Einstein’s great friend and intellectual sparring partner Niels Bohr had a nuanced view of truth. Whereas according to Bohr, the opposite of a simple truth is a falsehood, the opposite of a deep truth is another deep truth. In that spirit, let us introduce the concept of a deep falsehood, whose opposite is likewise a deep falsehood. It seems fitting to conclude this essay with an epigram that, paired with the one we started with, gives a nice example: “Naïveté is doing the same thing over and over, and always expecting the same result.”
American theoretical physicist
Frank Anthony Wilczek (born May 15, 1951) is an American theoretical physicist, mathematician and Nobel laureate. He is the Herman Feshbach Professor of Physics at the Massachusetts Institute of Technology (MIT), Founding Director of T. D. Lee Institute and Chief Scientist at the Wilczek Quantum Center, Shanghai Jiao Tong University (SJTU), distinguished professor at Arizona State University (ASU) and full professor at Stockholm University. Wilczek, along with David Gross and H. David Politzer, was awarded the Nobel Prize in Physics in 2004 "for the discovery of asymptotic freedom in the theory of the strong interaction". In May 2022, he was awarded the Templeton Prize for his "investigations into the fundamental laws of nature, that has transformed our understanding of the forces that govern our universe and revealed an inspiring vision of a world that embodies mathematical beauty."
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Ironically, conventional quantum mechanics itself involves a vast expansion of physical reality, which may be enough to avoid Einstein Insanity. The equations of quantum dynamics allow physicists to predict the future values of the wave function, given its present value. According to the Schrödinger equation, the wave function evolves in a completely predictable way. But in practice we never have access to the full wave function, either at present or in the future, so this “predictability” is unattainable. If the wave function provides the ultimate description of reality — a controversial issue! — we must conclude that “God plays a deep yet strictly rule-based game, which looks like dice to us.”
To put it crudely, theorists can be tempted to think along the lines “If people as clever as us haven’t explained it, that’s because it can’t be explained – it’s just an accident.” I believe there are at least two important regularities among standard model parameters that do have deeper explanations, namely the unification of couplings and the smallness of the QCD θ parameter. There may well be others.
In most theoretical embodiments of inflationary cosmology, the currently observed universe appears as a small part of a much larger multiverse. In this framework to hold throughout the universe need not hold through all space. They can be accidents of our local geography, so to speak. If that is so, then it is valid – indeed, necessary – to consider selection effects. It may be that some of the “fundamental constants”, in particular, cannot be determined by theoretical reasoning, even in principle, because they really are different elsewhere.
The phase transition paradigm: The standard model of fundamental physics incorporates, as one of its foundational principles, the idea that “empty space” or “vacuum” can exist in different phases, typically associated with different amounts of symmetry. Moreover, the laws of the standard model itself suggest that phase transitions will occur, as functions of temperature. Extensions of the standard model to build in higher symmetry (gauge unification or especially supersymmetry) can support effective vacua with radically different properties, separated by great distance or by domain walls. That would be a form of failure of universality, in our sense, whose existence is suggested by the standard model.
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A common habit of thought... is the idea that space is [a] simple receptacle in which bodies move around, with no two bodies present at the same point. ...In modern quantum physics generally, and in the standard model of fundamental physics in particular, physical space appears as a far more flexible framework. Many kinds of particles can be present at the same point in space at the same time. Indeed, the primary ingredients of the standard model are not particles at all, but an abundance of quantum fields, each a complex object in itself, and all omnipresent.
Intelligent creatures [that] evolved to live deep within the atmosphere of a gas giant planet could be deluded, for eons, into thinking that the Universe is an approximately homogeneous expanse of gas, filling a three-dimensional space, but featuring anisotropic laws of motion (which we would ascribe to the planet’s gravitational field). Are we human scientists comparably blinkered?
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E = mc<sup>2</sup> really applies only to isolated bodies at rest. In general, when you have moving bodies, or interacting bodies, energy and mass aren't proportional. E = mc<sup>2</sup> simply doesn't apply. ...For moving bodies, the correct mass-energy equation is
<math>E=\frac {mc^2} {\sqrt{1-\frac{v^2} {c^2}}}</math>
where <math>v</math> is the velocity. For a body at rest <math>(v=0)</math>, this becomes E = mc<sup>2</sup>. ...we must consider the special case of particles with zero mass... examples include photons, color gluons, and gravitons. If we attempt to put m = 0 and <math>v</math> = c in our general mass-energy equation, both the numerator and denominator on the right-hand-side vanish, and we get the nonsensical relation E = 0/0. The correct result is that the energy of a photon can take any value. ...The energy E of a photon is proportional to the frequency f of the light it represents. ...they are related by the Planck-Einstein-Schrödinger equation E = hf, where h is Plank's constant.
Different ways of writing the same equation can suggest very different things, even if they are logically equivalent. ...In Einstein's original 1905 paper, you do not find the equation E = mc<sup>2</sup>. What you find is m = E/c<sup>2</sup>. ...the title of the paper is a question: "Does the Inertia of a Body Depend on Its Energy Content?" …If we can explain mass in terms of energy, we'll be improving our description of the world. We'll need fewer ingrediants in our world-recipe.