Relativity and simple algebra II

[ralfcis]

Ok, while on break I read the link to John Rennie's PSX thread on circular motion and it was quite an eye opener for me. I was definitely wrong that angular velocity doesn't act like linear velocity because there is no direct linear change in distance between the orbiting guy and the guy at the center. I was also wrong that the centrifugal force acts like acceleration due to change in tangential direction which would make circular motion an example of the twin paradox. The key here is s (the spacetime path) is invariant from all perspectives in flat spacetime which allows the math to be manipulated such that t=Yt' between the perspectives of the two participants just like it is for linear relative velocity. But you, Q-rheesus, were qwrong in stating twin paradox type permanent age difference is accumulating with each orbit when it's just plain old time dilation age difference accumulating due to each orbit which is the same as adding distance between the participants. There is no way to make that type of age difference accumulation permanent without bringing the two clocks together in SR which requires a change in the constant angular velocity. In my math, both participants remain the same proper time age while in constant circular motion (the same as in constant linear motion) and any change in angular velocity will make permanent twin paradox age difference between them. It's simple. I thought it would be more time consuming than this so I was waiting to clean my plate first.

P.S. You'll probably insist that dt=Ydt' indicates time slowing but again, just like in circular motion linearized, time dilation is caused by relativity of simultaneity between the perspective of the two clocks as orbits accumulate. SR does allow the circular orbits to be normalized as linear separation which is the key to this entire example. Long live ralfativity.

 

[ralfcis]

I just thought of a problem with this explanation. If with each orbit the participants are building an equivalent linear distance between them, in order to compare the clocks they must be brought together by rewinding all the orbits. If the orbiting clock is stopped, it should be possible to fly the clock back along the radius which is a much shorter distance separation than the orbit count between them. I'll ask Rennie on the PSX about this.

 

[Q-reeus]

Ok, while on break I read the link to John Rennie's PSX thread on circular motion and it was quite an eye opener for me. I was definitely wrong that angular velocity doesn't act like linear velocity because there is no direct linear change in distance between the orbiting guy and the guy at the center. I was also wrong that the centrifugal force acts like acceleration due to change in tangential direction which would make circular motion an example of the twin paradox. The key here is s (the spacetime path) is invariant from all perspectives in flat spacetime which allows the math to be manipulated such that t=Yt' between the perspectives of the two participants just like it is for linear relative velocity. But you, Q-rheesus, were qwrong in stating twin paradox type permanent age difference is accumulating with each orbit when it's just plain old time dilation age difference accumulating due to each orbit which is the same as adding distance between the participants. There is no way to make that type of age difference accumulation permanent without bringing the two clocks together in SR which requires a change in the constant angular velocity. In my math, both participants remain the same proper time age while in constant circular motion (the same as in constant linear motion) and any change in angular velocity will make permanent twin paradox age difference between them. It's simple. I thought it would be more time consuming than this so I was waiting to clean my plate first.

P.S. You'll probably insist that dt=Ydt' indicates time slowing but again, just like in circular motion linearized, time dilation is caused by relativity of simultaneity between the perspective of the two clocks as orbits accumulate. SR does allow the circular orbits to be normalized as linear separation which is the key to this entire example. Long live ralfativity.

Did John Rennie, who I respect as someone really clued up on SR and GR, actually agree with your various claims expressed after "But you, Q-rheesus, were qwrong in stating..."?

 

[ralfcis]

Here's a link to the discussion.
https://physics.stackexchange.com/q...me-comparison-of-the-clocks-require-co-locati
Willo is just a troll but benrg is giving a surprising answer that seems to agree with my Loedel velocity method to establish perm age diff. SR has no term for twin paradox perm age diff so Willo has no idea what I'm talking about.

John Rennie said in the original link you posted. " It turns out that the time dilation of the circling body is the same as if it was moving in a straight line"

 

[Q-reeus]

Here's a link to the discussion.
https://physics.stackexchange.com/q...me-comparison-of-the-clocks-require-co-locati
Willo is just a troll but benrg is giving a surprising answer that seems to agree with my Loedel velocity method to establish perm age diff. SR has no term for twin paradox perm age diff so Willo has no idea what I'm talking about.

John Rennie said in the original link you posted. " It turns out that the time dilation of the circling body is the same as if it was moving in a straight line"

The answers by benrg (current vote 0 but that is a very fresh posting) agree entirely with me. Therefore disagreeing with your claims after "But you, Q-rheesus, were qwrong in stating..." in #361. One minor caveat is that γ = 1/√(1-v²/c²) should have been explicitly identified by benrg as the ratio of rotation axis located twin A's proper clock rate relative to orbiting twin's B's proper clock rate. But it's obviously assumed to be the case.

A fourth method not mentioned there is as follows. Do one run 1 comprised of a spin up time, then fixed number of orbits N at constant orbital angular frequency ω, followed by spin down exactly the mirror image as for spin up. Net clock differential of Δt1 = t(A) - t(B) clock readings, determined from initial co-location compared to after final co-location via slow transport along the radial direction.

Then conduct a second run 2 identical to the first, except the number of constant angular velocity orbits is N + m. Then t(A) - t(B) = Δt2. What is your answer for the difference in co-located final clock readings Δt2 - Δt1?

PS - regarding your comment:
John Rennie said in the original link you posted. " It turns out that the time dilation of the circling body is the same as if it was moving in a straight line"

I don't know how you pitched your question to him, but I can guarantee all he meant by that statement is acceleration makes no direct contribution - which is just the clock hypothesis.
I can further guarantee he was not saying there that reciprocal time dilation applies to circular motion case as set out by me in #237, unlike for constant linear relative motion.

Go ahead and ask John Rennie for clarification according to my comments above. And post his answers here - unedited. I suppose you should ask for permission to have his answers posted here.

 

[ralfcis]

The answers by benrg (current vote 0 but that is a very fresh posting) agree entirely with me. Therefore disagreeing with your claims after

I don't think you understand the difference between reciprocal time dilation building as equivalent linear separation between them increases under constant circular velocity and permanent age difference increases as the circular motion reverses and they end up in the starting config. Time dilation has no age difference because it's reciprocal and the perspectives cancel out the same way height perspective is reciprocal at a distance. It's not real, it's an illusion of perspective. But perm age diff in the twin paradox is not reciprocal nor cancelled out by perspective. How does he possibly agree with you? Can you explain it or is just your declaration of that perspective make it real somehow.

The HKX is not like the circular motion example as it is not circular motion that results in reciprocal time dilation where the linearized orbital distance keeps increasing between the two. It results in twin paradox age difference caused by a circular roundtrip journey that is flattened into a linear roundtrip journey. It's a circular journey not relative to the center but to a point on Earth's circumference. I'm sure you don't agree with this and maybe John Rennie can resolve this. I'm not asking the PSX any more questions because it will only get me banned permanently.

 

[Q-reeus]

I don't think you understand the difference between reciprocal time dilation building as equivalent linear separation between them increases under constant circular velocity and permanent age difference increases as the circular motion reverses and they end up in the starting config. Time dilation has no age difference because it's reciprocal and the perspectives cancel out the same way height perspective is reciprocal at a distance. It's not real, it's an illusion of perspective. But perm age diff in the twin paradox is not reciprocal nor cancelled out by perspective. How does he possibly agree with you? Can you explain it or is just your declaration of that perspective make it real somehow.

The HKX is not like the circular motion example as it is not circular motion that results in reciprocal time dilation where the linearized orbital distance keeps increasing between the two. It results in twin paradox age difference caused by a circular roundtrip journey that is flattened into a linear roundtrip journey. It's a circular journey not relative to the center but to a point on Earth's circumference. I'm sure you don't agree with this and maybe John Rennie can resolve this. I'm not asking the PSX any more questions because it will only get me banned permanently.

Oh dear. We shall never agree on what circular twin paradox really entails. That's obvious. Please just answer my question to you last post of mine. What is your answer for Δt2 - Δt1?
To ease it a bit, recall that rotation period T = 2π/ω (as measured in the non-orbiting frame of A). My answer btw is Δt2 - Δt1 = mT(1 - 1/γ). According to what you claim here and what I could decipher in #361, your answer should be 0.
Well is it?
[Note: I have edited my answer which originally showed a factor of (γ - 1), which is the time differential factor as determined by orbiting B's clock rate. Factor (1 - 1/γ) is the time differential factor determined by A's clock rate. Non-reciprocal aging by factor γ (seen in B's frame), or 1/γ (as seen in A's frame), during constant circular speed still applies as given in earlier posts of mine.]

 

[ralfcis]

We shall never agree on what circular twin paradox really entails.

Because we can't agree on the terminology. I'll answer your question tomorrow as I'm way too tired right now.

 

[ralfcis]

This is what I'll post as my answer on the PSX:

Thank you benrg for finally answering this question. I've been asking the same question over and over in many different forms and you are the first to understand and answer it. Getting banished from one forum after another for asking it has not deterred me. Now I have a handle on the problem and can generate an Md for circular motion: time dilation and circular motion: twin paradox. The circular velocity part is not important as Rennie explained circular motion has the same time dilation factor as linear motion. Here is the first Md for circular motion: time dilation:



Alice orbits Bob at .6c at a distance of .477 ly. I've set up the radius of the centrifuge such that each orbit = 1.5 ly linear distance units. The starting point between the center and circumference is separated by the radius distance. I could have used Bob's perspective or Alice's but I chose a half speed perspective between the two of them because it gets rid of dealing with the hysteresis caused by Bob and Alice's perspectives. At the end I can introduce either's perspective around this half speed velocity perspective which is one of benrg's recommended methods for comparing clocks. So I zero Alice's and Bob's start time using this perspective. At Alice's proper time t'=8, she has finished 4 orbits around Bob. Bob's horizontal blue line of simultaneity at t=10.17 (.17 is an offset introduced by the fact they started separated) is simultaneous with Alice's t'=8. Gamma is 10/8=5/4 when corrected for the initial offset and that's the time dilation from either Bob's or Alice's perspectives.

The Md for circular motion-twin paradox does not show age difference as being reciprocal. All perspectives agree that Alice is 2.17 years younger than Bob at t=10.17 and t'=8 because all perspectives are crammed into one point. Bob doesn't see Alice as 2.17 yrs younger than him while she reciprocally sees Bob as 2.17 yrs younger than her, they both agree that Alice is 2.17 yrs younger than him. From the half-speed velocity perspective, that constant difference began at t=8.17 and t'=6 and continues until the next change of velocity at a distance is initiated by one of them. Since the half-speed velocity perspective connects Alice's and Bob's proper times and eliminates their perspectives affecting their mutual time readings, this half-speed velocity perspective shows their proper time age difference which is the same value at t=10.17 and t'=8.

 

[ralfcis]

I just thought of a problem with this explanation. If with each orbit the participants are building an equivalent linear distance between them, in order to compare the clocks they must be brought together by rewinding all the orbits. If the orbiting clock is stopped, it should be possible to fly the clock back along the radius which is a much shorter distance separation than the orbit count between them. I'll ask Rennie on the PSX about this.

I just realized the only diff between the HKX and the centrifuge circular motion is there is no starting distance between the participants in the HKX. So the HKX is indeed an example of circular motion-time dilation not circular motion- twin paradox. The distance accumulation between the two is along the circumference and it builds with each orbit. This is not the same as permanent proper time age difference due to the twin paradox which would be induced if there was a change in either the constant angular velocity or if the stationary participant started moving.

 

[Q-reeus]

This is what I'll post as my answer on the PSX:

Thank you benrg for finally answering this question. I've been asking the same question over and over in many different forms and you are the first to understand and answer it....

You are lying. Go read #365 again. Then back to #237 and on. Everything benrg wrote I have presented to you earlier here. And I presented more - namely that nonsimultaneitythere is never present when stationary twin A is situated on the orbital axis. And that any off axis location of stationary A, the relative aging difference per orbit is unaffected by such offset. And of course various links to various experimental confirmations - not just HKX you fixated on. But you kept rejecting what should have been quickly obvious, presumably because you couldn't work circular relative motion into your beloved Loedel line obsession that you can't move away from. I guess you needed to save face. And still you have not answered the question posed in that #365 post. Why not?

 

[Q-reeus]

I just realized the only diff between the HKX and the centrifuge circular motion is there is no starting distance between the participants in the HKX. So the HKX is indeed an example of circular motion-time dilation not circular motion- twin paradox. The distance accumulation between the two is along the circumference and it builds with each orbit. This is not the same as permanent proper time age difference due to the twin paradox which would be induced if there was a change in either the constant angular velocity or if the stationary participant started moving.

Hafele-Keating experiment was not a very clean one, but the net SR component conforms to the 'centrifuge circular motion' situation when properly analyzed. You neglected to mention the complications owing to the 'stationary' observer being on the surface of a rotating planet. And that GR time dilation is involved and works against SR overall. I gave you other references to much cleaner and more accurate tests involving circular motion. Why are you fixated on HKX? I suspect because you think it can be 'linearized' but it can't be any more than the centrifuge one can or the circular accelerator muon decay one could or the various rotating Mossbauer ones could. And your last sentence is a red herring.

 

[ralfcis]

You can't read or understand plain text that's why you accuse me of lying. This is your entire argument in #237:

Clock readings diverge at an accumulating constant rate. The differing clock rates for circular motion are thus clearly nonreciprocal thus 'absolute' not 'illusory' in contrast to the reciprocal case of constant rectilinear relative motion.

Clock readings DO diverge at an accumulating constant rate just like it's shown in my Md. I don't think you either know how to read or construct an Md. Show me how you would construct one using constant angular velocity where the clock readings diverge and the distance does not. This is your problem understanding what relative velocity is: v=x/t. Plug in some numbers, acquaint yourself with the concept. Show me how your interpretation of what John Rennie says fits into an Md. I certainly did but you wouldn't know because you can't read or write Md's. Prove me wrong.

"The differing clock rates for circular motion are thus clearly nonreciprocal."

You clearly don't understand what "Circular motion-time dilation means." Time dilation is always reciprocal. The twin paradox is not about time dilation because the time difference is not reciprocal. Don't you get that? Benrg listed the different ways clocks can be validly compared to establish the non-reciprocal time difference. You show me in your Md proof that the permanent time difference you're claiming due to constant angular velocity is verified by one of these valid clock comparisons. I've come here to make mathematical arguments and you've come to make wild claims based on your wilfully ignorant misconceptions. I've entered a discussion with an obvious rank amateur and if you don't want to learn something then I'm wasting my time trying to explain it to you. What's stopping you from asking John Rennie yourself as anything I clearly reprint from him you'll determine must be a lie.

So thank you for educating me in concepts I wasn't aware of but I'm afraid your usefulness has come to an end until you work on your own self-education.

 

[ralfcis]

You neglected to mention the complications owing to the 'stationary' observer being on the surface of a rotating planet.

Irrelevant to this discussion; the orbits can be pole to pole longitudinal. I also didn't mention the complications of conducting the experiment in non-flat spacetime (a gravitational field); also irrelevant. These are the types of smoke bombs people who can only recite SR without comprehension use to distract from their ignorance. It's ok to be ignorant, I don't try to hide mine due to pride except that I pride myself on my honesty and integrity which may not be important to you, I don't presume to know.

Why are you fixated on HKX? I suspect because you think it can be 'linearized' but it can't be any more than the centrifuge one can or the circular accelerator muon decay one could or the various rotating Mossbauer ones could.

You brought up the HKX and so did Rennie. I at first wrongly said it was an example of circular motion-twin paradox when it's just plain old circular motion- reciprocal time dilation.

And your last sentence is a red herring.

Of course because you don't know what it means. You don't acknowledge how the twin paradox is about non-reciprocal time difference and not about reciprocal time dilation. Any part of the last 19 pages that deals with this would be redacted in the journey from eyes to brain which would be overloaded like a boatload of red herrings.

, presumably because you couldn't work circular relative motion into your beloved Loedel line obsession that you can't move away from.

Presumably? You can't read Md's, it's worked in the latest one.

And still you have not answered the question posed in that #365 post.

I've more than answered it with my Md's. You want me to punch in the numbers for you. Instead of ramping up or down I'll use instantaneous starts and stops and ignore the start time offset so the numbers won't include confusing decimal points for you. Each 1.5ly orbit takes 2 Alice years which is 2.5 Bob years. If she stops after 3 orbits, the permanent age difference is 7.5-6 = 1.5 yrs. If she had kept going, the age diff would have been zero but the time dilation from Bob's perspective would have been 7.5-6=1.5yrs which is not permanent age difference. If she stopped after 4 orbits, which is one more than 3 if you're wondering, then the permanent age diff is 10-8=2yrs. I'd have to show how my light signal delay analysis arrives at that number but hopefully you can figure that out for yourself from the previous examples I've shown how to do that. I've done this analysis by just reading off the numbers from my 2nd to last Md which you should be able to do for yourself some day.

And that any off axis location of stationary A, the relative aging difference per orbit is unaffected by such offset.

Correct. That offset only happens at the beginning as my Md shows. Maybe you're looking at some other Md on Wiki I don't know. This is my snarky side that I've been repressing until you called me a liar so you've unleashed the, I'd like to say, kraken but that would be korny.

'more positive charges exist between two electrons' mean anything other than local length contraction of the positive charge lattice

As I've said, oh never mind, go read it for yourself, I'm tired of spoon feeding you and trying to force you to read what I've said. Maybe an analogy will help. Let's say you have a window as wide as a flashlight that passes by. You measure the total light as the flashlight slowly passes by. But then you squish the flashlight so it narrows and you get more light through as it passes which turns out to be the same thing as slowing the flashlight allowing more time for the light to pass through. As I said, any explanation using length contraction can be explained by using time dilation.

Do you accept constantly accumulating differential aging between A and B?

As I've said, I've accepted constantly accumulating time dilation due to increasing distance separation but not constantly accumulating permanent age difference in the circular motion-time dilation example.

 

[ralfcis]

Anyhoo as I was about to write before I saw these posts, I do see some problem with the info I've been given on the PSX.

Benrg said one of the options for comparing the clocks is using light signals but in circular motion the distance separation is due to orbits and light can't follow a circumference. In a HKX scenario, two planes fly from the North Pole in opposite directions following longitudinal orbits. After one orbit they all end up back at the North Pole and send light signals to each other and the Pole. One plane has flown +1 orbit, the other - 1 orbit but the light signal delay would be inconsistent with the physical distance separation which is zero. What's worse is that this circular motion-time dilation example could be converted into a clock handoff twin paradox example which would establish non-reciprocal permanent age difference between the planes and the pole.

 

[ralfcis]

I'm going to reprint benrg's answer on the PSX on how to compare clocks to establish permanent age difference between them. I was told SR only uses the first method but I'm glad to see SR agrees with all 3 methods that I use in my theory.

"The times on the clocks have to be brought to a common spacetime point to compare them, but there's more than one way to do that:

• You can bring the clocks together.
• You can send time signals (light-speed or slower) from both clocks to a common point, which could be on the worldline of one of the clocks or not.
• You can set the problem up so it has some geometric symmetry, as a consequence of which a lot of different methods of comparing the times will have the same result, and implicitly assume that one of those methods is used, without saying which one.

I'm not a fan of the third approach, but it's very common in practice.

You could handle the thought experiment involving uniform circular motion in any of those ways:

• You could give the experiment a definite start and end time, with the clocks at a common location at the beginning and end. In this case the ratio of total times will not be Y, but as the duration of the experiment grows relative to the startup and shutdown times, the ratio approaches Y. You can take the startup and shutdown times to be negligibly small and approximate the ratio as Y.
• You could send periodic radio signals from the circling clock to the inertial one, or vice versa, and compare the reading from the signal to the reading on the local clock when the signal arrives. You could also send signals from both clocks to a common location, as long as it respects the symmetry – for example, sending the signals to any point on the rotational axis would work. In all of these cases you'll find that the ratio of the clock rates is Y.
• You could assume the signals are compared in some symmetric way, or brought together in a way that takes negligible time, but be vague about the details, and just say that any "reasonable" way of comparing the rates will give you Y, more or less.

'Others argue that if one twin comes to a relative stop at a distance, they being in the same frame, allows light signals to establish their proper time age difference even if they're separated.'

This is another example of assuming some "reasonable" method of comparing the clocks but being vague about the details. If the clocks are at relative rest then there is a family of spacelike hyperplanes perpendicular to both worldlines, and the difference between the clock readings on any of those planes is independent of which plane you choose, and that difference can be measured in any number of ways."

 

[ralfcis]

I retract what I said about Q-reeus being a rank amateur. Obviously he is not and I am. Q's view on there being no difference between reciprocal time dilation and the twin paradox's permanent age difference is held by almost everyone on physics forums. Unfortunately Brian Greene's online course, the only one I've taken, that I have provided links to, disagrees with this common misconception. He states reciprocal time dilation, even though contradictory where both can't be younger than the other, is equally true from each perspective. (I say each experience the same illusion of perspective, time doesn't slow but potato,patatoe.) There is no contradiction in the twin paradox where only 1 is younger than the other once measured by a valid clock comparison method. No one on any forum wants to buy this as definition so it's thrown out the window in favor of expert consensus between buddies who recite from the same hymnbook. Only rank amateurs like myself would question this "science".

 

[Q-reeus]

You can't read or understand plain text that's why you accuse me of lying. This is your entire argument in #237:

Q-reeus said: ↑
Clock readings diverge at an accumulating constant rate. The differing clock rates for circular motion are thus clearly nonreciprocal thus 'absolute' not 'illusory' in contrast to the reciprocal case of constant rectilinear relative motion.

Either you just continue to willfully lie here (all one has to do is compare your absurd statement above with my actual #237), or you are mentally ill. Either way it's become painfully obvious why you keep getting kicked off forums. The rest of your #373, and subsequent posts at least to #376, is a confusing and self-contradictory mishmash. You are lost in your Loedel diagrams world and can't see the SR physics forest for the trees.
In passing, I note your continued avoidance of answering my very simple question posed in #365. Tells me all I need to know. This time, bye really means BYE.

 

[ralfcis]

I note your continued avoidance of answering my very simple question posed in #365.

Nope I've answered it but maybe you could repeat the question so there's no misunderstanding.

The rest of your #373, and subsequent posts at least to #376, is a confusing and self-contradictory mishmash.

What parts are you confused about? I can help you. I for one don't argue against incomprehensible things. I try to understand what I'm arguing against but to each his own.

This time, bye really means BYE.

We both know that's not true.

 

[ralfcis]

Whoa, I just checked the status of my question on PSX and it looks like I'll not only be permanently banned from asking future questions but apparently they're going to send over a hit squad to silence me. Yet no one is saying why. One guy answered the question so how could it be such a bad question? At least if there was a flaw in my Md's they could have pointed it out.