Dimensions and Directions.

[throng]

I think we can express the four space/time dimensions as motion in four directions.

 

0 dimensions = point. It has no direction, so no dimension.

 

1 dimension = line. The distance required a moment to exist and it has length. The expanding line has movement in two directions. We can call these directions (dimensions) length and time.

 

2 dimension = triangle. The corners move outward in three directions (dimensions). Length, time and width.

 

3 dimension = tetrahedron. the four vertisies move in different directions to create the expanding tetrahedron. The directions (dimensions) are length, time, width and height.

 

So movement in at least four directions is required for expanding 3 dimensional volume, hence the 4 dimensions of space time.

 

I think we could express dimensions as directions in this way.

[throng]

A photon has zero dimensions.

 

Anything travelling at c is zero dimensional. (infinite mass). No time.

 

If a photon must travel a distance, it takes the one dimensional form and instantaneously arrives at the destined point. (From the photon's perspective).

 

The photon itself sees the universe as a point and it has no wavefunction, for movement is impossible in zero dimensions.

 

The delay in light arriving, say from the sun, is really the photons expansion from zero dimensions to three. We interpret the wave function of light as relative to our own wavefunction (speed).

 

So, whereas we percieve the phenoma of distance or volume in accordance with our own speed (frequency), the photon doesn't. At c there's no time or distance. the dimension is zero (zero frequency wave function).

 

It is our own wave function relative to zero (or infinity) that creates the perception of distance, movement and time. These phenomena don't exist at c.

 

So, we can express the experienced dimensions of space/time as directions, because the universe expands in four spatial directions relative to the observers 'speed' and the volume is the effect of wave function 'expanding".

[mooeypoo]

This is the weirdest wordsalad I've ever seen.

 

Your idea initially might have some potential in it, if it was a bit more elaborated (what does it mean other than a nice presentation?), and then your second post is.. just.. a mixture of comparisons between incomparable extremes.

 

A photon has zero dimensions.

Uh, you said in your first post that 0 dimentions is a point with no direction. Not only does a photon have direction, it's moving very quickly. According to your own definitions, that's supposed to be either 1 or 2 dimentions. Definitely not 0.

 

Anything travelling at c is zero dimensional. (infinite mass). No time.

Okay, hang on here.

A photon does not have infinite mass. It has zero mass.

Bsides, time seems to *slow down* as you approach the speed of light, but it still exists.

 

If a photon must travel a distance, it takes the one dimensional form and instantaneously arrives at the destined point. (From the photon's perspective).

Uh, so now you need to prove that a photon is created one way (in "zero" dimensions) and changes 'states'/'existences'/dimensions.

What makes it change? As far as we can tell, the universe is *against* change. Things keep doing what they're doing until SOMETHING changes them. Light keeps going in a straight line forever until *something* moves it - like a large massive object. Things in the universe tend to stay as they are; if they're moving with a certain speed, their tendency is to KEEP that speed, unless something (some force) makes them change it. If an object is standing still, its tendency is to keep standing still until something (a force) makes it move.

 

What caused your photon - first created with no direction or speed - to suddenly change its behaviour against everything we know in the universe?

 

The photon itself sees the universe as a point and it has no wavefunction, for movement is impossible in zero dimensions.

 

The delay in light arriving, say from the sun, is really the photons expansion from zero dimensions to three. We interpret the wave function of light as relative to our own wavefunction (speed).

Again, lacking proof and basic explanations.

 

So, whereas we percieve the phenoma of distance or volume in accordance with our own speed (frequency), the photon doesn't. At c there's no time or distance. the dimension is zero (zero frequency wave function).

First, speed is not frequency. If you claim otherwise, you need to be more specific.

Second, if your photon acts against what we know everything ELSE acts (hence, it acts against the *known* rules of physics), you need to do quite a bit more than just a claim.

 

You need to prove it. And explain why it is that photons are different than everything else.

 

It is our own wave function relative to zero (or infinity)

huh?

 

Which is it? Zero or infinity? Or are you saying that there are two points, zero and infinity where this is happening? is that why you are using 'wave functions'? You need to explain this.

And prove it. Wave function is mathematical. You need to supply mathematical proofs that support observations and evidence.

 

that creates the perception of distance, movement and time. These phenomena don't exist at c.

Why?

 

So, we can express the experienced dimensions of space/time as directions, because the universe expands in four spatial directions relative to the observers 'speed' and the volume is the effect of wave function 'expanding".

Err, that conclusion doesn't follow if you can't prove everything above and show it to be consistent with our observations of the Universe.

 

~moo

[throng]

This is the weirdest wordsalad I've ever seen.

 

THRONG: I lack eloquence.

 

Your idea initially might have some potential in it, if it was a bit more elaborated (what does it mean other than a nice presentation?), and then your second post is.. just.. a mixture of comparisons between incomparable extremes.

 

THRONG: Yes, that's true... I probably could elaborate, but it is a construct or metaphor, and the aspects are unproven.

 

Uh, you said in your first post that 0 dimentions is a point with no direction. Not only does a photon have direction, it's moving very quickly. According to your own definitions, that's supposed to be either 1 or 2 dimentions. Definitely not 0.

 

THRONG: Is a photon actually moving if time stops at c? Has space any dimension if, from the photon's perspective, distance is instantly traversed? I also think one dimension is a good metaphor for light speed. for motion is undetectable, so no observable time, unless observed from a higher dimension.

 

 

Okay, hang on here.

A photon does not have infinite mass. It has zero mass.

Bsides, time seems to *slow down* as you approach the speed of light, but it still exists.

 

THRONG: I was probably refering to matter with an entire lack of eloquence. If matter travelled at c it would be infinitely dence, yet from that perspective it would travel instantaneously, making it infinitely 'not dence'. Totally dence from our speed's perspective, but not from it's own.

 

 

Uh, so now you need to prove that a photon is created one way (in "zero" dimensions) and changes 'states'/'existences'/dimensions.

What makes it change? As far as we can tell, the universe is *against* change. Things keep doing what they're doing until SOMETHING changes them. Light keeps going in a straight line forever until *something* moves it - like a large massive object. Things in the universe tend to stay as they are; if they're moving with a certain speed, their tendency is to KEEP that speed, unless something (some force) makes them change it. If an object is standing still, its tendency is to keep standing still until something (a force) makes it move.

 

What caused your photon - first created with no direction or speed - to suddenly change its behaviour against everything we know in the universe?

 

THRONG: It depends on perspective. space/time is less speed than c. At c wouldn't the universe be point sized? If it takes 0 time to travel, are the two points in the same location.

 

Again, lacking proof and basic explanations.

 

THRONG: I cannot justify my second post, I like the metaphor in the first though

 

First, speed is not frequency. If you claim otherwise, you need to be more specific.

Second, if your photon acts against what we know everything ELSE acts (hence, it acts against the *known* rules of physics), you need to do quite a bit more than just a claim.

 

You need to prove it. And explain why it is that photons are different than everything else.

 

THRONG: I just meant massless particles don't 'experience' space/time whereas matter does, and that is supposition as nobody knows.

 

THRONG: I appreciate you tollerating the idiocy in my second post, I may have been intoxicated I think.

 

~moo

 

I actually only like my first post. Is this post at all sencible, even though it is wildly speculative?

[Riogho]

Okay, hang on here.

A photon does not have infinite mass. It has zero mass.

Bsides, time seems to *slow down* as you approach the speed of light, but it still exists.

 

Time does slow down as you approach the speed of light. For something that actually travels at c, in this case a photon, you will not experience time at all. Photons do not experience time.

[iNow]

Use of the word "experience" gets us into a bit of trouble, though. A photon cannot be said to have its own reference frame since it is never at rest.

[foodchain]

do experiments with photons have decoherence time?

[Klaynos]

A few points, speculations make predictions, word salads are useless. Your first post appears to just be stating the general definition of a dimension... Although a more formal definition would be mathematical, but an english equivalent would use the concept of orthogonality...

 

do experiments with photons have decoherence time?

 

Not in the way I think you mean, photons do not change unless they interact.

[throng]

A few points, speculations make predictions, word salads are useless. Your first post appears to just be stating the general definition of a dimension... Although a more formal definition would be mathematical, but an english equivalent would use the concept of orthogonality...

 

 

 

Not in the way I think you mean, photons do not change unless they interact.

 

 

Sorry about the salad, I'm unclear in thought. I only intended to use directions as dimensions and include time as one direction.

 

The general model for 3D is three directions (x,y,z), time being distinctly different in nature to spacial dimensions.

 

The original post says four relative spacial directions are required for 3D and time is identical in nature to the other three (a movement relative to other movement).

 

I just think it is a very simple expression which says, There are three dimensions which are 4 directions and time is one of them.

 

There's no new theory or revelation in it, it is just an original way of saying the same thing, but easier to visualize the time dimension.

 

 

 

I had another idea about dimensions too, so pass the dressing please.

 

0D is a point.

 

1D is a distance, and a maximum of 2 points can be equally spaced.

 

2D is a triangular plane and a maximum of three points can be equidistant.

 

3D is tetrahedral and only four points can be equally distant.

 

4D In 4D five points could be equidistant. In 5D, 6 points. In 6D, seven ... etc.

 

That is just another expression, not the standard (line)^n.

 

I like the direction one best because time is represented exactly like the spacial dimensions.

 

Nothing new here, it is just speculative thought, and origional expressions for dimensions. I'm sure they're sensible or reasonable.

Edited December 8, 2008 by throng
multiple post merged

[ajb]

You have the notion of dimension (of a topological space) independent of the notion of distance. See Lebesgue covering dimension. This gives the same notion of dimension for a manifold.

[Kyrisch]

Starting from 2D, there are an infinite number of points that can be equidistant... Circle, sphere, hypersphere, etc.

[D H]

Repeating the same thing over and over does not make it correct, nor does it communicate.

 

You are not talking about directions, you are talking about regular simplexes (simplices?). A 0-simplex is a point, a 1-simplex is a line segment, a 2-simplex is a triangle, and so on. These simplexes are the simplest geometrical shapes in N-space (hence the name).

[ajb]

I agree DH, Kyrisch is heading towards the notion of a simplex. These are not things I am very familiar with, other than the notion of a simplicial manifold, i.e. a simplicial complex (topological space) homeomorphic to a topological manifold. (Such things are useful in some approaches to quantum gravity, for example).

 

By direction on a manifold you mean a vector or possibly you could be specifying one (local) coordinate. The first notion is independent of the coordinates as where the second is clearly not. I think of the coordinates as defining "geometric directions", but again I will stress this is not really an invariant notion. The number of such directions is obviously the (topological) dimension which is invariant.

 

Now, what I have said applies to any (smooth) manifold (and some generalisations in fact). In particular I do not need any extra structure like a metric. In relativity, it is the fact we have a manifold with a metric that distinguishes between space and time. Even then, this relies on a choice of coordinates. What I am trying to say, is that one should not get too hung up on the distinction between space and time in relativity.

[throng]

Starting from 2D, there are an infinite number of points that can be equidistant... Circle, sphere, hypersphere, etc.

 

If only one unit of distance was used - 1m, the maximum no of points that could be only 1m away from any other is 3, equalateral triangle

 

Any other 2D shape requires relative distance.

 

---

Merged post follows:

Consecutive posts merged

Repeating the same thing over and over does not make it correct, nor does it communicate.

 

You are not talking about directions, you are talking about regular simplexes (simplices?). A 0-simplex is a point, a 1-simplex is a line segment, a 2-simplex is a triangle, and so on. These simplexes are the simplest geometrical shapes in N-space (hence the name).

 

 

Yes, thank you kindly I am refering to simplex, I just didn't know it. I guess the ones that exceed 4 points can't actually be made, because it would require more than one distance value between points (corners). 5 points would be a 4D shape wouldn't it?

 

The point is you need 4 points to create 3 dimensions, then and number of points can't possibly create more, because there are no directions where the a measure of 1m could lie between 5 points. Relative distance is inevitable after 4.

Edited January 27, 2009 by throng
Consecutive posts merged.

[ajb]

If only one unit of distance was used - 1m, the maximum no of points that could be only 1m away from any other is 3, equalateral triangle

 

Consider a circle of radius r in [math]R^{2}[/math]. Place the centre of the circle at the origin of a coordinate system if you like. Question, how many points lie on the circle?

[throng]

Consider a circle of radius r in [math]R^{2}[/math]. Place the centre of the circle at the origin of a coordinate system if you like. Question, how many points lie on the circle?

 

I can't see that a circle of radius r would fit inside a square with side r, I'm not sure what you mean.

 

Well the largest possible distance is 2r.

 

When r is squared the largest distance is a diagonal of the square.

 

A circle would require infinite relative distances but the set of distances lies between 2r and 0.

 

I don't think it is necessary to create area to make two dimensions, because dimensions are measurements, not only spacial, and three points in a line has two measurements, length and 180 deg.

 

So really, I think any three locations constitutes two dimensions, and a line is actually 2 dimensional. Only an empty distance between two points is truely one dimensional.

 

Is it true that if two measurements can be applied a thing is two dimensional?

 

Can distance angle area and volume be the actual definitions of geometric dimension?

 

 

 

A circle has infinite points, doesn't it?

Edited January 27, 2009 by throng

[ajb]

So, we have an infinite number of points a distance r from the centre of the circle. So by shifting the origin and the radius we have established that given any point in [math]R^{2}[/math] we have an infinite number of points a distance r away from any other.

 

This reminds me balls in metric spaces.

[throng]

So, we have an infinite number of points a distance r from the centre of the circle. So by shifting the origin and the radius we have established that given any point in [math]R^{2}[/math] we have an infinite number of points a distance r away from any other.

 

This reminds me balls in metric spaces.

 

I don't quite understand the concept.

 

I have a line length r. The origin is at the left end. draw circle radius r. Square r. Square occupied 1/4 of the circle.

 

I just can't visualise how the distance near the perimeter could equal 2r.

 

Thanks, all the info you and DH provided reassures me that my musings are not entirely crackpottery.

 

I see the dimensions can be considered as 'mediums' (measurements) which are the geometric relationships, namely distance, angle, area and volume.

 

The three spacial dimensions are distance, which is a medium of 4 perpendicular directions or locations. (the origin assumed rest).

 

But really there are four dimensions, so imaginary numbers etc. It seems clumsy.

 

Volume is enclosed by at least 4 locations and there are four primary geometric measurements, and an interesting interaction between the two definitions.

 

-----------------------------------------------------------------

 

So a point is a singularity, and a distance is a singularity, for each is defined by it's own measure, (because the two ends can't measure the distance.)

 

A point or two points the same, it can only be defined by a measure of itself, like the single distance between.

 

Is this founded in pure logic do you think?

 

Edited January 28, 2009 by throng

[D H]

Thanks, all the info you and DH provided reassures me that my musings are not entirely crackpottery.

Not entirely is the operative word. Simplexes are real concepts.

 

Is this founded in pure logic do you think?

No.

[PrinceOfDragons]

Time does slow down as you approach the speed of light. For something that actually travels at c, in this case a photon, you will not experience time at all. Photons do not experience time.

 

Is there math or obervations that proves that a photon does not experience time ?

[throng]

Not entirely is the operative word. Simplexes are real concepts.

 

 

No.

 

 

DH, people always think i'm a nut because I come up with new concepts, but I spend quite some time checking and rehashing.

 

I do like simplistic expressions, but if my logic is refuted by physics I read, I abandon it.

 

I have trouble formulating my thoughts so I come across all nutty.

 

I have an idea I would like to discuss, because someone highly trained in math would see more meaning than me. This will sound nutty but I don't see why light is considered speed when it behaves entirely differently to relative motions, and light is not mass, so it is a dimension.

 

I was toying with geometry and it dawned upon me that if light were considered a dimension, time would meld into spacial dimensions better.

 

I can explain the thing using two points (dots), and it is quaint.

 

If you are interested I will attempt a coherant explanation of the concept, which in the past I've been unintelligable.

 

It all starts with a point. The point is defined as a singularity, 'that which can only be measured by itself.'

 

Is that an adequate description of a 0 dimensional singularity?

 

 

 

[Quantoman]

It all starts with a point. The point is defined as a singularity, 'that which can only be measured by itself.'

 

Is that an adequate description of a 0 dimensional singularity? throng

 

 

 

 

it depends if that point (singularity) is not a 3 dimensional sphere..

 

at best the point would be 2 dimensional, but 0 dimensional

singularity is zero demension = nothing.

 

i guess?

Edited January 30, 2009 by Quantoman
erorr

[iNow]

You guys really need to read this recent post from Martin in another thread.

 

 

aaaarrrrgh! Please don't use the word singularity as if it was something real that actually existed!

 

Professionally, in cosmology, the word is used as a time-marker, it refers to the moment in time where the old classical model breaks down and stops computing. Only the public believes that there is actually a physical thing in nature called a singularity!

 

Since they don't exist in nature, you couldn't have an explosion of one.

 

In the new models, which don't break down, you still have the t=0 point.

You can still call that time-marker the "classical singularity" or as one of the experts in the fields calls it the "putative singularity".

It's just that the new model keeps on computing and continues on back before the t=0 point where the old model went bust.

 

The original meaning of singularity was in mathematics, a place where a function has a singularity is a place where it fails to be defined. Like the function 1/x isn't defined at zero. Physicists took the word over to mean somewhere a particular theory or math model broke or failed to apply or didn't give meaningful answers. It has a long history, not confined to cosmology, and doesn't necessarily mean that the failure mode is infinite density or infinite curvature. In other branches of physics other things can go haywire besides density and curvature.

 

Anyway it is not a feature of nature, it is a feature of manmade mathematical models. So it misleads people when one refers to a singularity as a physical natural something that could do something, like explode.

 

A singularity is a challenge to improve the theory. There've been a bunch of them in the past that have been fixed by improving theory, and that now no longer exist. They are ex-singularities.

Like the former Soviet Union, or the ex-parrot in Monty Python.

[ajb]

it depends if that point (singularity) is not a 3 dimensional sphere..

 

at best the point would be 2 dimensional, but 0 dimensional

singularity is zero demension = nothing.

 

i guess?

 

In geometry a point is defined as being zero dimensional. A line or curve is one dimensional and a surface is 2 dimensional. Higher dimensional "surfaces" are also defined.

 

Point being, a point is always zero dimensional, see topological spaces 101!

[throng]

In geometry a point is defined as being zero dimensional. A line or curve is one dimensional and a surface is 2 dimensional. Higher dimensional "surfaces" are also defined.

 

Point being, a point is always zero dimensional, see topological spaces 101!

 

 

Of course one can't say if zero dimensions is reality, and by no means can it be perceived, and since it will never be perceived, it alone speaks of it's existance.

 

It might as well be God.

 

E=m because Planck derived constants and experiments confirm.

 

S as a function of U. A unit in which nothing can happen, so a description of one dimension.

 

We want a singularity on which to base the Grand Theory Of Everything and seek Higgs boson, T=0 and immaterial concepts without mass. Might as well be God.

 

Of course E is the singularity that has been so long known, we measure change, but a changing singular thing.

 

So naturally the laws of physics lie on a very basic singularity, E, the truth. Which is 'I don't know'.

 

 

'All that is not known', zero dimensional?