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About Celeritas

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  1. Studiot ... Did you mean ... s = √( ∆x² + ∆y² + ∆z² + ∆t²) ? Best regards, Celeritas
  2. 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
  3. 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
  4. 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
  5. 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
  6. 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
  7. 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
  8. 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
  9. 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
  10. 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
  11. 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
  12. 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
  13. Michel123456, In my prior, I said the above. Better wording (edits are in red highlight) as follows ... For purely inertial spacetime systems, all events move downward at the steady rate of proper-time. However our animated GIF presents the POV of a properly accelerating observer, represented by a sequence of momentarily co-located and co-moving inertial reference frames (MCCIRF). For our non-inertial POV here (presented as stationary), there is a super-positional effect that occurs only within his spacetime system, that causes the downward rate of events to change from the steady rate (governed by the rate of proper time) to a faster downward rate, a slower downward rate, or even cause events to move upwards. This super-positional effect is greater with greater event-range, and with greater relative velocity. But in general ... Best regards, Celeritas
  14. michel123456, All events move downward at the steady rate of proper-time in the animated GIF. However, there is a super-positional effect that occurs only within the spacetime system of the properly accelerated POV, that causes the downward rate to change from its steady rate (governed by the rate of proper time) to a faster downward rate, a slower downward rate, or even cause events to move upwards. But in general ... An event that moves upward, means that the proper acceleration caused the event to become "a lot less in his past" than the normal downward rate of proper-time would place it (within only the spacetime system of he who properly accelerated). An event that moves downward slower than the normal rate of proper-time, means that the proper acceleration caused the event to become "less in his past" than the normal downward rate of proper-time would place it (within only the spacetime system of he who properly accelerated). An event that moves downward faster than the normal rate of proper-time, means that the proper acceleration caused the event to become "more in his past" than the normal downward rate of proper-time would place it (within only the spacetime system of he who properly accelerated). With a change in one's own state of motion comes a change in one's own sense-of-now. Sense-of-now (across the all-of-space) being depicted by a line-of-simultaneity. In this GIF, the line-of-simultaneity was removed, however it sits there always horizontal thru the origin. A proper acceleration causes a change in the angular orientation of his line-of-simultaneity (relative to others), but since it is fixed in this animation its rotation is instead manifested as a relocation of events (in space and time) accordingly. Best regards, Celeritas
  15. Hi bvr, I addressed the B experience per B, and the A experience per A. Intentionally, I omitted the A experience per B and the B experience per A. I just wanted to ensure the first case was understood first, before addressing the other ... However yes, you are of course correct ... the B experience per B does match the B experience per A. But the A experience per A does not match the A experience per B, given the 2 specific events identified. EDIT: I made an edit in red highlight on my prior post. Best regards, Celeritas
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