OK ... I have been hinting at this for a while and wanted to get some of you more math prone people to comment of this.

Can the compression of space-time be considered a dimension? Or would it rather be somehow a derived value?

here is a small thought experiment:

We are observing a point in space time. We notice that it is in a gravitational field and that its space-time is compressed relative to ours. Our friend is travelling at the speed of light and we perceive her space-time as being even more compressed than ours. However our friend is also observing the point we are observing and she perceives it to be expanded relative to her space-time.

Now lets say we name that point
0x, 0y, 0z, 0t
Can we then say it is at 1c or 2c for its compression dimension? where as we are observing it at its 1c position while our friend is observing it at its 2c position?

so for us the point is at ( in 5 dimensional space-time-compression )
0x,0y,0z,0t,1c


Or alternatively

Can the compression be calculated somehow as a dirivative ( hmm or integral ( forgetting /am confused by the math her ) ) of the scalar state of the space time possibly with relation to a gradiant of gravity?

Is there a way to change a title of a post ... I realized I had a misspelling there

Yeah. You meant dementia, right?

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compression is not a dimension, you are just talking about scaling, using different measuring rods, you still measure the same three dimensions. This has already been discussed to death in the thread that "scale" would be a dimension.

Spacetime is not scalar, I would hope that 3-space is vectorial.
Compression is just dividing the rods of one by a certain value.
I totally cannot make sense of what you want to say here.

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I was stating that gravitational fields are scalar. So that the gradiant of the gravitational force could be calculated. This is a question as I really done know. My thought is that the compression of space-time would related to the gradiant of the gravity. But in all honesty I have no clue what I am talking about.

Well this confuses me. Because my local scale is not the standard scale. In fact there is no standard scale. We only perceive that the something is a certain size. Even in 3 dimensional space the depth perspective is only percieved by the overlay of two 2 dimensional spaces.

it seems that similarly to some extent if we look at three dimensional space from two different perspectives us and our friend travelling at near the speed of light or sitting in a gravity well, Can we perceive the 4th spacial dimension or compression.

Firstly is there an infinite set of compressions that a point in space time can be at? My answer is yes.

Secondly if you plot three dimensional space x y z and then you expand the distances between the points, although the relative proportions of x,y,z hold. The distance changes. now lets say that we have a two dimensional space and we double the space. We draw the first graph on one sheet of paper and the doubled graph on a second. we gave the first graph an arbitrary value of one and the second graph a value of 2x1. We could then create a 3 dimensional space where the at point 1 of depth ( dont want to use z here so not to confuse it with the spatial dimension of z ), we have a point or a line or curve or whatever and at point 2 of depth we have each point, curve or line at proportionately double their x and y values. Now we fill in the spaces between with straight lines. We can then define the difference between point a at a compression of 1 and point 1 at a compression of 1, in fact point a ( in 2 dimensional space ) is represented in three dimensional space. I can then give you a distance of 1 between point a of compression level 1 and point 2 of compression level 2. What would the units be?
Actually I think we can draw a 2 dimensional space with a certain contraction factor to represent 3d sapce. This would be like a real picture. Kind of like a holgraph.

Now we switch from 2 dimension to 4 and add the one of compression and we have 5. We can now tell the difference between a light year at compression 1 and a light year at double the compression of 1. As t changes. the compression for each point relative to inself change would stay at 1 ( or 0 ). so at 1 second you would have a relative compression of 1 and if you moved you would have x', y', z', t' looking at it from one point over at a specific place in time you would have x + delta x, y, z, c' , 0 so at a certain point of time there would be a difference in compression for every point in the universe relative to us.

That is very hard to visualize from your words... can you draw a picture?

All I get from that is lines that are still in 3 dimensions connecting points that have moved in those 3 dimensions.

Your OP sounds like you are trying to state the rate of change of the compression. That would be a simple calculus example. But; the dimensions do not change.

If I want to get the rate of change of a curve (the slope) in 2d on a graph, I still get that rate expressed in 2 dimensions.

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Well that was my question ... however the curve is really defined by the level it is compressed. Another way to look at it would be to define the relativistic effect on space-time as the 5th dimension.

Now again you may be right ... maybe not a dimension but without out this number you can not compare two view points of one space-time can you?

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I guess that's a quick way to interpret my point...It is not a dimension.

In the same way we express 3d with x,y,z, but we express the distance two different points (x1y1z1)(x2y2z2) in length. Length is not a dimension, nor is it in the "language" of x, y, z. Yet the math is there and they are interpretations of the same things, but concentrating on the different properties.

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Is the rubber sheet analogy of any use to you? That the coordinate is in a gravity well pulling space? This only requires coordinates in a plane x,y and treats the dip in space (or lift for that matter) as a dimension.

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Yeah that is cool ... so the rubber sheet is representative of 2 dimensional space. Now. The compression factor would be the indent in the z direction ( not to be confused with z direction is xyz space). Now that should be able to be applied to 4 dimensional space to create 5 dimensional space.

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No.
Don't invent your own terms.
Use the existing terms to communicate clearly.

In order to understand these concepts you must have a clear set of basic definitions. Dimension, for instance, has a precise mathematical meaning. It is not to be confused with The Twilight Zone stories.

There´s a classic that is often indicated here, for those who want to get in touch with space-time warps and general relativity. Let me introduce to you Kip Thorne´s Black Holes and Time Warps: Einstein's Outrageous Legacy. Only 12.89 at Amazon in paperback edition.

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Thank you Argos,

That is an excellent reference. For dimension I was thinking lower order which would make it Hausdorff dimension. The most visible example would then be a solar flare. Hypothetically of course, a low region of heat and material form relative to the surrounding material in the sun and through turbulence a whirlpool forms. The opening of the whirlpool is circular and is described as a normal circular opening. A two dimension start.

As it grows it forms a tornado with an intensely hot centre that shifts out of the line of the circular opening. Since it is primarily linear it is one more dimension however curved. When the solar flare breaks the surface and arches into space before reconnecting it is still three dimensions.

But when the flare connects back into the sun at a new point that point connection adds one more to the structure. Topologically a solar flare is a four dimension structure. Because it is within our larger three dimensions we do get to see the solar flare although due to the workings of the sun we do not see either the opening or reconnection.

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The example could be worked slightly more in that reconnection back to a point along the whirlpool (or tornado because some groups but probably not this one like tornadoes) and reconnect as one would a mobius strip.

The effects could be twofold in that the solar flare may describe what appears to be multiple loops in a single flare or if the whirlpool was large enough and the camera was in the right spot a single flare form within the original causing rapid intensification of the original loop.

For the flare to dissipate then the centre of the whirlpool needs to locate a reconnection region not within the structure. There are a lot of very good quality solar images and a new solar cycle beginning so from an astronomy point of view a good thing

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"Nature is obliged to let reality determine its laws, whereas mathematics is under no such constraint."

well you have space + time ... what are the other 6 dimensions?

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Meanie.

Thanks, NF.

(Mean-ing, for our English as a second language posters. Oh well, it's been a long day.)