[Bill S]

  Define perfect.

You use the word, and you want me to define it?

This must flirt with the ideas of intelligent design. 

Is this where the idea of a perfect supreme being came from?  If so, I begin to suspect that imaginative thought might be superseding willingness to address issues, but that would be uncharacteristic, so, hopefully I'm wrong.

[jeffreyH]

The only proof you can ever have is a mathematical proof. This can lead to the idea of perfection. If intelligent design is linked to the mathematical nature of the world then it too should be considered perfect. Why then does everything ultimately decay? Is perfection a non term?

[puppypower]

An interesting observation about science convention, has to do with the question, why didn't Professor Einstein use polar coordinates to interface his theory of General Relativity? Gravity tends to move matter toward a sphere. While the terms bending of space-time and the curvature of space-time, interfaces naturally with the two angular coordinates of polar coordinates.

Why force the math to make it easier on man, when it could have presented by an analysis the way nature set up GR?  In the drawing below, a space-time well in GR, for any given mass sphere, uses constant angles and varies with radius.

In terms of time, hundreds of years ago we found out that acceleration is one part space or distance, and two parts time. Why approximate this with 1-D version of time? Nature showed us that acceleration is one part space and two parts time. If we use one clock; 1-D time, you can't measure two different accelerations at the same time. On a 2-D time grid, you have two lines.

[Bill S]

Why then does everything ultimately decay? Is perfection a non term?

I'm letting myself be drawn into philosophy, here, and I think that's unfortunate, because the further we go down this road, the less chance there is of getting answers to the real questions.  However, I like to try to provide some sort of answer to the questions that come my way.

"Why then does everything ultimately decay?" Because that is part of the regenerative cycle of nature.

"Is perfection a non term?"  Of course not, but what makes us think we know all there is to know about perfection?  Could it not be that nature has perfected a system that includes decay?

[Bill S]

In terms of time, hundreds of years ago we found out that acceleration is one part space or distance, and two parts time. Why approximate this with 1-D version of time? Nature showed us that acceleration is one part space and two parts time. If we use one clock; 1-D time, you can't measure two different accelerations at the same time. On a 2-D time grid, you have two lines.

Are you confusing "parts" with "dimensions"?

If I make a drink with one part squash and two parts water; and you make yours with one part squash and three parts water; does our water have different dimensionality?

[Colin2B]

An interesting observation about science convention, has to do with the question, why didn't Professor Einstein use polar coordinates to interface his theory of General Relativity?

Because it doesn't matter. Coordinates are only a way of describing geometry and it is possible to convert between the different systems. Also, he wasn't describing spheres but distortions of a flat spacectime.

In terms of time, hundreds of years ago we found out that acceleration is one part space or distance, and two parts time. Why approximate this with 1-D version of time?

As @Bill S points out you are confusing 4D dimentions with dimentional analysis and getting the wrong answer.
Acceleration can involve 3 spatial dimentions but the time quantity is the same one, there arent 2 - only one time line measurement (elapsed time) defines the acceleration completly.

[jeffreyH]

If we have an object with velocity v and vx = c/4, vy = c/2 and vz = 0 then the time dilation in the x, y and z directions are not equal. In this sense you could think of a multi-dimensional time. Except you would be missing the fact that it is the magnitude of the vector that is important rather than the components.

[Bill S]

Jeffrey, I’m trying to visualise this.

I see a 3D grid. 
The object is stationary in the z direction, but has motion in the x & y directions.  Its motion could be shown on a 2D sheet as movement in a diagonal direction.

The object is moving in a specific direction through 3D space, and 1D time.

I don't see how this lets in an additional dimension of time.  Have I missed something?

[jeffreyH]

The point is that examining individual components can give the impression that they can be separated out and still be valid. Since each one's value differs they can appear to be distinct entities. I think a lot of people seem to struggle with the concept of vectors. This is why people can end up thinking of multidimensional time. It can even lead to strange ideas of energy.

[Bill S]

I think a lot of people seem to struggle with the concept of vectors. This is why people can end up thinking of multidimensional time.

Jeffrey, would you say a bit more about the link between struggling with vectors and introducing multidimensional time?

[jeffreyH]

Ok. Say we have a velocity vector v with components x, y and z. Let's say we have multiples of a particular speed (s) in each component. So that x = 3s, y = 4s and z = 6s. We can then calculate the time dilation for each component as if the other two were zero. This can indicate that time is running at different rates in different directions. This neglects the fact that it is the magnitude of the vector that experiences time dilation in the direction it is pointing. So we need to get the magnitude using Pythagoras. That is m^2 = x^2 + y^2 + z^2. Then take the square root of m. We can always orient the coordinate system via a transformation so that the direction is along one axis and the other two components are zero. You are heading into linear algebra territory now which I think a lot of laymen avoid.

[opportunity (OP)]

Ok. Say we have a velocity vector v with components x, y and z. Let's say we have multiples of a particular speed (s) in each component. So that x = 3s, y = 4s and z = 6s. We can then calculate the time dilation for each component as if the other two were zero. This can indicate that time is running at different rates in different directions. This neglects the fact that it is the magnitude of the vector that experiences time dilation in the direction it is pointing. So we need to get the magnitude using Pythagoras. That is m^2 = x^2 + y^2 + z^2. Then take the square root of m. We can always orient the coordinate system via a transformation so that the direction is along one axis and the other two components are zero. You are heading into linear algebra territory now which I think a lot of laymen avoid.

That's a good explanation of time as unique considerations for time on each axis, and I am presuming it is still a different rate of time linearly in the same direction along each axis from the zero point.


How would the following be defined though as dimensions of time:

Lets say we have a hypothetical spatial and temporal zero point from which extending outwards in three dimensions in space is a wavefront of time most simply represented as light, moving at a constant speed. Let's say that the initial start point, zero point, is like the big bang, as a paradigm of time "before" (for the sake of argument) that the time/light front goes out at a constant rate in the 3 dimensions of space as a spherical wavefront from.

Now consider another type of event horizon, for the sake of argument. This time we have an infinitely sized spherical 3-d spatial sphere, and light/time as a front moves to the zero point inside that hypothetical infinite sphere. For the sake of argument, let us say that time here moves from the infinite perimeter as a realm of time "after" to the zero point in that sphere as time "before", an inwards spherical front, a spherical front moving inwards from that hypothetical infinity.

Now for the sake of argument, let us suggest that the "lap-over" effect of time "before to after" (zero space to infinite space) and "after to before" (infinite space to zero space) is somehow (for the sake of argument) an overall "now" event of space.

The question is, "how many dimensions of time are there in that one common 3-d space system with those given proposals for the properties of time"?

[jeffreyH]

You missed the point. You can't have multi-dimensional time. If a frame is inertial then you can always define coordinates where the origin is at rest in the frame of interest. In this case there is no motion in ANY direction. Therefore the velocity vector becomes (0, 0, 0) and the magnitude of the velocity is zero metres per second.

[opportunity (OP)]

You missed the point. You can't have multi-dimensional time. If a frame is inertial then you can always define coordinates where the origin is at rest in the frame of interest. In this case there is no motion in ANY direction. Therefore the velocity vector becomes (0, 0, 0) and the magnitude of the velocity is zero metres per second.

I do understand that, yet my previous question was a way of showing that although what you say is true (the inertial frame of reference consideration for time), yet "underneath" that layer of time, that "now" event as I suggested, could be (as per the proposal) a sub-layer to time itself beyond the consideration of the inertial frame of reference. "There" I'm thinking whether or not "dimension" is the right term to use.

In my opening post I suggested the following:

Think of it this way...as opposed to thinking time has to obey the idea of space-relativity, linearly so, a space that decides that its own position is based on observational references (?), why not let "time" be an observational reference more in line with Brownian motion equations, and not space?....that the observational reference of time is tuned to the chance played with Brownian motion, as an algorithm...

I've been dablling with an "algorithm" for time that doesn't corrupt the overal inertial frame of reference for relativistic equations, but those equations are theoretical sub-structures to the linear one-dimesional time we implement in relativistic space transformation equations. The point is that they don't interfere with our equations for space and relativity, yet offer "another way" of considering the idea of relativity. To me they're equations, and haven't yet considered them as "extra-dimensions" of time. I think what I am asking is what they should be termed if they're useful and represent different paradigms for time.

[jeffreyH]

Time is the measurement of change. The rate of change in an inertial frame of reference is independent of direction. Otherwise I think we would notice. In an accelerating frame things change. Within a gravitational field this results in tidal forces and a difference in time at different coordinates.

[opportunity (OP)]

I agree. I've been working on an algorithm though that gives overall time the very feature we understand it to be, yet by it's definition suggests a substructure to time, independent of direction, yet based on "before" and "after" parameters. It began as an algorithm of "imaginary time" (i), which became too complex (excuse the pun) and had to be simplified to a ratio according the idea of time-before with time-after that still gave "now" time the definitions you describe. I though went further with that "under the grid" algorithm and tried applying it to known equations and ideas in physics and it still fit. Yet, I'm not sure of its significance.

I've been advised by someone who has looked at the theory that it, the theory, is only significant if it can predict a phenomena contemporary physics can't, or can do something like combining mathematically electromagnetism with gravity and then demonstrating an artificial gravity field through electromagnetic means as per experiment.

Just as a footnote, what I put forward as an example for time in the post:

How would the following be defined though as dimensions of time:.........The question is, "how many dimensions of time are there in that one common 3-d space system with those given proposals for the properties of time"?[/i]

was for any theoretical point in space, and thus time as a direction could be anything for each reference of space as a "now-time" event.

As you said: Within a gravitational field this results in tidal forces and a difference in time at different coordinates

"That" difference in time is a feature already wired, I've found, into time's potential substructure, making the idea of relativity a process of understanding the substructure of time, and not vastly complicated mathematical matrices for space trying to resolve the issues of relativity and light. Essentially, the substructure "defines" the scale of the time-difference for light, mass, and thus the idea of relativity that Einstein proposed for space. Clearly it can't be any simple substructure, as it would need to represent the mathematics for a wave-function for light that resolves issues like the uncertainty principle and quantum entanglement.....issues of time-variance and spatial displacement regarding light.