# Is there a fourth dimension?

1. Dec 30, 2011

### metiman

Well? Is there? And if there is what kind of experiment could I perform to prove that there is? Or prove that there isn't?

2. Dec 30, 2011

### Pythagorean

what do you mean by dimension?

3. Dec 31, 2011

### Woopy

time

4. Dec 31, 2011

### Highway

^ this

(x,y,z,t)

5. Dec 31, 2011

### Number Nine

Sort of...sometimes...in some contexts. We really don't know what the OP is asking about without clarification; "dimension" has different meanings in different contexts.

6. Dec 31, 2011

### Jimmy Snyder

There's a 5th dimension.
https://www.youtube.com/watch?v=kjxSCAalsBE

7. Jan 1, 2012

### metiman

I was referring to a spatial dimension. As in the fourth dimension of a tesseract. You have length, width, depth, and some other thing. Maybe super-depth. In terms of cartesian coordinates you'd have something like x,y,z and s. The z vector is perpendicular to the xy plane and the s vector is perpendicular to, uh, the xyz plane? Or rather it would be perpendicular to the x, y, and z axes. I wasn't referring to time which I think might be somewhat similar to Einstein's theory. Although I'm a bit unclear as to whether his fourth dimension was purely temporal or some combination of spatial and temporal or whether he even intended for it to be taken literally.

8. Jan 1, 2012

### Fredrik

Staff Emeritus
The only thing that can answer a question about reality is a theory. In the established theories (general relativity, special relativity and pre-relativistic classical mechanics), spacetime is 3+1-dimensional (3 spatial, 1 temporal). In string theories, spacetime is 9+1-dimensional. There's also something called M theory in which spacetime is 10+1-dimensional. The problem is that no one has been able to make a testable prediction with any of these theories, except for the big one: string theories predict the existence of gravity. There are however no experiments that can test predictions of string theory that disagree with the established theories. So it's questionable if the string theory "theories" should even be called "theories" at this point.

Since we don't see a 4th spatial dimension when we look around us, a theory with more than 3+1 dimensions must explain why we don't. If it doesn't, it can be immediately dismissed. A simple possibility is that there's a 4th dimension that's like a very small circle instead of like a line, meaning that if you move any distance that you think should be large enough to be measured, in the direction that's orthogonal (i.e perpendicular) to the other three spatial dimensions, you will have made many laps around the entire universe. String theories actually do say something like this about their six extra dimensions, but since there are six of them, more complicated possibilities than circles must be considered.

Physicists expect that forces would behave differently at very small distances if there are small extra dimensions. For example, in a 4+1 dimensional spacetime, we would expect Coulomb's law for the electric force between two point charges to decrease with distance as 1/r3 instead of as 1/r2. This would have consequences in high-energy interactions between elementary particles, but we might not be able to see them. The particle accelerators that exist today may give the particles energies that are many orders of magnitude too small for these consequences to show up.

9. Jan 1, 2012

### Pythagorean

Do spatiotemporal dimensions exist at subplank scales?

10. Jan 1, 2012

### metiman

That's an interesting answer, Fredrik. Thank you. I should have ruled out very small dimensions. I forgot about those. I meant a fourth spatial dimension which was equivalent to the first three. The fourth vector would be exactly the same as the first 3 except that it would be orthogonal to 3 vectors instead of just 1 or 2.

I believe the usual science fiction idea is that the reason we can't see the fourth spatial dimension is not because it is too small or because it is curved, but rather because we are 3 dimensional creatures and cannot perceive anything that is four dimensional. Cannot even imagine it. The argument may even be that our senses have simply not evolved to detect 4 spatial dimensions or 4 dimensional objects. Sometimes the Flatland story and the analogy of two dimensional creatures living in a two dimensional world is suggested. Often there are 4 dimensional life forms in the story which can perceive both 4 dimensional objects and 4 dimensional space.

Of course 2 dimensional creatures do seem logically impossible to us. Even if they were only 1 atom or even 1 electron thick they would still have 3 dimensions. Perhaps the best analogy would be 3 dimensional creatures who can only perceive things in 2 dimensions. Perhaps they can only see projections or 'shadows' of the 3 dimensional world sort of like Plato's cave. Of course it would also mean they can only see a 2 dimensional 'slice' of themselves at any one time. This analogy would seem to imply that we actually were 4 dimensional creatures ourselves but, for some evolutionary reason, we just haven't evolved sufficiently complex brains to deal with more than 3 spatial dimensions in ourselves or the world.

Some specific examples of stories that use or at least mention the idea are: The Accidental Time Machine by Joe Haldeman, Sphere by Michael Crichton, a silly movie called Supernova (despite its flaws it has an interesting example of this), and one of my favorite books from my early childhood: A Wrinkle in Time by Madeleine L'Engle. I'm sure there are many more examples.

As far as the idea just being dismissible out of hand because it is not based on any observational evidence, haven't both relativity and quantum mechanics shown us that we cannot trust our senses or our intuition about what makes sense and what doesn't? The world is clearly very different from how we thought it was pre-relativity and even different from how it seems to us now. Perhaps we are not sufficiently advanced as a species to make such determinations. Maybe figuring out such things intuitively would be like a monkey trying to solve partial differential equations or do Fourier transforms or something. It's just not going to happen. At least not yet. It's almost like relativity theory and quantum mechanics have allowed us to get ahead of where we would normally be in evolutionary terms.

Note that I don't actually believe in any of this. The point is how to debunk the theory. Or alternatively how one could prove such a theory. If it were true, what kind of experiment could you perform to demonstrate it?

Aren't theories just generalizations of experimental results? Can't experiments also answer questions about reality? For instance, if you wake up in a strange environment and want to see if there is gravity you could drop an object and see if it moves anywhere when you do so. You don't need a theory to explain what causes the object to move to get useful information about reality by just observing that it does. Lacking a theory also doesn't prevent you from measuring quantities and deriving equations which describe relationships between variables. Experiments tell you that things are a certain way. Theory attempts to tell you why and sometimes how. But theory is dependent on experiment. Experiment is not dependent on theory. Not that theory isn't useful of course. It's just not the first thing that comes to mind when I want an answer to a question about reality. Instead I think, "What kind of experiment could be performed to prove or disprove this?".

11. Jan 1, 2012

### Fredrik

Staff Emeritus
In the established theories, yes. The planck scale has no significance in those theories. I'm not sure about the situation in quantum gravity theories. I suspect that different theories will give you different answers.

12. Jan 1, 2012

### Fredrik

Staff Emeritus
If all you want to know is if stuff falls to the ground or not, you don't need a theory that involves mathematics. But when we do, I prefer to think of experiments as doing nothing but telling us how accurate a theory's predictions are. I don't mind say that "experiments can only tell us how accurate a theory's predictions are" as if it's true in general, because strictly speaking, it is. It's just not always the simplest way of looking at things. If you measure the length of an object and find it to be 7 cm, you are testing the accuracy of the theory that says that length is 4 cm, the theory that says that the length is 5 cm, etc. So this way of looking at it is never wrong, but is sometimes kind of weird.

The idea that experiments reveal truths about nature is however a bit naive, since you often need a theory just to define the terms involved in the statement that you would like to prove or disprove. So that way of thinking of experiments doesn't always work. That's why I prefer my way.

Last edited: Jan 1, 2012
13. Jan 1, 2012

### moejoe15

No there is no 4th dimension. There isn't even 3. There is only one that we choose to describe 3 dimensionally. We also 'chose' to call time a 4th because we already made up the first 3.

One of our talents is to ascribe reality to our ideas as if just because we thought of it, it must exist. There isn't any consensus on whether time exists, let alone what it is. Saying it's the 4th dimension is a convenience, not necessarily a reality.

In case you are wondering what I mean, infinity and paradox are 2 concepts we made up which don't actually exist in nature. I think the current hysteria with string theory is also bogus. The only reason they can come up with 10 dimensions is because of the false premise we already have 3 or 4. I hope I am wrong about all that, it would make the universe much more interesting but also unnecessarily complex.

14. Jan 1, 2012

### Number Nine

...what?

15. Jan 2, 2012

### Fredrik

Staff Emeritus
There are things in our 3-dimensional world that can be described as 2-dimensional. For example, I think the behavior of electrons at the surface of a metal can be described by a 2-dimensional theory. I'll avoid making claims about the details, because I know almost nothing about them. My point is that for an (n-1)-dimensional theory to describe things in an n-dimensional space accurately, the nth dimension must not be equivalent to the others. It only works when something breaks the symmetry, as in my example of the surface of a 3-dimensional object.

You asked about how to prove that there's no 4th spatial dimension. Here you seem to be imposing the requirement that the extra dimension doesn't have any easily observable consequences. So what are its consequences? You obviously can't disprove something that doesn't have any consequences, but you also can't disprove something whose consequences are unknown.

It wouldn't make sense to add extra dimensions to a theory if those extra dimensions don't change the theory's predictions. It would be like adding an invisible blue giraffe named Leonard that doesn't interact with matter. If you add extra dimensions to the theory, then their effect on the theory's predictions will depend on what assumptions you make about them. If we assume that they don't change the fact that the electric potential changes with distance as 1/r, then we are also changing the 1/r2 in Coulomb's law to 1/r3, which probably contradicts every experiment ever made. If we instead assume that the observable universe is similar to the surface of a metal, i.e. if we assume that it's a 3-dimensional hypersurface in a 4-dimensional space, then what we have to do to test the theory depends on what assumptions we make about how the 4th dimension affects the observable universe.

16. Jan 2, 2012

### ryan7585

These were my thoughts exactly. We dont exist in any position to view our plane of existence as a whole, singular entity, so we must describe it in terms of its parts.

There is only one plane of existence but we use 3 dimensions of space to describe the positions of things within it. You can use ANY NUMBER of dimensions that is more than 3, to describe these positions.

So based on that, we could just say that string theory uses eleven dimensions, because it CAN, and that's what's necessary to make the math work out.

I can use 70 dimensions to describe the location of my pencil relative to the location of the floor. For every day purposes, I only need 3 to do this, but I can use as many as I want, and in M-theory, it is necessary to use 11

17. Jan 3, 2012

### moejoe15

Exactly.

18. Jan 3, 2012

### ryan7585

Are there any theories with this position? Everything I've read so far basically attempts to make additional dimensions metaphysical

19. Jan 3, 2012

### FlexGunship

Deepak Chopra has brought us all some word salad! Favorite dressing?

Obviously there are no theories that hold that position. If you don't know why it's obvious, then read!

EDIT: Look, dimensions are what are required to accurately describe the location of an event of object in the universe.

Imagine you're on a straight road. You cannot move side to side or up and down... only forwards or backwards. In this universe, you need only one value to describe your location. This is a "one-dimensional universe." Where are you? You could answer that question by simply saying (4) since it is a distinct location and tells you enough information to find that place.

Imagine you are in a small town with many roads but no hills and no buildings. You could overlay a grid and then, by using two values, describe your location. This is a "two-dimensional" universe. One number isn't enough to tell where you are, and three numbers would be redundant. You could be at location (4) but there are many places along location (4). You might call your staring point (4,0) and taking a few steps to your right leaving you along line (4), but in a new place. Call this place (4,5).

Imagine you're in a real-life town with many roads, and a few office buildings. Now it's possible to be in more than one location on the two-dimensional grid. The first floor of an office building might be given as location (4,5), but what about the second floor in that same location? You're still at (4,5) but you're not in the same place! You need another dimension to describe your location. Height! First floor could be (4,5,1) and the second floor could be (4,5,2). This is a "three-dimensional" universe.

Finally, imagine that you are at location (4,5,2), but then you leave. You need an additional dimension to describe WHEN you were there. (4,5,2,3:00PM) could be an example. This is enough information for someone to location you in a three-dimensional universe that passes through time. If your friend says meet him at (4,5,2) you might arrive there at the wrong time. So you need one more dimension.

Now... that is not an arbitrary number of dimensions. It is the fewest pieces of information to accurately describe you location in the universe of space-time. There is no extra information, and no information missing.

Do you understand why it's still to say "there could be as many dimensions as we choose" and why it's sillier to say "there is only one dimension"?

Last edited: Jan 3, 2012
20. Jan 3, 2012

### ryan7585

These are the reasons I rephrased his statement in my own words.

A dimension and a universe are not synonymous. There are no "one-dimensional universes".. There is simply the universe, and dimensions (measurements between points) can be used to describe the relative location of points within it. You can use any number of dimensions greater than 3 to describe the location of a point

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