Fred56

Right. But I used a travel metaphor, so saying "when you came from has disappeared" kind of destroys the metaphor.

Right. I'm kinda trying to sample how far others have got with this. Infinity is one of those things, like pi or e or i that keep "popping up" or squeezing between the gaps, sort of. I know there are lots (maybe an infinite number) of infinite series that have an actual, finite result. But infinity has no "actual" value, no eigenvalue. The set of terms in an infinite series is infinite but the result is finite, is this the same as saying an infinite series is finite, though (or bounded)?

In which case it will have it's own "objective" measure of time, one of the coordinates, right?

Ah, but what is the infinite set? Is it unbounded? Is there an infinite series which is finite (has a finite result)? Or an infinite set of mathematical descriptions of infinity?

Cheers, I read it already. Still doesn't get around the semantics that I think are the root of much confusion or misapprehension, or maybe misunderstanding (shudder) that's around, which of course includes my own.

Can you illustrate this? My limited mathematical grasp extends to the concept that something/something = 1, or something - something = 0, if the somethings are all the same symbol. But infinity doesn't do this huh?

Yes, what I'm saying though is that it is only represented this way, not because it actually has dimensions, but because it's just too convenient a model. We can't go and get some of this “time distance” from somewhere and compare it to another bit, like we do using a bit of “representative” distance, say, a ruler. We can't go and get 15 seconds and twack someone on the head with it, either, or “use” it (like a ruler or a thermometer) because it's “vapourware”. We only believe “time” is linear because we observe “regular” behaviour; because the clock ticks sound the “same” (or close enough for our inaccurate senses). Our belief in Time and our ability to measure it is due to change and is an artefact of the way we observe this change. Entropy is also change, so entropy explains our perception, or our belief in the existence of time. Even though it isn't really there. There is no time, only change, grasshopper. Other things, like our concept of energy, seem to have similar issues. Here's something I got back from someone on another forum about mass/energy equivalence: P.S. I hope this thread is viewed more as at least philosophy of science, maybe.

Infinity has a lot of odd, or amazing, or impenetrable, properties. Infinity can increase or decrease, but still be itself. Except that, even though infinity plus n (or plus infinity) is still infinite, infinity minus infinity is zero, but infinity minus n (some “ordinary” number that our brains can deal with) is still infinite. Infinity can be multiplied and divided and still be infinite. But infinity divided by infinity is 1. Infinity squared is infinite, as is infinity to any power. So infinity to the power of infinity is still infinity (to the power of 1). It's a really big huge meta-number that can't be transformed like other numbers. It's outside the normal behaviour range, or whatever. But Math would be lost without it. 'Specially those cosmologists and particle physicists.

I get some of the things you are saying, but I think you keep making mistakes in some of them too. For instance, you say when talking about the coordinates of something changing that: so you're saying when something moves, its coordinates don't change. I think. But you do say: And also: We have already tried to talk about the coordinates being the same (or not), and not all that successfully. But saying: Admittedly is a bit contorted, but I'm trying to say that if the coordinates are the same at different times this is because they haven't changed (which is the really obvious induction) or they are changing but returning to the same values, for some reason (like curvilinear motion, or oscillation, say), so every time they are measured, they are perceived to be the same. But you can't say that, in general the x,y,z coordinates at time t are or will be or were the same at time tn, because the object could be moving around like this (or in a "straight" line). Recall that space (distance) is also increasing in all directions, so there are more "points of spacetime" to consider now (than there were when this thread started, for instance). It isn't (usually) all that useful to just refer to some xyz coordinate, some point in space, unless it is in the world-line of some object, say, or represents some object (like a neutrino in which case its values would be changing "rapidly"), or is interesting for some other reason, otherwise it's just a point in space like the infinite, and rapidly increasing, set of points all over the universe. This is because: But: only follows if you are talking about some original point that the object has left behind. And what does this point have to tell us? What is the point of this point?

We believe that we measure time, we say that time “times” things, or events, and that there are “intervals” of time, there is a “time distance”. Indeed much of Physics is based on the singular concept of linear time. But we know that time doesn't really have “length”, or “width”, it doesn't occupy any space, like objects do, we can't “see” time. Time is dimensionless, in that sense. We also say things like “heat is transferred” or “heat is motion” which is like saying that “movement moves”, so why not say that time “times” things? Or space “distances” things or distance “spaces” things, or motion “moves” things? Isn't that, in fact all we ever really do when we measure anything? We measure the, er, measurement...

Don't quote me on this, but I can remember reading something about Albert being initially skeptical of black holes and how they are supposed to form. Because the infalling or contracting matter must necessarily exceed the speed of light, which would require infinite energy, according to his equations, he postulated that matter would not fall beyond the radius, but stop, or freeze, or something. But apparently that matter just keeps on going towards the centre, past the radius and into the singularity, smacckkk...! ...or something. My take on black holes is that if matter has fallen beyond some radius that requires infinite energy, or exceeding the velocity of light, then perhaps it already is a singularity and so beyond known Physics.

Um, this is actually something of a request. I posted something on another thread in Relativity about entropy which went something like: entropy is like a one-way ticket but when you arrive you find out there aren't any return tickets available because where you came from has ceased to exist. Which was shot down with an argument about heat-engines. Can someone explain what's wrong with my metaphor?

You do the same thing here, treating all variables as distance. But t stands for time, not distance. You are saying that x2-x1 is "similar to" t1-t. But meters aren't seconds.

Sure, but what happens to the entropy (the heat energy)? Doesn't work being done mean a change in entropy? I must have completely misunderstood my Physics on this. And I said this is incorrect. I still say it. (x,y,z,t1) certainly is not the same as (x,y,z,t2), and the (x,y,z) bit will only also be the same if there has been no motion, no movement or change in any of x, y, or z. (x1,y1,z1) will only be equal to (x2,y2,z2) at another time if and only if they haven't changed. A no-change universe means a no-time universe.

You are still confusing position in space with position in time. They are not the same thing. If the (x,y,z) coordinates of a past event are known, i.e. where it occured that is different from when it occured. Lots of people do this. I do it too because it's a "simple" model of time. But that doesn't mean it's correct. If time is like a line, why isn't it also like a 2d plane, or a 3d space? If "our past ... positions on the line" existed we would be able to see them or move to them, but we can't do either of these things. Nor do I, unless you are trying to find one of them, in which case an infinite number of them would make the job pretty tedious (just kidding).

But if the entropy returned to its original value wouldn't that mean the engine had not done any work? Doesn't a reversible system return to its original state only if the entropy change is =0 (a perfect reversal), and this means no work is done?

This is a straightforward solubility problem. You need to find out about the solubility of the "products" of interest: in this case caffiene and acetaminophen, in different solvents. Then you need to select a solvent which has a different density than the one the product is dissolved in, so you get two "phases" of liquid, usually one organic and one aqueous phase. One solvent will contain the product you wish to extract, the other will extract the product from this because the product is more soluble in the extracting solvent. All the info should be available in the Merck index, or somewhere on the web maybe. I'll leave the details of preparing an aqueous solvent to extract an amine from an organic solution up to you. Wikipedia should also tell you all about caffiene, acetaminophen and their solubilities. Caffiene is an alkaloid (actually an amine) and these have been extracted from plants using slightly acidic solutions for quite a while now.

Actually you initially said that you think the spacetime coordinates for "the past" are just as real or exist like the coordinates do for "now and "the future". So I asked where they are, or where you think these coordinates exist. If you are implying that the past and future coordinates (of everything) are the same this would only be true in a motionless (no change) universe (or maybe a universe with no objects, that would be odd, empty space with no motion or interaction, would it qualify as a universe?). I am also assuming that by coordinates you mean something like "all points in space", which isn't the same thing as the location of some event. I first thought you were talking about the coordinates of past events, but you seem to be talking about all coordinates, i.e. every point in space, which must be an infinite set. Can you see the point of my question now?

You mean you might be able to if you spent some time reading about it (which maybe you're too busy to find)? Einstein appears, to me at least, to be saying that the source's velocity has to be changing (i.e. the light source is accelerating or decelerating) in order for curvature of light to occur. But perhaps I have misunderstood his meaning. Scratch that, he is talking about propagation velocity, i.e. the velocity of light. Not sure what "velocity of propagation ... varies with position" then means. The speed of light varies with position - position relative to what?

No, entropy is disorder. How? By what mechanism? And how does it lead to theories and speculations (which are mental processes, and physiological, so require energy). Sorry, the rest of your post is quite difficult for me. Possibly even a bit impenetrable. Perhaps you could elaborate.

I think it might form something more exotic at the core, depending on how big the "planet" might get, like supersolid ice, whatever that might look like.

You're referring to a so-called "reversible" process. When these occur, entropy (heat) is transferred (to do work) but the overall entropy of the system is still >=0. Check it out.

Time, which doesn't move, or have any dimensions, presents a conundrum when it comes to measurement. How do you measure something dimensionless? Consider what we are actually doing when we "measure" time. If you look at your watch, or (if it has a Swiss movement) hold it up to your ear and listen to it ticking, you are observing a sequence of regular events. These appear regular only because your brain is able to "remember" each tick, and determine, or discriminate, that there is a very close correspondence to each individual "event" and its immediate set of predecessors. We sample these ticks like this until we are confident they are more or less copies of each other, and announce that we have measured time. But is that what has actually occurred? Or is there only one tick, and a string of remembered ones (and imagined future ones)? Only one now and a lot of nonexistent "past" nows?

Entropy is like having a one-way ticket. When you arrive, you see that not only are there no return tickets available, but where you came from doesn't exist any more. Exists where?

No, thanks for all the input. It has been interesting but I simply didn't get the depth needed, I suppose, from that course I did because we only did simple examples, and the concept of information entropy wasn't explored much except towards the encoding and so on, side of things. But it was a CS, rather than math or physics, class.