Four Observations
In this chapter, there is (1) evidence that anti-matter has anti-gravity, (2) evidence that the Earth absorbs and emits gravitons, which change its spin-vector, (3) an explanation of the temporary acceleration in the Hubble expansion, and (4) a new interpretation of Quantum Mechanics which is free of paradox and other mathematical impossibilities.
All these problems might have arisen because of an eleventh problem, which is the acceptance of logical and mathematical impossibilities such as paradox, singularities, and actual infinities. A paradox is a form of self-contradiction. Goedel proved one can prove anything from a logical system which contains a contradiction.
A singularity is a place where a variable goes to plus or minus infinity. Singularities are not allowed in mathematics. The function is undefined at that point. We can only say what happens as the function approaches that point. Nor do we allow actual infinities, though endless operations are allowed. We know there can be no actual infinities in nature, because they would gobble up the rest of the universe. Paradox, singularities and infinities have been accepted as part of the Standard Model in the 20th Century.
While I don't have solutions for all ten of the problems listed by Gordan Kane, I can solve some of them. It is not the equations that are wrong, but in some cases our use of them, for instance, applying Heisenberg's uncertainty rules to the vacuum, which results in the infinite energy of the vacuum. And in some cases, the problem is not the equations, but our interpretation of them. That is the problem with basic quantum mechanics.
p = h / L and W = C**2 / v where p is momentum, L is the de Broglie wavelength, W is the velocity of the de Broglie wave, v is the ordinary velocity of the associated particle and h is Planck's constant (6.6*10**(-27) erg-sec), while C is the speed of light (3*10**10 cm/sec). In Hawking's popular books, he usually refers to Planck's constant as h-bar, which is h/2pi, where pi = 3.14159.. Good idea, but h-bar is not on my keyboard.
The Schroedinger equation is obtained by plugging the de Broglie wave into the general partial differential equation for 3-dimensional waves, and then placing severe limits on the boundary conditions, in effect converting it to a probability equation. He used the greek letter Psi for the function, not to be confused with Psi research. What is Physics Psi? Nothing. It doesn't stand for anything. Furthermore, there are multiple solutions, all of which are true, until an observation of the system is made. That "collapses" the wave function. Quantum weirdness.
Any object can have a de Broglie wave, including a compound object, such as the 60 carbon atom bucky-ball. All his life, de Broglie could calculate any quantum mechanical problem correctly, just using his wave, rather than the Schroedinger equation. Not that I have anything against using the static Schroedinger equation to calculate orbitals. The problem is that it is an equation for nothing real. It is the de Broglie wave which corresponds to something real. It is by the de Broglie wave that the mind can see while Out-of-Body, without eyeballs to use. And it is by emitting de Broglie waves that the hands can "push the probabilities" to create the Geller effects.
The ideas of de Broglie excited immediate interest, because he could use his formula to calculate the orbits of atoms. Each orbit is determined by the standing waves (or resonances) of the de Broglie vibration. The ground state orbit will fit precisely one wavelength, the second orbit two wavelengths, and so forth to higher and higher overtones. These standing waves can themselves move, which indicates movement of their associated particle. This movement of the standing wave is never faster than the speed of light. Prince de Broglie's ideas are very similar to the theory of musical instruments, as he well knew.
A standing wave is sometimes called an Eigenstate, with a quantum number N=0,1,2,3..., with an Eigenvalue E(N) associated with each value of the quantum number. In a musical instrument, the Eigenstate is the note produced by the instrument. In music, the Eigenvalue would be frequency and the quantum number would indicate the fundamental tone and its first, second, third, etc., overtones.
If you have trouble understanding de Broglie waves, think of musical instruments. Louis de Broglie's theory is similar to the theory of a musical instrument, as he well knew. For a trumpet with a given length of tubing, there is a lowest note, one where exactly one wavelength of sound will resonate in the tube. It is possible to make higher notes on a trumpet, by producing overtones, but impossible to make a lower note. The same is true of electrons in orbit around a nucleus, although this analogy is only a teaching device and doesn't really explain the behavior of atoms.
So far so good. This picture even allows us to see why the first orbit of electrons around a nucleus can only hold two electrons, one somewhere under the maxima of the de Broglie resonance, and the other opposite to it under the minima. These two electrons have slightly different energies, because the magnetic pole of the up electron aligns with that of the nucleus, while the down electron has its magnetic pole alignment opposite to that of the nucleus. The picture even allows us to understand why we can never predict exactly where the electron is. The de Broglie wave is a probability wave. It shows us where the probability is greatest, but some of the time the electron will be anywhere its probability is non-zero.
Heisenberg's Uncertainty Rules: What we must add to this picture are Heisenberg's uncertainty rules, and Dirac's relativity, which gives us electron spin and anti-particles. I won't go into Dirac, beyond saying he is one of the handful of geniuses who produced quantum mechanics. If Z is some observable, then we will indicate the spread of its probability function (its Heisenberg uncertainty) by putting a "d" in front of it, dZ. The Heisenberg rules describe a curious coupling of position with momentum, and energy with time. Heisenberg's rules are:
dP * dx = h-bar, and dE * dt = h-bar where P is momentum, x is position, E is energy, t is time, and h-bar is Planck's constant divided by 2 pi. So if the positions are spread out, momenta will not be spread out. They will be "sharp." If the duration of an energy state has a large Heisenberg uncertainty, the energy will not. It will be "sharp."
If we assume that the de Broglie wave is not a mathematical fiction, we can make all the quantum paradoxes and all the quantum weirdness go away. The electron does not go through both slits in the famous two-slit interferometer experiment. But its de Broglie wave does, and produces the diffraction patterns on the far side. The electron goes through one slit or the other; we just don't know which, since the de Broglie wave intensity is equal at the two slits. The electron is always in one place or another. It does not have a ghostly presence in each of the places it could be. Thus, observing an electron does not "collapse the wave function," nor does it pick out one among an infinity of universes.
The de Broglie functions describe the experiment, such as the 2-slit interferometer. It describes what is possible, and the probabilities of each. For the detector on the 2-slit interferometer, we use wave theory and positive and negative interference to produce a curve of the intensity of the de Broglie wave at the plane of the detector. It might land on the right, or it might land on the left. What has collapsed? Nothing. The function for this apparatus remains the same. And if we keep on feeding electrons through it, the results will more and more closely match the probability function we have calculated for the plane of the detector. We do not change it by observing it.
The 2-slit experiment has now been done with atoms, molecules, and even a 60 carbon atom bucky-ball (Arndt, M. et al. (1999) Letters to Nature, vol 401, October 14, 1999 pg 680). This implies that one can calculate the de Broglie wave of an entire object, such as the bucky-ball, as if it were a single simple thing having a particular mass, velocity, and location. This is somewhat like the Center of Mass theorem in Newtonian physics. Of course, someone is sure to repeat the mantra of QM, which is that the position and velocity of an object cannot be known simultaneously. But this is not what the Heisenberg Uncertainty relationship says. It says we can simultaneously know each conjugate quantity to about 13 significant digits, if both variables are equally "broad." I am sure any experimenter would be very happy with that.
The de Broglie vibration explains the sometimes wavelike behavior of electrons. When a beam of electrons is reflected off a crystal, it forms diffraction patterns. This is because the de Broglie wave associated with the electron goes before, (since its velocity is always greater than that of the electron), and bounces off each atom on the surface of the crystal. The result is a whole series of reflected de Broglie waves, which add or subtract, producing a diffraction pattern. The probability of an electron hitting the detector screen in a particular place is proportional to the intensity of its de Broglie wave there.
Photons: Recall that the velocity of the de Broglie wave for an object traveling at velocity V is W = C**2 / V but V in this case is C, thus W=C and we know the frequency from E=hf, and by definition the velocity of a wave is its wavelength times its frequency so L = C*h / E, same as for photons. In other words, the de Broglie wave acts exactly like the classical EM (Electro-Magnetic) wave calculated from Maxwell's equations.
The problem of photons is quite different from the problem of atoms. In atoms, we have resonances of the de Broglie wave, which determine the orbits of the electrons. With EM radiation, the de Broglie wave does not form a resonance. It just spreads out like ripples in a pond, in three-dimensions, and has positive and negative interference with all the other de Broglie waves from other photons in the same quantum state. As usual, where the de Broglie wave is strongest, that is where you are most likely to find a photon. What does a photon look like?
I believe it looks just like a Schroedinger wave packet, except we must imagine a second wave at right angles to the first one. The first wave is in the electric field, and the one perpendicular to it is in the magnetic field. Photons are highly localized in space. They may all have the same size. One can get fewer long waves into a packet, which is why E=hf, that is, the energy of a photon is proportional to the number of waves of electrical and magnetic energy one can get into a photon. Thus, both Bosons and Fermions are particle-like, and it is the de Broglie wave which explains and predicts the wave-like behaviors of both.
There is no new physics here. I'm not changing the equations. This is just an interpretation of the equations, i.e., a word picture and a mental picture. This interpretation avoids the weirdness of later quantum mechanics, such as wave-particle duality, multiple universes, instantaneous action at a distance, the collapse of the wave-function and the entanglement of observer with observed, which crept in with Schroedinger, Heisenberg, and Bohr. My non-paradoxical interpretation is consistent with observation. We cannot ask more of an interpretation. I would make a stronger statement. Physics cannot simply accept paradox, any more than it can just accept singularities. To do so is the end of physics as a rational enterprise, because absolutely any proposition can be derived from a system of ideas which allows logical impossibilities.
It is possible to prevent infinity by cutting off the possible wavelengths when they are small enough to enter the realm of quantum gravity. But that ad hoc device still gives us a vacuum energy 120 orders of magnitude greater than the energy contained in all the matter in the universe! According to Lawrence Krauss, a well-respected neutrino physicist, "[This] discrepancy between theory and observation is the most perplexing quantitative puzzle in physics today (Scientific American, Jan. 1999, "Cosmological Antigravity," p. 55)." I am glad that Lawrence Krauss agrees with me.
Some would say that if the vacuum has any energy density, it would be infinite if the universe is spatially infinite. What is wrong with that? Only that space-time has been expanding from a Hawking no-boundary "South Pole" where imaginary time was zero, and it has been expanding for a finite time, exactly 13.7 billion years. So it cannot be spatially infinite.
Fortunately, it is possible to get rid of virtual particles, simply by saying that it is appropriate to apply Heisenberg's rules only when we can calculate a de Broglie wave. There is no de Broglie wave for the vacuum, since it has no momentum. So how then do we explain Casimir's force and other apparent confirmations of this idea? By applying de Broglie theory to the Electro-Magnetic field, which extends through all of space. As we bring two plates closer together, we begin limiting the wavelengths of photons that can exist between them. This draws the plates together. At least, that is one idea. Better than accepting an absurdity of infinite energy for the vacuum. Those people who are planning space-ships which will extract energy from the ZPE are just wasting their time.
It was Richard Feynman who suggested that anti-particles are like ordinary particles moving backwards in time. If that is true, anti-particles should have anti-gravity, a conjecture which has never been tested, although there is evidence for it. Newsweek (Newsweek, May 12, 1997, "Fountain of Annihilation") and Discover magazines have reported a fountain of 511 KEV gamma rays spouting from the center of our own galaxy, which is suspected of harboring an old quasar, also known as a giant black hole. 511 Kilo Electron Volts is the mass of an electron. The only way such a fountain of 511 KEV gamma rays could be produced is if there is a fountain of anti-electrons coming out of the North Pole of the old Quasar at the heart of the galaxy. This is exactly what we would expect if anti-particles have anti-gravity. Matter drawn towards the center of the Black Hole will rapidly pick up energy, which will produce particle and anti-particle pairs. Or the energy might arise from internal collisions of particles inside the Black Hole. When particle and anti-particle pairs are formed inside the intense gravitational field of a black hole or quasar, the anti-particle shoots out one pole or the other, producing the jet. It is nonetheless possible to have a stable black hole. All that is necessary is that all particles stay in their orbits around the central Hawking no-boundary zero point in imaginary time. They may eventually evaporate due to Hawking radiation.
I make use of this dark matter as a component of my theory of mind. Maybe it would be more accurate to say that mind is a component of dark matter. I suggest that dark matter consists in stable knots in the space-time geodesics. In my theory of mind, there is an intimate connection between mind-stuff and geodesics. Geodesics of space-time are like the flux lines of magnetic force, which can be made visible with a sheet of paper and iron filings. You may have done that experiment in high school. The geodesics of space-time determine the shape of space-time, which is locally distorted by the presence of mass, and can be locally distorted by mind to produce levitation and apports. These knotted geodesics could explain mass without needing the Higgs Boson.
Each large early Quasar produced a cloud of anti-matter, which created the voids we see now in the large scale structure of the universe. Bubbles of anti-matter will push out matter, both light and dark, until it collides on the boundaries of the bubbles. That is where superclusters of galaxies form, as long strings of matter. Anti-matter itself will not clump.
Why did the universe start out as matter, instead of equal parts of matter and anti-matter? We may never know. We can only speculate about the physics of the larger cosmos which gave rise to this bubble of space and imaginary time. The universe could be a zero energy quantum fluctuation in the primordial chaos, which produced a bubble of false vacuum. False vacuum is not part of this universe, so we can give it whatever properties are convenient. Let us imagine the bubble has space and imaginary time, and expands at an exponentially increasing rate, and then freezes out into matter, not a combination of matter and anti-matter. Somehow the expansion imparts to this matter something very close to escape velocity. Indeed, it is exactly the escape velocity out to at least 40 decimal points. After that, normal physics takes over. It could have zero energy because gravitational potential energy is negative, and could balance out all positive forms of energy.
This speculation has a consequence if the universe should turn out to be closed, and with the addition of all the anti-matter filling the voids between superclusters of galaxies, it just might be. When the stars and galaxies, black holes and sub-atomic particles (or whatever still exists in the year 2000 giga-year) come falling down like rain, there will be no big crunch. Zero energy fluctuation, remember? Somehow, by means I cannot guess, the positive and negative terms of energy will cancel out, and the universe will just quietly disappear. This speculation, if pursued, could have implications for the development of theoretical physics.
We have been looking at the absorption and emission of gravitons for 30 years, but not recognizing it as such. This is based on a little noted experiment, reported in Scientific American back in 1970 by Mansinha and Smylie, which shows that the Earth experiences abrupt changes of spin vector. In direction, the spin vector may change by 10 milli-arcseconds. In rotational speed, it changes on the order of 10 milli-arc-seconds per second. These abrupt changes look exactly like the absorption or emission of gravitational quanta, and thus could be the beginning of a theory of quantum gravity.
The field theory of gravity (Einstein's general theory of relativity) gives us misleading advice about the graviton, just as the field theory of EM gave misleading advice about the photon. Einstein's theory predicts that a graviton carries an extremely small amount of energy. So that is the kind of graviton being looked for, and not being found. And it is assumed in classical gravitational theory that a relatively small object can absorb a graviton, which is also not true. It takes a planetary sized object to absorb or emit a graviton.
Milli-arc-second jumps in direction and speed of the planetary spin vector have been observed by D.E. Smylie and L. Mansinha. See "The Rotation of the Earth," vol. 225, #6, December 1971, Scientific American, pp. 80-88. There is nothing in geology that could explain this. Magma movements are too slow, and the flow of currents in the liquid metal outer core of the earth cause continuous rather than discontinuous movements in the magnetic pole, with no associated change in the spin vector. The jumps in the spin vector are not caused by earthquakes. Abrupt changes of as much as ten milliseconds in sidereal time have been observed. Thus, Mansinha & Smylie's observations are a mystery...unless they represent the absorption or emission of gravitons of enormous energy. Add to this Bode's Law and we have the beginning of a theory.
No one has ever come up with an explanation of Bode's law. I suggest it makes our solar system resemble an atom, and we know that an atom's orbits are determined by the theory of photons. Likewise, it seems reasonable that a solar system should be explained by the theory of gravitons, with a touch of chaos thrown in. This means our Solar System is typical, and the ones currently being found are atypical. This increases the odds of finding life and intelligence in the universe.
How could we possibly integrate Bode's Law into gravitational theory? There is already a suggestion that the law of gravity may have higher order terms. We see this in the motion of space probes shot out of the Solar System. Eventually, their motion becomes non-Newtonian. It is as if there is an extra pull, more than is provided by Newton's law. In the F=M*A equation, there seems to be a higher order term, so F= M*(-A - a*A1**2). There may be other corrections, functions of Atomic Number, perhaps. Who knows?
In summation, we see that there are many interesting questions and problems in physics, but look as hard as you wish, you will find no basis in physics for jumping light-years.
Copyright © Dr.H 2004
Home