fluctuations in space(fields in the case bc of quantum topology)
It’s hard to say much about this, because it’s all highly speculative and unproven 
That depends on how deep you want to go. I’m assuming you’re talking about the geometry dealing within the Plank scales (ie string theory, LQG, and so forth).
There are indeed topological considerations involving the Schrodinger equation, quantum electrodynamics (tensor analysis, fiber bundles: U(1), and other areas where Hamiltonian and Lagrangian dynamics can be formulated with differential geometry), chromodynamics, and, of course, molecular quantum mechanics.
A fundamental quantum topology, if ever discovered, is going to involve something very radical that hasn’t been postulated by any of theories currently in quantum gravity.
“Time” is not a dimension. Time is not orthogonal to length, width and height and is thus not a dimension. Dimension refers to structure and is a static concept. Time is an abstract concept (you referred to duration which is a dynamic concept.)
I don’t know what a “moment of … consciousness” is. Also, I’ve never experienced pixelated vision.
I understand the analogy. I just don’t think it gets us anywhere. Saying that we’re “really” seeing timeless 4-D objects smeared through 3-D space+time, even if true, doesn’t help us reach any better understanding of the nature of time. And I think it’s silly to say the world is actually comprised of 4-D objects.
Clayton -
At “normal” speeds, time is, indeed, orthogonal to length, width and height. My bookshelf does not get narrower as I slide it across the floor to the other side of the room.
Clayton -
I’m not sure how else to explain it.
Well, let’s just try to take an example here.
A tiger running across your field of vision is fundamentally a sequence of “pictures”.
(For vision, one moment of your consciousness is a 2D picture.)
Well, it’s just an analogy.
Switch “colored pixels” to “colored points”, if that makes it clearer.
(By the way, are you experiencing a pixelated Mises forum page right now?)
Evidently not.
(See below for why.)
Really I have no idea what you are talking about.
(I didn’t say anything about 4D objects, space-time, smearing things, or whatever else.)
@Clayton, Time is orthogonal to Length, Width and Height?!?!?
If that is true, can you please point your finger in the direction of Time?
But you have to imagine at least something moving left/right, up/down, or forward/back.
(Whereas can’t you imagine something moving left/right without imagining anything else moving up/down?)
They are most certainly not conceptually similar. Length, Width and Height are conceptually static, they are a photograph. Time is abstract, when referring to an object in motion moving left or right, it is conceptually dynamic and necessarily refers to multiple locations in the universe, it is like a movie.
I don’t even understand what you want to say, Orthogonal. A dimension is simply an independent variable, charge or mass for example can be considered dimensions too but do not appear as often as time and space which, after all, are the basis of our thinking. Time and space are conceptually different in non-relativistic physics but this difference gets washed away in relativistic theories because it depends on the observer what he perceives as time and what as space, similar to the transformation of magnetic fields and electric fields.
Of course I am not able to point in the direction of time (or direction of charge for that matter) since “pointing in the direction of” is a concept of space. But that does not mean that time is something completely different from space.
I can’t point my finger in the direction of the fourth dimension of any orthogonal vector space because I simply cannot visualize a four dimensional vector space.
I may be misremembering my relativistic physics, but as I recall, spacetime is just a four-dimensional, orthogonal vector space (with time a complex dimension).
Clayton -
Is it? I’m not trying to be obtuse - I simply think that you’re asking me to assume with you that time is comprised of a series of “moments”.
I like to think of it this way. Imagine your tiger running across the field as an ordinary sequence of movie frames. Now, stack those discrete movie frames one on top of the other like a deck of cards. Now, take a specially designed lighter that “melts” the frames into one another so that if you were to slice the solid block of celluloid at any cut point, you’d see a well-defined picture of the cat in motion at that point in time. This is how we experience time. It is this indivisible, continuous thing that has a causal relation between “earlier” and “later”.
No, it doesn’t, because points are just infinitely small pixels. The problem is that even if you pack infinitely many points into a plane, you still do not have enough points to cover the plane.
Clayton -
Clayton,
Your first objection is invalid, since in a two-dimensional space you could very well visualise a three-dimensional space-time. But even there you are not able to point your finger in the direction of time, or any other non-space-like dimension for that matter.
Spacetime is a four-dimensional real vectorspace with a pseudo-metric, the Minkovski-metric, or a four-dimensional complex vectorspace with an actual metric, the Euclidian. In the latter case you loose much mathematical elegance and possibilities to generalise principles, in the first case you loose all the properties of vector spaces with scalar products. Though in both models of space-time, time and space dimensions are distuingishable in the metric or definition, they do not retain their ‘classical’ meaning. Two points seperated by time or space for one observer are not seperated for an other observer. The invariant distance between two points of space-time is the world-line, a mixture of space and time. But the mixture is observer-dependant.
If what makes up a 2D appearance isn’t a bunch of indivisible, colored points, then what is it?
As far as I can tell, that’s how my vision works.
Sorry, but I lost you at “slice the solid block of celluloid at any cut point”.
(By the way, if this has anything to do with that you are talking about, we know through experience that “trailing” indicates motion, but trailing is still nothing but a bunch of colored points arranged in 2 dimensions as to form what we call “trailing”.)
Permit the interjection…
Just because we humans perceive time as indivisible does not mean it is not quantised…so too for space. i.e. space-time…
Can you explain?
(I’m not sure what you mean, and don’t have enough information to make a good assumption.)
‘plank time’ is often referred to as smallest ‘meaningful’ unit of time, the issue of whether there are smaller ‘unmeaningful/unmeasurable’ units is then kind of metaphysical…
What’s it mean to be a “meaningful” unit of time?
by analogy in an abstract computer whose memory is stored in arrays of 1’s and 0’s (bits) … a meaningful unit of memory is a bit…
For vision, I see a sequence of groups of points arranged in 2 dimensions.
(I remember a bunch of 2D appearances, and arrange them in an order from “earlier” to “later”.)
I don’t understand what your argument is against that, or whether there’s even supposed to be one.