Celeritas

md65536, I understand Einstein's convention, and that it is by definition. But before responding further, I need to revisit differing conventions-of-simultaneity, make sure I understand that properly. I was thinking differing conventions would produce somewhat different LT solns, but now I'm thinking that's not the case. Given the LT solns are no different, I suppose it would not matter if the convention was true to nature or not. However, the LTs are simplest per Einstein's convention. Also, it's hard to imagine the ray not bisecting the roundtrip in the proper frame of the emitter/reflector, given there are no preferred frames. Best regards, Celeritas

I'm not sure why you posted this for me Markus? I only re-iterated that the length of the worldlines dictates the relative aging in the stated twins scenario. I mean, I've been saying that all along here. Wrt any of my prior posts, can you refer me to the part that made you think I did not realize that going non-inertial causes the lesser aging (or symmetry break). Wrt your last line ... same thing. I did mention that twin B's velocities (per A) are the result of its intial velocity and all the subsequent proper accelerations by B. I don't recall suggesting changing the motions of twin A or B wrt the defined twins scenario. I understand everything you say here above. If I had contradicted that anywhere, it went unbeknownst to me. Best regards, Celeritas

md65536, So, our discussion was regarding whether acceleration plays any role in the relative aging outcome. Everyone agrees that the LTs quantify relative time by the use of velocity, everything is inherent in the geometry of the worldlines, and it is ultimately about the length of the worldlines over the interval. Camp 1 ... says proper acceleration plays no role in the relative aging in the twins scenario. Camp 2 ... says (it does, ie) all relative velocities used by the LTs are the very result of the initial velocity and all subsequent twin B proper accelerations. The twins must be co-located at the ends of the interval to produce a relative aging that's invariant. It certainly takes twin B's proper accelerations, to make that happen. The fact that we reduce the periods of acceleration to zero, does not change that. It's about "the transitioning of inertial frames". Yet, no one disputes that the relative aging is quantified by the use of only velocities per the LTs. Regarding coordinate time, we call it coordinate time because observers disagree per POV, not because the LTs produce coordinate times that are merey apparent or even potentially incorrect. Is it possible they are incorrect? Yes. However, we assume the Einstein clock synchronization procedure is true to nature and hence correct, per Occam's Razor (until some future test proves otherwise). So at B/C flyby, we assume the A clock really does then exist at 3.2y-A per B, and the A-clock really does then exists at 6.8y-A per C. Ie that that's true to reality. If a future test proves 1-way <> 2-way, well, then we'll be changing the LTs to accomodate. Certainly, the accrual of proper time always dictates the relative aging result, instant accelerations or not. Yet the use of coordinate time in the relative aging prediction does not alter the outcome, although it is a less convenient calculation. One more ... at B/C flyby, C then holds A to exist at 6.8y-A. We call that coordinate time, because other observers (eg B at B/C flyby) can disagree. Yet, 6.8y is the proper time of the moving A-clock "when it displays 6.8y". Best regards, Celeritas

md65336, Maybe we should further address this point, regarding how real a coordinate time is. Lorentz considered coordinate time a mathematical artifact that arose during the derivation of his LTs. He called it "local time", to distinguish it from something "real". Einstein said that what Lorentz called local time, "was just time". Let's consider the ABC TIme Handoff scenario. At B/C flyby, B declares the A-clock to then read 3.2y-A but C declares the A clock to then read 6.8y-A. Are both correct, 1 correct, or neither correct? Are they all correct, but their predictions something less than real? Does a clock truly read what it's hands then display? The eventual receipt of light signals will reveal that all are correct, and their predictions (per LTs) represent the "real time" as experienced by the remotely located A-clock, per the observer. A clock is as old as it's time readout then displays, and we might assume that all clocks start ticking from zero at construction/birth. The fact that observers disagree, does not lead that LT coordinate predictions are something less than real. The fact that coordinate time differentials lessen with lesser range, and vanish when co-located with the observers (eg B&C at B/C flyby), does not lead that LT coordinate predictions are something less than real. The problem is ... what convention of synchronicity should twin B use during his proper accelerations? The Einstein convention does not work, because he's no longer inertial. What we do assume, is that LTs predict reality for inertial POVs within any locally-flat-spacetime far from gravity source. All that said, the Time Handoff and Twins scenarios produce the same result, because the geometry is the same. due to the specific scenario specifications and restrictions. The Twins scenario is reduced to inertial purely segments that match the Time Handoff scenario, because zero duration during proper accelerations are zero and hence ignorable (wrt the accrual of proper time). Again, the proper accelerations "are what causes" twin B to attain that geometry. As such, they play as much a role in attaining that result, IMO, as does the quantification of relative time per the LTs over the inertial phases of flight. Best regards, Celeritas

Hmm, not sure what you are talking about there md65536. I did not say that twin B would measure the outbound & inbound separation-lengths differently than B or C. Your response seems to imply you thought I said that. I said that twin B must properly accelerate, ie TURN in spacetime (which means "transition inertial frames") to age less than twin A. That causes the separation between the events to length-contract, as that length then goes into motion per twin B. Shorter length, he gets there quicker. Similarly on return, so twin B travels a shorter duration, and hence a shorter worldline. So when I said ... TURN (in spacetime), I meant "transition inertial frames". Far as the Turnabout event goes (at the halfway point), it is defined (unrealistically) as instantaneous. This means that the twin A-clock would (in the B spacetime system) swing from 2.4 ly away, thru 5 ly away, then to 2.4 ly away, instantly. The Twin A clock's readout would (in the B spacetime system) swing from 3.2y-A, thru 5y-A, then to 6.8y-A instantly. Of course, the receipt of light signals (a different thing) would not reveal any loss in A-clock time over the interval, per the doppler effect you pointed out prior. Relativity is an accepted theory, and it uses the Einstein convention for simultaneity. The 1-way speed of light equals the 2-way speed of light. I agree, that is a convention. However, it may very well be true to mother nature. Occam's Razor suggests we should assume it is, as everything works out far easier. However, no matter what the true simultaneity of mother nature is (even if 1-way <> 2-way), would not a proper acceleration cause similar results? ... ie, swings in remote clock "location and time-readout" in the spacetime system of he who transitions inertial frames. At face value, SR requires that all moments in time coexist. It's a fused spacetime "continuum". Time is laid out in the continuum as inches are laid out on the ruler. So the rapid change in A clock readout per B during his turnabout, is physical in the sense that twin A advances along his own worldline in a spacetime continuum (in only B's system), due only to a change in the twin B POV during his turnabout. What must happen in the B spacetime system (per LTs) has no effect on twin A's own experience ... ie time passes as usual per A. I agree with the OP in that the accrual of proper time is the very same for the Twins and Time Handoff scenario. That's because the geometry of the worldlines are the very same. But that's because the twin B proper-accelerations are considered instantaneous (impossible) and are hence ignorable, since no observer accrues proper time over that period. The matter regarding how A exists in the B spacetime system during B's turnabout is a separate thing from the OP, however it should be considered for a complete relativistic analysis. Best regards, Celeritas

md65536, So I've been trying to minimize the wording here ... The question is ... Why does twin B age less? One can say twin B ages less than twin A because B ages 8y over the interval, while A ages 10y. This is presented by the geometry of the worldlines. IOW, either twin may run the LTs to predict the aging of the other, and he with the lower result ages the least. Also (as you've said), each twin could just compare clocks upon return and the same result arises (so, no prediction of the other's clock necessary). However, the only reason that works out is because of the assumed relativistic effects that take place (length contracton), and so its not as though relativity (specifically the LTs) are ignored in that limited consideration. For example ... One can also say this ... Twin B must TURN in spacetime to record the separation between A/B departure and B-turnabout as a moving contracted length (L'=L/gamma), and by definition Twin A (and earth) records that separation at its stationary proper length (L, the longest recordable length for that separation). A & B always hold the same relative speed for the outbound and inbound legs, so he who records that separation the shortest, ages the least. And, that be twin B. That's why B ages less. His "turning in spacetime" causes that to happen, ie his own proper acceleration. It does not matter that B's proper acceleration is instant. It only matters what the result of those proper accelerations produce ... the resultant specific relative velocities (used by the LTs). Twin B must TURN in spacetime, and that answers the question. However, if we wish to predict the relative aging, we must quantify the relative time over the interval, and so the LTs must be run (which use velocities). We then find that A ages 10y while B ages 8y, from which it is easy enough to state that B ages the least (because the LTs require it). So, it's not as though I disagree with anything that's been said thus far. I just think the usual debates on this matter result from slightly different interpretations of the question ... who ages the least and why? Is the water boiling because its 212 degrees Fahrenheit, or because heat was first applied to reach that temperature? Best regards, Celeritas

md65536, The question that is always asked is this ... what causes twin B to age less than twin A? In the defined Twins scenario, if twin B does not properly accelerate, he cannot age differently than A. If B does properly accelerate, he always ages less. Did B's own proper acceleration cause him to age less? Indeed it did, but this does not address the extent of relative aging, ie why the worldlines geomtery ended up precisely as it did. How much younger is B? Well then you need to run the LTs, which use velocity. The fact that the LTs use velocity, does not change the fact that all velocities (and hence worldline geometry) are completely governed by all the proper accelerations over the interval. This is inescapable. So I completely agree with you, that the worldlines geometry is everything when it comes to quantifying relative aging. Inherent in that geometry, are all the relative velocities and relative accelerations over the interval. And indeed, the LTs use velocity. In regards to proper acceleration, it's not just about the feeling of an applied force (eg B experiencing equal and opposite forces applied to himself, eg a compression, with no net motion of himself wrt A). It's about what an accelerometer would measure (in collective) during applied force(s). Wrt twin B in the usual twins scenario, we usually assume a single point acceleration applied unto twin B, ie twin B changes in his own state of motion. B properly accelerates. Best regards, Celeritas

So ultimately, the relative aging is inherent in the geometry of the spacetime diagram and it's worldlines. It's the very same for the Time Handoff and Twins scenarios, given the turnabout is instant and hence ignorable. However, all this really means is that twin B must execute proper acceleration(s) to the precise tune that produces the outbound and inbound legs of the Time Handoff scenario. So the frame relations (LTs) dictate the outcome, but to attain those frame relations, twin B (not A) must execute the accomodating proper acceleration(s). So while there exists a geometry in the abstract that produces the relative aging presented by the Time Handoff scenario, twin B must attain that geometry by his own proper acceleration(s). So is it twin B's proper acceleration(s) that produce the relative aging? If B doesn't properly accelerate, he never ages differently from A. If A properly accelerates while B does not, A ages less than B (so that's out). Twin B's proper accelerations must produce all the velocities required to attain the Time Handoff worldlines (and hence its related relative aging result), which in this case are instantaneous accelerations. Velocities are governed by kinematic acceleration, and kinematic accelerations are governed by proper accelerations in any local spacetime. I think its fair to say that the twin's relative aging is quantified by their relative velocity, and the locations of the related events in spacetime. But I also figure it's fair to say that twin B's proper acceleration is what makes it all happen, and to the precise tune that it does. This is kinda like the chicken vs the egg deal. Best regards, Celeritas

Agreed, receipt of light signals from A shows he exists continguously over the interval. But I was speaking strictly of what exists in the spacetime system, not the receipt of light signals. The jump in A clock time (not per A himself) is something that must exist, because spacetime systems define what exists now across the all of 3-space for any moment in time. It's not that twin A himself skips that 3.6 yr A-duration, only that it becomes missing due to the instant change in POV at B turnabout (or B/C flyby). The Block universe is required to explain said A-time jump. Best regards, Celeritas

I think it is considered. If a twin makes the turnaround, it feels proper acceleration which (in accepted theory) contributes nothing to its proper time, so that feeling won't show up in the ageing equations. In changing inertial frames, its relative simultaneity with events at clock A changes. In the 3-clocks scenario, clocks B and C already have different relative simultaneity with events at A. So we're already accounting for those differences. There's no physical frame-independent difference between B and C, but measurements made in their respective inertial frames, are different. Simply by considering the two inertial frames properly in any relevent equations, everything's accounted. md65536, I've been trying to be careful in my response to your prior. I don't really disagree with what you said there, although I do consider the analysis more complete to consider the A-clock in the B spacetime system during his own turnabout. I realize that you (yourself) can look at the all inertial Time-Handoff scenario and envision what must happen during (say) a virtually instant twin B turnabout, but many trying to learn the theory may not make that leap (or maybe for some time) if not considering that. That is, to understand the meaning of a block universe. In the all-inertial Time-Handoff scenario, if we consider only the 2 inertial legs that coincide with the Twins Instant Turnabout scenario, one can say that B declares A to age by t/gamma = 4/1.25 = 3.2 yr. C declares A to age by t/gamma = 4/1.25 = 3.2 yr. Total aging for A per B+C = 3.2 + 3.2 = 6.4 yr. However, we know that A really ages 10 yr. That's a difference of 10 - 6.4 = 3.6 yr. So where does that required extra A-duration come from? It comes from "the difference in simultaneity" between the B & C inertial frames (which you've pointed out), so the LTs inherently handle that. In terms of the twin's instant turnabout scenario, it comes from the proper acceleration at B's turnabout, which leads many to argue that it is acceleration that causes A to age more than B. But this is also to say (once again) that it comes from "the difference in simultaneity" between the inertial frames occupied by B "before vs after" his instant turnabout. I would submit that it's more about 4-space geometry inherent in SR (as per Minkowski), than anything else. The geometry is dependent upon the relative motions, the relative motions are dependent upon (existing inertial motions) and any proper accelerations over the defined interval. All that, shapes the worldlines in spacetime. The jump in A-time that exists between inertial frames (B & C), or during the instant B turnabout, is a function of only the differential in inertial frames (and hence relative velocity), however it requires a proper acceleration for a single observer (twin B) to produce that jump in A-time, because he must rotate his sense of simultaniety to produce the same differential (that exists between the B & C clocks in the Time-Handoff scenario). I agree that "twin B's feeling his own inertia" is not the driving factor for quantification of B's lesser aging (it's velocity), but it is certainly true that the twin who properly accelerates is the one who ages less. Besides changing direction, he must produce that frame-differential that exists in the Time Handoff scenario (that produces the A-time jump, so A can age the most), and only a proper acceleration by B can attain that. Best regards, Celeritas

I'm not sure what the hoopla is about here. Scuddyx just says that the time-handoff (all-inertial) scenario explains the relative aging in the twins scenario (of instant turnabout). That's true. However, to ignore what happens during twin B's proper acceleration (per B) is to be incomplete in the relativistic explanation of the scenario, because the twin B prediction of the Twin A clock during that phase is never considered. If one never considers an acceleration phase, one is likely ignorant of a block universe. Best regards, Celeritas

scuddyx, So you point out that the Time-Handoff scenario using 3 inertial clocks (A, B, and C) produces the same aging outcome of an instantaneous turnabout (impossible) in the classic twins scenario, assuming (of course) that only the legs of transit common to both scenarios are considered. You therefore imply that acceleration may play no role in the relative aging. It's true that the all inertial Time-Handoff scenario produces the very same relative aging as the Twins scenario of instantaneous turnabout. But what the Time-Handoff scenario does not present, is what the Twin B records "for cosmic clocks in his own spacetime system during his own turnabout". It's there, that acceleration's role in the Twins scenario is explained. A proper acceleration produces a dynamic change in his own sense-of-simultaneity wrt all other cosmic bodies. For any complete description of relativity, the "entire experience" of all observers must be presented. And the more difficult experience to explain is that of he who properly accelerates, because other factors come into play (dynamic change in relative simultaneity) that do not exist in all inertial scenarios. There is always a debate as to whether acceleration plays any role in relative aging, since SR relates the relative measure of space and time on relative speed alone. It may have been pointed out already, however there can be no change in relative speed, without a change in at least one observer's own state of motion (acceleration). For the case of a non-instantaneous turnabout, how can you show that the predictions made by both twins A & B will concur wrt the relative aging outcome? You will find that the extent of aging of any clock is simply the accrual of proper time between the events (in the Twin's case, leave earth event, and return to earth event). Since each observer declares himself the reference for all motion, and passing only thru time, his time accrual is nothing more or less than the length of his own worldline between those 2 events. The events, just come to him as he waits. Because both twins (A & B) exist at both events, a valid relative aging comparison may be made between them. The acrrued duration between the events is dependent on nothing but the length of one's own worldine in spacetime. Best Regards, Celeritas

No I meant substitute a new variable tau.

Studiot ... Did you mean ... s = √( ∆x² + ∆y² + ∆z² + ∆t²) ? Best regards, Celeritas

Hi studiot. Just verifying ... The LTs are governed by the Minkowski Metric. You said "Euclidean metric" above. Did you mean "becomes a Euclidean-like metric", or were you thinking when relative velocity is zero, whereby the Minkowski metric reduces to the Euclidean metric (maybe since RAGORDON2010 had discussed 2 experiments of the same frame prior)? Best Regards, Celeritas

Tim88, I’m of the opinion that presentism can only apply to absolute time. The moment one allows light speed to be isotropic in at least one frame, eg Lorentz’s ether frame, the gamma factor arises in the model of space and time. The gamma factor requires some sort block universe IMO, a fused space-time continuum, the only reasonable explanation to date. While attempts have been made to validate LET using ad-hoc explanations, none have ever been satisfactory. The Fitzgerald length-contraction arose mathematically in the MMX null result analysis, however “Poincare stresses” certainly don’t explain the physical source of a length-contraction. The block universe does explain it, as the physical source is all in the geometry of space-time. You’ve stated in your car-scenario post (page 4) that … (real) length-contraction + (mis)synchronization = (apparent) time dilation However, no valid “physical reasoning” for real-length-contraction has ever been given in the very first place. That must be explained first, before the subsequent part (ie.) … + (mis)synchronization = (apparent) time dilation … may be validly argued. The physical source for real length-contraction was assumed to be ad-hoc "Poincare stresses". So apparent-time-dilation being the result of “Poincare stresses” plus human-error in clock-synchronization ... is a non-sequitur IMO. There is simply no good physical explanation for the source of the relativistic effects, other than some sort of block universe. I figure an ether exists, but no master frame is likely associated. How to define an ether as such, while making compatible a block universe and our experience of only an ever changing NOW? This is the challenge in my mind. Best regards, Celeritas

My vote is that an ether exists. All I know of its nature, is that it should uphold SR & GR, and play a role per QM in giving rise to energy and matter (fields). We may never be able to define it (except maybe by logical extrapolation) or prove it, but on the other hand. I am not so sure that the block universe precludes free will, even though it is carved in stone. Also, I can envision the block universe, also as an evolving universe. If presentism governs reality, then the relativistic effects would have to be un-real IMO. Therefore, I favor eternalism. However, I think that different people define eternal differently. If the universe has a finite temporal existence, it still may sit there in block format beginning-to-end. So we refer to it as eternal, because "all moments in time co-exist statically in a higher perspective", as opposed to "no cosmic beginning and/or no cosmic end". Its as though that higher perspective (we are not privied to) is outside-of-time (as we know it from experience), which could be interpreted as eternal. Best regards, Celeritas

Study the figure posted in → Post 240 → of the Clocks, Rulers … and an issue for relativity thread, then read what follows here. Just a quick note wrt that figure, where it says “spacetime system” should have been stated “2-space system (time implied)”. In the figure of Post 240, the light ray always travels the hypthenuse of a right triangle, which is always the longest leg per Pythagorus’ theorem. However, an observer at rest in the moving x’,y’ system records the photon to travel directly along +y’ during time t’. The photon must travel ct’ = y’ (= y) in the primed system. So why then is the polarity of ct of opposite polarity wrt x,y,z in the eqn for the length of the invariant spacetime interval? … s² = (ct)² - (x²+y²+z²) The reason … In the unprimed system … (ct)² = x² + y² … which for the given lightpath, and motion only along x/x’ is … (ct)² = (vt)² + y² but y = y’ = ct’ … as shown in the referenced figure, so (ct)² = x² + y² (ct)² = x² + (ct’)² Now, we have 2 light paths here, and so which is then the hypothenuse? The equation models the Pathagorus’ eqn per the unprimed POV, using ct’ for y as they are numerically identical, and so (ct)² is the longest leg of the right triangle. That then gives us … (ct)² = x² + (ct’)² ... where ct > ct' since t = γt' (ct’)² = (ct)² - x² as the above eqn is technically … y² = (ct)² - x² and so the eqn for the length of the invariant spacetime interval … (ct’)² = (ct)² - x² The spacetime interval is a relation between variables of 2 differing frames, that are related by a euclidean-like metric (the Minkowski metric), not a purely euclidean metric (that Galileo used). The minus sign on the right side of the equality is the result of that. Best regards, Celeritas

Not a problem. They see the bike at a specific bike location and corresponding bike time, although they then measure the range to the bike differently. However, they do see the car differently. For example, the blue-car driver sees the bike moving and length-contracted, while the red car driver sees the car stationary at its proper-length. Just extend a 45 deg light-path from the co-located cars into and thru the bottom right quadrant. Where it intersects the bike (an event) is the visual-image being received by the 2 cars at their co-location (another event). Best regards, Celeritas

Maxwell wisely made no mention of an ether in his EM theory, as the math worked without it and he could not define it. Einstein made no mention of any form of ether in relativity theory, as the math worked without it and he could not define it. However, this does not lead that an underlying ether does not exist. It's going to take a very special individual to give ether a great deal of thought, before any existent ether's inherent yet-unknown properties may be defined, and would need to be verifiable by test. I wonder whether an ether may be logically deduced (inferred) to exist (someday), even though it is not determinable directly by test. Certainly, we're going to have to learn something NEW first to ever cross that bridge. Matter, gravity, and light are energy. If they are all of the very medium, then energy is any variation or configuration of the medium within itself, and no matter whether it is immovable or not. If so, then the properties of any form of energy constitute a subset of the properties of any underlying ether. In such case, we see space and time when we see any form of energy, that is, we see (or feel) it when it exists in the required configuration for detection. Certainly, empty space is transparent and intangible. However, space and time are measurable. Unfortunately, the measure of space and time cannot reveal an underlying ether. I venture, that only quantum mechanics can reveal required properties of an underlying medium. And, I would guess that space and time alone will be insufficient, even at that level. Anyone who claims to have modeled an underlying ether using only space and time, others will argue that it is only a spacetime field and not an ether that gives rise to space and time. One might ask, what is the difference? Regarding Lorentz LET, I thought their presumption was that the EM field of electron orbs was altered by the motion thru the immovable ether. Poincare adhoc'ly added his Poincare-stress (induced by the ether upon moving bodies, and produced no force unto the atom) to define the length-contraction as "real and physical". Ie, it was not really about the size of individual electrons, but rather the size and geometry of their orbs in atomic structure. When considering LET, it's easier IMO to ignore all the ad-hoc notions of Lorentz and Poincare, and instead start from Einstein's SR and work backwards to Lorentz ether. The mistake IMO, was their ad-hoc assumptions to force fit an ether related physical-source to obtain clearly required covariant solns (based on Euler rotations). IOW, I'm suggesting that the source of LET's relativistic effects is caused by the relative measure of space and time per differing POVs (as in SR), except that a master frame exists. And remember, SR said any absolute frame was superfluous to the solns, not that they it did not exist. Of course, Einstein assumed any inertial frame was TRUE as a starting point. To extend SR to LET, one simply presumes that there exists one inertial frame that in fact measures what IS TRUE, and all others are merely APPARENT (untrue). YET, since it is quite impossible to prove a master LET frame via light signals, one can never ever know which inertial frame it is even if it does exist (Occam's Razor says ignore that model). Then one asks, if you guessed right about the master frame, does it make any difference at all, far as spacetime solns are concerned? The answer to this point, is NO. So ultimately, I'm saying that LET could be SR with the exception of "only the master frame measures what is true (eg what is simultaneous, what is contracted, isotropic c, etc)", versus "each frame measures what is true". IOW, LET without the ad-hoc'isms. Had Lorentz just assumed (as Einstein) that different frames measure differently, his ad-hoc'ities were never required, and he could have kept his presumption of a master ether frame. However, what good is a physical model that cannot be proven? Not that I favor LET, as "I favor SR". Yet, SR "assumes" the 1-way speed of light is c, which is nothing but a convention. While I cannot prove it, I sure would hope Einstein's convention matches reality, because of the simplicity and elegance of it. I do not understand why the ether must even possess a master frame. Why not approach an ether assuming that motion is meaningless wrt it? I mean, motion is meaningless wrt space-time. If spacetime is all there is, then spacetime is simply curved unto itself. If spacetime is the variation of an ether within itself, it seems impossible IMO to prove it exists by the measure of space and time alone. Something other than space and time seems required, to prove its existence. QM will likely have to prove an ether, IMO. Mordred, I must say, there is a nice appeal to the quantum geometrodynamics you mentioned. Time arising from introduction of matter waves. Does this model "model space after the bang but before matter came to be"? Does it help explain the double slit experiment any? Is it applicable to M-theory? Best regards, Celeritas

One can easily envision 45 deg light-paths drawn from events B & C (or any other event) toward to the car's respective world-lines. Where that light-path intercepts a car world-line (which is of course some duration after the event's occurrence) is when-and-where the driver sees the event, and that EM carries the proof that the event(s) occurred within the space-time system precisely as the figure presents it. The received EM could carry an image of a clock readout for clocks momentarily co-located at that event, and we envision clocks sysnchronized in each their respective frames. Remember, "event occurrences" in a space-time system are separate (but related) issue from "the event of SEEing it". Bets regards, Celeritas

Hi TakenItSeriously, Stars or galaxies would be represented by worldlines, which would dynamically translate downward and also rotate (in angle) during the stationary POV's dynamic proper accelerations. Same for the worldlines of the emitters that produced the GIF's depicted flash events. The designer of the GIF wanted to focus on events, and left the associated emitter worldlines out for a cleaner GIF. Events never move in spacetime, because they are represented by 0-dimensional points. However, since the GIF animates the passage of time as the downward progression of spacetime, the events move downward with the spacetime system as it goes. So instead of moving upwards (with the progression of time) within a static spacetime diagram (where events never move), the GIF keeps the accelerating POV fixed as spacetime moves downward carrying all events and worldlines with it. Just 2 different ways of presenting the exact same thing. Best regards, Celeritas

Tim88, Regarding whether space is a "physical thing", I would say yes. Space and time are both measurable.They exist, whether we have completely defined them as yet, or not. Tangibility is not the only requirement for physicality. Add, space is a continuum, and per SR spacetime is a continuum. You asked whether space is a "physical thing". Being of continuum nature, I say yes. And besides, the gravity-well (or curved spacetime, if you prefer) is an extension of the particle, always forever traveling with the body that creates it. Two aspects of a single underlying mechanism. To say particles have physical properties, while the other half of their own mechanism does not, makes no sense to me personally. Granted, there are debates in physics today as to whether time really exists. Some, actually argue that only time is fundamental. So I address your questions as per the consensus of today, ie that space and time are assumed to exist. I have little doubt personally, that our definitions of space and time will expand with time. Best regards, Celeritas I've never quite understood the "no time" arguments, even though I understand the block universe model. While the worldlines of a block universe are static in 4-space, this does not prevent the advancement of lines-of-simultaneity along those worldlines. That is, there could be "an activity" that exists within an otherwise static block universe. IOWs, even in the Minkowski 4-space model where time is a 4th spatial axis, time still advances along any worldline at the rate of proper time. No matter what rate one might imagine lines-of-simultaneity to advance, all events still occur at the same predictable clock readouts, regardless. So the rate of proper-time seems unrelated to worldlines or spacetime solns. Given we experience time's passage, the block universe must in some way comply IMO. Best regards, Celeritas

I would say it this way ... The gravitational-field is curved-spacetime. The effect of gravity, is the effect of directed inertial motion. Best regards, Celeritas

First question ... Yes. The vertical time axis and horizontal spatial axis (ie line-of-simultaneity) of the many momentarily co-located and co-located inertial reference frames (MCCIRFs) are not depicted, even though they exist there. Second question ... No. Making it a GIF just allows for the animation of the flow of time. For a standard spacetime diagram on a static page, one must envision a line-of-simultaneity advancing upwards with the passage of time (even if it were not depicted, by choice). On the animated GIF, the origin sits there stationary, and the passage of time is depicted as (generally speaking) a steady downward flow of events. There is no "time twice" issue, wrt the animation. Best regards, Celeritas