It seems the majority of posters here believe that space and time exist. However, I maintain that proving they do is not a trivial exercise; it's much easier to just assume they do. So, why is that? On the other hand, there are toy theories around that call the existence of space and time into question: Barbour holds that time doesn't exist, Markopolou maintains that space doesn't exist. Can either of these theorists or their colleagues be right? Why does time in GR/SR seem to be so different from time in QM? I've seen arguments that reconciling the difference might lead to a quantum theory of gravity, but so far, nobody seems to know how to do this. It also seems, to me, that 'structure' in the universe doesn't make a lot of sense without space, and some mechanism that allows change (be that time as we know it, or as we think we do). And, can a mathematical theory really describe what time and space are, other than, you know, mathematically? In that case, can we "do what we like" with time mathematically, the only restriction being that such treatment must be physically meaningful, and does that just close a loop, logically speaking? Time is mathematically fungible, but remains axiomatic, a "measure of change"? Say what?
Well, Aristotle though that, which is why you put it in quotes, I'm sure: http://faculty.uca.edu/rnovy/Aristotle--Time is the Measure.htm Aristotle: Time is the Measure of Change. From Aristotle's Physics (Book IV, part 10-13) For full text, Part 10. You mentioned what some or the majority the posters here believe, that space and time exist, and the variety of discussions on the topic are a bag full of different ideas. You close with, "Say what?" I say that space is where things happen, and time simply passes, but that is far to simple to satisfy most people. The thing that keeps coming up that keeps everyone from agreeing with my simplistic answer is that it can be shown that time, as measured by two identical clocks, will be measured to pass at different rates when the clocks move relative to each other. They also measure time at different rates when they are both stationary relative to each other if they are at different altitudes relative to a gravitational mass. Most everyone knows that acceleration changes the rate that clocks measure time, but the physical mechanism to explain the cause is what many of those discussions fail to answer, or at least what people fail to agree on. I am satisfied with the gravitational wave energy density explanation that I often mention. It is an explanation that makes the speed of light invariant in any frame, and it describes a mechanism that accounts for why relative motion through space makes clocks measure time differently. It is unpopular because it invokes the concept of a "medium of space", and posits that the medium of space is filled with gravitational wave energy. That hypothesis is saying that at any point in space, there is gravitational wave energy coming from every direction at the speed of light, at varying energy density levels depending on the distance and mass of the gravitational wave energy source. If one clock stays home and the other moves relative to it, the moving clock will experience higher gravitational wave energy density. The awkward part of the idea is that it says that particles function slower as the wave energy density of their local environment increases, which it does when there is any motion relative to a given rest frame. The moving clock, made of particles which when accelerated function slower, then measures time as if it has slowed down. The hypothesis is that time simply passes at the same rate everywhere, and the measurement of time between a rest frame and a moving frame will always feature one clock functioning slower than the other. Too simple, right?
I'd call space and time measurements, rather than things or stuff. If I say that the universe occupies a spherical space with a radius of 100 billion light-years (I'm not looking this stuff up so don't yell at me if my numbers are a little off), all I've done is tell you how big the universe is. I've said nothing about what the universe is. In fact the universe might be a gigantic sphere of absolutely nothing, punctuated at very large intervals by very small stars and planets, and criss-crossed by invisible beams of energy. (Oh wait, that actually is what the universe is!) If I say that the light from the stars at the very edge of the universe takes 13 billion years to get here, all I've done is tell you how fast light travels. I've said nothing about what time is. And I've also not explained how light can cover a distance of 100 billion light-years in only 13 billion years! My measurements aren't even useful enough to explain something that important! Space and time are concepts we have developed to facilitate measuring things, but space and time, themselves, are not things. We talk about the space-time continuum, but that is nothing more than a map. Like any map, it is an abstraction, not an actual thing unto itself.
Ok, suppose we do in fact measure space and time. Then there's an obvious distinction between the measurement of space and the measurement of time. That's without even going into what "measurement" is, but let's say it implies a geometry. Spatial measurements don't vanish; if you walk from your house to a bus stop, technically that constitutes a measurement and it doesn't disappear, but time (the time you spend walking there) does disappear. More prosaically, any measurement of time is always different, you can't measure the same interval of time more than once, with space you can measure intervals as often as you want. So space and time measurements yield very different "things". Just sayin'.
Spatial measurements don't vanish isn't that satisfactory a statement, because it implies chronological thinking--the distance I will walk from my house to a bus stop can wait until tomorrow. So even the concept of distances not changing is because they are also "carried through" time, we think. Really, the surface I will be walking on between my house and the bus stop won't be exactly the same as the one I can walk on now. Distance and measurement both imply persistence, which is again a chronological word. Is there no escape?
About dimensions and the way we represent functions. With two dimensions represented, we can write y as a function of x, or x as a function of y, we can permute two dimensions, essentially a transposition. With three dimensions, there is a lot more freedom, in fact six permutations exist, and in general n! permutations over n dimensions. This can be visualised as the number of ways to permute the n vector basis of R[sup]n[/sup], as n columns in a matrix. In each case you get a matrix representation of S[sub]n[/sub], the symmetric group on n letters. So big deal. But what about just one dimension, like the one we "assign" to time, and which is one of the four in R[sup]4[/sup]? Well, this can only be a 1x1 matrix, equivalent to a scalar, so time being "one of four" dimensions means it must not, in some sense, be one dimensional; likewise the three spatial dimensions we perceive are not "separate" since they depend on each other. In fact, "perception" (or observation) doesn't work in less than four dimensions, since it necessarily entails "storage", and hence space.
Space and time do not literally exist, but rather they contain everything that exists/existed/will exist. This may just be an issue of semantics. But now we need a technical word for "contain" and/or "contain everything that exists". I didn't see why it's hard to prove space and time "exists" (contains existence). All you have to do is prove radiation "exists" (radiates/propagates) and you've proved space and time "exist" ("contain" it). Once we settle on the correct word maybe we can revisit that. I wonder if either of them would settle for the idea of "containment"? Isn't that like asking why time in electrodynamics/QED seems different than time in QM? Just curious: why not first ask why time in SR/GR seems to be so different than time in common experience? And then, can't we roll these two together into one question why is time in electrostatics so different than time in electrodynamics of moving bodies? (or however you prefer to word that). I think the crux of this is simply that space and time are frame dependent, therefore all observations of events or phenomena are relative. I'm not sure what you're getting at, but you seem to be asking why stationary and moving frames (or moved frames) are so different. Not completely different, but they certainly can (their paths can) diverge (split) and merge. That would be the logical expectation of relating GR to QM. It's just not a direct correspondence. Does it bother you that this question remains open? Speaking of things people commonly retreat to, that seems like one of them. Why not start with the development of ideas based on differential calculus: that there are a number of first and second order derivatives, with respect to time, that have physical significance, and that by little more than these, and the derivatives with respect to direction, plus the integrals over space/surfaces and time--we have all of electromagnetics laid out as Maxwell's equations. Suppose I ask you what the inverse Fourier transform of the spectra coming from the Sun actually is ? I don't think you're going to dwell too much on whatever is bugging you here before telling me the answer. Or you might consider thinking what the convolution of the spectrum with a sine or cosine is and what it means -- or even just contemplate if the colors of light coming off of your screen really exist in a frequency-based reality or a space-temperature reality, or some other exotic twist on things. Not if it feeds some absurd conclusion. But how about dealing with practical matters? How about just talk about real radiation, and take it from there? It does stuff it time--it wiggles. It does stuff in frequency--it makes "fingerprints". It does stuff in temperature, or charge or whatever else you can find out that it's doing. But presumably it's real! Not in the case of the Fourier transform. Now take the result (frequency) and subject it to a quantum of action (h) and you get energy. That kind of says time is like energy. Both have something to do with persistence, and instances. The change you are looking for has something to do with derivatives. The integral over time has something to do with something else, be it frequency, or energy, or temperature, or total charge, or whatever the real world in manifesting that started all of this hooplah. How about say: real stuff is real, and it's up to us to classify it.
I can't see how that follows; you posit that space and time contain certain objects: "everything that exists/existed/will exist", a phrase which contains chronological references, but this container doesn't itself exist . . . Again, I can't see how this follows; frequency is only defined in a time domain, wavelength is a function of spatial distances between wavefronts. It's circular reasoning. Well, isn't that a consequence of Einstein's theories, and how does it explain what space and time are? Reconciling the difference between time in QM and classical theories is interesting, it doesn't "bother" me that this is the case, no. Well, these derivatives include the implicit assumption that 'distance' is a function of time; In electromagnetics, distance is exactly analogous to a difference in potential, hence potentials varying in time. The time rate of change of some physical quantity, as a derivative, assumes that such a derivative exists; what it doesn't do is prove from "first principles" that time and the time derivative exist.
