According to the holographic principle, our four-dimensional universe, consisting of three space dimensions and one time dimension, is a surface area of a five-dimensional spacetime called "the bulk." The remaining dimensions of string theory or M-theory are allegedly compacted and rendered insignificant.
Gravity, compared to the other fundamental interactions, is weak due to the graviton's unique ability to move between the surface area (our spacetime) and the bulk. Other particles remain fully in our spacetime and thus have more intensity. At least that's how the story goes. Unfortunately, the gravitational-wave test described in the above video failed to confirm the existence of "the bulk" or any extra dimensions beyond our four-dimensional spacetime. This does not surprise me, given the problems extra dimensions can cause (click here to read all about it).
So why did the gravitational-wave test fail? Do we really need "the bulk" to explain the nature of gravity? We will explore these questions. First, let's define the variables we will use:
According to general relativity, gravity is a function of energy density, so let's begin with the energy density of an atom. An atom is mostly space, so let's only consider the volume of space taken up my the average nucleus and the electrons. That approximate volume can be found in the denominator of equation 1 below:
Of course if we put that volume in the numerator, we get the energy (E):
If we put a larger volume (V) in the denominator (equation 3), we get a reduced energy (E'). Reduced energy is consistent with weak gravity, so we are on the right track.
We don't want Energy units, so at 5 and 6 we use meters and Newtons to adjust the units:
Now, coincidentally, 10^-45/N is approximately equal to G/c^4, so we make the substitution:
We use distance D and the alpha scale factor to make more substitutions at equation 9. From there we derive equation 12.
Equation 12 is Newton's equation. We were able to derive this equation because we started with the premise that the intensity of gravity is determined by the actual amount of space a particle interacts with. For baryonic matter, that actual amount of space corresponds with the gravitational constant G. Note that no extra dimensions are needed to get equation 12. Our 4D spacetime is sufficient. So why should we be surprised that the gravitational-wave test failed to confirm "the bulk"?
Caveat: the above mathematics may work just fine for ordinary matter such as atoms and molecules, but what about singularities such as black holes? Theoretically, a singularity takes up no space, so there shouldn't be any interaction between the matter and space, but there is! To resolve this conundrum, we first need to establish that light speed is truly the top speed in our universe. Consider the familiar Lorentz equation:
The main problem with this equation is time (t) is arbitrary. Let's make it precise. Let's make time (t) equal to the age of the universe. When I say universe I mean everything including the megaverse if such a thing exists. What we want is the longest time ever lapsed--so we set t accordingly and define the other variables we need:
Now we derive 21 below:
Line 21 shows that no velocity (v) can exceed light speed (c). So what does this have to do with gravity and black holes? Given the fact that light speed is the top speed, we can derive the following:
Take a look at 25 and 26 above. At 25, G stays constant as long as the change in time (delta-t) is equal to or less than the age of the universe. Note that delta-t increases as radius r decreases, so G remains constant. But delta-t has an upper limit of t. If r continues to shrink, G must also shrink. Thus it appears the intensity of gravity is determined by how much space interacts with matter. The smaller the radius r, the smaller the space the matter occupies. Equation 27 shows that the intensity of gravity never exceeds the speed of light squared no matter how much radius r shrinks.
In conclusion, "the bulk" and extra dimensions are completely unnecessary to describe gravity.
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