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1kWe have shown throughout this blog there would be numerous theoretical advantages to defining the universe in terms of four *spatial* dimensions instead of four-dimensional space-time.
One is that it would allow for the resolution of the conflict between the Newtonian assumption that space and time is continuous with the quantum mechanical assumption that it is composed of discrete quantized units by extrapolating observations of a three-dimensional environment to a fourth *spatial* dimension.
As Lee Smolim point out in his book “Three Roads to Quantum Gravity” these two disciplines define them differently.
“For example Newtonian physics assumes that space and time are continuous and can be arbitrary divided into smaller and smaller units. In other words there is no smallest possible unit of space or time.
However, quantum mechanics assumes that they come in discrete irreducible quantized bits. In other words unlike the Newtonian concept that length and time are infinitely divisible quantum theory assumes there is a finite limit to our ability to observe smaller and smaller segments of them.”
Yet one can qualitatively define the mechanism responsible for the fundamental quantum mechanical unit of length and time in terms of the Newtonian assumption that space and time are continuous and the quantum mechanical concept of the smallest measurable unit of space and time.
The smallest possible length according to quantum theory is determined defined by Planck’s constant (denoted h). Using it along with the speed of light in a vacuum one can determine Planck’s length or the smallest length that is measurable as being equal to 1.616252(81)-35 meters.Â
Using that knowledge it is possible to calculate Planck’s time or the smallest measurable unit of time as that required for light to travel, in a vacuum, a distance of 1 Planck’s length and because Planck’s length is the smallest measurable length it is the smallest measurable unit of time.
(Note those who are interested in a quantitative derivation of these units based on quantum mechanical interpretation of space and time should view the video to the right.)
In quantum mechanics Planck’s time is the limiting factor in one’s ability distinguish events because the fact that it cannot be divided in smaller units means that one could not determine if one event occur before another if they both took place within that interval.
Yet, one can derive the physicality of Planck’s or Quantum Time by extrapolating the laws of classical Newtonian space and time to a fourth *spatial* dimension.
However before we begin we must first derive Planck’s length or the smallest measurable length of in terms of four *spatial* dimensions.
In the article “Why is energy/mass quantized?” Oct. 4, 2007 it was shown that one can derive its quantum mechanical properties by extrapolating the laws of classical resonance a three-dimensional environment to a matter wave moving on a continuous “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 Newtonian 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 in one consisting of four.
The existence of four *spatial* dimensions would give the “surface” of a three-dimensional manifold the ability to oscillate with respect to it 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.
Therefore, these oscillations in a continuous “surface” of a three-dimensional space manifold, would meet the requirements mentioned above for the formation of a resonant system or “structure” in space.
Observations of a three-dimensional environment show the energy associated with resonant system can only take on the incremental or discreet values associated with a fundamental or a harmonic of the fundamental frequency of its environment.
Similarly the energy associated with resonant systems in four *spatial* dimensions could only take on the incremental or discreet values associated a fundamental or a harmonic of the fundamental frequency of its environment.
These resonant systems in four *spatial* dimensions are physically responsible for Planck’s constant and the incremental or discreet energy associated with it and quantum mechanical systems.
However it also defines Planck’s length in terms of the length of the fundament quanta of energy/mass because it defines the smallest unit of space that exists in terms of a resonant system in four-dimensional space. Therefore it also defines the physicality of Planck’s time as being the time required for light to travel, in a vacuum, a distance of 1 Planck length or as was just shown the wavelength of the fundamental resonant frequency of four-dimensional space.
This shows how one can resolve the conflict between the Newtonian assumption that time is continuous with the quantum mechanical assumption that it is composed of discrete quantized units because one can be derived in terms of a subset of the other
Later Jeff
Copyright Jeffrey O’Callaghan 2011
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