According to relativity spacetime is a continuum. A set can be be infinite, finite and unbounded, or finite and bounded. The case of finite and bounded is excluded for current theory, and maybe necessarily so since the term "universe" is all inclusive so it would include whatever was on the other side of the boundary. That leaves the cases of infinite or finite and unbounded.
The idea of finite and unbounded is like a basketball surface. It has no edge even though it is not infinite like a plane. If the universe were finite and unbounded and spherical then no matter which direction in space you went you would end up back where we are. Something like that may in fact be the case. Whether the universe is finite and unbounded or infinite is a question the answer to which is not currently scientifically known. My understanding is that the recent observations include a universe that is expanding at an increasing rate. If that is true then the universe is no longer behaving like current scientific theories predict and the theoretical physicists have work to do. If you want to know what a continuum is consider this... Imagine a point on a plane. Now imagine a small disc around that point. Now imagine a smaller disc. For every disc size you give me, if there is a continuum, I can find a smaller disc that is made up of points in the continuum. So if you draw a 1 inch circle then I can draw a 1/2 inch circle and if you draw a 1/2 circle I can draw a 1/4 inch circle etc. If that is true for every point then the set of points is continuous. The only problem with this idea is if there is a boundary point. If you choose a point on the boundary you cannot draw a circle all the way around but you could draw something like a half circle. But we are excluding bound sets so no problem! There are better more formal definitions on the internet in the wiki. Now imagine a line segment with a start and endpoint ... say the points on a line from zero to one. Then that set has a boundary. The points zero is one boundary and the point one is another. But if you take the line segment from zero to one and then exclude the point zero and the point one you now have an unbounded set! The numbers 1, 2, 3 etc are not a continuum because if you take the number 2 for example and I give you the number 1 for example you can't find a neighborhood around 2 that is closer to 2 than 1 but contains 2 and other numbers. But fractions are a continuum because if you give the number 2 for example and I give you the number 1 for example then you can say "all the points from 1 and 1/2 to the 2" All those points are closer to 2 than 1. If I give you 1 1/2 then you give me 1 3/4. Now try to find a number that that doesn't work for.... If I give you 1.9you give me 1.99. If I give you 1.99 you give me 1.999 etc. If I give you 1.999999999 you give 1.9999999999! In fact there was some theoretical work in physics that postulated that time and space were not continuous but were discreet or quantized. As far as I know the work never gelled into an acceptable theory. What is interesting is the relationship between time and space. Spacetime was a 4 dimensional continuum before Einstiein. What he found was that what is for one person two points or events imagined at the same time but separated by a distance and that therefore determine a length become two points that are not at the same time for the other person and so the points no longer are a length (which is an interval of space) but are now an interval of space and an interval of time. So a purely spatial interval becomes a space and time interval. So for example today now here a gun goes off and in Washington DC at the same time a gun goes off. That now becomes today here and now a gun goes off and then latter in Washington DC a gun goes off. Actually, it was a man named Minkowski who sort of summarized Einstein this way. It does not mean that time and space are really the same thing however. Locally, for any given observer they are very different. Also, time is related to material causality, so you can have a circle in space but not one in time. The universe may be spherical spatially but not in time because it causes problems with causality. (However, you can imagine a universe that repeats and in a sense that is a circle in time! Its just that if you are to preserve causality you describe it as a line that just repeats. How subtle the ideas of physics!) Relativity does preserve the ability to have material causality since no signal can go "faster than light" meaning that nothing here can cause something over there before light could reach it. If such an effect were discovered then the center of relativity theory would be destroyed. It is all based on that assumption. Therefore the future need not be determined in relativity. Causality can exist but its effect must be local. There can be no instantaneous action at a distance that is all. I can affect a star 4.5 light years away from the earth relative to the earth only 4.5 years from now relative to earth. (In the old theory of Newton the idea that everything was determined was also there. But that does not mean that there is no material cause. It just meant that if you know all of the causes and you know where everything is and how fast it is going at one point in time then you can predict the future forever. The same is true in relativity but what is interesting is that it is not true in quantum mechanics. That theory is non deterministic and only allows you to predict probabilities. Also remember that material cause is not the cause of the universe. It is only cause in the universe. ) What is interesting is that if I travel really fast it turns out that relative to me I can get to that star in as short a time as I want. I can get there in say 10 min and affect it - meaning cause something there....the catch is...I must measure that 10 minutes on my wrist watch. But someone on earth watching me would see me traveling for 4.5 years and would watch my watch moving very slowly for those 10 minutes! So the fact that it takes light 4.5 years relative to the earth to reach some star and the fact that nothing can go faster than light does NOT mean that I must take 4.5 years relative to my wrist watch to get there. In fact I can get there as fast as I want! Its just that everyone home will have aged a little more than me. Relativity and quantum mechanics are very interesting theories. There are deep philosophical reasons why they seem so strange. These reasons are because we are so confused about what "to be" means. We think it means to be a thing in the universe but that is not really it. Numbers are and they are not things. And even the universe is not best described as a bunch of things. There is for example color which exists but cannot be described just by using the idea of things moving around in space. So you end up back in philosophy and perhaps the best way to describe everything is that it is the experience we are having together. Describing that experience is where science comes in. Understanding what it means however... well... its just not scientific.... its philosophical... and when you start to become aware of the meaning of the universe certain experiences start to happen in you that are not describable within the current theories. That's why people who are only aware of science thing that the people who are not only aware of science are such raving lunatics. It is also why there is interest in this group. The term "Minds eye" is a very old term that refers to the experience of the meaning of the universe. The interesting thing about the charter of this group is that it purports to discuss these things rationally so you are at the meeting of science and the rest of the culture. On Aug 25, 8:47 pm, Michael Berkovits <[email protected]> wrote: > I actually disagree with your interpretation of the continuum (though > of course I'd be happy to hear more thoughts). This is what the link > said: > > "This new reality was that space and time, as physical constructs, > have to be combined into a new mathematical/physical entity called > 'space-time', because the equations of relativity show that both the > space and time coordinates of any event must get mixed together by the > mathematics, in order to accurately describe what we see. Because > space consists of 3 dimensions, and time is 1-dimensional, space-time > must, therefore, be a 4-dimensional object. It is believed to be a > 'continuum' because so far as we know, there are no missing points in > space or instants in time, and both can be subdivided without any > apparent limit in size or duration. So, physicists now routinely > consider our world to be embedded in this 4-dimensional Space-Time > continuum, and all events, places, moments in history, actions and so > on are described in terms of their location in Space-Time." > > A continuum doesn't have to be infinite. Dictionary.com defines a > continuum as "a continuous extent, series, or whole." It adds the > mathematical definition of "a set of elements such that between any > two of them there is a third element." Think of a line segment. It's > finite, but continuous - between any two points on the line, there's > another point. > > When the speaker says "there are no missing points in space or > instants in time," he is referring to the current set of space-time. > Doesn't mean that the set can't expand. Indeed, the universe is > expanding, thereby increasing the total amount of space in existence > (and hence, the total amount of space-time in existence, as space is > an aspect of space-time). > > If you could spell out more clearly what, from science, suggests that > the future has already happened, then I would be curious and grateful > to hear it. > > On Aug 25, 11:43 am, Pat <[email protected]> wrote: > > > On 25 Aug, 15:58, Michael Berkovits <[email protected]> wrote: > > > > Pat, > > > > What is your source for the contention that the space-time continuum > > > referred to by physicists means a continuum with defined endpoints? I > > > agree that the word "continuum" often means something with defined > > > endpoints, but as far as I am aware, its usage in the phrase "space- > > > time continuum does not." > > > But it does. Have a look at this > > link:http://einstein.stanford.edu/content/relativity/q411.html > > > But don't confuse 'missing points' with 'undiscovered points'. > > From our perspective, the entire future is filled with undiscovered > > points (thus appearing open), and there are many undiscovered points > > in the past. But, within the whole of the continuum, none of its > > points are missing. > > > > I think that the theory of relativity holds that we can see things > > > that happened far in the past (e.g., when we see an object that is 4 > > > light years away, we are seeing how it looked 4 years ago), but not > > > the future. As far as I kow, according to modern physics, the future > > > hasn't happened yet. Do you have more information? > > > Yes. You're mistaken about modern physics' view about the future. > > At least since Einstein. The fact of a space-time continuum implies > > that the continuum contains all of space and time. There is no space > > or time that can ever exist that is not, already, a part of the > > whole. And it is this point that I feel is vital to us understanding > > the true nature of the universe and our part in it. > > > > On Aug 25, 6:38 am, Pat <[email protected]> wrote: > > > > > On 24 Aug, 16:36, showmethehoney <[email protected]> wrote: > > > > > > Pat, how can continuum have ends points defined? > > > > > How can it not? A continuum is defined by its ends. For example, a > > > > line (a 1-dimensional entity) can be viewed as a continuum of points > > > > (zero-dimensional entities) from the beginning of the line to its > > > > end. Along the line, there are no missing points, i.e., the line is > > > > continuous. So, too, our space-time continuum is continuous from > > > > beginning to end with no missing points. The philosophical > > > > implications of us living in a space-time continuum are enormous, as > > > > it means that our conventional view of a future open to possibilities > > > > is simply not realistic/accurate. Einstein knew this, but only > > > > mentioned it rarely. To believe that the future is mutable is the > > > > modern-day equivalent of still believing the Earth is flat. We have > > > > to come to a new understanding of the universe and humanity's role in > > > > it and that will not happen until we've removed the comforting > > > > blindfolds we 'prefer'. > > > > > > On Aug 24, 8:22 am, Pat <[email protected]> wrote: > > > > > > > On 24 Aug, 12:51, "[email protected]" <[email protected]> > > > > > > wrote: > > > > > > > > > So, let me get this straight. You have a philosophy that, in > > > > > > > > philosophy, absolute truths are impossible. How do you get > > > > > > > > past the > > > > > > > > dichotomy of having such a contradictory absoloute truth in your > > > > > > > > philosophy? Alternatively, if you back off from the statement > > > > > > > > and say > > > > > > > > that your statement above is only a relative truth, it, then, > > > > > > > > logically allows for absolute truths to exist and {that they > > > > > > > > could} be > > > > > > > > duly ignored by you. Tricky stuff, Ian. Personally, I don't > > > > > > > > think > > > > > > > > you've stated your whole case, here. > > > > > > > > Heh I think Pat that if you do not belive in a creator God then > > > > > > > Ian's > > > > > > > strance is going to be the best you will get. > > > > > > > > Many of Ian's ilke may well (and justified too I believe) accuse > > > > > > > people like you and I of being philosophicly lazy, that we > > > > > > > practice a > > > > > > > kind of philosphy of the gaps, that we do not like to work out the > > > > > > > hard question of the absolute and so we call it God and have done > > > > > > > with > > > > > > > it. I don't think it is an acusation that we can easily defend > > > > > > > against, do you? > > > > > > > I think I've been fairly diligent in my attempts to discover the > > > > > > truth about the One (not that I'm finished, yet!!). In order to > > > > > > defend against the rallying cry of those who offer no comprehensive > > > > > > alternative, one must proceed from the point of ontology. Once > > > > > > we've > > > > > > determined what it is that exists, THEN we can look at what it can > > > > > > do > > > > > > and how it does it. The answer to all the 'why' questions to which > > > > > > atheists would have you believe there are no reasonable answers, > > > > > > leaves them only a pool of 'unreasonable answers' from which to > > > > > > choose > > > > > > and futher blocks progress. > > > > > > One of the main arguments against God is that atheists see no > > > > > > evidence that the universe is teleological, i.e., that it is heading > > > > > > in a particular direction with goals at the end. They overlook the > > > > > > FACT that we exist in a space-time continuum. The continuum > > > > > > contains > > > > > > ALL the past, present and future; that is, the ends are already > > > > > > defined (as is all the middle). If the ends are already defined, > > > > > > then > > > > > > the universe is, most definitely teleological, and the stumbling > > > > > > block > > > > > > (of no teleology) crumbles into dust before the weight of one stone > > > > > > (Einstein). > > > > > > My main point was that it should be obvious that some absolute > > > > > > truths exist. Some of these may not be particularly useful until > > > > > > one > > > > > > extends them. Einstein looked for truth and found special (and > > > > > > general) relativity. Absolute truths are, usually, things like > > > > > > physical constants. But it is how those truths work together and > > > > > > allow for the relativity in between that muddies the water and makes > > > > > > the absolutes seem less important or obscure.- Hide quoted text - > > > > > > > - Show quoted text -- Hide quoted text - > > > > > > - Show quoted text -- Hide quoted text - > > > > > - Show quoted text -- Hide quoted text - > > > > - Show quoted text - --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups ""Minds Eye"" group. To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/minds-eye?hl=en -~----------~----~----~----~------~----~------~--~---
