I haven’t looked into the latest research in a long, long time, but I remember hearing that all of the Unified Theories that come close to covering everything have something like 10-26 dimensions.
We’re all familiar with 4 (length, width, height, time). I can mostly conceptualize a 5th (space-time is “wrapped around” another dimension, making things like wormholes possible), and I can get a 6th if I accept multiple universes (your coordinatess would be length, width, height, time, whatever the 5d coordinate would be called, and then which universe you’re in).
Can anyone describe more? Thinking about this stuff is so much cheaper than pharmaceuticals…
Currently, M-theory proposes 10 spatial dimension and one time dimension, with three of the spatial dimensions being the extended dimensions we are familiar with on an everyday level, while the remaining nine are tightly curled up into shapes known as Calabi-Yau spaces, on the order of the Planck length.
It’s just not worth trying to understand most of this stuff on an intuitive level, cause it doesn’t make sense that way. Modern physics is inherently mathematical, and generally doesn’t make sense in any natural language.
At any given time, a particle has coordinates in three of the spatial (x, y, and z) and the one time dimension (the time at that moment). If the other dimensions are tightly curled up into Calabi-Yau space, that particle can’t have coordinates in those dimensions, right? If it can’t, how are they dimensions?
Here is a decent page on the subject, explaining the basics of it. It might help to visualize a simpler version or real spacetime by imagining space has only one extenteded spatial dimension and one “curled up” one. Let’s imagine the surface of a garden hose. it’s a two-dimensional surface with one long, extended dimension, and one circular “curled up” dimension. Up close, we need two numbers to describe the position of a point on the surface. However, as we zoom out, the circular dimension becomes smaller and smaller, eventually becoming imperceptible. At this point, we can use only one number to describe a position on the hose, which now appears as a one-dimensional line. The other six Calabi-Yau dimensions of our real universe are tightly coiled up and we can never observe them directly. But, the strings whci are believed to make up all the matter and energy in the universe can and do vibrate in these Planck-scale dimensions, and it is this vibration in the tiny dimensions that gives them the properties of all the observed particles that we can observe. The dimensions are only important when calculating the vibrational patterns of strings, and we need all the 10 (or possible 11) spacetime dimensions to do that. But on any scale we can observe, we need only refer to three of them.
No, that’s completely wrong. If you can demonstrably specify any arbitraty point in space with only one number, then I’ll buy that. There’s clearly at least three spatial dimensions. This is not arguable.
In “scientific” talk dimensions means unique (Orthogonal for the mathematic people) numbers that are needed to specify a system. They have nothing to do with the physical notion of length, breath and height (although the idea does come from there)
Say there are particles in a room and you want to specify their location. Then their location can be specified by choosing an orthogonal system - say the usual x, y, z. So the position of the particle is three dimensional or represented by the vector [x;y;z].
Now if you want to point out their location changing with time then you have the vector [x;y;z;t] - and thats four dimensional.
Further , if you also want to point out the temperature of each particle, then [x;y;z;t;T] (T denotes temperature) is five dimensional.
Temperature does not make a fifth dimension, because it is dependent on the other coordinates; you can’t have two objects with the same x,y,z,t but different T coordinates. If it were a true dimension, you could have two points with different x,y,z,t but different T values and the two objects would not be in contact.
(My bolding) I don’t think andy_fl was arguing T to be a spatial dimension. Rather, it’s pretty easy and common to come up with n-dimensional problems in the real world.
Example: given 50 different resources with associated costs and availabilities, and a number of different products that can be produced using those resources, each with its own profitability level, what’s the optimum (most profitable) combination of products to produce?
Assuming linear constraints, cost and profits, the solution is a point on a 50 dimensional polytope.
I don’t have a problem with your example. Well a nitpick, the number of dimensions is not the number of resources, but the number of different products. The 50 values for the different resources depends upon the number of each product. So, the number of dimensions in your example is the number of products. The dimensions are the independent variables; the dependent variables are just a function defined on the space of the independent variables.
Obligatory recommendation for Brian Greene’s excellent book. He explains all these theories in as simple terms as possible (he also uses the garden hose analogy).
What blows my mind is when he calculates the force compressing the superstrings, then what would happen if that force were suddenly removed…amazing.
If you have a system of n variables and m constraints, you can restate it as the dual problem with m variables and n constraints.
The dimensionality of the problem is the number of variables, and for large problems, you solve whichever version has the lower dimensionality.
But the number of constraints in the original problem doesn’t equal the number of products that can be made, because there are additional constraints, like: you’ve only got 20 units of resource 3, etc.
Thanks, I’ll definitely have to check it out! I find it especially funny that one of the reviewers on Amazon says, “However, total reliance on metaphor and analogy leaves a ‘mathematically inclined reader’ suspicious of the knowledge he has just (suposedly) acquired. Or so I thought, until I investigated further on the Internet the kind of arcane mathematics is really involved in string theory.” In other words, at least according to what this reader found, it’s easier to explain these things conceptually than mathematically… which is the opposite of what some have been saying in this thread…
IMO - and I maybe wrong to understand this - but dimensions are the number of numbers you need to completely specify a system (or give all the information abt the system). So if I have a ball in a box and it is moving around and it has a thermocouple in it which transmits its temperature - I donno why temperature is not a dimension.
x,y,z,t are physical dimensions. You just can’t have 2 bodies with the same x,y,z,t - regardless of if there is a fifth dimension or not.
That does’nt prove the dependence of T on x,y,z,t. You can arbitrarily change the temperature of any point in a box using a laser or any other energy source.
** If it were a true dimension, you could have two points with different x,y,z,t but different T values and the two objects would not be in contact. **
Yes - you can surely have that - whats the problem with that ? Imagine a few balls bouncing around in a box.
