Wild Surmise
July 1985 # MINUS 4
AN ALMOST INFORMAL NOTE
A PREPOSTEROUS NOTION OF THE UNIVERSE
It may be the case that time as we know it runs just the reverse of what we are accustomed to thinking. If that disturbs you, please read no further and think about it no further, or if you must, read on, not with an idea to believe or disbelieve, but only to exercise your mind.
Here is a list of some 19 things I will use. So far as I know, these things are sound modern science. This is my best effort to state them.
1. Newton’s Laws. To a close approximation, an object will remain at rest or travel in a straight line until acted on by a force. Every such action has an equal and opposite reaction. Every object is attracted to every other object by a force that is proportional to its mass and inversely proportional to the square of the distance between.
2. Einstein's special theory of relativity. As an object moves, it experiences a distortion of its shape, its mass and its experience of time. This distortion is such that as the object approaches the speed of light, its length approaches zero, its mass increases without limit and its specific time runs slower and slower. Thus no ponderable object can reach the speed of light. Furthermore, energy, which is what it takes to exert a force for some distance (say to accelerate an object that has mass) and mass can be interconverted; they are forms of the same thing. A lot of energy goes to make just a little mass.
3. Maxwell's Demon. If you had a little devil with a tiny little door to a chamber, and this devil were very quick, he could open the door every time he saw an air molecule coming from the outside toward the door, but close the door when a molecule came from the inside. Soon the chamber would be full of compressed air, which could be used as an energy source. Since the demon works for free and the door requires no energy to open and close, there is energy for free. Not so. The information that: the demon introduces into the system by "seeing" without altering the molecules is equivalent to the increase of energy in the system. Thus information and energy are forms of the same thing.
4. Maxwell's Field equations. For any conductor, any force, any electrical flow and any magnetic field will arrange themselves such that each is perpendicular to the other two. This is the basis of all electrical devices. Furthermore, if there is an oscillating electrical field, it will induce an oscillating magnetic field, which will induce an oscillating electrical field and so forth. The resulting field will spread out at the speed of light. Indeed, it is light, or radio waves or ultraviolet, or a large number of other waves, depending on the source and the wavelength.
5. Quantum mechanics. An atom consists of a nucleus, which contains most of the mass of the atom and is positively charged and one or more electrons, which have little mass and are negatively charged. The nucleus is well localized; effectively it is very small. The electrons are poorly localized, each lying in a zone of relative probability where the electron may be found if you go looking for it. (These zones, by the way lock like the harmonics of a vibrating sphere.) The electron is closely confined to a volume where it must almost surely lie, but it has a small but real probability of being located anywhere, only excluding the nodes of the distribution. In general, any particle has some chance of being located at or near any location in all of space, having no absolute location, although the chances of it being found more than a tiny distance from where it is expected is vanishingly small. An electron may change its energy state by moving from one probability distribution to another. In so doing, it accepts or releases electromagnetic radiation. Only certain shifts are permitted, corresponding to the harmonics of a sphere, each shift associated with a change of a certain amount of energy. The energy of electromagnetic radiation is such that a shorter wavelength is associated with a higher frequency, just as a more massive particle is more closely confined in the region where it will probably be found. Heating a mass of a given element will result in energy being radiated as the electrons jump around. The wavelengths of this radiation will be characteristic for the element heated.
6. Einstein's general theory of relativity. A massive object will distort the dimensions of space around itself. This distortion is such than anything passing close to the object will be deflected from its course in a way that bends it toward the object. Furthermore, time will be distorted near a massive object. Time close to the object will pass slower than time at a distance. Thus light rising from the surface will arrive with a longer wavelength than light from an identical source placed so that light did not have to climb out of a gravity wall. This should not be surprising; since the light climbing cut of the well must use up some energy (though weightless, it has a weight equivalent), and its lower energy should be perceived as a longer (redder) wavelength.
7. Wheeler's black hole. If a gravity well is deep enough, that is, if enough matter is placed in a zone of finite size, then light can never escape from the zone. Time within such a black hole will no longer be continuous with time in the universe outside the black hole. And nothing ever, ever can escape.
8. Singularity in a black hole. Once a black hole is established, all the matter in it will rush to the canter, where it will be crushed by gravity to a geometric point called a singularity. How long this takes is ambiguous, since time is not continuous between the inside of the black hole and the outside.
9. Schwarzschild’s event horizon of Wheeler's black hole. Knowing the mass contained within a black hole, it is possible to calculate radius of a sphere that is the surface of the hole. Outside this radius, time is continuous with time in space around. Within the radius, the rules for a black hole hold. That radius is twice the geometric measure of the mass. (1 solar mass 1.47 km in geometric units.)
10. Weird black holes. If the matter that collected to form a black hole came in a shape radically different from that of a sphere: long and skinny, flat like a disk, electrically charged, spinning, magnetized, full of holes, already much distorted by a neighboring black hole, then nobody is sure exactly what would happen. Matter might be able to escape. Matter might even escape to a point in time that was "before" the matter went in, resulting in 2 copies of the matter existing at the same time. Thus in theory, time and space could get all scrambled up. But that is only in theory and the theory is not very satisfying, since the mathematics involved gets unmanageable.
11. Hawking’s self distructing black hole. If you had a very tiny black hole, say with a Schwarzschild radius smaller than that of an atomic nucleus, than there is a way for matter to get out without climbing out of the well. Particles could merely blunder out courtesy of quantum uncertainty. If the hole is in very empty space, the rate at which particles locate themselves outside of it by turning up in relatively unused portions of their probability distribution might exceed the rate at which matter fell in. If electrons escaped faster than positively charged matter, the black hole would end by erupting, the contained positive charge finally overwhelming the remaining gravitational field and the contents exploding back into the knowable universe.
12. Ambiguous holes. One of the characteristics of a black help is that it is not reversible. Things fall in but not out. If one looked at time in reverse, one might refer to a "white hole." I will simply use the word "hole" to mean an object like a black hole but without specifying a direction of time. This "hole" has the same mass, possible singularity, and Schwarzschild radius as a black hole but might be a black hole or white hole depending which direction you assume time to be moving.
13. Laws of thermodynamics. While energy can change form, it cannot be created or destroyed. Any change in the form or distribution of energy must result not in the energy becoming more concentrated, but in the energy in the entire system becoming more dispersed.
14. Hubble's red shift of distant galaxies. Stars are collected in great whorls called galaxies. Galaxies themselves lie in great clusters. Astronomical distances can be measured thus. First weigh two things. Now hang them side by side and see how much they tend to come closer to each other than they would be if they hung straight down. You have now weighed the earth. Now measure a month. Calculate how far away the moon must be. Now watch the moon carefully through the month as it approaches the sun and as it moves away from the sun. The difference in its speed is a measure of how fast an object dropped from here but not traveling in an orbit would take to fall into the sun. Measure a year. Now calculate the distance to the sun. Now photograph a nearby star. Photograph it six months later and see how much it has shifted against the stars behind it. Calculate the distance to that star. Measure the star's brightness, color, and any tendency to vary in intensity. Measure enough stars so that you can predict at least for some stars what their absolute brightness must be, knowing their color and rate of pulsation. Proceed in an analogous way with star clusters, with galaxies and with galaxy clusters. At last, measure the wavelength of light from distant galaxy clusters. You will find that light from the distant clusters has a longer wavelength than light from nearer ones. In fact, there is a regular progression; the farther away you go, the redder the light is. The explanation is that the distant galaxies are rushing away with a speed that is proportional to their distance. The change in wavelength is produced by the Doppler effect, the same thing that makes an airplane sound like it is screaming when it is coming and roaring when it is going, even though the engine is running at the same speed the whole time.
15. The Big Bang theory of the universe. If every star is rushing away from every other star at a rate exactly proportional to its distance, then there must have been a time when they were all in the same place. This time can be calculated to be 10 to 20 billion BC. If the universe really began as a big explosion, there must have been a big burst of energy around that time, and we ought to be able to detect it. In fact, such a universally distributed low energy radiation has been detected; it has the characteristic distribution of energy radiated by matter at about 2 to 4 degrees Kelvin. (That’s for an ideal radiator -- it isn't radiation characteristic for any particular element.) The energy comes to us from all directions with about equal intensity.
16. Grand unified field theories. There are some recognized problems with the big bang theory. For one thing, it doesn't explain why electrical forces and the nuclear binding forces are related the way they are. (Their relationship seems quite arbitrary.) For another thing, we seem to be blessedly spared a lot of awkward things called antimatter stars and magnetic monopoles that would be predicted from a big bang. In the third place, a system blowing up could have three obvious fates. It could fall back in on itself, like a tennis ball returns to earth (as predicted by Poe.) It could accelerate away on a hyperbolic course, as a cannonball fired from a cannon in deep space would speed on its way never being slowed down much by the gravity of the cannon itself, though it traveled for billions of years. Or, against all probability, it could expand right at the knife edge of these two possibilities. Alas, it is the third, least likely, kind of universe we find ourselves in. In an effort to restore sanity, the grand unified field theories propose an even bigger bang from which countless universes (I think they should say firmaments) condense like a kind of froth, some with more antimatter, some with a different electromagnetic force and so forth, so that we are only a single case among a multitude.
17. Neutrino deficit from the sun. Radioactive matter is matter containing unstable nuclei, that decay according to a probability pattern, such that for any kind of unstable nucleus, there is a characteristic time during which half of the nuclei will undergo change, releasing particles, few or many, and changing their internal arrangement. Some of the released particles have an extraordinary penetrating power, having a better than even chance of traversing planets without hitting anything. Of course these particles, neutrinos, are hard to detects and it was a long time finding them at all. The sun is generally believed to be a great hydrogen bomb, converting hydrogen to helium and emitting energy by reactions that have been well characterized. These reactions are known to produce neutrinos and the rate of expected production is known. The distance to the sun is known, so the number of neutrinos that should be coming from the sun can be calculated. Alas, less than half as many neutrinos are counted as ought to be. What's worse, not all those neutrinos that are counted are necessarily coming from the sun. I suppose some day they will mount a neutrino counting instrument on a space craft and go farther from the sun. It should then be possible to tell how many neutrinos really come from the sun, how many are a sort of cosmic background flux and how many come from the earth.
18. Plate tectonics. A child looking at a globe can easily see how North and South America could fit against Europe and Africa. Recently, even scientists have noticed this. The earth is now understood to be, not an inert ball of rock, or a ball of hot, semi-solid matter covered with inert rock, but a dynamic shifting collection of plates, that crash into each other, slide under each other, draw apart from each other, and generally jostle each other with volcanic activity marking their movements. Light plates rise to be continents; heavy plates sag to become seas. This motion of the plates is not envisioned to go back far all the history of the earth, but only to go back to about the age of the dinosaurs, when a huge land mass, earth's great and only continent, began to break up and disperse into her great and only sea. No one suggests why the change should have occurred.
19. Quasars (quasi stellar objects). Among the remarkable things known to astronomers are a class of objects that are much like stars, except that their light is so drastically red-shifted that it was a long time before the pattern of their light wave lengths was figured out. A red shift could be due to local motion (but all quasars are red shifted, none blue shifted), to great distance, or to the light, having come from a very dense object so that it is red shifted by general relativity effects. Someone has calculated that if the red shift of a quasar is due to gravity, the quasar must be about seventy miles away; this seems unlikely. That leaves great distance. But the distances are so great (ten billion light years and more) that the quasars must be very bright beacons, far outshining ordinary galaxies. Yet quasars may be seen to change their intensity over time periods of about a day or so. In order to coordinate that activity, quasars must cram the energy release of a galaxy into the space of a solar system. The quasar's structure is not well understood.
All these points are public property. If there are any that are not familiar to you, that you doubt, or do not understand, a trip to any major university, a quick chat with the reference librarian and then a search for a book or an article or two should put you in command of more about the subject than I ever knew. If you still doubt any of them, (except maybe the grand unified field theories, which are quite new and which I think no rational person should be required to adopt against his instincts anyway) welcome to the lunatic fringe. If you believe all these things and take truth seriously, stop reading now. Watch a sun rise. Befriend an enemy. Plant a tree. This is your last warning.
At any moment, time, for an object at rest relative to neighboring galaxies and far from a very massive body, may be defined as the apparent size of the universe as seen from that object. (The apparent size of the universe is defined thus: Measure enough distant objects to establish the relationship between the velocity with which they are traveling and their distance; the radius of the universe is the distance an object would have to be to be traveling at the speed of light.) Two observers at widely different locations can agree on the age of the universe that each sees, and thus they can agree quite reasonably on how late in reality it is. Further, if we leave an object, having determined when the object is, and return at some different time to the same object, we can again take measurements and find that the universe has a different apparent size. Thus we can tell not only whether we have arrived earlier or later, but how much time separates us from the other visit. Time, than, can be defined as the radius of the knowable universe or firmament, the universe of potentially visible stars.
Having thus defined time, it becomes at once apparent why energy tends to disperse; the firmament is dispersing. That these two invariable observations, an expanding universe and dispersing energy, proceed lock step, yoked for cons, suggests a mechanism coupling them.
The obvious mechanism is this. At a given size, the firmament is able to accommodate a SINGLE particle in any one of a fabulously large but finite number of locations. At a larger size of the firmament, that number of locations is greater. (Of course if the particle is a bit of electromagnetic radiation, say of the background radiation from the big bang, it will increase in size right along with the universe and does net have a larger number of locations; so I am not referring to electromagnetic radiation. Besides, they say that time does not exist for light, because travailing at the speed of light makes time slow to nothing.) At a given size, the firmament is able to accommodate ALL the particles it now holds in an epically larger but still finite number of arrangements. This last number is so large it could not be written down explicitly using all the matter in the firmament as ink and all of space as a scratch pad, since each legible number would but represent one arrangement, and when the number of legible numbers was exhausted, there would still remain all the illegible states of the firmament, like the present one. Yet it is a finite number. When the firmament increases in size, the number gets even bigger.
Although as the firmament enlarges, each electromagnetic wave enlarges proportionately (so that it always occupies the same fraction of all of space and so specifying its location takes no more or less information at one moment than it does at another). As the firmament enlarges every particle traveling less than the speed of light occupies a smaller fraction of the universe, and takes more information to specify just where that fraction is.
If at one moment, say on Wednesday, we make a complete catalogue of what the state of the firmament is, the location, velocity, charge, spin, stability, temperature and force relationships of every particle and bundle of energy (writing it all down somewhere else, so as net to complicate our job) we would be able, in theory, to reconstruct Wednesday from our notes. But we would not be able to construct Thursday. Mighty though our catalogue would be, it would contain insufficient information to describe Thursday, because on Thursday the firmament would be bigger, would need a bigger catalogue to describe it, and we have already exhausted the firmament on Wednesday in compiling our pitifully inadequate tabulation.
Energy is dispersed on Thursday because those forces that confined it on Wednesday leak that energy into a void that Wednesday could in no way have accounted for. The decay of unstable isotope which could only be predicted as a probability on Wednesday may be a matter of documented record by Thursday.
We generally have the feeling that there is a lot of space out there for things to expand into anyway. What need for an atomic bomb to wait for the firmament to expand? The bomb will force its own way. Perhaps. At least it will force its way into voids already opened as the firmament has enlarged. And yet the void of space is over advertised. The atom, understood to be mostly empty space, is the domain of electrical forces of tremendous magnitude. Try to compress a ball bearing between your fingers, not deform it, compress it. Not much empty space there.
And even the void between the galaxy clusters is filled with the cosmic background radiation, the visible light of stars, stray particles, the fringes of electromagnetic fields everywhere, the trailing edges of the probability distribution of particles galaxy clusters away and the general gravitational field of the firmament as a whole. Nothing is really empty in a universe in which there is at least one particle, whose location is a probability field that extends through all of space. There are many.
Let us distinguish between two kinds of curvature of space. The surface of the earth is curved. This curvature makes it impossible to conduct a survey in which the surface of the earth is divided into rectangles. The surveyor tries to divide as much of the area he is responsible for into rectangles as he can. But if the area is large and his measurements accurate, he is left with a lot of long thin triangles where his rectangles did not quite match. On a plane, the sum of the angles of a triangle add up to 180 degrees. Start going east. Turn northwest, so that your new path makes a 45 degree angle with your first path. Turn south, making another 45 degree angle, and you meet your original line at right angles, making a 90 degree angle. The sum is 180 degrees. But now start on the surface of the earth at the equator. Go east one quarter of the way around the world. Turn north, making a 90 degree angle. Go to the north pole. Turn left, making another 90 degree angle. Arrive at your starting point for another 90 degree angle and you have a total of 270 degrees. The surface of the earth is thus positively curved. Try a similar measurement on the seat of a saddle, and you might find you had less than 180 degrees. The saddle is negatively curved. In this sense, space (or space-time) is flat. That has something to do with the fact that its rate of expansion is just on the knife edge between an expected collapse and unlimited expansion.
On the other hand, general relativity describes space as being distorted near a mass. This distortion is expressed as the force of gravity. Gravity reaches a long way. The distortion, the curvature, produced in space by all knowable matter averaged out over the entire firmament must produce some general uniform curvature of space even in regions devoid of much local matter.
This background curvature changes, of course, diminishing as the firmament increases in size, but keeps the same content of matter (plus energy plus information).
Thus a clock ticking in a bank vault has no trouble keeping pace with the expansion of the universe at large. It can deduce what is happening out there by local effects in here. Thus an unstable nucleus need not investigate the positions of far off stars to know when it can decay; the nucleus senses the gradual slipping of the bonds that hold it by the local change in the background curvature. The only odd thing in this is that most of the time the cosmic effect quite dwarfs local effects. We should expect clocks to run backwards in a descending elevator. They do not; the firmament is very large, very massive and moving very fast.
To review, time is the size of the firmament. As time proceeds, the firmament expands, there is an increase in the number of possible states of the universe. The effects of time: the tendency of energy to disperse, nuclei to decay, measurements of subatomic particles to be uncertain and Hawking black holes to explode are all due to the fact that the larger state of the firmament cannot be completely determined by the smaller state. A possible mechanism for transferring information about the size of the firmament throughout space is the gradual change in the curvature of space.
On the other hand, the past is quite determined. There is ample, nay redundant, information on Wednesday for specifying the state of the firmament on Tuesday. The classical picture of a particle reacting in a cloud chamber or film pack, generally shows one line coming in to a point and several lines radiating out from it; any two of the radiating lines are sufficient to locate the paint of collision or decay, while the incoming line is not. At any given size, the firmament completely and uniquely defines all states of the firmament that are smaller. As one moves from Wednesday to Tuesday, energy levels must pile up, and the pattern by which they do so may be predicted by absolute law. It is no trouble deciding when a nuclear reaction is going to happen if it is going to happen in the past.
To be sure, there is a problem here. With classical quantum mechanics, the past remains at least slightly ambiguous. Specifically, light is neither a particle nor a wave until it is observed. Then it may be one or the other but not both at once; it has not committed itself on what it started out as until it is observed, even if there is a long space between. I hope to avoid this paradox by saying that at the moment at which we stop the universe to do the inventory, all light, now that it has been observed, is either particle or wave. All the ambiguities have been resolved and under those conditions, the past (that is to say all times when the firmament was smaller) is determined and unalterable.
Having now got away from defining time subjectively or by use of one of its effects, we see that time is reversible. An outside observer might perceive our firmament as getting larger or smaller, and it would be much the same to us. We would still perceive an uncertain, relatively free future in the direction of the larger firmament, and a reassuringly fixed past in the direction of the smaller. We would even perceive a red shift associated with distant galaxies as they rushed toward us. The red shift would mean that the light was redder when it was in our instrument (would have a longer wavelength) than the same light when it was part of the shift of an electron's energy level in the galaxy in question. In the collapsing universe, the light would actually be outward bound and its red appearance here would just fit it to match what was needed there. How would it know were it was going? It would be in an absolutely determined firmament, in which every change of everything is fixed by law. A particle would "know" what it needed to know in order for energy levels to be systematically built up precisely because in such a firmament information is redundant. Information is the first thing to become overcrowded.
For the most part, we would be unable to tell which way the firmament was really changing. But under certain circumstances, we might indeed be able to tell if the firmament were enlarging or shrinking.
In order to decide how to tell which way the firmament is developing, let us imagine constructing a collapsing firmament. Such a construction would be a major engineering challenge, but it would be easy in concept. Simply locate a comfortable zone relatively empty space a few billion light years across. A little dirt, say some millions of galaxy clusters, would not present much of a problem, but you should exclude any weird black holes. Now scatter a lot of ordinary matter around, fairly uniformly distributed. Don't set the thing spinning much, or add a lot of anti-matter or electrical charge. Now stand back while mutual gravity pulls this floating junk yard closer together. At some point (and if you have built on a heroic scale, long before the matter you have scattered is in close contact, indeed while the pieces are far separated) an event horizon will develop. You will have created a black hole. The Schwarzschild radius of the black hole will already be very large when it first develops, and that radius will enlarge rapidly until it encloses all the matter you have placed. Do not let it enclose you too.
You are outside of the black hole you have created. It is a well behaved, that is a not-weird, black hole, and nothing can escape from it. Energy cannot escape as energy, as information or as matter. Still, there are some things we can reasonably suppose are going on in that black hole, even though we cannot be witness. First, at the initiation of the event horizon, the contents cease to be in continuity in space and time with the space we are in, and this change is abrupt. Second, all the contents of the black hole will rush to the center of gravity to produce a singularity -- a point of no finite size that still contains all the mass and other forms of energy that were initially present.
Third, along the way, things get more and more crowded, mass, energy and information piling up in a smaller space. Fourth, we may expect that prior to the final singularity, any number of subordinate black holes may develop as more crowded areas coalesce. At the end, there may be little or no ordinary matter, but only black hales devouring each other and sucking up any stray rags of energy not yet trapped. Fifth, and mast importantly, we would not expect to see any white holes. We do not expect to see any holes acting as fountains of energy. What goes in, whether into the Schwarzschild radius itself, into the final singularity or into any subordinate hole, goes in to stay, at least from our perspective outside.
Now here is my major point.
I propose that the Big Bang theory of the universe runs into its greatest difficulty because if the matter of the universe were collected into a small area, that area would be a black hole and nothing could get out of it. Such a primitive nugget could not expand. Since it could not expand, it did not expand. We cannot have come from a big bang.
Let me say that again. The concept of the universe expanding from a primordial nugget that was much smaller than it is now (say a hundred or a thousand times smaller) is in absolute contradiction with the theory of general relativity, which would require such a nugget to be a black hole, from which nothing could escape.
It does no good to say that for a long time after the big bang the firmament was all energy; energy and matter are forms of the same thing. Energy is subject to gravity and makes its own contribution to gravity.
It does no good to say that there were arbitrarily large energies at work pushing the firmament outward; the more energy in the system, the greater the mass, the deeper the hole.
It does no good to say that it was not force that caused the firmament to expand, but a progressive change in its curvature; the curvature of space is purely a reflection of the presence and distribution of mass.
It does no good to say that some black holes are weird and may spew their contents back out; our firmament is not charged, spinning or misshapen enough to be weird.
It does no good to refer to the grand unified field theories and say that there are any number of other firmaments adjacent to our own, pulling us outward by their gravity; the grand unified field theories also start with a big bang, only a much bigger one, which would in turn have been a much deeper hole.
It does no good to say that this is a question about something that happened in the first few seconds of time, when everything had a rather mythical quality anyway; enough matter has already been found in the firmament of stars to build a black hole some billions of light years across. If we escaped from a black hole, we did it since about the time the earth was formed. There is reason to believe that there is enough missing matter firmament to indicate we are in a black hole still.
If black holes are possible, our firmament could not have started with a big bang.
So to review again, time is the size of the firmament. Whether that firmament is getting larger or smaller would generally not be detectable by us day-to-day, since in either case, we would interpret the direction of the larger firmament as our future. The firmament cannot be enlarging because it would have to climb out of a black hole to do so. Therefore, the firmament is collapsing.
This is my second point. The firmament is collapsing into a singularity that it will reach around 15 billion years BC, which happens to be far in the future.
Me are now ready to discuss how we can tell if the firmament is getting bigger or smaller; there are three circumstances, ether than simple arguments from consistency, where we might be able to tell the difference.
If we were outside the firmament, we might be able to tell what was happening. But we are not outside.
If we waited until the firmament expanded another hundred billion years and nothing different had happened, we could safely conclude that it really was expanding, since there seems to be no way to hide enough mass in the visible firmament to make a black hole that big. But a hundred billion years is a long time to wait. (On the other hand, if in the near future, we suddenly find ourselves in continuity with the universe at large, if our Schwarzschild radius goes to zero and our event horizon disappears, then we will know that the firmament really was collapsing, but we will have failed to solve the puzzle in the time allowed.) However, if we could find a subordinate hole, we might be able to tell without waiting for the firmament to end.
Remember the fifth, and most important point of a collapsing firmament as described from the outside. It is not permissible to have a hole spewing out energy and matter, since we put nothing into that firmament but ordinary matter. Since an outside observer cannot see anything jumping OUT of a black hole, an inside observer (for whom time runs backwards, since he will always choose to call the larger state of his firmament the future) cannot see anything falling INTO a black hole. That is to say we cannot go from Wednesday small firmament, object outside of black hole to Thursday larger firmament object in black hole. That would be perceived by an outside observer of a collapsing firmament as a black hole spewing out matter. That is not permitted.
Therefore, find one black hole, see one thing fall onto it, and you have categorically disproved my shrinking firmament.
On the other hand, find a large number of holes that are indeed acting as sources of energy and matter, and you have given strong support to my idea. Where might we find such objects?
One obvious candidate would be the quasar. Quasars have stupendous power outputs and thus must be objects of great mass; yet they act as if they were relatively small. The common wisdom firmament would predict that an object so massive and so small should be a black hole, absorbing but not emitting energy. But there is no particular limit on how much energy can be dumped into a black hole of sufficient size, so in a reverse time firmament there is no limit to how much can come out of a hole. (Nor is there a limit on WHAT can come out. Remember that information and matter are forms of energy. A black hole can swallow energy in any form. So think of the hole in reverse time, not as a source of pure light, but more like a cornucopia, giving out an unlimited variety as well a great quantity. Like the cornucopia, such a hole is in danger of being buried in its own bounty.) But quasars are things of long ago and far away; at present, the feckless firmament offers us none convenient for study.
At the other end of the size scale, the Hawking black holes have been predicted to behave much like reverse holes. The difference is that with a Hawking black hole, there is always a chance that matter may fall back into the Schwartzchild radius. With a hole seen in reverse time, there is no such chance; anything thrust out stays out. A close study of small black holes would be very useful. Alas, none have been found.
I understand that at the center of the Milky Way galaxy, there is a quasar-like, black-hole-like object of great density and power output. (A black hole can emit radiation not from within its Schwarzschild radius, but from the acceleration of nearby matter.) Whether the object is a hole will be determined by measurements of its density and size. Whether it is a black hole will have to be determined by watching an object fall in, either by detecting a decaying orbit or seeing some radiation source suddenly become red-shifted as it falls. If either happens, this theory must be discarded. This leaves the one most obvious feature of the firmament of stars – the stars themselves.
As we examine the star closest at hand, the sun, we notice a problem. Consideration of the composition of the sun and the energy output requires us to believe that the sun is a huge hydrogen bomb. It must be producing its energy by the reaction of hydrogen to produce helium. To do so, it must be producing neutrinos at a certain rate, and we should be able to detect them. We do not detect enough neutrinos. One possible source of power for the sun would be that the sun contains a hole that is putting out energy, matter and information. Some of the matter put out drifts away as "solar wind," the force that blows tails of comets outwards. Much of the matter put out simply stays packed in a mass around the hole. As seen in reverse time, this packing is like material packed in a funnel, waiting for its chance to squeeze through the orifice.
Another odd thing about the sun is that it seems to be stable over billions of years. A self perpetuating process like an explosion should not be stable. There are well developed descriptions of how stars change, grow and develop, of their fuel use, structure and energy outputs. All are rather unsatisfying because there is no regulator to keep a star from developing a runaway reaction and exploding as soon as it could produce energy. But if the sun contains a hole where the firmament is packing away matter and energy that there is no longer room for, then that packing should proceed at a steady pace, just as the need proceeds at a steady pace.
If the material coming out of a hole at the center of the sun is not pure energy, but a mix of whatever might be stuffed down a black hole, we should not be surprised to see the surface of the sun troubled as things well up from inside. Indeed, while the sun seems to be quite still and tranquil as seen by visible light, pictures of the sun taken by x-ray, that can penetrate the luminous gaseous coat of the sun, show the sun to be restless indeed, with great disturbances continually appearing, for all the world like fruit pouring out of a cornucopia.
There is another odd thing about the sun. Certain measurements suggest that the surface of the sun is hotter than the interior. It is proposed that shock waves from inside come up and warm the surface making it hotter than the interior. Whatever the mechanism for heating the surface of the sun, only a tremendous power source can keep the interior from rising to the temperature of the surface; anything in an oven will rise to the temperature of the oven unless some process can pump the heat away. But suppose that the matter entering the sun through its hole is not hot. Just because matter, information and energy are coming out does not mean everything must be at thousands of degrees. Indeed, for some things to be highly ordered, they cannot be too hot. To be sure, we will never know what the material looks like the moment it comes out; the long trip out through the sun will crush it and heat it to ions. But a steady outward flow of initially cool material could account for finding temperatures deep in the sun lower than the temperature of the surface.
There are two measurements we might make on the sun to detect a hole deep within in. In the first place, if we had a neutrino detector on a space craft, inconvenient, as they consist mostly of vast reservoirs of extremely pure water, and if we had a source of neutrinos, awkward, since its unavoidable power output would rival the sun, we could try shooting neutrinos through the sun and see what happened. A hole would scatter neutrinos that came close to it. Nothing else would scatter them quite so much.
A second measurement, also quite inconvenient, would be simply to measure the size of the sun. If its diameter is increasing without a change in temperature or power output, it would be consistent with a hole putting out material from within. Covey the presence of the solar wind, even seeing it not shrink might be evidence enough. Unfortunately, such measurements would have to be very very precise. We expect the suns expansion to more or less parallel that of the universe. Since the sun has no solid solographical features to measure from, no place to stand on and is too hot to drag a surveyor’s chain across, it does not seem likely that we could measure its size down to fractions of an inch.
We might apply the same measurements to the earth more conveniently. Of course the sun, being bigger and more luminous, is a better candidate, but let us consider the earth.
First, the earth seems to get warmer as you go farther down; this is as would be expected. If the point were arrived at where the earth became cooler as you went down, we would have evidence for a source of cool matter within.
Second, consider shining a beam of neutrinos through the earth. We have a source, the sun. (Of course, it would be a good plan to send a neutrino counter far from the sun to be sure how bright a source the sun is; many of those neutrinos we do count may be coming from outside the solar system or from within the earth.) Since the earth rotates, it would not even be necessary to move the instrument we had on earth, provided it were built in the tropics. The trick would be to compare neutrinos arriving when the sun was on the opposite side of the earth from our instrument with the number arriving when the sun was on the same side and at right angles. It just might be possible to tell whether a hole at the earth's center was scattering the sun's neutrinos.
In order to predict the absolute size of the shadow cast by such a hole, some assumptions have to be made.
1) The size of the shadow is related to the Schwarzschild radius of the hole, which is proportional to the mass still in the hole.
2) The rate at which matter enters some particular hole (or comes out of it using normal time sensing) is constant or proportional to the area of the event horizon (the surface that is at the distance of the Schwarzschild radius from the center).
3) As the firmament collapses (in reverse time sensing) all subordinate holes develop at the instant the great event horizon of the firmament is established and all arrive at the final singularity simultaneously.
4) A moment must be assumed when the firmament "started" in reverse time, which is as much as to say when it will "end" using our ordinary sense of time. That will be the moment when great event horizon vanishes, we are in continuity with space at large and space and time cease to move in an orderly way.
Most of the assumptions are not intuitively appealing, and the list one looks like it should be quite arbitrary. On the other hand, given the first three assumptions and the size of it becomes possible to calculate when the firmament will end, in case you are interested. Root for a big shadow; that will mean a long time.
Finally, consider the size of the earth. Perhaps the earth is steadily growing from within. The rate at which Europe and America are drifting apart on their respective tectonic plates is just about in the same proportion to their distance as the drift of distant galaxy clusters. One of the puzzles of plate tectonics is that the continental plates, which are lighter than ocean plates, do not cover the earth. Presumably the light matter is matter that floated to the top just before hardening to form the earth's crust. Why is their area not as great as the surface of the earth?
Possibly they have been eaten up at subduction zones, dragged under and dissolved where continents collide. On the other hand, possibly their area is the same as the area of the earth's surface at the time at which they hardened. They have broken up and drifted apart, deep ocean clefts have formed and, as the curvature of the earth has decreased, mountain ranges have buckled up. Tectonics experts have constructed a hypothetical original continent; I wonder what luck they would have in fitting the plates together on a smaller ball.
Another test could be made. The earth has plenty of solid features, and you can drag a surveyor's chain across it. (Although I understand that the best measurements are made using lasers and satellites.) The earth is about 1.5 billion inches around and the firmament (known universe) is about 15 billion years old. If the size of the earth can be measured to a fraction on an inch, it should be possible in ten years to tell if the earth is expanding at the same rate as the firmament. Rather than surveying the whole earth, the same information might be gained just by measuring movement at enough geological fault lines.
There you have the preposterous theory of time and the universe. All it supposes is that we have been wrong about which direction time is moving.
It can be disproved by showing a single black hole into which an identified object actually falls.
It can be strongly supported by discovering a hole out of which matter seems to arise.
It has the disadvantage of demanding a profound change in thinking in return for little advantage.
It has the second disadvantage of making us, as seen from outside the firmament, to be inflexible automatons, ignorant of our past, doomed to a future we know, fated to end crushed at the bottom of a singularity, forever beyond the ken of the universe at large, our futile and mechanical existence at an end.
Don't look at it like that.
Advantages of taking time to be running in reverse are:
Booty
Editor's Note:
WILD SURMISE is an occasional newsletter on speculative matter. In coming issues, expect articles on 1) indoctrination 2) relativity 3) love. The bad news is that last month Booty said that of ten million Americans who fought in Vietnam, a million returned alive only to die months to a very few years after getting back. That statement, alas, stands unchallenged. Booty has promised to make some remarks on what might have happened to them in his piece on indoctrination next month.
We were wondering how much the envelopes weighed, so M lifted a box of 500 and said they felt like a 37 lb. dumbbell and thought Booty could calculate the weight of each envelope from that. Booty said he couldn't do it unless he knew how much the box weighed, so M is now looking for five hundred boxes to lift.
Obviously we are all staying anonymous around here.
Ed
Ó copyright July, 1985, WILD SURMISE
MILD SURPRISE
Years after the troop disbanded officially, we remained friends, most of a couple patrols, anyway. We'd meet after school and sometimes even go out to the old camp on the lake and pitch our old tents. Old enough by then to go without a scoutmaster.
The lake was "bottomless," that much we agreed on, but nobody was sure whether that meant it went right through to China, whether it was so muddy that water blended imperceptibly into quagmire or whether nobody had ever bothered to sound it. But the water was clean and cold.
One muggy night I slipped away from the bonfire, where the others were laughing and singing the old songs and made my way down to the water for a long quiet swim in the starlight. After a while, when I glanced back toward the camp, I could see three or four of my friends also leave the fire and go down to the waters edge where they crouched together.
They were telling ghost stories. No mistaking it. The hunched shoulders, the furtive gestures. It was a clear cut ghost story session. I went on with my swimming. Then the thought struck ale; I would play THE MONSTER RISES FROM THE DEPTHS on them. I would swim up underwater to the shore and then suddenly stand up and give them by best roar. Should put the fear into them good and proper.
Stealthily I swam toward the unsuspecting group. When I thought I was in range I gently submerged and started toward them. I would have been humming the shark attack theme from Jaws, but the movie hadn't come out yet. (Now Booty tells me it’s the poker theme from La Fanciulla; see what I have to put up with?) After a time, I ran out of air and since I hadn't reached the shore I knew I wasn’t going to make it without coming up at least once. I angled up gently hoping to just break the surface enough to get my air and not enough to let them know what was up. No surface.
OK, no surface, I'd have to go looking for it. I forgot about stealth and arched up steeply swimming with swift hard stokes. Still no air. Well it's up there somewhere, we're just deeper than we thought. Up. Up. Oof!
At first I thought I had come up in a cave, because I had crashed solidly into the mud. Freezing I settled onto what I now realized was a steeply sloping bottom. All right. If that way is down, then this way must be up.
After what seemed like a long time, I broke the surface like a jumping fish and a few minutes later came splashing ashore.
"Hi!" All you wonderful living people. "Good evening." Boy am I glad to see you guys again. "How yu doin'?"
"Shut up, M," they said. "We're telling ghost stories.
M