Each of the most basic physical laws that we know corresponds to some invariance, which in turn is equivalent to a collection of changes which form a symmetry group. ...whilst leaving some underlying theme unchanged. ...for example, the conservation of energy is equivalent to the invariance of the laws of motion with respect to translations backwards or forwards in time... the conservation of linear momentum is equivalent to the invariance of the laws of motion with respect to the position of your laboratory in space, and the conservation of angular momentum to an invariance with respect to directional orientation... discovery of conservation laws indicated that Nature possessed built-in sustaining principles which prevented the world from just ceasing to be. There were fewer roles for the Deity to play...
John D. BarrowRelated topics
angular basic ceasing conservation example form laboratory leaving linear momentum nature orientation play position respect space sustaining symmetry theme turn Laws built-in directionalRelated quotes
If, therefore, you've already considered that Signac and the others who are doing pointillism often make very beautiful things with it - Instead of running those things down, one [Bernhard] should respect them and speak of them sympathetically, especially when there's a falling out. Otherwise one becomes a narrow sectarian oneself, and the equivalent of those who think nothing of others and believe themselves to be the only righteous ones. This extends even to the academic painters, because take, for example, a painting by Fantin-Latour - and above all his entire oeuvre. Well then - there's someone who hasn't rebelled, and does that prevent him, that indefinable calm and righteousness that he has, from being one of the most independent characters in existence?
Vincent van Gogh
It is quite easy to include a weight for empty space in the equations of gravity. Einstein did so in 1917, introducing what came to be known as the cosmological constant into his equations. His motivation was to construct a static model of the universe. To achieve this, he had to introduce a negative mass density for empty space, which just canceled the average positive density due to matter. With zero total density, gravitational forces can be in static equilibrium. Hubble's subsequent discovery of the expansion of the universe, of course, made Einstein's static model universe obsolete. ...The fact is that to this day we do not understand in a deep way why the vacuum doesn't weigh, or (to say the same thing in another way) why the cosmological constant vanishes, or (to say it in yet another way) why Einstein's greatest blunder was a mistake.
Frank Wilczek
Don't forget that God sees you and watches you when you are in pain; He perceives even the beating of your heart. Consequently, He will not leave you without consolation and His fatherly protection. Naturally, the saints rejoiced in their afflictions; as for us, let us at least manage to accept affliction or pain patiently.
My child, pray within your heart, and the name of Jesus will become for you a comforting balm so that you can bear this trial of yours in a way which benefits you. You will greatly benefit from this trial if you submit yourself to it patiently. So again I say to you, with the almighty armor of prayer continually approach the omnipotent Lord more often, and you will come to know how He wondrously lifts the burden of pain and marvellously gives rest to sufferers.
Ephraim of Arizona
This spectrum is of the type known in spectroscopy as a line-spectrum. Its appearance is that of a group of bright lines on a dark background, indicating that the radiation divides itself between a number of clearly defined frequencies, and that there is no radiation in between. Before Bohr's explanation appeared, these frequencies had been supposed to belong to some sort of vibration taking place in the hydrogen atom - like frequencies of the musical note which is heard when a bell or piano wire is made to vibrate. It now became clear that they had an entirely different origin. The energy exhibited in the spectrum was not liberated by a vibration, or any kind of continuous motion, but by the sudden jump of an electron to an orbit of lower energy, and its frequency was determined by the compulsion put upon it to form a single quantum.
James Jeans
Why can stars do better than the big bang? ...During the big bang, there were only a few minutes when nuclei could form. Very rare processes, or slow ones, played little role. A case in point is the key process from which the sun derives its energy. In this reaction, two protons collide to produce a deuterium nucleus, a neutrino, and a positron. ...This reaction belongs to the family of weak interactions. ...It remains... a remarkable-and for humanity, remarkably fortunate-circumstance that the central reaction that drives the sun is so rare. It is only this extraordinary rarity that allows the average proton in the sun to last so long, billions of years, even though it is colliding with other protons millions of times a second. ...an entertaining example of Treiman's theorem.
Frank Wilczek