On page 33 of Sean Carroll book, “The Particle at the End of the Universe” he tells us that “The physicist John Wheeler once proposed a challenge: How can you best explain quantum mechanics in five words or fewer? In the modern world, itâ€™s easy to get suggestions for any short-answer question: Simply ask Twitter, the microblogging service that limits posts to 140 characters. When I posed the question about quantum mechanics, the best answer was given by Aatish Bhatia (@ aatishb): â€œDonâ€™t look: waves. Look: particles.â€ Thatâ€™s quantum mechanics in a nutshell.”
When Einstein was asked about the consequences of this particle wave dichotomy he replied “It seems as though we must sometimes use one theory and sometimes the other, while at times we may use either. We are faced with a new kind of difficulty. We have two contradictory pictures of reality; separately neither of them fully explains the phenomena of light, but together they do”
For example the paradoxical waveâ€“particle reality of energy/mass, one of the fundamental concepts defining Quantum mechanics defies the “reality” of the world we live in because of its inability to describe/define how quantum-scale objects can simultaneously exist as waves and particles. Many have tried to explain it as a fundamental property of the Universe, while alternative interpretations explain it as an emergent, second-order consequence of various limitations of the observer.
But Aatish Bhatia answer to Sean question brings up another troubling aspect of the reality behind quantum. How does the intervention of an observer force a particle to “choose” a state and how does it know when someone is observing it.
However Einstein may have provided us with an answer to both of these questions when he define the physical relationship between energy and mass in terms of the equation E=mc^2 and the geometry of space-time.
In other words, using the concepts developed by Einstein one may be able to derive a single reality for the wave-particle duality of the quantum world and how an observer interacts with it in terms four dimensional space-time.
However it will be easier to understand how by redefining Einstein’s space-time environment to its equivalent four “spatial” dimension counterpart because it will allow us to derive them in terms of the observable properties of the spatial dimensions instead not observable temporal ones of a space-time dimension.
Einstein gave us the ability to do this when he used the velocity of light to define the geometric properties of space-time because it allows one to convert a unit of time in his four dimensional space-time universe to a unit of a space identical to those of our three-dimensional environment. Additionally because the velocity of light is constant it is possible to defined a one to one correspondence between his space-time universe and one made up of four *spatial* dimensions.
In other words the symmetry of his mathematics means that he provided a qualitative and quantitative means of redefining his space-time universe in terms of the geometry of four *spatial* dimensions and the curvature or displacement he associated with the energy of a quantum system in a space-time environment to a spatial displacement in a fourth *spatial* dimension.
However defining its dimensional properties in terms of its spatial instead of its time components would allow one to not only understand why a quantum environment possess two distinct realities but also why observation determines which reality becomes predominate by extrapolating the laws governing cause and effect in the classical world to them.
For example the article â€œWhy is energy/mass quantized?â€ Oct. 4, 2007 showed one can derive quantum properties of energy/mass by extrapolating the laws of classical wave mechanics 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 occur in one consisting of four spatial dimensions.
The existence of four *spatial* dimensions would give a matter wave 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 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 space.
Therefore, these oscillations in a “surface” of a three-dimensional space manifold would meet the requirements mentioned above for the formation of a resonant system or “structure” in four-dimensional space if one extrapolated them to that environment.
Classical mechanics tells us the energy of a resonant system can only take on the discrete or quantized values associated with its fundamental or a harmonic of its fundamental frequency.
Hence, these resonant systems in four *spatial* dimensions would be responsible for the discrete quantized energy associated with the quantum mechanical systems.
Additionally it also tells us why in terms of the physical properties four dimensional space-time or four *spatial* dimensions an electron cannot fall into the nucleus is because, as was shown in that article all energy is contained in four dimensional resonant systems. In other words the energy released by an electron “falling” into it would have to manifest itself in terms of a resonate system. Since the fundamental or lowest frequency available for a stable resonate system in either four dimensional space-time or four spatial dimension corresponds to the energy of an electron it becomes one of the fundamental energy units of the universe.
Yet it also allowed one to derive the physical boundaries of a particle in terms of the geometric properties of four *spatial* dimensions.
For example 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 â€œupâ€ or â€œdownâ€ with respect to a fourth *spatial* dimension.
The confinement of the â€œupwardâ€ and â€œdownwardâ€ oscillations of a three-dimension volume with respect to a fourth *spatial* dimension is what defines the spatial boundaries of the resonant system associated with the particle “reality” of its wave properties in the article â€œWhy is energy/mass quantized?â€ Oct. 4, 2007.
In other words one can use classical wave mechanics to explain why a quantum system can possess both wave and particle properties.
However it also tells us how the intervention of an observer forces a quantum system to “choose” a state or how it “knows” when someone is observing it.
As was mentioned earlier its particle reality of is the result of it’s wave energy being confined to a specific volume.
However in every case, observing a quantum system requires one to confine its energy to the specific volume associated with the observing equipment. Therefore it will always display its particle reality when someone looks or observes it.
However if no one is looking at it its wave reality is free to move, interact and interfere with other quantum systems until they are observed and then they will revert to the back their particle realty as when observed in the double slit experiment.
In other words the reason why the particle reality of a quantum system takes the form an interference pattern associated with a wave in Thompson’s double slit experiment is because its wave reality can interact before it is observed and the act of observing it results in its wave reality being presented as a particle interference pattern.
Additionally it gives consistent explanation of why one can sum up quantum mechanics in these words “Donâ€™t look: waves. Look: particles” by extrapolating the “single” physically reality of our observable environment to one consisting of either four dimensional space-time or four spatial dimensions.
It should be remember that Einsteinâ€™s genius and the symmetry of his mathematics allows us to choose whether to define the reality of a quantum system in either a space-time environment or one consisting of four *spatial* dimension.
Copyright Jeffrey Oâ€™Callaghan 2015