dimensions

[Gil Fuller]

Would it be possible for this forum to require those who use the word 'dimension'to name the type of dimension: spacial, temperal, energy, mathematical, exotic, and give the 'unit' for this dimension. If we are ever to have any real understanding of reality, we must be more precise in the meaning of the words used, particularly when dealing with concept that are unobservable. To say that something has 11 dimensions means nothing unless we know the nature of these dimensions and their units. Also, anyone postulating the need for more than 3 spacial dimensions should should be required to state if this dimension is observable and by what means. Thanks

[DaVinci]

I would very much like for someone to explain that as well.

As of right now, I know that we live in a three dimensional world. I would guess this is refered to as our 'spacial' world. I have also heard many state that we model time as our fourth dimension... basically our spacial world passing through a state of time.

Now, I go on to read more scientific papers that speak of 11 dimensions and upwards to higher levels. I also read that scientists are beginning to think that some dimensions are actually 'FOLDED' inside of others.

What the heck does all that mean? :biggrin:

Edit: And where the heck are they? Or are they simply numbers on paper and as far as science is concerened, we have four in reality and the rest are numbers?

[selfAdjoint]

Physicists represent our physical world by four dimensions, three spatial and one time. This picture underlies special and general relativity and relativistic quantum theory up to and including the Standard Model.

Supersymmetry and string theory predict more dimensions than we see in our physical world. They have to have them to be mathematically self-consistent. These extra dimensions are spatial like length, breadth or height. Depending on the theory there might be ten, eleven, or even twentysix dimensions in total, always including our four in the set. Time is always distinguished and the other dimensions are of the same kind as our space dimensions, but in order to explain why they are not seen, the extra ones are thought of as compacted, reduced to tiny multidimensional nuggets, many times smaller than a proton and not detectible by our instruments.

[Xare]

Ill give a stab at trying to explain the small curled up dimensions... Imagine a power wire. Looking at it from a distance all we can tell is that it has 1 spacial dimension. It looks to us just like a line.

But now picture youself as an ant. As your crawling along the surface of the wire 2 more spacial dimensions show themselfs. You can crawl in a complete circle on the wire and come back to the exact spot where you started.

These small dimensions in string theory, are curled up so tightly that from a distance we cannot see them. But if we could shrink down to the quantam level maybe we could.

Thats about as good as i can do. These things still baffle me at times :yuck:

[DaVinci]

So are they useful in some way to us? Do particles use them to do things we do not know about? Or are they useless to us?

Or do we still not know? :biggrin:

[selfAdjoint]

I would say the answer is still don't know. String theory is still trying, without any success so far, to make some difference in the everyday world - or even in the world of physics experiments! Supersymmetry is hoping for some evidence to show up when they finish the Large Hadron Collider(LHC) at CERN in Europe.

[NanoTech]

String theory is a great system of thought to explain the quantum nature of the universe. I have read one of Kaku's books on very introductory string theory, mostly conceptual level reading without much mathematics. And what I have realized is that to truly understand string theory and "why" extra dimensions are needed to explain string theory correctly, then I would also need about 3-4 years of advanced college level mathematics!

Now I am guessing way past multi-variable calculus and n-th dimension differential geometry. Does anyone know the least amount of mathematical knowledge needed to seriously study string theory? I remember surfing through a webpage that listed mathematics courses up to cohomology and bundle fibers..but that was about 2 years ago, it's most likely changed now. Thanks. David

[hix]

I have no idea, but I think your best bet would be to take as much math as humanly possible. That is the road im taking.

[rick1138]

I remember surfing through a webpage that listed mathematics courses up to cohomology and bundle fibers..but that was about 2 years ago, it's most likely changed now.

If the page you are talking about was the one at superstringtheory.com it was correct, and still is - fortunately mathematics changes very slowly.

[Louis Cypher]

Dont stone me or anything but I think asking about string theory is kinda like asking does God exist :confused:

Snice idea but I and this only my opinion think it's all nonsense, wonderfully mathmatically elegant nosnense but nosnese all the same :devil: proove me wrong :smile:

I think if your an atheist you shouldnt try to poove god's existence and vice a veersa, to use the anology again.

String theorists call themselves scientist, we must remember most are doing PhD's in Physics, or Doctorates of Philosophy that's why we mock it as philosophy: not because it might not be true!?! Just because it encourages people to seek proof after all isnt that what science is all about? asking questions is sublime providing answers is heavenly

Come up with a hypothesis when you wake up dissprove it over breakfast then your ready for work

A scientist quote from s

:smile:

[Louis Cypher]

Dont stone me or anything but I think asking about string theory is kinda like asking does God exist :confused:

Snice idea but I and this only my opinion think it's all nonsense, wonderfully mathmatically elegant nosnense but nosnese all the same :devil: proove me wrong :smile:

I think if your an atheist you shouldnt try to poove god's existence and vice a veersa, to use the anology again.

String theorists call themselves scientist, we must remember most are doing PhD's in Physics, or Doctorates of Philosophy that's why we mock it as philosophy: not because it might not be true!?! Just because it encourages people to seek proof after all isnt that what science is all about? asking questions is sublime providing answers is heavenly

Come up with a hypothesis when you wake up dissprove it over breakfast then your ready for work

A scientist quote from s

:smile:
very funny 10 warnings in 2 minutes, I love playing devils advocate, sorry guys I'll leave now, lol, very funny, you couldnt make this stuff up really rofl

[nightcleaner]

There are as many dimensions as you like, an infinite number of them. The better question is not, how many are there, but how many are required to view a phenomena of interest? Some phenomena can be viewed quite well in one or two dimensions, others require more. For example, if you want to view the path of a ballistic missile, such as a cannon ball or a falling object, two dimensions are generally sufficient, one dimension (a line) in space and one dimension in time. We can display these two dimensions quite easily on a graph with the vertical dimension (y axis) being spatial and the horizontal dimension (x axis) marking off the position of the object as it moves in time. The result is a graph which shows the motion of the object quite naturally, with height, for instance, on the vertical axis and time on the horizontal.

Now if we want to consider the same object falling through a strong wind, we have to add another dimension to account for the effect of the wind on the object. Let us say for simplicity that the wind is directly across the path of the object. Then the two dimensional graph above is no longer sufficient, since there will be a displacement that cannot be shown in the plane of the graph. This displacement is vertical to the surface of the graph (z axis.)

In the real world, we might place a cannon on a cliff above the sea and fire a ball at a some vertical angle out over the water. Given the effect of the force of gravity on the ball, the muzzle velocity of the ball, the vertical angle of the cannon, and the height of the cliff, we can predict exactly where the ball will be when it reaches the water level. If we are trying to hit a target on the sea, this is all we need to know, as long as there is no cross wind. But if there is a cross wind of sufficient strength, the ball will be pushed aside by the wind and not hit the target after all. In this case we need to correct for the wind drift, and we need to consider a third dimension to do that.

Other examples of a two dimensional situation might include the path of a ball hit by a bat, or a ball thrown from the freethrow line at a basket, or a hockey puck, football, etc. Now consider a ball player who has to run across the field to intercept a pass. In that situation, just as in the cross wind in artillery practice, a third dimension is required, this time due to the movement of the player. The player must move in a way that will place body and ball in the same location at the same time. Too fast or too slow, and the ball will be out of reach.

Anyone who can catch a ball while running across a field has the ability to think naturally in three dimensions of space and one of time. Athletes don't usually have to do the math to figure out how to catch a ball. Therefore, I assert, it is quite possible to understand dimensionalities up to three space one time without college calculus. If you can do the math, it is easier to describe the various motions, but unfortunately for science students, doing the math does not really make it easier to catch the ball.

So, if you want to get an idea of how things work in three dimensions of space and one of time, play ball. If you want to be able to describe the various motions in precise language, study the physics and the math through calculus. Actually you can do the physics of ballistics with algebra, but it is easier and more beautiful in calculus.

I used to post on superstringtheory.com on the extradimensions board as rtharbaugh, but on pf it seems unfashionable to use given names, so I took the name nightcleaner, from my source of income.

I am now posting as nightcleaner and signing nc or Richard as the mood takes me.

As for the higher dimensions, I am trying to explore them in a natural, mostly non-mathematical way in the Strings, branes, and LQG board on Physics Forums. I welcome anyone here to join me there. I would be pleased to take any questions.

As it turns out, when trying to describe the motions of sub-atomic particles, we need more than the familiar three dimensions of space and one of time. My current research is directed toward the proposition that humans can achieve a "natural" view of events in higher dimensions. This is experimental work, and I should warn anyone interested that it is not established physics. Your high school and college math and science teachers cannot be expected to give you credit for any advances you might make in this area. If you are curious and just want to know more, without any prospect of financial, social, or academic gain, feel free to contact me.

If there is enough interest (ok, any interest) I will undertake an explanation of my findings from first principles and with no more mathematics than you might expect to find at a high school level.

Be well,
and happy holiday,

Richard T. Harbaugh
Nightcleaner

237

[godzilla7]

Indeed I have postulated myself that the number of dimesions is infinity, plug the infinites and indeed infinitessimals into the equations and we get a better looking theory.

[godzilla7]

There are as many dimensions as you like, an infinite number of them. The better question is not, how many are there, but how many are required to view a phenomena of interest? Some phenomena can be viewed quite well in one or two dimensions, others require more. For example, if you want to view the path of a ballistic missile, such as a cannon ball or a falling object, two dimensions are generally sufficient, one dimension (a line) in space and one dimension in time. We can display these two dimensions quite easily on a graph with the vertical dimension (y axis) being spatial and the horizontal dimension (x axis) marking off the position of the object as it moves in time. The result is a graph which shows the motion of the object quite naturally, with height, for instance, on the vertical axis and time on the horizontal.

Now if we want to consider the same object falling through a strong wind, we have to add another dimension to account for the effect of the wind on the object. Let us say for simplicity that the wind is directly across the path of the object. Then the two dimensional graph above is no longer sufficient, since there will be a displacement that cannot be shown in the plane of the graph. This displacement is vertical to the surface of the graph (z axis.)

In the real world, we might place a cannon on a cliff above the sea and fire a ball at a some vertical angle out over the water. Given the effect of the force of gravity on the ball, the muzzle velocity of the ball, the vertical angle of the cannon, and the height of the cliff, we can predict exactly where the ball will be when it reaches the water level. If we are trying to hit a target on the sea, this is all we need to know, as long as there is no cross wind. But if there is a cross wind of sufficient strength, the ball will be pushed aside by the wind and not hit the target after all. In this case we need to correct for the wind drift, and we need to consider a third dimension to do that.

Other examples of a two dimensional situation might include the path of a ball hit by a bat, or a ball thrown from the freethrow line at a basket, or a hockey puck, football, etc. Now consider a ball player who has to run across the field to intercept a pass. In that situation, just as in the cross wind in artillery practice, a third dimension is required, this time due to the movement of the player. The player must move in a way that will place body and ball in the same location at the same time. Too fast or too slow, and the ball will be out of reach.

Anyone who can catch a ball while running across a field has the ability to think naturally in three dimensions of space and one of time. Athletes don't usually have to do the math to figure out how to catch a ball. Therefore, I assert, it is quite possible to understand dimensionalities up to three space one time without college calculus. If you can do the math, it is easier to describe the various motions, but unfortunately for science students, doing the math does not really make it easier to catch the ball.

So, if you want to get an idea of how things work in three dimensions of space and one of time, play ball. If you want to be able to describe the various motions in precise language, study the physics and the math through calculus. Actually you can do the physics of ballistics with algebra, but it is easier and more beautiful in calculus.

I used to post on superstringtheory.com on the extradimensions board as rtharbaugh, but on pf it seems unfashionable to use given names, so I took the name nightcleaner, from my source of income.

I am now posting as nightcleaner and signing nc or Richard as the mood takes me.

As for the higher dimensions, I am trying to explore them in a natural, mostly non-mathematical way in the Strings, branes, and LQG board on Physics Forums. I welcome anyone here to join me there. I would be pleased to take any questions.

As it turns out, when trying to describe the motions of sub-atomic particles, we need more than the familiar three dimensions of space and one of time. My current research is directed toward the proposition that humans can achieve a "natural" view of events in higher dimensions. This is experimental work, and I should warn anyone interested that it is not established physics. Your high school and college math and science teachers cannot be expected to give you credit for any advances you might make in this area. If you are curious and just want to know more, without any prospect of financial, social, or academic gain, feel free to contact me.

If there is enough interest (ok, any interest) I will undertake an explanation of my findings from first principles and with no more mathematics than you might expect to find at a high school level.

Be well,
and happy holiday,

Richard T. Harbaugh
Nightcleaner

237


Am about to take a physics degree and am greedy for any info, dont worry about it being philosophy at the moment that's why they call it a doctorate of philosophy, hey you might be right, send us some info and I'll check you out on the srings b etc forum.

email me at the address given also if you wish.

I too tire somewhat of mathematical sophists, just want to turn up at there doors and shout proove it damn it?????

Bloody philosophers and sophists or are they both very quantum?

lol

[godzilla7]

speculation is good provided we realise that is all it is speculation on speculation is also healthy and eminently scientific, but do not accept it as truth for it is not wisdom you seek? :smile: the answers in the post

[godzilla7]

oh and before I forgot merry christmas prof et al

[nightcleaner]

Hi Godzilla7

Marcus is on a roll on the other thread so I may start a new thread to discuss 4d visualizations. Dr. Kaku says it is impossible for humans to see in 4d. Well you probably know the old saw.....if a scientist says something is possible, that is probably correct, but if a scientist says something is impossible, that is probably not correct.

Maybe the word "see" is the issue. Perhaps "imagine" would be better. I guess the retina is essentially two dimensional, although it is placed on the inside surface of an orb. But the nerves that lead to the eye get complex very quickly, as I recall from anatomy class. Different areas of the optical cortex in the brain respond to different patterns, shapes, textures, contrasts. It would appear to me that the brain is a three dimensional structure, and can therefore generate higher dimensional perceptions.

And then there is the continuity of time and memory. I havn't really looked at the literature for some years now because of other interests, but as I recall there was some work done in the ninety's showing that short term memory at least involved a loop of cells in the brain which sort of echoed information back and forth between them, with the intensity of the information dropping over time unless it was reinforced by additional observations.

Anyway the main point of my first post in this thread was that there is a better question than "how many dimensions are there?" A dimension after all is nothing more than a line on which we can make differential measurements. We choose which lines and how many of them to show the phenomena in question in the most clear way. For example we only need one line to tell us what the temperature is right now (cold where I am) but we need two lines if we want to show how the temperature changes through the day or the season. We put the fahrenheit or Centigrade or Kelvin scale on the up-down line (y axis) and the time of day on the horizontal line (x axis) and then plot a nice line through the measurement points, giving us a two dimensional graph, a picture in two dimensions of how the temperature changes over a given period of time.

But maybe our phenomena in question is the way temperatures change over a surface, like a map of the country you live in. Then we plot the temperatures in various places and connect the similar temperatures by isobars. If we want to know how the isobars over a region change through a day we set the isobars in motion and watch the temperatures drop or rise over time. My weatherman on television is fond of these kinds of video bites. A two dimensional map, changeing through one dimension of time. That is three dimensions.

I suppose if one lived in a mountainous region, the weatherman might be interested in showing the effect of altitude on temperature over time. Then the display might be of a landscape in some two dimensional perspective, showing the mountain by shading or contour lines, and then the temperature isobars could be graphed onto the picture of the mountain, giving the viewer the idea of how temperatures at different altitudes change over time. That would be a three dimensional surface changeing over time, so we would be showing all four dimensions on one moving two dimensional screen.

However, too much information on a graph quickly becomes confusing. For this reason, among others, we usually want to display the phenomena in question in the smallest possible number of dimensions that show the effects in which we are interested. Sometimes it is best to do this by showing two or more graphs, selecting which dimensions are displayed and allowing the viewer to correlate the two or more graphs to get a complete mental picture of the phenomena.

The question at the beginning of this thread had to do with how many dimensions there are, and what are they. I think it should be apparent now that there are any number of dimensions you wish to choose, but for practical reasons it is best to choose to show the phenomena in as few dimensions as possible. So the question becomes, how many dimensions are needed to show an interesting phenomena? And, second, how best to choose which dimensions to display to demonstrate the phenomena to an interested viewer?

Usually in classical and in relitivistic physics it is sufficient to display three dimensions of space and one of time to show any interesting phenomena. But in quantum physics, it isn't enough. We find, as expressed in the Heisenberg uncertainy principle, that the closer we get to knowing where in three dimensions an object like an electron is likely to be found, the less we know about where it is going to be in the next instant. So three dimensions of space and one of time do not seem to be sufficient to tell us what the real electron is doing.

My understanding has been that string theory has been able to show at least some of the observed masses and charges of particles by invoking the idea that there are other dimensions. However I do not have the mathematics to follow the arguments. I am not personally entirely happy with the image given by Brian Greene, Michio Kaku and others of "curled up dimensions" like the ant on the wire. It seems to me that the ant is still in the same 3d space as the observer, regardless of where it is on the wire, so the image gives an idea that the "different dimension" is a mere matter of scale. My sense is that that is not enough to justify calling it a different dimension. After all, using sufficiently fine scales, we can still locate the ant on the same three dimensional grid. The movement of the ant around the wire is not really movement in another dimension, just at another scale of measure in the same three dimensional space.

I have similar problems with the embedding diagrams which are widely used to show black holes, worm holes, budding universes and other ideas. It seems to me that there should be better ways to think about higher dimensions.

I am working on a geometric approach, starting with visualizations in zero, one, two, three, and four dimensions, looking for the rules for adding dimensions, and then trying to push the rules to give us ways to "see" directly in higher dimensions. The spacetime equivalence principle of Einstein seems to me to be a key element.

Other people are working on other approaches. Marcus is exploring dynamic triangulation and Regge algebra. I think this is exciting work and am trying to understand the math, but it seems I am better with words and ideas than with the language of formula.

Perhaps I will start a thread somewhere to try to build up from the foundations. It would be good to be able to insert images into posts, but I don't think PF supports that ability. I am trying to learn to make images in Power Point, and then when I am satisfied with my level of proficiency doing that, I will try to figure out how to post images somewhere so that I can provide links, at least.

Anyway thanks for the discussion. Let me know what you think.

Be well,

nc
293

[sd01g]

I would suggest the term HIGHER DIMENSIONS be replaced by the term

COMPLEX DIMENSIONS because these dimensions are HIGHER only because

they are more COMPLEX. These other mathematically complex 'dimensions'

are positional in nature and are not additions to the fundamental three

spacial dimensions. If M Theory (Math Theory?) is ever to join the real


world of science, it will have to accept the primacy of 3 spacial

dimensions + 1 time dimension. Anyone else agree?

[selfAdjoint]

Unfortunately the word complex has a particular meaning: complex numbers. Now by chance the Calabi-Yau manifolds on which strings may be compacted are complex manifolds. They are usually called six dimensional, but are actually of 3 complex dimensions. And the very name Calabi-Yau clls up a lot of structure (Kahler, Riemann-flat, vanishing Chern class) which is never mentioned in popular accounts, and which is severly tied to their bing complex manifolds.

[juju]

I would suggest the term HIGHER DIMENSIONS be replaced by the term

COMPLEX DIMENSIONS because these dimensions are HIGHER only because

they are more COMPLEX. These other mathematically complex 'dimensions'

are positional in nature and are not additions to the fundamental three

spacial dimensions. If M Theory (Math Theory?) is ever to join the real


world of science, it will have to accept the primacy of 3 spacial

dimensions + 1 time dimension. Anyone else agree?

Hi,

I think that M theory or other higher dimensional theories should be reducible to 3 space/ 1 time using a fractal type of description or possibly a fourier or other series type description. Either using real or complex numbers.

In some cases, a straight forward use of more spacial dimensions could be necessary to model real effects of interdimensional forces.

juju

[selfAdjoint]

Hi,

I think that M theory or other higher dimensional theories should be reducible to 3 space/ 1 time using a fractal type of description or possibly a fourier or other series type description. Either using real or complex numbers.

juju

A method of getting rid of the extra dimensions while preserving (most) of the physics goes by the name dimensional reduction. It was a hot topic a year or two ago. I suggest you search for it online.

[EvilEyeMonster]

I really don't belong in this thread as I am an amature thinker... But to me, the idea of multiple dimensions is as easy as understanding "muscle memory". You can close your eyes and still touch your nose. What kind of calculations did your brain have to make to know where in space your nose was in relation to your finger without seeing ANY dimensions?

[Rybo]

I would suggest the term HIGHER DIMENSIONS be replaced by the term

COMPLEX DIMENSIONS because these dimensions are HIGHER only because

they are more COMPLEX. These other mathematically complex 'dimensions'

are positional in nature and are not additions to the fundamental three

spacial dimensions.

http://www.rwgrayprojects.com/synergetics/s09/p86770.html#986.850

Fuller disposes of the word "dimenisons" an replaces it with "powering"
see specifically 986.853 in the link above.

His thinking was to be more akin to mathematicians usages. Define a mathmatical sphere and give it mathmatical powers of spin, expanison contraction, torque, orbit, crossings, openings, trajectories etc.....

Depending on the branch of science words do have very differrent meanings.

The number 10 is a numerically higher [more ergo stacked "higher"] than the number
3. Ten has inherntly more numerical and geometrically complex relatiosnhips, so yes, it is a "more complex number" than 1 through 9.

It always comes back to Gils orginal comments. To be specific as possible with our words and then we must elaborate exhaustively all relevantly related words to arrive at a near understanding/comprehension of what it is we imagine we mean and want to convey to others.

Fullers states that humans first words may have been spoken from a dire situation. There is also evidence that the oldest knon use of words was in numerics.

Dimension;
1) Spatial (in space) dimension (length, width, height ) [macro]
1a) hyper-spatial (more complex relationships) dimension (in space height, length width) [ micro ]

2) time (over time) generalized (abstract)
2a) time (over time) dimension (motional frequency per ????)

Rybo