md65536

I'm not quite following this. Are you saying that a "pacing back and forth" observer is the same as a stationary one? If so that's false. If for example you have a vibrating observer who can maintain a relative velocity of +/-0.866c with negligible time spent accelerating, it still ages at half the rate of a truly stationary observer. Scale that up and you get pacing back and forth. Scale that up and you can get orbiting the planet, and time dilation still applies relative to a stationary observer. Perhaps you have some other specific plan that could work, eg. you could implement the effect of post #283 with pacing, but it depends on the details. At the very least you would have to match the accelerations but at different times. For example, a rocket that follows the traveling twin but stops after negligible time, then spends a few years hanging around near Earth before accelerating back and arriving with the traveling twin, has the same acceleration as the traveling twin (out, stop, return, stop) but ages the same as the Earth twin, with which it has been relatively at rest for all but a negligible time. That could be expressed in terms of "pacing for a negligible time" and experiencing the same acceleration as a rocket. The whole point of the thread, which maybe wasn't clear at the start, is that you can measure the same difference in aging, as of the twins in the typical setup, using different setups, including ones where acceleration is taken out of the picture. As long as the different setups have the same essential components, ie. relative velocity maintained for a specific time, different inertial frames etc, the same aging can be calculated using the same equations of the same theory in different setups. And I agree with your other statements, ie. to make it a true "twin" experiment and measure it using only two clocks, acceleration seems to be needed to get one clock to use multiple inertial frames (perhaps by definition, because the clock is not inertial). However the theory doesn't distinguish one clock from another in identical conditions, and the equations don't change if a clock is substituted for a similar one. That is, if 3 clocks are used instead of 2, the experiment is different but the effects are the same, and the effects on an ideal clock's aging due to proper acceleration are postulated to be none.

That's like voting that the Earth is flat because you never plan to leave your village, and you can't imagine anyone else ever leaving their villages. People do have "access" to other frames of reference (GPS, particle colliders, astronomical observations, etc).

Okay, some of the things you've said in other threads are now starting to make sense to me. So if you have 2 events along a timelike path P and tau is the proper time between them according to some clock that follows P, any clock that is comoving with it follows the same path and passes through the events also? Thus not only agreeing on the proper time of the separated clock but also measuring it too. All along I thought that events at A were not passed through by (comoving) observer B.

Do clocks in different locations follow a common path through spacetime?

I was under the impression that different clocks measure generally different proper times.

Now try calculating the proper time according to a clock that stays on Earth.

With a clock. There's a clock at A. There's a different clock at B. There's another clock on your probe (depending).

You've got it right here! Letting Tau be the proper time measured by your probe, let tA be the coordinate time measured at A, with distance rA. Let tB be the coordinate time measured at B, with a different rB. Then tA and tB are not the same.

Do you understand that we're talking about 2 different clocks here, one at A and one at B? Do you understand that these two clocks do not pass through the same pairs of events? Do you understand that the proper time of 2 events at A is generally different from the proper time between two *different* events at B? Am I not understanding radar time correctly? A radar operator sends out a signal, and times the duration until receiving the reflected signal, using a clock that remains stationary relative to the observer... is that not what radar time is?

Does this give you the change in rate of proper time of a clock as it changes distance from the gravitational mass? No wait... I see, the change in proper time per change in distance. Is this for increasing radius only? By the way I haven't downvoted a single reply in this thread. I haven't even understood one. Please stop libelling me. ------ I think I understand now. If you took a ruler and a clock from A to B, and you measured the time it takes light to cross the ruler, then added it all up... This would be the equivalent of laying N rulers end-to-end, each with its own clock, and each measuring the time that light takes to cross the 1 light-unit ruler as 1/c units of time. It would be the same if you took a ruler and clock from A (at each step the ruler/clock would match the local ruler/clock) or from B. If this is what is called "ruler distance" then it is the same whether measured from A or from B. This might be the (invariant) "proper length" between an event at A and B. Radar distance, as measured from A or B without transporting the clock, doesn't have to agree. A's clock will tick at a different rate relative to any of the N clocks. Due to time dilation between A and B, it must be that the radar return-trip time calculated using only a local clock, must differ between A and B. If converted into the time of a transported clock, then those converted times will be equal. So radar times must be different, but radar distance would depend on how distance is calculated. Does it just use v=c?, or does it account for differences all along the length of rulers? I'm assuming it just uses v=c, otherwise it would probably need to know the ruler distance in order to compensate for it... Anyway this much seems certain: The distance and time measured by a transported ruler and clock would be the same, measuring from A to B or vice versa. The return-trip time of a radar signal would be different, measured from A verses from B.

Yes, you can work it out from any frame and it will be consistent. B and the destination counted the same number of wavelengths from Earth since B left. Where time dilation comes in is that B's clock is slower*; it has ticked 0.866 times as many as the destination's clock has during B's trip. So the frequency of the signals is also measured differently. Time dilation is real. The observed frequency is also measured differently... there is Doppler shift as well as time dilation. (Note the destination, at rest with Earth, receives the signals at the same rate they were sent, though still delayed. If Earth sent 104 signals over 104 weeks, delayed 52 weeks according to destination, they both receive 52 signals by the time B reaches the destination.) * This assumes B starts at rest relative to Earth, so that everyone can allow Earth's and the destination's clocks to be synchronized. Unnecessary complication: If B is already moving (eg. just passing Earth) then B and the destination both think the other's clock is slower than their own, but it still works out because they disagreed on the time at the destination when B passed the Earth!

I don't understand. For a photon with velocity c, the distance contracts to zero and the proper time is undetermined. A clock on the moon doesn't pass through any events on Earth so it is not measuring proper times of each leg of the journey. Similar for the clock on Earth. Whose clock measures Tau_EM etc and how do you figure out the round-trip times according to the Earth's clock using that?

Thanks, after struggling with it a bit I think the first half of what I wrote was misleading and plain wrong, but I'm 99% sure the second half is okay if the first half is ignored! Edit: Make that 50% sure. Or maybe 10%. Let me try again!... I guess velocity is rate of change of position, so velocity of one object relative to another is rate of change of position measured in coordinates where the second object remains fixed. To speak of a ship's velocity relative to Earth's, it is the change in position of the ship as measured with the Earth fixed, which is what is measured in Earth's frame. To say others "measure" the same thing is essentially translating what they measure into what the Earth would measure. This is essentially what you wrote, "everyone's measurements agree that the Earth [measures] the spaceship moving at 0.5c". Less misleading would have been to say "Everyone uses the same measure of the ship's velocity relative to Earth's, which is d/t as measured in Earth's frame." Definitely... I think one ought to approach learning about this by either striving to first look at only the simplest setup possible (eg. forget about a third observer or alternative measures of speed), until it makes sense, or consider more complicated situations with an expectation that it DOES work out consistently, but the calculations can get complicated.

I meant the second. I doubted what I wrote but after thinking about it figured it was right, even though I'm not 100% convinced. Edit: But I DO mean "relative velocity of Earth and the spaceship" and not just difference of velocities, or in other words we must use composition of velocities instead of just adding or subtracting them. Certainly it's an unnecessary complication to this discussion, I think, in exactly the same way that introducing a new observer is, and questioning whether what they see is consistent ("what about the sun's point of view" etc). But for sake of argument... Say traveling twin B is moving relative to Earth E at velocity v. Consider the measurements of an arbitrary inertial observer, for whom Earth is moving at relative velocity vE and the traveler at vB, then using composition of velocities *I think* you should find that in the new observer's frame, B is moving with relative velocity v relative to E. I know that velocity c is invariant regardless of who measures it. I'm not sure about other velocities but I can't think of any way to make two observers measure different velocities of two specific objects relative to each other. Edit: Yes, I see some additional possible confusion. I do mean "relative velocity of one object relative to another" and not anything like separation rate or closing rate, which is like... the rate of change of E relative to the new observer plus the rate of change of B relative to the new observer... or the relative velocities of two objects relative to a third... :S --- So like you said, velocity is relative to something, and we must be clear about what we're measuring relative to. So with an arbitrary observer's instruments, it should measure B moving at v relative to E, but generally not so relative to the observer. (For example if B is leaving E at v near c, an observer in the middle might see B and E receding at near c in opposite directions, at a separation rate that can approach 2c, but still measures the velocity of B relative to E (or vice versa) as v, using composition of velocities.) Edit: And one more complication!: In light of this, I must admit that an arbitrary observer can't simply take its ruler and clock measurements and divide to get v, it must deal with things like relative simultaneity ... and basically adjust for the differences between what is seen and what is measured. Or in other words the correct velocities must still be properly calculated from whatever observations are used to measure it.

Sure, recommendations of good learning resources are always appreciated.

Use a clock and a ruler, measure distance traveled and divide by elapsed time. Just make sure that you use a clock and ruler in the same frame. Correction: Re. post #205, 206, better safe than sorry, I think that's just wrong. Relative velocity between two objects, as measured by an arbitrary observer, isn't simply change in separation distance per time. The traveler is traveling at .5 c according to Earth's clock and ruler, and it is traveling at .5 c relative to Earth according to its own clock and ruler. Or .5 c relative to Earth according to the sun's measurements or according to some passing alien or according to anyone. There's no measure of velocity here that has it not traveling at .5 c relative to the Earth. One's the source and one's the observer. However they both can observe each other, they both can be both source and observer, and you can make it symmetrical. In that case there's no difference; both see the other distorted by aberration effects. The effect is symmetrical.

That's what I was asking about in the first post, the non-inertial observers located in gravitational wells, and redshifts of one-way signals between them, and relative lengths. You're now discouraging people from discussing the original topic because it apparently doesn't relate to your test probe. If the probe relates to the topic, how do you go from calculations of the probe's observations to what the observers located in gravitational wells measure?

Part of my confusion might come from failing to realize that radar distance and ruler distance are generally different measures of distance. So measuring the timing of light signals and placing rulers end-to-end probably won't give identical results. I think the redshift interpretation above is right, but I'm not so sure about the rulers.

Studied where? I'm just curious about how one attains your particular combination of knowledge and abilities. You've done the same thing in this thread as in the other thread you mentioned. 1) Introduce a new, marginally related observer and throw around some calculations for it (eg. the proper time of a traveling particle). 2) Ignore the observations we were discussing, which don't match your calculations, and justify this by claiming that the observations we were discussing are irrelevant to the alternate thing you were calculating. 3) Derail the conversation by focussing entirely on this alternate observer, no longer even bothering to relate it to the original topic. Eg. "The time dilation experienced by two observers with different gravity potential is irrelevant because the proper time of a single observer is invariant." You may be making some true statements, but you're falsely claiming they have any bearing on the topic at hand.

Where did you learn all of this? You definitely have a wealth of knowledge, but I question your ability to apply it (yes, I remember the other thread). So can radar time be measured by radar, ie. light?, and what would the proper time be then?

Wouldn't the same faulty reasoning apply to SR? If there's time dilation in SR, wouldn't you predict expanded distances?

How do you go from your example using proper time of a single observer and extend it to the measures of time made by two different clocks, which is what we were talking about here? Edit: By the way, radar time is measured by the radar transceiver observer, not a traveling particle.

Not if both are measured from one place. Measured from Earth vs from moon, yes... isn't that what length contraction implies?

Does this mean that the distance A measures to B is smaller than the distance B measures to A? (I always got this backward, guess I still don't get it.) In terms of a twin paradox, if A and B are together, and in negligible time A enters a gravity well and spends considerable time there, then returns in negligible time, A has aged less. If A and B are continuously bouncing signals off each other, A might say "each signal takes 1 second round trip to travel, so the distance is 1 light second" and ages 100 seconds per 100 signals, while B might say "each signal takes 1.1 seconds, the distance is 1.1 light seconds," and ages 110 seconds per the same 100 signals. Can they apply the local speed of light universally like that (neglecting inflation)? It still doesn't make sense to me, because... say you place metersticks between A and B, say 1000 of them, I would think that each measures a local ruler as 1 meter, and both agree that the rulers at B are bigger than the rulers at A ("rulers shrink in a gravitational field"???). Then A would measure the distance as being greater than 1000 m and B would measure it as less than 1000 m. Am I mistaking the meaning of rulers shrinking in a gravitational field? Is it A who observes a meterstick brought into the field as smaller than a meter, while B observes it as 1 m?

I've been trying to think about this in similar terms. Here's what I have so far... Some mistakes in what you wrote: Light doesn't have a slower clock. It doesn't have its own clock at all. The answer *is* length contraction, and corresponding time dilation and redshift... they all fit together so that velocity of light is c, locally according to any observer. One explanation of redshift comes from the equivalence principle. Here I have A with a higher gravitational potential relative to B, and they're relatively at rest; this is equivalent to A and B at the respective bottom and top of a box that is accelerating upward. So the explanation is, if A sends a signal to B, it takes time for the signal to cross the box, during which the box accelerates. So, B at reception is traveling faster away* from the source event (A at transmission), so the signal appears redshifted. *or something like that, I may have screwed up describing this correctly. I think a similar thing can be said about length contraction with the equivalence principle. If B views A's ruler end-to-end, the far end is farther away and appears slightly older. If A and B are in an accelerating box, then... uh... Okay I haven't figured this out, and anyway the link says that length contraction can't be deduced from the equivalence principle... :/ But in terms of redshift and length contraction: Similar to what I wrote in post #1... Suppose B receives a signal with wavelength of 1 m, redshifted from a source wavelength of 0.909 m. The same wave that is 1 m at B, is 0.909 m at A (measured by B?), so any length??? of 1 m at B is 0.909 m at A (measured by B). I guess this length contraction only applies in the direction of the line AB? Similarly in terms of redshift and time dilation: If A sends a signal with frequency 1.1 Hz (1 wavelength every 0.909 units of time) and B receives it as 1 Hz, then A's clock ticks 0.909 times for every tick of B's clock. This is just a sloppy interpretation of what I think are the right answers, forcefully made to fit into a hand-wavey explanation. I don't think I've got it yet. I agree, intuitively it seems like a shrunk ruler means less time for light to cross means a faster ticking clock, and I've always guessed wrong about it. I think it can be counter-productive to try to figure it out intuitively, because it's way too easy to come up with intuitive explanations for incorrect physics!