Scientist especially physicists should always remember that describing reality is different from defining it because history has shown that it is possible to accurately define or quantify an environment in terms of the mystical properties of a non-existent entity.
In other words even though one can find equations to accurately quantify or define an environment does not mean that they have found an valid explanation as to how and why it is what it is.
For example both Quantum Mechanics and the Standard Model of Particle Physics define and quantify the environment of particles in terms of what could be considered the mystical properties of a non-dimensional mathematical point.
Mystical in the sense that the definition of mysticism as being or having vague speculation: a belief without sound basis could be applied to it. This is because by definition no one has or ever will be able to observe the non-dimensional mathematical point they use to define a particle therefore we do not have an observational and therefore a sound basis for assuming its existence.
Most who have study the history of science are aware of the fact that many medieval and Renaissance astronomers assumed the planets were imbedded in rigid celestial spheres whose movement was guided celestial intelligences, souls or impressed forces.
Today many would classify that concept as being mystical because there is no observation evidence to support the assumption that the motion of the planets is control by some form of intelligence.
However many modern scientists would disagree with the assertion that a non-dimensional particle has similarities to the mystical ones we now associate with the Renaissance astronomer’s celestial intelligences by pointing to the fact that it permits them to accurately quantify its environment within the limit of our modern observational capabilities.
Yet the same argument could and most probably was used by them to justify their belief in idea that a celestial intelligence were guiding the planet because it also permitted them to accurately define and quantify the orbital environment of the planets within the limits of their observational capabilities.
The Standard Model of particle physics uses the concept of point particle only because it makes its mathematical description of their properties possible. However it assumes that a point is appropriate representation of any object whose size, shape, and structure are irrelevant in a given context. For example, from far enough away, an object of any shape will look and behave as a point-like object.
While Quantum Mechanics derives the world of the very small in terms of the probability function based on mathematical representation of particle as a non dimension point for reason similar to why the standard model does. In other words the only way to define the position of a particle in terms of a probably function is buy assuming that it does not have any spatial properties. Therefore it also assumes that it size, shape, and structure are irrelevant in a given context.
Unfortunately for the proponents of Quantum Mechanics the concept of a point particle is complicated by the Heisenberg uncertainty principle, which tells us even in the domain of quantum mechanics an elementary particle, with no internal structure, occupies a nonzero volume because of the uncertainty involved in determine the exact point where it is located in space.
As mentioned earlier both of these theoretical models assume that non-dimensional point is an appropriate representation of a particle because its size, shape, and structure are irrelevant in a given context.
But what if it is relevant?
For example what if the Heisenberg’s Uncertainty Principle which asserts there is a fundamental limit to the precision with which certain pairs of physical properties of a particle, such as position x and momentum p, can be simultaneously known is related to the spatial extension of a particle and not to its point properties as quantum theory assumes.
As was shown in the article “Why is energy/mass quantized?” Oct. 4, 2007 it is possible to understand the quantum mechanical properties of energy/mass in terms of an extended object by extrapolating the laws of classical resonance in a three-dimensional environment to a matter wave on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.
Briefly it showed the four conditions required for resonance to occur in a classical environment, an object, or substance with a natural frequency, a forcing function at the same frequency as the natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would be meet by a matter wave in four *spatial* dimensions.
The existence of four *spatial* dimensions would give three dimensional space (the substance) the ability to oscillate spatially on a “surface” between a third and fourth *spatial* dimensions thereby fulfilling one of the requirements for classical resonance to occur.
These oscillations would be caused by an event such as the decay of a subatomic particle or the shifting of an electron in an atomic orbital. This would force the “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension to oscillate with the frequency associated with the energy of that event.
The oscillations caused by such an event would serve as forcing function allowing a resonant system or “structure” to be established in four *spatial* dimensions.
Classical mechanics tells us the energy of a resonant system can only take on the discrete or quantized values associated with its resonant or a harmonic of its resonant frequency
Therefore the discrete or quantized energy of resonant systems in a continuous form of energy/mass would be responsible for the discrete quantized quantum mechanical properties of particles.
However, it did not explain how the spatial boundaries or volume of these resonant structures is defined.
In classical physics, a point on the two-dimensional surface of paper is confined to that surface. However, that surface can oscillate up or down with respect to three-dimensional space.
Similarly an object occupying a volume of three-dimensional space would be confined to it however, it could, similar to the surface of the paper oscillate “up” or “down” with respect to a fourth *spatial* dimension.
The confinement of the “upward” and “downward” oscillations of a three-dimension volume with respect to a fourth *spatial* dimension is what defines the geometric boundaries of the “box” containing the resonant system the article “Why is energy/mass quantized?” associated with a particle.
The mathematics of Quantum mechanics support the assumption that a particle occupies a finite volume berceuse it defines the smallest possible unit of space and increment of energy in terms of Planck’s length “h” while defining the size of an individual quantum of force in terms of the equation E = h c / L.
As mentioned earlier both the standard model of particle physics and quantum mechanics assume that a point particle is an appropriate representation of any object whose size, shape, and structure is irrelevant in a given context.
However, even though the size and shape of a particle may be irrelevant to someone looking at it from the macroscopic perspective of a human observer it may be very relevant to the process and mechanisms reasonable for what a human observes.
For example if one assumes, as quantum mechanics does that a particle is a non-dimensional point then according to the above concepts there would be an uncertainty in determining its position because that non-dimensional point could be found any with the volume of the three-dimensional “box” mentioned above.
Yet one could come to the same conclusion if one assumes that the quantum properties of a particle are a result of resonate system in four spatial dimensions because according to the above concepts there would be an uncertainty in determining its position because that non dimensional point could be found anywhere within the volume of the “box” mentioned above.
Planck’s length is one of fundamental components of Quantum Physics and along with Heisenberg’s Uncertainty Principle it defines the uncertainty in the ability to measure more than one quantum variable at a time. For example attempting to measure an elementary particle’s position (▲x) to the highest degree of accuracy leads to an increasing uncertainty in being able to measure the particle’s momentum (▲p) to an equally high degree of accuracy. Heisenberg’s Principle is typically written mathematically as ▲x▲p ³ h / 2 where h represents Planck constant
As mentioned earlier the resonant wave that corresponds to the quantum mechanical wave function defined in the article “Why is energy/mass quantized?” predicts that a particle will most likely be found in the quantum mechanical “box” whose dimensions would be defined by that resonant wave. However quantum mechanics treats particles as a one dimensional points and because it could be anywhere in it there would be an inherent uncertainty involved in determining the exact position of a particle in that “box”.
For examine the formula give above ( â–²xâ–²p ³ h / 2 ) tells us that uncertainty of measuring the exact position of the point in that “box” defined by its wavefunction would be equal to â–²xâ–²p ³ h / 2. However because we are only interested in determining its exact position we can eliminate all references to its momentum.
However if we eliminate the momentum component from the uncertainty in a particle position become 6.626068 × 10-34 meters or Planck’s constant.
As mentioned earlier the uncertainty involved in determining the exact position of a particle is because it is impossible to determine were in the “box” defined earlier the quantum mechanical point representing that particle is located. However as mentioned earlier Planck’s constant tells us that one cannot determine the position of a particle to an accuracy greater that 6.626068 × 10-34. This suggest that Planck constant 6.626068 × 10-34 defines the physical parameters or dimensions of that “box” because it defines the parameters of where in a given volume of space a quantum particle can be found.
Classical mechanics uses also uses the existence of a point at the center of mass to calculate the position of an extended object and to predict how it would interact with other objects in a gravitational field. Similar to quantum mechanics it assumes that the object position can be determined by measuring it from a point defining its center because from a distance they feel it gives them an appropriate representation of the size, shape, and structure of the object.
Therefore they can define the position of an irregular shaped object such as an asteroid by determining the distance from that point to whatever reference point they chose.
However Classical mechanics accepts the fact that there are limitation to the concept of using the center of an object to predict its position and how it will interact with other objects because as the resolution of the measurements increase or distance between decreases between it and the measure device it accepts the fact that the object shape has an effect on those measurements.
Similarly fact that Quantum mechanics tells us the individual quanta of energy/mass have a spatial extension defined by the equation E = h c / L means that there would always be an uncertainty in determining its position related to its shape because as mentioned earlier the resonant structure defining its particle properties is made up of the dynamic components of a matter wave and therefore there would be a predictable randomness when interacting with a measurement device.
Therefore on a quantum scale the size, shape, and structure of a particle would be relevant in determining a particle reality
This shows how one can not only mathematical describe the quantitative “reality” of a particles environment but also define how and why we observe them to interact the way we do based on the observable and therefore the verifiably properties of a three-dimensional environment instead speculating on the existence of a mystical non-dimensional particle.
As mentioned earlier assuming non-dimensional point particle can describe the quantum world is mystical in the same sense as the assumption made in the middle ages that celestial intelligences, souls or impressed forces were guiding the planets because there is no sound observational basis for their existence.
However history has shown that the greatest advances in science are made when one eliminates mysticism from the description of reality
As mentioned earlier Scientist especially physicists should always remember that describing reality is different from defining it.
Later Jeff
Copyright Jeffrey O’Callaghan 2013