Where does the Lake go, when the Geese fly to Canada?

 

My wife has lately suggested the plot for a SF story with a time-traveler as the hero. I may actually write the thing, and therefore I shall keep my lips zipped about what is happening, but before I can go down to business, I have to suffer every SF writer’s bane and figure out a means of propelling my hero through time, preferably in a way that, if not possible, seems at least plausible. Magic is not an option and the Bermuda Triangle is a lazy copout, I hate to be sloppy. On the other hand, physicists are beginning seriously to consider time travel as a viable option.

They speak of harnessing hypothetical “wormholes” and of getting dangerously near to the next black hole in our neighborhood in order to warp sufficiently the underpinning fabric of the Universe and so tunnel through space and time. Exotic physics, “dark matter” and “superstings” are prominent features in these speculations, yet neither of these gentlemen seems to pay much attention to the electricity bill. The annual budged of China, the USA and the whole of Europe will not suffice to provide even a fraction of the funding needed. Besides, my story begins in the late thirties of the 20th century, when people messed around with vacuum tubes and soldering irons and had not a clue about transistors and computer chips, and the budgetary requirements were absolutely pathetic. In other words I need to think about something cheep, something you can put together in your own garage. Something, that allows you to travel through time like stepping in and out of an elevator and to pinpoint the point of arrival as easy as turning a dial or throwing a switch. Something that doesn’t require you to get spagettified in “wormholes” or being compressed to a speck of mush in the face of a naked singularity.

In the days of CERN and our billion dollar super-colliders, powered by millions of giga-volts, this may sound naïve, but believe it or not, in other areas it has been done. These days we send particles through miles of tubing towards the collision point where they smash into other particles and in the general disintegration provide us with insights in the inner elements holding an atom together, but the very first time, when this was attempted, the experiment could be comfortably conducted on the tabletop of an ordinary desk, and it didn’t cost a whole lot.  On December, 17 in 1939 Otto Hahn conducted his celebrated experiment, the "radium-barium-mesothorium-fractionation," the first fission of an atom. It didn’t require much energy and there was little or no danger of radioactive fallout – a miniscule flash of X-rays, that was all. In fact the experiment was not even considered to be physics. Otto Hahn (1879 – 1978) was a chemist, and in 1944 he was awarded for his experiment the Nobel Price for Chemistry. It opened the road not only to nuclear fission and the Manhattan Project, but to the empirical exploration of the finer points behind Heisenberg’s “uncertainty principle.”

In 1927 Werner Heisenberg (1901 – 1976) had stated that short light-waves of high energy can measure the location of an electron with a certain degree of precision, yet the procedure will severely disturb the electron's impulse. Measuring the impulse of an electron with a longer light-wave will leave the impulse less disturbed, since long-waved light contains less energy, but then the electron's location eludes precise measurement, and diverges in a wave of statistical possibilities along the electron's orbit. From this Heisenberg drew the conclusion of a fundamental uncertainty in the correlation between impulse and location. A precise simultaneous measurement of location and impulse is just not possible, because the measuring light wave can only be short or long, not both at the same time.

In other words, the physical correlation between impulse and position ceases to exist because the agent we use to measure it interferes and in the process destroys one of the two data. The philosophical question here is: was there a correlation to start with? If a measurement is not even possible how are we to justify the stipulation that there is a correlation?

The answer should be simple! There is nothing to prevent us from choosing to measure either of the two data in this correlation and we will always get a result. Yet the fact that it is entirely up to our initiative to create an event in order to acquire a piece of information that otherwise would be unobtainable, has mislead otherwise sane and formidable physicists like the late John Wheeler (1911 – 2008), Eugen Wigner (1902 – 1995) and his colleagues in Copenhagen to speculate about a “Participatory Universe” in which “we are participators in bringing into being not only the near and here but the far away and long ago.” Obviously this is not happening. If we were really “participators in bringing about something of the universe in the distant past,” it should enable us to erase Auschwitz from the records. Merlin would return from his grave. And if somebody wishes to enthuse about the “fine tuning” of the Universe to our needs – also known as “anthropic principle” – he better explains why he thinks it is not us who are fine tuned to given conditions. It is just another flirt with the irrational, and I am not the only one with strong feelings about this.

The Austrian Nobel Laureate Erwin Schrödinger (1887 – 1961), devoted his entire working life to explain the movement of electrons in terms of waves. Schrödinger demonstrated that these electron-waves don't even move. They are stationary. Each time you check the position of an electron you will find it in a different place, but that doesn't mean that it is moving in between the checks. The equation describing the process became known as Schrödinger's wave function.

Accordingly a radioactive atom is characterized by the probability of its decay over a given period of time. Common sense would reason that at any given point in time there are only two possibilities, either the atom has decayed, or it has not. But the Copenhagen interpretation of quantum mechanics is telling a different story: the atom is understood to inhabit both states simultaneously before it is observed. It looks almost like a throwback to Bishop Berkeley (1685 – 1753). A tree will only fall if somebody is around to see it. (What about the already fallen trees? Are we going to deny that they had been upright before, because nobody saw it? Are we going to deny the actual correlation between standing and fallen trees? Or are we to assume that they are hanging in suspense half way fallen, and only when we look suddenly decide to stand upright?). To make an end of this nonsense, Schrödinger published in 1935 a series of three papers in which he lampooned the Copenhagen Interpretation in the notorious "cat paradox." Yet in quantum physics, things seem to have a strange way of backfiring. We know that the originator of the Copenhagen Interpretation, Niels Bohr, had a sense of humor, but people writing textbooks for students of physics don’t do humor. Schrödinger’s cat is now in the textbooks the example of quantum mechanics for beginners.

In Schrödinger’s own words “a cat is penned up in a steel chamber, along with the following diabolical device (which must be secured against direct interference by the cat): in a Geiger counter there is a tiny bit of radioactive substance, so small, that perhaps in the course of one hour one of the atoms decays, but also, with equal probability, perhaps none. If it happens, the counter tube discharges and through a relay releases a hammer which shatters a small flask of hydrocyanic acid. If this arrangement is left alone for an hour, one would say that the cat still lives if no atom has decayed, or otherwise would be poisoned. However before the container is opened, the wave-function expresses this by having in it the living and the dead cat (pardon the expression) mixed or smeared into equal parts.” The point in Schrödinger’s setup is the contention that according to the Copenhagen Interpretation, before we actually open the container, the cat is not only neither dead or alive, but that it is the act of opening, that decides the outcome of  the cat being either dead or alive. Very well Mr. Schrödinger, but why does it have to be a steel chamber? If the container is made of glass, then we should actually see the furry feline as a fuzzy cloud, or don’t we? Believe it or not, this has been put to the test.

A team of physicists – Christopher Monroe, Dawn Meekhof, Brian King and Dave Wineland – confined a charged beryllium atom in a tiny electromagnetic cage and then cooled it with a laser to its lowest energy state. In this state the position of the atom and its "spin" (a quantum property that is only metaphorically analogous to spin in the ordinary sense) could be ascertained within a very high degree of accuracy, though limited by Heisenberg's uncertainty principle. The next step was to stimulate the atom with a laser just enough to change its wave function. According to the new wave function of the atom, it now had a fifty percent probability of being in a "spin-up" state in its initial position and an equal probability of being in a "spin-down" state in a position as much as eighty nanometers away, which is a vast distance in the atomic realm. And lo and behold, the atom was indeed in two different places at the same time as well as in two different spin states, the atomic analog, so we are told, of a cat both being alive and dead. The piece of clinching evidence was the observation of an interference pattern. It is a telltale sign that the single beryllium atom had produced two distinct wave functions which now interfered with each other. It is like throwing a single stone into a pond but observing two circular waves rippling the surface as if from two different objects and see the two ripple patterns interfere with one another.

In the end, however, when the experimenters stop with their manipulation, i.e. feed no longer energy into the experimental setup – the equivalent to opening Schrödinger’s container – the beryllium atom finally will settle down in one of the two possible states, either spin-up or spin-down. Initially there is one object – the beryllium atom – then there seem to be two manifestations of the same object representing both possible states, and then only one again. Which is putting a question mark on an other theory, the so called “Many-Worlds” interpretation by Dr Hugh Everett III (1930 – 1982), a theory of growing popularity with scientists and filmmakers, Professor Stephen Hawking being its most prominent supporter. Like Schrödinger, Everett didn’t like the looks of the Copenhagen Interpretation and he came up with an alternative. He treated the process of observation and measurement entirely in terms of Schrödinger’s wave-mechanics. So when Everett opens Schrödinger’s container, he will find a cat either dead or alive, just like his colleague from Copenhagen. However he maintains that the act of opening the box has no effect on the outcome because Schrödinger’s equation gives a “superposition” of all possible outcomes and these do “exist” all the time simultaneously. In other words the observed presence of the same object in two different place simultaneously is supposed to be something permanent. By opening Schrödinger’s container, Everett maintains, the cat has split in two, one being dead, one alive. But the cat is not the only one affected. Box and observer have doubled as well together with the whole set of accompanying circumstances that have seen the observer confining a cat in the quantum limbo of Schrödinger’s box. Before we shoot down what appears to us lay-folk as a patent absurdity, let’s consider the obvious cosmological advantages of Everett’s proposal.

It is the only game in town that is unequivocal in embracing infinity. It is the only scientific explanation that makes the appearance of mind and intelligence inevitable without gambling against the odds of evolution or requiring the input of an intelligent designer or the assistance of some or other convenient “anthropic principle.” What can happen, must happen.

So timelines branch out and there emerge two worlds where formerly had been only one, all of them sharing the same history prior to the moment of forking off into opposite directions. In our own world just the one branch of recorded history is visible to us – fossils and the archives of the Vatican testify to the past existence of dinosaurs and of Pope Innocent III – yet we also may sit on a timeline that has branched out from an even more distant fork where Innocent and the Dinosaur’s had not been in the cards at all for the alternative timeline. There are observational horizons on both ends of a single timeline which prohibit the direct observation of forking apart. Yet in a Universe of classic gravity, the stars would bind not only to the observed galaxies but also to the host of unobserved parallel worlds.

This could be the explanation for the much vaunted but still elusive “dark matter” our cosmologies keep postulating had not Henry Cavendish, already in 1798, measured the torque produced by the gravitational force on two separated lead spheres suspended from a torsion fiber to determine the value of Newton's gravitational constant. Had the suspended lead spheres been gravitationally influenced by their parallel doublets in the parallel laboratories of parallel Henry Cavendishs, then the torsion would have been the averaged sum of all these contributions, which was not observed. In retrospect Cavendish established that the other worlds in Everett’s hypothesis are not detectable. And that shouldn’t surprise anybody. When the Messieurs Monroe, Meekhof, King and Wineland conducted their experiment on the beryllium atom, they needed to feed additional energy (in form of the laser beam) into the setup to effect the dispersion of the same atom in two different places. So the split is far from permanent. Even if we grant that quantum events can split the world in different directions, at the end the split will disappear and the world “collapse” to its normal state. Everett’s proposal seems a blind avenue, a mere convenience to operate the algorithms.

So far, all this is textbook.

I am not a physicist, I grew up with Immanuel Kant’s contention that in actual fact we are incapable of intuitively comprehending the true nature of time and space. Kant’s contribution is the understanding how and why certain aspects of the empirical world must go way beyond our intuition. The empirical world beyond our senses, does not know “order” and “chaos,” “time” or “space.” These terms apply only to our cognitive categories. Kant postulated that the human mind is as much the originator as it is the passive recipient of our perceptions. For instance “space,” Kant explained, “is merely a form of intuition for the external, but not a real object in itself; it is not a correlate of phenomena.” The same he maintained about time. When we are not looking the world “out there” is suspended in a timeless present that keeps eluding our grasp.

Then what is out there?

Carl Friedrich Gauss (1777 – 1855), János Bolyai (1802 – 1860) and Bernhard Riemann (1826 – 1866) have made us understand that even “empty” space is a mathematical manifold with intrinsic metrics. The physical properties of mass, charge and velocity of objects in space correlate with the metrical values of its geometry. The almost “flat” geometry of a near perfect void correlates to the low energy of the physical objects and electromagnetic fields it contains, while high energy and the masses of heavy stars, will bend and curve the geometry of space as well as the magnetic lines of electromagnetic fields. Drawing on this Einstein went a step further and postulated that the element of time has to be included too, and since then we refer to what is out there as the “Space-Time-Continuum” or “spacetime.”

 To us, “time” manifests itself in many ways, but always as a linear progression with one direction, from the past to the future. We age, gain time by running faster, synchronize our clocks, miss appointments. One thing we cannot do: retract our steps or better even return to a time before we were born. Or can we? I am not sure what it means to address the Universe as a “closed system,” but the overall amount of energy is “constant,” even if infinite, and therefore entropy, according to the second law of thermodynamics, is on the move towards “a maximum" (Rudolf Clausius, 1822 – 1888). Entropy is quantified in units of energy per units of temperature. In a steam engine fuel is burned to heat the boiler and water goes up in steam. The steam pushes a piston until the amount of energy from the fuel which initially had heated the water is consumed. Since the amount of available energy remains the same at any given time, it means that energy spent, is spent for good, and entropy has increased. So, every star and everything alive is on a one way trip to the future, towards the end of its resources, and no possibility of turning back. “Entropy” looks very much like the physical analog of time. (Scientists in their parlance, have a loose way to identify entropy with a state of order or disorder. What really happens is that it doesn’t really matter whether energy is burned in order to wreck havoc or build a palace, the result is exactly the same, an increase in entropy.)

The debate is still on whether we live in a very old Universe of limited size or a Universe of infinite duration and extension. Professor Hawking has suggested an alternative to both. In his book A History of Time, he gives a vision of the Universe expanding from Big Bang towards a maximum and then falling back into the “big crunch.” But instead of a linear progression, he proposes a permanent one-off, something beyond our cognitive categories of time and space. Hawking doesn’t mean to say that expansion and contraction occur in a cycle of infinite repetitions, but that the whole process is laid out and suspended in a timeless hyper-dimension of simultaneous occurrences. That’s how it would look from the outside, if an “outside” of the Universe were possible. For the inhabitant living “inside,” duration and distance continue to have their familiar features. We are born, we age, we die and experience this as a linear progression, but in the hyper-dimension these facts are laid out side by side and occurrences of the same time-withdrawn instance. Hawking uses the analogy of traveling the longitudes. From the pole (symbolizing Big Bang) the travel leads to the equator, the area of maximum expansion, and further on to the other pole, the point of collapse. We continue on our travel, reach again the equator and then the other pole, and so on, infinitely. “Time” is something that affects only the traveler who traverses the distance from point “A” to point “B,” while the planet itself is unaffected and remains unchanged on every turn. This is of course a mere analogy, but we do have good reason to consider the idea as more than a mere metaphor.

The pundits call this the “Block Universe.” It means time and distance sprawl out in a hyper-dimension that keeps the features of a progressing world simultaneously suspended in the eternal present. I am born, I grow up, I die. I live through these stages in a linear progression, but in the Block Universe the events are laid out side by side and remain immediately present. Mathematics can give expression to such phenomena.

Georg Cantor (1845 – 1918) has made us understand that infinite sets or transfinite numbers are as complete as any set of finite integers. Which means “eternity” is not simply an ever growing progression of time, but is complete and present right here and now. Infinite sets do not go on forever, they possess an actual, albeit infinite number of members and various infinite sets can vary in size. A transfinite set of integers is as "countable" as is every set that can be put in a one to one correspondence with other sets of integers. The total of the infinite set of all natural numbers is the transfinite number aleph-zero. The transfinite set of ordinal numbers – numbers transcending the total of all numerals – is greater than aleph-zero and is designated as aleph-one, aleph-two, aleph-three etc. There is an infinite number of these sets of ordinals. Cantor also proved that it is not a contradiction that any section of an infinite number has as many members as the collection as a whole. For instance, if, from an infinite set of integers, we take out all the prime numbers, then this class of integers will form a still infinite set.

In other words, time, or rather Space-Time, could be such complete and immediate presence, and our ageing and traveling towards the future is merely a ripple on the surface of something that is everywhere the same. Another metaphor, but I find myself in good company.

So, if space and time is a unified phenomenon, is it not logical to assume that in the experiment of the Messieurs Monroe, Meekhof, King and Wineland, the manifestation of the same beryllium atom in two different places at once, is not only happening in space but also in time? Einstein made us understand that no clock in the entire Universe can go absolutely in sync with any other clock. Everybody and everything is moving on an individual trajectory through space and time. Which raises the question when the beryllium atom eventually collapsed, what time did the “on board clock” show, and what was the time on the experimenter’s clock?” In fact we can be fairly certain that there must be a different time, if the atom collapses to a state of the opposite spin from the beginning. And is there any way to influence into which direction it should be going? It’s a bit like the old Zen master’s koan: “where does the lake go when the geese fly to Canada?” If you are this goose, the lake might be gone for ever.

So, although many questions remain unanswered, let’s consider a – watchama call it? – “quantum field operator.”

The first problem is of course that we want to transport a person, not just a single atom. Which means we pay for a larger, perhaps very much larger, electricity bill. The idea is to envelop a stationary chamber in a field of particles with down-spin, have it double in both spin states and then land safely in an up-spin state within the blink of an eye and with a minimum of discomfort for the chrononaut taking the ride. I think we can agree our physiology is as unsuited to be “smeared out” through the probabilities, as that of a cat, and the “collapse” back to one person may be a rather traumatic experience. Besides the question is not only when, but where we are eventually going to land. The experiment of the Messieurs Monroe, Meekhof, King and Wineland creates a distance of eighty nanometers between the two manifestations of a single beryllium atom. What is the distance for a much larger object? According to quantum mechanics it could go as far as to the far side of the Universe. The larger the leap through time, the more distant may be the drop point. This could make time travel an adventure of a mad hop through remote regions of the galaxy before we actually find the entry point to the moment in the past or future we wish to go to here on earth. We may arrive, as planned, at the time of Charlemagne, but actually very far away from France, may be in a real nasty place, like the interior of a distant star. Besides what does “enveloping” the chamber or cabin with a particle field really achieve? Anything at all? And if so, how to keep in sync the spin state of trillions of particles without violating Heisenberg’s principle?

I have no answer to any of these questions, that’s where poetic license is coming in, just don’t think an author isn’t aware of it. Yet we do already know, that, if feasible, this kind of transport through time will be instantaneous, faster than the speed of light. How do we know?

Albert Einstein was a great skeptic when it came to quantum physics and the Copenhagen Interpretation. To lampoon the concept he devised, together with the physicists Boris Podolsky and Nathan Rosen, a famous thought experiment – the EPR paradox. “It is possible,” he argued, “to obtain a pair of particles, say electrons, in a so-called singlet state where their spins cancel out each other to give a total spin of zero. Let us suppose these particles move widely apart in opposite directions, after which the spin of the particle to the left is measured and found to be in the “up” state. Because the two spins must cancel to zero, it follows the particle to the right must have “down” spin. In classical physics, this would be no problem at all. One would just conclude that the right particle always had “down” spin from the time of separation. However according to the Copenhagen interpretation, the spin of the particle to the left has no definitive value until it is measured, at which point it must produce an instantaneous effect at the particle to the right, collapsing its spin wave function into the opposite or “down” state.” And Einstein concluded: “This bizarre situation demands action-at-a-distance or faster than light communication, neither of which is acceptable.”

Einstein thought he had made his point. But in 1964 John S. Bell proposed his “non-locality theorem.” He accepted Einstein’s ridicule as a serious proposition and if he was right, this would mean there is such a thing as instant interaction regardless of distance, and were it to the other end of the Universe. And so, in 1982, Alain Aspect set into practice what Einstein had merely suggested to ridicule the idea.

As prescribed by Bell, the experiment polarized identically a pair of photons and then emitted it into opposite directions from a single light source at the center. Each photon passed through a polarized filter of which the angle was rapidly varied. Using quantum mechanics one can predict the probability that each photon will pass through a filter tilted at a given angle. But according to the same theory, the probability of one photon passing through depends on how both filters are tilted. Aspect made sure that the filters were sufficiently apart, and that their reorientation was varied quick enough, so that no signal from one end could reach the other in time to affect the second measurement, even if the signal traveled at the speed of light. In fact, Aspect changed the initial spin every ten billionth of a second, and made measurements on the opposite particles when they were separated by four times the distance that light could travel in the interval between the alterations of the spin. The results were as predicted by quantum mechanics. The experiment proved that some interactions are instantaneous and do not diminish with distance. The technology employed in this experiment to manipulate the spin of a particle field is already available. All we need to do is gradually to distribute through the ages a network of senders and receivers (spin filters), that allow us to pinpoint where we are going.

A venture fraught with danger. Where can we find safe places for our contraption, not only hidden from unwanted curiosity, but impervious to the effects of geotectonic changes in the environment? Perhaps on satellites?

It should be worth a try, however, let us worry about paradoxes later.

© – 7/11/2009 – by michael sympson, 4,700 words, all rights reserved