BEARSCARE

Memory corealization (Déjà Vu) is a phenomenon where an individual experiencing an instantaneous event recalls a real or imagined, past event as if the two were the same, occurring concurrently, while retaining a sense of separation in time. Starting with Aristotle, scientists, behavioral researchers and other experts have been unable to explain this phenomena. Today, a colleague and I conceived a theory which exhaustively explains Déjà Vu using logical deduction and proven scientific law.

The key to our theory is the fact that our universe is accelerating in its expansion; this is a relatively new discovery, but its implications are profound. Our theory derives from two propositions:

1) The universe’s expansion is accelerating outward radially. Therefore, our perception of time at a young age is different than our current perception of time (assuming adult age); that is, time apparently speeds up as we age since our absolute velocity through the cosmos is continually increasing, maintaining a gradient* of temporal perception**.

2) The well-known theory of the existence of a multiverse is true. More specifically, the multiverse is realized by infinite space and dimensions containing infinitely numerous “big-bang” events which, in some cases, can interact with each other .

Therefore, a nominally expanding sphere of temporal perception interrupted occasionally by distant or extradimensional effects of an alternate creative event can alter an individual’s perception of time, thus inducing familiar yet unexplainable effects in memory.

QED.

*The structure of this gradient is currently under debate. Theories of its nature vary between constant, linear, and high-order polynomial forms.

**This assumes that there is no absolute standard for perception of time, but only that there exists a relative difference between an entity’s first memory of the passage of time compared to his/her perception as he/she ages. The proposition does not address the question of the possibility of a continual shift in perception of time over the existence of sentience in the known universe; unfortunately, at this time, data are not known to exist to analyze this matter and probably will not until the theory posited here is accepted and subsequent studies are commissioned; even then, considering the magnitude of the distances and forces necessary to gather accurate data, hundreds of thousands of years’, if not millions’, worth of data would be required.

Prime spirals are a way to visualize the distribution of prime numbers within the set of natural numbers. Accidentally discoverd by Stanislaw Ulam in 1963, the prime spirals show that there is order in the distribution of prime numbers, where one would expect randomness.

Prime numbers are those which are not composed of other numbers. For instance, 3, 5, 7, and 41 cannot be described as the product of two or more smaller numbers. Considering the set of natural numbers, one would expect that, counting up from 1, the frequency of encountering prime numbers would decrease, since the subset being considered, the set of candidate numbers to form a larger, composite number, is increasing. Surprisingly, though, prime numbers can be shown to be prominent among large composite numbers. A program I wrote is calculating that approximately 8% of large (>1,000,000) numbers are primes.

Prime spirals show that, not only do primes appear much more frequently than we would expect, but that they have structure in their positions in the list of natural numbers. During a “boring” presentation, Ulam was doodling on paper. He began writing out natural numbers with 1 in the center of the page, and circling outward. See Figure 1 [1].

Figure 1: Natural Numbers Spiral

Removing composite numbers from the picture shows the beginning of the pattern (Figure 2 [2]):

Figure 2: Prime Spiral

Look at the following sets of numbers: {37, 17, 5}, {41, 19, 5}, {19, 7, 23, 47} and {3, 13, 31}. Each set is arranged as a diagonal line traversing the spiral space. Now consider a grid that is 200×200 numbers (Figure 3 [3]):

200x200 Prime Spiral

Figure 3 obviously shows order in the position of prime numbers (each pixel is a prime number). The image shows the space which the first 400,000 natural numbers occupy. It is clear that many of these numbers are primes and they exhibit the same behavior as those in the set of the first 50 prime numbers.

So, why does this matter? No one really knows. Intuitively, we would expect far fewer prime numbers than there are. And we certainly wouldn’t expect any pattern to their occurrence. The fact that an arbitrary visualization of a expectedly random process yields order is very profound. A simple conclusion is that the very fabric of nature is ordered, that looking even at the most primal systems, i.e., the set of natural numbers, we cannot escape order. Further, we would expect that our universe, the structure of mater, everything we know is a derivation of order from disorder, but prime spirals take us back one more level of abstraction indicating that, in nature, there is no fundamental disorder. The act of counting on your fingers, the number of fish in the seas, the number of cells in your body and the number of particles in the universe all exist in a framework which is fundamentally non-random. There is invisible order within the concept of numbers itself.

[1] http://en.wikipedia.org/wiki/File:Ulam_spiral_howto_all_numbers.svg

[2] http://en.wikipedia.org/wiki/File:Ulam_spiral_howto_primes_only.svg

[3] http://en.wikipedia.org/wiki/File:Ulam_1.png

In 1640, Isaac Newton discovered that the force associated with an object not in a state of equilibrium is composed of its mass and the rate at which its velocity is changing. That is, the famous, iconic declaration of F = ma. Physics purists claim that all physical laws can be derived from this one relationship. I believe them.

Let’s start with acceleration, a. Acceleration is the time derivative of velocity, which, itself, is the time derivative of position (displacement). Given, a constant a, we can calculate velocity by integrating from minus infinity to some time t in the future. This calculation yields v = at, assuming a is constant. We can further calculate any arbitrary position occupied by some object traveling at v by integrating again (assuming the object began its motion at the origin of its reference frame). This calculation shows that s = 0.5at^2, where s is displacement.

Integrating acceleration to find position, we see that force is proportional to mass divided by time squared ( F = 2m/t^2 ). This is fine, but what we really want is energy. Consider a very small particle. Einstein’s discover of mass-energy equivalence states that this particle’s energy is equal to it’s mass multiplied by a constant, the speed of light squared. We now have two relationships for this particle: F = 2m/t^2 and E = mc^2. Now, we all know that force is the time derivative of energy, so, 2m/t^2 = d/dt  (mc^2). The right side of this relationship has no dependence on time, so its time derivative is zero. Therefore, 2m/t^2 = 0. It follows that mass, as a physical quantity, actually has no non-zero magnitude and is completely irrelevant.

How can nothing have mass? It’s simple. Isaac Newton missed one very important point when he was writing his laws of physics. Energy is actually a vector, not a scalar. That is, energy occurs only in certain directions, such as moving forward in time. When direction information is ignored, the mass of small objects is always zero. Interestingly, however, Newton’s flawed equations are valid for massless objects, like photons. It’s problems like this that tortured Max Planck into researching the physics of very small things.

For years physicists have tried to reconcile Einstein’s theories of Special and General Relativity, his discovery of mass-energy equivalence, and Max Planck’s discovery of Quantum Mechanics. These old brains couldn’t figure out how really, really big things and really, really small things could be governed by the same physical laws. Today, I figured it out.

Let’s start with the small stuff. Max Planck discovered that energy itself could not be found in a continuum of magnitudes; that there must be some small quantity of energy by which every other quantity could be described. He named this small quantity quantum. One day, back in the early 20th Century, Planck and Einstein were arguing and Planck started working math problems to cool off. He noticed that his equations all reduced to a single number, whose units were energy-time. Although he knew this was big, he still shoved it Einstein’s face.

The number has come to be called the Planck Constant; its value is 6.626068e-34 J·s and is denoted h. This discovery spawned the largest rivalry the discipline of physics has ever seen: Einstein’s law of General Relativity governs the behavior of very massive objects whereas Planck’s theories of quantum mechanics accurately describe very tiny particles; and these two classes of objects act very, very differently. How can there be two discrete physical frameworks operating simultaneously and independently in one Universe?

The answer (this is where Einstein and Planck left off and I took over) lies in the Planck Length. I concede that I neither discovered, derived nor invented the Planck Length. It is a physical constant realized by combining Einstein’s Gravitational Constant, G, the Planck Constant, h, and the speed of light in a vacuum, c. The Planck Length is 16.163e-36 meters. This length is, literally, the smallest meaningful distance in the universe; that is, a particle traveling at an arbitrary velocity cannot traverse a distance smaller than 1 Plank Length. If 1 Planck Length is defined as the distance between two infinitesimally close points, A and B, a particle reaching point A will instantaneously be present at point B. That’s a Planck Length.

A trivial, though profound, corollary to the Planck Length is the notion of a Planck Volume. This is simply the Planck Length cubed, which equals 4.222e-105 cubic meters. Though evidence suggests that there are more than 3 physical dimensions (plus 1 or 2 time dimensions), considering observable, 3-dimensional space, the Planck Volume is the smallest “slot” any quantum of mass or energy can occupy. Though any conventional measure of volume can be described by any arbitrary solid shape, the Planck Volume is unique. Consider a vector of magnitude 1 Planck Length arbitrarily oriented in space. Now consider another vector of equal magnitude oriented in any direction not equal to that of the first. For a particle to legally traverse along a composite vector made from these first two, they must be orthogonal to each other. If the two are not, the particle would travel a distance which is not an integral number of Planck Lengths. Applying the same logic to a third vector, it is obvious that this vector must be orthogonal to the first two. Therefore, the fundamental quantum of 3-dimensional space is a perfect, x-y-z axis defining a cube. This unequivocally demonstrates that the observable universe is composed of very tiny cubes, though it offers no absolute structure or frame of reference.

Now consider Einstein’s theories. Combining the central tenant of Special Relativity, that no object can travel faster than the speed of light in a vacuum, that this velocity is a fundamental parameter of the universe, and the Planck Length, we can derive the Planck Time. That is, dividing the smallest quantum of distance by the largest possible velocity yields the smallest meaningful quantum of time. This value, (16.1636e-36 m)/(2.99792458e8 m/s) = 5.3915e-44 s, represents the smallest amount of time during which any event in our Universe can occur.  An equivalent calculation is the Planck Frequency, found by dividing the speed of light by the Planck Length, the smallest possible wavelength. The Planck Frequency is 1.85481e43 Hz (this frequency is 29 orders of magnitude greater than the highest frequency of visible light). Considering a discrete wave-particle at the Planck Frequency and using the Planck Constant, we can calculate this particle’s energy with the relationship E = hf. This energy, the Planck Energy is 1.2290e9 J. This represents the maximum energy a particle, oscillating at the Planck Frequency and occupying a single Planck Volume can have. But that’s not even the impressive part.

A little less than 14 billion years ago, during the infinitesimally small moments before the Big Bang, scientists believe that all the energy (mass) of the Universe was concentrated in a single point of zero-dimension, also known as a singularity. Such a point is obviously unobservable, as is a Planck Volume quantum. However, the latter represents a meaningful measure of space. So, consider a fundamental quantum of space, described earlier as a set of three orthogonal dimensions forming a cube with sides of 1 Planck Length, inside which is this singularity containing the entire energy of the Universe. At the exact moment at which the Big Bang occurred, energy would have been released from the singularity to expand outward. At some point, this energy would occupy the interior of the cubic Planck Volume and instantaneously be visible to an observer (the notion of an observer is obviously absurd, but reasonable for purposes of discussion). At this point, the energy would begin radiating out at the most fundamental frequency, the Planck Frequency, which corresponds to the Planck Energy. As an absolute value, this energy itself is unimpressive; however, the story changes when one considers the instantaneous Energy-time derivative, i.e., the power, produced by our young universe, the fundamental value of energy radiated during the fundamental quantum of time: (Planck Energy) / (Planck Time) = 2.2794e53 W.

Once inhabiting a single Planck Volume, the energy would propagate isotropically until it occupied 8 Planck Volumes, then 81, 256 and so forth. Within a tiny fraction of a second, this expansion would appear continuous, though the actual geometry of the young Universe would still, and will indefinitely, remain a cube with dimension of integral multiples of the original dimension, the Planck Length. This intensity is 26 orders of magnitude greater than the power radiated by our Sun. If that isn’t shocking enough, consider that the sun occupies approximately 3e122 Planck Volumes. That’s 1 Googol followed by 22 more 0s.

So, we have now characterized the initial, observable state of the Universe. We have also demonstrated that the Universe, if considered in the three physical, observable dimensions, is fundamentally described by a perfect cube expanding. Approximating the universe to be 14 billion years old, or 2.5966e53 Planck Times, the length of each side of the Universe is 7.7845e61 Planck Lengths, or 1.2582e27 meters. This distance is 8,410,930,211,398,689 times the distance from the Earth to the Sun.