Do Electrons Leave Our Universe When They Move Inside the Atom?

Using a quantum microscope, it is possible to view the wave function of the hydrogen atom (see diagram above). Note the electron can only be found in the lit areas and not in the dark areas between. When the electron moves between energy levels, it seems to mysteriously vanish from our universe and then mysteriously reappears, hence the alternating pattern of dark and light circular bands.

Of course there's a string theory that explains this phenomenon: when the electron leaves an energy level it literally leaves our 3D space and enters a higher curled dimension. It loops around then re-enters our space:

At the diagram above you can imagine the electron (red dot ) moving left to right. The loop represents the extra hidden dimension.

Now notice the diagram below. It is the famous double-slit experiment. Notice the target screen has light and dark areas. We could postulate that the dark areas are due to the light disappearing into a higher dimension or an alternate universe--or perhaps it was abducted by extraterrestrials.

Of course this is all nonsense. We know why the dark sections are dark and why the light sections are light: constructive and destructive interference wave patterns. Where the red and black lines are parallel there's light (constructive interference), where they cross or move in opposite directions, there is darkness (destructive interference).

Since there is no empirical evidence of extra dimensions, it makes sense to propound an alternate hypothesis that uses established physics as its basis--the established physics being constructive and destructive interference. If you compare the two diagrams above, you will note a striking similarity: both have alternating light and dark areas on their respective target screens.

We know what causes the interference pattern of the double-slit experiment--it's the two slits. But what could possibly cause the interference pattern (discrete energy levels) of the hydrogen atom? That's what this post shall cover. First, let's define the variables needed:

At equation 1 below, energy (E) is charge (q) times voltage (V). Assuming energy E is an eigenvalue, it must have a probability (P(E)). That brings us to equation 2. Quantum mechanics tells us the probability is an amplitude squared (A^2, see equation 3). A pinch of algebra gives equations 5 and 6.

At equation 5 we see the positive charge from the hydrogen atom's proton corresponds to a positive amplitude squared. At 6 the negative charge from the electron corresponds to a negative amplitude squared. To get a negative amplitude squared we multiply the positive amplitude of a sine wave with its negative amplitude:

Notice there's no way to get a positive amplitude squared using this method. To get the positive squared amplitude, we need to do the following:

We use the absolute value of sine to create a positive squared amplitude. We now have what we need to model the hydrogen atom's constructive and destructive interference wave pattern. Check out equations 7 through 10 below:

When we plug in values for equation 7, we get the wave pattern below which maps beautifully to the light and dark areas of the hydrogen atom:

No extra dimensions needed, just old-school physics.

Why Gravitational Waves Fail to Confirm Extra Dimensions

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.

Why Strings Don't Exist

Let's compare the point particle and the string. A point particle's dimensions all have a zero limit. By contrast, a string has a zero limit for its cross-section dimensions and a Planck-length limit on just one space dimension. So one could ask, if the Planck length is the shortest length, then how is it that a string has shorter dimensions along its cross section? Does space follow different rules along, say, the x-axis and y-axis than it does along the z-axis? It doesn't seem likely that it would--and we will mathematically prove it, i.e., we will disprove the string. First, let's define the variables we need:

Below we we define the Lorentz factor at equation 1; the de Broglie wavelength at equation 2; The Planck length at 3; and the Planck mass at 4. At equation 5 we express the Planck length in terms of the Planck mass and de Broglie function. The Planck mass is multiplied by c to give the maximum momentum theoretically possible: the Planck momentum.

If the momentum were larger than the Planck momentum, The Planck length would not be the shortest length possible. If equation 5 is true, then equation 10 below must also be true, but is it really?

If we check how much energy is involved in bringing, say, an electron up to the Planck momentum, we discover the amount falls far short of infinity. In fact, the the energy amounts to only around 300 lbs. of TNT. If we could somehow squeeze more energy into the particle, surely we could increase the momentum. The result would be equation 15 where the wavelength is less than the Planck length.

Unfortunately the particle's momentum is not only restricted by the light-speed barrier, but also by the Planck temperature, which we will discuss later. Right now, let's see if the Planck units are valid. To build the Planck units, the following assumptions are made (see equations 16 & 17):

But then there's the Heisenberg uncertainty principle. At equation 19 we see that h-bar (the reduced Planck's constant) isn't really the smallest value possible. H-bar/2 is smaller. If we use this smaller value, we can derive new and smaller units (see 23 and 24):

Let's plug in these new units into the uncertainty relation (see 25). Now, if we assume the Planck mass is valid, then the shortest length is half the Planck length (see 26). OK, we broke the Planck length barrier. Can we do better? Yes! According to special relativity, a particle approaching light speed has an upper mass limit of infinity (see 27). If we could somehow harness the energy of the whole universe, then surely the minimum possible length would be far shorter than half the Planck length (see 28 to 30).

OK, now is a good time to address the Planck temperature. The Planck temperature is allegedly the hottest temperature that can be achieved. If such is the case, then our particle maxes out at 300 pounds of TNT worth of energy and corresponding momentum, i.e., the Planck momentum.

The Planck temperature is defined at 31 below. Notice how equation 31 does not take relativity into account. Let's factor in relativity (see 32). At equation 33 we end up with a temperature that has an upper limit of infinity.

Some physicists have postulated that the Planck mass represents the mass of the smallest black hole possible. If such a black hole is at rest, we can certainly use equation 31 to find the Planck temperature. But what if the black hole is not at rest? Then its energy (E) would be equation 35 below. Once again we end up with a temperature greater than the Planck temperature (see 36,37). Even if we limited the energy to kinetic energy only, it seems highly probable such energy would exceed the Planck energy (Planck mass X c^2). Thus it seems probable the highest temperature would exceed the Planck temperature (see 38 & 39).

OK, we've laid the groundwork needed to disprove the strings of string theories. We begin our disproof with Gay-Lussac's Law. Using the Planck length and Boltzmann's for the constant and doing a bit of algebra we derive a temperature equation at 44:

Both a string and a point particle have zero volume due to one being one-dimensional and the other zero-dimensional. Zero volume yields infinite temperature (see 45 to 47). If we assume the Planck temperature is the highest possible temperature, then one-dimensional strings (and point particles) don't exist. If the string (or point particle) is at rest, there's infinite uncertainty re: the temperature, thus possible temperatures that exceed the Planck temperature (see 48, 49).

Now let's attempt to save string theory. If we assume there is a minimum distance greater than zero, then that minimum distance should exist in all directions. Given that assumption, is it possible to build a string? For illustrative purposes, let's assume the Planck length is the shortest distance possible. Here's what we get:

At 50 above we have the temperature equation. At 51 we shrink the dimensions down to the Planck length. We end up with a small volume of matter (circled in red) rather than a string. We use this object to derive equations 52 to 54. Of course, given what we have covered in this blog post, the Planck length could be cut by at least one half. However short the actual shortest distance, it is abundantly clear it doesn't make a one-dimensional string.

Debunking D-branes and other Extra-dimension Myths

According to string theory, d-branes come in one or more dimensions. They provide an anchor for strings. Some string theories have only even-numbered d-branes; others have odd numbered d-branes. As we shall see later in this post, the odd d-branes, or systems with an odd number of space dimensions, have a better shot at being real. One real example is space in our universe. We perceive it as 3D, and it can be thought of as a giant 3-brane.

But what about 4-branes, 5-branes and beyond? Today we are going to put various multi-dimensional branes to a rigorous test. The test is designed to show whether extra dimensions truly exist. It is the cross-product test. The diagram below shows how the cross product works in three dimensions:

The results are in red. When we calculate the cross-product of two dimensions, we get a third dimension that is perpendicular to the others. To test for extra dimensions, we need to define what we mean when we say "dimension." Dimensions are lines in space that are perpendicular to each other.

Because they are perpendicular to each other, their cross-products must yield a kind of symmetry, i.e., there must be the same number of each dimension. The indexes can also be added or subtracted to get the cross-product. For example, in 3D space, D3D1 = D2 (3-1=2) and D1D2 = D3 (1+2=3) However, there must not be any index sharing. For example, D4D8 = D4 is invalid, since the D4 on the left side of the equation is clearly the same dimension as the D4 on the right. We could change the index(s) to cover our tracks, but then we lose the index symmetry--and such a loss reveals the problem in a different way.

We also need at least three dimensions to get started. Applying the test to 1-branes and 2-branes yields a bunch of zeros. But at least there is symmetry, so the dimensions in the 2-brane might be perpendicular. The fact there is no index sharing is also a good sign.

As you can see, I put the results in tables. Each row element and each column element yield a corresponding result in the tables (let your finger be your guide). Now let's look at a 3D system or 3-brane:

You'll notice cross-products that share the same index yield zero as they should. Three dimensions obey the index rule and have perfect symmetry. The bottom table above shows there are two results for each dimension. A 3-brane is perfect; it meets all the requirements, and we'll use it as a yard stick to judge systems and objects with extra dimensions.

Let's check out 4D:

The 4-brane isn't looking good. The results in red violate the index-sharing rule. There is also a lack of symmetry--there is not the same number of each dimension (see right-hand table). The cross-products are also fake. I'll explain what that means later when I'm done laying the groundwork. For now, let's move up to five dimensions:

Ah! Perfect symmetry! Four of each dimension. Could we be living in a 5D universe? A 5-brane sure looks feasible--but then there are those nasty index violations in red. Oh well.

The 5-brane does show, however, that odd numbers of dimensions have symmetry. What is true for five dimensions is also true for seven dimensions and the nine dimensions of E500 string theories:

Once again we have perfect symmetry and index violations in red. What about the 10 space dimensions of M-theory?

Holy d-brane, Batman! What a mess! Ten dimensions lack symmetry and have bleeding-red index violations. It's unlikely these dimensions are perpendicular to each other. But what about the 9D system? That one looks pretty good, not perfect like 3D, but close. Thus it is time to explain why its cross-products are fake as a presidential campaign promise.

If there are really nine dimensions of space then any cross-product between any two dimensions should yield the remaining seven--since the remaining seven are allegedly perpendicular to the two. The above tables only show single results for each cross-product. Such a strategy is useful in that it exposes which cross-products aren't perpendicular (see index violations marked in red). That being said, D1D2 should yield D9 and the rest. D3D6 should yield D8 and the rest. If these extra dimensions were real, there would be more uncertainty due to multiple results. We would not get a nice, single result from any cross-product. If we could choose the ideal d-brane or universe, 3D would be the best choice. The marvelous thing about 3D is you have perfect symmetry and the same number of dot-products as cross-products. With higher dimensions this is never the case.

The diagram above shows how D1D2 equals seven possible results in a 9D system. Such a system has 81 dot-products and 567 cross-products! Not exactly a balanced system. Then again, what if all those extra dimensions are tiny and curled up? That would sweep the multiple results under the rug. However, if dimensions are curled, their angles are no longer perpendicular. The diagram below shows the x-axis being curled to the y-axis. Note how the angle is no longer ninety degrees.

If dimensions don't have to be right angles to each other, then we can have an infinite number of them within right-angled 2D or 3D space.

The above diagram shows how a 2D triangle can be expanded into a 4D triangle that occupies a flat 2D space. But why stop at four dimensions when we can have eight or more?

As you can see, it is easy to fool ourselves into believing there are extra dimensions. What we call extra dimensions could really just be a bunch of posers occupying a flat 2D or 3D space. If there are really four or more dimensions that are right angles to each other, cross-product results would be uncertain. A lack of symmetry implies extra dimensions do not exist.

For more on this topic, check out theses links: "Debunking Bosonic String Theory's 26 Dimensions" and "Are String Theory's Extra Dimensions Real?" and How to Derive M-Theory's Eleven Dimensions and Reduce Them to Four Dimensions.