E = mc2 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 = mc2 simply doesn't apply. ...For moving bodies, the correct mass-energy equation is E=\frac {mc^2} {\sqrt{1-\frac{v^2} {c^2}}} where v is the velocity. For a body at rest (v=0), this becomes E = mc2. ...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 v = 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.
Frank WilczekRelated topics
attempt body case color constant correct denominator equation frequency general light mass moving proportional rest result take value velocity zero photonRelated quotes
There were two problems which had to be faced. One was spatial and the other methodological. In the first case I had to do something about relational painting, i. e. the balancing of the various parts of the painting with and against each other. The obvious answer was symmetry – make it the same all over. The question still remained, though, of how to do this in depth. A symmetrical image or configuration symmetrically placed on a open ground is not balanced out in the illusionistic space. The solution I arrived at, and there are probably quite a few, although I only know of one other, color density, forces illusionistic space out of the painting at constant intervals by using a regulated pattern. The remaining problem was simply to find a method of paint application which followed and complemented the design solution. This was done by using the house painters technique and tools.
Frank Stella
Reconstruction is merely a special case of economic progress. If we are to understand its problems thoroughly, we must examine what is meant by economic progress and try to discover how it comes about... Economic progress is not altogether easy to define and is even more difficult to measure. Nevertheless, the phrase clearly corresponds to a meaningful idea. We have only to contrast a savage society with our own. In a savage society, the same customs, the same techniques, the same ways of doing everything, from ploughing to praying, are maintained generation after generation, son following exactly in the footsteps of his father and daughter in the footsteps of her mother, without deviating an inch from the well-trodden way. In modern civilized society, on the other hand, there is constant change and flux; we are constantly improving on the methods of our ancestors, and indeed one of the surest ways to discredit anything is to call it "old-fashioned!"
Kenneth Boulding
Though I remained insensitive to the subtleties and delicate gradations of colour.. ..my eyes at least did not deceive me when I drew back and looked at the subject in its broad lines, and this was the starting-point of new compositions.. .Slowly I tried my strength in innumerable rough sketches which convinced me.. .I could see as clearly as ever when it came to vivid colours isolated in a mass of dark tones. How was I to put this to use? My intentions gradually became clearer.. .I said to myself, as I made my sketches, that a series of general impressions, captured at the times of day when I had the best chance of seeing correctly, would not be without interest. I waited for the idea to consolidate, for the grouping and composition of the themes to settle themselves in my brain little by little, of their own accord; and the day when I felt I held enough cards to be able to try my luck with a real hope of success, I determined to pass to action, and did so.
Claude Monet
Science Of Energetics. Although the mechanical hypothesis just mentioned may be useful and interesting as a means of anticipating laws, and connecting the science of thermodynamics with that of ordinary mechanics, still it is to be remembered that the science of thermodynamics is by no means dependent for its certainty on that or any other hypothesis, having been now reduced, to a system of principles, or general facts, expressing strictly the results of experiment as to the relations between heat and motive power. In this point of view the laws of thermodynamics may be regarded as particular cases of more general laws, applicable to all such states of matter as constitute Energy, or the capacity to perform work, which more general laws form the basis of the science of energetics, - a science comprehending, as special branches, the theories of motion, heat, light, electricity, and all other physical phenomena.
William John Macquorn Rankine
Children are made to learn bits of Shakespeare by heart, with the result that ever after they associate him with pedantic boredom. If they could meet him in the flesh, full of jollity and ale, they would be astonished, and if they had never heard of him before they might be led by his jollity to see what he had written. But if at school they had been inoculated against him, they will never be able to enjoy him. The same sort of thing applies to music lessons. Human beings have certain capacities for spontaneous enjoyment, but moralists and pedants possess themselves of the apparatus of these enjoyments, and having extracted what they consider the poison of pleasure they leave them dreary and dismal and devoid of everything that gives them value. Shakespeare did not write with a view to boring school-children; he wrote with a view to delighting his audiences. If he does not give you delight, you had better ignore him.
Bertrand Russell