Does this make sense?

[Cecil]

This idea has been churning in my mind ever since I learned the relativistic equations for time/mass/length dilation and read that I should be thinking of spacetime as four-dimensional. I've never sat down to see if it's actually consistent, though it certainly appears that way to me now. I'm hoping some of the physicists here can help me out.

Basically, I conceive of all bodies moving at constant rates in straight lines in the warped 4-manifold that is our universe, regardless of velocity or forces. Bodies at rest are moving perpendicular to the spatial 3-plane (ie in the time direction) at the rate of one second per second. Bodies in motion (in some given reference frame) are moving slightly slower in the time direction, but exactly enough that using the Pythagorean theorem on the body's space velocity vector and its time velocity vector gives us a constant length of one regardless of the body's "space velocity".

Gravitional fields are like warpings of the coordinate system on the manifold. Clocks at rest in strong gravitional fields run slower than clocks in lesser fields - this is caused by the stretched coordinate system near the former clock. While in "reality" the time velocity vectors of both clocks have identical lengths of one, the stretching of the manifold near the former clock causes us (who live on the manifold) to perceive the vector as being shorter.

In this conception, moving from one reference frame to another is merely a rotation of the manifold relative to four "external" axes: 3 space and one time. Vectors which previously were perpendicular to the space 3-plane may now have some component in that plane, and vice versa.

Actually, while writing this post, I just came up with the idea that perhaps the "stretching" of the manifold due to gravitational fields is caused by the mass of the object "pushing" the manifold slightly deeper into the 5th dimension. What sort of tensile strength would be required for the manifold to adopt an inverse-square falloff pattern in that object's vicinity?

Right, so here's where you jump in and tell me how I'm a candidate for crank.net. It's probably glaringly obvious that I have had no physics since high school.

 

[Hellbound]

Um, actually, that's pretty much the idea behind general relativity. You just explained it in a nutshell.

 

[Cecil]

Um, actually, that's pretty much the idea behind general relativity. You just explained it in a nutshell.

Oh, uh, cool. I must have read it and not had it sink in immediately. It just seems intuitive to me that the sqrt(1-v^2/c^2) term in the dilation equations comes from the application of pythagoreas to a right triangle.

 

[Hellbound]

Oh, uh, cool. I must have read it and not had it sink in immediately. It just seems intuitive to me that the sqrt(1-v^2/c^2) term in the dilation equations comes from the application of pythagoreas to a right triangle.

That's pretty much it.

Have you read Einstein's "Relativity"? He published it in a book format. You can get it at most of the major bookstores. He talks about world lines, and how that right-triangle equation works (because of the relationship between spatial dimensions and time, graphed on a world line). He also gives a lot of his famous thought experiments, which helps to grasp some of the details of the theory.

Pretty good read, if a bit technical.