Dear Sir,
Your thought experiment replicates the arguments of a nineteenth century fiction called "FLAT LANDS", which inhibited 2-D creatures and the account of one of them after a visit to Earth. This has misguided everyone till date. Dimension of objects is the perception that differentiates the "internal structural space" from the "external relational space". Since such perception is mediated by electromagnetic interaction, where an electric field and a magnetic field move perpendicular to each other in a direction perpendicular to both, we have three mutually perpendicular directions. Thus, the face of a cube is 2-D, does it have independent existence? The "mathematics" involving n-dimensions is also a myth. Mathematics explains only "how much" one quantity accumulates or reduces in an interaction involving similar or partly similar quantities and not "what", "why", "when", "where", or "with whom" about the objects involved in such interactions. These are the subject matters of physics.
Measurement is a conscious process of comparison between two similar quantities, one of which is called the scaling constant (unit). The cognition part induces the action leading to comparison, the reaction of which is again cognized as information. There is a threshold limit for such cognition. Hence Nature is mathematical in some perceptible ways. This has been proved by the German physiologist Mr. Ernst Heinrich Weber, who measured human response to various physical stimuli. Carrying out experiments with lifting increasing weights, he devised the formula: ds = k (dW / W), where ds is the threshold increase in response (the smallest increase still discernible), dW the corresponding increase in weight, W the weight already present and k the proportionality constant. This has been developed as the Weber-Fechner law. This shows that the conscious response follows a somewhat logarithmic law. This has been successfully applied to a wide range of physiological responses.
Mathematics is also related to the measurement of time evolution of the state of something. These time evolutions depict rate of change. When such change is related to motion; like velocity, acceleration, etc, it implies total displacement from the position occupied by the body and moving to the adjacent position. This process is repeated due to inertia till it is modified by the introduction of other forces. Thus, these are discrete steps that can be related to three dimensional structures only. Mathematics measures only the numbers of these steps, the distances involved including amplitude, wave length, etc and the quanta of energy applied etc. Mathematics is related also to the measurement of area or curves on a graph - the so-called mathematical structures, which are two dimensional structures. Thus, the basic assumptions of all topologies, including symplectic topology, linear and vector algebra and the tensor calculus, all representations of vector spaces, whether they are abstract or physical, real or complex, composed of whatever combination of scalars, vectors, quaternions, or tensors, and the current definition of the point, line, and derivative are necessarily at least one dimension less from physical space.
The graph may represent space, but it is not space itself. The drawings of a circle, a square, a vector or any other physical representation, are similar abstractions. The circle represents only a two dimensional cross section of a three dimensional sphere. The square represents a surface of a cube. Without the cube or similar structure (including the paper), it has no physical existence. An ellipse may represent an orbit, but it is not the dynamical orbit itself. The vector is a fixed representation of velocity; it is not the dynamical velocity itself, and so on. The so-called simplification or scaling up or down of the drawing does not make it abstract. The basic abstraction is due to the fact that the mathematics that is applied to solve physical problems actually applies to the two dimensional diagram, and not to the three dimensional space. The numbers are assigned to points on the piece of paper or in the Cartesian graph, and not to points in space. If one assigns a number to a point in space, what one really means is that it is at a certain distance from an arbitrarily chosen origin. Thus, by assigning a number to a point in space, what one really does is assign an origin, which is another point in space leading to a contradiction. The point in space can exist by itself as the equilibrium position of various forces. But a point on a paper exists only with reference to the arbitrarily assigned origin. If additional force is applied, the locus of the point in space resolves into two equal but oppositely directed field lines. But the locus of a point on a graph is always unidirectional and depicts distance - linear or non-linear, but not force. Thus, a physical structure is different from its mathematical representation.
You say a person is just a wave packet, but consider the physics and the mathematics behind the concept. It is full of aberrations. We give you just one example. The wave function is determined by solving Schrödinger's differential equation: d2ψ/dx2 + 8π2m/h2 [E-V(x)]ψ = 0. By using a suitable energy operator term, the equation is written as Hψ = Eψ. The way the equation has been written, it appears to be an equation in one dimension, but in reality it is a second order equation signifying a two dimensional field, as the original equation and the energy operator contain a term x2. The method of the generalization of the said Schrödinger equation to the three spatial dimensions does not stand mathematical scrutiny. A third order equation implies volume. Addition of three areas does not generate volume and neither x+y+z ≠(x.y.z) nor x2+y2+z2 ≠(x.y.z). Thus, there is no wonder that it has failed to explain spectra other than hydrogen. The so-called success in the case of helium and lithium spectra gives results widely divergent from observation. The probability calculations, squaring of a complex variable, mathematical operations involving infinity, brute force approach, etc are un-mathematical manipulation in the name of mathematics. There are many such aberrations.
It is interesting to note that wherever both of us applied our mind independently, we have arrived at near similar conclusions. But whenever you relied on the views of other scientists, we have difference of opinion. The reason is: modern science is built on an incremental manner. Theories are built upon "established theories" without continuously evaluating them in the light of the results of latest experiments and observations. This blind acceptance of "established theories" is nothing but superstition. It is perpetuated by the books and papers eulogizing these as "in a brilliant deduction", "with a stroke of genius", "a highly successful theory", etc, to label these theories. which are unwanted misleading information to prevent free thinking and guiding the students in the right direction.
This has been compounded by the race for going ahead, which prevents students to look back. In the peer group, it generates the cult of incomprehensibility. For this reason, precise definitions are becoming rare in science. They use "operational definitions", which can be manipulated to suit their convenience. Look at the declarations by LHC regarding detection of the Higg's boson. Now there is a rush to change the name of the particle to share honors. Given the clarity level, we wonder how many people applauding the writers in this context really understand their views totally! The hurry also generates reductionism, so that totality of the theories is lost sight of. Many fundamental laws are applicable in multi-disciplinary areas. For example, Doppler effect is used in light, sound, cosmology, and SR (length contraction). Yet, no one used it to SR to point out that the length contraction is only apparent to the observer due to Doppler effect.
There is a necessity to scrap all theories and re-write them from the scratch based on the data available today. Even after more than a century, should we still persist with the concept of extra-dimensions? This will not undermine the effects of earlier scientists, as due to their efforts only we have come this far. But only to show honor to them, we cannot perpetuates myths - which most of the interpretations of quantum theory and latest cosmology are.
Regards,
basudeba
