Celeritas Posted February 11, 2020 Posted February 11, 2020 md65536, Wrt my prior post here ... on the other hand, if the coordinate time were to differ in that way (for example, say) 5.2y-B and 5.2y-C at their flyby event, whereas SR says 4y-B and 4y-C, then I would venture that a moving clock's tick rate would have to differ somewhat from what SR predicts. If so, then I see what you were saying prior, about ... "what are the specific things envisioned to vary" in an alternate theory (compared to SR). Wrt what I had been working on ... I've been trying to derive the LTs (in the OEMB way, but) for a non-midpoint reflection event. When I did that, it did not change any spacetime transformation solns, but I had kept Einstein's convention of 1-way = 2-way speed of light. So I've redefined the 1-way outbound light speed and 1-way inbound lightspeed to be consistent with the non-midpoint reflection event. Only problem is, the derivation gets very messy fast, as they do not reduce elogantly as in OEMB. It's pretty ugly, and Occam certainly would not favor it, but that's fine as a spreedsheet can handle it, elogant or not. I'm not assuming a master frame either. I'm assuming all frames use the same such convention. Anyway, I was just curious what the solns would be, and as to how they would differ from SRs. I was mainly interested in the coordinate solns and how they differ from SR, but really, it's about "the all of it". Best regards, Celeritas
Celeritas Posted February 11, 2020 Posted February 11, 2020 md65536 and studioT, First, I reread one of md's prior post. I should say that while I've been thinking in terms of 2 differing alternate theories (SR is 1 of them), I see now that md35536 has been responding strictly about 2 competing versions of SR (so with different conventions of simultaneity). However, I'd been assuming that a 1-way <> 2-way speed-of-light would produce LT solns that differ from SR (but I keep the 2-way = c). While I realize that coordinate time differentials diminish (between the 2 versions) for a moving clock that approaches intersection with my clock, and vanishes upon intersection (coordinate time becomes proper time), I was not sure that the intersection of remotely located clocks would be as such. The more I think about it though, and after rereading what you've posted, the more it seems it would be as such. In which case, the geometry of the worldlines is identical to SR's version, the time readout of the clocks are the same for all points on their worldline, and the change in time sync convention would have no impact on the time readout of intersecting clocks anywhere in spacetime (same as SR). If that's what you've been saying, and all that is true, then both versions produce the exact same results, even though the predicted coordinate (not proper) values differ (wrt SR). Before I go further, please let me know if I'm on track with your reasoning, or not. Thanx. PS ... StudioT brought up the inertial AB scenario. Two clocks A & B happen to read zero at their flyby. The question was ... Which clock ages 4 years first? Not sure why you bring up this scenario, as it's standard SR. The clock that ages 4y first (since flyby) depends on who you ask. Each clock will (of course) claim itself to age 4y first, and the moving clock to age 4y later, because of the Relativity of Simultaneity. I just was not certain what the precise impacts would be if the SR convention were changed, ie what all must change with a non-midpoint reflection event in Einstein's emitter/reflector frame, and how the transform solns might be impacted (if at all). It's one thing to imagine a reslanting of lines-of-simultaneity on a spacetime diagram, but is that precisely what a rederivation of the transforms (from scratch) would actually produce for a non-midpoint reflection event and 1-way <> 2-way? I wasn't quite certain. I'm now thinking it would produce the same. I gotta say tho, the transforms are very ugly when the 1-way <> 2-way (with 2-way = c). Nothing during derivation reduces much. Thanx Celeritas
md65536 Posted February 11, 2020 Posted February 11, 2020 10 hours ago, Celeritas said: In which case, the geometry of the worldlines is identical to SR's version, the time readout of the clocks are the same for all points on their worldline, and the change in time sync convention would have no impact on the time readout of intersecting clocks anywhere in spacetime (same as SR). If that's what you've been saying, and all that is true, then both versions produce the exact same results, even though the predicted coordinate (not proper) values differ (wrt SR). Before I go further, please let me know if I'm on track with your reasoning, or not. Thanx. Sure, I think I'm in agreement. Clocks passing or the intersection of world lines are events. Does it make it easier to deal with them as events? 10 hours ago, Celeritas said: I gotta say tho, the transforms are very ugly when the 1-way <> 2-way (with 2-way = c). Nothing during derivation reduces much. I think that 1-way speed of light differing from 2-way speed has turned out to be too complicated for me to handle. I don't even know if it can work, or how. In all the toy examples I've tried, if there's an easy-enough way to make some modification of simultaneity match the predictions of SR, I keep ending up with definitions where 1-way speed equals 2-way speed. Every time I've mentioned the definition of simultaneity I speak of the time it takes light to go in the 2 directions. It's easy to find alternative timing values that are still in agreement with SR; just borrow the measurements from another reference frame. Assuming standard SR agrees with reality in that frame, there's a set of definitions with which those same measurements agree with reality. But that trick doesn't work with the speed of light, because it's the same in the different reference frames. Even if you can get different speeds of light to work, there are other ways to get different working time/space coordinates that don't require a change in the speed of light.
Celeritas Posted February 11, 2020 Posted February 11, 2020 (edited) 4 hours ago, md65536 said: Sure, I think I'm in agreement. Clocks passing or the intersection of world lines are events. Does it make it easier to deal with them as events? Well, they are events. I wouldn't say it's easier, but rather that clocks intersecting are a best confirmation of the LT solns, because those clock carriers can tell everyone what their own clocks read on flyby. Of course, the eventual receipt of light signals are a confirmation of the LT prediction as well, if the owners of intersecting clocks refuse to tell us . Events in spacetime are what relativity is all about. Two postulates, a few assumptions, and events. The train arrives at the station when the small hand points to 7 and the little hand to 12. But no better event though than 2 clocks at flyby, because their readouts are then absolute. It does verify the prediction of the LTs. 4 hours ago, md65536 said: I think that 1-way speed of light differing from 2-way speed has turned out to be too complicated for me to handle. I don't even know if it can work, or how. In all the toy examples I've tried, if there's an easy-enough way to make some modification of simultaneity match the predictions of SR, I keep ending up with definitions where 1-way speed equals 2-way speed. My derivation of the LTs for a non-midpoint reflection event (but with 1-way = 2-way speed-of-light), resulted in this generalized transform eqns (for variable time sync convention) ... .... ((Eqn 1) ... t' = γ[ (1/γ2 - (2ec-v-c)v)t - (v+(1-2e)c)x)/c2 ] .... ((Eqn 2) ... x' = 2e(γ)(x-vt) whereby e defines where the reflection event occurs in the transceiver/reflector frame ... ie reflection at t'1 = e( t'0+t'2 ) where e is in the range of ... 0 > e < 1. So for e = 0.5 (the SR convention), Eqn 1 reduces to SR's transforms t' = γ( t - vx/c2 ) and x' = γ(x-vt) as follows ... .... ((Eqn 1) ... t' = γ[ (1/γ2 - (2ec-v-c)v)t - (v+(1-2e)c)x)/c2 ] .... (............ ... t' = γ[ (1/γ2 - (2½c-v-c)v)t - (v+(1-2½)c)x)/c2 ] .... (............ ... t' = γ[ (1/γ2 - (c-v-c)v)t - (v+(1-1)c)x)/c2 ] .... (............ ... t' = γ[ (1/γ2 + v2)t - vx/c2 )] whereby the terms (1/γ2 + v2) in the time transform always equals unity. So for SR's e = ½ ... then Eqn 1 reduces to SR's ... .... (................ t' = γ[ t - vx/c2 ] However ... for e <> 0.5, then the Eqn 1 solns say this ... Wrt the time handoff scenario (for easy reference), if the A observer runs Eqn 1 for the outbound B clock, it produces the same time solns (as SR) for the B clock readout anywhere on B's own worldline. However, for spacetime events NOT on the B worldline, the time soln differs from that of SR. However since the 1-way = 2-way speed of light, all it really means is this. The transforms for events "upon" the A and B worldlines, are as per SR. Event's off the worldlines, do not match SR. But since the 1-way = 2-way is maintained "while changing the reflection event" (e <> 0.5), all this really means is this ... Whereby SR says the reflector's clock should be set to t'1 = ½( t'0+t'2 ) upon photon reflection eg say 3y-X (X is a clock at rest with A where B turns around), it may be instead set to (say) 3.8y-X per the value of e selected (where e<> 0.5). Nothing else changes, so it's just a clock set to a different time readout than SR would. The relative velocity, relative rate of tick, and geometry of worldlines remain the very same. So it's just a clock that is set to a different readout than SR would dictate, nothing more, nothing less. It's NOT as though the 1-way light speeds were altered (wrt SR) to match the non-midpoint reflection event. That's what I want to derive next. What I want to do next, is verify (per A's POV) that ... intersecting clocks are predicted as per SR, given neither of those clock's worldlines are the A or B worldlines. I'm assuming they will. 4 hours ago, md65536 said: In all the toy examples I've tried, if there's an easy-enough way to make some modification of simultaneity match the predictions of SR, I keep ending up with definitions where 1-way speed equals 2-way speed. Well, I'm in the process of deriving the transforms for 1-way <> 2-way, as a function of the selected e, although I must say it's somewhat a mess because nothing reduces much. I'm not going to concern myself with the reductions though, I'm only interested in making the required substitutions as in OEMB. That's all you should need. A spreadsheet can handle anything you throw at it, ugly or not, assuming it's (of course) correct. So, I'll keep plugging along here, although I'm not moving fast because of other life related matters. I'll let you know what it reveals md. And, thank you for your time on this. Much appreciated. Best regards, Celeritas Edited February 11, 2020 by Celeritas
Celeritas Posted February 12, 2020 Posted February 12, 2020 (edited) 1 hour ago, Celeritas said: What I want to do next, is verify (per A's POV) that ... intersecting clocks are predicted as per SR, given neither of those clock's worldlines are the A or B worldlines. I'm assuming they will. Sorry, the EDIT feature locked me out before I could make this EDIT ... In my prior, under my response to the 2nd quote (last sentence), when I stated the above I meant this ... What I want to do next, given the derivation whereby 1-way = 2-way and e <> 0.5, is verify that per A's POV ... that Eqn 1 solns match SR prediction for intersecting clocks NOT on the A or B worldlines. I'm assuming they will. Whereby Eqn 1 was ... .... ((Eqn 1) ... t' = γ[ (1/γ2 - (2ec-v-c)v)t - (v+(1-2e)c)x)/c2 ] Best regards, Celeritas Edited February 12, 2020 by Celeritas
Celeritas Posted February 12, 2020 Posted February 12, 2020 (edited) On 2/11/2020 at 1:25 PM, md65536 said: I think that 1-way speed of light differing from 2-way speed has turned out to be too complicated for me to handle. I don't even know if it can work, or how. Temporarily under reconstrunction Thanx, Celeritas Edited February 12, 2020 by Celeritas
Celeritas Posted February 13, 2020 Posted February 13, 2020 (edited) On 2/11/2020 at 1:25 PM, md65536 said: I think that 1-way speed of light differing from 2-way speed has turned out to be too complicated for me to handle. I don't even know if it can work, or how. md65536, So I did put a derivation together for this. It allowed a reflection event at 0 < e < 1, versus SR's midpoint reflection event of e = 1/2. It also assumes the 2-way speed of light is always c (ie averaged), but does calculate the required 1-way light speeds (outbound vs return) based on the selected e. I derive the transforms in the same manner as done in OEMB. However, I had to make 2 assumptions ... (1) the linear coefficent alpha (that arises from integrating the partial derivatives eqn) is equal to a = 1/gamma, just as per SR. Einstein was able to deduce that a = 1/gamma per phi(v) = 1, but I could not do that because the transforms did not reduce much. Therefore, I just assumed what Einstein deduced, that a = 1/gamma. (2) there's that point in the derivation where you plug the interim eqn for time Tau (T) into X = cT. However, what speed-of-light to use? The 1-way outbound, the 1-way inbound, or the averaged 2-way speed-of-light? I had cout = c/(2e) and cback = c/(2(1-e)), and c (=cround_trip) being the averaged 2-way light speed (invariant c). When I got to that part, X = cT, I derived the x->X transform for all 3 light speeds options (cout = c/(2e) and cback = c/(2(1-e)) and cRoundTrip=c). Not sure if any of those are definitively proper, but in doing so I found "the results did in fact support what you've stated prior in this thread", given I understood you correctly ... The LT solns "for a clock that intersects you at some point", are the very same as per SR. So in relation to the OP's Time Handoff scenario, observer A obtains the same transform solns for the B POV (who passed him by prior), no matter if SR's LTs are used, or these modified transforms are used. For any clock that does NOT intersect you, such as a clock comoving with B (that's separated from B) never intersects A, the transform solns then DIFFER from SR for that clock. The transforms are ugly, compared to the nicely reduced LTs of SR. And I mean, ugly. Here's the transforms I got ... As derived from the 3 TAUs Eqn in OEMB Section 3, but where 0 < e < 1 ... ... e(T0 + T2 ) = T1 ... e [ T0(0,0,0,t0) + T2 { (0,0,0,t0 + x’/(cout-v)+x’/(cback+v) } ] = T1[ x’,0,0,t0 + x’/(cout-v) ] The transforms attained were ... ... (Eqn 3) ... X = c[ ( (1/(cout -v) - m )/ (γn) ) (x-vt) ] ........... ← for the leading c, I used each of ... cRoundTrip=c ...... cout = c/(2e) ...... cback = c/(2(1-e)) ... (Eqn 4) ... T = [ ( n + mv) t - mx ] / (γn) where … ... 0 < e < 1 ... cout = c/(2e) ... cback = c/(2(1-e)) ... m = [ (1-e)cback - ecout + v ] ... n = (de -v2) ... de = (cout*cback) + (cout-cback)v ... γ = 1/√(1-v2/c2) Thanx, Celeritas Edited February 13, 2020 by Celeritas
Celeritas Posted February 13, 2020 Posted February 13, 2020 On 2/11/2020 at 1:25 PM, md65536 said: I think that 1-way speed of light differing from 2-way speed has turned out to be too complicated for me to handle. I don't even know if it can work, or how. md, Yup, I see exactly what you mean now. It's beat the crap outa me here. In my most prior derivation here, while I believe I have the time transform correct (t -> T), the space transform x -> X seems to be mistaken. Been looking at it, but I don't see the mistake yet. It may have to do with my 2nd assumption I had mentioned prior, not sure? The spreadsheet that processes the transforms produces the correct B values per A, but only for events ON the B worldline, and no matter what the reflection event (e) selected. However, when I set e=0.5 in the derived eqns, and reduce it by hand, it does not seem to reduce to the SR LT for X (it should). However, for any coordinate inputs that are off the B worldline, they certainly don't match the SR soln. But while I would figure them not to, I doubt my solns differ "properly". That said, I posted thinking it was right, but clearly I posted too quickly. If I figure it out, and am 100% certain, I'll repost it. I do see what you mean though, about too complicated, and whether it can even work. Thanx, Celeritas
md65536 Posted February 13, 2020 Posted February 13, 2020 (edited) 16 hours ago, Celeritas said: (2) there's that point in the derivation where you plug the interim eqn for time Tau (T) into X = cT. However, what speed-of-light to use? The 1-way outbound, the 1-way inbound, or the averaged 2-way speed-of-light? I had cout = c/(2e) and cback = c/(2(1-e)), and c (=cround_trip) being the averaged 2-way light speed (invariant c). Ideally that would come from what you're trying to model. Or if you're seeing what happens with an arbitrary value, or if it's a value that can be chosen for convenience without modelling anything physical, then you can choose. 9 hours ago, Celeritas said: In my most prior derivation here, while I believe I have the time transform correct (t -> T), the space transform x -> X seems to be mistaken. Been looking at it, but I don't see the mistake yet. It may have to do with my 2nd assumption I had mentioned prior, not sure? The spreadsheet that processes the transforms produces the correct B values per A, but only for events ON the B worldline, and no matter what the reflection event (e) selected. However, when I set e=0.5 in the derived eqns, and reduce it by hand, it does not seem to reduce to the SR LT for X (it should). However, for any coordinate inputs that are off the B worldline, they certainly don't match the SR soln. It's beyond me at this point. I was surprised it worked for you, I'd assumed that with so many details and definitions that can be adjusted, it would be much likelier to come up with something that doesn't work. On the other hand, with all the measurements related, it might just need letting the related things conform to whatever changes you make. It's definitely messy that way, but maybe not a problem. For example, if you change the definition of speed, you might end up with a measure of momentum that is no longer constant for an inertial mass, and say "oh, this must be wrong," but if you're redefining everything, your alternative definition doesn't have to have the same properties as the standard definition. It might not be wrong, just less useful. I don't know what's happening with your x coordinates, but maybe something like that is expected? Proper time and proper lengths are measured differently. Proper times can be measured by a moving clock, but proper lengths are measured in a rest frame. The ruler distance along a world line is not invariant. In my example when I messed with the definitions, I ended up with an altered meaning of being at rest, and so distances didn't have the same intuitive properties as usual. It's a bit of a rabbit hole. If you're looking at something like the speed of light as "just a definition", and with distance defined by speed of light, it's also "just a definition." If that seems wrong, consider that the definition of a metre has changed several times in history, and each time the measured value of a given length changes slightly, but nothing physically changed with each new definition. Edited February 13, 2020 by md65536
Celeritas Posted February 14, 2020 Posted February 14, 2020 (edited) 11 hours ago, md65536 said: I don't know what's happening with your x coordinates, but maybe something like that is expected? md65536, This supercedes my prior related post. So it turned out to be a very silly misapplication of a parentheses in 1 spot. Couldn't believe it, but on the other hand, yes I can. My eyes were buggy from looking at pages full of parens. So with the correction (which applies to EQN 3 below), the spreadsheet shows it matches SR precisely for reflection event e=½, be it proper or coordinate values produced. It varies from SR the moment e <> 1/2, and it should. (1) e ... is a variable that specifies the point-of-reflection as percentage of the roundtrip, so 0 < e < 1. (2) I assume the 2-way speed of light is invariant c, but the outbound light speed (along +x) and inbound light speed (along -x) is determined based on the selected reflection event e. (3) Assumption I ... the linear coefficent alpha (that arises from integrating the partial derivatives eqn) is equal to a = 1/gamma, just as per SR. Einstein was able to deduce that a = 1/gamma per phi(v) = 1, but I could not do that because the transforms did not reduce much. Therefore, I just assumed what Einstein deduced, that a = 1/gamma. (4) Assumption II ... there's that point in the derivation where you plug the interim eqn for time Tau (T) into X = cT. However, what speed-of-light to use? The 1-way outbound, the 1-way inbound, or the averaged 2-way speed-of-light? The options are cout = c/(2e), cback = c/(2(1-e)), or c (=cround_trip) where c is the average 2-way light speed (invariant c). Well, I used cout = c/(2e) for the same reason Einstein substituted x'/(c-v) for t instead of t = x'/(c+v) ... so I used t = x'/(cout -v), and for X = cT I used X = coutT. I'm sure this derivation is correct, given the assumptions I made. How much use this is I do not know, but it is interesting to compare what happens for time sync conventions that differ from SR, and again, this matches SR for SR's e=0.5. Here's a repost of my most prior, with corrected space transform for x→X ... *************************************************************************************************** As derived from the 3 TAUs Eqn in OEMB Section 3, but where e specifies the reflection event ... ... 0 < e < 1 ............← Use e=0.5 to produce SR transformation solns ... e(T0 + T2 ) = T1 ... e [ T0(0,0,0,t0) + T2 { (0,0,0,t0 + x’/(cout -v)+x’/(cback+v) } ] = T1[ x’,0,0,t0 + x’/(cout -v) ] My interim substitutions were these ... ... where Einstein uses X=cT ... I used X = coutT ... where Einstein uses t = x'/(c-v) ... I used t = t = x'/(cout -v) ... and of course ... x' = x-vt The transforms attained were ... ... (Eqn 3) ... X = cout [ 1/(cout -v) - m/n ] (x-vt) / γ ... (Eqn 4) ... T = [ ( n + mv) t - mx ] / (γn) where … ... 0 < e < 1 ... cout = c/(2e) ... cback = c/(2(1-e)) ... m = [ (1-e)cback - ecout + v ] ... n = (de -v2) ... de = (cout*cback) + (cout-cback)v ... γ = 1/√(1-v2/c2) *************************************************************************************************** Thank you for the help md. Much appreciated! Best regards, Celeritas Edited February 14, 2020 by Celeritas
Celeritas Posted February 17, 2020 Posted February 17, 2020 (edited) Update to my prior post, which is the 7th post back from here. My apologies. My previous derivation of the time transformation for a non-midpoint reflection event (with 1-way = 2-way speed-of-light) was missing a 1/c2 term, which produced the correct numeric result (given c=1) but with incorrect units. The space transformation (for x→x') was correct. .... (Eqn 1, old) ...... t' = γ[ (1/γ2 - (2ec-v-c)v)t - (v+(1-2e)c)x)/c2 ] ....... ← incorrect time transform (posted prior) .... (Eqn 1, fixed) ... t' = γ[ (1/γ2 - (2ec-v-c)v/c2)t - (v+(1-2e)c)x/c2 ] ....... ← correct time transform (posted here) .... (Eqn 1) ............. t' = γ[ (1/γ2+(v+(1-2e)c)v/c2)t - (v+(1-2e)c)x/c2 ] ....... ← I reorganized the corrected time t coefficients this way ) The correct transforms are as follows ... .... (Eqn 1) ... t' = γ[ (1/γ2+mv/c2)t - mx/c2 ] .... (Eqn 2) ... x' = 2eγ(x-vt) where … m = v+(1-2e)c where … 0 < e < 1 where … γ = 1/√(1-v²/c²) For e = ½ , the above transformations reduce to the LT's of Special Relativity. Best regards, Celeritas Edited February 17, 2020 by Celeritas
RAGORDON2010 Posted February 20, 2020 Posted February 20, 2020 Just a thought in passing - Twin tales have been part of the Special Relativity public-discussion canon going back to the original Einstein paper. The message is always that the observer in the “moving” frame is aging slower than the observer in the “rest” frame. In my studies of situations where I apply the Lorentz transformations to move from one frame to the other, I’ve noted that on occasion the result is reversed. Below, I present an example of each case. Application 1 - Retarded Decays of Speeding Unstable Particles Let’s imagine that the unstable particle is at rest on your train, which is moving at speed 0.8c relative to me standing on the platform. Suppose you observe that the particle decays over a time interval t’, while I observe that the particle decays over a time period t. If we position the particle at the origin of coordinates in your frame, we may set its x’-displacement equal to 0. Then the Lorentz time transformation from your frame to my frame takes the same form as the classic time dilation formula and for your decay time t’ equal to, say, 24 units of time with v = 0.8c, my decay time t equals 40 units of time. So, you, standing in the “moving” frame are aging slower than I, standing in the “rest” frame. Award One Point to the Twin Tales. Application 2 - The Exploding Ball I would like to return now to the a situation I described in another post. I am again standing on the platform while you are on a speeding train moving at 0.8c. Next to you is a charged ball containing a small firecracker. I apply a strong magnetic field across the track causing the ball to undergo a series of vertical loops as I perceive the motion, while you perceive the motion as a series of “pogo stick” hops. Once the ball starts looping as I perceive it, and hopping as you perceive it, I zap the ball with a laser beam and set off the firecracker. Pow!!! The ball explodes at an object point (t,x,y,z) in my frame and at the corresponding image point (t’,x’,y’,z’) in your frame, where the object-image coordinates satisfy the Lorentz transformations. Now let's make it easy on ourselves. Suppose I zap the ball at the bottom or top of a loop, so I have no x-displacement to deal with, and suppose my clock reads 24 units of time at the moment the ball explodes, in whatever units of time are appropriate to our measurements. Here, with a zero x-displacement, the Lorentz time transformation takes the same form as the classic time dilation formula referenced above, and so your clock will read 40 time-units. So, I, standing in the “rest” frame, am aging slower than you, standing in the “moving” frame. Deduct One Point from the Twin Tales. So perhaps the best that can be said is that whether the observer in the “moving” frame is aging slower than the observer in the “rest” frame, or vice-versa, depends on the specifics of the experiment under consideration.
md65536 Posted February 20, 2020 Posted February 20, 2020 (edited) Celeritas, I haven't followed the math very well. But back to an earlier subtopic, I think I'll no longer say that B turning around "doesn't cause" the difference in ageing seen at event AC (when A and C pass), because I don't know the meaning of that statement precisely enough. Here, C can refer to OP's C clock, or to B after an instant turnaround at event BC. Speaking in terms of causality, event BC *can* be causally related to event AC. AB is also causally related to AC (and to BC). Indeed, all events on all three clocks' worldlines between the events mentioned, can be causally related to AC. So you could say "A remaining inertial causes the difference in ageing seen at event AC", and "The entire time A and B/C are separated causes the difference at AC". You could also say something like "A and B passing causes BC" and get into interpretations, just like "B turning causes AC" is interpretive, but causal influence is possible. In terms of causality, the event BC is not causally related to any events on A's world line between proper times 2 years to 8 years. Therefore technically, B turning around doesn't cause (or is affected by) any events at A within that range. Back to what the LT says, if there is some physical change in the relative time at A when B accelerates (which I don't accept), that change is causally restricted to within event BC's light cone. For example, if B randomly decided only at event BC, whether to turn around or remain inertial, then A would not be able to detect any change due to that decision, until it had aged 8 years since leaving B, at which point it is able to see whether B turned or not. 35 minutes ago, RAGORDON2010 said: So perhaps the best that can be said is that whether the observer in the “moving” frame is aging slower than the observer in the “rest” frame, or vice-versa, depends on the specifics of the experiment under consideration. Yes, "who is ageing less" ie. "whose clock is running relatively slower" is relative and generally depends on reference frame. That's why in the twin paradox experiment, the relative ageing is only compared when the twins are together (ie. at individual events). When they're together, the difference in their ageing is not frame dependent, so all observers agree on it. In your experiments, different observers disagree, as per special relativity, but that's no argument against the the twin paradox, in which everyone agrees on the outcome. Edited February 20, 2020 by md65536
Celeritas Posted February 21, 2020 Posted February 21, 2020 (edited) accidental post ... thanx, Celeritas Edited February 21, 2020 by Celeritas
Celeritas Posted February 21, 2020 Posted February 21, 2020 21 hours ago, md65536 said: Celeritas, I haven't followed the math very well. Well, I did not post the complete derivations, so that's understandable. I'm having some difficulty understanding exactly what they mean too. I derived transforms for 2 cases ... ... (1) 0 < e < 1 ... where 1-way = 2-way (speed-of-light) ... (2) 0 < e < 1 ... where 1-way <> 2-way (speed-of-light) ... unless e= ½ Case (1) seems improper IMO. The LTs are derived exactly as done in OEMB, with an invariant c, and closing rates of c-v (outbound) and c+v (inbound). Yet, to select a non-midpoint reflection event requires cout <> cback. So an invariant c and non-midpoint reflection event seem mutually exclusive. This is why I derived transforms for case (2). Case (2) determines the cout and cback for the selected e. My derivation seems proper, however I am not yet certain the 3 aformentioned assumptions that I made (during derivation) were proper. I must admit, the solns for a non-midpoint reflection event seem suspicious, but I'm still trying to understand it and verify it is actually right. I've been following your advice, in assuming that unexpected results may not necessarily be wrong. In fact, I'm still trying to convince myself that the derivation is logically sound, so this may take awhile. 21 hours ago, md65536 said: But back to an earlier subtopic, I think I'll no longer say that B turning around "doesn't cause" the difference in ageing seen at event AC (when A and C pass), because I don't know the meaning of that statement precisely enough. Here, C can refer to OP's C clock, or to B after an instant turnaround at event BC. Fair enough md. You quoted "doesn't cause", and wonder regarding the precise meaning of that. Your prior point regarding "proper-time accrual" being the important (and easiest) thing, is certainly a cause for the relative aging. That speaks to the comparison of the 2 worldline lengths. However ... It is equally true that the proper accelerations (ie frame transitioning) by twin B allows that worldlines geometry to become attained. That's about it, IMO. It really comes down to relative simultaneity. I like to say the same thing just a little differently ... It's about the relative angular orientation between the spacetime systems, which in the twins scenario is dynamic ... which also allows for re-location for an absolute age comparison. One twin must depart the originating common frame, or there be no relative aging differential. He who properly accelerates to transitions frames, always ages the least. So the geometry defines the relation of the worldlines and their lengths, the worldline length(s) define the proper time(s) accrued, and B's proper acceleration creates the worldlines geometry with re-colocation. 22 hours ago, md65536 said: Speaking in terms of causality, event BC *can* be causally related to event AC. AB is also causally related to AC (and to BC). Indeed, all events on all three clocks' worldlines between the events mentioned, can be causally related to AC. So you could say "A remaining inertial causes the difference in ageing seen at event AC", and "The entire time A and B/C are separated causes the difference at AC". You could also say something like "A and B passing causes BC" and get into interpretations, just like "B turning causes AC" is interpretive, but causal influence is possible. In terms of causality, the event BC is not causally related to any events on A's world line between proper times 2 years to 8 years. Therefore technically, B turning around doesn't cause (or is affected by) any events at A within that range. Back to what the LT says, if there is some physical change in the relative time at A when B accelerates (which I don't accept), that change is causally restricted to within event BC's light cone. For example, if B randomly decided only at event BC, whether to turn around or remain inertial, then A would not be able to detect any change due to that decision, until it had aged 8 years since leaving B, at which point it is able to see whether B turned or not. Very true, causality is dictated by locality, and hence by the transfer of light signals. I would only add that ... This does not then lead that when twin B executes his (instant, or virtually instant) turnabout, that twin A cannot sweep contiguously from 3.2y-A to 5y-A to 6.8y-A within the B spacetime system. Twin A must do so, if SR is correct. And IMO, that's the more interesting part. It matters not, that B does not "see this" via light signals. However, for the light received by twin B from twin A, the corresponding doppler shifts notable by twin B (during his transition of frames) provide a validation of this, per SR. The meaning of the theory seems incomplete IMO, if this point is not considered or understood. This is to say that when twin B arrives back on earth, before he even asks A to show his clock, B has already predicted that A must have aged 10 yr ... 3.2-A inertially out, 3.6y-A during instant (or virtually instant) turnabout, and 3.2y-A inertially back (=10y-A total). Each twin has each their own proper time accrual, but each twin also has their prediction of the other's aging over the common interval, and everyone's correct. Best regards, Celeritas
md65536 Posted February 21, 2020 Posted February 21, 2020 1 hour ago, Celeritas said: Case (1) seems improper IMO. The LTs are derived exactly as done in OEMB, with an invariant c, and closing rates of c-v (outbound) and c+v (inbound). Yet, to select a non-midpoint reflection event requires cout <> cback. So an invariant c and non-midpoint reflection event seem mutually exclusive. This is why I derived transforms for case (2). A possible way forward is to treat c as a constant local speed of light, as it is in GR. It might be possible not to worry about the speed of anything measured from a distance, in your equations? 1 hour ago, Celeritas said: I've been following your advice, in assuming that unexpected results may not necessarily be wrong. In fact, I'm still trying to convince myself that the derivation is logically sound, so this may take awhile. I don't recommend following any of my advice on anything, unless you agree with it! I'm 100% sure you understand the technical details better than I do. If you're interested in testing whether your results are in agreement with SR, you might try deriving the Doppler effect including any of your alterations. If it doesn't give the exact same values as SR, it's not going to agree with real measurements as SR does. But also, I'm not sure what you're working to accomplish, so I don't want to suggest more work. 2 hours ago, Celeritas said: This does not then lead that when twin B executes his (instant, or virtually instant) turnabout, that twin A cannot sweep contiguously from 3.2y-A to 5y-A to 6.8y-A within the B spacetime system. Twin A must do so, if SR is correct. I think we'll never agree, because of philosophical differences. Of course, SR doesn't depend on philosophy, and I think anything "purely" philosophical is not part of the theory. The way I see it... SR is correct, independent of experimental validation. The theory is purely mathematical. You start with some assumptions and mathematical rules, and you end up with some consequences. It is an exact, error-free model. Experimental validation deals with how well that model corresponds with reality, not whether or not it is correct (or complete, or whatever). We find that when measuring the universe, it really does seem to adhere to the assumptions and rules that SR uses, and thus the predictions made by SR are accurate in the real world. Philosophically, the only things I treat as "real" are what are measurable. If there's some mathematical prediction or description, like "A sweeping contiguously through time relative to B in the instant B accelerates", but it is not measurable, for me it's just a part of the model, not something real. For me, it makes so much more sense when everything "optional" is left out (cut off by Occam's razor). That's why I like OP's experiment. Changing from "B and C pass by each other" to "B turns around" doesn't change the prediction, so there's nothing real in that left to figure out.
RAGORDON2010 Posted February 21, 2020 Posted February 21, 2020 On 2/19/2020 at 9:54 PM, md65536 said: Yes, "who is ageing less" ie. "whose clock is running relatively slower" is relative and generally depends on reference frame. That's why in the twin paradox experiment, the relative ageing is only compared when the twins are together (ie. at individual events). When they're together, the difference in their ageing is not frame dependent, so all observers agree on it. In your experiments, different observers disagree, as per special relativity, but that's no argument against the the twin paradox, in which everyone agrees on the outcome. md65536 - Interesting observation. I wasn't aware of this distinction. Thank you for clearing it up for me.
Celeritas Posted February 21, 2020 Posted February 21, 2020 (edited) 9 hours ago, md65536 said: A possible way forward is to treat c as a constant local speed of light, as it is in GR. It might be possible not to worry about the speed of anything measured from a distance, in your equations? If you're interested in testing whether your results are in agreement with SR, you might try deriving the Doppler effect including any of your alterations. If it doesn't give the exact same values as SR, it's not going to agree with real measurements as SR does. But also, I'm not sure what you're working to accomplish, so I don't want to suggest more work. You had mentioned (prior) the momentarily co-moving and co-located inertial reference frames (MCCIRFs) that coincided with the twin B during his own own proper accelerations. At any moment during B turnabout, the local speed of light from A should be speed-c per twin B and the corresponding MCCIRF, and they should also agree on the doppler shift of the light from twin A. And, we may assume that we knew the frequency of the light transmitted by A per A in a pre-planned test event. Although, given superfast unrealistic proper accelerations by B, twin B may be required to coast momentarily to verify and validate that doppler effect. 12 hours ago, Celeritas said: This does not then lead that when twin B executes his (instant, or virtually instant) turnabout, that twin A cannot sweep contiguously from 3.2y-A to 5y-A to 6.8y-A within the B spacetime system. Twin A must do so, if SR is correct. 9 hours ago, md65536 said: I think we'll never agree, because of philosophical differences. Of course, SR doesn't depend on philosophy, and I think anything "purely" philosophical is not part of the theory. Consider this md ... We might imagine the twin's executing a pre-planned flight test precisely as we've been discussing here, with instant (or virtually so) B turnabout at a planet X. Planet X is at rest with earth, separated from earth by 3 ly proper, and it's clocks are synchronized with the earth (and twin A) clocks. Everytime the flight test is executed, the relative aging result is the very same, because the flight test is conducted identically every time. Next, imagine that at any point in time during the B turnabout at planet X, we have twin B "go to coast" and hence becomes inertial. Here, I am making a point as to "the validity of" the A clock sweeping continguously from 3.2y-A thru 5y-A to 6.8y-A (in the B system) during his turnabout (which I say is consistent with SR). Further, let's imagine that B is told to "go coast" precisely when he is momentarily co-moving and co-located with Planet X. The B clock then reads 4y-B, and twin B is now inertial. What do you think the twin B navigation system will declare of the current range to twin A (on earth), and for the current time on the clocks of planet X, earth, and twin A? Per B, I submit those clocks must then all read 4y, and with twin A 3 ly downrange. For that to happen, which I submit would be the only outcome consistent with SR (and reality), it must be true that the A clock contiguously swept from 3.2y-A to 5y-A in the B spacetime system during B's instant (or virtually instant) turnabout. Therefore, it must be true that the A clock contiguously swept from 3.2y-A thru 5y-A to 6.8y-A in the B spacetime system during B's instant (or virtually instant) turnabout, in the complete twins scenario we've been discussing here. Yes? Best regards, Celeritas Edited February 21, 2020 by Celeritas
Celeritas Posted February 21, 2020 Posted February 21, 2020 md63356, BTW, wrt my derived transformations for the case (2), where ... ..... 0 < e < 1 ..... cout ≠ cback ..... and where e ≠ ½ ........ ... (where e = ½ would be the SR convention) Considering the A and B worldlines from A/B flyby to BC flyby (Time Handoff scenario), while the gamma factor remains at γ = 1/√(1-v²/c²) for the relation between the A & B clocks, it also turns out that moving contracted lengths at rest in the B frame (as noted by A) must contract to values different from 1/γ. No doubt, because cout ≠ cback ≠ c, and spatial-offsets from the B worldline produce different coordinate values (of B per A) than does SR. All this, makes it very clear why Occam's Razor should win, and Einstein's convention be assumed as "the most likely" true-to-nature. Alas, it seems impossible to ever prove such, or so it would seem today. Best regards, Celeritas
md65536 Posted February 21, 2020 Posted February 21, 2020 (edited) 4 hours ago, Celeritas said: Although, given superfast unrealistic proper accelerations by B, twin B may be required to coast momentarily to verify and validate that doppler effect. There's another simplification that can be made. How do you know what's a realistic acceleration? We could be talking about twin neutrinos. If we're talking about rockets, the physical properties of the rockets aren't given. That's fine because they don't matter. The mass of the object that accelerates doesn't factor into the SR equations. Therefore it can be simplified out. We can talk about abstract twin particles. Imagining they're something specific, just adds red herrings. 4 hours ago, Celeritas said: Planet X is at rest with earth, separated from earth by 3 ly proper, and it's clocks are synchronized with the earth (and twin A) clocks. Sure, but they're synchronized only (generally speaking) in the Earth/A/X inertial frame. 4 hours ago, Celeritas said: Further, let's imagine that B is told to "go coast" precisely when he is momentarily co-moving and co-located with Planet X. Ie. B is momentarily at Planet X and at rest with it. 4 hours ago, Celeritas said: What do you think the twin B navigation system will declare of the current range to twin A (on earth), and for the current time on the clocks of planet X, earth, and twin A? B's now in A's inertial frame, and agrees with A's (X's) measurements: A is 3 LY away, and A's clock is Einstein-synchronized to X's, which reads 5 years (per OP's specs, halfway---according to any of A, B, C---through the experiment). 4 hours ago, Celeritas said: For that to happen, which I submit would be the only outcome consistent with SR (and reality), it must be true that the A clock contiguously swept from 3.2y-A to 5y-A in the B spacetime system during B's instant (or virtually instant) turnabout. Therefore, it must be true that the A clock contiguously swept from 3.2y-A thru 5y-A to 6.8y-A in the B spacetime system during B's instant (or virtually instant) turnabout, in the complete twins scenario we've been discussing here. Yes? Nah! How would you measure that sweep at A? You can definitely predict it, using SR, but if you didn't know SR but had any conceivable measuring device you can imagine, how would such a device measure (not predict) that sweep? If you can unambiguously measure it, I'll agree it's the only outcome consistent with reality. Just checking we're on the same page: What does X's clock read when B reaches it, comes to rest with it, and then leaves again (all in negligible B's proper time)? 2 hours ago, Celeritas said: All this, makes it very clear why Occam's Razor should win, and Einstein's convention be assumed as "the most likely" true-to-nature. Alas, it seems impossible to ever prove such, or so it would seem today. That's what makes it a philosophical argument, not a scientific one. Scientific theories do not pick a choice they think is "real" based on Occam's razor. You don't settle eg. Copenhagen interpretation or string theory based on Occam's razor. You also don't have to because the questions answered by science are about quantitative predictions, not "which model is the one true description of reality?". The conventions used in SR are not about picking a choice that one thinks is "real", it's about ... again, in Einstein's translated words: "that in every real case it must supply us with an empirical decision as to whether or not the conception that has to be defined is fulfilled." Ie. it is chosen because it is useful in making measurements. Any conventions that give you measurable predictions that equally agree with reality, are equally real. You need a different measurement given by different conventions, to be able to physically evaluate which is more "true-to-nature". Occam's razor tells you nothing about that, but it can tell you which are more practical than others. Edited February 21, 2020 by md65536
Celeritas Posted February 23, 2020 Posted February 23, 2020 On 2/21/2020 at 5:03 PM, md65536 said: There's another simplification that can be made. How do you know what's a realistic acceleration? ....... The mass of the object that accelerates doesn't factor into the SR equations. Therefore it can be simplified out. Agreed md, the LT derivation was based on a kinematic model. My point, was only to say that an instant acceleration is unrealistic, and anything less than instant "allows for continuity of" the A clock in the B spacetime system during his turnabout. It's not so easy to ignore it, if not instantaneous. You've argued that only proper time should be considered, because its absolute, while coordinate time is relative per POV. My point has been that coordinate time of a remote clock at a point in spacetime, is the proper time of that clock at that location in spacetime. Upon B/C flyby, each predict a different time of the A clock, but this does not mean they are wrong. They are both correct, and the eventual receipt of light signals will confirm that. As such, there is no reason (in my thinking) that the accrual of clock A coordinate time (per twin B) should not match the accrual of proper time (per A), ie 10y-A. And it does, and makes complete sense, using (for example) the MCCIRF method. It's certainly not the convenient method, but just as correct. If B ignores his turnabout, he must predict that twin A ages only 3.2+3.2 = 6.4y-A. However, we know he must age 10y-A. Therefore, the twin A existence in the B spacetime system during turnabout, cannot be ignored (instant turn, or not). On 2/21/2020 at 5:03 PM, md65536 said: Just checking we're on the same page: What does X's clock read when B reaches it, comes to rest with it, and then leaves again (all in negligible B's proper time)? The X clock reads 5y-A during twin B's complete turnabout, because no time can pass per anyone in the cosmos in an instantaneous turnabout (by definition). On 2/21/2020 at 5:03 PM, md65536 said: Nah! How would you measure that sweep at A? You can definitely predict it, using SR, but if you didn't know SR but had any conceivable measuring device you can imagine, how would such a device measure (not predict) that sweep? If you can unambiguously measure it, I'll agree it's the only outcome consistent with reality. Well, if B had no idea of relativity theory, he'd calculate the Newtonian predictions as he went. He'd be wondering how he got to planet X as fast as he did, with no good explanation. He'd be confused until he figured out how to derive the LTs In thought experiment, the sweep at A may be logically deduced. The eventual receipt of light signals verifies LT solns for any and all spacetime events in all-inertial scenarios. Now, imagine a clock D colocated and comoving with B. Twin B makes his turn at planet X, but D keeps on coasting. The eventual receipt of light signals will prove to D that when B turned, the A clock was 2.4 ly downrange and read 3.2y-A. That's a valid test. The B clock made that same prediction at the turn, so he was right, as confirmed by D's eventual verification. Next, B instantly lands on planet X. The eventual receipt of light signals will confirm that upon landing, twin A was 3 ly downrange with a readout of 5y-A. That's a test. So either the A clock truly advanced from 3.2y-A to 5y-A in no time at all (due to POV chnage), or it jumped in readout by magic, or B's SR prediction of the A clock readout while inertial is flawed (and Newton was right all along). The current A clock readout depends only on the current POV. When B transitions frames of reference at turnabout, his POV dynamically changes wrt those who remain inertial. His POV changes because his spacetime system rotates in 4-space. His sense-of-simultaneity rotates as his spacetime system rotates. The current A clock readout (and location) depends only on where B's sense-of-simultaneity then intersects the A worldline. Since his spacetime system dynamically rotates during turn, the remote A clock wildly swings in readout (and location). This has no affect on twin A or his clock, who always experiences time to pass steadily as normal. Turning your head at night, has no impact on the stars themselves. It's a POV change. What's required, is that all moments in time coexist, as inches on the ruler do. Ie, a fused spacetime continuum. That all worldlines are laid out in the continuum in their entirety, eternal in a sense. That we for reasons unknown, we do not experience that directly, however the measured relativistic effects (to date) are the proof of it. The required time desynchronization of moving bodies, is a clear example of why it should exist as such, IMO. But ... All that said, Lorentz's version of relativity (as re-interpretted after 1905) possesses the very same LTs, but means something completely different. It also uses the same time synchronisation procedure. Also, coordinate time means something different in Einstein's theory, versus Lorentz's theory. Therefore, I'll have to agree that the meaning of theories, and components of them, is subject to philosophical choice. The measurements, and noted predictability, are not. Does that sound fair md? Best regards, Celeritas
Celeritas Posted February 23, 2020 Posted February 23, 2020 (edited) 11 hours ago, Celeritas said: to md65536: All that said, Lorentz's version of relativity (as re-interpretted after 1905) possesses the very same LTs, but means something completely different. It also uses the same time synchronisation procedure. Also, coordinate time means something different in Einstein's theory, versus Lorentz's theory. Therefore, I'll have to agree that the meaning of theories, and components of them, is subject to philosophical choice. The measurements, and noted predictability, are not. Does that sound fair md? It was late when I posted last night, and I suppose "and components of them" was vague. The 1-way speed of light has never been verified by test, and may never be. So until it is, it's certainly fair to say that a convention used is a personal preference. It cannot be known that it represents something true in nature. I should add, while (say) Lorentz Ether Theory (LET) uses the same time sync procedure as SR, the meaning of "in sync" means something different for LET vs SR. In SR, you are assumed in sync after running the procedure, however in LET your assumption of such is mistaken while yet unawares. Philosophically, one theory (eg Lorentz Ether Theory, LET) may assume a master frame, while the other (eg SR) does not. One theory (LET) possesses a much more convoluted meaning than does the other (SR). So while they use the very same LTs, they mean something different. Light signals cannot prove which theory is right. So, it's a philosophical choice as to which theory one prefers. A block universe and a master ether frame are two such philosophical choices. Eternalism and Presentism are philosophies of spacetime. So, I agree in all that. The important thing, is that any valid theory (of space and time) must accurately predict the time readout of moving clocks upon flyby, anywhere and everywhere in spacetime. And, we may imagine virtual clocks of all frames at all points in spacetime, with virtual clocks replacable by real clocks. What is real, are the measurements and the predicatability of theories per measurements. With enough consistency of predictability, mathematically sound theories are then accepted. I'm still of the opinion that the accrual of twin A coordinate time must match the accrual of twin A proper time. If twin B does NOT consider the accrual of twin A coordinate time during his turnabout, then twin A ages only 3.2+3.2 = 6.4y over the interval (which is wrong, because it's incomplete). If twin B DOES consider it, then twin A ages the required 3.2+3.6+3.2 = 10y over the interval, which matches the proper time accrual of twin A. This is only to say that the present coordinate time of a remote moving clock is the proper time of that clock at that spacetime location, and while the use of coordinate time is less convenient it is no less correct. During turnabout, the fact that B's added consideration of twin A coordinate-time produces the total required aging of twin A (10y), lends weight that the rapid advancement of the A-clock readout (in the B system) is valid and representative of something real, just as proper time is assumed representative of something real. Just for a moment ... let's assume that all moments in time coexist in a fused spacetime continuum. IOW, let's assume that particular philosophy matches reality. As such, the wild advancement of the A clock in the B system during turnabout, is the result of a real mechanism, not (say) a mere mathematical artifact. The current readout of a remote moving clock then depends upon where your sense-of-simultaneity then slices the twin A worldline, and said intersection dynamically changes while transitioning inertial frames of reference (eg B's turnabout). Your sense-of-simultaneity is governed by the angular orientation of your spacetime system in spacetime which is dependent on your current velocity, and is dynamic during proper acceleration. So, it would then model what is real. Also, the rapid advancement in A-clock coordinate time has no impact on twin A, just as turning your head has no impact on the stars in the night sky. It's only a change in POV of the observer. Twin A always experiences the passage of time as completely normal, ans everyone else does. Lastly, I'm still studying the impact of differing time sync conventions, and I'll need more time before saying more in that regard. And as you (md) had mentioned, I'm not even sure (as yet) that these differing conventions make sense, or whether all the assumptions used in their derivation even make sense. It's been somewhat a challenge. One thing is for certain, if no convention can be proven true to nature, then you'd have to be a mascocist to use a non-midpoint reflection event. Best regards, Celeritas Edited February 23, 2020 by Celeritas
md65536 Posted February 23, 2020 Posted February 23, 2020 (edited) 13 hours ago, Celeritas said: If B ignores his turnabout, he must predict that twin A ages only 3.2+3.2 = 6.4y-A. However, we know he must age 10y-A. Therefore, the twin A existence in the B spacetime system during turnabout, cannot be ignored (instant turn, or not). That's wrong. B can SEE A ageing. B predicts that A's clock can be seen ticking at a rate of 0.5x its own, for 4 of B's years, and then ignores whatever happens at A while B turns around, then predicts A's clock can be seen ticking at a rate of 2x its own, for 4 of B's years. So it predicts A will be seen ageing 2+8 = 10 years, plus whatever it ignored. Why must it predict 6.4y, when it can predict the correct value? The rest of your post, you just keep repeating a similar false claim over and over. 13 hours ago, Celeritas said: His sense-of-simultaneity rotates as his spacetime system rotates. There's no such thing. Distant simultaneity isn't sensed. B doesn't "sense" a change in the time at A while it turns around (in negligible time). The coordinate time at A changes BY DEFINITION of simultaneity given by Einstein. Do you not accept that? You say his definition is a convention and then give pages and pages and pages of arguments that it's not. I've not convinced you of anything, and I'm repeating the same thing over and over, I give up. 2 hours ago, Celeritas said: IOW, let's assume that particular philosophy matches reality. No thanks. I don't think that all of the unnecessary complications you're adding will help to understand the uncomplicated case. 3 hours ago, Celeritas said: I'm not even sure (as yet) that these differing conventions make sense, or whether all the assumptions used in their derivation even make sense. So start with something that makes sense. Don't just make random changes, choose the idea that you're trying to model. If you only change things that do not influence any real measuring device readings then the end result should agree with reality. Assume your "fused spacetime continuum" if you want. Just *don't* change something that doesn't affect real measurements, end up with something that agrees with reality, and then conclude that your changes must represent "true reality". (For example, choosing a random privileged frame will agree with reality, that doesn't make its privilege real.) Also don't take existing definitions that don't affect real measurements and conclude that they must represent "true reality". Edited February 23, 2020 by md65536
Celeritas Posted February 24, 2020 Posted February 24, 2020 (edited) 3 hours ago, md65536 said: That's wrong. B can SEE A ageing. But I was speaking strictly of how the A clock exists "in the B spacetime system" over the round trip, to determine A's aging. Not "seeing" the hands of the A clock as B goes. Again, using everyone's proper time alone (per each themselves), produces the correct relative aging, and is the easiest approach. No dispute there. My point has been that B should be able to accurately predict the extent of twin A aging, using only A-coordinate values (per B), using the MCCIRF method. And, we could imagine a well preplanned flight test. Twin B cannot ignore how A exists in B's own spacetime system during his turnabout. If he does ignore it, B will predict A to age only 3.2+3.2=6.4y (not 10y) on reunion. That's wrong, only because it's incomplete. 3 hours ago, md65536 said: There's no such thing. Distant simultaneity isn't sensed. B doesn't "sense" a change in the time at A while it turns around (in negligible time). When I say sense-of-simultaneity, or sense-of-now across space, I mean line-of-simultaneity. If "sense" is a problem, just assume I said B's "simultaneous space", instead of B's sense-of-simultaneity. 3 hours ago, md65536 said: No thanks. I don't think that all of the unnecessary complications you're adding will help to understand the uncomplicated case. That's fine md. Nobody has a problem with the Time Handoff scenario, and it's certainly the simplest case. However, I've only been trying to point out what I mentioned above, in the 3rd para of my first response above. 3 hours ago, md65536 said: So start with something that makes sense. Don't just make random changes, choose the idea that you're trying to model. If you only change things that do not influence any real measuring device readings then the end result should agree with reality. Assume your "fused spacetime continuum" if you want. Just *don't* change something that doesn't affect real measurements, end up with something that agrees with reality, and then conclude that your changes must represent "true reality". (For example, choosing a random privileged frame will agree with reality, that doesn't make its privilege real.) Also don't take existing definitions that don't affect real measurements and conclude that they must represent "true reality". All good points, and I've been trying to do so. I've never worked on this before. There's a learning curve, as I go. For any two clocks momentarily intersecting in spacetime, they have a specific set-of-readouts. SR makes its prediction. Any valid theory must predict the correct readouts, and the owners of those 2 clocks know what their clocks then read. All in the cosmos must agree, if the transformations they use are valid. I'm primarily looking to see what changes in convention cause a change in that set-of-readouts (wrt SR), versus what changes do not. Best regards, Celeritas Edited February 24, 2020 by Celeritas
md65536 Posted February 24, 2020 Posted February 24, 2020 (edited) 1 hour ago, Celeritas said: But I was speaking strictly of how the A clock exists "in the B spacetime system" over the round trip, to determine A's aging. Not "seeing" the hands of the A clock as B goes. Again, using everyone's proper time alone (per each themselves), produces the correct relative aging, and is the easiest approach. No dispute there. My point has been that B should be able to accurately predict the extent of twin A aging, using only A-coordinate values (per B), using the MCCIRF method. And, we could imagine a well preplanned flight test. Twin B cannot ignore how A exists in B's own spacetime system during his turnabout. If he does ignore it, B will predict A to age only 3.2+3.2=6.4y (not 10y) on reunion. That's wrong, only because it's incomplete. What's the definition of a clock's "existence" in another observer's frame? What if B doesn't know of relativity, and says "A's existence spans 2 of its years on my outbound journey, and 8 years on my inbound, and I've measured that to be true"? How can you prove to B that it's wrong and that your description of existence is the right one? Can you convince it that what it measures (2 + 8 years observed) is wrong and your numbers (unmeasured, but later verified to be consistent with a particular definition of simultaneity) are the ONLY ones that can be real? And can you do this without relying on Einstein's definition of simultaneity or an equivalent? Do you think that when Einstein defined simultaneity in such a way that real-world events could be tested against that definition to determine if they fit it or not, he actually did much more than that, and actually defined existence? Or could it be that his definition so perfectly aligns with your assumptions about reality, that you figure he is proving your assumptions correct simply by definition? Edited February 24, 2020 by md65536
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