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Go ahead. Invent your own language. Invent your own axioms. Do it all without a bit of advanced mathematics. Do it without studying what the current theories are. The word is 'particle', and this word does not mean a hard little billiard ball zipping around in space.

In the minds of crackpots and politicians, repeating something enough times does make it right.

Anything that travels at the speed of light does so to all observers. What travels at the speed of light? Massless particles. Massive particles cannot move at the speed of light. Electromagnetism, the strong force, and gravity all propagate at the speed of light per current theories. Electromagnetism and the strong force are mediated by the photon and the gluons. That the photon is massless is about as solid as science can get. That gluons are massless is not as strong but the evidence is very good. We don't know what gravity is yet (it is axiomatic right now). The hypothetical graviton should also be massless.

Maxwell's equations in vacuum have a simple solution: Travelling sinusoidal plane waves. The velocity of these waves are equal to the inverse of the square root of the product of the electrical permittivity and magnetic permeability of free space. Maxwell, seeing that this value was very close to the speed of light, conjectured that light is an electromagetic wave. The equations dictate the electromagnetic fields propagate at some invariant speed c. The velocities of neither the transmitter nor the receiver come into play; the velocity is invariant. This is the paradox. The only invariant velocity per the Galilean transform is an infinite velocity. The Lorentz transform was explicitly developed to find some representation scheme in which Maxwell's equations are invariant. Einstein's brilliance was not in the development of the Lorentz transform. That development preceded Einstein by several years. What Einstein did was to replace the ad-hoc nature of those developments with two simple hypotheses.

Very good summary, Atheist. The water rocket (or any rocket, for that matter) accelerates because it ejects mass at some non-zero velocity relative to the rocket. Conservation of momentum dictates a corresponding change in the velocity of the rocket. It's pretty simple, conceptually. Welcome to SFN, Christie. Do you want the answer, Atheist (this problem is one of my jobs), or do you want me to help others get to the answer?

FYI, the cubics are soluble by analytical means, proven in the sixteenth century. See http://en.wikipedia.org/wiki/Cubic_equation.

Do you know what proper distance is? Your usage implies that you think there is some absolute reference frame in which things are measured "properly".

Sorry for the confusion. I misread Farsight's question. The velocity of any object as measured by some observer does not exceed the speed of light. Period. It doesn't matter if the object or observer is accelerating.

Good. Why did you do that? You were asked for the growth rate in 2006, not the when the population becomes stable. (Hint: You know [math]t[/math]. There is no reason to solve for it.) With regard to 280=0: You got that by multiplying both sides of [math]280/(2t+5)^2=0[/math] by [math](2t+5)^2[/math]. The result, 280=0, means there are no finite zeros. The population growth rate curve has zeros at [math]t=\pm\infty[/math]. Correct, assuming [math]t[/math] is non-negative. Negative values of [math]t[/math] yield some interesting results. July 2002 ([math]t = -2.5[/math]) was one heck of a month in Mathville by that population model.

No typo. Try it. Zanket's "logic" shows a to be false. I don't buy any of Zanket's arguments. Both a and b are true. And the difference between this and an absolute reference frame are what?

Using Zanket's logic, a is false as well. His star-rod-ball concept gives an arbitrarity high velocity even if the rocket is not accelerating. Try it. Give Zanket's 2 million light year long rocket an initial velocity that makes possible to travel 2 million light years (Andromeda observer) in 28 years (crew time). This does not show either a or b are false. I showed that you are mixing frames. That both are a and b are true is a direct consequence of the second hypothesis of special relativity. Note that this is an unproven hypothesis; it is axiomatic in relativity theory. The kinds of mistakes both of you are making makes me think you have some concept of an absolute reference frame hidden in your logic somewhere.

Sorry for being rude, Zanket. You will not find a flaw in the heart of relativity, special or general. The theories has been examined by some a vast number of people over the last one hundred years. Instead of spending your energy trying to poke holes in some well-thought out theories, spend your energy pushing the boundaries of the theories. The theories do have problems at the centers of singularities, in that they lack a causal mechanism, and in that they don't mesh well with quantum mechanics.

I see that this "theory" has finally been moved to "Speculations". Arguing with you is pointless. Go to school, argue with your professors.

No. I am using well established theories backed up by observed facts. Objects cannot exceed the speed of light; none has been observed to do so. Your "theory" flies in the face of observations. Your paper has one thing right: The velocity of an object relative to some other object asymptotes to c. You yourself disprove your own theory. You are mixing frames again. The rocket can get to Andromeda in 28 years because, to the crew, the apparent distance to Andromeda has shrunk from 2 million light years to a bit less than 28 light years. Andromeda can traverse the rocket in 28 years because, to an observer in Andromeda, the rocket has shrunk in length from 2 million light years to a bit less than 28 light years. Length contraction works both ways. There is no preferred frame of reference. Of course there isn't any jerk in a uniform field. The field generated by a massive body is not uniform. The acceleration in such a field is not uniform. Your treasured equations do not apply in such a field. What value of a do you propose to use in these equations when the test particle changes its acceleration every step of the way on falling toward the star?

No we aren't. It takes a beam of light 0.3336 microseconds to traverse a spacecraft that is 100 meters long (your example). 0.3336 microseconds is quite measurable with modern instruments. I guarantee you that a ball (assuming it has some mass) takes longer than this to traverse the spacecraft in the frame of the crew. Believe it or not, this is not the best source in the world. It is a Classics Illustrated version of physics. It is correct, but there is little explanatory background. It is mostly a compendium of equations that can be easily be applied incorrectly. Take the equations of a relativistic rocket, for example. You misapplied the equations for a rocket undergoing constant acceleration here: Equations 12-21 in your paper only apply to a constant acceleration. They do not apply when jerk is present.

Help improve your paper? You have nothing but words, wrong words to boot. If you can't do the math you aren't doing physics. The math was done and done well 101 years ago.

No, you cannot. One can traverse what appears to be a great distance to some other observer. It does not look like a long distance to the traveler himself. The frame mixing is highlighted. You are computing velocity as distance as measured in one frame divided by time measured in another. This is standard SR, so you can look up the math yourself. You left out a rather critical line: The effect is challenging to measure on a spaceship the size of the Earth: It is small. I asked you to show me the math. You did not. You showed a theoretical result, and no math. You did not quantify those effects nor did you show that the effects are uncompensatable. As long as it runs at the same rate as all of the other clocks along the "known distance apart", which it will only when that distance is zero in the limit. What other clocks? I said "I only need one clock."

Can you not see the inconsistency in what you are saying? One way to measure the velocity is to note how much time passes when some object passes between two points that are a known distance apart. For example, the time of passage between (1) the ball crossing the tip of the rocket and (2) the ball crossing the tail of the rocket. If it takes an arbitrarily short time for this to occur, the ball's velocity can be arbitrarily high. Forget the star, forget the rod, make the ball a single point. You are making this overly complex and thereby not seeing your mistakes.

PhysicsForum (kooks are banned) and sciforums.com (kooks-a-plenty). BTW, what is it with the kooks coming out of the woodwork lately? SFN is being inundated with "my theory of the X" posts. It's enough to make those of the conspiracy-nut mindset think the Democrats added something to the water to enable a win last Tuesday.

You have done nothing of the sort. Einstein started with but two postulates; you agree with both of them. With math, he derived all of special relativity from nothing but those two postulates. You have nothing but words until you develop the math skills to find his error. Good luck.

The rocket does not move with respect to the crew. The rocket remains a constant length in the eyes of the crew. That’s even more basic SR. And it is the key piece of information that you are ignoring. You are mixing frames. The ball cannot traverse the rocket in an arbitrarily short period of time. Doing so violates SR, and you claim no bones with SR. The tip of the rocket can get to the ball and star in an arbitrarily short period of time because the distance to the star can be made arbitrarily small in the crew's frame by making the relative velocity approach that of light. Suppose the ball is even with the tip of the rocket. The key question, and the one you refuse to answer, is how much longer does it take for the ball to traverse the length of the rocket as observed in the crew's frame? Certainly it is more than h/c, no? Remember, the length of the rocket is not subject to length contraction. In other words, the speed of the ball as measured by the crew, is less than one meter per some tiny fraction of a second. It is not a hundred thousand light years per fraction of a second. The crew must use its own ruler to measure time and distance.

TIme-of-travel is not sufficient to explain the relativistic effects observed everyday by those working at particle accelerators. Your "theory" needs to explain the observed confirmations of relativity. The first two items in your summary agree word-for-word with Einstein's postulates. Everything else in SR falls out of those two postulates mathematically, including the lack of a preferred reference frame and how velocities combine. How is it that you differ from SR when you agree with the only two postulates of SR? You have a vague notion of relativistic velocities not adding, that paragraph about "perportionallity" (use a spell checker, please). SR has a very detailed mathematical description of why this happens. These effects predicted by SR have been observed. You will not be able to convince one single physicist of the veracity of your claims without a lot of math to back it up. That math must agree with what the existing set of confirmations of SR. Finally, your new "theory" had better disagree with SR somewhere, otherwise there is no reason for using your new theory. You need to identify some physically achievable experiment in which your new theory predicts a measurably different outcome than that predicted by SR. Use math. I have a hard time parsing your words.

Wrong. If the crew is travelling at light speed, the crew cannot measure ANYTHING. Things blow up at [math]v=c[/math]. In particular, [math]\gamma\to\infty \text{\ as\ } v\to c[/math]. Time and motion stop. The crew sees nothing. You are mixing frames when you say the stationary ball takes zero time to traverse the interior of the rocket as far as the crew are concerned. The apparent speed of the ball to the crew is 0/0, indeterminate. It is not infinite. Forget the crew travelling at c. What does the crew see as the velocity of the ball when some other observer measures their relative velocity as something less than the speed of light? I don't care if you make [math]\gamma = 10^1\text{\ or\ }10^{1000}[/math]. But please do answer my question in light of a finite [math]\gamma[/math]. You can even take the limit as [math]v\to c[/math]. Just don't make [math]v=c[/math] when doing that.

Farsight, (1) You are still mixing reference frames here, and (2) the crew cannot go at the speed of light. You, as an observer in some other frame, see the ball pass through the vehicle at c. The crew, moving at the speed of light, see nothing. They are frozen in time. There is no motion. For this crew, time and the ball freeze the instant the crew achieves light speed. Fortunately, the crew are not photons. They cannot go the speed of light. Let us examine the case where the crew is moving relative to the ball with all but the tiniest fraction of the speed of light. Assumptions: The ball passes directly through the rocket, from top to bottom, much to the dismay of the crew, The ball is quite small, thereby avoiding extreme damage to the vehicle and the crew, The vehicle has extremely precise collision sensors that record the times (crew clock, of course) when the ball punctures the tip and tail of the vehicle, and The vehicle measures 10 meters, tip-to-tail, in the crew frame. What is the difference between the recorded times of the tip and tail collision sensors for this event? My answer: about 33.4 nanoseconds. Anything shorter than that violates the second hypothesis of special relativity, the speed of light in vacuum is the same to all observers.