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【Podcast：國際夢工場 050 ⚛️🎬】 陳志宏博士對談《奧本海默》：（二）科學、藝術、音樂、文學、社科、政治都在革命：奧本海默是Renaissance Man，還是 Alpha Male？（中文字幕） (Patreon)

Published:
2024-04-04 04:31:01
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2024-06
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金像獎最佳電影《奧本海默》對談第二部份，和陳志宏博士討論了奧本海默的多才多藝，究竟是真正融會貫通的 Renaissance Man，還是以顯示自己強勢、刻意支配他人的 Alpha Male DNA為出發點。究竟有多少觀眾，會明白奧本海默將科學、藝術、音樂、文學、社科、政治的革命扣連在一起的深層意義？

▶️ YouTube: https://www.youtube.com/watch?v=Qfpeawzzbkc

▶️ 陳志宏博士對談《奧本海默》（一）量子力學的顛覆性，究竟在於哪裏？

https://www.youtube.com/watch?v=aMPMKrNEC2I

⏺《奧本海默》（一）美德蘇的原子彈競賽，為何最終分出勝負？https://www.patreon.com/posts/99850847

⏺《奧本海默》（二）美國和納粹德國管理科學家，有哪些異同？https://www.patreon.com/posts/99891153

⏺《奧本海默》（三）廣島原子彈爆炸之前，曇花一現的「Deterrance 1.0」 理論https://www.patreon.com/posts/99887460

⏺《奧本海默》（四）廣島、長崎的悲劇：為甚麼未爆先降的核威懾理論失敗？https://www.patreon.com/posts/99916910

⏺《奧本海默》（五）大反派原子能委員會主席史特勞斯，才是猶太人心目中的救世主？https://www.patreon.com/posts/99888863

⏺《奧本海默》（六）奧本海默的對頭與「deep state」：史特勞斯影響力從何而來？https://www.patreon.com/posts/99921159

⏺《奧本海默》（七）國安角度，如何研判奧本海默極左思想的風險？https://www.patreon.com/posts/99891120

⏺《奧本海默》（八）有很多共產黨親密朋友，會否構成國安風險？https://www.patreon.com/posts/99982840

⏺《奧本海默》（九）科學革命、音樂革命、繪畫革命、文學革命、心理學革命、政治革命融為一體的「大革命時代」https://www.patreon.com/posts/100458529

⏺《奧本海默》（十）史特拉汶斯基、榮格、梵文，如何啟迪科學創見？https://www.patreon.com/posts/100011668

⏺《奧本海默》（十一）人文社科視角下的量子力學革命https://www.patreon.com/posts/100011534

⏺《奧本海默》（十二・最終篇）「矛盾中有統一」：奧本海默的多面人生https://www.patreon.com/posts/100011780

👉 科學新知Channel: https://www.youtube.com/@sciencefrontier852

Comments

George

After watching this interview, it brought to mind a discussion about exceptional scientists who, despite their brilliance, could not receive or have not won Nobel Prizes. Two such examples are Freeman Dyson and Edward Witten, both affiliated with the IAS in Princeton. Freeman Dyson was an unconventional physicist. He moved to the US for postgraduate study at Cornell after the WWII. He then moved to the IAS and returned to England in 1949. During his stay as a research fellow at the University of Birmingham, Dyson formulated groundbreaking work that demonstrated the equivalence between Richard Feynman's approach to quantum electrodynamics (QED) and the earlier mathematical calculations by Julian Schwinger and Shinichiro Tomonaga. The independent efforts of Feynman, Schwinger, and Tomonaga on QED earned them the Nobel Prize in 1965. Dyson's work held immense significance as it showcased the mathematical formulation of QED using Feynman's techniques and successfully resolved the issue of "renormalization." In 1951, despite not having a doctorate, Dyson secured a faculty position at Cornell University. His argument persuaded Robert Oppenheimer, who then recognized the equivalence between Feynman's theory and that of Schwinger and Tomonaga. Impressed by this accomplishment, Oppenheimer, who was the director of IAS at the time, offered Dyson a lifetime appointment at the institute. Dyson himself recalled that Oppenheimer made this offer as a result of “proving him wrong.” Dyson accepted the offer and continued to publish innovative papers throughout his career, delving into various topics, including the hypothetical detection of gravitons. In addition to physics, Dyson made contributions to various branches of mathematics, including topology, analysis, number theory, and random matrices. Notably, a mathematician presented a conjecture in 1973 concerning the distribution of zeros of the Riemann zeta function, which resembled work done by Dyson in mathematical physics. Reflecting on his own approach, Dyson remarked in 2009 that he believed winning a Nobel Prize often required a long attention span and dedicating oneself to a deep and important problem for at least ten years—a style of work that did not align with his own. Edward Witten, widely regarded as “the smartest living physicist,” plays a major role in the development of superstring theory, a prominent theory of quantum gravity. His exceptional command of mathematics and profound physical insights often lead to exploration of new research directions and the discovery of deep mathematical theorems. Witten's academic journey followed an unconventional path. Initially, he pursued a BA degree at Brandeis University, majoring in history and minoring in linguistics. Displaying interests in journalism and politics, he even contributed articles to publications like The New Republic and The Nation during the late 1960s. In 1972, he dedicated six months to working on George McGovern's presidential campaign. After a brief stint as an economics graduate student at the University of Michigan, Witten decided to return to academia. He first enrolled in applied mathematics at Princeton University in 1973. He then shifted his interest to physics, eventually obtaining his Ph.D. in physics in 1976 under the guidance of David Gross, a theoretical physicist who won the 2004 Nobel Prize. Witten has made remarkable contributions in the fields of quantum gravity, string theory, and quantum field theory (QFT). His exceptional achievements have garnered him numerous awards throughout his career. Notably, Witten holds the distinction of being the first and only physicist thus far to receive the esteemed Fields Medal, one of the most prestigious awards in mathematics. This recognition was bestowed upon him for his profound mathematical insights applied to physics, including the utilization of superstring theory concepts to prove the positive energy theorem in general relativity. Previously, mathematicians Richard Schoen and Shing-Tung Yau had proved this theorem using variational methods and minimal surfaces, albeit in a more intricate manner. Despite these achievements, superstring theory has yet to produce testable predictions, and due to current technological limitations, significant breakthroughs in the near future seem unlikely. Nobel Prizes are rarely awarded to physicists solely for theoretical work, no matter how elegant, without experimental confirmation. These examples underscore how even geniuses like Dyson and Witten can encounter challenges in winning Nobel Prizes, whether due to personality, research style, or the absence of experimental validation for their groundbreaking theories.

George

I'm a science enthusiast. While I’m not an expert in quantum physics, I would like to share my understanding of elementary quantum mechanics, first by the intuitive explanations and then through some mathematical equations. I welcome feedback from experts here who can kindly help identify any errors in my concepts or interpretations. Please feel free to provide your valuable insights and corrections. I would say the strangeness of the theory starts off with wave-particle duality: quantum objects have both wave and particle properties. If an electron has a definite single momentum, it has a single frequency, which behaves like a regular wave. This wave continues on in space forever, so the electron doesn't have a definite position. On the other hand, if we set up a wave with a definite position, we have to sum up waves of many different frequencies. So if an electron wave is localized in space, it doesn't have a definite frequency. This is called Heisenberg's uncertainty principle: the more accurately one physical property of a system is measured, the less accurately the other property can be known. We can illustrate this concept in a simple experiment where the position of an electron is measured. In order to measure the position of an object, a photon must collide with it and return to the measuring device. Since photons hold some finite momentum, a transfer of momentum occurs when the photon collides with the electron, in accordance with the law of conservation of momentum. This transfer of momentum causes the momentum of the electron to increase. Thus, any attempt to measure the position of a particle will increase the uncertainty in the value of its momentum. Conversely, if we measure the momentum of the electron with high precision, we use a photon with a longer wavelength (lower momentum) in order to minimize the disturbance to the electron’s momentum (the “push” it delivers is minimal). By gaining higher precision in momentum (minimal photon interference), we lose precision in the electron’s position in light of a larger spread of photons. If we consider this example with a macroscopic object, such as a basketball, it can be understood that Heisenberg's uncertainty principle has a negligible impact on measurements. Although there is still a transfer of momentum from the photons to the basketball, the mass of the photon is significantly smaller than that of the basketball, and therefore, the change of momentum in the basketball can be neglected. The world of quantum mechanics is very different from classical (Newtonian) mechanics that we're all much more accustomed to. We cannot derive quantum mechanics from classical laws. In fact, quantum mechanics is a more fundamental theory from which classical mechanics emerges. However, there are many close parallels between the equations of quantum and classical mechanics. To understand the origin of the uncertainty principle in mathematical language, we can refer to the canonical commutation relation [x̂, p̂] ≡ x̂p̂ - p̂x̂ = iℏ, where x̂ and p̂ are operators representing the position and momentum, respectively, in a quantum system, ℏ is the reduced Planck constant, and i is the imaginary unit defined by i² = −1. Its counterpart in classical physics is the Poisson bracket {x, p} = 1, where x and p are classical observables, i.e., number-valued quantities. It's worth noting that each observable in classical mechanics corresponds to an operator in quantum mechanics. The eigenvalue of an operator acting on the quantum state corresponds to the measured values of the observable. Examples of observables are position, momentum, kinetic energy, total energy, angular momentum, etc. If x̂ and p̂ are both numbers, they commute so the product does not depend on the order in which x̂ and p̂ are multiplied, x̂p̂ - p̂x̂ = 0, which contradicts the commutation relation. Nevertheless, this contradiction can be interpreted as the limiting case where quantum mechanics becomes classical mechanics when the Planck constant tends to zero. This means that, at the macroscopic level, quantum effects can often be considered negligible, and classical theory can be used instead. Yet in the quantum world, x̂ and p̂ are linear operators and they cannot be expressed into numbers simultaneously. Again, the commutator [x̂, p̂] = x̂p̂ - p̂x̂ can be used to clarify this concept. Note that the commutator itself is an operator. Let x and p be the observables, i.e., the eigenvalues of x̂ and p̂ respectively. We then have x̂ ψ = x ψ and p̂ ψ = p ψ. Acting the commutator on a quantum state (say ψ), which can be thought of as measuring an observable in a classical sense, gives x̂p̂ ψ - p̂x̂ ψ = x(p ψ) - p(x ψ) = 0. This implies the measurement of x and p doesn’t shift the state of the system, i.e., initial and final states are the same. However, the canonical commutator relation tells us that if we measure x, then measure p, the result for p would differ from directly measuring p. This’s because the first measurement for x has caused the system to “collapse.” In other words, positions and momentum do not actually have values in the conventional sense simultaneously. The more we confine one observable to be “almost a number” (by performing a measurement), the less the other observable will behave like a number, and vice versa. This does not mean that the quantum system cannot have exact positions and momentum at all times. In fact, they do exist, but they cannot be measured simultaneously in precise numbers. Interpreting this through a probabilistic view, the particle indeed exists in many locations at once. We can use our knowledge to predict the probabilities of where and when the particle will finally interact with a classical apparatus. It's worth noting that in classical mechanics, both position and momentum observables can be precisely measured simultaneously because they are represented by numbers. We can describe this phenomenon in a neat way using mathematics. The state of a quantum system is given by a wavefunction ψ(x, t), which is a complex function. The probability of finding a particle located between x and x+dx is given by P(x, t)dx ≡ |ψ(x, t)|² dx, where | • | represents the complex modulus used to define the probability density P(•, t). This means that if you start with a cloud of identical particles in the system, each with the same wavefunction ψ(x, t), and you measure the position of each particle at time t, you will obtain different results for different particles in the cloud. ψ(x, t) can be seen as the wavefunction in the position (x) space, while its Fourier transform Φ(k, t) is in the momentum (k) space. In a similar fashion, the probability of finding a particle with momentum between k and k+dk is given by Q(k, t)dx ≡ |Φ(k, t)|² dk. ψ(x, t) and Φ(k, t) are just two representations of the wavefunction, i.e., the state of the same quantum system, in different spaces. We can recover the certainty principle mathematically through the connection of these two spaces: when ψ becomes a very narrow spike in the position space (indicating a high likelihood of finding a particle around the spike), Φ becomes inversely stretched out, almost flat, in the momentum space (indicating a very low but equal probability of having a momentum between k and k+dk along the momentum space). Suppose we conduct an experiment repeatedly, using the same set of initial conditions, and tally the occurrences of different outcomes. If the outcome is always the same, it means that the system is deterministic, and the initial conditions fully describe it. If the outcome is not always the same, it indicates that the system is not deterministic in nature, or the set of initial conditions are insufficient to fully describe the system. Let’s say we toss a coin. We should be able to predict the outcome fairly accurately if we had a detailed description of the coin, its initial position, and motion, i.e., a full description of the setup in the experiment. However, under normal circumstances, we don't have access to that information, so our description of the system's initial conditions is incomplete. Quantum physics appears to be a “probabilistic” science because initial conditions cannot be purely given in terms of "classical observables," which are quantities that can be measured. As a result, we’re unable to predict the outcome of an experiment with certainty. Schrödinger's equation is a linear PDE that governs the wavefunction of a quantum system. It is often regarded as the quantum counterpart to Newton's second law of motion, F = ma. In my viewpoint, it is a deterministic equation per se, much like a system without any built-in state simulator. However, certain properties of the system are not fully accessible through observation. Therefore, the probabilistic nature of quantum physics arises from the relationship between initial conditions and outcomes when repeatedly observing a large number of times.

HTTT17
>>134242351

I think I used to love Physics and understand what you described above. But I no longer remember any of these after I worked for 10 years in the society : (