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  1. The spacetime graphic plots light motion ct on the vertical scale, and object motion vt on the horizontal scale. The object position is plotted for successive clock events, producing a history of positions. The slope of a straight line thus represents vt/ct or constant speed, thus a speed profile. In the graphic, relative to the U frame (x, ct), A moves at .3c and B moves at .6c. In Newtonian physics, using t=x/v, A (black) arrives at 3x at Ut=10, and B (green) arrives at 6x at Ut=10. In SR physics, a clock rate is slower the faster it moves in space relative to a ref. frame. U concludes the A-clock rate is .95 his local clock rate, and the B-clock rate is .80 his local clock rate. If the B speed profile reverses (magenta) at R, and B rejoins A at .6c, the example becomes a 'twin' scenario. There is no acceleration at R, since the change involves a zero time interval. The outbound and inbound segments can also be replaced with two profiles crossing at R. The speed profile of B can vary anywhere within the blue profile for light. The out and back speeds are only equal in this case for simplification. The graphic demonstrates that any speed profile that departs from that of A, loses time relative to A. If the graphic is rotated 180 deg, by symmetry, the same method will produce the same results for speeds in the opposite direction. Additionally, even though the Lorentz/gamma factor is a function of (v/c) squared, speed as shown is a ratio or scalar, thus a negative speed is not a real world solution. You can’t move slower than zero. There is also an inconsistency with ‘velocity’ defined as ‘speed’ in the 1900’s, with the additional mention of direction, and today’s definition of ‘velocity’ as a two-component concept. Doppler shift is an altered perception of a constant frequency, caused by the observer’s motion relative to the source. It does not indicate the rate of a moving clock. An observer’s motion cannot alter the rate of a distant clock, but it can alter his perception.
  2. Wasn't length contraction of the slab in the x axis the solution?
  3. [Ships moving past your ship at various speeds don't alter your equipment. Their speed does alter their measurements. It's the same as moving observers assigning different x and t coordinates for the same event, based on their relative speed.] md65536; [Yes]
  4. md65536; An anaut Al, leaves Earth for a target object Q 12 ly distant by an earth star chart. Al's flight plan is to orbit Earth at a large distance until his ship reaches .3c. From reading his 'relativity' manual, he knows he has two options. 1. remain an anaut moving at .3c, or 2. assume a pseudo rest frame, with Q approaching him at .3c. If 1, he arrives at 38 yr, knowing he and his ship have lost 2 yr due to time dilation. If 2, Q arrives at 38 yr. He knows that a clock at rest does not lose time. His watch and computer both agree with the onboard clock. He can verify the speed of Q using light signals. The only other variable is distance. He concludes the universe has apparently contracted in the direction of motion, to explain the time difference, i.e. a mental reconciliation, without any physical processes. No.1 is believable since SR predicts on the basis of physical processes, fast moving clocks run slower. No.2 is absurd, since a fast moving space craft cannot influence distant parts of the universe, but it can influence the perception of an occupant. When this is accepted, there is no need for no.2. When an observer measures lc of objects, he does not conclude lc of the space between objects. This also points to the anaut's conclusion in no.2 as perception, not corresponding to anything physically real. _________________________ Your puzzle would imply you accept time dilation as a physical phenomenon. When the anaut twin returns to the earth younger than the other, isn't that proof that the anaut twin biological processes occurred at a reduced rate, even though the anaut was not aware? That's the implication of postulate 1, 'physics is the same for all inertial frames', thus the observer cannot detect any differences. Being 'aware' contradicts postulate 1. SR does not say you can't determine the how and why of td and lc. ________________________ Inanimate muons need someone to speak for them.
  5. When the atomic clock returns to earth and is compared to the ground based clock, there is a real measurable difference in readings. How can that be if the time dilation isn't real? The length contraction of the atmosphere is the human interpretation of the muon time dilation, to explain the early arrival of the ground. It's a form of reciprocity.
  6. Why should time have a direction if it's a scalar? A clock accumulates 'time'. A complete clock has registers for sec, min, hrs, etc, like an odometer. In practice the larger units day, month, yr. etc, are posted as a calendar, but still a record. So where's the direction? It's 3:21 pm, 9-6-2019, which way do I go?
  7. md65536; When high altitude high speed muons show their decay times extended, allowing more to reach the ground, is the decay process really slowing or are the scientists imagining it? In the H-K experiment, precision clocks were flown around the world, in both directions. The SR and GR effects of timekeeping were revealed when compared to ground base clocks, though they weren't aware of them while in the air. You may not like the idea of 'things happening without your awareness', but that's the essence of relativity. Mental activity is chemistry, which is EM activity. It was unthinkable before then, that motion can alter perception and measurement. NIST, who's business is time standards, will tell you all clocks drift. GPS will not work without constant periodic adjustments. The world is not the 'ideal' setting people imagine/want it to be.
  8. md65536; In the graphic, the arc of radius 1 represents one unit of ct (sec, yr., etc). The red curve is the perception of distance traveled by the observer based on his speed and local time In the interesting scenario of an anaut moving outward from the center of a spherical system of objects, over a range of speeds, the sphere has a maximum radius at v/c=.707c, and two different speeds for each calculated distance. Relative to your puzzle, the green curve is 1/2 the local time for any given speed. Any pair satisfies 'equal distance'. Only one satisfies the '2:1 aging'. A horizontal line between the intersection of the green line and blue diagonal (light speed) projected downward to the red should provide the answer. A speed is .4472 and B speed is .8944. What do you think?
  9. md65536; In the 1905 paper, clock B moved away at constant speed from clock A and returned, with clock B recording less time than clock A, even though they were synchronized initially. The thought experiment was done in an SR environment. Two clocks A and B are sent away from location U, in the direction x, at constant speeds a and b respectively. They reverse direction in zero time simultaneously relative to U and return at constant speeds a and b respectively. Each clock does not experience acceleration for the entire trip. This is irrelevant in SR, since gamma (Lorentz factor) only contains 1st order terms v/c, and nothing for acceleration. For political correctness, two clocks can be used, one outbound and one inbound, exchanging data at reversal.
  10. What about length contraction? A similar case. The anaut measures his 20 m capsule interior, lc to 90%, with his 1 m tape, lc to 90%, and gets 20 m.
  11. There is nothing in my response that implies a moving object causes a distant clock to run slower. An observer A perceives a moving clock B run slower, which results from the B clock's motion.
  12. ...when in relative motion to an observer. I.e. slow clocks are perceived by others. Local time always appears normal, since the clock owner is affected by time dilation to the same extent as his clock. It's physics, not relativity enforcement by decree.
  13. Can't agree. The constant independent speed of light is the reason why EM processes run slower when in relative motion to an observer. A clock is just a periodic process, serving as a measuring tool for human activity. The light clock is simplicity and precision. When the clock is in motion, the light has to chase moving mirrors, for all modes of oscillation. Why doesn't the observer moving with his clock notice, his biological clock is also running slower. A simple analogy is the hunter who aims ahead of the target, to compensate for the target motion.
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