M-Theory Brief

Comment:  This science brief was intended to prepare readers for another series by establishing a rational perspective of cosmological concerns about other dimensions. I am coupling this to the leadership series with the intent to demonstrate how a leader's rational thought and the ability to communicate complex ideas is important. I choose M-Theory because of its widespread recognition but has literally no practical understanding by the general public which has lead to some irrational cosmological beliefs. By the end of this, I hope that readers have a functional understanding of the theory and concepts.

M-Theory

M-Theory has been  popularized in many movies such as Timeline, The Matrix, and many others. Hollywood took a creative license when investigating the many possibilities of the theory. Nonetheless, M-Theory is relatively new being introduced during 1997 by Physicist Edward Whitten who sought a unifying theory for the everything. The theory stunned the science community because of its well supported and demonstratable applicability. The meaning of M-Theory designation is just a serialized name for the theory to distinguish from other theories like G-Theory or Q-Theory. Scientists do not know what to call it yet.

Whitten in developing M-Theory, took the well establised equations of space-time, the theory of relativity, quantum loop theory of gravity, superstring theory, and others  into a mathematical relationship that demonstrated a ten dimensional universe with a mathematical error as a 11^th dimension. The error is generally thought of as insignificant and indicates the model may not be complete yet.  The underlying support for strings is that everything is in a natural resonance or vibrational state, known as harmonics, which is characterized by an oscillating string linking the quantum realm to the physical realm.

Conventions In Physics

Let us first consider some conventions used in physics. Many people hear about particles and strings but have little grasp as to what these things really are about. They are abstractions that represent a local grouping of collective behavior physicists are observing.

Particles generally appear in the Planckian realm at an order of magnitude of about 10^-30 meters. In lay terms, particles are generally thought of as soupy fields of local goop (not plasma fields as they occur at a higher order of magnitude) that demonstrate a common behavior. Physicists assign the concept of a particle to the field in order to conduct 'combinatory play' or foley with the behaviors. Consider love and hate. They are intangible and not empirically observable but we know they exist and have some general traits. If a love particle and a hate particle are assigned traits such that they resemble something like pool balls, then we can assign the qualities of love and hate to the respective particles. In this way, we can begin to explore their interactions.

Likewise, harmonics and waveforms resemble an oscillating string and can take on many other shapes. Please recall when as a child you took a long rope or string and shook the end such that a wave or bump travelled down the rope, this is the  concept of strings as used in physics. Strings describe the behavior of lightwaves, particle waves, and a variety of wave shapes.  The string is mathematical formulation of the harmonic state of the waveform. Thus, innumerable strings are possible. Edward Whitten used the most probable strings in formulating M-Theory which are a closed loop string as opposed to an open ended string.   

Harmonics and M-Theory Formulation

In M-Theory, strings are infinitely thin and run through the substance of space-time forming the 'fabric' of space time. The natural resonance of all things is a natural harmonic that requires a time basing association of the waveforms or strings representing the resonance. Looking at M-theory, the first four dimensions are space-time and the remaining six dimensions are natural but cannot be explored by humans directly. Let's look at some of these equations briefly to understand what is going on.

The equations for space-time are expressed as functions of time and annotated as X(t) for example. A is acceleration, V is velocity, and X₀ is the intitial displacement in space. The equations of space-time are:

X(t) = 1/2 At² + Vt + X₀
Y(t) = 1/2 At² + Vt + Y₀
Z(t) = 1/2 At² + Vt + Z₀

The dimensions are X, Y, Z and t or Time. In a simliar fashion the Theory of Relativity is developed into a function of time.  E = MC² is the Theory of Relativity that must be transformed into a function of time as the common point of reference. The equation for velocity is distance over time or distance as a function of time, D(t). Thus, the speed of light;   C = V(t)  where V(t) can be in any one of the first derivative (velocity) of the three spatial directions X(t), Y(t), or Z(t) or a combination of directions known as a vector as well as their formulas on the other side of the equal sign.  The equation becomes:

E(t) = M [ V(t) ]²

On a side note, many scientists hold the speed of light constant in order to make their theories work properly. However, there is evidence that the speed of light may vary. Theories indicate that the universe has been / is expanding. This has the effect of dilating time and subsequently affecting the speed of light. For example, relax a rubber band and put two marks one inch apart, name the span between the marks 1 second, then place the rubber band under tension. The marks spread apart making the distance between them greater but the definition between the marks remains one second. The dilation is related to the delta in the distance between the marks before and after tension. The universe is also said to be under tension of expansion forces counter by equal and opposite particle forces that want to draw the universe back to a singularity. 

The fifth dimension becomes energy, E(t), which includes three of the four natural forces and is now tied to space and time. Gravity is a sixth dimension as string's tension describes quantum gravity. While seemingly complicated this is the approach Whitten took. All these equations were based on time and used to formulate unified equation of reality. Common to linear algebra methods, a matrix of simultaneous equations was formed to solve the equations for various conditions and instances.  Hence, the movie The Matrix draws its dichotomy of reality (the red pill) or the matrix versus illusion (the blue pill) or the results produced by the matrix from this analogy.

Looking Deeper



Figure 1

Whitten went farther than we did here as he used 11 dimensional strings that tied the quantum to the physical in Superstring Theory. Please refer to Figure 1: Wave form Basics, in the following discussion. Note that vibrating strings can occur in 2 or more dimensions.  Velocity of a vibrating string is frequency. Acceleration is the rate of change in velocity. Additionally, vibrating strings' amplitude is associated to the energy in the system. Tension or stiffness in the string is associated with gravity. Time is associated with the period and wavelength of a string. For example, a second of time is one wavelength of Argon gas.  The remaining dimensions are related to the harmonics of vibrating strings and may be attributed to other natural dimensions as well. Time basing the equations is necessary in harmonics. The mathematical error consists of the eleventh dimension which is technically insignificant.  Whitten Discusses.

The significance of M-Theory is that it illustrated to scientists that the parts or pieces of the universe were well understood and science had been too close to the puzzle preventing them from seeing the picture being assembled. Many scientist equated the discovery to stepping back and looking at the whole elephant from a distance rather than up close and only seeing the individual components.

Subset Theories

When the ten dimensions of M-theory are conformally mapped into three dimensions to see what they look like the process reveals an infinite number of spheres called Worlds and large infinitely thin sheets known as membranes or Branes for short.  This model has become known as the Brane-World model of the universe. Scientist then hypothesize that the worlds (spheres) collide with each other or are slapped by the membranes flapping like a flag in the wind. These collsions between Worlds results in new universes that are merged together or bounce around like pool balls on a billard table. Meanwhile, a World slapped by a membrane, The Many Slap Theory, results in a reordering of the World or Universe. Such a slap from a membrane would be considered a Big Bang from within the universe.

There are many implications for M-Theory and it has some profound impacts on the human perception of reality and the human place in the cosmos.

I hope you enjoyed the read and gained some valuable insight into the theory. My goal was to communicate as best possible a complex concept. Please fell free to email me and let me know your thoughts. james.bogden@gmail.com. Thanks!