# A 4th Dimension

### #1

Posted 16 July 2014 - 12:00 PM

### #2

Posted 16 July 2014 - 02:27 PM

Reading an article in the current SA about a 4th spacial dimension got me wondering. I can only see or just as valid feel, three. I've read about time and the arrow of time and was left with the impression that it's always in one direction. So what happens if that's not exactly accurate? Might there be a reality where there are 2 times? Don't we in a round about way, experience and notice evidence of that when we ponder that light doesn't age?? The convoluted 11 or so spacial dimensions predicted by String Theory to satisfy problems in quantum theory never seemed to make any sense. How would objects FEEL in such a reality? OTOH, time isn't seen or can it be touched. Three spacial dimensions looks and feels right as a limit. I'm bad with math but could more then 1 time smooth out the same problems with quantum theory as does more then 3 spacial dimensions?

I've always felt that the dimension of 'Time' can be thought of in terms of 'enduring'.

You have a measurement of length. You have one of width and one of height. You also have one of duration.

"The shoebox is 14 inches long. It is 6 Inches wide and 8 inches in height and has existed for a duration of 2 years."

So it takes reporting on all 4 dimensions in order to correctly define the shoebox in the Universe. For example, if the shoebox only existed from 2012-2014' and a time traveler went looking for it in 2011' he won't find it.

All objects, in order to be said to exist, must extend into all 4 dimensions.

Pesse (Unless they extend into the Fifth Dimension in which case they sing music) Mist

### #3

Posted 16 July 2014 - 03:27 PM

Retrocausality although not necessarily related to another dimension may also be an engaging topic related to your post.

And then there is the notion that physical processes may work perfectly well regardless of which direction the arrow of time is facing in the quantum world but on the macroscopic level, not so much.

### #4

Posted 16 July 2014 - 04:05 PM

Then have a stiff drink.

### #5

Posted 16 July 2014 - 04:54 PM

### #6

Posted 16 July 2014 - 05:01 PM

Google "imaginary time" and "

CPT symmetry"...

Then have a stiff drink.

OK. My teeth hurt but it's too early for a stiff one.

### #7

Posted 16 July 2014 - 06:18 PM

"The shoebox is 14 inches long. It is 6 Inches wide and 8 inches in height and has existed for a duration of 2 years."

So it takes reporting on all 4 dimensions in order to correctly define the shoebox in the Universe. For example, if the shoebox only existed from 2012-2014' and a time traveler went looking for it in 2011' he won't find it.

All objects, in order to be said to exist, must extend into all 4 dimensions.

Pesse (Unless they extend into the Fifth Dimension in which case they sing music) Mist

That's the narcissistic, Earth-centric way of looking at the shoebox. What if its existence/endurance depends on literally everything else in the universe? Its presence in our reality might be explained by a different and unified way of looking at space and time. Taking a page from the

*Hitchhiker's Guide*novel, Twistor theory alludes that your shoebox existed because that was the least improbable configuration for the Reimann sphere known as your closet.

### #8

Posted 17 July 2014 - 02:52 AM

If the vector can change direction (time travel, etc) then the universe might have to store position*time for every minimum unit of time (unless there is no minimum and Planck time is meaningless) and then reproduce physical processes all over again, faster than they happen.

There might not even be 3 dimensions, instead of width [1] x length [2] x height [3] it could be:

distance [1] from one point (the point is always the same so it doesn't count, it could even be the location of the big bang haha) and two angles [2] compressed into one ... if the universe supports infinite numbers

There could even be only 1 dimension w=x*y*z, where the space is a continuous line of Planck length units or something. Instead of moving from point A (1,1,1) to B (10,10,10) you move from 1 to 1000 without factoring 1000 into 10,10,10.

### #9

Posted 17 July 2014 - 09:55 AM

Einstein was the first to describe spacetime as a true 4-dimensional structure. It is in the form of Minkowski space, which is Euclidian, for Special Relativity and Riemannian monifolds for General Relativity, which are non-Euclidian. A 4 vector in Minkowski space has time as dimension. Transformations are made that are essentially rotations in the 4 dimensional space. Time and space get longer and shorter based on the rotations. It is exactly like the x-axis getting shorter while the y-axis gets longer as you rotate constant length around the origin in flat plane. It gets much more complicated fir General Relativity where tensors replace 4-dimensional vectors. A length in Minkowski space is described as s^2=-c^2*t^2+x^2+y^2+z^2, where s^2 in the square of the length. If you notice, time squared takes on a negative value to make the math work. If you took the square root, it would take on an imaginary value.

### #10

Posted 17 July 2014 - 11:09 AM

A length in Minkowski space is described as s^2=-c^2*t^2+x^2+y^2+z^2, where s^2 in the square of the length. If you notice, time squared takes on a negative value to make the math work. If you took the square root, it would take on an imaginary value.

sqrt(-c^2*t^2) = ict

This sign usage is denoted -+++ and is called the "spacelike" convention.

Many modern physicists use +--- which is known as the "timelike" convention,

so the equation takes the form s^2 = (ct)^2 - x^2 - y^2 - z^2

In the book

*Gravitation*by Thorne, Misner, & Wheeler, they have a table

of sign conventions used by various physicists over the years, and a section

called "A Farewell to ict."

### #11

Posted 17 July 2014 - 11:43 AM

For example, if you are moving or accelerating along the x-axis only, there is no motion in the y or z axes.

Maybe but one objects X axis may be another observers Y or Z axis depending on their perspective. So who is really to say?

### #12

Posted 17 July 2014 - 12:11 PM

### #13

Posted 17 July 2014 - 01:24 PM

If you have to go to great lengths to "make the math work", perhaps that means the equation is invalid?There is the concept of orthogonality when describing dimensions. Things happening along one dimension have no impact on other dimensions if the axes are orthogonal. For example, if you are moving or accelerating along the x-axis only, there is no motion in the y or z axes.

Einstein was the first to describe spacetime as a true 4-dimensional structure. It is in the form of Minkowski space, which is Euclidian, for Special Relativity and Riemannian monifolds for General Relativity, which are non-Euclidian. A 4 vector in Minkowski space has time as dimension. Transformations are made that are essentially rotations in the 4 dimensional space. Time and space get longer and shorter based on the rotations. It is exactly like the x-axis getting shorter while the y-axis gets longer as you rotate constant length around the origin in flat plane. It gets much more complicated fir General Relativity where tensors replace 4-dimensional vectors. A length in Minkowski space is described as s^2=-c^2*t^2+x^2+y^2+z^2, where s^2 in the square of the length. If you notice, time squared takes on a negative value to make the math work. If you took the square root, it would take on an imaginary value.

### #14

Posted 21 July 2014 - 12:48 PM

Having a 4th dimension (time) makes sense to me only if an "arrow of time" can go faster or slower, like a vector that can change magnitude, but not its direction. Otherwise if the vector is always constant then the 4th dimension is redundant.

If the vector can change direction (time travel, etc) then the universe might have to store position*time for every minimum unit of time (unless there is no minimum and Planck time is meaningless) and then reproduce physical processes all over again, faster than they happen.

There might not even be 3 dimensions, instead of width [1] x length [2] x height [3] it could be:

distance [1] from one point (the point is always the same so it doesn't count, it could even be the location of the big bang haha) and two angles [2] compressed into one ... if the universe supports infinite numbers

There could even be only 1 dimension w=x*y*z, where the space is a continuous line of Planck length units or something. Instead of moving from point A (1,1,1) to B (10,10,10) you move from 1 to 1000 without factoring 1000 into 10,10,10.

How do you know the Universe doesn't experience time as individual quantized 'instants' strung together?

Sort of like how we make cartoons today: Draw a bunch of 'instants' and then flip through the stack and, viola', we have a video pulled from distinct quanta of 'instants'.

Pesse (..and, according to quantum physics, each 'instant' can break off into all possible follow-up quanta) Mist

### #15

Posted 21 July 2014 - 01:38 PM

I really don't know. But then wouldn't we live in a pre-determined (with 1 stack) or redundant (choosing a frame from many stacks which also require more storage) universe? I call the 2nd possibility redundant because events could just happen in-place, on the fly, without needing time.How do you know the Universe doesn't experience time as individual quantized 'instants' strung together?

Sort of like how we make cartoons today: Draw a bunch of 'instants' and then flip through the stack and, viola', we have a video pulled from distinct quanta of 'instants'.

Pesse (..and, according to quantum physics, each 'instant' can break off into all possible follow-up quanta) Mist

### #16

Posted 21 July 2014 - 01:50 PM

That's an interesting idea, but I guess there'd have to be as many extra time dimensions as there are extra velocities (or maybe I should say "speeds").I'm bad with math but could more then 1 time smooth out the same problems with quantum theory as does more then 3 spacial dimensions?

### #17

Posted 21 July 2014 - 04:15 PM

### #18

Posted 21 July 2014 - 09:34 PM

### #19

Posted 22 July 2014 - 07:56 AM

Time (as we know it) is only relative to us here on earth. Dictated by the sun and rotation of the earth, correct? We may say the speed of light is 186,286 mps, but that's just our perspective on it.

Actually, one of the central facets of relativity is that the speed of light © is constant. It is always measured as exactly 186,282.4 mps, or 299,792,458 meters per second, no matter what reference frame you measure it from. Different reference frames will measure time differently, and they will measure distance differently, but time and distance vary in a manner that maintains C as a constant.

Jarad

### #20

Posted 22 July 2014 - 09:27 AM

### #21

Posted 22 July 2014 - 10:27 AM

As I interpreted the question, it's about why we should use earthly parochial measures like miles, meters, seconds. If one uses different units of measure, different figures for c result.Time (as we know it) is only relative to us here on earth. Dictated by the sun and rotation of the earth, correct? We may say the speed of light is 186,286 mps, but that's just our perspective on it.

Actually, one of the central facets of relativity is that the speed of light © is constant. It is always measured as exactly 186,282.4 mps, or 299,792,458 meters per second, no matter what reference frame you measure it from.

### #22

Posted 22 July 2014 - 11:10 AM

### #23

Posted 22 July 2014 - 01:50 PM

Everything, as they say, is relative.

### #24

Posted 22 July 2014 - 01:59 PM

I only ask because I'm curious. This (in my mind) doesn't explain how c changes near a black hole (singularity?). If c is supposed to be constant, "unchangeable" , and a lot of theory revolves around this, then why are these theories made from uncertainties? But taken as gospel? I must be confused. I understand that c is supposed to be a fixed value, but clearly it isn't. It can't be. C maybe a fixed value, but from who's view point? It's not the same, (near a black hole, for instance) as it is relative to you're position in space.

### #25

Posted 22 July 2014 - 02:17 PM