I just edited the previous post to add some more information, including about how Jack can use the same reasoning to show the time delay in Jill clock is by a factor of .8, without using the Lorentz transform. This post will be about how Jill can make the same observation for clock1 (although the calculation is different), and an observer at clock1 would be able to make the reciprocal observation about Jill. Details are below the fold.
Since Jill and clock1 are moving away from each other, rather than toward each other, the diagram is different (and actually simpler). Jill still sees her clock move from 0 to 8 on her journey from clock1 to Jack, however, at the end of the trip cloc1 is read 4. That means Jill sees two of her own seconds to pass for every second that passes on clock1, or that the images of consecutive seconds on clock1 are two light-seconds apart for Jill.
So, if clock1 waits for t seconds between sending the image of 0 and sending the image of 1, the separation distance between the image of 0 and the image of 1 will be 1.6ct. Since 1.6ct = 2 ls, we get t=1.25 seconds. Thus, the fraction of seconds as measured by clock1 to seconds Jill measures for clock is 1/1.25, which is again .8. This means Jill measures clock1 to tick off 6.4 seconds on her trip between clock1 and Jack, the same as she measured for Jack.
In the reciprocal, when an observer (Jerry) at clock1 sees Jill pass Jack, Jerry has seen 8 seconds pass on Jill's clock, but 16 seconds pass on clock1 (the ten for the trip itself plus another 6 to see the image). So Jerry sees Jill's clock move at half the rate his clock does. Jerry can make the same calculations Jill does to measure Jill's clock ticking off .8 seconds for each of his.
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Eric, I made a number of comments in "part 1," which you have ignored. Many of them would apply here as well, but I won't repeat them. I will simply repeat this question:
I asked: "Why all this work to "prove" that she "sees" something that she does not see, and cannot see if she is moving, as is supposed?"
I will make one further comment, which is elaborated on at much greater length in the original thread (where there are a number of additional comments which you have so far ignored).
I suspect, without even wanting to take the time to think it through, that you have now (in "part 2") actually done what I asked Colton to do, i.e.: reverse your assumptions about who is moving.
This is what Fowler did also, by basing his whole analysis on "looking back" at clock 1, rather than dealing with the reality which Jill was confronted with when she encountered clock 2 in his example.
Applying (inappropriately and irrelevantly) Minkowski "conventions for absolutizing time and distance" in reverse, you have made (by those standards) Jill the stationary party (and Jack the moving party) in this "part 2." She is no longer viewed as moving past clock 1, but instead, in effect, clock 1 is treated as moving past her.
Clarification:"I will make one further comment, which is elaborated on at much greater length in the original thread ..."
By "original thread" I did not mean "part 1," but rather the 2000 comment thread which parts 1 and 2 were spun off from.
I can't resist...
One Brow said: "However, in particular I'm trying to point out that Jill, regardless of whether she is moving, does not measure Jack's clock to be going faster."
Yet that's what Colton said she would do, regardlesss, and which (incorrect) answer you wish to cling to as an absolute. He said Jack's time would always be faster, moving or not (10 is faster than 8, aint it?).
She will never measure Jack's clock to be going faster IF:
1. She is stationary, and
2. She (correctly) views herself as being stationary.
Of course with incorrect assumptions she can come to any conceivable conclusion. But she cannot, using Hogg's definition, "measure" things which support any conclusions she reaches which are based on false assumptions. Even if her fallacious logic happened, by sheer accident, to agree with the actual facts, that would not be an "observation," per Hogg
One Brow said: "I don't know if this has been done, but experiments like this could certainly serve as another validation of SR."
It's not clear what you mean by "this," but, yes, you're right. It could also serve as an invalidation of the relativity postulate of SR (insofar as it tries to ratify Jill's conclusions inferred from false assumptions).
To answer your question, yes, it has been done. Read up on the GPS system and you'll see that.
aintnuthin said...
I made a number of comments in "part 1," which you have ignored.
You didn't notice the sentences I added in part 1 were in response to your comments?
I'll respond to your comments directly over the weekend, but I have been reading them and thinking about them. I am not ignoring them.
I see this addition: "So, Jack sees the entire trip in 4 seconds. In that time, Jill's clock moves from 0 to 8. Jack can use the same logic as above to measure Jill's clock to tick off .8 seconds for every seconds of his.
Same logic? Same lack of logic? If Jack sees the entire trip in 4 seconds, how is that .8 of his?
By your own "logic" Jill sees 16 of his seconds tick off to her 8 (a 50% rate, not 80%), and Jack sees 8 of her seconds pass in 4 of his (also a 50% rate, not 80%).
Of course your own logic doesn't square with the facts, either, because he ends up seeing her 8 to his 10, and she sees the same. Light delay, which can affect the way a clock appears, but not the clock itself, is indeed "mutually reciprocal," but time dilation is not.
I said:"...and Jack sees 8 of her seconds pass in 4 of his (also a 50% rate, not 80%)."
I don't think you figure(4 seconds for Jack is even right), but if is notice that although the 50% "rate" is the same, then Jill sees double (16 to her 8) while Jack sees half (4 to her 8). How can you possibly get .8 out of each of these?
One Brow said: "...in particular I'm trying to point out that Jill, regardless of whether she is moving, does not measure Jack's clock to be going faster...So, if clock1 waits for t seconds between sending the image of 0 and sending the image of 1, the separation distance between the image of 0 and the image of 1 will be 1.6ct. Since 1.6ct = 2 ls, we get t=1.25 seconds."
If t (Jack's frame) is 1.25, then that times 8 = 10.
You go on to say "Thus, the fraction of seconds as measured by clock1 to seconds Jill measures for clock is 1/1.25, which is again .8."
You appear to have the numerator and demoninator reversed. 1.25(Jack's frame) divided by 1 (Jill's frame) = 1.25, not .8.
That said, you still have you ratios wrong, either way. The images will not come at a constant rate, so you can't take any ratio (right or wrong) for reception of the first image and project it over the whole trip.
Time for a reprint of a post I made back in the 1000 range:
I said: "He can explain to you exactly why the poor chump on the train is deceived by motion which he insists doesn't exist. But, then, they show how their theory is quite willing to call these mistaken assumptions "correct" (to get a relativity principle")."
And this exact same model of scenario permeates virtually every explantion of SR. First you must:
1. Establish 2 observers, each with their own unique "frame of reference." Recall that "frame of reference" is code for "motionless" in this context.
2. Now you start talking about one of them moving while they continue, (by virtue of the "frame of refence" they have been assigned) to see things as though they were both simultaneously motionless.
3. Now you have handy points of equivocation along virtually every front, which you can cleverly exploit to "prove" any point you want, just depending on what pieces of information you take from what frame of reference. Especially handy is that you at all times keep a third frame of reference in your back pocket which you can haul out as needed: The God frame of reference where you can point out what's really happening as needed.
These guys end up confusing themselves more than the hapless listeners they suck in, I swear. When every conceivable piece of evidence (subjective perception) can be called true, false, or "unknown" depending on your polemical requirements at the time, it's quite a rhetorical advantage. They all seem quite satisified with themselves after an extended journey into such sophistry, too. I guess it could be kinda fun...."
This part, in particular, seem appropriate: These guys end up confusing themselves more than the hapless listeners they suck in, I swear.
That last (reprinted) post makes more sense in light of the one which preceded it, and to which it (partially) referred, so I'll include that (prior) post as a reprint too:
I said: ""Mainstream SR" (our physicist friend and many others in his position) says that if a guy insists he's not moving on a train, and then, solely on account of the motion he denies exists, see one flash from the front (coming toward him) sooner that he does one from the rear, he will (erroneously) conclude that the one he's see first occurs first. And guess what? HE IS ABSOLUTELY CORRECT!
That's one problem with all these thought experiments. The "explainer" plays God, and sees and knows all things. He can explain to you exactly why the poor chump on the train is deceived by motion which he insists doesn't exist. But, then, they show how their theory is quite willing to call these mistaken assumptions "correct" (to get a relativity principle"). The chump's mistaken perception's end up being "the truth," so he does end up controling simultaneity and the "speed of light" with his misperceptions. The theory transforms his (mistaken) impressions into "reality."
One Brow said:"However, in particular I'm trying to point out that Jill, regardless of whether she is moving, does not measure Jack's clock to be going faster."
In the main thread One Brow said:"In particular, my understanding is that...she can calculate Jack will see/observe 10 seconds to pass on his clock."
Eric, you're always gunna get yourself into trouble, and display an inordinate amount of conceptual confusion, when you routinely think(and try to disprove) today the OPPOSITE of what you thought (and thought you proved) yesterday.
Edit: Meant to say:
"...when you routinely think(and try to prove)[not "disprove"]
One Brow said: "However, in particular I'm trying to point out that Jill, regardless of whether she is moving, does not measure Jack's clock to be going faster."
She NEVER measures Jack's clock by deduction. She "measures" it to read 10 seconds when she looks at it, however. The conclusion she reaches if she tries to deduce it will vary according to her assumptions. If she (falsely, here) assumes she is stationary, she will deduce it to be 6.4 seconds. If she (properly) acknowledges herself to be moving, she will deduce it to be 10 seconds (which is in perfect accord with her observations).
SR forbids the second(correct) deduction. Unfortunately for SR, it cannot, by mere fiat, prevent or invaldate her observations.
LR forbids the first (incorrect) deduction, and insists that empircal observations be respected.
You and Colton implicitly adopt the LR view, yet you struggle hard to apologize for the SR view, which your stated view flatly contradicts. I should put the term "your stated view" in scare quotes, however, since it may change from minute to minute, just depending on what point you want to try to "prove" in order to make an incorrect claim of yours appear to be correct.
I said: "The conclusion she reaches if she tries to deduce it will vary according to her assumptions. If she (falsely, here) assumes she is stationary, she will deduce it to be 6.4 seconds."
So, the question becomes, how does she square her actual observation (10 seconds elapsed on Jack's clock) with her erronous conclusion? Obviously she should question her erroneous conclusion, not her indisputable observation, but she chooses NOT to do that. So, what does she do?
In denialist fashion, she simply rejects that empirical evidence and insists (without cause or basis) that Jack's clock 2 read 3.6 seconds when clock 1 read 0.
If you're really trying to prove her view, you must honor her claims. She would NOT see clock 2 to read -6 when she is at clock 1, she would read it as only -2.4. But she doesn't (and can't) see that. She can only falsely assert it in an attempt to justify and rationalize her unsound logic.
There is so much equivocation and frame-switching in your examples that it is hard to keep track of them all (and not worth the effort to try).
But here's one: You say she will see -6 seconds on clock 2 when she is at clock 1. But that is based on a distance of 6 light seconds between the two (taken from Jack's frame). Why would she "see" a separation of 6 light seconds when, it her frame, the distance is only 4.8 light seconds?
Are the reasons why I thought that a "reprint" of comments made long was appropriate any clearer, now?
Like this part, I mean?:
"Now you have handy points of equivocation along virtually every front, which you can cleverly exploit to "prove" any point you want, just depending on what pieces of information you take from what frame of reference. Especially handy is that you at all times keep a third frame of reference in your back pocket which you can haul out as needed: The God frame of reference where you can point out what's really happening as needed."
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