JVNY

Can anyone help explain whether gravity slows light going directly up or down a gravity well over an extended (not infinitesimally small) path, if possible using the two uploaded Minkowski diagrams of linear acceleration to help a student of Special Relativity understand the answer? For figure 1, consider two ships that begin at rest in the lab frame: Rear at x=0.5 and Front at x=1.0. Simultaneously, each flashes a light toward the other and begins to accelerate at a constant proper rate (Rear at a=2, and Front at a=1). These assumptions ensure that the ships maintain their proper distance in their own frame and that lines of simultaneity for the ships in their own frame go through the origin in the lab frame. The first observation is that the flashes arrive at the two ships simultaneously in their own frame. Analogizing to gravity, the speed of light between two directly vertical points is the same regardless of the direction of travel. This seems consistent with gravity not being a force; it does not retard light moving out of the well, nor advance light moving into the well. The second observation is that the light flashes cross to the left of the center point between the ships. Analogizing to gravity, light seems to travel vertically slower when lower in the well (regardless of travel direction), and faster when higher in the well (regardless of travel direction). This seems consistent with gravity being curvature, if there is an invisible dimension in which there is more curvature toward the rear in acceleration, and toward the bottom in gravity. To test this, see figure 2, adding a third ship (Center) that starts at x=0.75. Simultaneously, Center flashes light forward and backward, and the ships begin to accelerate in order to maintain proper distance in their own frame (Rear at a=2, Center at a=1.33, and Front at a=1). When the flashes hit the other ships, they reflect and return to Center. The flashes strike in the following order: (1) the forward flash from Center strikes Front; (2) the rearward flash from Center strikes Rear; (3) the forward flash returns to Center; and (4) the rearward flash returns to Center. Analogizing to gravity, this seems to confirm that light travels slower deeper in the well, and faster higher in the well. The above seems consistent with sources saying that light travels at different speeds depending upon where it is in gravity. But other sources say that complete General Relativity shows that light always travels at the same speed regardless of gravity. These sources refer to the effects of gravity on clocks and measuring rods. The analysis above does not depend on clock rates; it uses only the order of arrival of simultaneous flashes to determine whether a flash is faster, slower, or the same speed as another flash. So, does this mean that General Relativity says that measuring rods at the rear shrink, such that a flash is actually traveling a greater distance when it is toward the rear (or deeper in the well)? Even though the acceleration rates were set such that the ships maintain their proper distance (as all of the discussions of Born rigid motion say can be done)? Has there been an experiment like the second diagram above, sending simultaneous signals up and down, then reflecting and returning them to the same source? One author suggests such an experiment, although he appears to conclude that the downward flash will return to the source first (rather than the upward flash). See Petkov, "Probing the anisotropic velocity of light in a gravitational field: another test of general relativity," http://arxiv.org/abs/gr-qc/9912014. Thanks. Diagrams.pdf

This posting presents a scenario with different relative aging absent acceleration (it does not include any change of magnitude or change of direction). Three women are in a row along the axis of motion in the order C, A, B. A and B are at rest with respect to each other on space stations 1LY apart. A and B agree on simultaneity and have synchronized their clocks. C is on a spaceship. C and AB are in inertial relative motion at 0.9c. All three women become pregnant (thus each child is inertial from conception). A and B give birth simultaneously in the AB frame, and each sends a message to the other at the speed of light identifying the time of birth. By coincidence, C passes by A and gives birth at the same time that A does (both A and C have the same coordinate on the axis of motion and therefore agree on the simultaneity of the births). C and her child continue toward B, in inertial relative motion. According to special relativity, B's child ages more slowly in C's frame than C's child. However, when C passes B's space station, B's child is older than C's (and A and B agree that A's child is also older than C's, because A and B's children were born simultaneously in the AB frame and have remained at rest with respect to each other). How can B's child age more slowly, yet end up older? The relativity of simultaneity. A and B give birth simultaneously in their own frame. A and C give birth simultaneously in both frames. However, A and B do not give birth simultaneously in C's frame. In C's frame, her child is born at the same time that B's child is 0.9 years old. The rear of the approaching AB frame presents in C's frame older by the product of the proper distance in the AB frame (1LY) and the relative velocity (0.9c). As C and her child continue in relative motion along the length contracted distance from A to B (only 0.44LY), B's child ages more slowly than C's child. However, this slower marginal aging over the contracted distance is not enough to overcome the 0.9 years of additional age at inception, so B's child is older than C's child when they pass. You can elaborate on this by considering a string of clocks between A and B, each at rest with respect to A and B, all synchronized in the AB frame. In the C frame, each successively distant clock is slightly more ahead (at the product of its distance from A in the AB frame and 0.9). Each individual clock runs slower in the C frame, as special relativity states. However, if C observes each clock in the series as she passes it, time in the AB frame runs faster by the inverse of the usual time dilation. Think of someone taking an express train across country and observing station clocks as he passes through (which is more practical than trying to look back at the clock of his departure station). Several authors have pointed out the initial clock advancement in the C frame as described above. See for example Fowler at http://galileo.phys.virginia.edu/classes/252/lorentztrans.html, and Gollin at http://web.hep.uiuc.edu/home/g-gollin/relativity/p112_relativity_9.html. McHugh has expressly explained the twin paradox using this analysis, at http://mathforum.org/kb/message.jspa?messageID=6688895.