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Klope3

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Thu Nov 12, 2009 6:08 pm Post subject: Is it possible to reach the Fourth Dimension? 

So the question of whether or not the fourth dimension exists has already been asked. But what if it does? Do you think we could ever be able to reach itor cause an inanimate object to be forced into it? Thoughts please




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loki_clock

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Fri Nov 13, 2009 5:23 pm Post subject: Re: Is it possible to reach the Fourth Dimension? 

Well that depends on whether or not we're already interacting with it. String theorists believe there are already higher angular spatial dimensions by which the natural forces work, and it might one day be possible to exploit these forces to cause other things to rotate into them. However, I don't believe it's possible to create a force along an axis out of forces that are flat along that axis, so unless we discover some method of synthesizing completely arbitrary force vectors, I don't think it's possible to move something into a higher linear spatial dimension. Besides that, I'd worry about the integrity of the object we're pushing around, since hydrostatic equilibrium will, if I understand its nature correctly, cause the spheroid forms of the particles to collapse into glomular ones.




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Klope3

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Sat Nov 14, 2009 1:25 pm Post subject: Re: Is it possible to reach the Fourth Dimension? 

I got lost on a few of your vocabulary words, but its seems we're about on the same wavelength. It would be hard to cause strictly threedimensional objects (such as pistons or human muscles) to accelerate an object (such as a cube or a human body) in a fourdimensional direction. Such 3D objects create force *because* they move in 3D directions.
And I have also wondered what would happen to a 3D object once it's in 4D. It seems to me that if a hypothetical 2D creature somehow entered our 3D world, gravity would pull all its internal organs out because they would no longer be held in by a restriction to two dimensions of movement. If dimensional analogy applies here, and if gravity behaves similarly (or at all) in 4D, then entering 4D could be very dangerous for a human...




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loki_clock

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Sat Nov 14, 2009 2:04 pm Post subject: 

What terms in particular? I can explain any of them pretty easily.




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Klope3

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Sun Nov 15, 2009 2:59 pm Post subject: 

 Hydrostatic Equilibrium
 Glomular/Glome (heard this before but don't know what it means)




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loki_clock

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Sun Nov 15, 2009 4:22 pm Post subject: 

Glomes are 4D hyperspheres.
As for hydrostatic equilibrium, I'm pretty surely misusing the term. It's the balance of gravitational compression with an outward pressure gradient. Once celestial objects reach a certain size, hydrostatic equilibrium causes their irregular shapes to move toward an overall form, a reflection of the forces acting on it. In simple cases, those will be spheroids, hence the shape of the planets.
That's mostly irrelevant (since we're going on the assumption that I used it wrong), except to understanding my analogy. When a force acts from all vectors equally inward (gravity) on a central point, the things moving toward the point will form a sort of ball. Then if there's some method of distributing the matter evenly, the result, in a perfect example, is a sphere. In the case of the celestial bodies, the method of distribution is rotation. In the case of particles, it's the insustenability of its own form. Its essentially an extremely topheavy object, bound to fall apart with just the slightest offset in its negligible dimension. It doesn't, however, collapse to a singularity, because of the repelling forces of whatever's first to collapse to a stable, repelling particle, or one that attracts them. That's where the equilibrium part comes in.
The other problem with sending something into a tangent dimension is the possibility that if something is singular along an axis, then it has infinite density, thus gravity, along that axis, like cosmic strings and domain walls. This would make it impossible to send anything with mass into the tangent dimension, or at least translate it once it was relieved, because it could not escape the infinite gravity of the particles it would be passing over.




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ChaimLeib

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Thu Nov 19, 2009 9:03 pm Post subject: Re: Is it possible to reach the Fourth Dimension? 

loki_clock is right that it could be dangerous to enter the fourth dimension, but if I am understanding string theory and spatial dimensions correctly (I'm only an EE/CS major), it would not be possible to attain infinite mass density.
To explain why, we can think of Flatland, a 2D universe. If we took Mr. Square and tried to align him in way to make him infinitely dense, it would be impossible, no matter how we rotated and translated (moved) him around. If we rotated him in the third dimension, he would appear as a crosssectional line in Flatland, but that line would contain a tiny fraction of his mass, most of which is outside of Flatland in 3D space.
At the same time, Mr. Square would be extremely vulnerable, if someone decided to try poking at his crosssection, because it has practically no inertia. Ripping him in half becomes a distinct possibility. The same goes for the rest of the inhabitants of Flatland, should Mr. Square happen to reenter Flatland in a place that was occupied by someone else. (Mr. Square wouldn't crumple if he is perfectly flat.)
Similarly, if a 3D person were rotated in the 4th dimension, we would see his 2D crosssection. He would have the same problems if someone collided with him in this state.




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ChaimLeib

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Thu Nov 19, 2009 10:04 pm Post subject: Re: Is it possible to reach the Fourth Dimension? 

Another problem with travel to the 4th dimension involves string theory. Science currently tells us that there are four basic forces in the universe (and as far as we know, there aren't any more). They are:
1) gravity (carried by the yetundetected graviton);
2) electromagnetism (carried by photons),
3) the weak interaction (carried by bosons, and apparent in radioactive decay), and
4) the strong interaction (carried by gluons, which bind atomic nuclei together).
Although gravity is the most familiar force, the other forces are actually much more powerful, by at least 25 orders of magnitude. The strongest of these, the aptlynamed strong force, is more powerful than gravity a factor of 10^39.
Theorists say that close the time of the Big Bang, the electromagnetic force and the weak weak interaction were unified due to the extremely high energy levels that were present. They call this the electroweak force. After energy levels decreased, they became two separate forces (with the electromagnetic force stronger by nine orders of magnitude).
This presents the possibility that other forces were similarly unified and later separated. This is the Unified Field[/Force] Theory. (If this is true, we may only be seeing a sliver of the graviton's true power in our three dimensions; gravity may actually be an incredibly powerful force! In that lies the problem of sending an object into the fourth dimension, if it has mass.)
Unfortunately, there are limitations to modern science that make it impossible to extrapolate back in time to verify the Unified Field Theory. The laws of quantum mechanics break down before a certain point in time near the Big Bang. Beyond that point, it is impossible to tell what happened before, because causeandeffect as we know it no longer apply.
All this is an active area of theory and research. Currently, the primary focus of string theory efforts is to use huge particle accelerators to create subatomic particles in the hopes of creating... the elusive graviton. This would be strong circumstantial evidence to support string theory, which calls for the existence of such a particle. If a graviton is created in one of these smashers, there will be a energy difference between the input particles and output particles due to the escaping graviton transferring energy... to the fourth dimension.
If we could produce these highenergy, massless particles, it may even be possible to communicate with intelligent beings that live beyond our common 3D universe.




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loki_clock

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Fri Nov 20, 2009 10:03 pm Post subject: Re: Is it possible to reach the Fourth Dimension? 

ChaimLeib wrote ( View Post): › If we rotated him in the third dimension, he would appear as a crosssectional line in Flatland, but that line would contain a tiny fraction of his mass, most of which is outside of Flatland in 3D space. 
That's the problem the assumption that it's merely flat as possible in our dimensions. If it's a truly 2D object, it will be singular along the third axis, and will have at least effective infinite density, even if it has fluctuations.
Quote: › At the same time, Mr. Square would be extremely vulnerable, if someone decided to try poking at his crosssection, because it has practically no inertia. Ripping him in half becomes a distinct possibility. 
Yes. And if an event horizon does not form as the hypothetical result of the flatness, I think it would also be infectious. The slightest knock from the tangent axis would cause the particles to collapse into a hypersolid form, then attract the surrounding particles with no resistance on their part, and so on and so forth.. Molecular bonds would mean nothing at all to a hyperdimensional vargi.




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ChaimLeib

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Sun Nov 22, 2009 5:05 pm Post subject: 

loki_clock wrote ( View Post): ›
That's the problem the assumption that it's merely flat as possible in our dimensions. If it's a truly 2D object, it will be singular along the third axis, and will have at least effective infinite density, even if it has fluctuations.

How can this be? If objects (like parts of Mr. Square's body) can have gravitational effects on the 2D universe as if it were inside the 2D universe, even though they are not in actuality; that would mean that any 3D mass, no matter where it existed in the 3D universe, would have essentially infinite 2D mass density, whether it intersects the 2D universe or not. Is this what you are implying?
If so, since there are no locations of infinite mass in our universe (we know this because if that were so, all the objects in the universe would be converging to that place close to the speed of light, and current observations show the universe to be expanding at an accelerating rate) there is no mass in the fourth dimension, besides what exists in the confines of our common 3 dimensions.
loki_clock"; p="463 wrote: ›
Yes. And if an event horizon does not form as the hypothetical result of the flatness, I think it would also be infectious. The slightest knock from the tangent axis would cause the particles to collapse into a hypersolid form, then attract the surrounding particles with no resistance on their part, and so on and so forth.. Molecular bonds would mean nothing at all to a hyperdimensional vargi.

It seems you are describing the gravitational "clumping" of 2D mass into the 3rd dimension, like a bunch of sand falling on a single point piling up into a cone. This coneshaped pile could only come about if the grains of sand are landing slightly off of their target. If they were precisely falling on the same point, and there was no net force in any direction besides that of gravity, the particles would actually pile up in a thin, towering line.
Also, I've never seen the term "vargi" anywhere, and Google doesn't give me anything. Could you explain that last sentence?
Quote: ›
...then attract the surrounding particles with no resistance on their part...

Be careful not to confuse mass density and mass itself. If all of Mr. Square's mass were concentrated at one line (which I don't think is possible, as explained earlier in this post, above), he would nevertheless have the same, finite total mass as before, provided we retain the Law of Conservation of Mass. If the mass in a human were converged to a singularity of infinite mass density, the resultant black hole would be a *very* tiny one, with the diameter of the event horizon on the submicroscopic scale.
Furthermore, it is safer not to say "no resistance" without qualification in this case. Mass is generally held to be the resistance of an object to acceleration, and any object with mass therefore has inertia/resistance (inertial mass). If you hold that inertial mass and gravitational mass are different quantities (an unconfirmed hypothesis; the General Theory of Relativity actually contradicts this with the strong equivalence principle) and you refer to zero gravitational mass here, that of course would mean that the mass is wholly unaffected by gravity, which is unfortunately not true, as Mr. Square will tell you.
In summary my hypotheses are:
Mass that doesn't intersect our universe does not have the same gravitational effect as when it does intersect. This is because I am hypothesizing that gravitons originate at the location of the mass and propagate in straight lines as a general rule; they don't first head to our 3D universe and then suddenly turn 90 degrees midtransit and propagate from there.
The Law of Conservation of Mass and Energy (remember that conversions can take place through E=mc ^{ 2 } ) still holds in 4D.




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ChaimLeib

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Sun Nov 22, 2009 6:07 pm Post subject: Re: Is it possible to reach the Fourth Dimension? 

In the beginning of my post, it appears as if I am confusing mass density and mass; what I was actually doing is assuming that a finite 3D mass is infinite 2D mass. I realize now that that is probably another big question, which I'll address here.
I reasoned that:
if a 1D slice of Mr. Square's 2D body is an infinitely small fraction of Mr. Square's mass;
it follows that a 1D Mr. Line sees Mr. Square as being infinitely more massive than he, since he is, after all, the size of a 1D slice of Mr. Square.
From there I generalized to higher dimensions that an (n1)dimensional object has a mass that is an infinitely small fraction of the mass of an ndimensional object. Or in reverse, an ndimensional object is infinitely more massive than an (n1)dimensional object.




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loki_clock

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Mon Nov 23, 2009 4:41 am Post subject: 

I'll try to respond to the best of my ability, but it doesn't look like we're on the same page here at all.
Quote: › How can this be? If objects (like parts of Mr. Square's body) can have gravitational effects on the 2D universe as if it were inside the 2D universe, even though they are not in actuality; that would mean that any 3D mass, no matter where it existed in the 3D universe, would have essentially infinite 2D mass density, whether it intersects the 2D universe or not. Is this what you are implying? 
No, I mean that any purely 2D mass has maximum gravitational effect along the axis it's flat on, so that it has finite density on two axes and infinite on one. Then also a 3D mass would have infinite 4D mass density, not 2D. This is, as I understand it, the implication of spacetime singularities.
Quote: › If so, since there are no locations of infinite mass in our universe 
Not infinite mass, infinite density.
Quote: › (we know this because if that were so, all the objects in the universe would be converging to that place close to the speed of light 
Ah, but the problem is, only the particles closest to it would be accelerating at the speed of light. This is the maximum intensity. Everything further away from it has to be drawn in slower than the speed of light. Infinite mass would affect the radius of the singularity's horizon, making the region of maximum effect cover the whole universe, but again I'm referring to (effectively) infinite density, which can be acquired by any amount of mass, but more importantly here is automatically acquired by anything with 0 size. Black holes have effectively infinite density, but because everything has to be drawn in slower that's further away from it we're not all being drawn into the nearest black hole at the speed of light.
loki_clock"; p="463 wrote: ›
Yes. And if an event horizon does not form as the hypothetical result of the flatness, I think it would also be infectious. The slightest knock from the tangent axis would cause the particles to collapse into a hypersolid form, then attract the surrounding particles with no resistance on their part, and so on and so forth.. Molecular bonds would mean nothing at all to a hyperdimensional vargi.

[/quote]It seems you are describing the gravitational "clumping" of 2D mass into the 3rd dimension, like a bunch of sand falling on a single point piling up into a cone. This coneshaped pile could only come about if the grains of sand are landing slightly off of their target. If they were precisely falling on the same point, and there was no net force in any direction besides that of gravity, the particles would actually pile up in a thin, towering line.[/quote]
Hmm, no. I'm describing the 2D world as this thin tower, and the influence of gravitational forces from 3D objects as the first deviation the tower has ever encountered. Since the particles knocked out will soon, I'm proposing, become higherdimensional particles, they too will exert 3D forces on their 2D neighbors, spreading all the way down the tower like a game of Jenga.
[/quote]Also, I've never seen the term "vargi" anywhere, and Google doesn't give me anything. Could you explain that last sentence?[/quote]
Dative of vargr, which is an Old Norse idea of the wolf as a destroyer, especially of worlds. Whither Tolkein's "wargs."
From the rest about resistance, you can probably tell now that I understand that already. But now that I think about it, if they have truly 0 mass, their event horizon must also be infinitely close to them. As long as you never touched it, you would never be trapped in it, but you could still never go past it.




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