Disclosure: I am not trained in advanced physics. My training/degrees are in the fields of mechanical engineering (solid mechanics, fluid mechanics and heat transfer) and nuclear [reactor] physics – not the theoretical stuff discussed earlier. Oh, and I have a high school diploma, which is just about all I needed in my quest to debunk TW… Anyway, this is my first post here; I saw TW’s ad, now appearing in Popular Science, and couldn’t resist looking it up, which ultimately led me here.
Although this thread has mostly been devoted to debunking TW’s theories in the realm of advanced physics, I think you’ve sold yourselves short on how easy it is to prove him wrong and reduce his arguments to utter rubbish. Let’s explore the simplest premises that are available from his book, shall we? To quote from his website:
SURFACE BOUNDARIES
In general, any (N+1)-dimensional space can have an N-dimensional surface subject to the following related criteria:
Ψ THEOREM 2.9 - CLOSURE BOUNDARY {Ψ2.4, Ψ2.8}
(A) ANY (N+1)-DIMENSIONAL REGION CAN BE BOUNDED BY AN INFINITELY
THIN N-DIMENSIONAL SURFACE
(B) THE MAXIMUM DIMENSION AN INFINITELY THIN N-DIMENSIONAL
SURFACE CAN BOUND IS (N+1)
A circle is bounded by an infinitely thin line; a sphere is bounded by an infinitely thin area.
Similarly, a line is too dimensionally small to form a spherical boundary. In reference to our
universe, no boundaries of any kind exist along its three spatial dimensions. This means space is not a bounded interior region; it is a bounding surface.
Let’s start with the first sentence. It begins clearly enough, because any N+1 dimensional space can, in fact, contain an N dimensional surface (provided you don’t bound the N+1 surface to be too small). Unfortunately, his logic heads south by the end of the sentence. The statement made at the beginning of the sentence is not subject to any additional criteria; that is to say, an N+1 dimensional surface can ALWAYS accommodate an N dimensional surface. TW’s theorem, regardless of whether it is true, is proposed to support a flawed premise (and conclusion, but we’ll get to that later).
Now, to look at theorem 2.9 (A) – Can any N+1 dimensional surface be bounded by an infinitely thin N dimensional surface? Short answer: No.
There are four available examples in classical physics: 0-to-1 dimensional bounding up through 3-to-4 dimensional bounding. TW discusses two examples: using a line to bound a circle and a shell to bound a sphere. However, a circle (defined in Euclidean geometry as the sum of all points equidistant from a single point – not a line) cannot be circumscribed by a 1-dimentional object (line). By virtue of bending the line, it is no longer 1-dimensional: it is now 2-dimensional. Similarly, a sphere shell, although of zero thickness, is still a 3-dimensional object (if you doubt it, look up the formula: it requires inputs in 3 dimensions).
Lest anyone suggest that the above argument is semantic, let’s look at the two cases TW doesn’t explore. Is a 1-dimensional object (line) bounded by a 0-dimensional object (point)? Clearly not. At a minimum, at least two points are required to bound a line (segment). This is an important distinction, because theorem 2.9 (B) and the conclusions that proceed from it require the bounding object to be singular. Similarly, a 4-dimensional object (3D w/ time component) cannot be bounded by a 3D object. Perhaps a 4D object could be said to be bounded by a 3D object at the beginning of the specified time and by another 3D object at the end of the specified time (really the same object at two different times), but by no means does the “3D” object bound the “4D” version.
Based on this, it naturally follows that theorem 2.9 (B) cannot be true because it is premised on 2.9 (A). All further assertions based on these theorems are also wrong.
In summary, TW has, for no valid reason, taken 50% of the available examples and via improper geometric definition has created a false theorem. This theorem (2.9 (A)) is used to justify another theorem (2.9 (B)). This theorem is used to draw the conclusion that the universe, but virtue of extending infinitely in 3D, cannot be bounded and thus must be a bounding surface by virtue of 2.9 (B).
Incidentally, this conclusion doesn’t mean anything, and doesn’t even make sense. Although wrong, it seems to be the cornerstone for many more of TW’s theories to come (try reading the next few paragraphs that follow these theorems – they all rely on it heavily). Thus, we can state that null physics is indeed, null (and void).
Alternative method of disproving TW:
Theorem 2.9(B) requires the N dimensional object to be infinitely thin in the N-1 dimension. For example, a shell (or, for TW, plane) circumscribing a sphere has no thickness. However, when using 2.9 (B) to draw conclusions about “universal closure,” the universe is presumed to be infinitely large in 3 dimensions, not infinitely small in any dimension. TW has conveniently inverted the use of infinity here in a fashion that is not logically supported, and is thus invalid.
Second Alternative method:
Let’s offer a “true” version of 2.9(A) – namely, that any N+1 dimensional object can be bounded by a finite number of N dimensional objects. (For geometric (up to 3D) objects, the number required is N+2, but this doesn’t necessarily translate to time.) From this, a “true” version of 2.9(B) would be that only N dimensional surfaces can be used to bound an N+1 dimensional surface (i.e., lines cannot be used to circumscribe a sphere – only planes). Realistically, it should be N or N+1 dimensions, because an N+1 dimension object can be contained in a larger N+1 dimension object, but this is irrelevant to this particular argument.
Hmm, let’s apply this to the universe. The 3D universe can bind the 4D universe (i.e., there is a beginning to the universe, and presumably and end as well). Why can’t the 4D universe be binding a 5D universe? Or a 5D universe bind a 6D? In fact, there is no reason that the universe cannot extend into infinite dimensions using this train of logic. It thus follows that the “universal closure constant” (whatever the heck that is) is not 4, as stated by TW, but infinity. The term is one of TW’s invention for all I know, so I doubt it means anything (feel free to correct me if I’m wrong), but isn’t it a lot more plausible that a “closure constant” for an infinite object is infinity vice 4? Maybe I should write a book about it. Would anybody pay me $59 for it (I’ll make sure to throw in some nice, glossy graphs and everything!)?
