• I: A brief history on the concept of time
• II: Intrinsic Spin and Supersymmetry
• III: Superstring Theory
• IV: Summary of Supersymmetry & Superstring Theory
• V: Cosmological constant
• VI: The Real-Ghost symmetry
• VII: Conclusion

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.

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.

• One, space and time are absolute different entities.
• Two, there are absolute yardsticks for both space and time.
• Three, all events (dynamic or static) will not alter the absoluteness of both space and time.
• Four, although there is no preferred absolute point in space, every point is the center of universe, that is, every point is absolute relative to the rest of universe. This is relative absoluteness. On the contrary, Newtonian time does not have relative absoluteness but is absolute absoluteness.

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

• One, there is no absolute yardstick for space nor for time. Both yardsticks of space and time can be compressed or stretched.
• Two, space and time are no longer different entities. Time is the fourth dimension of space.
• Three, time is no longer absolute absoluteness. Every point in space needs its own (absolute) watch. This relativeness is, in fact, a relative absoluteness.
• Four, all events can change the yardsticks of space and time, that is, space and time are no longer independent of events.

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.

• The expansion (direction) of universe.
• The arrow of entropy (thermodynamics).
• The arrow of human psychology (the brain is a thermodynamic system, so it senses the arrow of entropy).

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?

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.

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.

• First, there is an important difference between the graviton and the photon, that is, the photon couples only to charged particles, but the graviton couples to all particles, including the graviton itself. This kind of self-entanglement can give rise to infinity.
• Second, in quantum physics, the quantum vacuum has a nonzero energy. Since gravity is supposed to interact with every form of energy and should interact with this vacuum energy. Thus, a vacuum would have a weight. On the one hand, quantum vacuum does not have weight in the real world. On the other hand, this quantum vacuum energy causes many gravity theories to produce meaningless answers -- infinity.
• Third, all theories seemed to diverge to infinity when they regard the fundamental particles as mathematical points.

• Quarks are the rock bottom building blocks, that is, they are not the composite of any sub- or pre-quark particles.
• Although a quark is not the composite of any prequark particles, it does have an internal geometrical structure, that is, it is not a point particle but a vibrating string. The size of this superstring is the 20th power of 10 smaller than the original string in the strong nuclear force model.
• Supersymmetry is an essential element of superstring theory.

• First, since its simplicity, there was the freedom to choose the particular symmetry structure to be used in defining a theory. With this freedom, superstring theory was able to select a particular symmetry structure from an infinite number of possibility, and a particular symmetry structure SO(32) magically canceled out the anomalies whereas for all of the others it didn't. Later, the second symmetry E8 x E8 was also found to be capable of producing a finite theory. For many physicists, this was a great triumph in the history of quantum gravity. On the other hand, many Nobel laureates of physics, such as Sheldon Glashow and Richard Feynman, do not think that the finiteness of a theory shall or can be the only yardstick to judge the validity of any theory. Feynman said, "I never thought trying to get rid of the infinities would be a good way to discover correct physical laws." I, nonetheless, will give this achievement of superstring on finiteness, especially based on two particular symmetries SO(32) and E8 x E8, a thumb up.
  
• Second, although superstring theory cannot yet make contact between the world of gravity and the world of elementary particle physics, it does provide some sort of connection between gravity and quantum fluctuation, at least on a conceptual level. But, it cannot explain the common fact that gravity is a long range (seemingly infinitely long) force and is transmitting seemingly instantaneously. I, nonetheless, welcome this direction of thought.

• First, there is just one type of string in superstring theory. Then, how does this string give rise to different types of elementary particle? They (superstring physicists) say that a string vibrates like a violin string. It has different harmonics. But, there is an infinite number of different ways for this superstring to vibrate. So, there shall be an infinite number of elementary particles! Where are they? Which vibrations correspond to the known elementary particles? They say that the lowest vibrations correspond to be the known particles. But, how many lowest vibrations are there for a string? Some say 496 (16 x 31), which is 20 times more than we actually know of today. Where are those fictitious particles?
  
• Second, how does the superstring squeeze out electric charge, particle's mass, etc.. Some say that superstring theory is at least 100 years ahead of its time, that is, much of the mathematics required to solve those complicated equations has not even been worked out yet by mathematicians. John Schwarz, the founder of superstring theory, said, "Another concern one might have is that the mathematics which is required just gets so difficult that the human mind is unable to deal with it."

• Edward Witten, a superstring physicist, said, "Superstring theory is only understood in a rather crude way, and the proper foundations for it aren't known, it might prove difficult to carry out these calculations [particles' masses, etc.]." Some say, "When those equations can be solved mathematically, all answers for those questions will fall right out then." Do you believe that? I don't.
  At any rate, the issues of the origin of electric charge and of particle's mass are not fair questions for superstring theory because all other models (Standard model, Quark model, QCD, etc.) do not have answers for those questions neither.
  Nonetheless, many superstring physicists do admit that they do not know what they are talking about at least on one aspect. The three cornerstones (quark, string, and supersymmetry) of superstring theories are very poor guiding principles. They do not provide a framework to distinguish which version out of many superstring theories is a better theory. Worse yet, they cannot even be guidelines to determine which solution out of many possible answers of a given theory is valid.
  
• John Schwarz said, "So there is not only the problem of trying to solve the theory and fit it to experiments, but also, at a more fundamental level, we have to deepen our understanding about what the theory is all about.... We don't really have a deep understanding of the principles that underlie those equations."
  
• David Gross, another superstring physicist, said, "it is, however, slightly embarrassing that we have so many solutions but no good way of choosing among them. It is even more embarrassing that these solutions have, in addition to many desired properties, a few potentially disastrous properties. These include symmetries of the theory that do not appear in the real world, and so must be broken somehow. Then there are massless particles that have never been observed, and, in fact, are ruled out by experiments. so something is wrong with all of these solutions that we have so far."
  
• Sheldon Glashow said, "They [superstring physicists] have the feeling that they require, as Ed Witten says, the construction of five new fields of mathematics before they have any reason to become confident that they have a theory. In fact they do not have a theory. They have a complex of ideas which do not evidently form any kind of theory and they cannot even say whether their structure describes the successful accomplishments that have been obtained in the laboratory, and in theoretical physics."

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.

• Supersymmetry:
  • Good points:
    1. It provides the quantum intrinsic spin a geometrical meaning.
    2. It provides a linkage between fermions and bosons.
    3. It seems to have prevented the four observable spacetime dimensions from being curled up into a little sphere smaller than an atom, that is, the supersymmetry seemed to be the reason to keep cosmological constant to be zero.
    4. Supplemented by Higgs boson, it seems to give masses to particles in the standard model.
  • Bad points:
    1. It predicts the existence of too many fictitious particles (the hidden matter, squarks, sleptons, etc.). Not a single one of them has been observed.
    2. Supersymmetry is obviously broken in nature, but no one knows what mechanism breaks it.
• Superstring:
  • Good points:
    1. It found two symmetries, SO(32) and E8 x E8, which give finite results in a quantum gravity theory that describes the scattering of gravitons from a graviton.
    2. It provides a conceptual description of quantum gravity as quantum fluctuation.
    3. It demands more spacetime dimensions than the old Einstein four spacetime continuum.
    4. It speculates that the mathematical point has an internal geometrical structure.
  • Bad points:
    1. It cannot describe gravity as a long range (seeming infinitely long) force, and why it transmits seemingly instantaneously.
    2. It lacks guiding principle to explain why more spacetime dimensions are needed. Today, many superstring physicists try to eliminate those extra dimensions in some modified superstring theories.
    3. It does not know the internal geometrical structure of a superstring.
    4. It cannot give a convincing explanation of how different elementary particles, the origin of electric charge and the particle's mass arise.
    5. It cannot make contact with known physics.

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.

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.

• One, gravitation and electric charge arise from time quanta bouncing (flip-flap) from the real and the ghost universes. See The Rise of Gravity and Electric Charge.
• Two, a Prequark Model is the direct consequence of Equation zero. N (the real-ghost field) generates 64 subspaces, and N^2 has four values (+/- 1, +/- 3). When N^2 = +/- 3, that subspace is a pure vacuum. When N^2 = +/- 1, that subspace is an elementary particle. Thus, there are 48 elementary particles --- particle and anti-particle both have three generations of particles, each generation has 8 particles (two leptons, two quarks with three colors for each), that is, 2 (particle / anti-particle) x 3 (generations) x {2 (leptons) + [2 (quarks) x 3 (quark colors)]} = 48. That is, we have reconstructed quark theory with equation zero.
• Three, in Prequark Model, quark is, in fact, a string (not a point but having three seats). Furthermore, the real-ghost field (N) contains SO(32) and E(8)*E(8) symmetries. Not only is the superstring theory a subset of this new physics but all its problems which I have mentioned in the previous sections vanish in this new physics.
• Four, the real-ghost symmetry is already a broken symmetry, and thus the difficulty in the supersymmetry theory disappears. This real-ghost symmetry can give rise to intrinsic spin and a zero cosmological constant at the same time. Supersymmetry is only an approximation of this real-ghost symmetry.
• Five, there is a great mystery in physics. Why are here three generations of particles? Together with the concept of infinity, this real-ghost symmetry will provide an answer on this issue.
• Six, together with John Conway's Life Game, Prequark Model can explain how biological lives arise in terms of the laws of physics.
• Seven, there is another great mystery in physics. How does particle's mass arise? In Standard Model, Cabibbo and Weinberg angles give rise to elementary particle's mass, but they (Cabibbo and Weinberg angles) are free parameters in the Standard Model. In this new physics, both angles can be calculated.
• Eight, there is another great mystery in physics. How does electric charge arise?
• Nine, the electron fine structure constant can be derived with the following equation.
  Equation of Wonder
  Alpha = the fine structure constant
  = {e^2/[4 pi * h(bar) * c]}
  = 1/Beta
  Beta = 64 ( 1 + first order mixing + sum of the higher order mixing)
  First order mixing = [1 / Cos (A)]; The mixing angle A = 28.743 degree
  Sum of the higher order mixing = 2(1/48)[(1/64) + (1/2)(1/64)^2 + ...+(1/n)(1/64)^n +...]
  The value for the first two terms of the higher order mixing = .0006561
  Beta = 64 (1 + 1/Cos(A) + .0006561) = 137.0359
  
  Beta = 137.0359895 (the measured value)
  (see http://www.chemie.fu-berlin.de/chemistry/general/constants.html)
  
  According to Standard Model, when the Structure Function
  Q^2 = m(W)^2, Beta is about 128.
  
  [back to top]

  VII: Conclusion

  Where is tomorrow? Tomorrow resides in the ghost world (as the imaginary time), and when it jumps into the real world, it becomes today. At exactly the same time when today jumps into the ghost world, today becomes yesterday. Not only these jumping acts in the real-ghost symmetry give rise to gravity, to electric charge, to space, to prequark, it also gives time a direction. This jumping (flip-flap) process of real-ghost time is, in fact, a ball to donut transformation process.

  [back to top]
  [To other topics]