The basic scenario: clock1 and Jack are at rest, sitting six light-seconds apart, and Jack has a clock (clock2) synchronized to clock1. Jill, holding a clock, passes by clock1 traveling inertially at .6c and synchronizes her clock to clock1 (so they now both read 0), and them passes by Jack. When Jill passes Jack, her clock reads 8 seconds and Jack's clock reads 10 seconds. If you use the Lorentz Transformations (LT) from the view that Jill's inertial state is the rest frame, Jill gets 6.4 seconds for clock2. The disagreement is over whether the 6.4 seconds is supposed to be what jack sees on his clock, as far as I can tell. My answer is below the fold.
My response is that the 6.4 seconds is the time Jill measures for clock2, not the time Jack measures for clock2. You can show it is the former with basic algebra. First, because of light-speed delay, Jill sees jack's clock to read -6 when Jill passes clock1. As Jill passes Jack, her clock has gained 8 seconds while Jack’s has gained 16 seconds. Jill can use that and her relative velocity of .6c to tell how much time passes on Jack's clock for her, without using the LT. I will load a diagram to help illustrate this.
This diagram is based on clock2 sending out an image reading -6 and then an image reading -4, and Jill receiving those images 1 second apart in time. Jill can measure how far apart the images were when they were sent, and therefore how much time passed in Jill's frame between when the first image was sent and when the second image was sent.
In between the times when clock2 reads -6 and clock2 reads -4, the image of clock2 reading -6 travels at c (as measured by Jill), while the clock2 itself travels at .6c. (Edit: adding sentnces) That means the rate of separation between the image of clock1 readin -6 and the actual clock 1 is c-.6c, or .4c. Thus, the ratio of the distance traveled by the image of clock1 reading -6 to the distance traveled by clock1 is c/.4c, or 1/.4 (End of edit). Since the image of clock2 reading -6 and the image of clock2 reading -4 are 1 light-second (ls) apart, the total distance from where clock2 generates the image of -6 and where that image is when clock2 generates the image of -4 is 1/.4 which is 2.5 ls. Since the image of clock2 travels at c, the image takes 2.5 seconds to travel 2.5 ls. So, Jill measures 2.5 seconds to pass while Jack’s clock moves from -6 to -4, or two seconds. 2/2.5 = .8, so for every second Jill observes on her clock, she observes .8 seconds to pass on Jack's clock, the amount predicted by the LT. Over the course of all 8 seconds Jill observes on her clock, this becomes 8 * .8 = 6.4 seconds. Again, this is what she observes to pass on the clocks, not a prediction of what Jack observes.
To forestall an objection, none of this is an explanation for the time delay. It is only a measure of the time delay that Jill can make without using the LT.
(Edit: adding sentnces) I also want to note that Jack can use the exact same process to measure the time delay for Jill, without using the Lorentz equations. Jack does not see the image of Jill passing clock1 until 6 seconds after it happens, when his clock read 6. 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. (End of edit).
Posts
228 comments:
«Oldest ‹Older 201 – 228 of 228Physics uses, and has ALWAYS used, LR, not SR, when dealing with accelerating frames. LR has ALWAYS made accurate predictions in these cases while SR NEVER has.
Since they make the exact same predictions (as in my example), this will be hard for you to sensibly defend.
Here is it again, with you right back to claiming (contrary to your "standard response") that SR "makes predictions" about accelerating frames.
Which one will it be, next time?
"If you say the HK experiment or the GPS, I will respond that every mainstream source sees these results as a confirmation of SR/GR. Find something that has a direct comparison, where there could be a real difference in the numbers read."
So you're claiming, supposedly contrary to "every mainstream source," that SR DOES NOT apply is the GPS case? How could the GPS "confirm" SR, when, according to you, it does not even apply? GPS confirms the validity of the Lorentz transformations. It does NOT confirm SR. It uses LR, not SR, as the basis for it's operation.
" Find something that has a direct comparison, where there could be a real difference in the numbers read."
A. Without going into the details about how it would change our entire cosmology, interpretations of QM, etc., I just gave you an example where LR makes correct predictions where SR either a. makes none, or else, if applied, makes the wrong predictions. LR makes correction predictions in ACCELERATING frames, get that?
Do you understand this? Do you dispute any of this?
"I understand the passage, and dispute your interpretation."
Really? Just what, in what way, and why do you dispute it?
To reinforce the point (I'm not sure that any amount of reinforcement will help in your case, but....): You say that SR "does not apply" in non-inertial frames. What you leave out (or completely forget about) is that even SR holds that acceleration is absolute (not "frame-dependent'). So, then, the natural question would be "what theory *does* apply in non-inertial frames?"
GR.
We have just seen the answer, which is, "Why, a theory of absolute motion (LR), of course." Which is, in fact, what the GPS uses and relies on, not SR.
If the GPS relied on LR only, it would fail, because LR does not allow for time changes from gravity/acceleration.
GR is not a theory of relative motion. It is irrelevant to shis topic, but you keep mentiioning it as a red herring. We're discussing LR vs SR.
For what it's worth:
"[GR's]name, however, is something of a misnomer. The theory does not extend the principle of relativity for uniform motion to nonuniform motion. It retains the notion of absolute acceleration—that is, acceleration with respect to space-time rather than with respect to other bodies....
Einstein was not satisfied with special relativity for very long. He felt strongly that the principle of relativity for uniform motion ought to be generalized to arbitrary motion....Einstein did not give up his crusade against absolute motion so easily....
Einstein—understandably perhaps, but mistakenly—thought that extending Lorentz invariance to invariance under arbitrary transformations would automatically extend the principle of relativity from uniform to arbitrary motion...It only takes a cursory look at Einstein's calculations in support of this claim to see that this attempt to relativize rotation is a nonstarter.....
He still believed at this point that general covariance guarantees the relativity of arbitrary motion. The Dutch astronomer Willem De Sitter disabused him of this illusion in the fall of 1916...
Another one of Einstein's attempts to relativize all motion had failed. Einstein thereupon lost his enthusiasm for Mach's principle. He accepted that motion with respect to the metric field cannot always be translated into motion with respect to other matter."
Einstein's struggle to relativize all motion, uniform and nonuniform, illustrates the old travelers' saying that the journey is more important than the destination. Although Einstein never reached the destination he originally had in mind, he found many valuable results along the way.
Einstein had found a new theory of gravity, which does away with the artificial split between space-time and gravity of Newtonian theory. Even some of the dead ends in Einstein's crusade against absolute motion led to interesting physics....The cosmological constant, originally introduced in the context of Einstein's ill-fated attempt to make general relativity satisfy Mach's principle, has made a spectacular comeback in modern cosmology
http://www.encyclopedia.com/science-and-technology/physics/physics/relativity
If the GPS relied on LR only, it would fail, because LR does not allow for time changes from gravity/acceleration.
You just can't seem to contain yourself to relevant comments, Eric. Yeah, we both know that gravation ALSO affects clock, but that's NOT what we're discussing. We're talking about the manner in which relative motion, NOT GRAVITY, influences clocks.
My turn to repeat:
"In the example in this post (the two directly approaching each other), has Jill seeing Jack's clock tick off two seconds for every one she sees tick off on her own clock. Jack sees two seconds tick off on Jill's clock for every second on his. You can run an experiment on this in a lab for sensitive enough clocks."
Do you understand this is what happens?
====
What? We just went through this at great length. I denied that this is what happened, and said that's Jill's conclusions about Jack's other (synchronized it his frame) clock were DEDUCED, not "seen on her/his clock." You agreed, I thought. She DENIED what she did in fact see (which was only at the end of the journey, not "during" it.
It's hopeless, Eric. You just seem to make assertions, without argument, consistency, or explanations, and present them as "facts." Over and over and over again, even when the defects of your claims are pointed out to you.
You responses are perhaps most revealing for what they ignore, and do NOT respond to, than what you do respond to.
Incidentally, the following, from Lawrence Berkeley National Laboratory, mentions a few of the differences that the acceptance of absolute simultaneity would make (and reasons for accepting it):
"The theory of relativity does not offers an adequate framework for superluminal processes, at least not without refering to logical paradoxes, but a Galilean theory does. As is pointed out in the following section, several arguments can be found which indicate the non-generality of covariance and the existence of superluminal processes. The resurrection of absolute time in physics is therefore possible, if not even necessary.....
Both Galilean space-time and Minkowski space-time have appeared to be valid physical concepts. However, the absolute generality of relativistic covariance is set into doubt....it is well known that one can define a universal time, which appears in cosmological models. For instance, general relativity leads one to the Robertson-Walker metric [11], which describes the long-range structure of our universe: Here, the time parameter t defines an universal time, the cosmological time.
...recent investigations of electromagnetic radiation propagating over cosmological distances seem to reveal a true anisotropy in the structure of our universe, suggesting that the speed of light might be not a true constant, but dependent on direction and polarization. These results might possibly represent a further indication in favour of the existence of an absolute reference frame...There exists a measurable preferred reference frame, which can be determined, for instance, from the absolute motion towards the uniform cosmic background radiation....If our universe has a Newtonian background, ie. if there is an absolute time underlying the space-time continuum, then there is no threat on causality by superluminal processes, because time travel and its paradoxes are excluded a priori"
http://aether.lbl.gov/www/classes/p139/speed/space-time.html
Copyright 2007 by David Morin, morin@physics.harvard.edu
"One might view the statement, “A sees B’s clock running slow, and also B sees A’s clock
running slow,” as somewhat unsettling. But in fact, it would be a complete disaster for
the theory if A and B viewed each other in different ways. A critical fact in the theory of
relativity is that A sees B in exactly the same way that B sees A."
http://www.people.fas.harvard.edu/~djmorin/chap11.pdf
A "complete disaster for SR," to assert YOUR view of it, eh? If all inertial observers reach the same conclusions in all inertial frames, there would be no SR. You don't understand the most fundamental premises of SR or their implications it seems. Clearly what the GPS demonstrates is this "complete disaster." The GPS satellites do not "see" the and ECI clocks as going slower than its own. They see them as going faster. The time dilation is NOT "reciprocal."
What is a "disaster" for SR is LR, which adopts the very premise that SR FORBIDS, and thereby makes the GPS possible.
You say: "In all three frames, clock C reads 34.64, clock A reads 40"
That's simply saying that you KNOW one of them is wrong. That you KNOW that simultaneity is not "relative," that you KNOW that speed is absolute. And you think, that by saying this, you are "proving" SR. You are disproving it, that's all.
More from Morin: Here he merely restates what I have already quoted the Baez physicist as saying:
"Our assumption that A is at rest on the train was critical in the above derivation. If A is moving with respect to the train, then eq. (11.9) doesn’t hold, because we cannot say that both A and B must agree. In everything we’ve done so far, we’ve assumed that A and B are in inertial frames, because these are the frames that the postulates of special relativity deal with....If, however, you are accelerating, then all bets are off, and it’s not valid for you to use the time dilation result when looking at a clock."
====
And Morin makes it clear that the travelling twin is the one who will be younger BECAUSE he is the one who is moving:
"If both A and B are blindfolded, they can still tell who is doing the traveling, because B will feel the acceleration at the turnaround."
Once again, the twin paradox just applies LR instead of SR to get it's resolution. In effect, it says the earth "really is" the preferred frame it this context because only that frame gives the correct answer. As between the two only one is "travelling," That can be determined and that twin will be younger, because the MOVING (not the non-moving) clock is the one (not both) that slows down.
To the extent the travelling "believed" or "assumed" that the earth clock was slowing down (which, incidentally he can do only be ignoring all observed empirical facts and instead slavishly adopteing a belief that SR it "true"), then, to that extent, he was just plain WRONG. That's because SR is wrong in it's most basic assumptions.
As Morin (and every other physicist, even if YOU don't) acknowledges, for SR to "work out" as a viable theory (and not face "complete disaster") it must suppose that each clock runs slower than the other. Of course this is logically impossible, so it's certainly no surprise that such a premise never comports with empirical observation.
LR posits that, as a matter of objective reality, only one clock will "really" slow down.
In contrast, SR, the solipsistic theory, says that each clock runs slower than the other. I don't see how anyone could believe that is "literally" true, even if it does allow you to get correction prediction if and you when you posit either one clock or the other, as you desire, to be the one that is "really" moving.
The resolution to the twin paradox does NOT say (because it can't say) that "both are right." Only the stay-at-home twin is right, they say. The travelling twin is wrong, because the earth clock did NOT, as he assumed, "actually" slow down.
2 x 2 = 4. Now I can get the "same answer" (4) mathematically, can by saying that -2 x -2 = 4. But getting the same answer does not mean both are, or could possibly be, true as a matter of fact. Me having $2 in one pocket and $2 in another is NOT the same thing (even if I get the same absolute answer when multiplying) as me not having a single cent, but owing you $2 and your brother $2. Both situations can't be true.
""In all three frames, clock C reads 34.64, clock A reads 40"
B, to A: In MY frame, your clock reads 40
A, to B: Really? Cool, that's what it reads in my frame too!
A & B: We have absolute simultaneity now. We agree. That's just what SR tells us....Uh, wait...that's not SR, that's LR.
The empirical definition of a physical quantity requires an etalon measuring equipment and a precise description of the operation how the quantity to be defined is measured. For example, assume we choose, as the etalon measuring-rod, the meter stick that is lying in the International Bureau of Weights and Measures (BIPM) in Paris.
The reference frames of the etalons are not an inertial frame.
I think I have cited you to this "logical analysis" before. Perhaps you would like to read it some time and show, line by line, why it is false, it you deny his claims, eh?
He doesn't understand what an inertial frame is, or realize his etalons are not contained in one. Good enough?
Good enough for HIM to know that YOU can't read, I suppose. He says "for example," to illustrate a point, He doesn't EVER say a god-damn word about any frame being "inertial" in this illustration of his point, nor is that the least bit relevant.
It's only "relevant" to someone who sees non-sequiturs as "relevant."
What he did say is this: " The empirical definition of a physical quantity requires an etalon measuring equipment and a precise description of the operation how the quantity to be defined is measured."
He does say, later, however that it both SR and LR the "privileged" frame is the one where the etalons for time and distance are "at rest." It is my understanding that a frame that is "at rest" in an inertial frame. What do you think?
"He doesn't understand what an inertial frame is..." <---Heh.
""In all three frames, clock C reads 34.64, clock A reads 40"
A to C: In MY frame, your clock reads 34.64 and mine reads 40. How do you read it?
C to A: Exactly the same way.
A and C: That's means we have been in the same inertial frame all this time, eh? I have no clue why we ever thought we were moving toward each other. Parmenides was right! All motion is an illusion.
C to A: No it means that I was the one moving, that's all. My time slowed down, see? A: Well, that's better. Good to know we have an easy way to know who's moving faster and who isn't. That's just what SR tells us! Uh, wait...that's not what SR tells us, that's LR. How about B? Does he get the same answers? C to A: He has to, because ALL inertial frames predict exactly the same thing, see!
A: Yeah, I get it, he was moving slower than me too. He was going at exactly the same speed you were all this time. I don't know why anyone would ever think the two of you were moving at different speeds, relative to each other.
A: Actually, I'm getting kinda confused here. C: Me, too.
If someone tells me that 3 + 13 + 16 + 9 + 37 = 1,869, I don't even to add those numbers up to KNOW he is wrong, know what I'm sayin?
Nor would I have any idea how he came up with that ridiculous conclusion. Only HE could possibly know that.
If you're going 80 mph, how long does it take you to go 80 miles?
A: 8 eight hours.
Q: Suppose you have two twins, Mike and Ike, and one of them, who we shall call the "travelling twin" for now, is travelling and the other twin is not. Now suppose that Ike is the one who is NOT the travelling twin. Who would the travelling twin be?
A: Both of them.
Q. Who is buried in Grant's Tomb?
A: Abe Lincoln.
The essential difference between SR and LR:
LR says light is "Measured to be" constant in all inertial frames (but not accelerating frames)
SR says light *IS,* as a matter of ontology, constant in all inertial frames (but not accelerating frames)
So, the question becomes this: What is light "measured to be" in SR? Answer: It is it ALSO measured to be constant. This would seem to make perfect sense, since, according to SR, light *IS,* is fact constant. But there's one problem. SR ALSO posits that rod shrink and clocks slow down with speed. If that were true, AND IF the speed of light was in fact, as an ontological matter, "really" constant, then our "measurement" of it in an accelerated frame would have to be WRONG. We could not possibly measure it's "true" speed with distorted instruments.
Do you see a way around this problem, Eric? Let me guess--it's all illusory, right? "Time" slows down, not clocks. Can you explain how that works in terms of the objective world?
"Time" slows down, not clocks. Can you explain how that works in terms of the objective world?"
Also: Distance shrinks, not rods.
How does that work, exactly?
The Lorentz Transformation, which assumes that rods shrink and clocks slow down with speed, i extremely well-tested and deemed to be true. It is so obviously "true" that SR uses it too. But, according to SR, as YOU interpret it, anyway, the LT is false.
Tell me, then, since the LT is false, what is the formula for the "true" situation?
What is the formula for the supposition that rods do NOT shrink at all, they remain completely unaltered, but instead distance shrinks and that clocks do NOT slow down, they remain completely unlatered, but instead time does.
Ya got one?
"Do you see a way around this problem, Eric? Let me guess--it's all illusory, right? "Time" slows down, not clocks. Can you explain how that works in terms of the objective world?"
Before you are in with some nebulous metaphysical hocus pocus, let me explain what I mean by "in terms of the objective world."
The HK experiment, GPS, etc., have proven that clocks DO in fact slow down at increased speeds, as an objective, observable, physical matter.
Since that just happens to be "true," and not an illusion of some sort, address the contradiction first, OK?
How can the "true" speed of light "really" be the same in all frames, yet STILL be measured to be the same in all frames with distorted instruments?
"How can the "true" speed of light "really" be the same in all frames, yet STILL be measured to be the same in all frames with distorted instruments?"
It doesn't really surprise me that you haven't responded to this. It's just one inherent contradiction with SR. It is (unanswerable) questions like these that lead many to claim that clock retardation and length contractions MUST be illusory.
But that doesn't work either. If it's all illusory, there is no need for any relativistic adjustments. Clocks and rods stay the same in all frames and nothing "really" changes. But that doesn't solve the problem which led Al ("out of desperation," he said) to propose this illogical "solution." If that were the case, there would be no problem. Clocks, rods, and time would all stay the same in every frame, just like Galileo and Newton supposed. There would be no reason to "rethink" them, except one: Empirical observation such as the Michaelson-Morley experiment.
There is a perfectly logical and consistent "resolution," but it ain't SR. It's LR, which makes perfect sense and has no inherent logical contradictions or "paradoxes."
A solipsistic theory of physics, such as one that says that if two people assume opposite things, then each is right, is sheer folly. Al must have been REALLY desperate, eh? He has thrown objectivity and "truth" out the window; the baby with the bathwater. His "solution" is worse than the problem.
Know what I'm sayin?
In 1905, Einstein was a great admirer of Ernst Mach. Why? What was he about? Well, let's look, eh?
As a philosopher of science, he was a major influence on logical positivism, American pragmatism...Mach defended a type of phenomenalism recognizing only sensations as real.
https://en.wikipedia.org/wiki/Ernst_Mach
Only sensations are "real," eh? As Karl Popper noted Mach's philosophy was in the tradition of Berkeley (the quintessential solipsist), and he basically founded the (now thoroughly discredited) logical positivist school of philosopy (and philosophy of science).
Mach once said: "the motions of the Universe are the same whether we adopt the Ptolemaic or the Copernican mode of view” of the Solar System, and “both views are, indeed, equally correct.”
Both views are "equally correct?" What does this mean? Does he mean as an objective, or a subjective matter? Obviously he is talking from a strictly subjective point of view. He immediately clarified this by adding that The geocentric and the heliocentric views are merely two “interpretations” of a Universe that “is only given once.”
Only given once, eh? Obviously they cannot BOTH be correct from any kind of objective view (which Mach eschewed). The universe is not, he said, "given twice." Even this proto-positivist knew that both "interpretations" couldn't be literally true. I guess Al didn't read that part.
Of course, as I have previously noted, as Al's philosophy matured, he came to reject Mach's "solipsistic" views. But unfortunately he never went back and cleaned up the mess he had made with SR.
"But unfortunately he never went back and cleaned up the mess he had made with SR."
Well, in a way he did, I guess. I think it is commonly known and acknowledged that motion is not "relative" in GR and the speed of light is NOT constant in GR. This is ultimately a rejection of SR. Those who say GR "reduces" to SR in certain simplified situations overlook the fact the fundamental premises of SR are rejected in GR.
One could just as easily say that, in inertial frames, LR can be "reduced" to SR.
"How can the "true" speed of light "really" be the same in all frames, yet STILL be measured to be the same in all frames with distorted instruments?"
It doesn't really surprise me that you haven't responded to this.
I answered it in the comment 7 of the new thread on this subject.
http://lifetheuniverseandonebrow.blogspot.com/2016/10/you-cant-tell-relativistic-rest-frame.html
Post a Comment