A thought that keeps popping into my head.

[xiphias]

So, gravitation and acceleration have such similar effects that it feels like they ought to be the same thing -- that one of them ought to be a special case of the other. My gut feeling is that acceleration is a more basic sort of thing, so I just keep feeling like gravity ought to be a special case of acceleration. And then I keep thinking of the "rubber sheet" metaphor for gravity wells in space. And I don't want to take that TOO far, because I'm not even sure that the "rubber sheet" thing is even a MODEL, but it does stick in the mind effectively.

(You know, imagining a two-dimensional version of space as a rubber sheet, and then you put objects with weight on them, and it deforms the rubber sheet, and that gives you a way of visualizing what happens as mass in space creates gravitational "fields".)

So I just sort of think of that rubber sheet thing. And you could imagine that rubber sheet floating in space, but accelerating in a direction, and, with constant acceleration, the objects would have the same effect of deforming the rubber sheet.

So, I just have this thought -- what if gravitation happens because our three-dimensional space is accelerating along an axis perpendicular to all of our spacial dimensions?

Now, where my brain starts having trouble is I'm trying to imagine what happens if the dimension it's accelerating along is time. I just can't get the math. I feel like, if I understood the math, the equations on relativistic time dilation would either prove that this is NOT what is happening -- that the universe accelerating along the time axis is not compatible with the way relativity works -- or that it would give a possible way of explaining time dilation. And I don't know which, 'cause I don't have the math.

Ah, well. I thought I'd throw that out there, anyway.

Comments

[gingicat]

Whatever else it may be, it would make an awesome SF story.

[530nm330hz.livejournal.com]

Channeling Einstein again, are we?

[wcg.livejournal.com]

OK, let's take this by parts. First, gravity as we feel it *is* an acceleration caused by the force, commonly called the gravitational force, which is an attractive force between two objects dependent on their respective masses and the distance between them. Newton wrote it out as F = G*m1*m2/r^2

Second, there are other types of acceleration. The one we see all the time is the electromagnetic acceleration of charged particles which produces the images we see on our computer screens, TV screens, cellphone screens, etc... All accelerations are caused by some kind of physical force. The four known physical forces acting in our universe are gravitation, the electromagnetic force, and the two nuclear forces, which only manifest at sub-atomic distances. Those two are the strong and weak nuclear forces, and about 20 years ago some of the bright sparks out at Fermilab showed that the weak nuclear force split off from the electromagnetic force way back when the universe was a few seconds old.

The rubber sheet model of gravitation and spacetime comes from General Relativity, where Einstein gave us the rubber sheet to illustrate Reimannian geometry, where the surfaces are not necessarily flat. In Reimannian geometry, the dimensions are not defined by the x,y,z unit vectors you're familiar with from regular Euclidian geometry. Rather, the dimensions are defined by surface differentials (the basic form of derivatives) which are orthogonal to each other. So the Euclidian unit vectors are a special case in the classical limit where spacetime is not warped by the presence of mass. When a mass is placed into the spacetime manifold, the manifold warps with the amount of warping proportional to the mass. This warping induces a curvature and the curvature can be measured by changes in the unit differentials.

Which (finally) brings us to your core question: what if gravitation happens because our three-dimensional space is accelerating along an axis perpendicular to all of our spacial dimensions?

The answer is, no, gravitation is not caused by that. General Relativity is a very, very, very well tested theory of gravitation most recently confirmed by the Gravity Probe B results.

Now, the three spatial dimensions we perceive are indeed all perpendicular (or orthogonal) to the time axis. This is most obvious in the Special Relativistic case of a "flat" spacetime manifold (without any mass) where the unit vectors are x, y, z, and -t. (If you want to know why the minus sign has to be there, just ask.) But we're not accelerating along the time axis. The time axis is, itself, an integral part of the spacetime manifold. Time dilation happens if we move very fast in the spatial dimensions, but time dilation is a localized phenomenon limited to the small volume of spacetime that's been accelerated in the spatial dimensions. It's not an acceleration of the spatial matrix relative to the time axis.

Clear as mud?

of astronauts and elevators

[thnidu.livejournal.com]

Bravo, wcg! That's much clearer (and much more detailed) than anything I could've said to this.

To amplify one line -- gravity as we feel it *is* an acceleration caused by the force, commonly called the gravitational force,:

We don't actually feel gravity at all, but the effects of resistance to it. That's why the "zero-g" experienced by astronauts in orbit is also called "free fall", and part of their training for it is in aircraft that for brief periods (a minute or less?) move just as they would if they were falling freely. That's why we feel heavier as an elevator starts upward or stops downward, and lighter in the opposite cases: It's accelerating against or with the force of Earth's gravity, forcing us upward or letting us fall (partially) with it.

[mrmorse.livejournal.com]

Just to reinforce what others have stated, under General Relativity, acceleration and gravitation are the same thing. This is known as the Equivalence Principle.

[felis-sidus.livejournal.com]

Didn't some quantum physicist or other come up with a theory that time doesn't really exist and the calculations to support it? Was that ever accepted or disproven by physicists in general?