Thread: Are dimensions real, or just our way to describe what we experience?

For sure, we can imagine 1, or 2 dimensional space and we can say that we live in reality which can be divided in 3 space-dimensions. But are the dimensions real phenomena in our universe, or are they just our way to describe it? Can we separate our 3 space dimensions from each other to see that they really exists in a way that we see them in mathematics? For example, i havent ever heard physicists speaking about bending just X or Y or Z or time in separate, but only to bend them in one trough the gravity. Doesn't this sound like that there is really no such things as dimensions, but just a space that human brain wants to divide in pieces to have a better look on it? Do we have a good reason, a proof to think otherwise? That the dimensions REALLY exists, or is it just we?

ALL physics is based on mathematical models. The definition of what is real is more of a philosophical question (Plato) than a physical question.

Originally Posted by mathman

ALL physics is based on mathematical models. The definition of what is real is more of a philosophical question (Plato) than a physical question.

So you say that we have no proof that there really are dimensions?

I say yes dimensions really do exist. But there is no "first", "second", "third", or "fourth" dimension, just like when you have two cups of water there is no "first" or "second" cup. We live in a four dimensional universe.
What I don't understand is how time seems so different when relativity (I think) says that time is exactly the same thing as space. Perhaps it only seems different because of some factor, just like up/down seems like a distinct dimension but only because of the earth's gravitational field?

Dimensions are a way of counting the number of ways something can move. If you restrict yourself to the surface of the Earth, it's clear you can move north/south and east/west and that's enough to get you anywhere on the globe, therefore the surface of the Earth is 2D. Note, north/south and east/west are arbitrary, but any system you come up with will require at minimum two directions.

Now, if you allow yourself to jump, you've just added a direction that can't be described by some combination of north/south and east/west.

If you also want to specify an exact event, you also need to specify when that event takes place. If I just said "you're invited to my party at the hotel downtown," you wouldn't have enough information to actually get to the party, despite knowing where the hotel downtown was. That's another direction you can move in.

Again, the labels on a lot of these directions are somewhat arbitrary. You can specify the location of the hotel in latitude, longitude and altitude or as XYZ coordinates or in a few other ways. Time seems a little different though and that's because we see time, in some ways, backwards. Things farther away in time are actually closer than things nearer in time. Think about it this way. If you needed to get from A to B in one hour, it's going to be much harder than if you needed to get from A to B in one day, in exactly the same way that getting from A to B in one hour is harder than getting from A to C in one hour would be if C were closer in space than B.

And when you try and write this out mathematically, you get that . Notice that minus sign there. It's still possible to alter the coordinates in various ways though, but no matter how you do it, you'll still end up with 4 dimensions in total. (I don't actually know enough about the details to say whether it's possible to rotate the coordinates in a way that gets rid of the minus sign though.)

the difference between physics and math is that physics has to discribe and apply to the real universe which we observe with our senses, math does not. You can question whether the math discribes a real thing but the real thing, in this case dimentions, are a matter of our direct physical preception. So the correct question is does the math discribe the behavior or the real dimentions. Sometimes math can say something that while true can't be real. Example: "The average American family has 2.2 children". This a presumptively true statement that none the less cannot discribe a real thing. No actual family has 2.2 children.

Originally Posted by Neuntoter

.... But are the dimensions real phenomena in our universe, or are they just our way to describe it?...
...Doesn't this sound like that there is really no such things as dimensions, but just a space that human brain wants to divide in pieces to have a better look on it?....

So, are numbers real?
If we accept they are ideas and have an existance as ideas then I have to say they are real.
Yet at the same time I have to admit they have no concrete existence because they are only ideas that exist in our minds.
I suppose you could think of numbers, and the idea of dimensions, separately from the words we use to label the ideas but I am not sure I could actually do that.
So I am going to guess that words and numbers share the same sort of realities.

The mind is created by (at least from) the material world and so ideas (created by the mind) are ,insofar as they are indirectly created by the material world "real".

If you go the other way and say that the mind creates the material world then the outcome is more or less the same.

Oddly though ,while our ideas can be wrong the outside world never is.

So maybe our ideas are never wrong but only misplaced and right for the momentary perception.

If dimensions are directions of movement is there any limit to the number of them there could be?

Originally Posted by geordief

If dimensions are directions of movement is there any limit to the number of them there could be?

The number of dimensions is not arbitrary, since the form the laws of physics can take is dependent on them. Wikipedia had a nice little diagram of what happens if you vary the number of space and time dimensions, but it appears that page no longer exists.

Originally Posted by geordief

If dimensions are directions of movement is there any limit to the number of them there could be?

The limit is 3, because the directions have to be mutually orthogonal to count for dimensions.

Dimensions can be thought of, but can they be seen?

Yes. To a degree.

1 - 3, can.

4 - etc. can only be conceptualized (though, mathematically proven)

Wrong.

Originally Posted by mathman

Originally Posted by geordief

If dimensions are directions of movement is there any limit to the number of them there could be?

The limit is 3, because the directions have to be mutually orthogonal to count for dimensions.

Not necessarily true.
Four-dimensional space - Wikipedia, the free encyclopedia

Originally Posted by mathman

The limit is 3, because the directions have to be mutually orthogonal to count for dimensions.

The basis vector of the time-like dimension is linearly independent of the three spatial basis vectors; you can have as many dimensions as you want that fulfil that condition. Mathematically, there is no limit.

Originally Posted by Neuntoter

For sure, we can imagine 1, or 2 dimensional space and we can say that we live in reality which can be divided in 3 space-dimensions. But are the dimensions real phenomena in our universe, or are they just our way to describe it?

I go for the latter. Dimensions are a useful construct to map a projection of a system from a vantage external to the system being described. The reality however may be that such an external vantage is in 'reality not possible'. The result may therefore be a description of a sub-system that is frame dependent.

For example in general relativity from the frame of reference of an accelerated observer escaping the gravitational curvature, they see an event horizon which is a terminal boundary to their notion of spacetime. From their vantage, they never see the infalling observer move past this boundary of no return but rather see a static representation of that observer spatially extended over the horizon. There is no inside of the black hole from their frame of reference.

For the infalling observer on the other hand who is inertially following the curvature, no such boundary exists. It is still the same old space they are travelling through. For large enough black holes, there is no experiment they can perform that deduces anything special when they pass through what another accelerated observer sees as an event horizon. Spacetime continues on for them until their demise as scale becomes important gravitationally towards the proposed singularity.

For such radical different takes on the geometry of spacetime from these two different points of view.....who is right. Most likely they are both right. The dimensionality of spacetime from these two vantages appears to be frame dependant. You can have one description OR the other. They are both equally valid descriptions of the same system taken from different frames within the one system. Unfortunately you cannot have hoth descriptions at once, just one or the other. A duality of two valid descriptions of the same system. In QM you bump into this duality frequently.

Sometimes I have read about " 2 dimensional worlds" where a conscious being lives in such a way as to be unaware of the 3rd dimension - for example perhaps a starfish like creature that crawls along just on the surface of its perfectly spherical planet .

Is this really possible?

Is it possible for there to exist a living organism with only 2 dimensions or is this some kind of fictional character just created for display purposes?

Surely this "starfish" has to have an idea of what is its top and what is its underside?

Originally Posted by geordief

Sometimes I have read about " 2 dimensional worlds" where a conscious being lives in such a way as to be unaware of the 3rd dimension - for example perhaps a starfish like creature that crawls along just on the surface of its perfectly spherical planet .

Is this really possible?

Is it possible for there to exist a living organism with only 2 dimensions or is this some kind of fictional character just created for display purposes?

Surely this "starfish" has to have an idea of what is its top and what is its underside?

If a 2d lifeform existed in a 3d context, there would be clues for the existence of further dimensions even if they could not adopt a gods eye view to observe that context. For instance they might circumnavigate a spherical earth to arrive back at their commencement point. Things might suddenly appear in their 2d vantage to suggest these things emanated from an unobservable new dimension. Where things get harder however is an appreciation of additional dimensions when both observer and observed are constrained by the same geometry. A good book that discusses hyperdimensions where you can almost intuitively understand them is Flatterland by Ian Stewart which expounds on the classic novel Flatland.

Originally Posted by Implicate Order

For instance they might circumnavigate a spherical earth to arrive back at their commencement point.

Does this sound like a general test then for a new dimension?

If you can travel along a line in a known dimension and return to your starting point

Better still are tests used to interpret the geometry and topology of our universe using triangles and the angle between vertices to identify whether the geometry is flat (Euclidean) or closed and curved (spherical) or open and curved (hyperbolic).

We might be able to infer extra dimensions from techniques such as covariant analysis. For example assume you are a flatlander that can only see in 2d. Assume a 3d hand (the fingers) entered your 2d arena. You might see a cross section of 5 seperated circles enter your domain. You would not necessarily conclude they were related to each other but through covariant analysis you might establish that the 5 circles move in repetitive patterns that may suggest they are representations of an object from a higher dimensional context.

The notion of dimensions often raises questions - I suspect that part of the problem stems from the tendency to visualise them as orthogonal straight lines stretching out from an origin, but that isn't the only way of specifying coordinates. "Dimensionality" appears to be more fundamental. To specify the position of a point in space we need to give three numbers, so space is three-dimensional. If we want to talk about events, then another number is required - the time when the event happens. How these numbers are used to find the point (or event) depends upon the type of coordinates used, and that is arbitrary.

What about the way dimensions are treated in other disciplines besides mechanics?
Almost any measure that can be multiplied by itself can be a dimension. (The measurement needs to be a measurement not just a "yes or no" type test)
Multiplying a length by itself gives you an area, that is two dimensions. If multiply a length by itself three times and you have a cube which is three dimensions.
If you multiply a length by itself n times you would have an n dimensional figure.

At one time in the history of math european mathematicians rejected the idea of raising anything to the power of 4 because they didn't think there could be any real objects with more dimensions than three, and they considered exponents as expressions of geometry.

It is also true that we commonly multiply different types of measurements together. When we multiply force times distance we get work (energy) as a result.
So in a sense we are using force as another dimension in our maths. There are other examples and if you look in different disciplines you see them soon enough.

Dimensional models of personality disorders - Wikipedia, the free encyclopedia

Within the context of personality psychology, a "dimension" refers to a continuum on which an individual can have various levels of a characteristic, in contrast to the dichotomous categorical approach in which an individual does or does not possess a characteristic.

Originally Posted by geordief

Originally Posted by Implicate Order

For instance they might circumnavigate a spherical earth to arrive back at their commencement point.

Does this sound like a general test then for a new dimension?

If you can travel along a line in a known dimension and return to your starting point

No, that's a general test for curvature. A space can be curved into a closed shape (like the surface of a sphere) without adding another dimension. Humans find it very hard to separate the surface of the sphere from the embedding of that surface into a 3D space, but the 3D space is not required for the surface to curve.

Originally Posted by MagiMaster

Originally Posted by geordief

Originally Posted by Implicate Order

For instance they might circumnavigate a spherical earth to arrive back at their commencement point.

Does this sound like a general test then for a new dimension?

If you can travel along a line in a known dimension and return to your starting point

No, that's a general test for curvature. A space can be curved into a closed shape (like the surface of a sphere) without adding another dimension. Humans find it very hard to separate the surface of the sphere from the embedding of that surface into a 3D space, but the 3D space is not required for the surface to curve.

I think I have heard that in theory a beam of light was to complete its journey out into the universe without being absorbed it would eventually return to more or less the same spot (so that you could see the back of your head if you waited long enough).

Not that that could happen I am sure but I think that is supposed to be the geometry of the universe if I understood (and recall) correctly.

Not that I actually understand that geometry .....

That is one possible geometry. If the universe isn't infinite, it will almost certainly not have a boundary like the edge of a piece of paper, but will be closed (wrap around to itself) like the surface of a sphere. The leading theory I've heard of puts the shape as some weird dodecahedron, but last I heard, they haven't found the supporting evidence they were looking for.

For a beam of light to get back where it started, it'd have to head out in the right direction (I think) and even then would take something like 100 billion years to get back.

Originally Posted by MagiMaster

Originally Posted by geordief

Originally Posted by Implicate Order

For instance they might circumnavigate a spherical earth to arrive back at their commencement point.

Does this sound like a general test then for a new dimension?

If you can travel along a line in a known dimension and return to your starting point

No, that's a general test for curvature. A space can be curved into a closed shape (like the surface of a sphere) without adding another dimension. Humans find it very hard to separate the surface of the sphere from the embedding of that surface into a 3D space, but the 3D space is not required for the surface to curve.

Good point MagiMaster. I am one of those humans that have real difficulty wrestling with notions such as intrinsic curvature :-))

Originally Posted by mathman

ALL physics is based on mathematical models. The definition of what is real is more of a philosophical question (Plato) than a physical question.

Reality is a mathematical model as are human beings. So reality is becoming more aware of itself and the number of dimensional relationships is growing. The fantastic thing about dimensions is that the first one must be infinite for a second one to grow.

No.

Originally Posted by Markus Hanke

Originally Posted by mathman

The limit is 3, because the directions have to be mutually orthogonal to count for dimensions.

The basis vector of the time-like dimension is linearly independent of the three spatial basis vectors; you can have as many dimensions as you want that fulfil that condition. Mathematically, there is no limit.

I agree mathematically. However I understand the question refers to physical space dimensions.

Originally Posted by mathman

I agree mathematically. However I understand the question refers to physical space dimensions.

The geometrical description of space-time is a mathematical model; this is all we can ever do to describe the world around is. The relationship between the model and reality is the same one as between the map and the territory - they mightn't be the same, but there is a definitive relationship.
What is the fundamental difference between a mathematical dimension ( as in - geometry ), and a physical dimension ?