Relativity and simple algebra II

railcis,

You need to re-read my post #329. You are convoluting-wrapping yourself to try to disprove me. Sometimes you try to take the perspective of the person in the center not in revolution. Sometimes you try to take the position of the person in the center in revolution. Try to take a consistent approach to what that person the center is doing.

The denial I gave was to what you were saying. That varies over time.

A person orbiting the Earth feels no more force than someone on the surface of the Earth, WTH anyone else orbiting the center of the Earth. That doesn't discount anything I said about circular motion. In fact it goes to prove it.
 
A person orbiting the Earth feels no more force than someone on the surface of the Earth
Well that's just blatantly wrong. Ever hear of gravity. A satellite is in free fall so it is weightless. A person on Earth is not weightless, he feels a force. In GR that force is acceleration without motion.
 
I find the same true of everyone else. No one understands the difference between closing speed, relative velocity or even what velocity means. If someone is neither approaching or receding from you in a direct line, there is no relative velocity between you. That's why you can walk much slower across the surface of the earth and maintain zero relative velocity with a satellite in space if you are walking on the same radius line. Your angular velocity is the same but your relative velocity is zero. That's why the brief instant that a bullet is right beside you, in between the time it is changing from approach to recession, that bullet is at zero relative velocity to you in that instant. Do you disagree with everything I've just said?
You persist in claiming there is no relative velocity in circular motion scenarios I have presented. Despite everything explained in #323, #324. That's your choice. Which is a very mistaken one.
 
...As long as Q brought up pet peeves on forums, I have 2. One is Q did not answer some of my questions and 2 is when I take the trouble to answer questions and there is no subsequent response.
There was no point answering SR related issues given your very mistaken grasp of what circular motion is about. Hence the sole quote in #323.
 
That is easily resolved by if the person in the center is rotating along with the ball bearing, then there is relation motion between him and the 3rd object but not the ball bearing. If the person in the center constantly gazes at the 3rd object, then there is relative motion between him and the ball bearing, but not the 3rd object. And so the relative motion between the ball bearing and 3rd object doesn't present any problems....
Your analysis is flawed. ralfcis often talks about Lorentz contraction and 'genuine' time dilation being just 'perspective' artifacts of SR math. Not true as circular motion nicely demonstrates. Stop and think it through. If the notionally point sized observer spins really fast, at a quite small radius, the apparent 'relative velocity' of objects observed there will exceed the speed of light c. By many orders of magnitude if one projects out to even the nearest stars. Those 'hypervelocities' are obviously nothing more than actual perspective optical illusions.

All that matters in my examples in #323, #324, is the location of observer. If offset laterally from orbit axis of traveling twin, there will be periodic modulation of observed Doppler shift, rather than perfectly steady transverse Doppler shift. The observed period T is unaffected by any lateral shift. Whether he/she/it spins or not is irrelevant. As far as Newton's bucket/Mach's principle is concerned, I refer you to posts on that when I was back at Physics Forums:
https://www.physicsforums.com/threads/does-gr-contradict-machs-principle.505896/
See my #27, #29 on p2 there.
 
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There was no point answering SR related issues given your very mistaken grasp of what circular motion is about.
I'm still not sure if you're trying to prove me wrong about 1 thing or 2 (unrelated to each other) and are you saying there are no linear examples that can prove me wrong? It all boils down to our disagreement, or my disagreement with the rest of the world, whether circular motion on the z-axis is relative velocity or not. We started on the electricity/magnetism example in circular motion. What happened to that?
 
Your analysis is flawed. ralfcas often talks about Lorentz contraction and 'genuine' time dilation being just 'perspective' artifacts of SR math. Not true as circular motion nicely demonstrates. Stop and think it through. If the notionally point sized observer spins really fast, at a quite small radius, the apparent 'relative velocity' of objects observed there will exceed the speed of light c. By many orders of magnitude if one projects out to even the nearest stars. Those 'hypervelocities' are obviously nothing more than actual perspective optical illusions.

All that matters in my examples in #323, #324, is the location of observer. If offset laterally from orbit axis of traveling twin, there will be periodic modulation of observed Doppler shift, rather than perfectly steady transverse Doppler shift. The observed period T is unaffected by any lateral shift. Whether he/she/it spins or not is irrelevant. As far as Newton's bucket/Mach's principle is concerned, I refer you to posts on that when I was back at Physics Forums:
https://www.physicsforums.com/threads/does-gr-contradict-machs-principle.505896/
See my #27, #29 on p2 there.
Q-reeus,

Thanks for your post. And I respect it, but I don't really follow it. To me it is not about rotating on a small enough point to where it can be disqualified per SR. Surely the person in the center could not experience hi-per velocity if the person rotating could not go faster than the speed of light? Am I wrong? I'm not talking about observing the background, I'm talking about observing the object, which cannot go faster than the speed of light.
 
the apparent 'relative velocity' of objects observed there will exceed the speed of light c. By many orders of magnitude if one projects out to even the nearest stars. Those 'hypervelocities' are obviously nothing more than actual perspective optical illusions.
This is an example of closing speed and I mentioned others (two light signals observed by a 3rd party crashing at 2c and laser dot zooming from earth across the surface of the moon exceeding c from the Earth's perspective).
 
I'm still not sure if you're trying to prove me wrong about 1 thing or 2 (unrelated to each other) and are you saying there are no linear examples that can prove me wrong? It all boils down to our disagreement, or my disagreement with the rest of the world, whether circular motion on the z-axis is relative velocity or not. We started on the electricity/magnetism example in circular motion. What happened to that?
What happened was you gave a hand-waving argument that made no sense and had no math behind it. What else is there I can add that would alter your viewpoints? Your claim that final relative age differences in any traveling twin scenario is purely owing to nonsimultaneity is simply false. Manifestly false in the circular motion cases since nonsimultaneity is always absent, whether during spin up, steady circular speed, or final spin down. And I have explained why quite a number of times by now. No point repeating again here.
It's no good you simply asserting otherwise. If you persist in claiming your theory can explain relative aging difference for circular motion of one twin, then provide the math showing it.
I say you cannot.
 
Q-reeus,

Thanks for your post. And I respect it, but I don't really follow it. To me it is not about rotating on a small enough point to where it can be disqualified per SR. Surely the person in the center could not experience hi-per velocity if the person rotating could not go faster than the speed of light? Am I wrong? I'm not talking about observing the background, I'm talking about observing the object, which cannot go faster than the speed of light.
The two are intimately linked. Following the motion of an orbiting object by spinning at the same angular speed is still just an optical perspective. Try and recall the central observer has no translational motion while the orbiting object does have a constant speed ωr. That the velocity v = ω x r is constantly changing direction does not alter there is always relative speed ωr
between orbiting twin and stationary twin located on the orbit spin axis. How many times must I repeat that?
 
If you persist in claiming your theory can explain relative aging difference for circular motion of one twin, then provide the math showing it.
I first need to look at your links to find out what you're talking about. If it's the HK experiment then it's just like the non-circular the twin paradox for which I've already provided the math.
 
The two are intimately linked. Following the motion of an orbiting object by spinning at the same angular speed is still just an optical perspective. Try and recall the central observer has no translational motion while the orbiting object does have a constant speed ωr. That the velocity v = ω x r is constantly changing direction does not alter there is always relative speed ωr
between orbiting twin and stationary twin located on the orbit spin axis. How many times must I repeat that?
Q-reeus,

Please don't label me a "railcis", as I will take it to heart if I get a good argument, but this "twin" you talk about is not necessarily stationary. That was the gist of my original post, that there were different observations if the "twin" was stationary WTR to the orbiting object VS stationary to distant objects. My link to the wiki article of Circular Velocity bore that out. The scenario you originally wrote about has different outcomes for different observations of a person in the center. And I am not talking about distant observations (this is to my way of thinking/understanding).

Your last post didn't talk about that twin in the center. If you tell me now the observations of the person in the center will be the same for your original thought experiment if that person rotates or fixes his gaze on distant objects, then I will leave it alone.
 
I first need to look at your links to find out what you're talking about. If it's the HK experiment then it's just like the non-circular the twin paradox for which I've already provided the math.
Wrong wrong wrong. Circular motion is not linear motion. 'Linearizing' circular motion is changing the physics. It introduces nonsimultaneity that is, to repeat yet again, completely absent for circular motion, steady or not. Transverse Doppler shift is always recorded for any observer located somewhere on the orbital spin axis. I grow weary of repeating such things. Just once should have sufficed.
 
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Q-reeus,

Please don't label me a "railcis", as I will take it to heart if I get a good argument, but this "twin" you talk about is not necessarily stationary. That was the gist of my original post, that there were different observations if the "twin" was stationary WTR to the orbiting object VS stationary to distant objects. My link to the wiki article of Circular Velocity bore that out. The scenario you originally wrote about has different outcomes for different observations of a person in the center. And I am not talking about distant observations (this is to my way of thinking/understanding).

Your last post didn't talk about that twin in the center. If you tell me now the observations of the person in the center will be the same for your original thought experiment if that person rotates or fixes his gaze on distant objects, then I will leave it alone.
To answer your last question - yes it is the same. Of course a real observer can never be point sized and having finite lateral extent, will experience centrifugal forces when spinning. But it's irrelevant. What counts is transverse Doppler shift applies to the frequency of light emitted by the orbiting twin when received by the twin lying on the orbital spin axis. Which can only mean the orbiting twin is aging at a slower rate. Sorry to say this is becoming comical. I was confident getting ralfcis to study circular motion would quickly end the issue but it just keeps going like the in out linear examples did. So unnecessary.
 
To answer your last question - yes it is the same. Of course a real observer can never be point sized and having finite lateral extent, will experience centrifugal forces when spinning. But it's irrelevant. What counts is transverse Doppler shift applies to the frequency of light emitted by the orbiting twin when received by the twin lying on the orbital spin axis. Which can only mean the orbiting twin is aging at a slower rate. Sorry to say this is becoming comical. I was confident getting ralfcis to study circular motion would quickly end the issue but it just keeps going like the in out linear examples did. So unnecessary.
Good enough. Thanks. I'm out of the discussion.
 
Good enough. Thanks. I'm out of the discussion.
No problem. Thanks Nacho for participating and doing so in a sincere and respectful, courteous manner. Which is a refreshing change from the usual situation some others here at Sciforums choose to engage with.
 
Believe it or not Q, your answers did clarify things for me. I'll get right on this after I attack my backlog of questions. I'm on page 9.
 
Before I continue with my backlog of questions from James (at least I answer questions and give feedback to answers) and then discuss with John Rennie on the PSX (and hopefully return with an answer to Qreeus) I'd just to finish up with my answer to Neddy.

Here is an Md showing the orderly linear change in the slope of the Loedel lines of simultaneity and the orderly linear change in the Loedel velocity lines. The second Md deals with the same in an example where a return is made instead of a stop. The Loedel velocity lines no longer have a linear change in slope and it looks like the change to negative slope of the Loedel velocity lines happens in the last 1.4 yrs before the end of the velocity imbalance period. It's just interesting that the progression of proper age difference after the turnaround is not symmetrical even though the time spent going out at +15/17c is the same as the time coming back at -15/17c. I don't expect anyone to understand what I'm musing about here, this is just more of a note to myself.

.8824ce.jpg


.8824r2.jpg

SR has no comparable diagram that shows permanent age difference progression. It's determination of permanent age difference can only be done at re-unification when t=10.2 and t'= 4.8 for a difference of 5.4 yrs. But my method determines the permanent age difference by the Loedel line of simultaneity with t=9.6 on one end and t'=4.2 on the other. The permanent age difference will continue at 5.4 yrs after this point where the slope of the Loedel lines of simultaneity stop changing which is much earlier than SR can call it.
 
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I'd also like to add that SR only considers "age difference" down perspective lines of simultaneity. For example, the blue line represents an age difference of 2.4-1.13 = 1.27 yrs while so does the thin red line. The green Loedel lines of simultaneity are no different like the first one is 2.4-2.4=0 yrs age difference. I spent months trying to explain this on the PSX and it was beyond them completely even though there was a Wiki article explaining what a Loedel diagram was. They just couldn't understand how Loedel velocity lines could have Loedel lines of simultaneity. They're still refusing to answer the latest question I posted on age difference because they have no idea what terminology I'm using and SR has none of its own that fits my descriptions.
 
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