Leaderboard

Multiplication is a term with a very wide scope in both Mathematics and Physics, where it means (in both) Multiplication is a binary operation combining two mathematical objects or physical entities to produce a defined result according to stated rules. Binary means there are two participating objects or entities. That wide meaning gives rise to a whole host of uses or interpretations since it depends upon the objects or entities and the rules of combination and in some cases the order in which the operation(s) are carried out. In Mathematics we would expect the result of the multiplication to be another mathematical object In Physics we would expect the result to be another physical entity. The nature of the physical entity give rise to both the meaning and motiviation. But In Physics it is possible to have more than one result. For instance Force x Distance can result in a moment or energy, which are different physical entities. Does this help?

I recently read a very good book called "The Web of Belief" by W.V. Quine and J.S. Ullian. Its basically a compact introduction to rational belief and an entry point to areas of philosophy, methodology of science, and philosophy of language. Here are some excerpts from the section on the virtues of a hypothesis. I thought it would be beneficial to any aspiring scientist. There are five in all, but I don't have time to type them all up atm, so here are the first three. I will finish them up tomorrow. Virtue I: conservatism: In order to explain the happenings that we are inventing it [hypothesis] to explain, the hypothesis may have to conflict with some of our previous beliefs; but the fewer the better. Acceptance of a hypothesis is of course like acceptance of any belief in that it demands rejection of whatever conflicts with it. The less rejection of prior beliefes required, the more plausable the hyothesis--other things being equal. Often some hypothesis is available that conflicts with no prior beliefs. Thus we may attribute a click at the door to arrival of mail through the slot. Conservatism usually prevails in such a case; one is not apt to be tempted by a hypothesis that upsets prior beliefs when there is no need to resort to one. When the virtue of conservatism deserves notice, rather, is when something happens that cannot evidently be reconciled with our prior beliefs. There could be such a case when our friend the amateur magician tells us what card we have drawn. How did he do it? Perhaps by luck, once chance in fifty-two; but this conflicts with our reasonable belief, if all unstated, that he would not have volunteered a performance that depended on that kind of luck. Perhaps the cards were marked; but this conflicts with our belief that he had no access to them, being ours. Perhaps he resorted to telepathy or clairvoyance; but this would wreak havoc with our whole web of belief. The counsel of conservatism is the slight-of-hand. Conservatism is rather effortless on the whole, having inertia in its favor. But it is a sound strategy too, since at each step it sacrifices as little as possible of the evidential support, whatever that may have been, that our overall system of beliefs has hitherto been enjoying. The truth may indeed be radically remote from our present system of beliefs, so that we may need a long series of conservative steps to attain what may have been attained in one rash leap. The longer the leap, however, the more serious an angular error in the direction. For a leap in the dark, the likelihood of a happy landing is severely limited. Conservatism holds out the advantages of limited liability and a maximum of live options for each next move. Virtue II: modesty: One hypothesis is more modest than another if it is weaker in a logical sense; if it is implied by the other, without implying it. A hypothesis A is more modest than A and B as a joint hypothesis. Also, one hypothesis is more modest than another if it is more humdrum: that is, if the events that it assumes to have happened are of a more usual and familiar sort, hence more to be expected. Thus suppose a man rings our telephone and ends by apologizing for dialing the wrong number. We will guess that he slipped, rather than that he was a burgler checking to see if anyone was home. It is the more modest of the two hypotheses, butterfingers being rife. We could be wrong, for crime is rife too. But still the butterfingers hypothesis scores better on modesty than the burglar hypothesis, butterfingers being rifer. We habitually practice modesty, all unawares, when we identify recurrent objects. Unhesitatingly we recognize our car off there where we parked it, though it may have been towed away and another car of the same model may have happened to pull in at that spot. OUrs is the more modest hypothesis, because staying put is a more usual phenomenon than the alternative combination. It tends to be the counsel of modesty that the lazy little world is the likely world. We are to assume as little activity as will suffice to account for appearances. This is not all there is to modesty. It does nto apply to the preferred hypothesis in the telephone example, since Mr. Butterfingers is not assumed to be a less active man than the one who might have plotted burglary. Modesty figured there merely in keeping the assumptions down, rather than in actually assuming inactivity. In the example of the parked car, however, the modest hypothesis does expressly assume there to be less activity than otherwise. This is a policy that guides science as well as common sence. It is even erected into an explicit principle of mechanics under the name of the law of least action. Virtue III: simplicity: Where simplicity considerations become especially vivid is in drawing curves through plotted points on a graph. Consider the familiar practice of plotting measurements. Distance up the page represents altitude above sea level, for instance, and distance across the page represents the temperature of the boiling water. We plot our measurements on the graph, one dot for each pair. However many points we plot, there remain infinitely man curves that may be drawn through them. Whatever curve we draw represents our generalization from the data, our prediction of what bioling temperatures would be found at altitudes as the slimplest curve that passes through or reasonably close to all the plotted points. There is a premium on simplicity in any hypothesis, but the highest premium is on simplicity in the giant joint hypothesis that is science, or the particular science, as a whole. We cheerfully sacrifice simplicity of a part for greater simplicity o the whole when we see a way of doing so. Thus consider gravity. Heavy objects tend downward: here is an exceedingly simple hypothesis, or even a mere definition. However, we complicate matters by accepting rather the hypothesis that the heavy objects around us are slightly attracted also by one another, and by the neighboring mountains, and by the moon, and that all these competing forces detract slightly from the downward one. Newton prpounded this more complicated hypothesis even though, aside from tidal effects of the moon, he had no means of detecing the competing forces; for it meant a great gain in the simplicity of phyysics as a whole. His hypothesis of universal gravitation, which has each body attracting each in proportion to mass and inversely as the square of the distance, was what enabled him to make a single neat system of celestial and terrestrial mechanics. Another famous triumph of this kind was achieved by Count Rumford and later physicists when they showed how the relation of gas pressure to temperature could be accounted for by the impact of oscillating particles, for in this way they reduced the theory of gases to the geenral laws of motion. Such was the kinetic theory of gases. In order to achieve it they had to add the hypothesis, by no means a modest one, that gas consists of oscillating particles or molecules; but the addition is made up for, and much more, by the gain in simplicity accruing to physics as a whole. I will continue with the other two at a later time.

This is awesome. A picture of the dust cloud around a star 520 light years away. But better than that, there are signs that a planet is forming. Full story here: https://www.eso.org/public/news/eso2008/ Note that this is a real image, not a simulation or "artists impression"

"I am not sure what I am asking"

To paraphrase George Carlin, her thrust was to prick holes in the stiff front erected by the porn dealers.

Why does that matter? Most of them are very short-lived, so we could not use them anyway. But I think we do well with the neutrons, protons and electrons that persist. Because it's not a mechanical effect, i.e. it's not a force or interaction. However, it is an easily-derived consequence of c being invariant. It's not like relativity was fabricated from nothing. Models work if they match experimental results, and allow us to predict results before we do the experiment. Models describe behavior, not truth/reality. e.g. a phonon does not need to physically exist for it to be useful in describing nature. Don't make the mistake or reifying what is used in models as an argument against the model. The ultimate question is whether or not your (or anybody's) model matches what nature does. For the ones you have described that comprise mainstream physics, the answer is "yes, the model matches experiment"

It's a good thought, but I believe in this very thread we've had links showing that linear momentum is a source of gravitational attraction.

Venus orbits the same direction as all the other planets. But it spins on its own axis backwards, so it has one more day per year than its sidereal spin rate, as opposed to one less like all the other planets. Earth for instance experiences 365.25 days per year, but spins at a rate of about 366.25 times. Venus spins so slow that it goes around about once per Venus year, giving it just two days in its year.

I believe that in accordance with the third law of Hegel's dialectics ( development goes in a spiral), physics will somehow return to the ether as a medium for the propagation of interactions. Of course, not to the Lorentz model, but on a new level. Most likely, the term "ether" itself will be replaced with another one.However, this is already happening, because the vacuum in the modern sense is not a void.