What Shapes Can We Visualize in the Fourth Dimension?

AI Thread Summary
The discussion explores the concept of the fourth spatial dimension, emphasizing that it can be visualized through analogies like the book "Flatland," which illustrates how a two-dimensional being perceives three dimensions. Participants mention the tesseract as a representation of four-dimensional objects and discuss the unique directional properties of the fourth dimension, termed "ana" and "kata." The conversation also touches on string theory, suggesting that higher dimensions can be constructed from points or strings, leading to complex geometric interpretations. Overall, the participants grapple with the challenges of conceptualizing dimensions beyond the familiar three, highlighting the intricate relationships between geometry, physics, and our understanding of space. The dialogue underscores the difficulty of visualizing higher dimensions while proposing intriguing theories and analogies to aid comprehension.
  • #51
This Zeno thing has been hashed to death on other boards of this forum,. I will just say this, 1/2 + 1/4 + 1/8 + 1/16 + ... + 1/2{sup]n[[/sup] adds up to 1 if you include all the terms. Convergent sequences have limits, and that disproves the simple minded version of the Zeno paradox. But no doubt you will have some other phony argument about limits.

Your ideas about string theory are another matter. They are just as wrong as your ideas about real numbers. String theory does not say "A point is a string".
 
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  • #52
I don't agree with the simple minded Zeno thing either. But all my life I have questioned the meaning of numbers.

String theory does say that instead of numerical points we have strings, and that idea answered all my questions. It also lead me to realize how we can have a space with 10 dimensions and wormholes.
 
  • #53
Okay, I just realized string theory talks about point particles being strings. It was me who extended that idea to all of space, and there, I found the six extra dimensions of string theory. When you create space out of equal length strings instead of non-dimensional points, you find that you can only travel back and forth in six directions. The number six is extremely important! To go in any direction you have to zigzag through three of the extra dimensions, to arrive at any point.

Many tetrahedrons is what space would look like if it were made from strings. The edges of the tetrahedron, which would be the strings you construct space from, go in six directions.

Smolin's Loop Quantum Gravity suggested that space may be made of little faceted structures, exactly like my tetrahedrons.

Molecules and objects are a collection of point particles. All the point particles would ride along the strings of space as the object moves freely through space, or maybe the molecule is precisely projected through space (this idea can be used to explain the "how" behind a lot of the conclusions in Relativity). The point particles of a molecule guide and govern the motion of all objects though space, but the point particles themselves can only go in six directions as they ride along the strings.

When I head that Voyager slowed down for no reason, it precisely fit one of the conclusions I had drawn. Space itself would be more densely packed far away from any massive objects, and an object would slow down.
 
  • #54
Originally posted by John

When I read that Voyager slowed down for no reason, it precisely fit one of the conclusions I had drawn. Space itself would be more densely packed far away from any massive objects, and an object would slow down.

Did it? I never knew that. So, your estimation of this finding is that space must be more densely packed (with?) the farther away from massive objects. Is there an upper and lower limit to the label 'massive'? Do you summize that the relationship between the amount space is packed is directly proportional to distance from these massive objects? Does that correlate to gravity? Does this explain all the missing matter in the universe? Couldn't it just be that Voyager drifted through an undetected 'cloud' of dark matter which caused friction and drag on the spacecraft ?

Your thinking regarding these non-dimensional points being strings that 'suck' matter (and intertransferable energy) along is intriguing. It reminds me of some of the current speculative fictions available on the bookshelf.

As for this debate between corresponding points on differing lengths, my logical mind agrees with selfAdjoint, whereas my creative mind likes your reasoning (however wrong, misguided or anti-establishment). Like I've said before, perhaps (in a very circumventive way) you're on to something. Who knows?

I think the trouble with tertrahedrons (or any figure for that matter) is that they are three-dimensional constructs. Thinking multi-dimensionally, the actual composition of the ultra-microscopic space fabric will be something utterly different. The tertrahedron is a shape recognizeable to both our three-dimensional mind and eyes - and so it fits in nicely with your theories. Application, however, interdimensionally would result in something quite removed from this familiar shape. I think the key to working it all out is to discard our three-dimesionally-crippled mind-sets and try to think multi-interdimensionally. Flatlanders trying to envisage our 3D world would draw flat projections of shapes they recognize in order to imagine them applied to the invisible third dimension. You have to do the same with your tetrahedrons - try to envisage them on another plane entirely. Will the 3D shape hold up to the test? The flat image the Flatlanders drew didn't!

I see where you're coming from with your lengths and points issue. For your argument to hold water, you must accept that a string must be of a finite length in order to use it as a measuring stick with which to size out the universe.

For collections of molecules to all move along from point to point in the correct direction (as my fingers now move across this keypad, with every atom choreographed precisely) all the points my atoms interact with must all allow my atoms to follow the same path - or else whenever I tried to move I'd disintegrate! This implies that my atoms actually 'control' the direction of flow. This implies that (unawares to me) I have complete control over the fabric of space in which I exist! The macro masters the micro!
 
  • #55
You said, “Perhaps (in a very circumventive way) you're on to something.”

I say, Yes! and all I need is help from experts, rather than arguments against the details.

You said, For collections of molecules to all move along from point to point in the correct direction (as my fingers now move across this keypad, with every atom choreographed precisely) all the points my atoms interact with must all allow my atoms to follow the same path - or else whenever I tried to move I'd disintegrate! This implies that my atoms actually 'control' the direction of flow. This implies that (unawares to me) I have complete control over the fabric of space in which I exist! The macro masters the micro!

When I came up with that picture in about 1984, I knew it couldn't be exactly right for the same reason you say, "How do the molecules choreograph themselves?" Although I knew the basic idea was right.

You asked, What is space made of? What gets denser? Since we haven't gotten past the idea of physical strings of matter that are like tight rubber bands or violin strings, I'll call them strings, and say that space forms like a 3-dimensional elastic macramé stretching outward. If the strings are shorter, the space is denser and objects move slower.

Another point you made was, tetrahedrons can't be right because they are too simple. Agreed. In one of my posts I say how the strings are constantly changing in length. The six dimensions of tetrahedron space is able to change, which produces a space with a total of 16 string dimensions. That’s adequately complex, so we aren't stuck in a world of tetrahedrons.

How do objects and molecules stay together and choreograph themselves through a space made of matter? Imagine cutting a flat piece of string fabric out of space. It takes two flat pieces of leather to make a baseball. But the shape of the two pieces of the baseball are precise and intricately joined, which is hard to come up with in nature. The least number of simple pieces you can use make a hollow sphere are three. And we know three quarks make a proton.

Imagine three pieces of flat space fabric, quarks. When you take a section of triangular strings out of expanding space, it immediately becomes a denser chip, a flat chip. Take three of those flat chips and put them together; it’s a proton, a dense particle of contracted strings, but it’s hollow. The strings, in triangles, are all over the surface. Imagine electrons (which aren’t really electrons but vibrating strings) traveling along the strings over the surface. The strings are vibrating mass, and the moving mass causes the proton to inflate like a balloon. It's a brane. You could have several protons forming one brane. All of their quarks arrange themselves like panels on a soccer ball, so a few protons form one single bane. They also form in layers or shells, which we call energy shells of the molecule. When the electron is on the brane, it vibrates all the strings of the brane and the electron loses its identity, thus you can’t know where it is, but you can pick one point and recapture all the energy of the electron and send it out along the strings of space.

So molecules are neatly organized membranes, separate from the dimensions of space. That’s how they stay together. How do they move through space?

Remember, we are moving though a matter field, not through empty space.

If molecules are made out of the same fabric as space, then molecules would suck up the space around them in order to form. Like building a sand castle. You have to dig a depression around the castle to get enough sand to build the castle. If you just sweep it all in and build the castle, and if the sand was perfectly flat, then water would run downhill into the castle. If a molecule sucks up space, that makes the space immediately around the molecule less dense, and things would tend to fall into it. That’s what I think is the operating principle behind gravity.

But it’s more complex. Quarks were cut neatly from space at an early stage in the expansion of the space we are in. The quarks organized into hollow protons. The surface of the hollow protons became excited and the vibrating strings inflated the proton. But they are a brane, totally separate from the dimensions of space. What connects the protons to space? The only candidate is neutrons. A wave in the ocean is a mound of water preceded and followed by a trough. A neutron is like a wave in space. It moves like a wave. The strings of the neutron don’t move, but like molecules of water, the wave moves and the individual molecules of water stay put. A neutron moves like a wave. As it approaches a string that is in space, the string expands becoming part of a trough. Then the string gets compressed as it becomes part of the neutron, and then the neutron passes and the string expands to form another trough or gravity well, and then returns slowly to normal.

The strings in the proton are more densely packed than the strings in space. The strings of the neutron are connected to space but they match the density of the proton just under the surface of the proton. So electrons, which are trapped on the surface of the brane can go down into the neutron and then up into space. Since the strings of space around the neutron and the strings of the proton are approximately the same length, electrons can pass from the skin of the proton into the neutron, and then to the strings of space; and the vibrating strings in the protons can throw off many photons using the same process. The proton is not connected to space, but the neutron is.

I’ve tried to give a sketchy picture, but there’s an experiment here. I'm saying only neutrons create the conditions for gravity. The idea is that protons are hollow branes disconnected from space, and neutrons interact with space and generate gravity. Therefore, according to my idea, a hydrogen cloud in a nebula would not generate gravity. Nebulas with their random shapes don’t appear to have gravity in them. If we ask the question, “How much gravity do giant hydrogen clouds have?” And if the answer is, “Less than their mass would suggest.” We have the seed of a major idea.
 
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  • #56
Interesting concepts.

Are they yours alone, or gleaned from the minds of others?

There's something about your assesment of the generator of gravity that doesn't really sit well with me. Your description of matter 'falling' toward a denser mass describes the general view of gravity - but what causes the less densely-packed matter to 'fall' toward the denser?

There's a natural trick in biology called osmosis. An example of which is when a cell 'sucks' oxygen out of the passing blood supply. It does this because of the difference in the pressure gradient between the blood flow and the cell internal environment. There is less pressure inside the cell. Nature cleaves to balance. And so the pressures are equalled out, and oxygen 'falls' through the cell wall. Could your assesment of gravity work along similar lines?

Is the universe forever trying to maintain balance? Do the more densely-packed regions of space have a 'lower pressure gradient on the quantum fabric' than the sparser, higher-pressured regions?

This would explain (in overly simplistic terms) how gravity operates on a large scale.

In an ideal universe all the matter and energy would be equally spread out. Uniformity rules! Ours is unfortunately rather 'lumpy' and quite thinly spread - and so everything is forever trying to even the score. All the matter in the universe is pulling all the other matter in the universe, trying to make everything uniform. The denser aglomerations pull harder, attracting even more matter. Unfortunately, our imperfect universe will never achieve complete uniformity - because it looks like there isn't enough matter to stop it expanding!

So perhaps your idea of neutrons being the principle catalyst in the production of gravity could be put to the test. Hydrogen is the most abundant atom in our universe. Any physicist would (I think) be hard-pressed into believing that they play no part in the generation of gravity. In fact, there seems to be a direct link between dense conglomerations of hydrogen AND gravity. Take our physical universe as example. Jupiter is 82% hydrogen and has a priddy huge gravity well! So maybe the link with neutrons might be the wrong path.
 
  • #57
Your description of matter 'falling' toward a denser mass describes the general view of gravity - but what causes the less densely-packed matter to 'fall' toward the denser?

In Newtonian or linearized Einstein gravity both bodies fall toward their common center of gravity, so it's symmetric in this sense. But of course the center of gravity is nearer the more massive body - perhaps inside it - so that breaks the symmetry.
 
  • #58
Sorry! I didn’t see your answer until now. Jupiter is 82% hydrogen. That would certainly disprove the idea that neutrons create the conditions for gravity. So I looked up the stats for Jupiter.

From the stats: [The fact that Jupiter’s radius is 11.2 times larger than Earth’s means that its volume is more than 1,300 times the volume of Earth. The mass of Jupiter, however, is only 318 times the mass of Earth. Jupiter’s density (1.33 g/cm3) is therefore less than one-fourth of Earth’s density (5.52 g/cm3). Jupiter’s low density indicates that the planet is composed primarily of the lightest elements—hydrogen and helium.]

And so, scientists determine the mass of Jupiter from its gravitational pull. They are saying the mass is always going to be equal to the gravitational pull. I would guess that the gravitational pull would be less than its mass if it has a lot of hydrogen.

[The force of gravity at the level of the highest clouds in Jupiter’s atmosphere is about 2.5 times the force of gravity at Earth’s surface.]

To me, that seems like a low figure for its gravitational pull, only 2.5 times that of Earth at its highest clouds? They got those figures from accurately measuring its gravitational pull. They haven’t actually measured its real mass. They aren’t going to say, “The gravitational pull is less than its mass.” But looking at its size, the figures for its mass and the amount of gravity seem low.

[Beneath the supercritical fluid zone, the pressure reaches 3 million Earth atmospheres. At this depth, the atoms collide so frequently and violently that the hydrogen atoms are ionized—that is, the negatively charged electrons are stripped away from the positively charged protons of the hydrogen nuclei. This ionization results in a sea of electrically charged particles that resembles a liquid metal and gives rise to Jupiter’s magnetic field. This liquid metallic hydrogen zone is 30,000 to 40,000 km (19,000 to 25,000 mi) thick—about half the radius of the planet.]

An ionized hydrogen nuclei is very similar to a neutron. It is a hard little ball of matter. So the sea of liquid metal would tend to distort space, like neutrons do. An inflated proton, which looks like a balloon, or a brane has a harder time distorting space. I say hydrogen may not create gravity at all, and doesn’t react to gravity as efficiently as it if had neutrons.

How does gravity work? If an electron is moving in an energy shell, there is a gradient in the energy shell caused by the distortion of space. Like this:

Point...Point...Point...Point

I say the electron always moves from one point to the next in the same amount of time. So if the electron is moving in a flat circle laid on that line, it is moving faster on one side of the circle than the other. The mass of the electron pulls the object to the left. This is what causes the gravity effect. It has no relation to a force, but happens because electrons always move from point to point in the same amount of time. If the points are farther apart, the electron speeds up. If closer together, the electron slows down. If the electron is moving in a field that is distorted, the electron will always be moving faster on one side of its orbit, pulling the object in that direction.

There is enough ambiguity in Jupiter's mass, makeup, and gravitational pull not to disprove my idea about neutrons, yet. What about hydrogen clouds, nebula, that don't seem to collapse or expand?
 
  • #59
Firstly, Happy New Year!

Secondly (and I don't have time to get into any lengthy discussion right now), electrons do not have mass.

Your idea that the electron's mass pulls the atom and creates gravity doesn't tally if you accept that electrons have no mass.

Also, electrons (unless acted upon by external forces or by transition through varying densities of matter) keep their speed constant. In a perfect situation (i.e. where elctron flow isn't impeded by the resistance of the medium through which they are moving) the electron speed is unchanging. My take on your thoughts about them speeding up to bridge bigger gaps and slowing down to cross smaller ones, is that the warping of our 3D space at fundamental levels actually allows the electron to nip across any varying length or 'gap' between points in the same time. The space fabric between points is 'stretched' between points farther apart, but it is the same amount of space fabric. This allows for an apparent speed up of the electron when actually the electron is only crossing the same apparent distance on the space fabric. If you draw two lines the same length on two bands of elastic that are the same length and then stretch only one of them, the line on the stretched elastic becomes longer than the other. However, the amount of material covered by that stretched line (the molecules that make up the elastic) remain the same. To our eyes the lengths or gaps between the points looks longer and so we assume anything moving along it would take longer - or have to speed up to do the trip in the same time. When actually, to any traveling electron, there is no apparent change in length at all.

As for Jupiter ... if you can imagine the density and mass of the planet's liquid metal core, you'd see why Jupiter's gravity is so strong. The thousands of miles of 'gases' forming the Jovian atmosphere are somewhat insignificant in the gravity equation. It's that metallic core that warps space to produce gravity. All the surrounding gases are just accessories in comparison.

:smile:
 
  • #60
The electron's mass has been measured many many times, and is known pretty accurately. In energy units it is 511,000 electron volts/c^2, or as usually stated but the same number .511 MeV, in units with c=1.

See Weisstein
 
  • #61
It's certainly interesting to note that we can accurately state the mass of something we cannot accurately locate. Uncertainty states we cannot accurately predict the location of the electron at any given moment ... so how can we so accurately state it's mass?

My mind's still groggy from New Year - so no doubt you'll elucidate.

As for this apparent electron mass being enough to determine an atom's 'movement' through space (as implied by John), I'm still not convinced. Let's face it, anything with a mass so teeny tiny is pretty much insignificant in gravitational terms ... isn't it?

[b(]
 
  • #62
The uncertainty principle states that you can't accurately measure BOTH of a pair of complementary observables AT THE SAME TIME. For this discussion the two important pairs of complementary observables are momentum and position, and energy and time (say, duration). If you don't care about one of a pair, you can measure the other one as accurately as you want. The thing about mass is that, unlike momentum, energy, or duration, it is persistent. So you can exploit that. The mass of the electron is determined from seeing how it scatters.
 
  • #63
Originally posted by theriddler876
hey, anyone out there care to offer their thoughts on the fourth dimension? as in what would it be, all I have is that a fourth dimensional object would seem like a 3 dimensional object moving down and then disapearing?
Try stronger questions. For instance how many regular (or platonic) bodies can you visualize (or find) in four dimensions? How many in five? How many in three? (In two there are infinite).
 

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