Those "other factors" are what our debate is about, since we both agree that in the scenario you proposed as a poll, A will read a lesser time than B when they meet. So now please address the two questions in my last post, which I think will clarify what it is we actually disagree about:yogi said:
and
As Ich says, this is not a "spacetime event". A spacetime event is something that happens at a single point in space and a single moment in time--any description of two clocks separated in space cannot qualify as a single event. But this is just an issue of your using incorrect terminology, I understand the scenario you are describing and as I've said practically every time we discussed this scenario, I agree that the clock that accelerates will read a lesser time when they meet. If you ever thought I disagreed about this, you haven't been reading my posts very carefully.yogi said:
So do you refuse to answer my questions?yogi said:
Illusory? What the hell does that mean? If A and B are out-of-sync in C's frame, is this somehow more "illusory" than the fact that A and B are in sync in B's frame. If so, then it seems you do indeed think the description in B's frame is more valid than the description in C's frame, even if you are not willing to be straight with me and come out and say it in response to my question about this.yogi said:
Not if you are consistent about which inertial frame you use throughout the problem. The shifting hyperplanes only happens if you insist on trying to understand what things look like from the perspective of a non-inertial observer, meaning you have to switch from one frame to another in the middle of the problem. But really, the theory of SR was never meant to tell you anything about the "reference frame" of a non-inertial observer, it is just supposed to tell you how a given physical situation can be understood if you analyze it from beginning to end in one inertial frame or another. In the case of the A-B scenario, if you analyze the whole thing from the perspective of B's frame, or if you analyze the whole thing from the perspective of C's frame, there is no shifting of hyperplanes or sudden jumps in clock readings whatsoever.yogi said:
Yogi, you sound like a creationist taking quotes by scientists out-of-context to make it sound like they're supporting positions they obviously don't. If you notice, the only mathematical ideas I'm using in discussing how things would look in B's frame vs. C's frame are the Lorentz transformation equations, which Einstein himself derived in section 3 of his 1905 paper! And the whole concept of the Lorentz transformation is not that they represent some arbitrary mathematical transformation, they are the formulas for relating physical measurements made on systems of measuring-rods and synchronized clocks of different observers. If observer B has a system of measuring-rods spread throughout space which are at rest relative to him, with clocks mounted along them that are synchronized using the assumption that light travels at a constant velocity relative to B, and C also has a system of measuring rods at rest relative to him, with clocks mounted on them that are synchronized using the assumption that light travels at a constant velocity relative to him, then what the position and time coordinates they get by reading off their respective measuring-rod/clock systems will be exactly the ones I gave in my numerical example earlier. For example, if C sees that the clock in his system that was next to A when it accelerated read 2005 at that moment (at which moment A's own clock also read 2005), then if he looks at the moment that B was next to a different clock in his system that also read 2005, he will see that B's own clock read 2005.5 at that moment. This shows the physical meaning of the statement that in C's frame, the event of A accelerating, and of A's clock reading 2005, happened at the same moment that B's clock read 2005.5. So don't give me that nonsense about this being just a matter of abstract mathematics, Einstein explains in detail the physical meaning of the coordinates of different inertial observers in section 1 of his 1905 paper.yogi said:
All frames are "relatively moving" relative to something--for example, the frame where B is at rest is moving relative to C. Again, are you saying there's some reason to believe the measurements in B's frame are any less "illusory" or "apparent" than the ones made in C's frame?yogi said:
Just a quibble--in Einstein's example it's the B clock that is the inertial one, the A clock is the one that accelerates. But even if you switch the letters, I'm not sure I understand your point--he certainly talks about what the clock that was moved measures, he says that it lags behind the clock that didn't move by (1/2)t(v/c)^2. Maybe that's not what you meant by "what the moving clock measures in the clocks' frame", but if so, what did you mean? Did you mean that Einstein doesn't talk about how things look in the frame of the clock that was moved? Well, I don't either, since the clock that was moved (A) moved non-inertially and thus doesn't have a "frame" in SR. I did talk about how the whole situation would look from the frame of a third observer C who is moving inertially at velocity v relative to the inertial observer B. So is your point just that Einstein didn't talk about how the whole situation would look in a different frame? No, he didn't, but anyone who comprehended the previous sections of the paper would understand that Einstein believed it's an arbitrary choice which frame you use to describe a given physical situation, no inertial frame is more valid than any other. Would you disagree that this is clearly Einstein's view?yogi said:
Yes he does. He first talks about how objects look in a reference frame K (which he has labeled 'the stationary system') when they are moving relative to K, then he says "It is clear that the same results hold good of bodies at rest in the 'stationary' system, viewed from a system in uniform motion".yogi said:
Because that's not all that you consider. You also say that the clock which moved "logged less time" than the other clock, or that it "aged less". And you also seem to think it is somehow more valid to say that the two clocks were initially in sync than it is to say they were initially out-of-sync. If you want to renounce all such statements and just say that in Einstein's scenario, the clock that accelerated will be behind the clock that didn't when they meet, then I certainly agree with that much, but if you continue to make statements which go beyond that and seem to implicitly privilege B's frame over other frames, then I still say you're wrong.yogi said:
Yes, but SR also says that the only truly physical facts are the ones that would be true in every inertial frame. The fact that A is behind B when they meet will be predicted in every frame, but the statement that A and B were initially synchronized is not a frame-independent truth, nor is the statement that A's clock was ticking more slowly as A and B approached each other.yogi said:
I wasn't accusing you of being a creationist, just of taking quotes out of context like a creationist.yogi said:
OK, I have been calling A the traveling clock since that's how Einstein wrote it in his example. But I'll switch from now on so we're using the same convention.yogi said:
Sure. Or this other point could have a clock that was synchronized with A's clock in A's rest frame, and then you could compare what B's clock reads at the moment it passes this clock, and you'd see B was behind this other clock. This would be the idea described in section 1 of Einstein's paper, where the coordinates of an event (in this case, the event of B's clock reading a certain time) are determined by local readings on a network of measuring-rods and clocks spread throughout space which are all at rest relative to the observer and with the clocks synchronized according to Einstein's procedure.yogi said:
What I am saying is that this is not a "real age difference" unless they meet, because nothing is physically "real" in relativity unless it is agreed upon in all frames. It's true that if B reads 2010 at the same moment he's passing a clock in A's network which reads 2015, then at that moment B is five years younger than A, in A's frame. But in C's network of clocks, at the moment B reads 2015 he may be passing a clock in C's network that reads 2020, and at the moment that A passes a clock in C's network that reads 2020, A may read 2014. This would mean that in C's frame, A is one year younger than B. Since the question of whether B is older or younger than A at the moment that B reads 2015 cannot be decided in a way that doesn't depend upon an arbitrary choice of reference frame, there is no physically real age difference between them until they meet at a single point in space.yogi said:
I am not sure what your interpretation actually is. Why is it, exactly, that your interpretation tells you that the age difference in A's frame is more "real" than the age difference in some other frame? Is it simply because Einstein chose to describe this example from the point of view of this frame? Or is it because they were initially brought into sync in this frame? If they had been initially brought into sync in some frame other than their rest frame, would you say that the "real age difference" would be the one in this other frame, or would you say that their real age difference should still be viewed in terms of their initial rest frame, but that it would no longer match the difference in their clock-readings since they were out-of-sync in their initial rest frame? If you want me to try to find an experiment that shows why your interpretation doesn't make sense, then please answer these questions about how your interpretation works.yogi said:
Synchronized in their rest frame, presumably?jdavel said:
No, I'm pretty sure we both agree that B would be behind A2. But I think yogi would say this means that B really aged less than A2 did between the time it passed A1 and the time it passed A2, while I would point out that in B's frame, A2 aged less than B between the times of these two events, and I'd say that no inertial frame should be preferred over any other.jdavel said:
In B's frame, the event of E1 does not happen simultaneously with E2--instead, at the moment B passes A1 and both read 0, A2 reads vL/c^2. So, define the event E2b: "A2 reads vL/c^2". If you want to compare how much A2 ages vs. how much B ages in B's own rest frame, then you must compare how much time elapses on B between events E1 and E3 with how much time elapses on A2 between events E2b and E3. Saying that event E2 is somehow more important than E2b is equivalent to saying that one inertial frame's definition of simultaneity (the A1/A2 rest frame) should be preferred over another inertial frame's definition of simultaneity (B's rest frame).jdavel said:
As I said, because I'd say the only "real" physical quantities are those that all frames agree on. Do you agree that as long as the two clocks are separated in space, different frames will disagree on the time difference between them? Are you saying the time difference in A's frame is more "real" than the time difference in C's frame?yogi said:
Yes, this looks fine to me.jdavel said:
Dragongod said:
What does gaining more energy have to do them living longer?Dragongod said:
So you think the Lorentz equations are correct, even with this -vx/c² term?yogi said:
So are you saying that the "real" answer to the time difference between two clocks separated in space can be found by using length and time measurements in their own rest frame? Does that mean that if two clocks are in motion relative to each other, you think there's no real answer to the time difference between them at any given moment, that only when they come to rest relative to each other can a real time difference be found?yogi said:
So those transforms that you prefer are just the LT without vx/c^2?yogi said:
If you don't discuss what these events mean in english, and what you want to find in english, then we can't really say whether these are all the events you "need." (what do you need them for?) But if we say as before that there are two clocks A1 and A2 at rest in S and synchronized in S, and another clock B moving at v relative to them (at rest in S'), and B first passes A1 (with both reading 0 at that moment) and then passes A2, then these three events will tell you how much time elapses on both B and A2 between the moment when B passes A1 and the moment when B passes A2, in the S' frame. If you want to know how much time elapses on both clocks between the times of these events in the S frame, then instead of E2 you need this event:jdavel said: