eh

Let's try to imagine our universe eventually coming to it's death. Imagine there is enough mass in the universe to reverse the expansion, and also imagine that the big crunch will in fact occur. For the sake of the conversation, let's imagine that when the universe reaches zero volume, everything literally vanishes. The universe is dead, and time has ceased to be.

First, we picture the galaxies getting closer and closer. They begin to 'crunch' together, and form a massive fireball. Now this fireball starts to shrink. It gets smaller and smaller, until it's the size of a basketball. It continues to shrink. Now it's the size of a baseball, then a marble.

It continues to shrink even still, becoming the size of a grain of salt, an atom, and even smaller. Then, when it reaches it's smallest possible size, it's game over. Time stops. The volume of the universe is zero. In fact, nothing exists anymore.

This seems easy enough to imagine. But if we can say that the universe has ceased to exist, and time has ceased, at what point do we say nothing exists? In other words, if we let the number 1 represent the lowest state the universe can get before coming to and end, what exactly is the transition between one and zero?

1 (let's say the last second or so of existence)is clearly the last state of existence before the end. Time should come to an end after that. Easy enough. But wait. If time only exists while the universe exists, then there cannot be an 'after' the end of the universe.

But if this is the case, how do we make the jump from 1, to 0? If we can never go lower than 1. or whatever minimum state you want to define, how can the universe ever fail to exist?

Bill

The plethora of infinities contemplated by Einstein's Theory of Relativity as he "wound the clock back towards zero" caused every physicist worth his salt to believe that there had to be something more that would prevent such a state (with a plethora of infinities) from every actually being reached. The exact same argument exists with respect to your "end of the universe" scenario. If the universe contains anything at all (and the Heisenburg Uncertainty Principle seems to mandate that the universe MUST contain SOMETHING), then the "size = 0" state can never be reached in actuality.

Stephen Hawking's later writings seem to rest on an idea of a cyclical universe that reaches some minimum size and then generates another "Big Bang" in some way. The theory would seem to be that the huge force of the implosion of the entire universe would generate the energy needed to start the next "bang" cycle. Hawking sees the "Big Bang" as a limit beyond which no previously existing state of affairs can have any current meaning. The "Big Bang" is the ultimate universal version of a Waring Blender on Puree. All that comes out is distinctly energetic quanta.

And again, later theories do not depend upon the universe having some minimum amount of mass in order to reach the "recycle" state of collapse. In the "heat death" scenario, the universe expands to a state of total "false vacuum" (where only the Heisenburg Uncertainty Principle causes anything to exist within the universe). The collapse happens at that point because the fully expanded universe stops responding to the outward pressure of expanding matter (the hypothetical cause of the increasing accelleration that we think we might be observing at present) and, due to the huge quantity of built-up "potential energy," a rapid collapse back towards zero size becomes inevitible.

However, it cannot reach zero size. But collapsing from the huge size of the fully-expanded universe, a lot of "random quanta" will be swept up in the path of the collapsing "event horizon" such that, by the time the whole thing is collapsed down towards your "T = 1" state, there is enough energy stored up to account for the soon-to-be-released "Big Bang" of the next cycle.

=====

In any case, your stated conditions are just a modern version of Zeno's Paradox, and that, in turn, is about all we get from a Christian's employment of the Muslim "Kalam" argument for the existence of God: another Zeno's Paradox.

Calculus provides the solution to Zeno's Paradox. We know, somewhat intuitively, that Zeno's Paradox always does resolve in favor of the event in question actually occurring. Calculus can provide the mathmatical model to ascertain exactly when that state of affairs will pertain. Your postulate about "T = 0" time for a collapsing universe is no different. Given that the universe will not actually collapse to zero size and/or "disappear," all we are legitimately concerned with is when it will reach its minimum size and begin to expand ("Big Bang") again. That is a soluable problem using readily-available mathmatical techniques.

== Bill

tronvillain

Bill:
Are Steven Hawkings "later writings" from after A Brief History of Time? It's just that I didn't get that sort of impression at all from that particular bit of writing.

John Page

Bill:

Doesn't calculus rely on the assumption that you've sliced reality up into sufficiently small chunks?

My understanding of calculus (and I could be completely wrong) is that it provides an approximation. Let's say you have a nice equation that predicts the behavior of time/matter at the super-quantum level but there is a discontinuity at quantum/sub quantum levels.

A historical precedent could be the discovery of atomic energy which wouldn't be detected by using calculus on "conventional" thermodynamic formulae.

Just curious, especially with the increased popularity of Zeno (after Heisenberg, was it).

Pleasure to see your erudite posts again. Cheers, John

Bill

No. I would call that his "earlier writings" (for mass consumption, anyway).

I was referring to <a href="http://www.secweb.org/bookstore/bookdetail.asp?BookID=848" target="_blank">The Theory of Everything: The Origin and Fate of the Universe</a> in specific because I've just finished reading it. But that book is just a transcript of some older lectures from Cambridge, so I believe he has written more or less the same comments elsewhere too.

== Bill

Bill

John: Its been over three decades since I took calculus in high school and college. I haven't used it since, so to say that I'm a bit rusty on the finer points of theory would be a gross understatement.

But it is my clear recollection that calculus provided as exact of an answer as you could ever hope to obtain. The reason for this is that you are measuring "the limit" that is approached as you slice reality up into more and more chunks, approaching an infinity of chunks that are virtually zero in size.

And certainly, calculus does recognize the idea of a discontinuity in any given calculation. That sort of discontinuity can be called (ta-da) a "singularity." The "singularity" of the relativistic Big Bang model is just such a discontinuity. It is a place where infinity appears in the numerator or denominator (or both) of various division problems, thereby negating the reality of the resulting answer. The "singularity" can also be viewed as a "limit" in the classical sense of calculus.

The breakthrough occurred with quantum mechanics because quantum mechanics set a lower boundary on the size of the chunks into which reality could be divided. This, of course, "breaks the mold" of classical calculus calculations. However, quantum mechanics introduces its own set of weirdnesses to the "solution" of what might have actually happened when the "Big Bang" occurred.

The real bottom line here is that we don't really know, and we probably won't have anything more than just speculation until we can solve the riddle of quantum gravity.

== Bill

tronvillain

Bill:
I think you meant "Yes" rather than "No.", but I get the idea.

strubenuff

Perhaps M-theory hold the answer...there are no 0's and no infinities in its equations. I'm aware it's a highly speculative theory, but it's a possible solution to the apparent contradictions in logic.

Afghan

Didn't Stephen Hawking say somewhere, in fact, I think, in A Brief History, that arguing about what happened before the beginning of the universe was like arguing about what was north of the North Pole. Presumably, something similar happens at the end of a closed universe. The universe gets smaller and smaller as you get closer and closer to the end just as circles of latitude get smaller and smaller as you get closer to the pole. But there is no discontinuity when they finally stop. You run out of time at the same time you run out of stuff. There simply is no point in time when it goes from 1 to 0.

Bill

It is true that the "North Pole" analogy is frequently invoked to cut off debate about the time of T=0 and before. However, the polar analogy just isn't an equivalent situation.

First, the polar coordinate system is suitable only when you are measuring a rotating sphere or something else that has obvious poles (such as a quasar). It just isn't true that time has any obvious poles at all. Thus, this particular analogy is being forced upon the "Big Bang" situation.

Second, you might have an argument if our "Big Bang" universe actually did devolve (in reverse time order) into a singularity (or a "single point of existence"). That is what happens mathmatically at the North Pole. However, our present understanding of the "Big Bang" is that, at T=0 time, our "Big Bang" universe is not a point, but is just an extremely small (but very multi-dimensional) space. Thus, again, the forced analogy of the North Pole just doesn't fit!

Accordingly, I maintain that the time axis is continuous through the T=0 time of the "Big Bang" and the illusion (in this instance) is that the singularity operates as a wall that prevents us from traversing that instant in time. Again, there are no zeroes or infinities at T=0 in the modern view. Small, but not zero. And thus not even close to infinity in any other respect.

The problem with Hawking's book, <a href="http://www.secweb.org/bookstore/bookdetail.asp?BookID=121" target="_blank">A Brief History of Time: From the Big Bang to Black Holes</a>, is that it was written way too long ago; certainly before the resurrection of string theory, from whence these new ideas about the "Big Bang" all spring. I doubt that Hawking would stand by this particular view of the "Big Bang" today, and I can state unequivocally that he does not take that position in his newer book, <a href="http://www.secweb.org/bookstore/bookdetail.asp?BookID=848" target="_blank">The Theory of Everything: The Origin and Fate of the Universe</a>. Instead, Hawking backs off to the somewhat more justifiable stance that, even though it is at least theoretically possible to transit the occurrance of the "Big Bang," in point of fact the size and pressures of our "Big Bang" universe at T=0 time will totally dissolve everything contained within the universe so as to make it virtually irrelevant what went on before T=0 time (the "Big Bang"). Saying that the earlier time line prior to T=0 is not relevant to our current circumstances is a very far cry indeed from stating that such a time line does not, in fact, exist.

Since Hawking has obviously changed his position on this point, I would rather say that it is time for you to change yours.

== Bill