In The Halcyon Dislocation, I postulated the existence of time quantization as a means to setting up parallel, sibling worlds. Here is the description of this concept in an exerpt from the book:
Tired and hungry, Dave and Glenn returned to their room and turned on the TV to see if broadcasting had resumed. To their surprise Jennifer McCowan, the blonde talk show host of Halcyon Music, was on the air.
“Even without social media,” said McCowan in her gentle, lilting voice, “I know that everyone is asking ‘where are we?’ and ‘what’s happened to us?’ To answer those questions I’ve asked a friend of mine to the studio. Please welcome Vlad Sowetsky.”
Canned applause welcomed Vlad.
“So, Vlad,” said McCowan, “please tell our viewers what you do.”
Vlad, a tall, big boned youth in his mid-twenties, had a long, narrow face and close-set eyes, so that the overall impression vaguely reminded one of a horse. He had shoulder length hair and stubble on his face.
“To cut to the chase, I’m a graduate student with Professor Hoffstetter, and I was in the control room when the dislocation occurred.”
“So what actually happened during the accident yesterday?”
“Well,” said Vlad, “we were running the largest test on the force field to date. The plan was to—”
“Whoa,” said McCowan, “I think you are going much too fast. Tell the audience how the Hoffstetter force field works, but no jargon, please!”
Vlad screwed up his face as if he were being asked the impossible. “The force field appears as a bubble about the size of a soccer ball when we first generate it. The time inside the bubble is slightly behind our time. When we first make the bubble, the time delay—or offset—is very, very small so that the field is thin. That is to say, anything can cross it. We expand the bubble to the desired size and then thicken it. By ‘thicken’ I mean that we increase the time offset so the field begins to have an effect. First it stops large objects. If we increase the time offset even more, we could theoretically stop air molecules or light from crossing the force field boundary.”
“Field boundary,” said McCowan. “Now you’re lapsing into jargon again and losing me.”
“By field boundary I mean the edge of the force field bubble. Shooting a missile through this barrier is, as Hoffstetter would say, ‘like trying to shoot into last week.’” Vlad was beginning to get exasperated.
“Okay,” said McCowan, “please go on. Even if I don’t understand all of the physics, I’m sure there are many listeners who will.”
“Well, we had intended to expand the force field so that it enclosed the central building in the experimental area. However, while we were expanding the bubble, the first lightning strike overloaded the equipment and the expansion continued unabated.”
This was followed by a momentary pause and a baffled look on McCowan’s face. “How big did the bubble get?” she finally asked.
“I think it expanded to a sphere about four miles in diameter,” said Vlad.
“Then a second series of lightning strikes overloaded the offset controls, and the time offset increased enormously,” said Vlad. Beads of perspiration had appeared on his forehead.
McCowan uncrossed her legs and leaned forward. “Tell the audience what you think happened next,” she prompted.
Vlad took a deep breath. “I only have a half-baked theory. Do you know about quantization of energy?”
“Vaguely,” said McCowan, a blank look on her face.
“Let me see if I can make it as simple as possible. Macroscopically, that is, in the world of meter lengths and kilogram masses, energy seems to be continuous. It flows like a stream or a river. So if I ask how much energy it takes to lift this book,” he lifted a book from the table, “you can calculate the energy in joules to as many decimal places as you like. I can lift the book to any height and calculate the lift energy for each height. But when you go down in size, ten orders of magnitude to angstroms, the world changes. When lifting electrons away from the atomic nucleus, all the rules change, and one can only ‘lift’ the electron to discrete ‘heights,’ or energy levels. It’s like being able to lift this book in little jumps.” He demonstrated by rapidly lifting and stopping the book at various heights.
“Yeah, I know what you’re talking about. You’re bringing back unpleasant memories of first year chemistry. But what has that got to do with the Hoffstetter field generators and the accident?”
“Everything!” said Vlad. “I think time is also quantized.”
“You’ve lost me again. How can time be quantized?” asked McCowan. “And if it is, what difference does it make?”
“Well, think about it in relation to the quantization of energy that you learned about in first year chemistry. We think of time flowing past us like a stream moving at a constant rate. That may appear true in our macroscopic world, but what happens if, at very short time intervals, one reaches a minimum time (I call it a mintival for minimum time interval)? What if our existence at the time interval of a mintival consists of little jumps, like a jump second hand rather than a sweep second hand? Or putting it another way, what if instead of a flowing stream, time consisted of a series of pools,” and here he paused to let his words sink in, “and our existence is a discontinuous series of jumps from one pool to the next?”
“Your theory is fascinating, Vlad, but what has that got to do with the Hoffstetter field generators?”
“I just told you that the Hoffstetter field generators cause the matter inside the field to lag normal time by a very small amount, say ten to the minus thirty-second of a second—that’s a decimal point with thirty-one zeros after and then a one. Now let’s suppose…” Sowetsky turned and kneeled on the sofa and drew three contiguous rectangles on a white board behind his seat “…that these three rectangles represent three sequential mintivals in our world, or universe, if you like. Another world can coexist with ours, as long as the mintivals of that world are offset from those of our time.” He drew three more rectangles adjacent but offset to the first three, like bricks on the side of a building. “It would be like a single reel of film containing two movies, with the odd numbered frames representing our world and the even numbered frames representing another world. If two projectors played this interlaced film with one displaying the odd numbered frames and the other the even numbered frames, one film could give rise to two motion pictures. Similarly, although two solid objects cannot occupy the same space at the same time, they can occupy that space at different times, so to speak.”
“Keep going,” ventured McCowan doubtfully. “I hope our viewers are following you through all this.”
“Well, normally, when the Hoffstetter field generators shut down, they collapse back to the nearest quantized mintival. When the field generators overloaded, I believe we kicked over into the trailing mintival—hence the new world!”
“Well, I’ll be!” said McCowan, genuinely shocked. “Can we get back?”
“I don’t know,” said Sowetsky, frowning. “We only know how to make the Hoffstetter field lag time, not precede time. If we tried it again, we might jump into yet another world that lags this one!”
“You can’t be serious!” said McCowan.
“I’m deadly serious,” said Sowetsky evenly.
“We’re never going to get back, are we?” asked McCowan, her voice fading to a whisper as tears began to fill her eyes. She turned away from the camera for a moment. “I have one final question, Vlad,” she said, regaining her composure with obvious effort. “Did you tell Professor Hoffstetter about this possibility?”
“Of course! I told him not once but several times!” said Sowetsky. “That’s what burns me up so much.”
“What did he say when you told him?”
“At first he told me ‘science requires us to take risks,’ and finally he told me to stop raising the matter.”
Is this even possible? Normally in quantum mechanics, quantization comes about because of boundary conditions. Think of a guitar string. A loose guitar string doesn’t produce a pure tone. Only when it is stretched between two points (think boundary conditions) does one obtain a pure fundamental frequency along with the overtones. These frequencies represent quantization of the sound (the fundamental and overtones are related mathematically). It’s not easy to see why time should have boundary conditions and so quantization seems unlikely at first glance.
However, in 1899, the great physicist, Max Planck, proposed a natural unit of time based only on universal constants such as the gravitational constant, Planck’s constant, and the speed of light. Planck’s time (ca. 5.39 x 10^-44 seconds) is a small number indeed and is considered by many physicists as the shortest time interval possible. Similarly, the inverse quantity, 1/tp, is a frequency and may represent the maximum frequency possible. Perhaps there are boundary conditions for time and the idea of time quantization are not as far fetched as it seemed at first glance.
Relationship to Time Paradox
In any case, Planck Time, or the Mintival described by the character Vlad Sowetsky in The Halcyon Dislocation are very short time intervals indeed. They are much shorter than the time of one vibration of a hydrogen molecule or the shortest time observed experimentally (8.5 x 10^-19 seconds (2010)).
This provides a trivial solution to the time paradox. In the time paradox, one short circuits a chain of cause and effect events. That is to say, travelling back in time means the traveler invariably makes changes or initiates new causes that change the future. Or does he? There are usually two solutions. In one possible solution, each change initiates a new multiverse or parallel world strand.
A second solution (illustrated in C. S. Lewis’ The Great Divorce (he references getting the idea from a science fiction novel) centers on the idea that the traveler cannot affect the past at all. It’s like adamant. Not even a blade of grass could be bent by the visitor.
With very short time intervals, traveling backward in time does not generate a violation of the time paradox because over these time intervals nothing happens so nothing changes. So you see time travel should be possible as long as the trip backwards is very short!