There is a famous metaphor used to illustrate General Relativity's description of gravity as the warping of space-time. It is the Rubber Sheet Illustration, and it goes like this. Take a flat rubber sheet suspended in the air. When flat, this sheet pictures empty space. If one were to place a bowling ball in the center of the rubber sheet, the sheet would no longer be flat. The weight of the bowling ball would create a depression, warping the formally flat sheet. A marble placed within the depression created by the bowling ball would naturally roll down toward the bowling ball.
The idea here being that the bowling ball and the marble represent matter, and the rubber sheet represents space-time. Just as the bowling ball warped the rubber sheet causing the marble to fall towards it, so too a massive object like the sun warps space-time causing smaller massive objects like the earth to fall towards it.
It is a pleasing metaphor that illustrates the relationship between matter and space-time quite nicely. However, it suffers from a glaring flaw. Notice I did not say the mere presence of the bowling ball causes the rubber sheet to warp. No, I said the weight of the bowling ball does so.
How could an illustration of gravity invoke gravity itself as an integral part of the illustration? That's like explaining why a strawberry is red by saying that it looks red.
If we changed the setting of the metaphor to outer space, devoid of gravity, would the illustration work? No. The bowling ball would have no effect on the rubber sheet whatsoever.
Here's my take.
What if we accelerated the rubber sheet upward against the bowling ball? The effect would be the same in that case. So to fix the flaw, we substitute gravity for accelerated motion. This is OK since they are the same thing anyway.
This small change reveals something further about the nature of gravity.
Why does space-time warp in the presence of matter? To answer this question, let's ask another. Why does the rubber sheet warp in the presence of the bowling ball in the modified metaphor? The answer is inertia. The bowling ball is stationary, and it resists the movement of the rubber sheet, causing the depression. Translate that and you have the reason why matter warps space-time. Space-time is moving and is warped by the drag of matter, which tends not to move.
But this brings up more questions! What is space-time moving through, and why does matter tend not to move through it?
My suggestion is this, what is moving can be thought of as a slice of space-time at an instant of time. This slice is moving through time, at the speed of light. If we imagine space-time being made up of non-vibrating strings, then these strings are all moving through time at the same speed, they therefore form a flat surface. This pictures flat space-time, and the flat rubber sheet. When strings vibrate they manifest particles or matter. The energy necessary to vibrate is taken from the energy needed to maintain their speed through time. As a result they slow down. In fact the more energetic, the more massive they are, and the slower they go. These slower strings are the matter that drag space-time as it speeds through time. That is why space-time warps in the presence of matter. It's the result of energetically vibrating strings slowing down relative to their non-vibrating neighbors as they all speed through time.
Just something I wanted to get off my chest. Let me know if you would like me to clarify any of the points.
QUOTE (imfromthepast+Jun 7 2006, 09:45 AM)
What if we accelerated the rubber sheet upward against the bowling ball? The effect would be the same in that case. So to fix the flaw, we substitute gravity for accelerated motion. This is OK since they are the same thing anyway.
This small change reveals something further about the nature of gravity.
Why does space-time warp in the presence of matter? To answer this question, let's ask another. Why does the rubber sheet warp in the presence of the bowling ball in the modified metaphor? The answer is inertia. The bowling ball is stationary, and it resists the movement of the rubber sheet, causing the depression. Translate that and you have the reason why matter warps space-time. Space-time is moving and is warped by the drag of matter, which tends not to move.
But this brings up more questions! What is space-time moving through, and why does matter tend not to move through it?
My suggestion is this, what is moving can be thought of as a slice of space-time at an instant of time. This slice is moving through time, at the speed of light. If we imagine space-time being made up of non-vibrating strings, then these strings are all moving through time at the same speed, they therefore form a flat surface. This pictures flat space-time, and the flat rubber sheet. When strings vibrate they manifest particles or matter. The energy necessary to vibrate is taken from the energy needed to maintain their speed through time. As a result they slow down. In fact the more energetic, the more massive they are, and the slower they go. These slower strings are the matter that drag space-time as it speeds through time. That is why space-time warps in the presence of matter. It's the result of energetically vibrating strings slowing down relative to their non-vibrating neighbors as they all speed through time.
Just something I wanted to get off my chest. Let me know if you would like me to clarify any of the points.
I'm a little confused about acceleration part. The idea of the sheet accelerating upwards works fine for the rubber sheet analogy, but how would this translate to 3-D (space-time would be moving in every direction at once in order to create a sphere of gravity)? Also, what would cause the strings to take energy in the first place and vibrate, creating matter?
I wouldn't mind just dismissing the string/vibration thing as "just because", but I can't really dismiss the moving space-time thing.
Anyway, I think this is an interesting theory - it got my brain working.
QUOTE (amac+Jun 9 2006, 07:19 AM)
I'm a little confused about acceleration part. The idea of the sheet accelerating upwards works fine for the rubber sheet analogy, but how would this translate to 3-D (space-time would be moving in every direction at once in order to create a sphere of gravity)?...
This was a point I glossed over. My apologies. In essence three dimensional space-time is accelerating in the direction of time, the fourth dimension. This is difficult to imagine because it is a four dimensional illustration, so let's simplify it.
Imagine that we discard one of the three spacial dimensions, leaving us with a two dimensional representation of space-time. In this stepped down analogy, time would become the third dimension. In this scenario, space-time would be the two dimensional rubber sheet. When we thereafter speak of the rubber sheet accelerating upward, we are not describing the sheet moving in a spacial direction, but a temporal one. In other words, the flow of time is the slice in space-time (the rubber sheet representing all of space at a single instant) moving upwards through time.
It takes energy to move through time at the speed of light. When the constituent strings composing space-time are left to themselves, all this intrinsic energy is spent moving through time only. Nothing is left over to power the vibrations that would manifest matter, they therefore manifest empty space.
Once a string begins to vibrate, part of their intrinsic energy is diverted from moving through time into the vibration. Their speed through time therefore lessens. This has the twofold effect of producing the warping of space-time known as gravity, and the time dilation effect that is associated with gravity.
As far as what causes the string to start to vibrate, I imagine space to be composed of strings much in the same way a table is composed of molecules. When something hits the table, a vibrational pattern is generated that is passed from molecule to molecule. I picture particles moving through space as happening in much the same way. A vibrational pattern is produced that is passed from string to string. In this scenario, a particle is not a vibrating string moving through empty space, but rather a vibrational pattern moving from string to string.
This was a point I glossed over. My apologies. In essence three dimensional space-time is accelerating in the direction of time, the fourth dimension. This is difficult to imagine because it is a four dimensional illustration, so let's simplify it.
Imagine that we discard one of the three spacial dimensions, leaving us with a two dimensional representation of space-time. In this stepped down analogy, time would become the third dimension. In this scenario, space-time would be the two dimensional rubber sheet. When we thereafter speak of the rubber sheet accelerating upward, we are not describing the sheet moving in a spacial direction, but a temporal one. In other words, the flow of time is the slice in space-time (the rubber sheet representing all of space at a single instant) moving upwards through time.
It takes energy to move through time at the speed of light. When the constituent strings composing space-time are left to themselves, all this intrinsic energy is spent moving through time only. Nothing is left over to power the vibrations that would manifest matter, they therefore manifest empty space.
Once a string begins to vibrate, part of their intrinsic energy is diverted from moving through time into the vibration. Their speed through time therefore lessens. This has the twofold effect of producing the warping of space-time known as gravity, and the time dilation effect that is associated with gravity.
As far as what causes the string to start to vibrate, I imagine space to be composed of strings much in the same way a table is composed of molecules. When something hits the table, a vibrational pattern is generated that is passed from molecule to molecule. I picture particles moving through space as happening in much the same way. A vibrational pattern is produced that is passed from string to string. In this scenario, a particle is not a vibrating string moving through empty space, but rather a vibrational pattern moving from string to string.
Thanks, imfromthepast. One more question about the acceleration thing, though. How and why is space-time accelerating at the speed of light through time? How can we even define the speed of light in a dimension of time - it is generally defined in meters/sec, but in a dimension of time, there are no meters or any other distance measurements - just time.
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