Expert: James Gort - 2/28/2007

Question
Greetings Professor. I hope I'm not monopolizing your time. I appreciate the answer you gave to my other question.

My question is about a concept I have in my head and whether or not it is a multi-dimensional object or some other thing.  I'm trying to get a grip on the whole 11 dimensional space idea. I'm not a student of physics - this is just for interest. I shouldn't preamble, this is going to be long enough...

11 dimension space is a mindwracking concept because my comparative logic is 3 dimensional. Would imagining a 11 D world be as simple as imagining a multifaceted jewel, with intersecting planes of a more complex nature than a cube? Or to say it a different way, a plane has 4 points and a cube has 8, so you would multiply by 2 again to get the next "connect the dots" geometric pattern? The physical effect on any matter within must be very complex. Gravity would be interesting...

Here's another way I'm thinking about it and I'm wondering if my end result a multidimensional object or some kind of phased 3D object/knot?: This first part is basic but I have to start here. A pair of 0 dimensional points will make a 1D string (length only). Along this 1 D string there is a number of points, perhaps infinate number (this is important later). Add an additional dimension of width or, in other words, lay a bunch of strings side by side and you have a 2D plane. Up to this point I think I'm correct to assume these objects cannot be directly observed by us in our 3D universe because they lack depth. (A 2D plane could not cut a person in half like a knife because it lacks the 3rd dimension of depth. It would be "anti-blunt". Is this correct?

Moving on: So if you take the strings we have neatly lined up in a row to form a plane and add similar planes in all directions, 360 degrees, we end up with a 3D shape, I'll call it a string ball but it could be a string cube too. That's about the end of where I find this easy to understand - 5 oclock shuttle departing the 3D universe, starting now :)

...If you take each individual plane in this 3D shape and displace the entire cubic shape to a point (or a finate/infinate number of points) along each plane of all 3 dimensions, like melding a number of these string ball objects together, would these identical displaced realities cohabitate the same space time or would this be an extradimensional object with different space time issues? I'm assuming that a particle can be displaced along it's wavelength, if they are correct that a particle has wave properties.

I'm just an amateur, possibly missing something obvious here. This sounds like science fiction, where another version of me could exist in an identical finite universe, at a different particle wavelength but we would all be contained within the "infinate universal knot" (or at least the 11D's that they are able to prove mathematically). Perhaps you could even displace the object along the time dimension as well.

So well, my point (oh the puns) is that I'm just wondering if this is multidimensional or just a complicated geometric shape? I spent too much time in a car where I wonder about things like this.

Thank you for your time.

Answer
Hi Paul,

No problem on the time.  I see you've been thinking this through!

First, answers to some of your specific questions.  Yes, a 2D plane through a person would not cut a person in half, because there is no thickness.  It would only produce two "zones" - the "upper body" and the "lower body".

Regarding the displacement of your 3D body (formed by many strings).  I'll assume you have an infinite number of planes to form your solid 3D body (in other words, there's no holes).  In that case, if you displace it in "space", the original object and the displaced object would cohabit space-time, but if the 3D overlapped, there would be some redundancy.  Mathematically, you can superimpose 1-dimensional strings or 2-dimensional planes with no problem.  When you get to real particles, there is a problem.  A quantum mechanical principle applies here (google the following for more info) - Heisenberg's Uncertainty Principal and Quantum Fluctuation.  Basically, physics says we can't isolate a real particle to a point.  So your 3D object is really not composed of an infinite set of 2D objects, but a finite set of particles whose position in space-time is fluctuating.  So you can't apply pure mathematics in this case to real particles.

By the way, you could have also displaced your 3D ball in time rather than space.  Construct your ball on Tuesday, and then tear it down.  Then make an identical ball (same points) on Thursday.  The 2 objects are also separated in space-time (in this case, only time).  

Similarly, you MIGHT be able to displace the objects on other dimensions (but I'm not sure how you'd go about it, and whether you could test it, if you did!).

As another point, it's better not to refer to particles with "wave properties".  All known physical interactions between electrons and photons can be predicted by assuming photons are particles.  Assuming they're waves makes some calculations a bit easier, but some calculations can't be done at all!  See "QED" by Richard Feynman.  Great little book.

I think you got the 11 dimension concept from "string theory" - which requires multiple dimensions to be self-consistent.  In that case, yes, there could be different versions of you if only one of those dimensions was changed (or you were displaced). It is sounding more like science fiction all the time.  But don't believe everything you read!  I suggest you get another little book entitled "Not Even Wrong" by Peter Woit (a Princeton theoretical physicist).  In it, he explains that multi-dimensional string theory is not a theory at all, since it can NEVER be proven.  It cannot be shown to be right (or wrong).  So is it science?  Probably no more so than another theory that says there are an infinite number of co-existing universes (some of which can be connected by worm holes!).  Science fiction?  Yes.  But legitimate science has proposed these ideas!  To me, it isn't science (it's fiction, philosophy, theology, or something else) unless it can PREDICT something that can be tested.  I don't think multi-dimensional universes fall into that category.  I'm not saying that they don't exist - I'm just saying that we don't know, and I wouldn't call the theories I've seen so far "science".  

Try and find those books and you'll be amazed!

Prof. James Gort