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 Forum index » Archive » Archive: Perplex City » PXC: Questions/Meta
Four-dimensional Rubik's Cube
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Rolerbe
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thebruce wrote:
interesting... re:gravity... I think if we apply physics that we know in our 3D world to a 4D world, the physics won't apply... I don't necessarily think a 4D object won't have any gravity - I think the concept of gravity won't apply to a 4D object in our 3D world... we just can't conceive of a 4D object, given our physics rely on 3D objects existing in theoretical 4 dimensions... so the 4D object would likely have similar effects - existing in 4 dimensions, with an effect in the 5th...


It is becoming more and more probable that we already live in a 10 or 11 dimensional universe. Perception is not the same as reality. We don't percieve the additional dimensions (for a variety of reasons), but that doesn't mean they don't exist. Gravity is, in fact, implied in the 11 dimensional string theory. So, a 4D object has no problem being affected, and space-time distorted by the presence of a large nearby mass.

Exert force to accelerate the object. Measure the force applied and the resultant acceleration. Gives measure of mass. "Rest mass" can then be determined using either Einsteinian or Newtonian equations, depending on the relative speed.
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PostPosted: Tue May 24, 2005 11:07 am
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Rolerbe
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hamatoyoshi wrote:

Here, however, is a discussion of what you're asking scaling from three dimensions down to two-dimensions and using lasagna for an example. Very-unscientific, but the only discussion I could find on it.

weight = mass * gravity

Assuming we scaled down to a three dimensional object in the two-dimensional world (back to the hand again; only using this since it's easier to visualize), I don't think gravity would change at all.

I'm assuming it would work the other way too.


I think the only possible remaining correction to make would be to determine the projection of the acceleration (gravity or otherwise) into the 3 dimensions that we perceive. But ultimately it makes no difference. Assume the 4D mass is greater than the 3D mass (i.e. some of the mass is 'projected' in the 4th dimension). Now apply a force and measure the acceleration. Since we can only apply 3D forces, we measure the force applied and calculate the 3D (projected) acceleration. Hence we come up with the 3D projected mass. If we really have no perception with the 4th dimension, then none of our (simple) experiments will reveal it.
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PostPosted: Tue May 24, 2005 11:12 am
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hamatoyoshi
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Rolerbe wrote:
If we really have no perception with the 4th dimension, then none of our (simple) experiments will reveal it.


I think that's it. Perhaps it's merely a matter of perception, but for all intents and purposes, this fourth dimension wouldn't apply to us, because it doesn't exist for us.

Think about passing your hand through a 2-dimensional world again, only the "cross section" of your hand that is within that world exists within the bounds of that dimension, the rest of your hand is entirely unaffected by the laws of that world, though actions in that world may lead to consequences only perceptible in our 3-dimensional world.

Suppose a 2-dimensional car collided with your hand, would it have any consequence (such as cutting your hand through)? This is probably why you shouldn't go sticking your hand into other-dimensional worlds should you ever have the opportunity.

PostPosted: Tue May 24, 2005 12:30 pm
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tanner
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 		the maximum volume a 3d slice of a tesseract that can affect a 3d space such as ours is the volume of one of its bounding cubes -- given a constant density and composition this will give the maximum mass (weight) -- the mass could vary if the 3d slice were a lower volume (all the way down to zero) IMO Smile
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PostPosted: Tue May 24, 2005 3:28 pm
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Rolerbe
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 		Projection physics
Along the lines of our discussion of mass projection into the various dimensions (real or imagined), here's an interesting way to think about time, space, and the speed of light.
(I accidentally wrote "the speed of life" here -- not much different, given my current lifestyle Smile )

We, and all the matter in the universe is travelling at the speed of light, right now. But the velocity vector is all in the time dimension. When we 'travel' in space, we are changing the direction of the velocity vector, but not its magnitude. Some of our speed is projected into the spatial dimensions. The more force applied, the greater the projection. As we project more of the velocity vector into the spatial dimensions, the projection in time is reduced (i.e. time dilation). The mathematics for this 'view' actually works out and is synonymous with Lorentz and Einstein.

Time flows at the speed of light!
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PostPosted: Wed May 25, 2005 7:57 pm
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invfish
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hamatoyoshi wrote:


I think that's it. Perhaps it's merely a matter of perception, but for all intents and purposes, this fourth dimension wouldn't apply to us, because it doesn't exist for us.


I wouldn't go so far as to say 'doesn't exist for us'. I would say that it is yet to be discovered (and if discovered have a possible means to return to the 3rd dimension or even find words to describe the 4th dimension) or we are yet to become 'aware' of it's existence as our perception evolves.

One major flaw with science is that the tools it uses are made to give the answers they are looking for. I.e. there is no tool created to find the 4th dimension and prove its existence because they do not know where to begin (i.e what exactly is the 4th dimension?). If they knew where to begin, you could bet that there would be a tool to experiement and make observations with Wink

PostPosted: Thu May 26, 2005 10:32 pm
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invfish
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 		Re: Projection physics
Rolerbe wrote:
Time flows at the speed of light!


Even within a dream?
Wink

PostPosted: Thu May 26, 2005 10:34 pm
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Violet
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invfish wrote:

I wouldn't go so far as to say 'doesn't exist for us'. I would say that it is yet to be discovered (and if discovered have a possible means to return to the 3rd dimension or even find words to describe the 4th dimension) or we are yet to become 'aware' of it's existence as our perception evolves.


I don't think it's merely a case of not knowing where to begin, or having the right tools to find the 4th dimention: as far as humans are concerned there are only 3 dimentions that we can ever comprehend because our own brains don't have the tools to deal with it. Just as we can't ever comprehend the humungousness of the universe. It doesn't mean we just haven't stumbled across the 4th yet and somebody really really clever will one day, I don't want to put our species down, but we just aren't equipped for it! Perception comes only through what the brain experiences.

PostPosted: Sat May 28, 2005 1:10 pm
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invfish
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Violet wrote:
It doesn't mean we just haven't stumbled across the 4th yet and somebody really really clever will one day, I don't want to put our species down, but we just aren't equipped for it! Perception comes only through what the brain experiences.


Expand your mind Wink
It will happen. We haven't stopped growing yet =)

There is nothing our minds can not think of.

PostPosted: Sun May 29, 2005 7:35 pm
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NovacaineX
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Quote:
There is nothing our minds can not think of.


There might be plenty of things our minds cannot think of, but we'd never know because we can't think about them! Razz

PostPosted: Sun May 29, 2005 11:54 pm
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Violet
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 		Well said!

PostPosted: Mon May 30, 2005 8:55 am
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