y_feldblum

If one can travel 1m to the right and 1m forward, one comes to a position 1.717...m away from where one starts. The ancient Greeks took one look at this and gave up with mathematics. It took two millennia for mathematics to pick back up with the inclusion of polynomial roots, transcendentals, and complex numbers into the mathematician's toolchest. Quantum tunneling is based on the notion of a "probability cloud" where a particle's position is a continuous probability distribution over an unbounded region of space.

Zeno's Paradox itself never referred to the universe as discrete. Your resolution does. I am completely baffled how a view of the universe as discrete can avoid requiring a privileged coordinate system. Tunneling and instantaneous teleportation are vastly different phenomena with vastly different properties. One of them is real and one of them isn't. Attempting to resolve Zeno's Paradox by reference to quantum tunneling does not help in the slightest, because quantum tunneling assumes a continuous universe.

First, on Newtonian and Einsteinian physics, location is not absolute. It is a meaningless statement that "this object is here, in an absolute sense." Location is not a property of the universe or of entities as such. Instead, it is a relationship among entities, and it must not be reified. Second, it is clear from all observations that entities move continuously. Anything else would require instantaneous teleportation.

Our mathematical understanding of the world is correct. The fact that, when you depressed buttons with letters on them, corresponding letters showed up on a screen is living proof. The runner does in fact occupy an infinite number of positions, and occupies each position for a quantity of exactly zero time, in moving from the start to the finish. The runner is not moving discontinuously; he is moving continuously. Zeno's paradox states that, given a certain understanding of motion, motion is impossible. Well, we do not use that understanding of motion. We use a better, accurate one, immune to Zeno's paradox, and we have Newton and Leibniz to thank for it.

Caveat: I have a good understanding of the motivation for, the math of, and the philosophy behind (an objective interpretation of) special relativity; and an OK understanding of general relativity. I know very little about quantum mechanics or the Standard Model of elementary particles, but enough to speak a little on the topic. There is no such existent as a "gravitational field," "electric field," or "magnetic field." Fields are mathematical abstractions from forces due to physical interaction. The gravitational force of one body on another is carried by gravitons emitted by one body traveling to and interacting with the other. Likewise with the electric and magnetic forces and photons. The interaction of the magnetic force is far more complicated than the interaction of the electric force, which is why the simple weathervane experiment applies to the electric force but not the magnetic force. "why would the gravitons only be emitted on the opposite side of the moon?" They are not. The mathematics is complicated wrt forces and fields and surfaces enclosing volumes of various shapes, of course. "So, by observation, we know that something must be going on in between, say, the earth and the moon leading to gravitation" That does not follow. We know, by observation, that the earth acts on the moon via some mechanism or other. We have investigated and determined that a particle called the graviton, which travels between the two, is responsible for this interaction. But it does not follow that there is something "going on in between." Dark matter and dark energy are matter and energy for whose existence there is indirect evidence, but which cannot be directly observed by ordinary means. The indirect evidence includes, for example, the fact that the gravitational effect which a certain quantity of matter at a certain location would exhibit is in fact exhibited, but we currently have no means of seeing this matter more directly. Physicists suspect the existence of vast quantities of matter because there is indirect evidence for it and it would easily explain many things, and so now physicists are looking for this matter, and are looking for new techniques of finding it. It cannot be seen, with current methods; it is therefore called "dark".

My question is: what observations of reality lead ultimately to the conclusion of the universe as full plenum. So far the argument for that conclusion has been: it is necessary because denying it amounts to claiming that there exists a thing, "nothing", which is not anything but which nevertheless is. But that is not sufficient. Objectivism does not begin with "Existence exists. Now let me go out and observe it." Quite the opposite. Objectivism begins with "all this that I see ... is." Every philosophical conclusion must be reducible to observation of reality. What observations of reality give rise to this particular conclusion?

The Standard Model lists numerous elementary or subatomic particles (some of which are composed of others) which have been discovered, and predicts others which have yet to be discovered (and which occur only in very unusual circumstances, such as in proximity to extraordinarily large quantities of energy). These, which include electrons, protons, neutrons, and photons, and gravitons, are the basic primary substances making up everything that there is which we have to date observed (leaving "dark matter" aside). All matter and all interactions among pieces of matter are explained through the elementary particles of the Standard Model.

What of the case of a "patch" where no matter whatever has been detected. For example, no light originates from that patch, and casting various particles into that patch elicits no phenomena indicating any kind of interaction between those particles and anything that might be in that patch? Physicists have been looking for just this kind of matter for centuries, but have so far been unable to discover it by means of observation, whether direct or indirect. I do not understand the philosophical argument against saying "there isn't anything over here." It sounds like one is simply reifying space and reifying the void. When you say "one could [...] say that existence does not exist inside the box", you are neither using the definition "the sum total including everything that exists" nor using the definition "the property of an entity whereby that entity is instead of is not." Neither is applicable, and neither makes sense in the context. What do you mean by that statement?

Thomas, the part about fields is correct. A field is a double abstraction from actual physical forces. One might say that the Earth exerts a specific quantity of force f on the Moon, which is a certain distance d away from the Earth and is of a certain mass m. If one abstracts away from the specific distance and the specific mass, the concept is a field: the Earth will exert some force on an object given its distance away from the Earth - but omitting the the particular distance - and given its mass - but omitting the particular mass. The field is a very powerful mathematical tool. Whereas to describe a force exerted by one gravitating body on another, one had first to describe each body and the distance between them, to describe a field exerted by one gravitating body, one need only consider that gravitating body. In essence, the tool allows the physicist to abstract away from the second body and to focus only on the first body alone. The physicist can analyze the shape of a body and in a first step decode its impact on the field the body exerts, keeping in mind that the field is a mathematical abstraction and not actual stuff, and then in a second step decode how the shape of the field exerts actual, physical forces on other bodies of whatever mass they are and in whatever location they are; without fields, the calculations of the actual forces would be made more far complicated. Einstein observed that objects under the influence of gravity are always in free fall if there is nothing obstructing the effects of gravity. Such objects under the influence of gravity do not feel the influence of gravity. They do not feel force; neither do they feel acceleration. Falling feels exactly like not moving at all, or moving in a straight line without accelerating - even though, clearly, that is not the impression one gets from observing another person falling. (This is an observed fact.) Einstein went for the conclusion that falling is moving in a straight line through spacetime. The way to explain this conclusion, according to Einstein, is to consider space as curved (in a highly mathematical sense - not in the sense of an object being curved) wherever there is mass. Is his conclusion correct? It is extremely odd, to say the least. However, his general theory follows from accepting the observation that free fall feels like constant motion and going to the conclusion that free fall is constant motion, in accordance with observation.

That is how sense-perception works. A single full property of an entity is broken down into its component parts, which are more easily perceived. This approach is accurate to whatever degree any animal requires. You see redness and you feel hotness; you do not see or feel both at once. The length of a spacetime interval, by the way, is exactly how long it takes to traverse it. It can be measured directly with a clock and a transportation device capable of accelerating, steering, and keeping up a life support system. Or, we may send particles which tend to undergo decay along a spacetime interval and count how many decayed in transit.

It is a question of metaphysics. I have seen it asserted a few times that materially "the universe is a full plenum." The meaning often given is: "there is no such thing as a vacuum; there is something everywhere." It is generally asserted that philosophy justifies and mandates this conclusion. This conclusion is typically leveled at the conclusion from the Michaelson-Morley experiment that there does not exist an aether. I am curious, what is the proof of the conclusion that "the universe is a full plenum?"

Extent and duration are components of timelength and so are perceived independently. Extent in the forward direction and extent in the right direction are, likewise, components of distance and so are perceived independently. A single displacement (directed distance) may be specified by "3 steps forward and four steps right", if one is facing a certain way, and "five steps right" if one is facing another way.

The very existence of the IMF is collectivist/statist in nature. The promised reward for which the IMF is demanding "free market reform" is collectivist/statist in nature. The means of accomplishing said "free market reform" are collectivist/statist in nature. Everything the IMF/World Bank is and does is dictatorial socialism beneath a veneer of freedom. What more evidence is necessary?

I have seen people here state that "the universe is a plenum" from time to time. I have never fully understood what was meant by this statement, and I have never seen a full philosophical justification for it. What does "the universe is a plenum" mean? What is the evidence of the senses which supports this statement? What is the philosophical justification, stemming from the evidence of the senses, for this statement?

The point was that there is a single root point of difference between the mathematical framework of Newtonian physics and the framework of Einsteinian physics. The single root point of difference is in whether time and space (i.e., extents and durations) are to be treated mathematically as fundamentally distinct or as fundamentally similar and integrated. From all the evidence available, the mathematical framework of Einsteinian physics is correct and true, while the framework of Newtonian physics is a very close approximation under the conditions considered normal at the time of its development. The difference between these two frameworks in the field is due solely and entirely to the single root point of difference identified above. The implication is: the single root point of difference between the mathematical frameworks must be abstracted to become the single root point of difference between the philosophical justifications. In other words, Newton's mathematical framework treated time and space as fundamentally distinct: so too did his philosophical framework; Einstein's mathematical framework treats time and space as fundamentally similar and integrated: so too does his philosophical framework. Einstein's philosophical framework, which treats time and space as fundamentally similar and integrated, is justified ultimately by the evidence of the senses.

There is. Not a priori, of course. But when one understands that Newtonian physics treats time as completely separable from the three dimensions of space while Einsteinian physics treats time and the three dimensions of space as four dimensions, and that Einsteinian physics more accurately describes observed phenomena and more accurately predicts phenomena than does Newtonian physics because Einsteinian physics treats time and space as four dimensions (that is the root difference and, fundamentally, the only difference between the two theories), one is led to the conclusion that the treatment of time and space as four dimensions is justified and mandated philosophically. Length does not contract and time does not dilate. The measurement of length and the measurement of time depend on the velocity relationship between observer and observed, but the combination of length and time ("timelength" taken as a whole) does not depend on the velocity relationship between observer and observed, because it is a "whole" property (as opposed to length and time taken individually, which are component parts of timelength). The math does not state that entities depend on how fast they are going. The math states that entities are what they are, that a ruler of length 4in will always be of length 4in, that a trip of duration 1yr will always have duration 1yr.

A previous post explains that the Lorentz equations are very analogous to the equations modeling rotation about an angle. In fact, that is not exactly true: the Lorentz equations can be immediately derived from the much simpler equations which are the equations of rotation about a hyperbolic angle (which are very similar to the equations of rotation about an angle). That is not to say that rotation is a good physical explanation of the Lorentz transformation. Contrary to certain popularizations, it does not assert that entities actually change length, duration, or mass simply by changing velocity with respect to another entity - it asserts that partial observations of interrelated aspects of an entity depend on the relationship between entity and observer, but full observations of the actual properties of an entity do not so depend, as philosophically expected. Moreover, it is a very simple theory and does not assume into existence any new entities, thus abiding by Occam's Razor. By contrast, any and every aether theory proposed sports a distinct lack of physical evidence - while assuming into existence new entities, namely, the aether.

The Lorentz equations are known to hold experimentally, independently of the principle of relativity (Galileo's, Newton's, or Einstein's).

http://ageofhooper.blogspot.com/2008/04/ro...us-capitol.html That's why not.

They often purchase oil futures years in advance.

The principle of relativity (going back to Galileo) states that the motions of and interactions among bodies remain independent of the bodies' locations and velocities with respect to yet other bodies, because there is no causal connection between these other bodies and the moving and interacting bodies in question. It is a very good natural explanation.

CF, on the one hand, to date there has never been physical evidence found for an ether. On the other hand, of the many theories of an ether that have been offered, they have generally all been disproven: the results which these theories predicted simply did not accord with the results of experiments designed to test these theories. Tensorman, the nonsense is in stating that an object moving faster gets heavier, etc. It is not so. The observed mass of an object gets larger as the object moves faster with respect to the observer. That is because mass is not an independent, self-contained property of an entity. However, there is a certain combination of observed mass, velocity, and energy which is an independent, self-contained property of an entity. This combination is given the name momenergy (or momentum-energy or 4-momentum). The particular mass observed depends on the relationship between observer and observed; the particular momenergy observed is independent of the relationship between observer and observed, because it is an existential property of the observed. Mass observed depends on the momenergy of the observed and the relationship between observer and observed. (The same principle is true of the combination of time, space, and velocity.) Yes, it is true that two objects which take different paths from A to B (to events, separated by time interval and space interval) will have different lengths, and the length of a path is the proper time interval of an object moving along that path. But the clock of an object moving along one path rather than another does not change. One path is simply shorter than the other. "Paradoxically," the curved path is shorter, so the grandfather accelerating and decelerating in his spaceship will travel a shorter path through space and time than his grandchild taking a nonaccelerating path through space and time, at rest on earth. Traveling a shorter path takes the traveler less time, so he ages less. This fact arises from the mathematical relationship between space and time.

Me for one. Yes, but for me it is primarily philosophical. MM is corroborating evidence. MM is: "given the expected properties of the ether which current theories predict, we performed experiments designed to detect these expected properties, but no evidence of these expected properties could be found." That does not suggest that there is an ether. Neither do the Lorentz equations suggest that there is an ether. The Lorentz transformation requires a physical explanation - it is itself not a physical explanation - but it does not itself suggest the existence of an ether. The "everything is relative" theory begins with Galileo and continues with Newton. It is a phenomenally objective and sound theory with vast quantities of evidence to back it. F = m A hinges entirely on "everything is relative."

Quantum mechanics answers this: gravitons sent from a mass interact with other masses, and photons from moving charges interact with other moving charges to induce the various effects of electromagnetism.

The mathematical equations used in relativity to describe the fact that two observers moving at different speeds see different phenomena are almost exactly identical to the mathematical equations used to describe the fact that two observers looking in different directions see different phenomena. We all know that when two observers look in different directions, they see the same actual phenomena, although they may measure the component parts of the actual phenomena differently. For example, one person may say "the Starbucks is one block forward" while another person standing in the same spot but facing a different directio may say "the Starbucks is one block to my right." The standard interpretation of relativity - the one you learn when you study relativity at anything beyond a 101 level - says that we should treat space and time as interrelated in the same way that we treat forwardness and rightness as interrelated. As you turn to your left, that which was forward becomes that which is to your right. As you speed up, space and time are interrelated in a similar way. The reason for this interpretation is that the equations describing turning about an angle are almost identical to the equations describing speeding up. The next time you hear "objects get shorter and heavier when they go faster and their clocks slow down", understand that it's nonsense and is nothing at all like what the standard interpretation of relativity states. It is the naive interpretation of the Lorentz transformation, but of course that is only the naive interpretation, and the Lorentz transformation predates relativity theory, which gave the foundation for a vastly different interpretation: that speeding up is a kind of analog of turning about an angle. The standard interpretation says that as an observer's speed relative to the observed changes, he will measure changes in various interrelated quantities such that the combined sum of these quantities remains the same. The measures of the various interrelated quantities are, taken separately, affected by the speed relationship between observer and observed. But the actual physical quantities involved can always be calculated from the measures of the various interrelated quantities. The matter is analogous to observing an object through a magnifying glass: the measure of the object's size changes, but we know there is a magnifying glass in the way, so given the object's measured size and given certain information about the magnifying glass, we can always calculate the object's actual size.