phyti

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eric 5; A definition: The measurement of 'time' is matching world events to clock events (reference events). This provides a means of ordering and comparison for human purposes, similar to measuring lengths, etc. Therefore to qualify, a clock must be a source of periodic uniform events, sun, moon, pendulum, cesium atom, etc., depending on the precision needed. For an explanation of time dilation, refer to http://wizdum.awardspace.info For experimental evidence search the internet for 'muon time dilation'.

asprung; ---- Forget 'time is passing', and think 'events are happening throughout the universe'. The rate of activity for the traveler in his spacecan, his clock, and everything that moves with him is slower because of his motion. Why, because all interactions at the atomic, molecular, and biological level are mediated by em/light exchange, and the speed of light propagation in space/vacuum is constant. When he reads the slow running clock, his slow running memory can't detect it. Similar to 'length contraction',...if his spacecan did shrink 50%, he couldn't tell with his measuring rod which is 50% shorter. It's a matter of scaling, the difference being the clock events (ticks) are fewer and farther apart. If his clock intervals are longer, and he sees the same number of events happening in the outside world, then his clock intervals contain more events than those of his earth-twin. The same number of events happen for both, the traveller just partitions his 'time' into bigger pieces. Both persons remain in the 'now' world because there is no where else to be!

Complex analysis is a more recent concept. As stated, subtraction is not presented as a complex operation. Think of j as i^2.

When numbers are directed (pos and neg, relative to zero), they are treated as vector. Historically they were not viewed as such, and a makeshift rule was used, "the product is pos if like signs and neg if unlike signs". Technically the neg number was the first use of a complex number. In that context, j is a 180 deg rotation, so jx = -x, and j(-x) = x. Eg. (-x)^2 = (jx)^2 = j^2(x^2) = x^2.

My quote: "However your reference frame, which includes you and the mirror," does not imply they are moving with respect to each other. "Remember light speed is independent of the source" This is the principle of constant light speed (in vacuum) from SR. The light is moving and therefore not part of the reference frame of the boy. The constant speed for any observer is the result of the constant speed and time dilation. This can be demonstrated in a simple light clock. No one gets ahead or behind anyone else relative to time. Time does not accelerate or decelerate, moving clocks just parse it into different length intervals.

Any motion alters the process of light serving as a messenger. As he moves faster, the light takes longer to reach the mirror. Remember light speed is independent of the source, so light is chasing a moving target. However your reference frame, which includes you and the mirror, are effected by time dilation. At the particle level the light is also chasing moving targets, thus the biological functions, neurons, etc. are effected. Time does not slow down but the activity does and you are not aware of this. Only observers not in your ref. frame notice this. Think of it like length contraction. If your spacehip contracted to 1/2 length. everything in it would also contract to 1/2 length including your ruler. When you measured the length of the ship you would not detect a change from its design length. When you time a light signal to the mirror and back, you use a shorter time (unknowingly) to calculate the distance. Now the distance is also shorter by the same factor. When you divide the short distance by the short time, you get c, the speed of light. From your perspective everthing seems normal. Ultimately whatever clock sytem you use, at light speed a clock cycle cannot be completed, therefore it is indeterminate.

All knowledge is by definition, which would include math. The root of the problem/disagreement is the concept of infinity. The integers/(natural numbers) and rationals, have a constant value, and they can be formed in a finite number of steps. The irrational numbers are formed by an infinite process which can never be completed. The integers and rationals can be constructed and correspond to real world objects because they are discrete models. The irrationals cannot be constructed because they are continuous. The representation '.9...' can be defined as '=1' but that doe not make it '=1'. It has to be defined as '1' to make it work, because the process cannot do it. It really is a variable by definition, it approaches 1 in the limit. Note it only equals 1 when it reaches 1. Irrationals are beneficial in the analysis of complex problems. Their value as an analytic method is not in question. The continuous process issue is not confined to irrationals but all concepts that depend on it. Pi is a good example. No one knows what the millionth decimal is until it is constructed. All applications use an approximation because no one can wait for the theoretical/ideal value. For a wagon wheel 3.1 is sufficient. For a ball bearing 3.1416 is sufficient. The precision depends on the purpose, but in each case a different value is used. The ideal value of pi is never used because it can never be known. For some the leap from the finite to the infinite does not need justification. The mind does not experience anything infinite, so it imagines what it could be. In simplistic fashion it extrapolates the properties and processes of the finite to the infinite. Eg. we can list a finite set of objects, but can we list an infinite set? Eg. we can count a finite set of objects, but can we count an infinite set? The objection is the assertion without proof that the irrationals, transcendentals, etc. exist, even as mental constructs. The result, as the limit of an infinite process, exists only if the process is completed. This is the failure point and not a proof. The mind has no experience of the infinite therefore it has no basis for a concept of an object or a process.These objects can only exist as approximations and not absolute values or constants (a misnomer). The step from finite to infinite is as great as the step from 0 to 1.

10^k=(9+1)^k expand this into 9^k+...+1^k all the terms are divisible by 3 except the last hope that helps

When Klaynos listed 3 ref frames it got clearer. That's why someone else looking from a distance sees the things that are right under your nose. Thanks

SR implies (or is interpreted as) the space contraction and time dilation depends on the relative velocity of the two reference frames. B moves at .6 c relative to A. B sees objects of known dimensions passing in the opposite direction appearing contracted to .8 their length. A accelerates to .2 c in the direction opposite of B. The relative speed of separation is now approximately .8 c. This would require the contraction B sees to be approximately .6 c. The objects moving past B do not speed up when A moves. How do you explain this?

When you observe a star, you are aware that what you perceive happened in the past some light years ago. Extending this reasoning to closer objects, the light from the sun takes a few minutes, the chair across the room takes a few nanoseconds. The zero reference time ends in your mind. This would imply that we really live in the past. Now is a fictitious concept with no correspondence in the real world. Time is a mental construct to order events and measure the amount of activity/change in the world. The concept future can only be possible outcomes for human activity. The future of inanimate matter on its own is limited by the laws that govern it. Animals are essentially programmed to a repetitive life style. The human is unique because we have free will and can act contrary to natural laws and form alternate histories, i.e. the future is not a predetermined 'place', its a process. We may predict an event only if our theory is correct, but verification(knowledge) is always historical (after the fact). A key requirement for the concept of time to work is memory.