Neddy Bate
Valued Senior Member
So. Have we figured out whether SR is correct, or whether Mike_Fontenot is correct? I prefer the one without the 'Absurdities', but what do I know
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I can perhaps help if I know what you're trying to achieve.
I made a mistake as well in the graphs of post 292. I switched the labels on the axes of all the pictures. Time should be horizontal (the way you do it), and X vertical. Too much habit doing it the other way.I now know that to be wrong.
No, that equation was (incorrectly) used to compute the velocity relative to S after time t in S.The bottom curve on my plot of the initial inertial observers' view of the position of the trailing rocket t is given by the equation
X = tanh(A*t).
All the correct equations can be found at https://en.wikipedia.org/wiki/Hyperbolic_motion_(relativity), which I posted in 294.I want see what the corrected curve is, and I want to know the equation of that new curve, and how the equation is derived.
In the accelerating frame of the rocket, the rocket is by definition stationary at all times and has traveled nowhere, but the launchpad recedes from the rocket over proper time tau.Also, if we replace "t" with "tau" in the above equation, does that give the view of the people on the trailing rocket about how far they have traveled from the initial inertial observers?
Not sure where -0.9497 came from. The speed of the launchpad in S' should be -0.9487All these numbers come from post 292.
Position of launchpad at time 0 in S' : 2.162
Speed of launchpad in S' at any time: -0.9497
Current position of launchpad in S' at τ=1.8184: 2.162 - 3*0.9497 = -0.687
// Compute distance to lauchpad from ship frame at ship time tau
#include <stdio.h>
#include <math.h>
#define ITTERS 36 // itterations
#define STEP 0.05
int main()
{
int itter;
double ctime; // Coordinate time of inertial frame
double tau = STEP; // Proper time of ship
double pos; // Computed position of ship in S
double lpad; // Computed position of lauchpad relative to ship
double vel; // Relative velocity between pad and ship
puts(" tau ctime S pos launchpad v gamma");
for (itter = ITTERS; itter-- >= 0; tau += STEP) {
ctime = sinh(tau); // coordinate time
vel = tanh(tau); // speed as a function of proper time
pos = cosh(tau) - 1.; // distance traveled by ship
lpad = pos - ctime*vel;
printf("%.4f %.4f %.5f %.5f %.5f %7.4f\n",
tau, ctime, pos, lpad, vel, 1 / sqrt(1 - vel*vel));
}
}
tau ctime S pos launchpad v gamma
0.0500 0.0500 0.00125 -0.00125 0.04996 1.0013
0.1000 0.1002 0.00500 -0.00498 0.09967 1.0050
0.1500 0.1506 0.01127 -0.01115 0.14889 1.0113
0.2000 0.2013 0.02007 -0.01967 0.19738 1.0201
0.2500 0.2526 0.03141 -0.03046 0.24492 1.0314
0.3000 0.3045 0.04534 -0.04337 0.29131 1.0453
0.3500 0.3572 0.06188 -0.05827 0.33638 1.0619
0.4000 0.4108 0.08107 -0.07499 0.37995 1.0811
0.4500 0.4653 0.10297 -0.09336 0.42190 1.1030
0.5000 0.5211 0.12763 -0.11318 0.46212 1.1276
0.5500 0.5782 0.15510 -0.13428 0.50052 1.1551
0.6000 0.6367 0.18547 -0.15645 0.53705 1.1855
0.6500 0.6967 0.21879 -0.17952 0.57167 1.2188
0.7000 0.7586 0.25517 -0.20329 0.60437 1.2552
0.7500 0.8223 0.29468 -0.22761 0.63515 1.2947
0.8000 0.8881 0.33743 -0.25230 0.66404 1.3374
0.8500 0.9561 0.38353 -0.27721 0.69107 1.3835
0.9000 1.0265 0.43309 -0.30221 0.71630 1.4331
0.9500 1.0995 0.48623 -0.32715 0.73978 1.4862
1.0000 1.1752 0.54308 -0.35195 0.76159 1.5431
1.0500 1.2539 0.60379 -0.37648 0.78181 1.6038
1.1000 1.3356 0.66852 -0.40067 0.80050 1.6685
1.1500 1.4208 0.73741 -0.42443 0.81775 1.7374
1.2000 1.5095 0.81066 -0.44771 0.83365 1.8107
1.2500 1.6019 0.88842 -0.47046 0.84828 1.8884
1.3000 1.6984 0.97091 -0.49262 0.86172 1.9709
1.3500 1.7991 1.05833 -0.51417 0.87405 2.0583
1.4000 1.9043 1.15090 -0.53508 0.88535 2.1509
1.4500 2.0143 1.24884 -0.55533 0.89569 2.2488
1.5000 2.1293 1.35241 -0.57490 0.90515 2.3524
1.5500 2.2496 1.46186 -0.59380 0.91379 2.4619
1.6000 2.3756 1.57746 -0.61202 0.92167 2.5775
1.6500 2.5075 1.69951 -0.62956 0.92886 2.6995
1.7000 2.6456 1.82832 -0.64643 0.93541 2.8283
1.7500 2.7904 1.96419 -0.66264 0.94138 2.9642
1.8000 2.9422 2.10747 -0.67820 0.94681 3.1075
1.8500 3.1013 2.25853 -0.69311 0.95175 3.2585
I wrote something to plot distance to lauchpad relative to the ever-changing CMIF of the rocket, as a function of ship time tau
What absurdity exactly does this lead to? I'm not sure what you consider absurd. It it that the rocket accelerating away should be far away after quite some time, but also that it has 'come back' so to speak? Or is there a different thing you find absurd?Much later, the rear rocket (with Harry) gets to Tom. At that instant, Tom knows that the front rocket is VERY far away from him, and the speeds are VERY large, and gamma is VERY large. Tom knows the length contraction equation (LCE) of special relativity, and so he knows that, in HIS frame, the two rockets are now separated by the distance L/gamma. That means that the leading rocket, and the trailing rocket, and Tom, are all essentially at the same place. And it means that the front rocket, which was previously very far away from Tom, has backed up to Tom, even though its rocket has been pointed away from Tom the whole time, with its rocket blazing. Clearly, that is an absurd situation. So we must reject the contention that the lowest curve should be according to the people on the rockets, because it leads to an absurdity.
Because the CMIF picture is that of an inertial frame (which is what the CMIF part stands for). It being an inertial frame, inertial (unaccelerating) things like the green launchpad line are straight lines.Sorry, I couldn't follow what you are doing. Why wouldn't the CMIF results be exactly the same as the "tau" (accelerating) results?
They do. That's how I generated post 306. Each data point was calculated in a different CMIF frame. The rocket is always at location zero in any of those frames at the time in which it is stationary in that particular frame. I didn't bother to draw a picture plotting the launchpad curve. No point in plotting the rocket since it follows the time axis.I would think the collection of CMIF results at each instant precisely give the "tau" (accelerating) results.
It is relative to the accelerating frame of the rocket and has nothing to do with the choices of the people on the rocket. They're quite free to choose frames other than that of the rocket. I never use people's choices as a frame specification since nothing in theory of relativity obligates what they should be.Assuming you correctly get the curve according to the people on the rocket
Don't agree with the logic, but I do agree that the curve in question does not depict motion relative to any rocket.That seems to imply that the curve you're starting with (which is the curve we've been discussing for the last month) can't be the view of the people on the rocket.
OK, by switching signs you're saying that the rocket is accelerating in the negative direction and leaving the lauchpad behind in a positive displacement from the rocket. That can be done, but inconsistent with the story up until now where we had the lone rocket accelerating forward in the +x direction.I THINK your computations say that at tau = 1.0, the distance of the curve above the horizontal axis is 0.35195.
OK, it fits on the graph better that way. So the launchpad is above the rocket, not below it.(I've switched the sign on your result, so I can plot it on my previous plot with the initial inertial observer view).
Yes, we noted your unconventional habit of putting t horizontal. I expected this, and have tried to use this convention in my latest post where the one picture (of the CMIF S') did exactly that. I never drew a picture of the rocket PoV since it is confusing. For instance, the time axis only works at x=0 and at different x values, time scales differently, so a clock stationary at x=5 would not be in sync with the clock at x=0. There might be discontinuities in worldlines, stuff like that. Such is the nature of attempts to draw non-inertial frames. You rarely seem them drawn on physics sites, but you requested the data.But I plotted your value of 0.35195 at the horizontal location 1.0 on my old chart
What curve are we talking about? The column labeled S-pos? That curve is the location of the rocket relative to S, an inertial frame, not something relative to the rocket. The curve relative to the rocket is the launchpad curve, the only object that moves in the rocket frame.which is the "t" value there ... maybe I should be converting your tau value to the corresponding "t" value, and plotting that. OR, maybe I just need to not try to compare the two curves in a quantitative way, but rather just in a qualitative way. They definitely look like they both have essentially the same shape.
That's why I don't worry about what your inertial observers say. They're morons. I just graph where the rocket is relative to S and let the observers delude themselves if they choose.But despite all that, I THINK when I take your curve, and then ask the question "What does the initial inertial observer say about that curve", he will get the same absurd result that I have described.
Don't they now... They look pretty weird right out of the gate to me.One other comment: The weird things that happen that I have described don't show up until gamma is very large.
Your story, not mine. Answer the questions if you have any faith at all in this assertion.So you need to extend your computations to larger tau to get to large gamma ... that's when the rocket will start moving back toward the initial inertial observer, according to the initial inertial observer (even though it's still pointing away from him, and still thrusting).
Full denial of physics texts. Where in the text does T&W say that the first equation is an assumption?Taylor and Wheeler assumed that
...
I now believe that they were incorrect in that assumption
You only asserted that you found something absurd. No specific absurdity was described, so your statement above is pretty empty.it leads to the absurd result that I have described in my post #305
Why hasn't this topic been long ago moved to Alternate Theories with all the other denialists?Have we figured out whether SR is correct
This is a old and repeated quote which I present as evidence that being in the presence of a rocket that literally vanishes and appears a finite distance away constitutes an absurd situation.she WOULD see the leading rocket instantaneously move a finite distance from her (in the direction away from the trailing rocket), and THAT is an ABSURD situation.
I said that a ways back, and wanted to illustrate it.One can observe the same rocket in three separate locations at once. That is also absurd
Because (a) this thread could possibly be viewed as educational, in that it attempts to lead somebody who is confused about relativity through to a correct analysis of a particular scenario; (b) because nobody has asked for it to be moved, up to the current time; (c) there is no self-consistent "alternative theory" on display here. If anything, the thread could be moved to our Pseudoscience subforum, which will probably be the clearly appropriate course of action if it turns out that Mike is unwilling to accept correction or education. Currently the signs are not encouraging, seeing as Mike is apparently unable and/or unwilling to answer a couple of straightforward questions, for reasons best known to himself. I mean, why would it be hard to agree that acceleration is the first derivative of velocity? Who knows? *shrug*.Why hasn't this topic been long ago moved to Alternate Theories with all the other denialists?