Originally posted by Eh
We deal with the relations of events. Like I said, in continuous time, an event is separated by a serious of events, which themselves can be broken into smaller events continuously.
Eh, we still can't get on the same page here.
I repeat, my main point is that there is no meaning for relation of rates of events if there is no comparison between duration of similar discrete events. Continuity doesn't change this the slightest. It only obfuscates this.
Given 2 chains of events: a) 1->2->3 and b) 1->2 where each change is precisely +1, we can say chain (a) has 2 times the rate of chain (b). BUT, if you don't have finite duration for each individual change, then there is no cause in principle WHY such finite rate difference can exist, why the rate ratio isn't
infinite.
Its obvious that if we assign chain (b) duration=1 then chain (a) event 1->2 has duration 1/2. If we claim that there is no concept of duration for events, then we must assume that (b) duration =0 and (a) 1->2 duration=0/2=0. For correlation to be possible, duration of any event must be >0.
But you haven't defined time as anything beyond change, and so aren't really arguing anything. Like I said, loops do seem to have change as a fundamental property, and that seems to be enough to give us a working definition of time.
Of course, I haven't even tried. Whats the point in trying to define it if you don't even agree that there is merit in that. You CAN do without it as is obvious from our successes, but it gives birth to MANY mysterious properties instead of just few when dig into fundamentals. Things don't fit together easily.
Btw, maybe you can give working definition of 'change' through which you try to define time. As I see it, without underlying time there can be only one way: change is instantaneous, zero duration event, and as such, infinite amount of changes is possible for ANY other pair of relative discrete events.
The only way to get away without time is to postulate static 4D universe, where everything already is.
That doesn't give a definition of time, and as such is hardly an example of "change" being a circular definition itself. When we ask how fast something changes, we are always comparing it to our reference frame. Whether you want to take that notion and break time into discrete events that can vary, or a continuum is another story.
There is no 'our reference frame' without separate time. Every single fundamental event is separate frame. How can we compare anything at all if we don't have a 'glue', ground for finite ratios for difference of duration?
I understand exactly what you're saying, and this is similar to continuous space in geometry. Take a line, and you can divide it into an infinite number of smaller lines. But the line itself is ultimately an infinite collection of points, which themselves are zero dimensional. In fact, points have no existence without the line. Either a line or point without the continuum have no existence. You must have the infinity of the line in the first place, in order to go anywhere else. That's just the problem with continuous space.
The same will apply to continuous time.
Consider segment: -- when you take any segment of line, you can always divide it into 2 equal segments. You get 1 point that separates the segments. You can continue that infinitely. But always you will have 1 segment more than there are points. You take position that there are infinite amount of points and that therefore line consists of points, but that is misleading. Line consists of infinite amount of finite segments that are separated by imaginary points of coordinates. When you collapse segments to 0 length, you loose line and segments, and all that's left is single unique point. There is no way how you could get (in)finite amount of points between coordinates 0 and 0. Yet you can safely say that there are infinite amount of points and segments in a line or segment. Because in coordinate centric geometry you care about points, that becomes definition of line, ignoring segments as secondary.
Same with time. You speak of points in continuum of time, ignoring that you need to have segments. When you bend spacetime, you work with point coordinates, but infact are changing lengths of segments. While you make calculations of equations, it doesn't matter, points and segments are pretty much equivalent, but when you talk about definition of time concept, you can't confuse time coordinates for concept of time itself. To have points on time axis, you need to define segments too.
I propose that we should not ignore the segments as undefinable, but ponder about this, instead of just hiding them into properties of loops and defining that time is just points of the contiinum.
Finite value? Only relative to larger events.
Whatever. It (minimum time duration) just can't be zero.
A fundamental unit, by definition would be constant. Even so, if you want to argue for time without change, you'll need to define it first. Otherwise, you're not really arguing for anything.
Fundamental means undivisible into components with new properties. It doesn't mean constant. By your view field lines can't be fundamental, geometry can't be fundamental if can be curved. You talk about fundamental Constant, not fundamental unit of existence.
I am NOT arguing anything. You still don't get that all I'm doing is to try to make you consider that time has 2 aspects not one: one aspect is what we call change, event sequence whose relative rates we can detect and correlate, and other aspect that you so strongly want to ignore - aspect that is the REASON that different rates can exist at all. This aspect is present in all theories in some form, I only try to take it out for a review.
I'm saying that any defined fundamental unit in current theories can be split into distinct timeless properties, and their change dynamics, where latter can't be separated from concept of time.
How far have we gone from the claim that time cannot have any existence without space? I haven't seen any arguments that support either that, or the notion that time itself is more fundamental than space. As per my original claim, take away space and time would be gone with it.
Take away energy, and universe will be gone with it. What kind of argument is this? Of course space is crucial component of existence.
What is fundamental concept? That which is common to all things is fundamental. How many spacetimes can you construct? 1D, 3D, 32D? How many time dimensions can you introduce to make it dynamic? 1 is enough for any number of spatial dimensions. Time is common for spacetime with any number of dimensions, any kind of geometries. Time as concept is fundamental for any kind of dynamics.
Problem with space is that it isn't absolute. Any 2 distinguishable concepts can be immediately praised as 'space'. So when you say remove space, WHAT space are you talking about? Number space, 1D space, 32D space, fractal space, chess move space, hilbert space, thought space?
When I say "time makes space" I mean it quantifies single anything (incl continuum) into comparable finites. Flat or curved 3D space is only subset of many possible realities, and its time that makes distances comparable, ie illusion of uniformity and structure.
Singularity of existence whose property is unspecified finite time duration between changes (for eg. split into 2), will give rise to space of distinguishable points. Whether that space is geometric or is at some point perceived as geometric is secondary.