S.R. Defining the present

Discussions on classical and modern physics, quantum mechanics, particle physics, thermodynamics, general and special relativity, etc.

Re: S.R. Defining the present

Postby BurtJordaan on June 26th, 2017, 9:32 am 

ralfcis » 26 Jun 2017, 01:08 wrote:If Charlie passes near a planet 4 ly away and

a) all the clocks there are sync'd to earth time and
b) he sync's his clock to earth time as he passes and
c) his relative velocity to earth is .8c then
d) as he passes earth, his clock will say 3 yrs have passed while the earth clock will say 5.
e) the spacetime pah has a valid start and stop so this is not reciprocal time dilation but real age difference.

True or not?

Only partially true. Only Charlie traveled the spacetime path, so only Charlie's aging difference is known. You have no idea by how much Earth aged "at the same time", because there is no common "at the same time" for Charlie and Earth.

PS: if you have followed my Space-propertime threads, you should have been able to answer your own question.
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Re: S.R. Defining the present

Postby ralfcis on June 26th, 2017, 10:40 am 

Only Charlie's aging difference is known relative to what? You're saying not relative to the earth? The distant planet and earth are in the same frame. You're saying they're not because they start out separated.? But if the planet sent out a signal to earth when Charlie began the journey, it would have reached the earth at yr 4 earth time. Charlie would have reached the earth at yr 5 with only 3 yrs having elapsed on his clock sync'd to earth time when he passed the distant planet. The earth is aware of both start and stop times.

The facts are in the clock comparisons yet because of some rule i don't understand, earth's clock reading has been invalidated. I know the rule, that the spacetime path must begin with the two participants being co-located, but I don't understand why. I hope our agreement still stands that the spacetime path need not end with them being co-located. That they can end separated but in the same frame relatively stopped and the official end is when the signal of that stoppage reaches the far participant (earth). If those rules are good enough to establish an end to the spacetime path, why are they not good enough to establish a beginning?
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Re: S.R. Defining the present

Postby BurtJordaan on June 26th, 2017, 11:25 am 

Ralf, I have been trying to correct your misunderstandings of the relativity of simultaneity for something like 5 years now. I'm not willing to be dragged into the endless cycle of repeats of the same old stuff again. :(
Maybe someone else might try.
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Re: S.R. Defining the present

Postby Positor on June 26th, 2017, 12:07 pm 

Two clocks in the same frame, and sync'd in that frame, are not sync'd in a frame moving relative to it. So, two clocks that an earth observer calculates as being sync'd, Charlie (who is in a different frame) calculates as being un-sync'd.

Correct?
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Re: S.R. Defining the present

Postby BurtJordaan on June 26th, 2017, 12:14 pm 

Positor » 26 Jun 2017, 18:07 wrote:Two clocks in the same frame, and sync'd in that frame, are not sync'd in a frame moving relative to it. So, two clocks that an earth observer calculates as being sync'd, Charlie (who is in a different frame) calculates as being un-sync'd.

Correct?


Yup.
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Re: S.R. Defining the present

Postby ralfcis on June 26th, 2017, 1:32 pm 

Charlie's sync offset with the clock on earth is vx/c2 = 3.2 yrs. He also sees the earth clock time as dilated at 1.8 yrs. So when he arrives on earth he knows the earth time is 3.2 +1.8 = 5yrs. Charlie's proper time sync'd to the planet's clock is 3 yrs. That is the present they share at the moment they cross. So his age difference with the earth clock is 2 yrs. No? Is this not how relativity of simultaneity works? What am I not getting?
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Re: S.R. Defining the present

Postby ralfcis on June 27th, 2017, 5:25 am 

Hi everybody, welcome to groundhog day on the forum. This is the day when I make my usual claims that most of my questions have not been answered. And of course they have been. The answer is I don't understand relativity of simultaneity and haven't for the past 5 yrs. So I've provided a brief explanation of it without anyone acknowledging I understand. Maybe I need a little more detail such as going right back to the beginning of basic principles. I can even post Brian Greene's video explanation of it. I'll do that because if I again prove I understand relativity of simultaneity and that it is not the answer to my specific questions, then that should open the door to getting answers.

Let's go back to the STD I've been using. Alice travels at .8c from earth to a planet 4 ly away. She hands off her clock info to Charlie passing in the opposite direction back to earth. At the handoff, Alice's line of present intersects and includes Earth at the 1.8yr mark. Earth's present is at the 5 yr mark and the relativity of simultaneity is how these 2 presents from different perspectives are joined. That missing time of 3.2 yrs is handed off to Charlie whose line of present intersects and includes Earth time at 8.2 yrs. So right from the handoff, Charlie adds his own lump sum of sync offset of 3.2 yrs. This is added to the time dilation he sees of earth time of 1.8. Add that earth time all together and you get 1.8+3.2+3.2+1.8 = 10 yrs while the round-trip journey time is only 6 yrs.

The same answer for Charlie would occur if Alice stopped on the planet or turned around with Charlie except that if she passed the planet, there would be no age difference between her and the earth. If she stopped at the planet, she will have aged 2 yrs less than the earth. If she turned around and flew beside Charlie, she would have aged 4 yrs less than the earth.

My question is if Alice stopped on the planet, that would be a valid spacetime path end so would that not be a valid spacetime path start for Charlie. Relativity somehow forbids Charlie's journey from being separated from Alice's because that would mean his start is separated from earth. Yes I know the shortest spacetime path is for the participant who is at the closest to both events. Charlie's separation from earth at his start somehow causes a problem for SR to determine that he has aged less than the earth even though we can calculate relativity of simultaneity to arrive at the same answer for Charlie as it was when he was connected with Alice. You're saying no. Why not and some answer beside I'm still not understanding how things work.
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Re: S.R. Defining the present

Postby ralfcis on June 27th, 2017, 9:39 am 

So Positor, you had an answer. How is your answer any different from my answer? Am I not permitted to use relativity to be able to compare Charlie's 3 yrs travel with Earth's 5 yr aging? The example is exactly the same as the Muon example and that has an answer. The muon coming in from the upper atmosphere has aged less in order to strike the Earth. A valid time comparison can be made but you rename the Muon, "Charlie" and suddenly SR throws up its hands and declares no age difference can be determined? And no one can see the question I've been asking for 5 yrs that has never been answered.
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Re: S.R. Defining the present

Postby Positor on June 27th, 2017, 10:16 am 

The point, I think, is that no age difference can be agreed unless the two bodies in question are co-located — whether these be a Muon and Earth, or Charlie and Earth. This is because, as Burt has pointed out, there can be no agreed simultaneity between spatially separated events (even after the light-travel delay has been taken into account).
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Re: S.R. Defining the present

Postby ralfcis on June 27th, 2017, 10:36 am 

The point, I think, is that no age difference can be agreed unless the two bodies in question are co-located


Jorrie and I hashed out that was not true but I tried to get him to re-commit to that answer. If Alice stops in space relative to Earth, an age difference is established once Earth receives the signal that Alice has stopped. The two participants just have to be in the same frame. My question was that since Alice and the Earth can start out co-located and end up separate but stopped, why is the reverse not true according to SR? Why can't they start separated/stopped and end up co-located to establish an age difference as what happens in the muon example?

(even after the light-travel delay has been taken into account)


All the factors of relativity can be taken into account in post processing. The present may not be known in the present but it can be determined what the present was in a past time and definitive judgments can be made.
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Re: S.R. Defining the present

Postby Positor on June 27th, 2017, 10:57 am 

ralfcis » June 27th, 2017, 3:36 pm wrote:If Alice stops in space relative to Earth, an age difference is established once Earth receives the signal that Alice has stopped. The two participants just have to be in the same frame.

But what about other observers who are not in the same frame? They will calculate different age differences between Alice and the Earth.
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Re: S.R. Defining the present

Postby ralfcis on June 27th, 2017, 11:03 am 

Anyway the whole point of this thread is to determine how SR defines the present. SR has a different line of present going through space for each participant's time. This is what causes relativity of simultaneity: events that happen in the present (simultaneously) for one participant do not happen simultaneously for the other. But if the slopes of their lines of present align, then the same events happen simultaneously for both. In order for the lines to align, they have to be in the same frame relatively stopped or so close together that their lines converge into a point which means no slopes to align. When either happens, an age difference between the two participants can be determined.
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Re: S.R. Defining the present

Postby ralfcis on June 27th, 2017, 11:12 am 

But what about other observers who are not in the same frame? They will calculate different age differences between Alice and the Earth.


According to SR, 2 participants engaged in relative velocity will not have a determinable age difference, they will have reciprocal time dilation so long as they remain in constant relative motion. SR says its not determinable to avoid the paradox that each will see the other reciprocally younger.

Other people in different frames will have different perspectives and different line of present on Alice and Bob on Earth. So long as they are in constant relative motion, there is no determinable age difference until there's a change in relative velocity. As near as I can gather, SR can only make age difference determinations under only 2 conditions, either both are stopped relatively to each other or they co-locate.

Trying to get a definitive answer on SR's rules has been impossible so far. The "answer" I have gotten when asking for a clarification of the rules on how they apply to a particular scenario is that I shouldn't look upon it in terms of rules. That's what's considered an answer in the SR world.
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Re: S.R. Defining the present

Postby nameless on June 27th, 2017, 8:27 pm 

ralfcis » Mon May 01, 2017 9:08 am wrote: Defining the present

How simple; Here! Now!
All that exists is the ever 'present', the past and future only exist in (y)our thoughts/ego.

All that complexity would have Occam spinning on his Razor!
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Re: S.R. Defining the present

Postby ralfcis on June 27th, 2017, 9:55 pm 

The title is SR defining the present. Defining the present is in the philosophy forum section. Don't let me keep you.
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Re: S.R. Defining the present

Postby BurtJordaan on June 28th, 2017, 4:42 am 

ralfcis » 27 Jun 2017, 17:12 wrote:According to SR, 2 participants engaged in relative velocity will not have a determinable age difference, they will have reciprocal time dilation so long as they remain in constant relative motion. SR says its not determinable to avoid the paradox that each will see the other reciprocally younger.

Ralf, how many times do we have to repeat that reciprocal time dilation has nothing to do with "aging". What I have shown in the space-propertime diagrams, both Alice and Bob age identically and independently from what the other one does, provided that they are permanently inertial.
Image

Each just have a reciprocal (shortened) view of the other ones space-propertime progress. That's reciprocal time dilation and Lorentz contraction. There will be a detectable aging difference after one of the two does a non-inertial stint that brings him/her to rest relative to the other party. Or any other, more complex scenario that is not perfectly symmetrical for the two.

We have been through this many times before. I still fail to understand why you struggle so much with it.
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Re: S.R. Defining the present

Postby ralfcis on June 28th, 2017, 8:57 am 

Ok I'll translate what I have written for you:

According to SR, 2 participants engaged in relative velocity will not have a determinable age difference, they will have reciprocal time dilation so long as they remain in constant relative motion.


What this means is:

reciprocal time dilation has nothing to do with "aging both Alice and Bob age identically and independently from what the other one does, provided that they are permanently inertial"


I don't know what you're reading but it's not what I'm writing, not even close.
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Re: S.R. Defining the present

Postby ralfcis on June 28th, 2017, 9:59 am 

You know, the last good discussion we had was a few months ago where you actually answered my questions. There was the usual heckling and abrasive attitude but if it leads to an answer, I don't really care. However, I feel that's just not going to happen again. You're just not interested in asking or answering questions for clarification so there's really no fruitful or polite discussion anymore. So what's the point? I know there's no one else here that either knows enough about relativity or is willing to engage but I'd rather have silence over unconstructive and baseless heckling. However, if in the future you have something relevant to add, feel free to contribute. Now I'd like to continue in my exploration of how SR defines the present.
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Re: S.R. Defining the present

Postby BurtJordaan on June 28th, 2017, 12:02 pm 

ralfcis » 28 Jun 2017, 15:59 wrote:You know, the last good discussion we had was a few months ago where you actually answered my questions. There was the usual heckling and abrasive attitude but if it leads to an answer, I don't really care.

Ralf I honestly don't understand what your problems are. Just a few posts back you were complaining:

ralfcis » 27 Jun 2017, 17:12 wrote:Trying to get a definitive answer on SR's rules has been impossible so far. The "answer" I have gotten when asking for a clarification of the rules on how they apply to a particular scenario is that I shouldn't look upon it in terms of rules. That's what's considered an answer in the SR world.

Now I have, in a nutshell, 'regurgitated' the proper "rules" for you and you complained about that!

Are you attempting to create your own set of "rules" that "defines the present" in SR? Why not just use Einstein's (and Minkowski's) simultaneity rules that are now standing up to scrutiny for more than a century?
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Re: S.R. Defining the present

Postby Positor on June 28th, 2017, 9:56 pm 

Ralf,

It would be helpful at this point if you could list your unanswered questions in a concise form, and briefly state where you differ from SR, particularly as regards (a) aging, (b) time dilation, and (c) relativity of simultaneity. That would help to focus the discussion.

To what extent is this thread about SR's definition of the present, and to what extent is it about your definition/idea of it?
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Re: S.R. Defining the present

Postby mitchellmckain on June 29th, 2017, 1:27 am 

If you want a definition of the present which is Lorentz invariant (i.e. doesn't change with velocity), then it is as I have said, everything between past and future light cones. Of course this is relative to a particular point in space-time and that is the part which would be conquerors of the universe typically have trouble accepting. They want a thin here and now which is the same for everybody over which to wield their power and exercise their control/influence. But relativity makes it clear that power and influence only exists in the future light cone, and that is far too limiting for those dreaming of carving out an empire among the stars. Scientists accept that the present of the universe is beyond our reach and that is why they often give it quite a different name, "absolute elsewhere."
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Re: S.R. Defining the present

Postby ralfcis on June 29th, 2017, 7:42 am 

Yes I will do what you asked. I am not pushing my agenda here because it will lock down and split this thread. I'm only working from the STD's and trying to interpret in English what the math is saying. Right now it's telling me some really bad things that may force me to change my theory yet again but it's even worse for relativity. It's telling me that if earth sets up a universal network clock and Alice only has her on-board clock, then her reciprocal perspective doesn't really matter. It doesn't matter because it looks like either party can't become aware of any paradox reciprocity may cause (needs to be checked). It does not cancel out Bob's earth clock based reality which can be documented in the messages between Bob and Alice. At the 4ly point where Alice reaches the earth clocked planet, her clock can be compared with the earth clock network. Sure, Alice is 3, Bob is 5 seems to contradict when Alice is 5, Bob is 3 but if Alice doesn't have a fleet of her own network clocks flying with her, Alice's perspective doesn't matter (which I will show in further analysis of the STD). If Alice passes the far planet, she will read the earth sync'd planet clock as 5 and her clock will be 3. This is not negated by what Alice does at this point. It is also not negated by what Bob does. If he takes off and catches up to Alice, he will end up overcoming her advantage and end up aging slower (regardless of whether you consider it age difference (not permitted by relativity) or reciprocal time dilation at 4ly).

Now I'm against this because it messes up my nice neat little theory I had up until 2 days ago and it definitely goes against relativity. I haven't begun to explore this idea yet but I'm tending to believe any paradoxes in the messaging between the two that reciprocal time dilation would create are avoided by the speed of light delay.

Yes this is revisiting the same old conflict yet again. SR sets up rules under which age difference can be determined to avoid the paradox caused by time dilation reciprocity. The relativity of simultaneity is part of those rules. Your argument is this has already been looked at from every angle by the best minds for over 100 yrs and it's settled. Then that should make my specific questions easy to answer and I can join the club, So I'll prepare that list of questions based on the STD I've been using.
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Re: S.R. Defining the present

Postby ralfcis on June 30th, 2017, 12:21 pm 

Sorry, I know I'm missing a big opportunity here but I've got to continue and delay re-phrasing the questions to some future date.

So when Bob's line of present at 3 yrs intersects Alice = 1.8, what does it really mean? Possibilities:

1. Is Alice's past concurrent with Bob's present as Prof Brian Greene has stated in his relativity course? His take is that since Alice's line of present is slanted, she can intersect the past or future of the participant she is leaving or going towards which means past, present and future exist concurrently. I will show why this is not true because option 3 is the only correct answer.

2. Is it an illusion of Bob's perspective of Alice? Is reciprocal time dilation real or an illusion of perspective? Is it valid to say that when Bob=3, Alice =1.8 in his present it cancels out the reciprocal fact that when Alice=3, Bob = 1.8 in her present? SR states both perspectives are independent realities that only need to be resolved when they either co-locate or share 0 relative velocity. If that's the only time it matters, I see no problem about making definitive statements of who is actually aging slower when it doesn't matter so long as the age results are the same when resolution matters.

3. The answer is this: Alice =1.8 is not a fair comparison to bob=3. Since the motion is relative, these values must always be equal so Alice's total time is being diminished by her motion through space relative to Bob's network of clocks. Alice doesn't have a network of clocks to care about what her perspective of Bob is.

8c5cnew.jpg


If you look at the STD, when Bob =3, Alice = 1.8 forms a pythagorean triangle where ct is the y-axis, x is the x-axis and the hypotenuse ct/Y ends up being shorter than the y-axis. I'm not familiar with the math terminology but it's some sort of hperbolean pythagorean formula like this:

(ct/Y)2 = (ct)2 - x2

It's not a sum of squares but a subtraction. Bob stays in one spot so his time of 3 is not diminished by travel through space. Alice actually travels the same time but it is partly expressed as her travel through space. So however you draw the STD, the times from both perspectives are equal but a mix of time through time and time through space (I'm not sure of the SR terminology).

So I feel this makes you free to choose only 1 perspective to determine age difference and when they are relatively stopped, the time through space component becomes automatically converted to all time through time. This final result is not affected by ignoring the space through time component throughout the analysis. So, in effect, whether reciprocal time dilation and age difference are the same or not doesn't really matter to the end result. Choosing the earth perspective or the LHC perspective for particles and assuming the time dilation from only this perspective will yield age difference. I guess the other questions don't really matter anymore.



Just as a side note, the math works out the correct formula for Y:

(ct/Y)2 = (ct)2 - x2
(ct)2 * (1-1/Y2) = x2
(ct)2 * (Y2 - 1)/Y2 = x2
c2 * (Y2 - 1) = Y2 * (x2/t2)
c2Y2 - c2 = v2Y2
Y2 =c2/ (c2 - v2)
Y=c/sqrt(c2-v2)
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Re: S.R. Defining the present

Postby ralfcis on June 30th, 2017, 6:16 pm 

Oops, I was so rushed I didn't develop the formula that converts the distance separation and velocity into a time equivalent. So when Bob=3 and Alice =1.8, the missing time component for Alice is 1.2. Monday.
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Re: S.R. Defining the present

Postby ralfcis on July 3rd, 2017, 12:17 pm 

I should have known better that there is no simple addition in relativity. The original formula allows conversion between time in the moving frame as a composite of time through time and time through space compared to the stationary frame which is 100% time through time.

As the velocity through space approaches c, for t=1, the hypotenuse (t') approaches 0 while x approaches 1. Another way of looking at it is the unit spacing of t' approaches infinity while the unit spacing ratio of t and x approaches 1. As the velocity goes to zero, x goes to zero and t approaches t'.

Since it doesn't matter how we relate the stationary frame (the one with the network clocks) to the two participants (on-board clocks) engaged in relative motion, we will choose the orientation that is easiest. The easiest is to put Bob with the stationary frame of Earth with an Earth clock network and have Alice as the moving frame. Everything will be judged from Bob's reality and there is no need to consider Alice's lines of present because there is no Alice's clock network and there's no need for one. According to Bob's reality, Alice has only aged 3 yrs when Bob has aged 5. I'll show in the next post how this reality can be verified in many different ways. If Bob then starts to move off the stationary frame, then he has to travel much faster to make up the time Alice has already saved on him.

All this is rather tedious to visualize using Minkowski STD's so I'd like to explore using a new type of STD (I don't know if it has already been invented). I'd like the y-axis to be ct/Y and the slanted line which used to have a slope of 1/v to now have a slope of 1/Yv. So for example, v=.4/5c, Y=5/3, Yv = 4/3c = x/(t/Y). I've produced a graph of how velocities would look at .4c, .6c, .8c, .8824c but I'll have to bring a scanner in tomorrow to attach it here.

In this graphing method there is no light cone. As velocity increases, the slope of the line approaches horizontal. As velocity approaches zero, the slope of the line approaches vertical. I don't know where this will lead without doing some examples. First I'll do the examples using the more familiar Minkowski STD's.

I hope I can continue this week.
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Re: S.R. Defining the present

Postby ralfcis on July 4th, 2017, 12:42 pm 

Here's the new form of the minkowski STD I promised yesterday. Took me all day to do it on the computer whereas it took only a few minutes with paper and pencil.

graphchlipalski.jpg


So much easier to understand this way. There are no weird slanted axes and reciprocity for all speeds is a perpendicular line to the velocity line.

To help you orient to our example, for v=.8c the distance to the planet is x=4 ly. The circles represent t is the same value on that circle for any velocity. The value of t is read vertically from 4 and it intersects the circle t=5 so t=5 for Bob. The value of t' for Alice is read horizontally from that (t'=3). Enjoy.
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Re: S.R. Defining the present

Postby ralfcis on July 5th, 2017, 11:40 am 

Anyway, let's leave that for now and go back to the Minkowski STD for our example:

graphm8c.jpg


Alice is leaving the Earth and approaching the planet 4 ly away at .8c. All problems in SR involve approach, departure and the time between which is stoppage. The Earth and planet are relatively stopped and have sync'd clocks so that despite the distance separation, all clocks read the same time. So if a signal is sent from the planet at t=5, Earth will get that signal at t=9 and know that subtracting the speed of light delay, the time on the planet was 5 four years ago.

I'll continue tomorrow hopefully.
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Re: S.R. Defining the present

Postby ralfcis on July 6th, 2017, 4:12 pm 

I just got to write a quick note for tomorrow before I forget.

correction: the line t'=1.65 should be t'=1.667

When Bob =1, he signals Alice who gets it at 3. When Bob = 1.8, he's in her line of present. When Bob = 5, Alice =3 is in his line of present. She can verify this by checking the time on the planetary clock and since she knows Bob is 4 ly away, it took 4 yrs for the signal to reach her. She can also verify calculating the relativity of simultaneity and adding it to bob's time on her line of present that he is indeed 5 when she is 3.

But she's got that pesky conflict that Bob is 1.8 on her line of present when she's 3. Bob = 1 was 4 yrs ago and just .8 yrs later, Bob's in Alice's present. 4 Bob yrs = 1.2 Alice yrs. So 1.2 Alice yrs ago, Alice was 1.8 which corresponds to Bob=3. The aging Bob does between yrs 1 and 1.8 is the equivalent of 1.2 yrs of Alice aging. That 1.2 yrs is the time equivalent of the 4ly she traveled. Her pure time through time is 1.8 yrs. 1.8+1.2= 3 yrs for her which aligns with Bob=3 as discussed above. So the reciprocity is that they have both aged 3 yrs but Alice's total time is reduced to 1.8 yrs because it's reduced by the time through space. So Alice is 3 and bob is 5 in bob's present. Alice is 3 and bob is 1.8 in Alice's present. And Alice is 3 and Bob is 3 in some other kind of present that safeguards reciprocity between the two. This must be related to some kind of proper time present. I need to figure this out.
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Re: S.R. Defining the present

Postby ralfcis on July 7th, 2017, 6:10 am 

Sorry, I tried the same analysis on .6c and it turns out to be a fluke of the numbers at .8c. Unless I've made a mistake on the .6c STD, it doesn't look like there is a 3rd type of present.

graphn6c.jpg
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Re: S.R. Defining the present

Postby ralfcis on July 7th, 2017, 8:03 pm 

I can see this is going down a dead end; a nice math fix that doesn't reflect the physics.

RELATIVE motion is what causes both clocks to go slower relative to each other. Aging is the result of the passage of time. So long as they are in constant relative motion, the reality is both ARE aging slower than the other. Relativity of simultaneity supports this as a fact.The TV signals each receive of the other confirm the same relative velocity and that they appear to be moving at the same slow motion video. I don't think the speed of the slow motion video is exactly the same as how slowly each is aging relative to the other.

When one changes his velocity to 0 relative motion, he can immediately see the other's TV picture run at normal speed. The other guy has to wait for the speed of light delay to see that he has moved from a relative velocity to 0 relative velocity. So if relative velocity causes the other guy's clock to move slower (hence he ages relatively slower), then the guy who stopped sees the other guy at 0 relative velocity and hence that guy is no longer aging slower. That guy still sees the stopped one at the old relative velocity during the delay so the guy who stopped is seen to remain aging relatively slower. When the signal catches up to the oblivious guy, he'll see the guy who stopped finally moving at normal TV picture speed. So now they are both at 0 relative motion and hence neither is aging slower than the other. But during that signal delay time, the oblivious guy saw the stopped guy aging slower for longer.

Now the question remains, why does this imbalance of perception cause a real age difference? The reality should be that when 1 guy stopped, they were both at 0 relative velocity whether 1 knew it or not. It's only because 1 guy didn't realize it that the age difference became reality? Is there a better answer than this?
ralfcis
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