"Oh....... you like "embedded" better than "encompassed"???"
In the sense that you are now using it to denote a fundamental equivalence of predictive value--yes. If you now were to use "encompassed" in the way you've just used "embedded", I think it would be less accurate:
"to separate 2 theories emcompassing each other... ie. that aren't separate, but really simply the same thing in different stages of evolution, so to speak</b?"
I don't get you 'lens' analogy... but maybe that's just me?"
Yes, I see that. Perhaps this will help: Earlier in your post you made the statement, "you win". This demonstrates that you are viewing our discussion as a competition between people rather than as a test of ideas. This could be viewed as observing the interplay of our posts through different lenses of perception, I hope this helps.
"Einsteins THEORY IS MORE PRECISE in ALL circumstances"
NO. They are equivalent in all but extreme circumstances. Again, gravity is a fact regardless of how we call it, define it, or describe it. Neither Einstein or Newton has said the last word on it. They simply described how things move toward one another and they developed a means to calculate that movement that was predictive and reliable. The work of Einstein is not exhaustive by any means.
"What I’m going to do here (with a little math) is show that Einstein’s equation reduces to one of Newton’s. So Einstein’s theory is not a replacement for Newton’s, but just an extension. In other words, Einstein’s theory holds for the same phenomena that Newton’s does, plus some more. Newton’s laws still work, in the range that Newton and his followers tested them; Einstein’s work in that same range, plus more. If we’re interested in speeds much less than that of light, we can use Newton’s Laws – or we can use Einstein’s for those cases too.
One of the formulas, derived from Newton’s laws, that’s familiar to high school physics students, is the following: The energy of motion of an object (the amount of work required to move the object from rest to a certain velocity) is half the product of the object’s mass with the square of the object's velocity:
Ek = ½ mv2
Another one of Einstein’s results (and one of the things that makes Special Relativity so hard to understand) is that the mass of an object increases with velocity. The increase isn’t noticeable until the velocity is a large fraction of the speed of light, and the mass goes to infinity as the velocity approaches the speed of light. This is one reason why faster-than-light speeds are believed to be impossible. The equation:
m = mo/sqrt(1 - v2/c2)
where I am denoting the square root of 1 - v2/c2 by sqrt(1 - v2/c2), since I don’t have the square root symbol handy. What this tells us is that, given an object with mass mo at rest, the actual mass m increases with velocity in the manner shown. If the velocity is 5% of the speed of light (quite fast - over nine thousand miles a second), the denominator is sqrt(1 - 1/400) = sqrt(399/400) = 0.99875; m becomes 1.00125 times the rest mass. The mass increases by a little more than one tenth of one percent.
So you might think the mass never changes much. Wrong. If the velocity is half the speed of light, v/c is one half, the denominator is sqrt(1 - ¼) = sqrt(3/4) = .866 so that m becomes 1.1547 times the rest mass. The mass increases by about 15%. A velocity of 60% of the speed of light gives v/c of .6, the denominator is sqrt(1 - .36) = sqrt(.64) = .8, and m becomes 1.25 times the rest mass; this is an increase of 25%.
At 80% of the speed of light, v/c is .8, the denominator is sqrt(1 - .64) = sqrt(.36) = .6, and the mass increases by 67%.
If the velocity is 90% of the speed of light, the mass more than doubles - it is 2.294 times the rest mass. At 95%, the mass is 3.203 times the rest mass. At 99%, it is 7.089 times the rest mass. At 99.9%, it is 22.37 times the rest mass. At 99.99%, it is 70.71 times the rest mass. You can see that, when v = c, the denominator becomes zero – the mass goes to infinity.
Let’s do a little more algebra. Let’s use the binomial theorem, which says
(1 + x)n = 1 + nx to first order (for small x)
An example of this is 1.12 = (1 + .1)2 = 1.2 to first order. We know 1.12 = 1.21, so 1.2 is close.
Likewise, sqrt(1.1) = 1.11/2 = 1.05 to first order. We know sqrt(1.1) = 1.0488, so this is also close.
Now expand
1/sqrt(1 - v2/c2) = (1 - v2/c2) -1/2 = 1 + 1/2 v2/c2 to first order.
Then
m = mo/sqrt(1 - v2/c2) becomes
m = mo (1 + 1/2 v2/c2) or
m = mo + 1/2 mv2/c2
The mass has two components – the rest mass mo and a component due to the velocity. If we multiply by the speed of light squared, to get the energy, we get
E = mc2 = moc2 + 1/2 mv2
The two components of the energy are the rest energy, plus a velocity-related component. The latter is the same as Newton's prediction. So, for small velocities (relative to c, the speed of light), the energy = rest energy + 1/2 mv2, which is exactly what Newton derived."
home.earthlink.net
"So Newton used to be thought of as "UNIVERSAL" as YOU described it"
Newton's law of gravity has universal application. ALL objects attract each other with a force of gravitational attraction. This force of gravitational attraction is directly dependent upon the masses of both objects and inversely proportional to the square of the distance which separates their centers. This is true throughout the universe under all but extreme conditions. That is why our children are still educated and tutored regarding Newton's Law of Universal Gravitation. The what, the why, and the wherefore of gravity is irrelevant. There may, for instance, be "gravitons" or there may not. It may be solely the distortion of the "fabric" of space/time--or it may not. What matters is that this "force" or this "effect" may be calculated with reliability throughout our universe under normal conditions. It is predictive and verified. It is thus rightly called "UNIVERSAL". |
