Summary of Supersymmetry & Superstring Theory

The above is a brief description about the current mainstream physics. Now, I will summarize it again into a checklist form in order to compare it with a new physics.

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V: Cosmological constant

In 1916, Einstein discovered a major flaw in his general relativity, that is, the universe must expand or contract according to his new theory. Then (about 13 years before Edwin Hubble discovered that universe is, indeed, expanding), Einstein believed that the universe must be static. Thus, he modified his new general relativity theory by adding a new so-called cosmological constant into his equation to balance the expanding or contracting froces. Later, he called this Cosmological Constant 'the biggest blunder of my life,' because he missed the opportunity to make the greatest scientific prediction of all time: the universe is expanding.

Today, this biggest blunder of Einstein becomes a very important constant of nature. It must be exactly equal to zero, that is, there absolutely cannot be a cosmological constant. But, why? and how?

If this cosmological constant is not zero, we wouldn't have had four big spacetimes that we could walk around in; they would be curled up into a point. But, the fact is that we do have a nice universe in which we are walking around and that cosmological constant is exactly equal to zero. The actual measurement of this cosmological constant is the best experimental determination of a zero quantity we have ever come up with.

Physicists need to find a reason for that, and supersymmetry got the credit. They said, "It is supersymmetry that prevents cosmological constant from developing a nonzero value." But, they have no idea of how supersymmetry can be broken (because it is broken in reality) and yet not produce a nonzero cosmological constant.

In the Standard Model, all particles' mass come from a mysterious and fictitious particle called the Higgs boson. In order to make a sensible description of the Higgs boson, the standard model must rely on the idea of supersymmetry. In short, supersymmetry seems to be necessary for consistently giving masses to particles.

In summary, on the one hand, there is no evidence that supersymmetry is a reality in nature. On the other hand, supersymmetry remains to be an attractive idea at least on the mathematical and theoretical level.

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VI: The Real-Ghost symmetry

The intrinsic spin of quantum particles was only an observed fact before 1927. Then, Paul Dirac developed relativistic quantum mechanics, which provides a mathematical and theoretical explanation for it. In the mid-1970s, supersymmetry explains that intrinsic spin arises from a Superspace which consists of one ordinary four spacetime dimensions plus four additional spacetime dimensions generated from supersymmetry operation. And, supersymmetry is credited as a mechanism to keep the cosmological constant to be exactly equal to zero. Together with Higgs boson, supersymmetry gives mass to elementary particles. But, there is no experimental evidence that shows supersymmetry to be a reality in nature. That is, it must have been broken. But, how? Today, no one has any idea how that supersymmetry can be broken and yet produce a universe like ours.

In fact, the supersymmetry as it is defined (as there are two identical copies of universe) does not truly explain the property of intrinsic spin. You can try this yourself very easily.

Use two identical chairs (for example, both red) as two identical universes and put one in front of you, one behind you. If there is no other reference point around, you will come back to your original position after only 180 (not 360 nor 720) degrees of rotation.
If you broke that symmetry slightly (one red chair, one blue) and again there is no other reference point around, you will come back to your original position after 360 degrees of rotation.

Now, if these two chairs (one red, one blue) exchange their positions once while you rotate 360 degrees, then you will find out that you must rotate 720 degrees before you get back to your original position. Thus, the property of intrinsic spin cannot truly be explained by the traditional sypersymmetry concept.

That is, the partner universes of Supersymmetry cannot be identical. In fact, the symmetry partners do not need to be identical. As a round CD disk, it has a perfect symmetry along its center axis. Now, if you chip off a very small chunk from the edge of the disk, this small chunk breaks its symmetry, and it is a symmetry partner of that defective CD disk. They two together form a symmetry, and they are symmetry partners of that symmetry.

The partner universes of Supersymmetry have the relationship as the above example. We do know that there is ordinary spacetime in the ordinary universe. Then, what kind of spacetime the partner universe has? If it has the same kind of spacetime as the ordinary universe; then, these two universes cannot be distinguished, and the intrinsic spin should be 180 degrees, not 720 degrees for electrons.

Twenty years ago, I realized that the Schroedinger equation has a symmetry for space but not for time. The only way for Schroedinger equation to have a time symmetry is by introducing the concept of imaginary time. Although then there was no physics reason to demand this type of symmetry, I was simply wanting to see that if this kind of symmetry, indeed, exist; then what kind of new physics can come out from it?

With these reasonings, a new concept of time could be formulated, and it has four characteristics.

  1. There are two types of time --- real and imaginary.
  2. The totality consists of two symmetry partners --- a mortal universe with real time and a ghost world with imaginary time. When imaginary time jumps into the real world, tomorrow becomes today. When today (real time) jumps into the ghost world, today becomes yesterday. The real world has a space which is billions light years across. The ghost world is only a point, a singularity which is, in fact, an infinity.
  3. Any delta T can never be zero. That is, time is a quanta. If delta T can be zero, then the real and the ghost universes cannot be distinguished.
  4. The velocity for the imaginary or the real time moving between universes is light speed.
With these four points, I formulated a space-time euqation.
Delta S = (i^n1, i^n2, i^n3) * C * (Delta T) ..................... Equation zero
= N * C * (Delta T)
"i^n1" is n1th power of "i", the imaginary number, C the light speed, N a real-ghost field (the creation tensor). With Equation zero, a new physics flew out from it.