xyzt

[math]\frac{dr}{d \tau}[/math]

Post 3 says essentially the same thing (with more detailed math).

How can my challenge be "off topic" since you made a false claim? A claim that you are now retracting as false. Yes, I just explained that to you in an earlier post. Why are you trying to make it look as if I am disagreeing with this? Try Philosophy of Science and/or Foundations of Physics. Let us know what they answer.

You are a prime example of that. False. Since you think otherwise, I challenge you to cite the experiment that "confirms" relativity of simultaneity. Please. I didn't say you did, what I said is that you are mixing simultaneity with clock synchronization methods. You still persist in this error, even after all the information I provided you with. I am pointing the errors in your paper. You cannot answer by saying "look at my paper, I am right". This is a standard crackpot type of response. Tell you something, why don't you submit your paper to a peer reviewed journal, let us know when you get an acceptance. I am done trying to correct your misconceptions, I see no point in trying to educate you. I would still like an answer to my challenge above.

Einstein clock synchronization method has nothing to do with simultaneity of events. As the name says it, it is a method of synchronizing clocks (there are others). None of them has anything to do with the definition of simultaneity. Simultaneity has nothing to do with light propagation, this is why I recommended that you buy the Zhang book. It is really simple, if the transform for time is : [math]t'=\alpha t+\epsilon x[/math] then, a time interval [math]dt[/math] between two events transforms as: [math]dt'=\alpha dt+\epsilon dx[/math] If the events separated by a distance [math]dx \ne 0[/math] are simultaneous in one frame , F, ([math]dt=0[/math]) then, in any other frame F': [math]dt'=\epsilon dx[/math] [math]\epsilon dx[/math] encodes the amount of lack of simultaneity between the two events in frame F', nothing to do with "the time required by light to travel from A to B is equal to the time required for it to travel from B to A.". You keep persisting in your confusions in an attempt at justifying your paper. Experiment rules out this hypothesis, we already talked about this in the first posts. The only part that is true is that indeed, the concept of simultaneity is conventional (and, as such, not testable, there are no tests for relativity of simultaneity).

I already corrected the same exact errors earlier (twice), I corrected it again following your suggestion. So, this is the third time I correct his same exact errors.

You were talking Newtonian mechanics, i.e [math]F=m \frac{d \Phi}{dr}=\frac{GMm}{r^2}[/math]. Potential. In Schwarzschild coordinates: [math]\frac{f_1}{f_2}=\sqrt{\frac{1-r_s/r_2}{1-r_s/r_1}}=\sqrt{\frac{1+2 \Phi_2/c^2}{1+2 \Phi_1/c^2}}[/math] The Earth gravitational field is not uniform, it is (approximately) radially symmetric, it can be described by the Schwarzschild metric to a very good approximation. The potential is not constant, [math]\Phi =-\frac{GM}{r}=-\frac{r_s c^2}{2r}[/math] , so the field is not uniform. This explains the [math]\frac{f_1}{f_2}=\sqrt{\frac{1-r_s/r_2}{1-r_s/r_1}}=\sqrt{\frac{1+2 \Phi_2/c^2}{1+2 \Phi_1/c^2}}[/math] above.

The radial distance , it is the universal law of attraction, no?

You are mixing GR concepts with Newtonian ones, there is no "force of gravity" in GR. Moreover, in the framework of Newtonian physics, your statement is false, the "force of gravity" is different, [math]\frac{GMm}{r_1^2}[/math] for observer 1 and [math]\frac{GMm}{r_2^2}[/math] for observer 2. Since [math]r_1 \ne r_2[/math] the force is different. This is a non-sequitur, the coordinate acceleration has nothing to do with the Doppler shift. Besides, it isn't a Doppler shift to begin with, it is a gravitational shift since the observers are stationary. You keep piling up mistakes. .

I know, this is why I pointed out that you are mixing up the two concepts. Yet, your confusion persists. You are just repeating the same error I already pointed out: you are mixing up "Einstein synchronization method" (what you are trying to describe, incompletely) with what you call Einstein "standard" simultaneity (a non-existent term; based on the description and your intentions, the correct term would be "relativity of simultaneity"). If this is what you want, your description is wrong.

...in 21 you did not address your errors. You compensated by introducing fresh ones. No, I am saying you are wrong. Very wrong. Like you, phyti confuses relativity of simultaneity with clock synchronization. You need to learn your basics.

But you make a gross mistake in your opening stance. A mistake that you stubbornly refuse to admit to. I even colored it for you in order for you to understand it. Do you understand your mistake? Err, no. It is called "Einstein synchronization METHOD", not "Einstein simultaneity". uncool is correct, you are wrong (yet on another issue). If you want to make your own stuff, you need to start by getting the foundations right. As it stands, you don't.

Like I said, you need to educate yourself, here is a good start. You can continue by buying the Zhang book. I highly recommend it. What "assumption" are you talking about?

I didn't call your paper crap, I called vixra crap. Besides, at the time, I had no idea it is your paper. Good, because you have a lot of errors to think about. If you were as quick with the upvotes as you are with the downvotes, you would be grateful for the showstopper errors that I pointed out to you.

Neither did I , until he started defending it. He's very quick to neg me when I point out the errors in his posts. This is a non-sequitur, I told you that mainstream physics sees no connection between light delay (transit time) and relativity of simultaneity, you come back with a discussion between light delay and time dilation. Time dilation is not the same thing as relativity of simultaneity. You keep piling up errors.

I beg to disagree. Look at his "paper"and at his answer to the criticism leveled against his "paper". The whole thread belongs in pseudoscience, just as the "paper" found a home in vixra. Where it will rest . Forever. This is the third falsity. May I suggest that you get educated in the foundations of the experiments involved in constraining light speed anisotropy?

Well, it is not the first time he's been pushing fringe ideas, only to retaliate with negatives when this is pointed out to him.

What comes from vixra is crap. By definition. Vixra was created specifically for this reason: a repository of crank papers that have been rejected by mainstream, the "answer" to arxiv. You can see the errors right from the opening stance: "In the definitive work [1] on special relativity (SR), Albert Einstein acknowledges that an assumption is required in order to define a common time between two separated clocks. The assumption used which defines standard simultaneity is that the time required for a light signal to travel from an observer O to an observer P is the same as the time required for a signal to travel from P to O. While it is generally acknowledged that this remains an assumption, it is consistent with observation and is used in the physical representation of time throughout modern physics. Einstein justifies the assumption by its practical benefit of independence of observer standpoint with the clock, but it is tempting to presume that the assumption has a fundamental physical basis, since it is consistent with observations of an invariant speed of light" One paragraph, two gross errors: 1. Light transit time has nothing to do with relativity of simultaneity, conversely, relativity of simultaneity has nothing to do with light transit time, this is a classical error, oft repeated by people ignorant on the subject. 2. Light speed isotropy (what the author calls "the time required for a light signal to travel from an observer O to an observer P is the same as the time required for a signal to travel from P to O.") has been confirmed by countless experiments. I did not see any point in reading past this point.

...brought to you from vixra, the crackpot repository....

Radian.

Firstly, you will never get any relevant answer if you persist in reducing everything to numerical calculations, you NEED to LEARN how to use fully symbolic calculations. Secondly, the transverse case is quite difficult, I can post the radial case and you are going to glean how difficult it is to deal with "photon orbits". Thirdly, you can wait for your Rindler book to arrive and read the appropriate chapter on "photon orbits". The chapter gives the "easier" treatment, based on the metric. You can use that to try to produce the more difficult solution, based on the equations of hyperbolic motion.

I disagree, he clearly mixes up things when he says: This is a very bad way of attacking the issue , as I said, length contraction is an effect that can not be easily translated from SR into GR (and , more importantly, it shouldn't). The GR mathematical machinery is more than capable of dealing with all the effects by itself, no need to resorting to mixing in length contraction. This is not to say that the effects are not physical, it is just to say that you need to stay withing the confines of the GR math, no point in mixing in SR. Rindler does it in a few places in his book and it looks very ugly (most likely it is incorrect as well). I think so. I did not do the calculations for the amount of bending of the transverse ray of light but I once did the calculations for the transit time for a ray of light moving radially (up and down the elevator) and , though the symbolic formulas were a little different, when I did a Taylor expansion, they agreed to the third term. Considering that the third term is [math](\frac{gh}{c^2})^2[/math], this is an amazing precision.

Not clear where this is coming from. The actual statement, verifiable through math, is that the light bending predicted by GR is exactly double the light bending predicted by Newtonian physics ([math]\Theta_{GR}=\frac{4GM}{Rc^2} [/math] vs [math]\Theta_{Newton}=\frac{2GM}{Rc^2}[/math]). So, the IM Egdall guy must have misinterpreted what he read. I do not understand your fixation with length contraction. In GR, calculating the length of an object in motion wrt to an observer is a complicated problem that cannot be reduced to calculating length contraction. Length contraction is an artifact of the Lorentz transforms, while it is true that the spacetime is locally Lorentzian , you can't really use length contraction.

The coordinate speed of light does not intervene in the explanation of the Shapiro delay, so, not. Shapiro delay is an exercise in the calculation of the total elapsed time done in the context of assuming light speed constancy, not variability. Perhaps you can do the math and post it, the way I did it? I would be very interested in your proof. Frankly, I would prefer you, JVNY and Iggy opened a different thread , this exercise is just a sideshow to the false claim made by Iggy who got this all started. Let's concentrate on the main show, the false claim about the Shapiro delay confirming the slowing of light speed.

No , they don't, I have shown this repeatedly. The posts aren't inconsistent since the particles in YOUR example DO NOT have the same speed, contrary to your drawings they are not accelerated in a Born rigid fashion. Math contradicts your drawings (and drawings never form a valid form of proof). Besides, your exercise is just a sideshow, the main show is the incorrect claim that Shapiro delay somehow proves light "slowing down". I would like you and Iggy to retract this false claim. Nothing to do with any length contraction. The speeds are unequal, each rocket moves at a different speed as I have demonstrated several times.