favorite theories

Parent Cafe
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<p>I found a book the other day which contained over 5000 theories in the various fields of human endeavor, ranging from physics to mathematics to philosophy to psychology to sociology to economics to political science (a rather oxymoronic term!), etc.</p>

<p>One of my favorites is the theory of “infinite divisibility” of matter, which apparently has not been discredited yet, but the book rests on the supposition that matter would have to have infinite size for the theory to work. It seems to begs the question though – obviously if matter is infinitely divisible, it has infinite size! </p>

<p>I like to think that the theory is true, and it seems at least reasonable when matter is reduced into smaller and smaller particles. But the problem I am having with it is that if an object is taken, such as a baseball, why is it the size it is and not some ever expanding (as well as diminishing) sphere? If matter does not “grow” infinitely, then it must be finite at least in that direction, leading us to conclude the very real possibility that there are absolutes. Make sense to anybody?</p>

<p>Other favorite theories?</p>

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<p>

As the universe expands, it is not overtaking volumes that pre-exist. So the question is: Is the universe is actually creating additional “fabric” to incorporate into its expansion? -OR- Is the fabric itself “stretching” to provide the expansion. It it’s the latter, then the ruler by which you would measure the baseball is expanding at the same rate as the baseball. But that cannot be, because then we would not be able to observe the expansion!</p>

<p>A really simple mental model can illustrate. Three dimensions get complicated quickly, so let’s imagine a two-dimensional universe: a flat piece of paper that extends infinitely in all directions. The surface of the paper (not the paper itself) is the “fabric” that I’m referring to. </p>

<p>But let’s make two assumptions: First, that space itself is curved. And to keep the model simple, let’s assume that the curvature of space is the same everywhere. Now if we mentally curve that paper uniformly, we can see that the resulting shape is a sphere (or more accurately, the surface of a sphere). Suddenly, our one assumption has carried us from an infinite universe to a finite one (but also one without "edges’). We’ve also added what looks like (from our omniscient point of view) a third dimension - but more about that in a moment.</p>

<p>The Second assumption will be that the velocity of light through this fabric is constant. What the constant (c) is, who cares, but what that does is give us a fixed relationship between distance (d) and time (t): c=Δd/Δt. Why is this important? Because now we can phrase questions about distance (es: How far did you go?) in ways that use time: (eg: How long did it take?). If the velocity is constant, the answer to one will allow you to compute the answer to the other.</p>

<p>So back to our sphere, Think of standing at a point on the sphere (the universe). What is the answer to the question “What is the farthest distance that you can see?” If we follow the light coming to your eyes (back along the path of the longest distance you can “draw” on this sphere), we find the answer to be: the point on which you’re standing. But we can also ask the equivalent question: “How long would it take for that light to get here from the farthest point you can see?” The answer to that can be computed by t=(circumference of the sphere) divided by c, the velocity of light).</p>

<p>So now the critical leap to lead to some interesting results: The farthest you can see is the spot on which you’re standing. But you don’t see the back of your head. You see the spot you’re standing on as it existed back in time equal to the time it took the light to circumnavigate the universe! So what is the “farthest back in time we could possibly look?” The obvious answer to that is “the creation of the universe.” So I - in my little model - am going to relate the two: The farthest back in time I can “see” is the creation of the universe and the farthest distance I can see is the spot on which I’m standing, then I can make the conclusion that the universe was created right at the spot on which I’m standing!</p>

<p>…continued in next post…</p>

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<p>Nice, but why “assume” that space is curved and thus finite? And, if it does not have “edges”, what about its surface, is that not an edge?</p>

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<p>…BUT…</p>

<p>Another person in another part of the universe can make the same observation: that the universe was created at the spot on which THEY’RE standing. How can that be? Not a paradox, as we will see…</p>

<p>Let’s assume that our universe was created 12 Billion years ago. That says that the circumference of our spherical universe model is 12 Billion light years, the time it would take the light to circumnavigate the universe from the spot on which I stand (as it was at the creation) to the spot on which I now stand. But suppose I were asking the question 6 Billion years ago? The universe would only be 6 Billion light years in circumference. And if I asked it 10 Billion years ago, our universe would be only 2 Billion light years in circumference. And you can see that if I went all the way back to t=0 (creation), the size of the universe would be 0 light years across. Which means that every point in today’s universe was the SAME point at the creation (t=0).</p>

<p>So from our theoretical simple model, you can see that the “expansion” of the universe is closely related to the passage of time, increasing at a point to “accomodate” the movement of light from the creation to every point in the universe today.</p>

<p>This model leads to lots and lots of other cosmology topics:</p>

<p>Suppose that the arrow of time were going backwards, the universe would be collapsing to a point, but our observations would be the same, since we perceive time as progressing in a certain direction.</p>

<p>Inside a black hole, the fabric of space is collapsing, so the model would show that time in a black hole is actually going in a negative direction (but if we were inside the black hole, wouldn’t we see it in the positive direction and perceive time outside the black hole as negative?. And how far negative can time go? When space collapses to a single point (singularity) the point at which that happens is t=0! Creation and the Death of the universe are the same event occurring at the same time!!!</p>

<p>So “Where is the matter of this universe coming from since creation?” is one question. The other one is “In a black hole, where does the matter disappear to?” Hmmm… If I am asking -for the same event at the same moment of time (t=0) - where something went and how did it appear, it seems like the same event just viewed from two different directions. So did our universe result from the collapse of another universe or from the collapse of our own?</p>

<p>Which leads to another interesting possiblity: Since there are multiple black holes in the universe, our universe is collapsing in multiple locations to create multiple universes, the creation of which we observe (actually, we can’t really observe beyond the radius of a black hole) as black holes.</p>

<p>Whew - Interesting stuff…</p>

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<p>Your second post was really amazing. Great job!</p>

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<p>Back to the concept of “dimensions:”</p>

<p>The surface is not an edge because there is nothing above the sphere or inside the sphere. Remember this is a two dimensional model.</p>

<p>But, you say, a sphere is a three-dimensional model. That “third” dimension is the passage of time, growing larger (at the rate of c), as time passes. A positive direction in that dimension is expansion of space; a negative direction in that dimension is the collapse of space.</p>

<p>Simple.</p>

<p>The reason for the curvature of space is to make the model a LOT more interesting than the flat 2-D universe, and one that allows us to make deductions that match with observable phenomena within our “real” universe.</p>

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<p>Really interesting, but what is the use of working up an elaborate analysis if the premise is not true – that space is curved?!</p>

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<p>Infinite divisibility is more a philosopher’s question than a matter of physical inquiry. You can cut stuff up, that’s true, but at some point the pieces will reach the Planck limit - see Planck’s constant, Planck length, Planck time, etc. When an object hits 1.616 </p>

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<p>Everyone taking notes?? Pop quiz tomorrow!</p>

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<p>Lergnom,</p>

<p>Aren’t the “proofs” themselves based on theory?</p>

<p>Also, regarding infinite divisibilty. Are you saying that there is an ABSOLUTE point at which we cannot get beyond, despite whatever technology we may develop to do so – and thus we show that “relativity” is false (if relativity applies to matter)? Or, do you think it is because our technology is limited that we must conclude that matter is finite?</p>

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<p>Planck’s constant gives us the relationship of the uncertainties between the position of a sub-atomic particle and its momentum (Heisenberg’s Uncertainty Principle). What that means is that in the sub-atomic world, as you go to smaller and smaller scales, you can no longer talk about the position of a particle, but only about the probability of where that particle is. As a matter of fact, even the concept of a “particle” breaks down in this “quantum mechanical” world.</p>

<p>But you are right about one thing, leanid: It is a theory, which means that it’s a mathematical construct to model and explain the workings of the universe. It may not necessarily be HOW the universe really works. But of course we can only know it at the quantum level by the mathematics which predict/explain/illuminate what observations we can make and predict the results of experiments which verify/“prove” the theories.</p>

<p>The popularization of physics concepts can be fascinating (especially cosmology), but when the scales become sub-atomic, it’s harder and harder to put those concepts into any kind of visualization about what’s going on. </p>

<p>That’s why I like to go the other way, towards the scale of the universe itself. Much more able to visualize what’s going on.</p>

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<p>By the way. Even though I have an undergraduate degree in Physics (and taught HS physics for 2 years), I am really not a physicist in any way, shape or form. My first Quantum Physics class made me realize that I would never succeed at being a physicist. Any real physics student could laugh at my ramblings, but I still enjoy following the simple models to whatever speculations can be gleaned from them.</p>

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<p>digmedia,</p>

<p>I, for one, appreciate your taking the time to explain things. I am no science whiz by any means, just curious about things.</p>

<p>For instance, aside from breaking things down into quantum quarks, or whatever has been determined to be the smallest particle (and I appreciate your inclination to look at the “big” picture, ie the universe, as a way to actually “see” things), in my simplicity I cannot get away from the fact that matter must have a beginning point and an end point, regardless of size, so that there MUST be a point between them, thus making that matter divisible. </p>

<p>If you are saying that “at some point” matter loses its beginning and its end then it has become LESS than matter. Is that “less than matter” really nothing?! If so, how is matter created/formed/evolved from nothing?! I don’t know, maybe god knows…</p>

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<p>

Ah… that’s the question, but one I was trying to answer in the posts above. On the one hand (expansion of the universe from a single point), we have the question, “where is all this matter and energy coming from?” On the other hand (collapse in a black hole), we have the question, “where is all this matter and energy disappearing to?”</p>

<p>Hmmm…, since the appearance and disappearance happen at the same instant (t=0), maybe… just maybe… the questions are related and one answers the other. It boggles the mind to think that our expanding universe is just another way of viewing a collapsing universe and we are just traversing across the “time” dimension.</p>

<p>But here’s an area of physics that’s really important here that I do not know about. Maybe someone could answer this: Are there any laws that fail if the arrow of time is reversed?</p>

<p>Take the Second Law of thermodynamics, which says that Entropy increases over time. Entropy, expressed as S is the ratio of the change in heat, dQ, absorbed by a given system when that system is at a given temperature, T. So S=dQ/T. The Second Law says that entropy increases over time, t, so mathematically, that is dS/dt > 0. Another way of saying this is that heat dissipates over time. </p>

<p>But if we reverse time, we will see the heat returning to the system rather than dissapating. So the change in entropy, dS would be negative. But the change in time running backwards would also be negative. So if dS and dt are both negative, the law holds: dS/dt is STILL greater than zero.</p>

<p>If there are physical laws which do not hold in the negative direction, it would blow my simple model. I think there are, but I don’t know which ones.</p>