[yor_on (OP)]

Yeah, I thought so to. Like making it into spiraling pattern when time is involved as one of the parameters, which, as it will be never-ending could be seen as a line without end, or, as you see it stop, make an ending, turning in it into a line for sure. Still, will have to think about it some more as it, to me, seems perfectly correct. I mean, those geodesics are really straight paths, but it may be the nomenclature that dizzies me there, you could call it paths of least energy expenditure too, couldn't you?

[LeeE]

Yes, good old Pythagoras, but I don't follow that generalisation.   This seems like an odd and unwarranted way to treat time.

That minus sign is what makes SR and GR work and gives them a geometrical interpretation.  If you choose not to follow it, I don't think you'll get the physics of relativity to work out...

That response was of no help whatsoever, as well as being offensive.  I was asking a question and at no point did I reject anything.  Your response was just an unwarranted and unjustified accusation, and one that also failed to give the origin and explanation of the generalisation I was querying.

The Lorentz equations at the basis of SR & GR that I'm aware of do not follow the form you gave and instead use the conventional Pythagorean form.

If you can give a link to an article that explains the derivation of that generalisation, then fine, I'll have a read of it.

[JP]

That response was of no help whatsoever, as well as being offensive.

I'm sorry you thought that.  Sometimes trying to be succinct comes off as being aggressive, I suppose.

You can think in Pythagorean terms, but the geometric interpretation of general relativity (and the geodesics Yor_on has asked about) rely on that extra minus sign on the time coordinate or they don't work.  I don't know of a website that covers it, but textbooks on general relativity will do so.  Many on special relativity will as well.

[kenhikage]

I may be way off base here, but I thought that plotting circular movement over time resulted in a sine wave~ That is, of course, plotting two-dimensional space against time. I would think then that plotting three-dimensional against time would result in a sort of wave sheet.

Is that why particles also behave like waves? []

I hope I'm not derailing this topic btw.

[yor_on (OP)]

Not as I can see? There seems to be different possibilities for how to describe it mathematically? But you really need to give some examples to how you think kenhikage so that we uninitiated see what you mean, why it have to be a sine curve in 2D and possibly a wave sheet in 3D? Wave-sheet btw? What would that look like?

[Joe L. Ogan]

Could be wrong though, happened before, and will happen again

Don't worry about it Yor_on. I used to make mistakes too.

Could be wrong though, happened before, and will happen again

Don't worry about it Yor_on. I used to make mistakes too.

  Geezer, I believe that you that you thought you had made a mistake once but found out later that you had not.  Thanks for comments.  Joe L. Ogan

[Geezer]

Could be wrong though, happened before, and will happen again

Don't worry about it Yor_on. I used to make mistakes too.

Could be wrong though, happened before, and will happen again

Don't worry about it Yor_on. I used to make mistakes too.

  Geezer, I believe that you that you thought you had made a mistake once but found out later that you had not.  Thanks for comments.  Joe L. Ogan

Joe - I didn't want to come across as being too arrogant, but what you say is true. There was one occasion when I thought I was wrong, but I later found out I was mistaken.

[Joe L. Ogan]

Oh, Geezer, one would never think about you being too arrogant.  The occasion that you reference is the one that I was talking about.  Thanks for comments.  Joe L. Ogan

[kenhikage]

Not as I can see? There seems to be different possibilities for how to describe it mathematically? But you really need to give some examples to how you think kenhikage so that we uninitiated see what you mean, why it have to be a sine curve in 2D and possibly a wave sheet in 3D? Wave-sheet btw? What would that look like?

http://www.mathimage.com/images/see_mi_UnitCircleToSineWave.jpg

A wave-sheet would be a plane of intersecting waves. I'm wondering if gravity, and thus matter, doesn't simply collect in these troughs and crests. This idea treats matter as an effect rather than a cause of "gravity."

[CPT ArkAngel]

Everything can be described by vibrations of strings in multiple dimensions (String Teory). It is just a matter of perception and how far you can go with it...

[kenhikage]

Everything can be described by vibrations of strings in multiple dimensions (String Teory). It is just a matter of perception and how far you can go with it...

As true as that may be, I wasn't meaning to describe the dimensions as waves. But, in hindsight, perhaps that is the natural progression of my thoughtlette. Although, in thinking about it again, crossing waves could never create singularities.

I didn't really mention it before, but I came across this idea when thinking about OP's question. A circle is the natural path of bodies orbiting a center of gravity. Mapped over time, on a 2D graph, it's a wave. Then I was thinking about the natural shape of most bodies being spheres, a circle with an extra dimension. So, I added a dimension to my wave and got a waved plane. So, rather than thinking of each dimension as a string, I was thinking of 4 dimensions as 2 strings, and matter as energy that got caught up in the folds of that plane.

Sorry, I'm just throwing ideas around. I think some outside the paradigm thinking is needed to get to a decent theory of gravity. Or, in other words, I have no idea what I'm talking about.

[yor_on (OP)]

Ken, sweet thinking that one. Transforming a wheels motion into a sine curve. Had forgotten about that one, but you're perfectly correct. So our conceptualized orbit of a sphere around a sphere will indeed be able to transform the orbit into a sine-curve, or as I see it, also transform it into a 'spiraling motion' as time comes into play. A nice animation.

Then again, where does my ring produce those sine curves, at all 'points' of its motion? Won't that become an infinity of points?  It's easier for me to see it when looking at a defined sphere orbiting, but when looking at a ring the concept becomes fuzzy.

And a 'waved plane' becomes even more complicated.
Got any visual aids to that one?

And yes, string theory do try to define it all:)
Ahem..

Now, that are some really deep mathematics..

[kenhikage]

Based on the animation you linked to, I think we are using different words (wave & corkscrew) to express the same idea. There is a slight problem with said animation though. There are two Ys which intersect, one of sine, one for cosine. If we label Cos's Y as Z and intersect the waves you get the plane I was mentioning. Depending on where the waves intersec you get differently shaped planes. As there is no perfect sphere (or circle), I suspect this field (plane) wouldn't be a perfect crossing of sine waves as in this image: http://upload.wikimedia.org/wikipedia/commons/0/0e/Complex_sine_im.png . But that is an idealization of what I'm throwing out there.

Let's add to the mess with this: http://biocab.org/Coplanarity_Solar_System_and_Galaxy.html#anchor_22 .  []

[yor_on (OP)]

Heh

Weird movements through the void, well, as long as it don't sidestep?
Looking at that it's a wonder that we still have 'motion sickness'
Ahem

Aha How did you think of those sines? As intersecting at all points and then either quench or reinforce gravity, nah? And how did you think of them to be in a wave-plane? An infinity of wave-planes then? But gravity has no 'valued' direction, right? If you look at it, it seems an attraction toward a gravitational 'center' working from all directions? So how would those 'layers' be placed?

Or am I just taking a stroll in the great beyond

[kenhikage]

Sorry, I didn't address your ring concept. You have the right idea about a circular path in space, but even a ring spinning around an object makes a spiral in time.

First, think about the single object (or better yet, point) circling your massive object. Now think about looking at that motion form the side; it would just look like it is going up and down. Sometimes it travels in front of the massive object, other times it disappears behind it. Now think of time as your X coordinate. As time plays out the bodies move to the right, but the movement path is traced out. What results is a sine wave. If you looked at it from a less than dead on view, it would look like a spring or coil.

So, in your ring you simply have a bunch of particles (with empty space between them) all tracing this coil shape. If you were to look at it it would be so tightly packed as to seem like a tube. But the fact remains that each particle would be orbiting in space and moving forward in time.

[yor_on (OP)]

Nope, it's not a sine wave. A sine wave would be a single point as you say, in a orbit. What you do here is to define one point of a ring as that 'single' object me thinks. And then you are correct. But as I see it there is no single isolated point existing there, more than in my imagination as I define it so. A closed ring, of matter or not, is closed, no matter how you fold it, as I believe. So to make it a sine seems to me truly hard. What one might do is to lift in the time aspect as just another 'material' dimension and then 'displace' the object in time, but it would still be a 'whole object', well, to me it would
==

What you are doing is to assume that there is 'spaces' that somehow invalidate the aspect of a closed ring, in reality that is, but we are using abstractions here. If you accept that a 'closed ring' in theory exists, then it's difficult to define it as having intermediate 'breaks' all the way around. Also in the end matter is a definition of the 'forces' gluing it together. If it is that way this glue have no breaks, as if they had, what should I assume those 'breaks' between matters interfaces to be? And why would they not 'split' if so? As you then would have to assume that those forces stops in those interfaces?

[kenhikage]

Just as an aid: http://www.g-o-springs.com/wp-content/uploads/2009/04/v8-spring.bmp

Sorry if I've been less than specific. When I'm describing a sine wave, I'm removing a dimension of space (which we see) and putting in time (which we don't). As I described in the the post just after yours, It's like looking at a spring from the side. It's still a spring, but we've "removed" a dimension by looking at it from a certain angle. In our spacial way of thinking we look at that spring from above, so it looks like a circle.

The reason I came up with the field way of thinking about it is because I was adding back in that other dimension. The corkscrew or spring-shape is the (true) path of a circular orbit. To think about all of space-time, I was imagining a plane (of things corkscrewing around.

My concept wasn't that it affects gravity, but that gravity is our concept of what is really the bending of the wave-plane. I suppose where my postulation differs from GR (?) is that Einstein saw mass (or energy?) as bending space-time. I'm looking at it the other way around. Bent space-time is causing energy to collect into pools of what we experience as mass.

[kenhikage]

Nope, it's not a sine wave. A sine wave would be a single point as you say, in a orbit. What you do here is to define one point of a ring as that 'single' object me thinks. And then you are correct. But as I see it there is no single isolated point existing there, more than in my imagination as I define it so. A closed ring of matter is closed, no matter how you fold it, as I believe. So to make it a sine seems to me truly hard. what you could do is to pick in the time aspect as just another 'material' dimension and then 'displace' the object in time, but it would still be a 'whole object', well, to me it would

You can't think of any object as "whole." Even neutron stars have some space between the neutrons. But supposing your ring has no space between the subatomic particles (and supposing it isn't a black hole), and supposing the ring IS rotating, then by definition each little particle is moving in the same way that a non-ringed single point would. So you have an immeasurable number of tiny spiraling particles.

If you color coded each one you would see corkscrews of color. The whole object would look like a rainbow colored tube or pipe. I don't dare link to an image, but just look up "rainbow pipe" on Google image search (unless you're at work).

[yor_on (OP)]

Well, I think we can synthesize it somewhat, and what we get if so is in a way a spiral pattern in a 3D + time. A very fuzzy spiral pattern assuming time is a flow. But if you froze any of those 'time segments' it would still be a whole object. I'm not sure if it's treatable this way as I on one side say that time 'flows', on the other speaks about 'time-segments' though. If time was 'instants' instead though

But then you meet the same problem as always, a circular thinking. If time are 'instants'?
What's in between those instants? And as you fill them up with something You will find that those also needs to be explained in their 'interfaces' with times 'instants' ad infinitum.

A flow seems simpler to me
==

Oh yes I can
In the end you have geometrical definitions, even string theory use two. A open string and a closed.

[yor_on (OP)]

"My concept wasn't that it affects gravity, but that gravity is our concept of what is really the bending of the wave-plane. I suppose where my postulation differs from GR (?) is that Einstein saw mass (or energy?) as bending space-time. I'm looking at it the other way around. Bent space-time is causing energy to collect into pools of what we experience as mass."

Nice thinking again Ken, I love turning things all around, just as you seem to do.

And mine thinking is in the end all about time, what it is and what it does. Consider if we could 'stop' it all, getting a whole block of 'jelly' out of it. Time as well as matter and space. What would it do to our comprehension and definitions? Without treating them as 'separated'? Where would the 'causality flow' go?