The Copenhagen interpretation of quantum mechanics is baffling, while the many-worlds interpretation is unrealistic. The time travel model attempts to provide a comprehensible explanation.

In this model we assume that the presence of a particle causes vibrations in the time coordinate of spacetime. The wave function may be identified with the displacement of the time coordinate from the present. The square of the wave function is proportional to the strength of these vibrations and gives the likelihood of finding a particle in the vicinity.

The time waves at present overlap the time waves of a moment ago, and so on, so that a particle becomes spread out over all the spacetime between the last interaction and all possible points of the next interaction. If a particle's time coordinate is uncertain, its position and momentum are also uncertain.

The wave function is the displacement of the time coordinate from its normal position at a specified time. So the wave function forms a longitudinal time wave carrying the particle back and forth in time between the present and the last interaction. If a time-travelling particle should interact in the past, we would have perceived this interaction as occurring in what was then the present. So particles cannot interact in the past. If particles can produce free time waves, then like gravitational waves, they carry negligible energy.

When an interaction occurs, the particle is no longer available for time travel and the wave function collapses backward in time to the point of the last interaction. Since we cannot observe the past, the collapse appears instantaneous. The collapse is itself not observable, so nothing observable changes in the past.

The Schrodinger equation states that the frequency of temporal vibration is proportional to the energy. Its complex nature is a mathematical way of describing vibrations. The many-dimensional nature of the wave function is a consequence of the Hamiltonian formulation. There is no implication that the world is actually complex or many dimensional.

The relativity of simultaneity causes a uniform vibration to become a traveling wave when seen from a moving coordinate system, which is why the momentum is obtained by taking the spatial derivative of the wave function.

The antisymmetric Fermi statistics of the wave function under exchange of a pair of identical fermions is a way of stating that the particles cannot occupy the same space at the same time. If all fundamental particles are spin one-half rishon fermions, then the symmetric Bose statistics are simply obtained by exchanging rishons two pairs at a time.

Let us consider two classic examples. In the two-slit experiment, a particle may go through one slit, then back in time, then through the other slit. In the case of two quantum entangled particles, when one is observed, the wave function for that orientation collapses backward in time, leaving only the wave function for the opposite orientation.

If a time wave curved around into a circle, the entire whirl would appear to oscillate back and forth in time. The whirl could not dissipate due to conservation of energy and angular momentum, or other quantum numbers. We suggest that these whirls are in fact the rishons. It is also a law of nature that a rishon cannot disappear unless it meets its antirishon. This model explains how a particle can produce time waves: particles simply are trapped time waves.

The observed intrinsic spin of a rishon is far greater than what could be possessed by a small rotating mass. In our model, the internal rotational phase velocity of the time waves may be much greater than the speed of light, since no information is conveyed. This may explain how a rishon can have a large angular momentum but little mass. Since a rishon is a cloud of time waves, it would have eigenstates of angular momentum. When its angular momentum (or energy) is measured, one would always find it to be an eigenstate, in accord with general principles of quantum mechanics. This cannot be understood if a rishon is viewed as a point particle.

The V rishon may be the lowest possible energy state, while the T rishon may be the highest possible energy state, perhaps because the phase velocity has slowed down to the speed of light. Any slight instability would cause intermediate states to gain or lose energy and move toward one extreme or the other. This may explain why there are just two stable rishons, light and heavy. The bare mass may be much larger than the observed mass, due to renormalization. Unfortunately it is not known how to calculate this, so hard numbers cannot be given.

The large spin of a rishon eliminates the spherically symmetric S states, leaving the three P states to correspond with the three colors. The T rishon constantly emits and absorbs a cloud of V anti-V particles, corresponding with gluons and photons as the pair carries net color or not. The V rishon does not have enough mass to do this. The weak force arises from the transfer of a group of rishons, the W particle.

A rishon might have a polar temporal field caused by the circular motion of time waves, analogous to a magnetic field. Particles would be ejected preferentially along the direction of this field, because time flows in that direction, thus violating parity. The temporal field would be aligned with or against the direction of external time, corresponding to rishons or antirishons. Because of the time difference, the two would have slightly different reaction rates, producing an excess of hydrogen over antihydrogen, which have the same rishonic content. The photon and gluon are symmetric with respect to matter and antimatter, but the W is not, so only the weak force violates parity.

Time dilation and the relativity of simultaneity are features of special relativity, while in general relativity mass influences the flow of time and gravitational radiation consists in part of time waves. Therefore our concept of time waves has some precedent. Quantum mechanics and general relativity both describe disturbances of spacetime and together provide a complete picture. Everything can be explained as waves, whirls, or bends in spacetime.

When a particle interacts, it stops time-travelling into the past, because the coherence of the time waves is broken. The wave function collapses, or disappears, backward in time. It is as though the wave function never existed at all, so it vanishes instantaneously in all frames, in agreement with the fundamental principle of relativity, that there is no preferred frame.

In the rishon model, all neutral matter has equal amounts of T and anti-T rishons. Under sufficient pressure, theses would be forced together and annihilate, so matter would convert to photons or neutrinos and escape before a naked singularity could form, or in a big crunch.

The collapse of a wave function is an irreversible process, so quantum mechanics does not conserve information, in a black hole, or anywhere else. Gravity is a curvature of spacetime, so the need for gravitons is questionable.

In the rishon model, a photon consists of a V anti-V pair, so, like the neutrino, it might have a small rest mass.

The P states mentioned above are conjectured to be states of intrinsic spin having spin one-half.

The photon and vector bosons have different masses because they are made of different rishons. Symmetry breaking is not needed.

Particles are disturbances in spacetime and according to general relativity would therefore have mass. The Higgs mechanism is not needed.

It would be of great interest to discover and study the equations which govern the structure of the rishons.

It is shown in quantum field theory that the vacuum appears warmer when viewed from an accelerated frame, so the exponential term in the vacuum polarization may represent the reduction of the polarization *g* by the temperature.

As waves on a rope shorten the rope, so time waves may shorten spacetime, which we perceive as gravity.

A cat is much too big to travel through time, so it cannot be in a true superposition of states connected by time travel. It is only the observer's knowledge that is uncertain.

The Planck frequency may simply be the frequency of precession of a particle around the time axis. This is not the same as the internal frequency. The direction of the time axis is not observable, so the time waves would be isotropic, as observed.

A free time wave cannot propagate, so the surface of a rishon would appear perfectly reflective from the inside. Hence a rishon would resemble a wave guide which could have waves that go faster than light. The energy of a rishon is contained in the time waves.

The V rishon may be the lowest energy state, having low mass but very high phase velocity. The T rishon may be a local minimum energy state produced by the formation of the photon-gluon field. As the internal mass grows, the field also grows, reducing the total energy at first but then raising it, as nuclei may lower their energy by growing larger until electric repulsion dominates, like an iron nucleus.

The size of the rishons may also be a minimum energy state. If a rishon were smaller, the electric repulsion and the internal momentum and hence the energy would be greater, If a rishon were larger, the strong or color force would pull it back together.

If a tablecloth represents spacetime, a wrinkle is a wave function which pulls in the surrounding space. As light goes slower in a denser medium, time goes slower where space is pulled in by matter. If a car were driven parallel to the time axis, and the left wheel turned slower than the right, the car would veer to the left, which we call gravity. The average pulling in of space is proportional to the number of crests of the wave function along the time axis, and hence the frequency or energy.

The quarks and leptons consist of three rishons in a triangle. A T anti T pair could be added to each side of the plane of the triangle, explaining why there are exactly two higher generations, and why the highest generation decays in two steps. A V anti V pair could be added to each side of a neutrino. These pairs have so little energy they could appear and disappear spontaneously, explaining the three shifting types of neutrino. Perhaps one should not dismiss the possibility that the alleged Higgs particle may be made of rishons.

A rishon does not have a sharp boundary, so the rotating time waves extend a short distance outward. If the waves of two nearby rishons partly cancel, the energy is reduced and a bond forms, which we call the color force. These waves also agitate the spacetime around the heavy T rishon, creating a cloud of virtual particles. Rishons occupy three P states, so in effect a rishon itself occupies one state, leaving two states as valence states. So a rishon resembles an atom with valence two. Two rishons with spin up and spin down cannot occupy one state, because time waves cannot go in opposite directions at the same time. The T and V would likely have different bond strengths, like different atoms, or in the old terminology, different color charge.

On a spacetime diagram, the circular time waves of a rishon can go clockwise or counterclockwise around the time axis, corresponding to rishon or antirishon. These are intrinsically different because one cannot turn a rishon over relative to the time axis. They are not even exactly symmetrical because time goes forward, not backward. A rishon cannot fly apart as it would become free time waves, which is impossible.

A rishon would be stable if the time waves both generate and follow geodesics. The scale may be set by the distance a free time wave can propagate.

In this model, the internal phase frequency generates the angular momentum, while the group frequency generates the Planck frequency. Many small waves could pile up to form a group wave that circles at the Planck frequency.

The color magnetic force may help hold a rishon together, or bond rishons to each other, or comprise the energy of a V. Since all mass is positive, any color magnetic force would be attractive.

If rishons have a finite size, the wave function must be antisymmetric so they do not overlap.

Everything is made of time waves, so time is certainly not an illusion. Interactions occur in the present, wave functions disappear in the past, and the future is unknown.

The T may be just a V surrounded by a cloud of V anti V's, so the V in effect is the only truly fundamental particle. The cloud around a T would become polarized, causing the apparent color charge of a T to be somewhat less than that of a V.

If the V is the only fundamental particle, all particles would have a multiple of the same spin, obey the Planck relation, and have three colors, as observed. A T cannot change into a V, or vice versa, as this would change the net color, which is not allowed.

A V anti V pair can annihilate if it can dispose of its energy and angular momentum. A T anti T pair can annihilate when the V and anti V particles at their centers combine.

The total spin of a V is h bar, but since the radius and spin vector are both tilted at a 45 degree angle in time, the spin we see along a given direction is one-half h bar.

A wave function, or time wave, pushes the local time axis out of alignment with external time, causing local time to go slower as seen from afar, producing gravity.

In the big bang, space was greatly stretched, and time was also stretched, causing the antirishons to be more massive than the rishons, since the antirishons point against the flow of time, an effect which is negligible today. This asymmetry would cause an excess production of hydrogen over antihydrogen, favoring the lower energy configuration.

Stretching of space would induce a curl in the temporal field, as in electrodynamics, oppositely affecting rishons and antirishons, creating enough matter for a trillion galaxies.

A rishon's internal time wave cannot propagate into the future or past, as this would disrupt the rishon. Therefore the present must have a finite width, and by covariance, the size of a rishon is determined, like a spherical well, having the familiar P states. If the de Broglie relation holds, the angular momentum mvr of a rishon is h bar, and since the radius is known, so is the internal momentum mv, where v is the phase velocity. A rishon would seek to minimize its energy, so the mass m becomes very small, while v becomes very large. So the V rishon is very light, while the T rishon is a V surrounded by a large cloud of virtual particles, making it much heavier.

A spin-zero rishon would have no conserved quantum numbers, and so could not exist. Higher-spin rishons would be unstable or nonexistent. If the W and H are the spin states of the TantiT, the rishon model would be in good agreement with observation.

The external waves can overlap coherently over a long interval, but the internal waves cannot because of their high frequency.

Since the wave function is the displacement of the time coordinate from the present, the time derivative is the deviation from the normal flow of time, and according to general relativity, causes a gravitational field, which we interpret as arising from mass, as stated by the Schrodinger equation, as any child can see.

Deviations in the flow of time act as the source of the gravitational field. We interpret this source as gravitational mass, which according to general relativity is the same as inertial mass, which we can of course observe, as stated by the Schrodinger equation. The Planck relation and the de Broglie relation can be derived from the Schrodinger equation.

A particle generates a time wave that carries the particle back and forth in time, which may create a standing wave. The wave reflects from the present because the future does not yet exist, and reflects from the last interaction because the prior wave function has collapsed. When the particle interacts in the present, it stops travelling through time and the wave collapses, and the process repeats.

Free time waves are confined to the width of the present and form rishons. The width determines the amplitude.