Here is a thought experiment about a way to perhaps detect gravity waves.
All around the Earth at strategic points, attach transducers to solid bedrock. These transducers would output electrical waves in response to mechanical waves in the Earths crust, much like a seismometer. However, the...
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Please let me explain a bit more where I'm comming from.
Case 1.
As a ship is moving through space at say 0.9c, but is 'coasting' at steady velocity.
Here it seems clear that to me, that an Earthly observer would see.
t=t'[T]
Now assume the same scenario...
Hi
I thought I was done, but now I have a followup question.
Let [T] = Gamma
Usually, I see this
t=t' [T]
But since for an accelerating ship along the axis of flight
m=M[T]^3
It seems intuitive that perhaps
t=t' [T]^3
I got some answers from my spreadsheet that suggest this...
For all newcomers to this thread, the two equations that I derived and posted previously are incorrect. Please accept my apology for those errors.
Thanks to jtbell, whom I think first had the insight into exactly what my problem was.
After additional study and some computer experiments...
I got that point long ago, as you have so often pointed out.
I'm searching for a computer validation of "any" function that works. Its not about who is right or wrong.
If the function, which you offered is proven, I'll admit that and perhaps discuss the reason(s) why it turned out to be...
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I took the existing spreadsheet and changed the relativistic mass multiplier from [T] to [T]^3. (third-power). With that computation made on some 30,000 intervals for t, the total time sum jumps to a very large value of 7,967.1 days (86,400 seconds/ day). The arc...
Re; JTBell Post
You cannot use this in F = ma when the force is parallel to the direction of motion. It works only when the force is perpendicular to the direction of motion. You need to use instead, which is m = M[T]3 in your notation.
(End quote)
Assume a rocket under propulsion in the...
Computer spreadsheet solutions track the derived inverse sine function output for time over the entire velocity curve from start to 99.9% of light speed. The difference of both solutions is within 0.0234%, for all points on the velocity curve.
I’m offering a gentle challenge for someone to...
After some digging in my old calculus book, I was able to directly integrate the desired function by trigonometric substitution. Consult the attached .jpg image for details. Please excuse the hand writing. Thanks
Revised Derivation
The original posting was correct, however it needed some refinement. Notations and extra steps have been added for clarity. In the mean time, the integration by form from CRC tables has been proven. This was done by differentiating the function back to the original...
Thanks for your feedback. I have made a considerable effort to prove the formulas offered by both you and Janus. However, I can't replicate the computation results of those formulas with a computer. Basically, it should be a matter of integrating simple physics relationships over time...
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Derivations that my friend and I provided have been revisited and thoroughly checked. The integration solution, by form from a CRC table, was differentiated and the result was then compared with the integral from which it was derived. As a result of this recheck...
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In your equations, the acceleration (A) is held constant. But in my example, the force (F) is held constant while acceleration is permitted to decline over a relativistic curve. I think that this could be a critical difference.
Two equations below are the...