Is it possible to define the “reality” behind the quantum world of probabilities in terms of the physical concepts of causality in the space-time environment defined by Einstein? 

Quantum Mechanics
Probability and Uncertainty

Quantum theory defines the existence of particles in terms of a mathematically generated probability function created by Schrödinger’s wave equation and assumes that particles do not exist until a conscience observer looks at it.  In other words it assumes the act of observation or measurement creates their reality.

However because it is based on probabilities it also assumes that the predictability associated with the laws of causality that govern our macroscopic universe do not apply to a quantum world.

In other words in quantum theory, everything is unpredictable.

Einstein hated this uncertainty, famously dismissing it when he said "God does not play dice with the universe" even though he was unable to give a reason.

However he gave us a clue as to why God must play dice when he said "If a new theory was not based on a physical image simple enough for a child to understand, it was probably worthless"

In other words we may be able to understand why a quantum environment lacks causality if we can transform the abstract or non-physical aspects or the probabilities associated with Schrödinger’s wave equation to one that more closely resembles the physical properties of our classical world.

For example Einstein told us that our physical environment is made up of four dimensional space-time however no one has ever observed the physicality of time or a space-time dimension.

Therefore it is extremely difficult to form a physical image of the quantum world or any other based on the existence of time or a space-time dimension because it is not part of our sensory environment.

Granted Einstein’s theories give us a detailed and very accurate description of how an interaction of time with the three *spatial* dimensions is responsible for the "reality" of the sensory world we inhabit and he was able to give us a clear physical image how a curvature in space-time can be responsible for gravity.

For example the most common physical image use to explain gravity does not use time but instead extrapolates the image of an object moving on a curved two dimensional "surface" in a three dimensional environment to four dimensional space-time.  However this image only contains reference only to the sensory reality of the spatial dimensions and not a time or space-time dimension.

Yet, the fact that most humans define our physical "reality" in terms of the spatial dimensions instead of a time or space-time dimension suggests that one may be able to form a physical image of how and why the quantum world is what it is by viewing our universe in terms of its spatial instead of its time properties.

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 space.  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 by mathematically defining the geometric properties of space-time in terms of the constant velocity of light he provided a qualitative and quantitative means of redefining it in terms of the geometry of four *spatial* dimensions.

The fact that one can use Einstein’s equations to qualitatively and quantitatively redefine the curvature in space-time he associated with gravity in terms of four *spatial* dimensions allows one to form an image of its causality in terms of the physical properties of the spatial dimension instead of the non-physical ones most of us associate with time or a space-time dimension. 

As was mentioned earlier one of the advantage to redefining Einstein space-time concepts in terms of four *spatial* dimensions is that it not only allows one to understand gravitational energy in more direct terms but also allows on to form a physical image in terms of a classical environment for the unpredictability of the quantum world.

For example in the article “Why is energy/mass quantized?” Oct 4, 2007 it was shown one can derive the quantum mechanical properties of a particle by extrapolating the laws governing resonance in a classically three-dimensional environment to a matter wave moving on a “surface” of a three-dimensional space manifold with respect to a fourth *spatial* dimension.  Additionally, it was showed why all energy exists in these resonant systems and therefore must be quantized.

Briefly it was 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 its natural frequency, the lack of a damping frequency and the ability for the substance to oscillate spatial would also be found in one consisting of four.

The existence of four *spatial* dimensions would give three-dimensional space (the substance with a natural frequency) 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.

However, these oscillations in a “surface” of a three-dimensional space manifold, according to classical mechanics would generate a resonant system or “structure” in space.  These resonant systems are known as particles.

(In an earlier article “The geometry of quarks” Mar. 2009 it will be shown how and why they join together to form these resonant systems in terms of the geometry of four *spatial* dimensions.)

The energy in a classically resonating system is discontinuous and can only take on the discrete values associated with its fundamental or a harmonic of its fundamental frequency.

However, these properties of a classically resonating system are the same as those found in a particle in that they are made up of discreet or discontinuous packets of energy/mass.  This is the basis for assuming, as was done in the article “Why is energy/mass quantized?” that its quantum mechanical properties are a result of a resonant system in four *spatial* dimensions.

The reason why we do not observe energy in its extended wave form is that, as mentioned earlier all energy is propagated through space in discrete components associated with its resonant structure.  Therefore, its energy appears to originate from a specific point in space associated with where an observer samples or observes that that energy.

This is analogous to how the energy of water in a sink is release by allowing it to go down the drain.  If all we could observe is the water coming out of the drain we would have to assume that it was concentrated in the region of space defined by the diameter of the drain.  However, in reality the water occupies a much larger region.

However, treating the quantum mechanical properties of energy/mass in terms of a resonant system generated by a matter wave also allows one to form a physical image of its unpredictability by extrapolating the laws of our classical three-dimensional world to a fourth *spatial* dimension.

Classical wave mechanics tells us a wave’s energy is instantaneously constant at its peaks and valleys or the 90 and 270-degree points as its slope changes from positive to negative while it changes most rapidly at the 180 and 360-degree points.

Therefore, the precise position of a particle quantum mechanics associates Schrödinger’s wave equation with could be only be defined in terms of the peaks and valleys of the matter wave responsible for its resonant structure because those points are the only places where its energy or “position” is stationary with respect to a fourth *spatial* dimension.  Whereas it’s precise momentum would only be definable with respect to where its energy change or velocity is maximum at the 180 and 360-degree points of that wave.  All points in between would only be definable in terms of a combination of its momentum and position.

However, to measure the exact position of a particle one would have to divert or “drain” all of the energy at the 90 or 270-degree points to the observing instrument leaving no energy associated with its momentum to be observed by another instrument.  Therefore, if one was able to determine precise position of a particle he or she could not determine anything about its momentum.  Similarly, to measure its precise momentum one would have to divert all of the energy at the 180 or 360 point of the wave to the observing instrument leaving none of its position information left to for an instrument which was attempting to measure it.  Therefore, if one was able to determine a particles exact momentum one could not say anything about its position.

The reason we observe a particle as a point mass instead of an extended object is because, as mentioned earlier the article “Why is energy/mass quantized?” showed its energy/mass must be packaged in terms of a resonant system.  Therefore, when we observe or “drain” the energy continued in its wave function, whether it be related to its position or momentum it will appear to come from a specific point in space similar how the energy of water flowing down a sink drain appears to be coming from a “point” source with respect the extended volume of water in the sink.

However, this allows one to form a physical image of the unpredictability of a quantum environment because it give us a Classical reason why we cannot precisely measure the both the momentum or position of a quantum object because the measurement of one effects the measurement of the other. 

For example, if one wants to measure the position of a particle to within a certain predefined distance “m” its wave energy or momentum will have to pass through that opening.  However, Classical Wave Mechanics tells us that as we reduce the error in our measurement by decreasing that predefine distance interference will cause its energy or momentum to be smeared our over a wider area.  Similarly, to measure its momentum one must observe a portion the wavelength associated with its momentum.  However, Classical wave mechanics tell us we must observe a larger portion of its wavelength to increase the accuracy of the measurement of its energy or momentum.  But this means that the accuracy of its position will be reduced because the boundaries determining its position within the measurement field are greater.

However, because of the dynamic interaction between the position and moment component of the matter wave responsible for generating the resonant system associated with a particle defined in the article a ”Why is energy/mass quantized?” the change or uncertainty of one with respect to the other would be defined by the product of those factors.

Another way of looking at this would be to allow a particle to pass through a slit and observe where it struck a screen on the other side.  One could get a more precise measurement of its position by narrowing the slit however classical wave mechanics tell us this will increase the interference of the wave properties associated with its resonant structure.  However this will cause the interference pattern defining its momentum to become more spread out and therefore make it more difficult to accurately determine its value.

Therefore, Classical wave mechanics, when extrapolated to Schrödinger’s wave equation in an environment consisting a fourth *spatial* dimension tells us the more precisely the momentum of a particle is known, the less precisely its position can be known while the more precisely its position is known, the less precisely its momentum can be determined.  In other words it tells us in terms of a physical image based on a classical environment the reason why God must play dice is because the physicality of a quantum environment prevents us from precisely determining the initial condition of a particle through observation.

Later Jeff

Copyright Jeffrey O’Callaghan 2014


 

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Can we influence reality?  Some misguided scientists think we can.

For example the Copenhagen model of Quantum Mechanics suggests the act observing an environment defines its reality as is shown by its interpretation of Thomson’s double-slit experiments because it holds that the myriad of probabilities it defines are unreal and only become real when their outcomes are observed.

Quantum Physics And How We Affect Reality!

In other words they feel reality is an emergent property of observation because it suggests that before one is made an environment does not exist or is unreal and only appears after being observed.

This is because, in the case of the double slit experiment many assume that the classical concepts of "particle" and "wave" cannot be used to fully describe the wave particle behavior of quantum-scale objects exposed by this experiment  Therefore many interpretations of quantum mechanics explain this paradox as a fundamental reality of the Universe.

In other words they feel that the act of observing creates its reality because as was mentioned earlier according to most quantum mechanical models an object does not exist as a particle or wave before it is observed and that its final reality, whether it is particle or wave is dependents on the act of observe it.

This prompted Einstein to say “I like to think that the moon is there even if I am not looking at it”.

However it would not be necessary to for anyone to assume that the moon was not there if they were not looking at it if it was possible to explain in terms of classical properties of space and time the wave/particle behavior of quantum-scale objects.

As mentioned earlier Thomson’s double-slit experiment clearly demonstrates the wave/particle behavior that is associated with the reality of a quantum mechanical environment.

This may be why Richard Feynman the farther of Quantum Electrodynamics believed Thomson’s double slit experiment provided the perfect mechanism for its understanding because it clearly demonstrates their inseparability.

However, as of yet no one has been able to explain in classical terms the behavior of the quantum environment encompassed by this experiment.

Yet Einstein may have given us a clue as to why when he said "If a new theory was not based on a physical image simple enough for a child to understand, it was probably worthless."

For example Einstein told us that our physical environment is made up of four dimensional space-time yet no one has ever observed the physicality of time or a space-time dimension.

Granted Einstein’s theories give us a very detailed and accurate description of how an interaction of time with the three *spatial* dimensions is responsible for the "reality" our world and he was able to give us a clear physical image how a curvature in space-time can be responsible for gravity by extrapolating the image of an object moving on a curved two dimensional "surface" in a three dimensional environment to four dimensional space-time.  However this image only contains reference to the physicality of the spatial dimensions and not a time or space-time dimension.

However, the fact that most humans perceive or define reality in terms of the physicality of the spatial dimensions instead of a time or space-time dimension suggests that one may be able to form a physical image of how and why the quantum world is what it is by viewing our universe in terms of its spatial instead of its time properties.

Einstein gave us the ability to do this when he used the constant 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 that is physically identical to those of our three-dimensional space.  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 by mathematically defining the geometric properties of time in his space-time universe in terms of the constant velocity of light he provided a qualitative and quantitative means of redefining it in terms of the geometry of four *spatial* dimensions.

The double slit experiment is made up of "A coherent source of photons illuminating a screen after passing through a thin plate with two parallel slits cut in it.  The wave nature of light causes the light waves passing through both slits to interfere, creating an interference pattern of bright and dark bands on the screen.  However, at the screen, the light is always found to be absorbed as discrete particles, called photons.

When only one slit is open, the pattern on the screen is a diffraction pattern however, when both slits are open, the pattern is similar but with much more detailed.  These facts were elucidated by Thomas Young in a paper entitled "Experiments and Calculations Relative to Physical Optics," published in 1803.  To a very high degree of success, these results could be explained by the method of Huygens–Fresnel principle that is based on the hypothesis that light consists of waves propagated through some medium.  However, discovery of the photoelectric effect made it necessary to go beyond classical physics and take the quantum nature of light into account.

It is a widespread misunderstanding that, when two slits are open but a detector is added to determine which slit a photon has passed through, the interference pattern no longer forms and it yields two simple patterns, one from each slit, without interference.  However, there ways to determine which slit a photon passed through in which the interference pattern will be changed but not be completely wiped out.  For instance, by placing an atom at the position of each slit and monitoring whether one of these atoms is influenced by a photon passing the interference pattern will be changed but not be completely wiped out.

However the most baffling part of this experiment comes when only one photon at a time impacts a barrier with two opened slits because an interference pattern forms which is similar to what it was when multiple photons were impacting the barrier.  This is a clear implication the particle called a photon has a wave component, which simultaneously passes through both slits and interferes with itself.  (The experiment works with electrons, atoms, and even some molecules too.)"

Yet as mentioned earlier one may be able to understand the wave particle duality of quantum objects such as a photon as is demonstrated in Thomson’s double slit experiment in terms of our classical reality if one converts or transposes Einstein’s space-time universe to four *spatial* dimension equivalent.

For example the article, "Why is energy/mass quantized?" Oct. 4, 2007 showed that one can explain and understand the physicality of the wave and particle properties of quantum object’s by extrapolating the laws of classical resonance in a three dimensional environment to a matter wave moving on “surface” of a three dimensional space manifold with respect to a fourth *spatial* dimension.  It also explains why all energy must be quantized or exists in these discrete resonant systems when observed.

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 a matter wave moving in 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 with respect to a fourth *spatial* dimension to oscillate with the frequency associated with the energy of that event.

However, 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.

As was shown in that article these resonant systems in four *spatial* dimensions are responsible for its quantum mechanical properties.

However, it does not explain in classical terms why the energy of these waves not continuously distribute throughout space instead of being package in discrete units we call particles. 

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 spatial boundaries of the resonant system associated with all quantum objects including a photon in the article "Why is energy/mass quantized?".

This provides the ability to understand, in terms of our classical reality the inseparability of the wave-particle duality of energy/mass because clearly demonstrates how the one is dependent on the other.

However, it also defines why the interference patterns remains in Thomson’s double slit experiment when one photon at a time is fired at the barrier with both slits open or "the most baffling part of this experiment" is because, as mentioned earlier it is made up of a resonant system or "structure" therefore it occupies an extended volume which is directly related to the wavelength of its particle system.

This means a portion of a particles energy could simultaneously pass both slits, if the diameter of its volume exceeds the separation of the slits and recombine on the other side to generate an interference pattern. 

It also explains why the interference pattern disappears, in most cases when a detector is added to determine which slit a photon has passed through.  The energy required to measure which one of the two slits it passes through interacts with it causing the wavelength of that portion to change so that it will not have the same resonant characteristics as one that passed through the other slit   Therefore, the energy passing thought that slit will not be able to interact, in most cases with the energy passing through the other one to form an interference pattern on the screen.

However it also explains why, as was mentioned "there are ways to determine which slit a photon passed through that will cause a change in the interference pattern but will not completely wiped it out.

The fact that the interference pattern can still occur even if a measurement is made is because if the energy passing through one of the two slits is altered by a relatively small amount compared to what it originally was, classical wave mechanics tells us it will be able to interact to form a slightly different resonant system with a slightly different interference pattern on the other side than would be the case if no measurement was taken.

It should be pointed out that the fact that an interference pattern can be observed when a detector is added is a direct contraction of the Copenhagen interpretation of quantum mechanics.  It demands when a detector is added to the experiment to determine which slit a photon has passed through the interference pattern can no longer form.

However, this also means there should be a quantifiable minimum value of interaction between a measuring device and a photon that will permit the interference pattern to be reestablished on the other side after measuring which slit the photon passes through.

It also defines in classical terms the reason, why the measurements always takes the form particles and not waves in Thomson’s double slit experiment

As mentioned earlier, the article "Why is energy/mass quantized?" showed energy must be propagated through space in quantized resonant systems if one applies the concepts of classical reality to a matter wave on "surface" of a three-dimension space.  Therefore, because its energy must be propagated through space to be observed the energy impacting the screen always will have the discrete non-wavelike characteristics of a particle.

The above article demonstrates why it is not necessary for anyone to assume that observing a quantum environment influences or changes its reality to explain the results of the double slit experiment because it clearly shows they can be explained in terms of the unchanging reality of our classical physical environment.

Latter Jeff

Copyright Jeffrey O’Callaghan 2014


 

The Imagineer’s
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Vol. 4 — 2013



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