1. Oops, how do I move this to the Physics Forum?
I'd most humbly like to pose a question. If anyone can answer this I'd like to discuss relativity with you.

From Earth's perspective, if Alice does a linearized 3 ly round trip out and back at .6c, what will be her rate of time due to time dilation, doppler shift ratio, and age difference just before the end of each leg.

.8, .5, 1 for outbound and .8, 2, 2/3 (average) for the return leg. The last number is where the discussion begins. I say she will be the same age as Bob on earth just before the end of the outbound leg because they are engaged in constant relative velocity before the frame jump (turnaround). So they're both 4, no age difference has occurred. When they re-unite at the end of the inbound leg, she will have aged 2 years less than Bob. Bob ages 6 yrs (total =10) and Alice ages 4 yrs (total =8) hence the answer is she ages 2 yrs for every 3 bob yrs on the inbound leg. The answer most people give me is Alice ages 1 yr less than Bob on the outbound leg and 1 yr less than Bob on the inbound. I don't see what is the mathematical support for this result if there can be no age difference for constant relative velocity in the outbound leg.

At t'=4, Alice's line of simultaneity swings from Bob's time t=3.2 to t=6.8. I don't see how this would translate to an instantaneous 1 yr less ageing for Alice at the turnaround and then another 1 yr less at the re-unification point. Wouldn't the ageing difference be spread out and appear smoothly incremental on the tv signals they continually broadcast to each other. Yes the doppler shift ratio would result in a sudden speed up (from a tv picture at half speed to double speed fast forward) on Alice's screen but there would be no evidence of a discontinuity in Bob's ageing rate.

I'm also seeing another problem. If Alice had relatively stopped at the turnaround point, she'd have to wait until the news of that stop reached Bob 3 yrs later at t=8 in order for the spacetime path to be officially closed in order to validate Alice had aged 1 yr less than Bob. If that method is valid for a stop, wouldn't it also be valid for the turnaround scenario? Instead of Bob and Alice re-unifying, isn't it enough for the info of the stop to reach Bob. And once that info reached Bob, wouldn't that re-establish a new common Doppler shift ratio between them which would mean they were re-engaged in constant relative velocity and hence no more age difference could accumulate for the rest of Alice's journey to re-unification?

I'm hoping someone out there will understand what I'm saying because most people don't understand the difference between reciprocal time dilation and permanent age difference due to a frame jump.

Here's an STD (spacetime diagram) you may want to use:

2.

3. Hard to respond - I suffer from MEGO.

4. You can PM a moderator and ask them to move it to the physics section, or if you don't one of them might see it and fulfill your request.
From Earth's perspective, if Alice does a linearized 3 ly round trip out and back at .6c, what will be her rate of time due to time dilation, doppler shift ratio, and age difference just before the end of each leg.
From Earth's perspective, the time dilation factor experienced by Alice will be = 0.8. She will also travel 6 light years (to and back), and at a speed of 0.6c this will take 6/0.6 = 10 years. And with a time dilation factor of 0.8 this means that Alice will age by eight years.

Now let's see what happens from Alice's perspective. She notices the Earth whizzing behind her at a speed of 0.6c, and the distance to the star (or whatever) is not 3 light-years but 3*0.8 = 2.4 light-years (since 0.8 is also the length contraction factor). Therefore, from her point of view, it takes 2.4/0.6 = 4 years to get to her destination, and then another 4 years to get back, so it will take a total of eight years.
When she looks at the Earth, she notices that time has slowed down by a factor of 0.8, so after 4 years, she will determine that 0.8*4 = 3.2 years have gone by on Earth. When she turns around, she will notice that Earth instantaneously aged by 3.6 years, and she will then observe another 3.2 years go by on Earth in her return trip, so in total she will observe ten years go by on Earth.

The hardest part is understanding why she observes the Earth instantaneously age by 3.6 years. First, understand that she is decelerating infinitely fast, which is impossible in real life, so you couldn't observe this in real life. Instead, by an extremely quick (but not instantaneous) turn-around, you would simply observe the Earth aging extremely fast. But in our case, we can assume instantaneous turn-around which means instantaneous time jump.
And to understand this, we are going to use a Lorentz transformation. This transforms a point in spacetime (x, t) to another point (x', t'), from the point of view of an observer traveling at speed v (as a fraction of the speed of light) who is currently at position x.

Here, x and t must be in units whose ratio gives the speed of light (so x being in light-years and t being in years is good). Plugging in (x, t) = (0, 10) (the place and time that Alice returns) we get (x', t') = (0, 8), which is what we want*. And this means that that frame of reference hits Earth with Alice after eight years, which means it takes four years from when Alice turns around, so all is good.

*Actually, I only got this result when I changed the minus signs in the transformation to plus signs. I hope someone else can fill you in a little better.

5. I am a carrier and very contagious.

I was hoping this would be moved to the new physicsforum which I can't register in due to the captcha shutdown.

Maybe if I include my colorful STD it may temporarily alleviate your MEGO.

Nope constant error message even if I put the diagram on a 3rd party site. Does anyone know how to upload images here?

6. Sorry anticorncob, you're not answering the question and you're just giving me the standard spiel confusing ageing with time dilation. The twin paradox is all about the difference between permanent age difference and reciprocal time dilation and I'm looking for someone who understands this right off the bat. Just answer 1 question: If Alice didn't turn around and kept going for 4 more years, what would be her age difference with Bob? The answer is zero and why? Your time dilation is still in effect yet it yields no age difference, why?

Hint: It's one of the 1st 2 tenets of relativity and it's not the one about the constancy of the speed of light.

7. From the Earth's perspective, Alice travels to 3 light-years away at 0.6c then returns. This is a total distance of 6 light-years, and takes 10 years to complete. From Alice's perspective, due to time dilation, it takes 8 years for the total journey. From the time Alice leaves Earth to the time she turns around is 4 years. Since the start and end points are definite points in spacetime, the interval between them is invariant, and thus the 4 years which Alice has aged does not depend on the observer. By contrast, how much Bob (on Earth) has aged over this time does depend on the observer. This is because the point in spacetime on Bob's worldline which is simultaneous to Alice's turnaround depends on the frame of reference in which the notion of simultaneity is being applied. Thus, in Bob's frame of reference, Bob has aged 5 years from when Alice leaves Earth to when she turns around. But in Alice's frame of reference, Bob has aged only 3.2 years because in her frame of reference, Bob is moving away from her at 0.6c, and the time dilation applies to him (relative to her 4 years).

8. Good. You didn't answer the original question but at least you know relativity and not the popular science version most people ascribe to on forums. However, may I rattle your cage a little bit? It would be easier to do so if I could post some spacetime diagrams but I have not yet found a way to do so here.

Yes spacetime paths are the way relativity determines age difference. But there are rules to them. I understand the reason behind those rules and we could discuss that in further posts but those discussions are very long so let's leave them aside for now.

Bob and Alice start out with the same time on their atomic watches. Time ticks at the proper time rate for all inertial frames. This is invariant as you alluded to. So the time on their watches, just before the turnaround is 4. If Alice continued on for 4 more years without changing their relative velocity, the time on their watches would be 8. But if Alice turns around and takes 4 yrs to return, her watch says 8 and Bob's 10. I'm not talking about the perspective time or coordinate time they or any other frame have of them or each other. The proper time is on their watches and it is invariant and it is each of their ages = 4 before the turnaround point.

As you said from Bob's perspective, Alice is 4 when he's 5. From Alice's perspective, when she's 4, Bob's 3.2. From a 3rd party perspective going at "half speed" (1/3 c between them), they're both 4. These numbers are superficially meaningless to their actual ages and are just coordinate time much like time zone time (just because your watch says 6 am doesn't mean it's 6 am around the world).

A contradiction arises because it is also not a valid end to their spacetime path so how is it possible to make a conclusion that no age difference occurs if two frames are engaged in constant relative velocity? Ok, maybe relativity considers one of its main tenets an exception to the spacetime path rule. Seems odd unless you have another explanation for this. The spacetime path rule that is broken here is that both clocks must re-unite for the spacetime path to close. (There is another exception to this rule which I'm coming to.)

So what is behind this rule? Distance separation due to a relative velocity allows relativity of simultaneity to creep in and mess up the time readings due to perspective. Co-locating the clocks eliminates the perspective and allows the proper times on the wristwatches to be compared without perspective messing things up. Co-location allows age difference to be independent of perspective. It's a common misconception that the clocks need to stop to co-locate. They can whiz right past each other at full relative velocity and that still constitutes a valid end to the spacetime path.

But there's another kicker; in order for two clocks to re-unite, there must be a break in the constant relative velocity somewhere in the path. Bob and Alice continue to see their watches tick time at the proper rate before, during and after the break. They don't see any time change or jump on their watches and both started at the same time but when they re-unite, their proper times don't match. All your talk about perspective time due to reciprocal time dilation and lines of simultaneity is irrelevant as age difference is purely a phenomenon of proper time magically being altered on their wristwatches right before their eyes.

Relativity's spacetime path rules only allow a determination of age difference at the end of the spacetime path. For reasons I could explain at length, any attempt to look at how age difference unfurls before the end would result in paradoxes using relativity's method so that region of the math has been deemed off limits.Even the question I posed is off limits and it resulted in me being permanently banned from the physicsforums after 1 day. Even though relativity states frames in constant relative velocity can't cause age difference, the spacetime path rule does not allow you to conclude that because there is no valid end to a spacetime path before Alice turns around.

Relativity makes an exception to the rule in the case where instead of turning around, Alice relatively stops. There's no way for re-unification of the clocks and the distance separation between the two allows for perspective time to come in and mess up the readings of their ages. Yet, in this one exception, Alice's light signal back to Bob (in the form of her televised broadcast of her wristwatch (so the Doppler shift ratio can be established)), at the stopping point (3ly) allows the spacetime path to be closed when that signal reaches Bob. Seems like a lot of legal fineprint all of a sudden.

What does this rule mean for subsequent theorizing? Well it throws out the idea that age difference is caused by a sudden swing in Alice's line of simultaneity because the age difference determination has to wait for the news to reach Bob. This in turn throws out the misconceptions that acceleration causes age difference due to general relativity's equivalence of acceleration and gravity. If people would just look into relativity a little further they'd see in clock handoff scenarios, where their is no acceleration involved in instantaneous frame jumps, yet age difference still occurs.

I avoid all this mess by taking the two exceptions to relativity's rules and making them the rules. The math that comes out is the music of the spheres and I have been searching for years to find the right people who understand relativity to show them that math. But the problem is people who know relativity don't want to see it or hear anything about it (thanks to forum nuts who have made similar wild claims over the decades and it turns out to be mostly mindless word salad). The people who think they know relativity are even more closed minded and probably don't know math anyway so no point in showing them either.

9. Originally Posted by ralfcis
Bob and Alice start out with the same time on their atomic watches. Time ticks at the proper time rate for all inertial frames. This is invariant as you alluded to. So the time on their watches, just before the turnaround is 4.
No, it's not the time on their watches that is 4, it's the time on her watch that is 4. The time on his watch depends on how the end point of his path in spacetime is defined. In order to define a proper time, it is necessary to have a path in spacetime including both the start and end points. The start point of both Alice and Bob are defined, but the end point is only defined for Alice. That is why some notion of simultaneity is required to define the end point for Bob, and the notion of simultaneity is dependent on the frame of reference. In the case where Alice and Bob meet at the end of Alice's journey, this defines the end point of Bob's path, and both start and end points are defined for both Alice and Bob, without requiring any notion of simultaneity.

Originally Posted by ralfcis
But there's another kicker; in order for two clocks to re-unite, there must be a break in the constant relative velocity somewhere in the path. Bob and Alice continue to see their watches tick time at the proper rate before, during and after the break. They don't see any time change or jump on their watches and both started at the same time but when they re-unite, their proper times don't match. All your talk about perspective time due to reciprocal time dilation and lines of simultaneity is irrelevant as age difference is purely a phenomenon of proper time magically being altered on their wristwatches right before their eyes.
Simultaneity is not the same as what the observer actually sees. What the observer actually sees is delayed by the time it takes for light to travel the intervening distance. Because the intervening distance is changing, the relative rate at which clocks are seen to tick is based on the Doppler effect rather than the time dilation. By considering how Bob sees Alice's clock tick, and how Alice sees Bob's clock tick, one can determine that indeed Alice ages 8 years compared to Bob's 10 years for the total journey. In particular, one gains a clear perspective on how the asymmetry between Alice and Bob arises. When Alice turns around, she sees Bob's tick change from slower to faster immediately, whereas Bob doesn't see Alice's clock tick change from slower to faster until the light from Alice's turnaround has reached Bob. This reflects that it is indeed Alice that is turning around and not Bob.

10. Thanks, makes sense but I need more time to absorb it. It looks like the rules for spacetime paths rule. They must start and end properly. The clocks can't be separated without bringing in perspective to determine age difference. So what about the scenario where Alice relatively stops. How is the spacetime path properly ended by a light signal when they're still separated?

P.S. Ok I'm mulling over what you said but the question is still what are their ages before the turnaround point not because of the turnaround. According to the point you brought up, the answer must be indeterminate as they are both calculating the other as younger both through reciprocal time dilation of .8 and the 1/2 doppler shift ratio they see of each other.

If my interpretation of what you're saying is correct, at the turnaround Bob's age from Alice's perspective either jumps from 3.2 to 6.8 or from indeterminate to 6.8 or from indeterminate to 5? Ok, I'm confused.

PPS According to the forum rules I can't reply to myself so here's an alternate way of looking at what I'm saying.

Say Bob and Alice want to go away on vacation in separate ships but still be the same age when they arrive. They can do this by agreeing ahead of time Alice will turn towards earth when her watch says 4 and Bob will take off from earth towards Alice when his watch says 4. Without showing the STD I can give you the answer that Alice's supposed year less ageing at her turnaround will be cancelled out by Bob's year less ageing at his takeoff when they meet. But if Bob misinterpreted Alice's instructions and takes off when he calculates Alice's wristwatch hits 4, which is when his watch hits 5, they will not meet at their intended destination in neither time nor space. So doesn't that imply a proper time simultaneity outside of relativity of simultaneity? Doesn't it imply that they are the same age from a proper time standpoint just before each changes the relative velocity?

11. Originally Posted by ralfcis
The clocks can't be separated without bringing in perspective to determine age difference.
The problem isn't the separation of the clocks. It's how to define the path in spacetime including the start and end points. Once one has a path including the start and end points, the proper time along that interval is defined and invariant. In the case where the paths of two clocks intersect, the point of intersection is a natural definition of a point on the paths of both clocks.

Originally Posted by ralfcis
the question is still what are their ages before the turnaround point not because of the turnaround.
Actually, it's not because of the turnaround, but at the turnaround. But infinitesimally before the turnaround is ok.

Originally Posted by ralfcis
According to the point you brought up, the answer must be indeterminate as they are both calculating the other as younger both through reciprocal time dilation of .8 and the 1/2 doppler shift ratio they see of each other.
It seems to me that you are still trying to hold onto the notion of an absolute time. The age is simply the length of a (timelike) path in spacetime between two points. There is no ambiguity or inconsistency once the path and the two points on that path are specified. The differences that result from a change in perspective is because different intervals are being compared, not because the intervals themselves are different.

Originally Posted by ralfcis
If my interpretation of what you're saying is correct, at the turnaround Bob's age from Alice's perspective either jumps from 3.2 to 6.8
Although I did say that, it is actually incorrect because it treats Alice's frame of reference as two separate inertial frames rather than the single non-inertial frame that it is. In the single non-inertial frame of reference, at the turnaround, Bob has aged 5 years. Although Bob and Alice do not agree about simultaneity everywhere, they do agree at Alice's turnaround.

12. [duplicate post deleted]

13. Ok, while I try to understand this, what are their ages infinitesimally before the turnaround? Are they both a tad shy of 4 or Bob a tad shy of 5? I also added another paragraph to my previous post. I will admit that I view proper time as an instantaneous present that can only be calculated once the info, delayed by the speed of light, is received to know what that present was. I don't view this as a newtonian universal time or absolute time because it can be changed, started by changes in relative velocity, during the delay it takes to relay the info of a change from the initiator of the change.

PS. I don't like this rule of not being able to reply to your own posts.

I feel like your response is the closest I've come in years to getting my questions answered but I don't have any formal training in relativity (except a mickey mouse on-line free course) so I can only understand by parsing each sentence:

1." The problem isn't the separation of the clocks."

I thought the more you see someone move through space, the less they move through time. So a distance separation between two frames can be converted into time. So the 3ly separating Bob and Alice at the turnaround can be converted into 1 additional year for Alice (5 Bob yrs =4 Alice yrs +1 Alice year converted from the 3ly separation) or .8 (1yr/Y) additional yr for Bob ($Alice yrs = 3.2 bob yrs + .8 converted distance). This is how I look at it but in relativity it's probably the invariance formula. I don't know. 2. " It's how to define the path in spacetime including the start and end points." Does this require me knowing more rules on how to do this? 3. " Once one has a path including the start and end points, the proper time along that interval is defined and invariant." Are you saying Bob's interval for the outbound leg is 0-5 and Alice's interval is 0-4? You also say " The differences that result from a change in perspective is because different intervals are being compared, not because the intervals themselves are different." Differences do result from a change in perspective so that must mean 2 different intervals are being compared but the last part of your statement is they are not different intervals? 4. So your last paragraph definitively states at the turnaround Bob= 5 and Alice =4. Then at the end Bob gains another year for Alice's 2nd inertial frame for a total of Bob=10 and Alice =8. But how does this progress from start to finish? Does Alice lose .25 yrs for every Bob yr or are there lump sum jumps in age difference at the end of each of Alice's inertial frames? 5. " Although Bob and Alice do not agree about simultaneity everywhere, they do agree at Alice's turnaround." Why is that? Alice's line of simultaneity swings wildly and only in mid swing does her line line up with Bob's line for an instant. Is that the reason? 14. Originally Posted by ralfcis Ok, while I try to understand this, what are their ages infinitesimally before the turnaround? Are they both a tad shy of 4 or Bob a tad shy of 5? I also added another paragraph to my previous post. I will admit that I view proper time as an instantaneous present that can only be calculated once the info, delayed by the speed of light, is received to know what that present was. I don't view this as a newtonian universal time or absolute time because it can be changed, started by changes in relative velocity, during the delay it takes to relay the info of a change from the initiator of the change. PS. I don't like this rule of not being able to reply to your own posts. I feel like your response is the closest I've come in years to getting my questions answered but I don't have any formal training in relativity (except a mickey mouse on-line free course) so I can only understand by parsing each sentence: 1." The problem isn't the separation of the clocks." I thought the more you see someone move through space, the less they move through time. So a distance separation between two frames can be converted into time. So the 3ly separating Bob and Alice at the turnaround can be converted into 1 additional year for Alice (5 Bob yrs =4 Alice yrs +1 Alice year converted from the 3ly separation) or .8 (1yr/Y) additional yr for Bob ($ Alice yrs = 3.2 bob yrs + .8 converted distance). This is how I look at it but in relativity it's probably the invariance formula. I don't know.

2. "
It's how to define the path in spacetime including the start and end points."

Does this require me knowing more rules on how to do this?

3. "
Once one has a path including the start and end points, the proper time along that interval is defined and invariant."

Are you saying Bob's interval for the outbound leg is 0-5 and Alice's interval is 0-4? You also say "
The differences that result from a change in perspective is because different intervals are being compared, not because the intervals themselves are different." Differences do result from a change in perspective so that must mean 2 different intervals are being compared but the last part of your statement is they are not different intervals?

4. So your last paragraph definitively states at the turnaround Bob= 5 and Alice =4. Then at the end Bob gains another year for Alice's 2nd inertial frame for a total of Bob=10 and Alice =8. But how does this progress from start to finish? Does Alice lose .25 yrs for every Bob yr or are there lump sum jumps in age difference at the end of each of Alice's inertial frames?

5. "
Although Bob and Alice do not agree about simultaneity everywhere, they do agree at Alice's turnaround."

Why is that? Alice's line of simultaneity swings wildly and only in mid swing does her line line up with Bob's line for an instant. Is that the reason?
Ralf, I'm pleased to see you are getting some traction here with KJW, as I had hoped you might.

15. Thanks exchemist for directing me here. So far I have some answers but they're in direct contradiction to what my former mentor taught me. Then again I may have misunderstood my former mentor as he avoided committing to specific answers and I'd have to make up my own like a hermit in a dark cave trying to describe what the sky would look like.

16. Originally Posted by ralfcis
1. "The problem isn't the separation of the clocks."

I thought the more you see someone move through space, the less they move through time. So a distance separation between two frames can be converted into time. So the 3ly separating Bob and Alice at the turnaround can be converted into 1 additional year for Alice (5 Bob yrs =4 Alice yrs +1 Alice year converted from the 3ly separation) or .8 (1yr/Y) additional yr for Bob (\$ Alice yrs = 3.2 bob yrs + .8 converted distance). This is how I look at it but in relativity it's probably the invariance formula. I don't know.
That's not a good way to view relativity. The "master equation" of special relativity is:

where:

is the differential of proper time along a given curve,
, , , and are differentials of the coordinate variables , , , and along the curve.

If the curve is a straight line, then the above equation can be rewritten as:

where:

is the proper time from coordinates to along the straight line between them.

Originally Posted by ralfcis
2. "It's how to define the path in spacetime including the start and end points."

Does this require me knowing more rules on how to do this?
The problem being solved implies particular paths in spacetime including their start and end points. The use of a spacetime diagram makes it easier to work out the paths, start and end points.

Originally Posted by ralfcis
3. "Once one has a path including the start and end points, the proper time along that interval is defined and invariant."

Are you saying Bob's interval for the outbound leg is 0-5 and Alice's interval is 0-4? You also say "The differences that result from a change in perspective is because different intervals are being compared, not because the intervals themselves are different." Differences do result from a change in perspective so that must mean 2 different intervals are being compared but the last part of your statement is they are not different intervals?
In the last part of my statement, I was simply saying the intervals are invariant. Differences caused by a change in perspective is because different intervals are being compared.

Originally Posted by ralfcis
4. So your last paragraph definitively states at the turnaround Bob=5 and Alice=4. Then at the end Bob gains another year for Alice's 2nd inertial frame for a total of Bob=10 and Alice=8. But how does this progress from start to finish? Does Alice lose .25 yrs for every Bob yr or are there lump sum jumps in age difference at the end of each of Alice's inertial frames?
To work this out, progress smoothly along one path and work out the corresponding point of simultaneity along the other path. In Bob's frame of reference, this is quite straightforward. In Alice's frame of reference, it is less straightforward due to that frame of reference being non-inertial.

Originally Posted by ralfcis
5. "Although Bob and Alice do not agree about simultaneity everywhere, they do agree at Alice's turnaround."

Why is that? Alice's line of simultaneity swings wildly and only in mid swing does her line line up with Bob's line for an instant. Is that the reason?
No. That Alice's line of simultaneity swings wildly is based on the view that Alice's frame of reference is regarded as two seperate inertial frames of reference, and that the simultaneity suddenly changes from the simultaneity of the first inertial frame to the simultaneity of the second inertial frame. But in fact, one should consider simultaneity for the single non-inertial frame itself. To do this for any frame of reference, consider a pulse of light that is emitted at one time along the path, reflected at some point away from the path, then received at another time along the path. Then the spacetime point at which the pulse was reflected is simultaneous to the point on the path that is halfway between the emission point and reception point. In determining the halfway point, it is necessary to measure time entirely along the path.

17. I'm going to have to go away and feast on this for a while, break it down into some sort of nuggets I can absorb.

18. "To work this out, progress smoothly along one path and work out the corresponding point of simultaneity along the other path. In Bob's frame of reference, this is quite straightforward. In Alice's frame of reference, it is less straightforward due to that frame of reference being non-inertial."

So from Bob's perspective in the STD I can't post, his ageing progresses( 1yr bob, .8yr alice), (2 bob, 1.6 alice), (3 bob, 2.4 alice), (4 bob, 3.2 alice) ( 5 bob, 4 alice) . No wild swings from Bob's perspective, Alice loses . 2 yr for every yr bob ages.

From Alice's perspective in the 1st inertial frame, (1 yr alice, .8 yr bob), (2 alice, 1.6 bob), (3 alice, 2.4 bob) (4 alice, 3.2 to 5 bob) . Everything looks the same from both perspectives except when Bob jumps in age 1.8 yrs instantaneously.

Now if that were true, this ageing spurt would show up in the televised signals of their daily life between Bob and Alice. (Most people use telescopes but televised signals give so much more resolution.) Right up until Alice is 4, both Alice and bob see each other in half speed slow motion due to the doppler shift ratio at .6c. At the start of Alice's next inertial frame, Bob will still see her life at the half speed time rate but Alice will immediately see Bob's tv life at double speed. The tv signal will be delayed so she'll see Bob's life start at double speed from when he's 2. For Alice's last 4 years, she'll be watching all of bob's tv signal at double speed. At no time watching bob's telecast will she see the jump in ageing when he instantaneously goes from 3.2 to 5 years in your explanation of how ageing unfurls if I've understood you correctly. Add the same jump at the start of Alice's next inertial frame and the total jump will be 3.6yrs for less than a second of Alice's time. Ageing must progress smoothly and I'm saying that intuitively.

Bob will begin to see alice's broadcast signal at double normal rate of time when he's 8. My take is whenever the two see each other's doppler shifted tv signals reflect the same rate of time, they are experiencing the same relative velocity and hence reciprocal time dilation where an age difference can't be determined because they equally see the other as ageing less. All the age difference progression occurs between Alice = 4 to Alice =6 which is equivalent to bob =8 from her perspective. You seem to have a similar idea because each ages at the same rate from each other's perspective until the turnaround point and there's this instantaneous swing. The swing continues into Alice's 2nd inertial frame so it looks like all the ageing difference occurs within these two swings. Then each sees the other in a normal reciprocal progression which I can't possibly see as accumulating an age difference because it's reciprocal and must be cancelling out.

Although my explanation gives the ageing difference process 2 years to progress, I should still see that ageing progression superimposed in the doppler shifted tv signal. I don't because that ageing progression occurs at the proper time level and can only be seen at the perspective time level delayed by c. I have not worked out the math to see if the delay smooths out the age difference progression that is occurring at the proper time level. You can ignore all this personal theory stuff as it's outside of relativity and I'm trying to understand how relativity works for age difference.

I'm still working on the rest. I don't need to look at your equations in 3D so I'll just use x for space.

P.S. See why the swing is 1.8 yrs for each of Alice's inertial frames. The normal progression is .8yr per yr if they had remained in constant relative motion. But an extra yr appears for each bob yr per swing. There are 2 swings so there are 2 extra yrs for bob (which is really 2 less yrs for Alice) over the roundtrip journey.

I think I'm understanding you correctly now.

P.S. Ok I thought about it and I know we're on the same page now. Relativity uses a different method than I do to calculate age difference but it is not because we define ageing differently (I use my former mentor's definition and he did publish a book on relativity so I thought every relativist was on board). We both ignore the "ageing" due to reciprocal time dilation in order to calculate age difference. Now I did make a misstatement above, Bob = 8 is not on Alice's line of simultaneity when she's 6. I can still state what is without going outside the bounds of relativity but I'd like to be able to post an STD. In the meantime let's do verbal and I'll reply to myself to keep this post short.

19. This post is split off from the post above to explain a small point in it.

First a definition of terms and numbers we'll be using:

Examples of "half speed" or "half" the relativistic velocity combination are:

.6c relative velocity is the relativistic velocity combination of two frames at 1/3c.
.8c relative velocity is the relativistic velocity combination of two frames at .5c.
.8824c (15/17 c) relative velocity is the relativistic velocity combination of two frames at .6c.
.9756c (40/41 c) relative velocity is the relativistic velocity combination of two frames at .8c or 3 frames at .6c.
.3846c. (5/13 c) relative velocity is the relativistic velocity combination of two frames at .2c.
.2c relative velocity is the relativistic velocity combination of two frames at .1c.

The slopes of the lines of simultaneity x/t for each of these half speeds is the inverse of the slope of their velocity lines x/t so:

.33c half speed slope of simultaneity line is 3.
.5c half speed slope of simultaneity line is 2.
.6c half speed slope of simultaneity line is 5/3.
.8c half speed slope of simultaneity line is 5/4.
.2c half speed slope of simultaneity line is 5.
.1c half speed slope of simultaneity line is 10.

So we're still on the same scenario but we're going to study a host of turnaround speeds and what the resultant age difference is. Looking at my STD, I get this table:

If Alice turns around at .9756c, Bob will be 8.075 and she will be 4.675 for an age diff of 3.4 at re-unification.
If Alice turns around at .8824c, Bob will be 8.4 and she will be 5.6 for an age diff of 2.8 at re-unification.
If Alice turns around at .8c, Bob will be 8.75 and she will be 6.25 for an age diff of 2.5 at re-unification.
If Alice turns around at .6c, Bob will be 10 and she will be 8 for an age diff of 2 at re-unification.
If Alice turns around at .3846c, (you need a big STD for relativity) for an age diff of 1.6 at re-unification.
If Alice turns around at .2c, (you need a big STD for relativity) for an age diff of 1.3 at re-unification.
If Alice stops, Bob will be 8 and Alice will be 7 for an age diff of 1 with no reunification.

What's interesting to note is that the slope of the "half speed" perspective's lines of simultaneity from Bob t=8 intersect the full relative velocity lines at points that reflect the age difference as shown in this spacetime diagram (STD) which you can't see because I can't post it.

All the half speed lines emanate from t=8 and intersect the velocity lines at the following points:

.9756c (half speed = .8c) at t'= 4.6 for an age diff of 3.4 as above.
.8824c (half speed = .6c) at t'= 5.2 for an age diff of 2.8 as above.
.8c (half speed = .5c) at t'= 5.5 for an age diff of 2.5 as above.
.6c (half speed = 1/3 c) at t'= 6 for an age diff of 2 as above.
.3846c (half speed = .2c) at t'= 6.4 for an age diff of 1.6 as above.
.2c (half speed = .1c) at t'= 6.7 for an age diff of 1.3 as above.
0c (half speed = 0c) at t'= 7 for an age diff of 1 as above.

The table can also show how age difference unfurls for each Bob year, it uses the exact same method.

Of course the table continues into forbidden territory for relativity so I can't show you without permission. The graphs are beautiful, like butterflies but no way to put a needle in them and post.

You may ask why "half speed"? The explanation is also outside the bounds of relativity. But everything I've shown you thus far is perfectly legal so there is no justification to throw this post into the trash or ban me from this forum. Consider it a curiosity, a mathematical coincidence with no reason behind it. I'll withdraw if people find it offensive as they have on other forums. In fact I've been accused of corrupting the young impressionable minds of prospective relativity students and possibly compromising promising careers. I took that as a compliment.

20. Originally Posted by ralfcis
From Alice's perspective in the 1st inertial frame, (1 yr alice, .8 yr bob), (2 alice, 1.6 bob), (3 alice, 2.4 bob) (4 alice, 3.2 to 5 bob). Everything looks the same from both perspectives except when Bob jumps in age 1.8 yrs instantaneously.

Now if that were true, this ageing spurt would show up in the televised signals of their daily life between Bob and Alice.
This is wrong for two reasons: First, it treats seeing as the same as simultaneity. They are not. What you see is in the past, never simultaneous. Second, you are disregarding what I said about Alice's worldline not being two inertial frames of reference, but a single non-inertial frame of reference. In the single non-inertial frame of reference, the points of simultaneity along Bob's worldline is continuous, there is no jump. The numbers you provide for Alice's perspective in the 1st inertial frame are incorrect when the full non-inertial frame is taken into account. To determine the space of simultaneity for my worldline at this instant in time requires not just my worldline at that this instant in time, but also my past worldline and my future worldline. Thus, even during the first part of Alice's journey, simultaneity also involves the second part.

21. "This is wrong for two reasons: First, it treats seeing as the same as simultaneity. They are not. What you see is in the past, never simultaneous."

I said exactly what you just said. Alice at her turnaround sees Bob's televised picture from the past when he's 2 and she's 4. Her line of simultaneity from her at 4 hits Bob at 3.2. 3.2 comes after 2. What she sees is Bob's televised signal from Bob affected by the Doppler shift ratio. You can't see simultaneity, only calculate it.

"
Second, you are disregarding what I said about Alice's worldline not being two inertial frames of reference, but a single non-inertial frame of reference."

I thought you were directing me to break it up into 2 parts and you even said the jump in Bob's age from Alice's perspective is not 3.2 to 6.8. I don't see how it matters, the result is the same whether you consider the spacetime path in 2 parts (which I think is invalid) or the entire round trip as 1 valid spacetime path. The question is how does relativity determine permanent age difference between the two independent of perspective as opposed to the age difference due to time dilation dependent on perspective. Everything outside of Alice's line of simultaneity swing at t'=4 is reciprocal time dilation and does not result in a permanent age difference between the two over the entire roundtrip journey. Hence, the permanent age difference between the two must occur inside her line of simultaneity's swing and I could see how that was happening with Alice's perspective of Bob instantaneously ageing 3.6 yrs minus the 1.6 yrs she would have aged anyway without the swing leaving Bob gaining 2 yrs on her during the swing. This interpretation is wrong? So I'll continue trying to figure out what you're saying.

"Thus, even during the first part of Alice's journey, simultaneity also involves the second part."

I totally agree but I thought you were giving me equations to figure out how to properly define spacetime paths that don't end in a re-unification so I could break her roundtrip into two inertial frames. But that's no? Defining a spacetime path requires only the rules I stated before? Just to confirm, there are no others?

P.S. I suspect we may be talking about 2 different things. I think you're talking about how to determine the length of a spacetime path thereby arriving at either Bob or Alice's age and I'm talking about the mechanism of where in the spacetime path the ages start and end differing between the two. Is that what's happening? I don't know.

P.P.S. I just drew me a 4ly .8c round trip STD. When Bob is 10, Alice is 6. This must mean, if I use the same analysis I did for .6c, 4 years are lost during Alice's line of simultaneity sweep from Bob =1.8 to bob = 8.2 for a total of 6.4. Now to get the answer we need of 4 Bob years, we need to subtract 2.4 from 6.4.

In the .6c example we had to subtract 1.6 from 3.6 to get 2. With a Y of 1.25, so 2 Bob yrs divided by Y was the required 1.6 year correction. In the .8c scenario, Y= 5/3 and 4yrs * 3/5 =2.4 which is the required correction for .8c. The correction is all about what Alice would have aged if there was no turnaround for 4 bob years and since she doesn't age those 2.4 yrs, bob ends up 4 yrs older due to relativity's mechanism of age difference.

This method works for asymmetrical velocities on the two legs so I don't see why it's mathematically unreasonable to split the roundtrip into separate legs.

Now I'm not saying this is the correct way of understanding how Bob ends up older in relativity but what I'm specifically asking for is a method as dependable as this that relativity uses to explain age difference due to a turnaround. One where I can say Bob gains 2 yrs just at the end of the 1st leg and another two years just at the beginning of the 2nd leg. Otherwise people are coming up will all sorts of unfounded scenarios of how the extra Bob years are appearing. I myself have come up with many possible explanations and only my latest one is correct. Just an example, or some plain English with some numbers thrown in, anything so I can get a foothold and work my way to some understanding of what you're saying.

My former mentor said relativity does not allow such a method before the end of the spacetime path even though it's mathematically possible to do so. Other limitations of the spacetime path method are that only a re-unification or a stop allow for the establishment of age difference between the two. But I know it's mathematically possible to establish age difference if Alice slows down or speeds up instead of executing a turnaround which relativity doesn't allow because there's no valid end to those spacetime paths. I feel relativity can't arbitrarily overrule the math just because it violates the spacetime path rules. My math does not require spacetime path rules but it can't be discussed here because it's outside of relativity.

22. Ok I've figured it out and here's how age difference works in relativity in the .6c turnaround scenario:

Alice spends her 1st 4 years watching the Bob show in half speed slow motion due to the doppler shift ratio. So she's only seen the 1st 2 years of the bob show at her turnaound. Since it takes 3 yrs for light to travel the 3ly to Alice t'=4 from Bob t=2, Bob is 5 (the proper time on his watch is 5) when his signal from t=2 reaches Alice at t'=4 (the proper time on her watch). Alice's swing of her line of simultaneity won't even begin on Bob's timeline for another 1.2 bob years.

So at the turnaround, Alice starts watching the Bob show at double fast forward. She's not going to run out of show because there's 3 yrs of backlog stuck in space. Bur let's see if anything weird happens to bob's picture when the supposed swing in his age starts when he's 3.2. Will Alice see Bob instantaneously age from 3.2 into 6.8 when he's only actually reached the age of 5? Alice is 4.6 when she receives Bob's signal from t=3.2. It takes 2.55 yrs to reach Alice so Bob is 5.75. The backlog in his show is diminishing, her binge watching is paying off.

Let's see what the status is at the end of her line of simultaneity swing. The light signal from Bob at t=6.8 reaches Alice at t'=6.4 and it has travelled 1.2 yrs so Bob is 8 when Alice is 6.4. From t=6.8 to t=10 which is 3.2 yrs of bob show to watch, Alice has from t'=6.4 to t'=8 to watch it at double speed. So when they re-unite, she will be all caught up and viewing his present directly and he will have aged 2 yrs more than her. No sudden jump in Bob's age has been witnessed by Alice. So what's the swing in Alice's line of simultaneity telling us about age difference, absolutely nothing.

There's been nothing funny in Bob's apparent ageing during the total swing in Alice's line of simultaneity. In fact the times on both their watches would be the same (Bob 10, Alice 8) if Alice had never turned around. So where's this permanent age difference due to Alice's turnaround because this all looks like reciprocal time dilation to me. I'm going to do the analysis from Bob's perspective and see if it's hiding there.

From Bob's perspective, he's seeing the Alice show at half speed slow motion until he's 8. That's when he'll finally see the Alice show from t'=4 going at double speed fast forward. The light takes 3 yrs to reach bob but I guess you must apply gamma (Y=1.25) to it to get Alice ageing 2.4 of her years in the time it takes for the light to reach bob. In the 2 yrs bob has left before re-unification, he will see 4 yrs of the alice show and they will again be both up to speed with each other. But if Alice had kept going and not turned around, it would take her light signal longer and longer to reach Bob. He'd fall further and further behind in his watching of the alice show. Nevertheless, the instantaneous proper time on both their watches would be t=10 for Bob and t'=8 for Alice.

So what does getting behind in a tv show have to do with establishing permanent age difference as opposed to reciprocal time dilation? If the analysis had been done with Bob being depicted as moving, the reciprocal time dilation would have shown Bob's watch at t=3.2 when Alice's is at t'=4 at the turnaround but it would have corrected itself by the end where Bob's t=10 and Alice's t'=8. If Alice had never turned around in this analysis, when Bob hit 10, Alice would be 12.5. There's something deeply wrong about the reverse analysis in that it doesn't tell the same story at all. It must because however you depict relative velocity, it must give the same results no matter the depiction. This is actually a statement of faux outrage because I know that when Alice changes velocity, they are no longer in a known state of relative velocity and until they re-establish that state, that's where age difference is actually occurring and can be properly depicted consistently independent of who's depicted as stationary. This, relativity can't do unless you show me otherwise.

Relativity knows this is a logical inconsistency between 2 mirror image analyses that should give identical results so it is hidden behind spacetime rules that do not allow description of how age difference unfurls. Or maybe explain away the inconsistency but no one I've asked has even tried to do so. Rule 1 of relativity, there are no inconsistencies and rule 2, if you find one refer to rule 1.

Maybe the moderator could fix the download of images problem here or show me how it's done because I'd like to talk math in graphical form instead of arithmetic.

P.S. I assume I'm asking questions that have never been asked before because I've been asking them for 13 years and they have been mostly unaddressed in that time. (My initial question took 6 yrs for an answer so I no longer ask it.) Mostly I get irrelevant wiki articles thrown at me or book suggestions.

23. While I await your answer, (I hope one is coming as most people never come back to finish a discussion) I went back to re-read your posts.

"That's not a good way to view relativity. The "master equation" of special relativity is:"

I don't see how your formula is an any different way of looking at relativity from the way I worked out those numbers. Anyway I don't view that as the master equation. I see c2 = vt2 + vx2 to be the master equation which translates to we are always moving at the speed of light which is a combination of our speed through time and our speed through space. All the formulas of relativity are derived from this equation but more importantly it always groups Y with v for a new concept of Yv that really works some eye popping miracles that I can't discuss in a thread about relativity.

"
But in fact, one should consider simultaneity for the single non-inertial frame itself. To do this for any frame of reference, consider a pulse of light that is emitted at one time along the path, reflected at some point away from the path, then received at another time along the path. Then the spacetime point at which the pulse was reflected is simultaneous to the point on the path that is halfway between the emission point and reception point. In determining the halfway point, it is necessary to measure time entirely along the path."

Oops I see you did tell me not to separate Alice into 2 inertial frames which I agree with.

After that I don't understand your instructions. Can you draw what you want me to do or just give me numbers on the STD and what line you want coming out of those numbers?

24. I'm a vagabond without a forum. I've been exploring a question about special relativity for years but have now only started peddling it from forum to forum hoping someone knows the answer and can answer my specific questions to his answer. So far I've found 2 knowledgeable people but no definitive answers yet and why differing answers are wrong. Full disclosure: while waiting I've come up with my own answers over the years.

What conditions define a spacetime path? The answer is supposed to differentiate ageing from reciprocal time dilation and permanent age difference due to a change in relative velocity as in the twin paradox. I won't be communicating with anyone posting links to wiki articles. If you see no difference between reciprocal time dilation and age difference, please don't try to respond.

1. True permanent age difference can only be established if the two participants start together, one makes a change in relative velocity and they both re-unite. Hence, relativity forbids making any determination of permanent age difference if the change in relative velocity is a slow down (not quite a stop) or a speed up.

2. An exception is when the change ends in a relative stop, they remain separated but the end of the spacetime path is when the news, via light signal, of the change reaches the other party. It's somehow not as valid as point 1 because their separation allows another frame's line of simultaneity to calculate a different permanent age difference from the one they see between them (I don't agree) or the space between them has a time value that does not appear on clocks and can only be exhausted by re-unification. I never got a clear answer on this.

3. Unchanged constant relative velocity does not result in age difference. Some contend age difference is a matter of perspective, and so constant relative velocity does result in age difference, equal from each perspective. Others say age difference can't be established because there is no valid end to the spacetime path. Others say because time dilation is reciprocal, the two perspectives cancel out and that's why there's no age difference.

4. At what point in the spacetime path does the age difference occur? Relativity's answer is that age difference can only be determined at the end of the spacetime path. Any attempt to look at how it progresses during the path is forbidden. Others say there is a jump in age difference during the swing in the initiator's line of simultaneity. Other's say there are two jumps, one at the velocity change and another at the end. Most say age difference progresses incrementally and identically to reciprocal time dilation in a spacetime path. They say there is no difference between the two even though the twin paradox proves there is.

5. If relativity does not forbid looking at how age difference unfolds, then why are there two different answers depending on which party is depicted as stationary?

25. Originally Posted by ralfcis
I'm a vagabond without a forum. I've been exploring a question about special relativity for years but have now only started peddling it from forum to forum hoping someone knows the answer and can answer my specific questions to his answer. So far I've found 2 knowledgeable people but no definitive answers yet and why differing answers are wrong. Full disclosure: while waiting I've come up with my own answers over the years.

What conditions define a spacetime path? The answer is supposed to differentiate ageing from reciprocal time dilation and permanent age difference due to a change in relative velocity as in the twin paradox. I won't be communicating with anyone posting links to wiki articles. If you see no difference between reciprocal time dilation and age difference, please don't try to respond.

1. True permanent age difference can only be established if the two participants start together, one makes a change in relative velocity and they both re-unite. Hence, relativity forbids making any determination of permanent age difference if the change in relative velocity is a slow down (not quite a stop) or a speed up.

2. An exception is when the change ends in a relative stop, they remain separated but the end of the spacetime path is when the news, via light signal, of the change reaches the other party. It's somehow not as valid as point 1 because their separation allows another frame's line of simultaneity to calculate a different permanent age difference from the one they see between them (I don't agree) or the space between them has a time value that does not appear on clocks and can only be exhausted by re-unification. I never got a clear answer on this.

3. Unchanged constant relative velocity does not result in age difference. Some contend age difference is a matter of perspective, and so constant relative velocity does result in age difference, equal from each perspective. Others say age difference can't be established because there is no valid end to the spacetime path. Others say because time dilation is reciprocal, the two perspectives cancel out and that's why there's no age difference.

4. At what point in the spacetime path does the age difference occur? Relativity's answer is that age difference can only be determined at the end of the spacetime path. Any attempt to look at how it progresses during the path is forbidden. Others say there is a jump in age difference during the swing in the initiator's line of simultaneity. Other's say there are two jumps, one at the velocity change and another at the end. Most say age difference progresses incrementally and identically to reciprocal time dilation in a spacetime path. They say there is no difference between the two even though the twin paradox proves there is.

5. If relativity does not forbid looking at how age difference unfolds, then why are there two different answers depending on which party is depicted as stationary?
I got your post asking me to answer your question about "what constitutes a space-time path" ? I got it kind of late this evening but tomorrow I'll try to explain it

26. Yay, I'm very excited. This could be the end to my quest!

27. Originally Posted by ralfcis
P.S. I suspect we may be talking about 2 different things. I think you're talking about how to determine the length of a spacetime path thereby arriving at either Bob or Alice's age and I'm talking about the mechanism of where in the spacetime path the ages start and end differing between the two. Is that what's happening? I don't know.
Ultimately, arriving at an age difference between Alice and Bob involves determining the lengths of the spacetime paths of both Alice and Bob. To determine the length of each of the paths, one needs to define a start point and an end point for each of the paths. Also, in order for the age difference to be meaningful, one needs to relate the start and end points of one path to the start and end points of the other path. The problem is that unless the start points of both paths are the same point, and the end points of both paths are the same point, there is no unique way to relate the start and end points of one path to the start and end points of the other path such that the age difference is unequivocally determined. For example, one would usually choose simultaneity to relate one path to the other, but in general different observers do not agree about simultaneity, and there is no way around this (it is not a flaw of relativity, but the nature of reality).

It should be noted that given two points in spacetime, the distance between them depends on the path. (from the "master equation") is not an exact differential. This means that there is no function of spacetime location.

28. Originally Posted by ralfcis
"But in fact, one should consider simultaneity for the single non-inertial frame itself. To do this for any frame of reference, consider a pulse of light that is emitted at one time along the path, reflected at some point away from the path, then received at another time along the path. Then the spacetime point at which the pulse was reflected is simultaneous to the point on the path that is halfway between the emission point and reception point. In determining the halfway point, it is necessary to measure time entirely along the path."

Oops I see you did tell me not to separate Alice into 2 inertial frames which I agree with.

After that I don't understand your instructions.
Do you know how radar works? What I'm saying is the reflection of the signal from the object is simultaneous to the time that is halfway between the signal being sent and the echo being received. The important point is that this definition of simultaneity is true regardless of the motion of the radar unit.

29. "The important point is that this definition of simultaneity is true regardless of the motion of the radar unit."

Yup I now get what you're saying but you may not like how I'm going to use what you're saying because it really fits into my theory and a new way to see how relativity handles age difference. You're going to have to put some effort into following what I'm saying. I can tell when people just scan for recognizable words and end up putting them back together in their own interpretation.

Let's look at the outbound leg. Add a "half speed" (1/3 c) perspective between Bob and Alice. The line of simultaneity from that half speed perspective intersects the same proper times of both and it intersects the half speed relative velocity line at an equidistant point from each. You define this as a kind of "true" simultaneity and I define it as a shadow of the true simultaneity but both essentially (meaning not at all except for this instance)) are the same concept in slightly different terms.

Now we throw in the equation for tau2 = t2 + x2 where c2=1 so I don't need to write it into the equation. I use this to convert distance into time and back again. Einstein said time is what clocks measure but I say age is what clocks measure and the time that doesn't appear on those clocks is stored as space or distance travelled between the two. This is what the formula for tau is telling us.

To put some numbers to it, when Alice is 4, she is 3ly from Bob and he is 3ly from Alice. The formula for tau =5 from Bob's perspective is 52 = 42 + 32 which is correct. The formula for tau =4 from Alice's perspective is 42 = 3.22 + 2.42 which is also correct. The 2.4 is from 3/Y where Y=1.25 at .6c. But these results tell us nothing about what is really happening here. We want results that convert the distance separation into time. Another formula does that but you can read it right off the STD.

The 3 ly @ .6c is equivalent to 1 yr time. How does that relate to the half speed perspective and tau for Bob and the age on Alice's clock? Graphically tau - time for 3ly = alice's age (5-1=4). The "true line of simultaneity from the half speed perspective joins Alice =4 and Bob =4. Let's do the same calculation for Alice's tau. The 1 yr time equivalent for the 3 ly separation must be divided by Y for Alice's perspective so it's .8 yrs. It gets added to 3.2 to equal Alice's tau of 4. You'll need to do other examples to prove to yourself the math is consistent. I do not wish to burden you with the formulas because they've been derived on another forum and I'd have to go dig them up. The formulas are not important here, it's the understanding of how they're used.

So what does this mean? On the journey where Alice turns around, for each 3 ly she travels at .6c, time gets stolen off her clock and is converted into distance travelled. The time equivalent for 3ly distance at .6c is 1 Bob yr. She travels a total of 6 ly so 2 yrs are stored in the distance she travelled and have disappeared off her watch.

But you may say that's poppycock, how can time be in a form of distance? That's how relativity works, the more time you spend travelling through space, the less time you spend travelling through time which is what clocks measure as age. Alice's turnaround established she was the one doing 2 legs through space whereas before the turnaround both were going through space reciprocally and, accounting for this, the time they stored in the distance separation cancelled out. This is the same thing the half speed perspective does. By being equidistant from both, the time converted from the distance separation cancels out.

So how does all this relate to the scenario where Alice doesn't make a change in relative velocity? The exact same calculation applies as at just before the turnaround point. Alice's line of true simultaneity (which is the same as the half speed line of simultaneity) shows she and Bob are both 8. When Alice is 8, she has gone 6ly which is 2 yrs stored in distance travelled and you subtract that from Bob's tau =10 to get the result that in the true simultaneity perspective he is also 8.

Now I'm just trying to explain how relativity handles things and my personal theory gets the same results but with a much different and clearer explanation of how things happen. Again, I can explain how relativity arrives at the same results in several different plausible stories. All of the "popular science" explanations I've seen on various forums are easily mathematically disprovable but math hasn't convinced anyone of the believers so far. Only my former mentor truly understands relativity but he won't speak to me since I branched off with my own theory before he could clearly explain relativity's point of view.

I'd just like to hear which one of these plausible stories relativity actually uses. I don't want some vague smoke and mirrors jargon explanation that falls apart as soon as I ask a question about it and then the person just walks away which has always happened in the past. Just a yes or no without being qualified by the word "essentially" or "sometimes". Have I described how relativity handles age difference or, at least, is my explanation thoroughly consistent and plausible without violating any of relativity's tenets? Actually I don't care about the second part of the question because my true goal is to fully understand relativity's point of view.

P.S. The most important thing to consider about the story here is that even in the reverse analysis, with Alice depicted as stationary, as soon as she takes off to catch up with bob, she is the one who is 1 yr younger. Because she is the one who initiated the change in relative velocity, she is the one who actually travelled through space despite what the depiction shows. Other stories which depict Bob as moving say he is 1 yr younger and Alice makes up 2 yrs younger by the time she catches up with Bob. This is a completely wrong interpretation because the depiction of relative velocity does not change the results of relative velocity.

30. Moved to Personal Theories.

31. I have personal theories but none of the discussion discloses my personal theories. I did not present my personal theories and nothing I said is outside of relativity. I'm trying to understand relativity by using relativity. I was very careful not to cross any boundaries. The discussion was pure relativity and math. Please show me otherwise you, you, . . . Probably I offended one of the cartoon interpretations of relativity some readers might be holding on to. I guess we'll let the webmaster decide. I hope he's a fair chap.

32. Originally Posted by ralfcis
I have personal theories but none of the discussion is about my personal theories.
Riiight:
I'm going to use what you're saying because it really fits into my theory and a new way to see how relativity handles age difference

my personal theory gets the same results but with a much different and clearer explanation

and especially
my true goal is to fully understand relativity's point of view before I replace it

How can you seriously expect to replace a theory you admit you don't understand?

I guess we'll let the webmaster decide. I hope he's a fair chap.
Good luck with that: WE (i.e. numerous forum members including admins and moderators) haven't been able to contact him for years.

33. KJW do you have some pull with this moderator to get me out of jail?

34. I was forthright, I mentioned I have a personal theory but did not present it. What I showed here is not my personal theory at all. Mine is very very different. This was all about understanding relativity and what I do with that understanding is my business, that's why I want to fully understand it "before" to be fair. What if this thread made me realize there's no need to do so. Won't find out now. Also, there are many wrong interpretations of relativity. How do you know the ones calling for this to be trashed have the right ones. Where were their voices in the thread which was mostly questions and asking for clarifications by presenting my understanding of what was being said? Please show me any part of what I said, any part of the math that's wrong. And if you do, that's what I want to find out, Have I interpreted relativity correctly! That is all.

35. Originally Posted by ralfcis
I mentioned I have a personal theory but did not present it.
Ah, goal-post moving....
but none of the discussion
Oh yeah "I avoid all this mess by taking the two exceptions to relativity's rules and making them the rules" also qualifies as "personal theory".

What I showed here is not my personal theory at all.
Apart from referring to it and using as a "yardstick" to check the maths.

This was all about understanding relativity
And yet you say - more than once - that (essentially) the current theory is correct because it agrees with your "theory".

that's why I want to fully understand it "before" to be fair.
Then don't you think that taking something better than "a mickey mouse on-line free course" would be a good start?

What if this thread made me realize there's no need to do so. Won't find out now.
Why not? It's not locked.

Please show me any part of what I said, any part of the math that's wrong.
How about the numerous KJW posts that have used those exact words: "that's wrong"?

36. Exceptions to the rules are still accepted as part of the rules. The rule is the twins must reunite and what is also acceptable is they can relatively stop or continue at constant relative velocity which still allows determination of age difference (0 in the last example).

If I in anyway showed what my personal theory states then you should be able to quote it. You'd know it because it's based on information theory. I can easily write out the opening paragraph but that would definitely get me kicked off. By your logic you should kick me off because I have a pet theory that would definitely get me kicked off. See how your logic works?

Again mentioning you have a theory and that parts agree with relativity is not disclosing a personal theory. Everyone has a pet theory. Why am I in jail for it.

I took a course then found a very knowledgeable mentor who published a book on relativity and who tutored me personally for 10 years. Again you're fishing for excuses.

No one of the level of expertise I'm looking for is going to fish around the personal theories. I personally talked to Don Lincoln of Fermilab and he said, do you know how many people approach me to review their papers every day. I have no time for that. Do want proof, I have it in writing.

"That's wrong" is a part of normal discourse. Then i went on to ask well is this right then. This was not a contentious discussion where i stubbornly stuck to my personal theory which I didn't disclose. However, when I saw correlation I mentioned that to say yes i think i understand what you're saying. I'm going to put it in my own words. Do you see a correlation. I changed my interpretations many times to try to understand what he was saying.

Doing the right thing is not a sign of weakness in front of your buddies who want to silence me, it's actually a sign of strength. I feel I'm so close to the end, there's a guy who said he had the answers and was going to write them out today. Once I get what I need, I'll leave and never come back.

37. Originally Posted by ralfcis
Exceptions to the rules are still accepted as part of the rules.
Here for clarification:
exception

someone or something that is not included in a rule
So no, you're wrong.

If I in anyway showed what my personal theory states then you should be able to quote it.
Those goalposts again...

I can easily write out the opening paragraph but that would definitely get me kicked off.
That's twice you've invented a rule for the forum that actually doesn't exist.

By your logic you should kick me off because I have a pet theory that would definitely get me kicked off.
Right. Because we don't have any sub forum for, say, Personal Theories. Or Pseudoscience.
Oh, wait...

Nope, but I see that grasp of facts is pretty tenuous.

Again mentioning you have a theory and that parts agree with relativity is not disclosing a personal theory. Everyone has a pet theory. Why am I in jail for it.
Because it's been referenced in this thread, more than once.
(Jail?)

I took a course then found a very knowledgeable mentor who published a book on relativity and who tutored me personally for 10 years.
A "mickey mouse course" in your own words.
And, despite 10 years of being tutored1, you still have questions that you expect to get answers to on a forum (and rapidly2)?

Again you're fishing for excuses.
Nope. Don't need 'em.

That's wrong is a part of normal discourse.
Certainly. When you're wrong. (Which was what you asked: Please show me any part of what I said, any part of the math that's wrong.)

1 Which, given the errors in this thread didn't teach you much.
2 Viz. the PM you sent me because KJW hadn't replied to one of your posts within 18 hours or so...

38. Questions are not errors.
Ok, you did make one valid point. I should be kicked off for impatience. Also it is laughable to think a forum can answer questions but it really did in my case. Too bad you had to end that.

You guys really take great pleasure in your work.

39. Well this is not a good day for me. First I get thrown here and now my IP has been blacklisted from accessing all my years of posts on my former SPCF forum. They have my only copy and I was really excited I could upload my STDs from there to here, but no more. They must really hate me. I can't even start my theory of ralfativity thread. Oh well, I'll find a way around it.

40. Originally Posted by ralfcis
KJW do you have some pull with this moderator to get me out of jail?
You're not in "jail". You are still able to post on this forum. All that has happened is that this thread had been moved to "Personal Theories & Alternative Ideas". What's the problem with that? But arguing with a moderator over that decision is a quick way to get suspended or even banned.

41. Well I finished arguing. Ok, not jail but banishment to a no man's land. I'm glad you're still here but if you leave, no other expert is going to find me here. If I'm wrong in my last post or if we have terminology troubles, you may leave.

42. Originally Posted by ralfcis
Well I finished arguing. Ok, not jail but banishment to a no man's land. I'm glad you're still here but if you leave, no other expert is going to find me here. If I'm wrong in my last post or if we have terminology troubles, you may leave.
With the exception of "Trash Can" (which can't be viewed unless logged in), all subforums are equally accessible. There is no problem with having one's thread in "Personal Theories & Alternative Ideas". I've started threads in the "Personal Theories & Alternative Ideas" subforum.

43. Originally Posted by ralfcis
Let's look at the outbound leg. Add a "half speed" (1/3 c) perspective between Bob and Alice. The line of simultaneity from that half speed perspective intersects the same proper times of both and it intersects the half speed relative velocity line at an equidistant point from each. You define this as a kind of "true" simultaneity and I define it as a shadow of the true simultaneity but both essentially (meaning not at all except for this instance)) are the same concept in slightly different terms.
You are not allowed to do this. This "half speed" frame of reference is a valid frame of reference, nothing more. You are not allowed to declare this as "true" or anything else that suggests this is a preferred frame of reference. The existence of this frame of reference does not solve the problem of determining an unequivocal age difference because the problem is with the existence of all the other frames of reference that provide different answers to the question. You can't declare one frame above all others by fiat. That is against what relativity is about.

Originally Posted by ralfcis
tau2 = t2 + x2
The equation is

It should be noted that and are coordinates, while is proper time.

Originally Posted by ralfcis
So what does this mean? On the journey where Alice turns around, for each 3 ly she travels at .6c, time gets stolen off her clock and is converted into distance travelled. The time equivalent for 3ly distance at .6c is 1 Bob yr. She travels a total of 6 ly so 2 yrs are stored in the distance she travelled and have disappeared off her watch.

But you may say that's poppycock, how can time be in a form of distance? That's how relativity works, the more time you spend travelling through space, the less time you spend travelling through time which is what clocks measure as age.
While there may be a mathematical equivalence between this view and the correct view, I fail to see how this is a better explanation of relativity. If one is given the coordinates of two points in a particular coordinate system, the metric which is just a generalisation of the Pythagorean distance formula, provides the spacetime distance between those two points. What could be simpler than that? And relativity is more than just the twin-clock paradox. The view you are putting forward seems to disregard the principle of relativity which is an extremely important principle. And how does your view generalise to general relativity?

44. So in my equation I got tau and t mixed up? So when Bob =5 and Alice =4, tau is Alice's time and t is Bob's? Well that's fine, the answer's still the same. However the meaning is different. If the proper time is 4 for Alice and since proper time rate is universally the same in frames of constant relative velocity, and since they both started at t = tau= time =0 (sync'd), then Bob's proper time must also be 4 relative to Alice in a theoretical instantaneous present that can only be experienced simultaneously if the two parties are co-located. If they are separate, that instantaneous present (that relativity does not recognize), must be calculated once the speed of light delay between the two is accounted for. Is there such a legally binding contract stated somewhere in relativity or have I just disqualified this thread from ever being taken out of the personal theories section (not implying that the previous disqualification wasn't already valid).

Ok, I see how my personal theory is bubbling through from your last two sentences and the misinterpretation of the equation. You picked up on that which is very impressive. I'm blind to that, it keeps creeping back into my brain. There are 3 main tenets to my theory that would make any relativist cringe. Actually you picked up on the 1st one (a universal time rate of all frames engaged in constant relative velocity ticking at the normal time passage rate which is the velocity c through time, i.e. all watches ticking at the same rate but not sync'd) in an earlier post. I was going to say at least you didn't call me an absolutist but "preferred framer" at the top of your post kind of implies that. But, in fairness, an absolutist believes all time is relative to the CMBR which I don't. Also use of the the half speed frame is equivalent to choosing to depict either Bob as the stationary frame. It does not imply they are how they're depicted. But let's not get into that now. Let's concentrate on how relativity works.

I'd like to work backwards from this sentence:

"While there may be a mathematical equivalence between this view and the correct view"

with the formula for tau, possibly the invariance formula and maybe the lorentz transforms thrown in for good measure, how does relativity calculate the same step by step results I get from my math which you said works (equivalently). I still don't know what is "the correct view" for this specific example. The question still remains, how does age difference unfurl during the spacetime path especially under the spacetime path rules which I was told only allow determination of age difference at the end of the spacetime path? And can relativity calculate age difference outside of the re-unification rule and its two inclusions (which I used to call exceptions) of Alice stopping and Alice not making a velocity change? So if Alice's change involves a slow down or a speed up, do those scenarios result in a permanent age difference using the correct relativistic method? On a philosophical note, wouldn't mathematical equivalence validate a competing theory despite the fact everyone says there is no need for one? (I can't yet address how this hypothetical competing theory would affect general relativity and the math behind this hypothetical theory is different from that presented in the last post.)

P.S. The on-line mickey mouse course I took went through this example of the twin paradox but it never mentioned spacetime path or how age difference unfurls. It did show how the doppler shift ratio (without calling it that and getting it mixed up with reciprocal time dilation) would work in a side by side video of how Alice and Bob would see each other age in real delayed time but that's not the same thing as how age difference unfurls.

45. Originally Posted by ralfcis
So in my equation I got tau and t mixed up? So when Bob =5 and Alice =4, tau is Alice's time and t is Bob's? Well that's fine, the answer's still the same. However the meaning is different. If the proper time is 4 for Alice and since proper time rate is universally the same in frames of constant relative velocity, and since they both started at t = tau= time =0, then Bob's proper time must also be 4 relative to Alice
One point in the mentioned "paradox" at the set should be more stressed. Not only that Alice's and Bob's watches are being synchronized at the start, but, while both are being stationary they measure the equal reference distance e.g. to some Star as turn around point. When Alice moves she can say that she is still stationary and that Star is moving at the same relativistic speed toward her, but the distance will now suffer length contraction. Therefore she cannot be of the same age as Bob when she is adjacent to turn around point. Alice will calculate the trip to turn around point to last for 4 years, but Bob because there is no path contraction and the Star remains fixed, a 5 years. No change in Alice's velocity and there is age difference near the turn around point.

Even when you include time dilation from Alice's perspective to Bob's watch, all the missing years of Bob's life occur in the short time when she is changing velocity. So, she will calculate that Bob is older even from her point of view Bob's clock ticks slower in no-changing velocity outgoing and ingoing trip.

See:
The Twin Paradox in Special and General Relativity. &mdash; physicsmatt

That is good example of twin paradox which also shows how it is resolved even when there is no change in velocity (stop and turn around) i.e. on torus. I was very interested in your line of reasoning, but Relativity deals well with all the variations of twin paradox, as shown.

Sincerely,
Zlatan

46. I just gave it a quick glance but he says at one point Alice does not age during the sweep of Alice's line of simultaneity across Bob's time line. In the example here, the sweep is from 3.2 to 6.8 which is 3.6 yrs. Bob only ages 2 more years than Alice so Alice must age 1.6 yrs during the sweep. That can only be determined if you consider what Alice would have aged if she hadn't made a change in velocity unless he can explain that differently.

I'm hoping KJW's explanation does not follow the same instantaneous age difference that occurs from a line of simultaneity sweep. The math I proposed in my last post has a regular .25 yr loss for every yr travelled no matter who ends up making the change. The math for my personal theory ends up with a different result, as age difference only unfurls during the imbalance of relative velocity caused by Alice's change and Bob's receiving the news of it and establishing a new constant relative velocity after which further age difference no longer occurs. The delay of the information causes age difference. What this method allows is a determination of age difference if Alice's change is a slow down or a speed up of relative velocity because this method does not depend on spacetime path rules. I have not mentioned this before and I will start a separate thread to discuss it as soon as I can gain read access to my posts on the forum I was banned from. I do not wish to pollute this relativity thread with my personal theory.

I gotta say, this guy KJW, I don't know who he is but he must be way up there in the field of relativity. I haven't encountered anyone close to him, although my former mentor was very good except he wouldn't answer questions specifically.

47. Originally Posted by ralfcis
all watches ticking at the same rate
It's quite common for it to be said that in their own frame of reference a clock ticks at one second per second regardless of its motion. Although ultimately meaningless, what this statement is attempting to express is that motion doesn't actually affect the rate at which clocks tick, and that one second on a clock is a true second even if that clock is time dilated in some other frame of reference. This is a consequence of the principle of relativity.

Originally Posted by ralfcis
I was going to say at least you didn't call me an absolutist but "preferred framer" at the top of your post kind of implies that.
I should point out that the reason why there is no preferred frame of reference in special relativity is because the Minkowskian metric (the "master equation") is invariant to Lorentz transformations. That is, all inertial frames of reference are indistinguishable as a result of having the same metric.

Originally Posted by ralfcis
my math which you said works (equivalently).
I said it may be equivalent. I didn't say it was equivalent. That would require more analysis than I've given it, but I don't see any obvious difference in the maths that would allow me to say it's not equivalent. But understanding relativity is more than just doing maths. It is about understanding why the maths is the way it is. One needs to understand the principle of relativity. I recall a rather heated debate I had with someone about reflections from a mirror that is moving parallel to its surface. The other person claimed that the motion affects the reflections and produced relativity equations to support that view. I argued from the principle of relativity that the motion does not affect the reflections. Thus, maths doesn't necessarily produce the correct answer if one is incorrectly applying the maths due to an improper understanding of the underlying principles. I didn't need to use maths in my argument.

Originally Posted by ralfcis
The question still remains, how does age difference unfurl during the spacetime path especially under the spacetime path rules which I was told only allow determination of age difference at the end of the spacetime path?
Relativity doesn't allow an unequivocal answer to this question because different calculations produce different results and no particular calculation can be regarded as the preferred calculation above all the others. It could be argued that your question as stated doesn't really make sense. For example, what does "age difference unfurl during the spacetime path" really mean? It's like having two pieces of string and asking how the difference in length progresses along the strings.

48. Ok I think I have your answer. So long as they're separated (during the spacetime path) and there's no such thing as a preferred frame, there is no unequivocal way to determine how age difference unfurls. So I can go on forums with this answer and every theory people have is wrong. It's not due to Alice's line of simultaneity sweep of Bob's time line resulting in an instantaneous jump in his age. It's not due to or during acceleration and whether acceleration is fast or slow. It's not due to acceleration's equivalency to gravity in general relativity. It's not due to 2 separate legs of Alice's travel adding up to what reciprocal time dilation would give as the answer. It's not due to time being stored as distance travelled and therefore not appearing on a clock which only measures age (ie time through time). I don't know how many other theories there are but they're all wrong if they reason age difference either incrementally accumulates or happens at points or over points of the spacetime path. I hope I understand you correctly. If so, I'll spread the word and have every moderator on every forum call me a nutcase, heap abuse on me for trying to answer this question and get ripped apart by every ignorant hyena patrolling every forum. But if this is the truth, it's worth it.

Thank you so much for spending the time with me.

P.S. Believe it or not this answer gives my own personal theory a huge boost. You can tune into that once I understand how to upload my STDs here and start writing it under personal theories (which it totally is and I see that even though it deals with relativistic phenomena, it has nothing in common with how relativity explains them).

Just one last question you didn't answer. I just need confirmation. I'm now certain relativity cannot determine age difference if instead of stopping or turning around, Alice's change in velocity away from Bob is either a slow down (e.g. to .5c) or a speed up (e.g. to .8c) at the 3ly mark in this thread's .6c example. True? If true, my theory is now falsifiable through experiment.

However there must be something special about the turnaround point because if Alice returns to Bob at .5c or .8c, the age difference from those changes in relative velocity is calculable by relativity. In a related question, so when Alice makes a stop and there's distance between her and Bob, that should also be indeterminate age difference or is the 0 relative velocity frame like a universal large proper frame not subject to outside perspectives? Is there some rule in the relativity handbook that gives some special importance to both being in the 0 velocity frame at some point in the spacetime path?

49. Originally Posted by ralfcis
I hope I understand you correctly.
Suppose I were to say that Alice ages uniformly at 0.8 Bob's rate of aging throughout the journey. How would you reply?

50. I added a last paragraph. To answer your question Bob is also ageing at .8 Alice's rate from her perspective so until the spacetime path is validly closed, there's no way to determine an age difference. They are engaged in reciprocal time dilation. And according to my last paragraph, the path has no chance of being closed without one of the two making a change in relative velocity that temporarily puts them both through the 0 relative velocity common frame at some point during the spacetime path that is not the start or end point.

51. Originally Posted by ralfcis
To answer your question Bob is also ageing at .8 Alice's rate from her perspective
But I prefer to answer the question from Bob's perspective.

Now do you see the point I'm making?

52. Bob is ageing at the normal rate from his perspective. That's 1 not .8.

53. Originally Posted by ralfcis
Bob is ageing at the normal rate from his perspective. That's 1 not .8.
I said Alice was aging at 0.8 Bob's rate.

54. Your statement is not complete. Alice was ageing at .8 Bob's rate from whose perspective.

55. Originally Posted by ralfcis
Your statement is not complete. Alice was ageing at .8 Bob's rate from whose perspective.
Does it matter?

56. Yes the perspective matters but are you asking does the answer from that perspective matter? It does because in the relative velocity component of GPS time which is due to time dilation, there can be many perspectives of that giving different answers but the one from our perspective does matter and creates the GPS network. Age difference can't be established because there is no valid spacetime path according to the spacetime path rules.

57. One thing I should stress: the answer that Alice ages at 0.8 Bob's rate is correct.

58. You know anyone can parrot what I've said above and all the parrots on this forum will say, "Oh ralf finally got it." But the real question is, did they finally get it. An easy test is to ask them the difference between time dilation, doppler shift ratio and age difference and even if they read this entire thread again, they still won't have any answer.

59. Sure the answer is correct but how much she ages is not the same question as what is their age difference. It also doesn't answer the question of whether she or Bob will be the one who ends up ageing at .8 the others age rate by the time the spacetime path ends.

60. Originally Posted by ralfcis
Age difference can't be established because there is no valid spacetime path
It isn't that there is no valid path, but many valid paths. The different perspectives produce correct answers (assuming they've been calculated properly) even though they are different answers. The solution is to qualify any particular answer by how it was obtained.

61. Oh wait, I see what you're trying to get at. It's Einstein's definition of time. It's all personal time. That is reality. There is no universal newtonian present, there's an individual present for every matter particle in the universe. I typed this before i got your reply.

"It isn't that there is no valid path, but many valid paths." When the spacetime path closes, that's the valid path to establishing valid age difference. It's the ageing part during the path that is all valid when qualified from which perspective. I'm talking age difference, you're talking ageing.

62. Originally Posted by ralfcis
Sure the answer is correct but how much she ages is not the same question as what is their age difference. It also doesn't answer the question of whether she or Bob will be the one who ends up ageing at .8 the others age rate by the time the spacetime path ends.
Yes it does. When the two meet again Bob is 10 years and Alice is 8 years, an age difference of 2 years.

63. Originally Posted by ralfcis
I'm talking age difference, you're talking ageing.
Once one has the age of both people, then one has their age difference.

64. Let's say Bob makes the change at 4 instead of Alice. Before he makes the change, they calculate each other to be ageing at .8 the other's age rate (but they actually see each other age at half their age rate due to the doppler shift ratio.) After Bob makes the change, their reciprocal time dilation is unchanged at .8 the others age rate. Bob immediately sees Alice age at double his rate while Alice, unaware of Bob's change, still sees him age at half her rate. She can only calculate that Bob is ageing at .8 her age rate due to reciprocal time dilation. Even though Bob has seen her age rate double his, that doppler shift ratio still indicates that alice's age rate is still .8 of his. But at the end Bob is two years younger than Alice. The ageing rate has been unchanged and yet an age difference has appeared. The individual ageing rate of both people from each other's perspective has not added up to the correct age difference.

P.S. So I don't know what you're trying to make me say. I thought the conclusion we drew from our discussion is that trying to arrive at an unequivocal age difference by analysing the ageing process that each one goes through cannot work because as long as they are separated there are so many perspectives of their ages that each perspective has its own correct answer to how each is ageing.

P.P.S This last statement made me invent another explanation of how age difference unfurls (that is totally wrong because that is not possible in relativity). The theory is whoever initiates the change in relative velocity becomes the preferred frame. If Alice makes the change at 4, her line of simultaneity becomes law and the sign of the slope does not change so it keeps pointing downward towards Bob's timeline. So this means for each yr Alice ages on her wristwatch, Bob starts ageing 1.7 yrs on his. 4 x 1.7 = 6.8. So he ages 6.8 yrs from when Alice's line of simultaneity intersected his timeline at 3.2. Alice ages 4 yrs before and after the turnaround. So the math works! Bob =10 and Alice =8 and there are no sudden jumps in Bob's age from Alice's perspective. But relativity says no to this math as well, it works but is invalid. You cannot work out age difference from their individual ageing progression. Just as well because then there would be huge battles over which math treatise relativity actually supports for age difference progression.

65. Originally Posted by ralfcis
Just as well because then there would be huge battles over which math treatise relativity actually supports for age difference progression.
Ralfcis;
Your complaint that you can't find anyone on forums knowledgeable enough to explain SR is incorrect. After 12 yrs of interacting with the most popular ones, there was always a few who had a working knowledge of SR who could explain it using text, or math, or graphics, or all of these methods. It seems presumptuous for you to impose your own inability to understand the subject onto others whom you don't know,as to work experience, education, etc.
On the negative side, there are scientists who put their own spin on interpretations, and unintentionally mislead a novice via their authority status.
Eg. Brian Greene using the metaphoric 'moving in time'.

Your quote:"I thought the more you see someone move through space, the less they move through time."
My reply: "Truth exists in the statement, not the one who proclaims it."
------------
There is no unfurling of ageing!

P.S. unfurling of ageing is not the same thing as unfurling of age difference. This is the last point I made to KJW and am awaiting his response.

67. Originally Posted by ralfcis
So the math works! Bob =10 and Alice =8 and there are no sudden jumps in Bob's age from Alice's perspective. But relativity says no to this math as well, it works but is invalid. You cannot work out age difference from their individual ageing progression. Just as well because then there would be huge battles over which math treatise relativity actually supports for age difference progression.
Interesting. But when Alice reunite with Bob she would know that Bob was the one who was stationary in regard to experiment's starting frame and that he was travelling only in time. She was the one moving in space. So assigning any physics to Bob's moving in experiment's starting frame is her error.

Yes, implications are very interesting.

P.S. This is one of debates which I missed the most, after site breakdown. KJW was one of the leader participants. I miss some other guys like SpeedFreek, Boing3000 etc… Good discussions were lost.

Cheers!

Zlatan

"she would know that Bob was the one who was stationary in regard to experiment's starting frame and that he was travelling only in time."

All wrong. Bob may have never been stationary wrt Alice if Alice flew past him at the start. (The start is significant for the co-location of the two, not their relative velocity.) Bob was depicted as stationary but he had the same relative velocity as Alice during the journey. He was also moving at .6c through space relative to Alice despite that the STD depicts him as not going anywhere. The starting frame was not Earth or the entire background universe. The starting frame just had Bob and Alice, the background doesn't matter. That's a separate frame; confusing because that separate frame is always included in the STD as the background cartesian coordinates. STDs are very bad for causing everyone's confusion and especially for implying a preferred frame.

He was also not the only one travelling through time. Both were travelling through time at the velocity of light through time which manifests itself as the normal rate of time. For example, a VCR has slow motion, fast forward and play. Play is the normal rate through time. The other two are other velocities of time through time. The doppler shift ratio is like a VCR where the two can see each other at different apparent time rates but they see themselves at the normal time rate. Everyone in his own frame passes through time at the normal time rate which is the maximum rate events can progress through time.

So at first Bob and Alice were both moving at c through time and at, let's say, .6c through space. They saw the doppler shift ratio from each other, manifest as the tv signal they broadcast of their daily lives, as half speed slow motion. They both looked to be moving in slow motion from the others perspective and so were the others clocks even though everything within their own environment was looking normal. From that they could calculate their relative velocity was at .6c and from that they could calculate their time dilation as .8 of each other. For every year one was aging, the other was aging .8 yrs from each other's perspective. From other perspectives moving at different relative velocities to them, the ageing rates were something else. Also don't get confused with their ageing rate due to time dilation and the apparent rate they seem to be ageing due to the doppler shift ratio and the age difference between them at re-unification, which is not due to any universal ageing rate. It's a one-time endpoint number that had as many derivations as perspectives watching it get there.

The person who initiates a change in relative velocity that ends in their unification, will be the one who ends up ageing less than the other because his spacetime path is proven to have been through space and therefore less through time. (I don't know how relativity establishes that proof because if the guy on earth performs the velocity change, he is still at the same point where he started while the other guy isn't.) However that determination can't be made until they re-unite because any distance separation before that point brings in perspective from other frames. Any determination of age difference has to be referenced to the frame making that determination. It's only when they are together that the universe can say what their age difference is from all perspectives (the same) and hence, independent of perspective just like c which is also independent of perspective.

You need to forget everything you've ever been taught from wiki articles, popular science magazines, people on forums, on-line mickey mouse courses and probably most books.

P.S. I suspect the proof of who actually travelled through space is somehow connected to who entered the 0 velocity common frame (a party has to stop at some point temporarily to make a turnaround). Is this the lost spacetime path rule that explains why Alice can make a stop at a distance from Bob and still have a valid age difference with him? It's like the spacetime path doesn't need to go all the way to re-unification if the party runs out of gas trying to make it there and sends a note of apology. The age difference is established when the note reaches the other party.