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The scientific methodology (often called "Effective Theory") adopts essentially a reductionist's approach, which break down the investigation into many levels mainly defined by size and from small to large (see a few examples in Figure 01). Usually, the higher level does not involve the detail of the lower one, which just provides a few parameters as linkage between the two. These parameters serve as macroscopic description of the more |
Figure 01 Reductionist's Systems |
complicated microscopic domain, and often can be measured by experiment or observation. |
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Figure 02 Particle, Definition |
characterized by its electric charge, mass, spin, and color charge. The ratio R ~ 10-3, which is much larger because the strong interaction in this case is a short range force. Actually, not much is known about this system. |
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random directions as shown in Figure 03. The thermal energy becomes work if they can be coaxed to move in an unison direction such as in the "Heat Engine". It is called a wave when the organized motion is propagating through the medium such as the sound wave in Figure 04. Thus, particle and wave seem to be very different. Each particle is a single entity with certain characteristics, while the wave involves coherent motion of a collection of particles at macroscopic level as it is understood until the advent of quantum theory which treats these two entities as the flip side of each others and creates severe conceptual problem. |
Figure 03 Thermal Motion |
Figure 04 Sound Wave |
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The wave nature of light (as Electro-Magnetic, EM wave) has been demonstrated conclusively by its diffraction pattern since 1801 in Young's experiment (Figure 05). The particle aspect of light was first revealed by Max Planck's "quanta of light" to account for the discrepancy in blackbody radiation; it was finally confirmed by the discovery of photo-electric effect (Figure 06) in 1905. It was found subsequently that electrons can produce similar diffraction as light. The diffraction pattern is attributed to matter wave (or probability wave, see Figure 07) similar in form to the EM wave but with different origin. |
Figure 05 Diffraction of Light (EM Wave) |
Figure 06 Photo-electric Effect [view large image] |
The EM wave is actually at macroscopic level - one step away from quantum. |
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In 1924, de Broglie derived a relation between the wave length of the matter wave ![]() Ek = pc, which also can be expressed in term of quanta in quantum theory as Ek = hf, where the frequency f ~ c/ ![]() p = h/ ![]() |
Figure 07 Matter Wave (Probability Wave) [view large image] |
In Figure 07, P1 and P2 are the probabilities of finding the particle (from slit 1 or 2) along the screen , and P12 is the result of interference - hence the nomenclature of "probability wave". |
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Figure 08a Traveling and Standing Waves [view large image] |
It shows that starting from a non-linear equation for r, i.e., (m/2)d2r/dt2 + V(r) = E, quantization has it linearized into the Schrodinger equation for the wave function ![]() |
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Figure 08b Standing Waves [view large image] |
Figure 08c Superposition |
See "Harmonic Oscillator" and "Infinite Square Well". |
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There is a deeper level of quantum theory than the particle and wave as mentioned above. In the Standard Model (SM) of elementary particles, it is the quantum fields that are ubiquitous in the formulation. In contrary to the classical fields such as the electro-magnetic fields in Maxwell's equations and the metric tensors in General Relativity, in which there is always a source such as charge and current or mass-energy tensor to generate the fields, the quantum fields in SM has no source - it is assumed to be everywhere and at all time in this Universe. That's why there is always a |
Figure 09 Quantum Fields [view large image] |
Figure 10 Virtual Particles [view large image] |
suspicion about an even deeper level to describe the detail of their origin - according to the the reductionist's view point. See "Quantum Fields and Vacuum Energy Density" for more on vacuum state. |
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The interaction is expressed in the covariant derivative D ![]() ![]() ![]() |
Figure 11 Lepton Largranian for WS Model of SM [view large image] |
The quarks have a slightly different form of the Lagrangians by the title of quantum chromodynamics (QCD). |
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Figure 12 Quarks and Gluons [view large image] |
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indicates that the matrix element Sif has an inverse, which in turn implies that it is possible to return to the initial state from the final state at least in principle although the probability is almost zero in practice so that the second law of thermodynamics is "almost" never violated. This property is also related to the so-called "conservation of information", which caused so much trouble for Stephen Hawking in the "Black Hole Information Paradox". |
Figure 13 S-Matrix |
Note: For example in the electron positron scattering process, there are three possible finally states as illustrated in Figure 13. The sum of the probabilities for each one of these has to be: S*11S11 + S*21S21 + S*31S31 = 1 to insure that the final state is in one of the three possibilities. |
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Similar to the superposition of waves in quantum mechanics, the unitary condition ![]() |
Figure 14 Possibility in Life [view large image] |
Figure 15 Probability in Lottery [view large image] |
The unitary condition for Lottery can be expressed as : ![]() |
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For example, in case the game is rigged such that only 6 balls (digits) would fit the exiting hole (representing the hidden cause to be discovered or invented), then the unitary condition is still :![]() |
Figure 16 Bell's Theorem |
This is an extreme example of Bell's Theorem, which was proposed to test if there is any (not yet discovered) hidden elements in quantum theory. Since then, many tests have been performed to show there is no hidden variables in quantum theory (no cheating). |
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What irked Einstein and friends even more is the phenomena of entanglement which is the superposition of states between two or more particles (Figure 17). It bothered them to witness the simultaneous collapse of corresponding states even when the detectors are separated beyond the distance allowed by the speed of light (called non-locality). They blamed the in-completeness of quantum theory and proposed the "Hidden Variables" interpretation as mentioned above. |
Figure 17 Entangled States |
Figure 18 Entanglement, |
Traditional definition of "probability" is : "likelihood", "chance", ... always associated with incomplete knownledge. In quantum theory however, "probability" can be calculated from well-defined equation and becomes deterministic, which is the oft-missed difference. |
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After all is said and done up to this point, there is still plenty of doubt about how to make sense of the quantum theory. For example, Sean Carroll in his 2019 book "Something Deeply Hidden" states that "the Copenhagen approach is difficult to swallow for several reasons. Among them is the fact that the wave function is unobservable, the predictions are probabilistic and what makes the function collapse is mysterious." It seems that the decoherent interpretation is still ignored by many people, physicist included. They still believe that the "Many-Worlds interpretation" is more creditable (Figure 18a). In another 2019 article "Proof of Parallel Universes ?", it is argued that instead of proofing non-locality is correct; the Bell test could mean the existence of parallel universes (while local causality is preserved). |
Figure 18a Parallel Universes [view large image] |
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Then in his 2019 book titled "Einstein's Unfinished Revolution" Lee Smolin mentions that decoherence cannot be derived from the Schrodinger equation because the latter is reversible while former is irreversible (as measurement cannot be undone). The problem can be resolved by invoking the "Quantum Poincare Recurrrence Theroem", which permits the reversibility of measurement under certain rarely occurred circumstance. The other way is to invent another equation such as the Pilot Wave Theory" by de Broglie to describe the measurement process. Quantum mechanics is not complete without such supplement to address this so-called "measurement problem" - his said. |
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The same Lee Smolin has a even more radical idea to formulate a new theory which would merge General Relativity with Quantum Theory, i.e., another "Theory of Everything". He repeats the same kind of criticism of quantum theory in an August 24, 2019 New Scientist article "Beyond Weird". In his view, the faults of quantum theory are in its mysterious nature (superposition, entanglement), the phenomena it doesn't explain (dark matter, dark energy), the answers it doesn't give (why gravity |
Figure 18b New Reality |
is left out ???), and the measurement problem as stated earlier. The foundation of his new theory is based on a "Manifesto" including 6 hypotheses as shown in Figure 18b. He claims certain successful attempts so far, but there is still a long way to go. |
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phenomena is different from "Quantum Theory" for small scale particle. Problem occurs only at the beginning of the universe, which becomes very small and requires quantum treatments. Actually, such combination has been successful implemented in "Origin of Time (2019 Version)" by "Quantization of the Friedmann Equation (Matter-only)". Lee Smolin's obsession to unify the large and small domains would be cooling down if he accepts the view that mathematics has its own limitation; it is not designed to represent the reality of the world. It is to the credit of theoretical physicists who managed to work out some equations at different levels that can be stitched together to portray a picture of the whole (see "The Eight Most Important Equations in Physics"). |
Figure 18c Theory Of Everything (TOE) [view large image] |
Progress in theoretical physics can be served better by building on existing foundation, rather than starting anew from scrap turning everything upside down. |
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Way back in 2004, half-a-dozen experiments have been designed to determine the boundary between the classical and quantum world. One experiment shown in Figure 19 fires C70 fullerene balls (70 carbon atoms in the soccerball-like crystal of about 1 nm across) at 190 m/sec toward two diffraction gratings. The first grating creates the matter wave from the fullerenes. The wave is then diffracted by the second grating and the interference pattern is formed on the detecting screen demonstrating the wave property of the fullerenes. However, the interference pattern fades away if the fullerenes are heated by a laser heater (to about 2700oC) or collide with gas (leaking into the vacuum chamber of the experiment). No one has a definitive answer for how the striking photons or molecules switch the quantum to classical domain. One explanation is that the interaction causes an uncertainty in the position of the fullerenes, blurring the interference pattern. Another argument asserts that the disappearance of the quantum property is caused by entanglement between the photons/molecules, the fullerenes, and the rest of the world (the wall of the chamber). |
Figure 19 Matter-Wave Experiment and quantum-classical boundary |
See explanation by "Decoherence". |
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In an article commemorates the 50th anniversary of the "New Scientist" magazine, Roger Penrose suggests that there are three kinds of reality: the physical, the mental and the mathematical, with something (as yet unknown) profoundly mysterious in the relations between them. According to this view, the various "Quantum Interpretations" are attempts to link the mathematical reality to the physical or mental reality. Figure 20 shows the mathematical reality as the patterns of interference computed from a mathematical formula, while the physical reality is in the form of photographic plate with the darker strip corresponding to the higher value of the curve. The mental reality is the image of dark and white strips formed in the retina and perceived by our consciousness. |
Figure 20 The Reality
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Interpretation | Feature | Status |
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Copenhagen | Measurement plays a key role in decoherence of quantum states | Healthy |
Hidden Variables | Hidden variables carry missing information about quantum states | Challenged |
Many Worlds | All quantum possibilities play out in a multiplicity of universes | Dubious |
Penrose | Outcome of experiments is a result of gravitational interactions | Under investigation |
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A modern interpretation around early 21st century suggests that the measurement is a continuous process similar to the diffusion of an air particle going from one spot to another making collisions with other particles many times on its way. In the quantum world, the particle is identified to the quantum state while the interacting particles in the intervening space are replaced by the Hilbert states of the environment (such as the the detector for the measurement), which is a collection of huge number of particles (see a much simplified illustration in Figure 22). This theory about quantum paths is called Quantum Trajectory Theory (QTT), while the process is what used to be called "decoherence". |
Figure 21 Two States Superposition |
Figure 22 Quantum Trajectory Theory (QTT) [view large image] | Meanwhile in 21st century, the technology in time scale measurement has been refined to the level of nono-second. It enables experiment to trace the time development of the collapsing process as shown in Figure 23,a. |
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The 2019 experiment uses an artificial atom made of superconducting qubits having a ground state G and an excited state D. Microwave is used to excite the "atom" from ground to excited state. It is found that back-action (actually decohence) keeps sending the superposition (in the form of 2 linear probability functions for G and D) back to the Ground state. Then transitions to the excited state occur after a quiet interval (see Figure 23,a). The sequence of events happen in time scale of about few hundred micro-second - definitely not instant as thought 100 years ago. |
Figure 23 Modern Quantum Jump Experiment (ill.) [view large image] | Here's the details (see the original article "To Catch and Reverse a Quantum Jump Mid-flight") : |
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350 ![]() PG + PD = 1 as shown in Figure 23,a and similarly in Figure 24. The quantum trajectory is any one of those evolution tracks (in Figure 23,a). |
Figure 24 Two-Level Rabi Drive
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Figure 25 RF Signal and I, Q Basebands [view large image] |
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Figure 26 Neo-Quantum-Jump Experiment, Time-Record [view large image] | See "Has Quantum Theory's Greatest Mystery Been Solved ?" for an Introduction to QTT and the Experiment. |
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Such effect has been observed experimentally by observing the "entanglement measure" for the electrons in various diatomic molecules. It is drastically shown in Figure 03k where the H2 molecule having 2 electrons attains much higher entanglement than the Cl2 molecule having 34 electrons. Thus, the collapse to an unique state by decoherence can be attributed to the weakening of the entanglement measure to zero by all the Hilbert states in the environment. |
Figure 27 Entanglement [view large image] | See a detailed treatment of " Quantum Decoherence". |