In general a universe cannot be isotropic and not homogeneous, BUT it can APPEAR isotropic from a central location and not be homogeneous. If the grapes in the above example are lined up (say in a uniform cubic mesh) then the Jello is not isotropic because the lines of grapes select specific directions (along the grapes versus diagonal); like bishops versus rooks in chess. But if the Jello and grapes have the same properties everywhere then it is homogeneous. One location in the grape Jello is pretty much like another location when considered on a scale that is big enough to include a representative sample of grapes and Jello.
We don't simply assert the cosmological principle so that we can understand the universe; the cosmological principle is consistent with how the universe is observed to be. This in turn implies that the universe is understandable. Einstein is said to have remarked that the hardest thing to understand about the universe is that it is understandable. I suppose it is possible that we are totally deluded in thinking that the universe is understandable, but I don't know how we would ever be able to appreciate that if it is so.
No one would deny that cosmological principles and religion were compatible in the middle ages! That's sort of what got Galileo in trouble later; he was messing with that compatibility. Cosmological principles try to describe the universe is it physically is. The Earth is physically a sphere, and it orbits around the Sun. The stars are distant objects similar to the sun. In the 18th century the rise of deism (a religious movement asserting the creation of natural law to the Creator, but denying active interference with those laws) was an attempt to reconcile religion with developing scientific thought. Trouble comes when religion is tied to concepts that are demonstrably false. (Flat Earth worshipers are never going to be compatible with modern science.) To the extent that religion deals with the spiritual and the transcendent there will (by definition) be no overlap and hence no conflict. However, this represents a significant retreat from the domain that religion once occupied human society. For more on this point of view, see Steven Weinberg's book Dreams of a Final Theory.
Although it is sometimes popular to believe that the Big Bang necessitates the existence of a creator, this seems to me to be an error in logic. If you wish to argue that the fact of existence necessarily implies the existence of a creator, then you don't need a big bang specifically. A steady state, infinitely old universe would equally imply the existence of a creator (by virtue of it existing). The creator must necessarily be transcendent of space and time and could (presumably) create a big bang universe, or a steady state universe, or whatever, in keeping with the creator's inscrutable will.
Discussions of events in the time of quantum gravity are highly speculative, and at this point they probably don't deserve to be called theory. Generally this sort of question is approached by considering whether the laws of physics, either as we understand them, or as we may someday understand them (e.g. what a quantum gravity theory might be like), permit things like multiply connected universes, wormholes, ``chaotic inflation,'' etc. This would change what we mean by t=0, since what we think of as t=0 would be equated with the beginning of only our little subset of the universe. How time and space might be defined in the larger metauniverse, I don't know. Would these ideas be testable? First ask would a theory of quantum gravity be testable? If it were, and something in that theory required these multiple universes to exist, then maybe we would regard it all as testable. It is hoped that that might be the case, but at this point we don't have a quantum gravity theory, so who knows?
Possibly there is some sort of metatime and metaspace that are higher dimensional and out of which our little ol' universe formed. The chaotic inflation models have this sort of feel. But then you will ask, "What happened before this metaspace was created?" Or "How did this metaspace come into being?" How does one avoid an infinite regression without simply invoking a "first cause" or something similar?
Remember first that we are dealing with the two dimensional surface of the cylinder. Homogeneity means that every point on the surface of the cylinder is like any other point. If the cylinder is infinite then this is true. No point will be different from any other point. The cylinder is not isotropic, however. In one direction it is circular, and in the other linear. So if you set off walking in one direction you return to where you start, but walking in the other direction you go on forever.
If the question of what was before the creation of the universe is not scientifically valid, what about asking "What happens afterward?" Can time and space be destroyed if they have been created?
The big crunch would reverse whatever happened in the big bang, so presumably time and space could be destroyed. If there is a big crunch and time and space cease to exist, you can't ask what happens next, because there is no next without time.
A cube is made up of squares and has 3 dimensions. Is there an object made of cubes in 4 dimensions? Is there a fourth dimension other than time?
8 cubes put together in four dimensions is a hypercube. It has some interesting properties. Mathematically speaking there can be arbitrary numbers of space dimensions and geometric shapes in those dimensions. It just so happens that we seem to live in a universe that has 3 space dimensions and one time dimension, but you can create mathematics for all sorts of multidimensional things.
Does the failure of the perfect cosmological principle have a consequence for the nature of time?
It means that time doesn't have to be infinite. A more subtle question is whether the fact that the universe evolves (and the arrow of time, i.e., the sense of it evolving forward in time) tells us something fundamental about the nature of the universe and physical theory.
The PCP posits that the universe always looks pretty much the same at any time in its infinite history. The cosmic microwave background is light coming to us from a time in the past when the universe was hot and dense, and hence much much different from the way it is today. This and other evidence shows that the universe is evolving and changing as time proceeds.
The Copernican model with Keplerian ellipses simply fit the observations better. That was sufficiently compelling for most scientists. The first direct observation of the explicit motion of the Earth in its orbit was the detection of the aberration of starlight.
We say there is no center to the universe but there is a t=0 point in time. How can there be a starting time but no starting place?
The "starting place" was everywhere. Turn it around: How can we say there was a starting time if everything didn't start at that time?
The following is going to be my speculation on the subject. The way humans perceive time seems to be dependent on how we create and store memories. Some of this involves language (or related symbology), and some does not. We are aware of the immediate passage of time at a emotional, sensual, and experiential level, as well as a rational level. Animals presumably have a similar experience, only with little or none of the rational component (depending on the animal). Humans remember the past and are able to relate events in the past to those in the present through language structures, as well as through emotional ones. Contrast remembering a passage from a book that relates to what you are currently experiencing, with the sudden rush of memory that might come from the sudden smell of bread baking in the oven. I would guess that much of our perception of advancing time is on the rational level; it is hard to remember exactly what time a memory that rises unbidden is associated with. You smell bread, and you become happy with some vague memory, and only later do you realize it corresponds to a particular visit to your grandmother's house. Animals must experience time passage at least at this vague emotional level, but probably don't have a way to make those memories ordered, and hence don't perceive time passage in quite the same way we do.
Do you think it would be ever possible to come up with a theory of everything" that explains the entire history and future of the universe and answers all unanswered questions? How can a product of the universe (humans) be capable of understanding that which created it?
There are several issues here, all of which are hotly debated. First, is it possible to come up with a "theory of everything" which describes all the basic interactions, unifies all the forces, and explains the reason why the constants of nature have the values they do? Possibly. That at least is the aim of much of modern physics research. This is discussed in Steven Weinberg's book Dreams of a Final Theory. Note, however, that even with such a theory things are too detailed for a complete description (e.g. we understand fluid mechanics and nuclear reactions pretty well, but there are details of the sun that have so far proven too complex to sort out.)
Now, another question is, is it possible, even in principle, for something (us) that is part of the universe to conceive of a complete model of the universe, including itself. A complete model must contain even the model. (Can the human brain ever understand the human brain? to take a simpler example.) Feel free to debate this point. It seems to me that we are so far from hitting such a practical limit (if it exists) as to make the question unimportant from a scientific point of view. We have made tremendous progress in understanding the cosmos so far, so why not just continue exploring rather than worry whether or not we will ever (or can ever) reach the end?
Is it wrong to assume that if the cosmological principle is true that there must be other life in the universe?
No, in fact the cosmological principle would tend to imply that other life in the universe does exist; otherwise the Earth would be quite unique in a significant way. However, this doesn't mean that other life, especially intelligent life, has to exist in the Milky Way. Any particular galaxy can be unique in any number of ways. The cosmological principle would just suggest that life ought to be distributed relatively uniformly throughout the universe. The nearest civilization might be somewhere in the Virgo Cluster without violating the principle at all. And it is also possible that life is unique to Earth; the cosmological principle is a guide and an axiom, not a proven assertion.
There really isn't any hard information to determine this. By virtue of the Copernican Principle we would assume that ours is not the only planet in the cosmos that contains beings contemplating the meaning of the cosmos. But there are just too many unknowns. The standard procedure for estimating life bearing planets is described in this web page on The Drake Equation.
What about this recent claim by radio astronomers of evidence for an anisotropy in the universe?
All claims that appear to violate well-established scientific knowledge must be evaluated very carefully. The observations must be replicated by others, and the result must be verified. This criterion applies to all fields of science, not just astronomy. Occasionally a sensational result turns out to be correct, and science gains important new knowledge, but the usual outcome is that somebody was mistaken.
In this case, that seems to be what happened.
What one feels is acceleration. In fact you are experiencing acceleration right now due to the Earth's gravitational field. You are feeling one g of acceleration (32 ft/sec2). Now let's consider the acceleration felt by going around in a circle on the Earth. At the equator you would move 1000 mph due to the rotation of the Earth. In 12 hours you would be going the opposite direction at that same speed so the acceleration is 2000 miles per hour per 12 hours, or 166 miles per hour squared. There are 3600 sec/hour and 5280 feet per second so this is 0.068 ft/sec2. Not very significant compared to g.
Copyright © 2003 John F. Hawley