Tuesday, July 26, 2011

Finding the delay of a clock without using the Lorentz transformations

For my readers who are not following the almost 2000-comment thread, aintnuthin and I are discussing Special Relativity. In particular, there is a question about whether a specific number is a prediction of what Jill measures, or a prediction of what Jill predicts Jack will measure.

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).

13 comments:

J said...
This comment has been removed by the author.
aintnuthin said...

What does Jack see on Jill's clock using this "method?"

aintnuthin said...

A few questions:

1. You first say "without using the LT," at one point, then later say "for every second Jill observes on her clock, she observes .8 seconds to pass on Jack's clock."

Where does the ".8" come from?

2. Who's frame tells her that only .8 seconds pass in her frame?

3. You say:"Since the image of clock2 reading -6 and the image of clock2 reading -4 are 1 light-second (ls) apart."

How does she determine that they are 1 light second apart?

4. You say: "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..."

If she's looking at this second clock the whole time (beginning with "seeing" it read -6) why does she "see it" end up displaying (according to you) 6.4 seconds when it actually says 10 seconds when she gets there? She blind, that the idea? Or does she, like many people, have a way of "seeing" whatever she feels like seeing?

J said...

Physicists typically prove time dilation at very high velocities, don't they, OB?? And use the LT, which are not exactly algebra but calculus (the old delta notation in Einstein's own book on SR and GR, and space and time collapsed via Minkowski) ...Gold nuclei in an accelerator, etc. At even high speeds (supersonic jets) it is negligible--few nanoseconds. At 60% C...still negligible, wouldn't it be--though the different frames of references has been demonstrated empirically (ie the clocks in planes--no shit you probably say): either way, if the LT are not used, then's it's still the Gallilean-Newtonian tran.. So Jill (and Jack) needs to ramp her ride near to C, IMHE--tho another issue (yll probably scoff) presents itself.. would human vision/eyes even function near C? Not very well, if at all.

aintnuthin said...

One Brow said: "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."

The issue arises from the question of what Jill, not Jack, sees on Jack's clock 2 when she reaches it (which is 10 seconds, not 6.4).

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?

aintnuthin said...

I'm serious, Eric. You give an entire thread the heading
"Finding the delay of a clock without using the Lorentz transformations" and then, within seconds, you are using the lorentz factor of .8 to "prove" your claim.

All of this without ever realizing that you quickly disproved your own claim. What is it about your thinking process that leads you to such obvious self-contradiction, all while being oblivious to it? Ever try to answer that question? You really should.

aintnuthin said...

Let me apologize for my last few comments. I couldn't follow your example and I thought you had drawn the .8 factor from the LT. I still can't follow it, but it does appear that you are getting the .8 figure by some other means.

I really can't follow your example at all, and get lost as soon as you say this: "is 1/.4 which is 2.5 ls."

Where does the .4 come from?

In any event, you have clearly overlooked the fact that each succeeding image will have less far to go to reach her.

To illustrate this, if the total distance for her in her frame is 4.8 light seconds, then, after 7 seconds, she will be only .6 light seconds away from clock 2. Yet you have tried to establish an implicitly "constant" travel distance of 2.5 light seconds for every subsequent image received.

By your reasoning, when she saw his clock read 8 (i.e. when her clock reads 7), it would have to travel 2.5 light seconds to reach her. How could it travel 2.5 light seconds if the TOTAL distance is only .6 light seconds?

The whole example is inherently illogical. I can see that much even if I can't discern how you arrive at your figures

aintnuthin said...

I do think it shows something about your thought patterns, all the same. You start out with a goal in mind, i.e. to establish a "constant rate" of .8. As soon as you think you have found the "answer" you are seeking, all further reflection on your part ceases.

aintnuthin said...

Eric, I don't think you'll understand this, but you seem to having completely ignored, or misunderstood, the crucial distinction Hogg was trying to make between "seeing" and "observering." You consistently claim to be honoring, respecting, and adhering to this distinction when you are in fact abusing it and crapping all over it.

Hogg is trying to make the crucial distinction between subjective and objective factors. Between fundamental (objective) differences and mere differences of perspective. He is insisting that all subjective factors be eliminated, not intensified and emphasized.

He says, for example:

"A common confusion for students of special relativity
is between that which is real and that which is apparent...How [moving things] appear depends on the particulars of the observation,
including distance to the observer, viewing angles,
times, etc...All apparent e ects, including the Doppler
Shift, stellar aberration, and superluminal motion...[should be separated] from the basics,
which are not dependent on the properties of the
observer."

What does he mean here by "the basics?" He is trying to distinguish the "fundamental details of
the observational procedure"(i.e., the "basics) from the "non-fundamental" ones (i.e., those which are dependent on the properties of the
observer).

One can only discover the "basics" by separating "real" (objective)phenomena from "apparent" (subjective) phenomena. He tries to illustrate the diffence in the context of length contraction:

"A common confusion for students of special relativity
is between that which is real and that which is apparent.
For instance, length contraction is often mistakenly
thought to be some optical illusion. But moving things
do not "appear" shortened, they actually ARE shortened...The observer nds that they are shortened
only after correcting for these non-fundamental details of
the observational procedure."

The above is from his introduction. In his text he uses the word "see" to encapsulate apparent, subjective factors. He says: "to see" will be reserved for
apparent e ects, or phenomena which relate to the fact
that we look from a particular viewpoint with a particular
pair of eyes."

In a somewhat circular fashion, he reserves the word "observe" as something which is applied to "real" effects. He says: "to observe" will be
used to mean "to measure a real effect with a correct experimental
technique." But even that "measurement" is a highly qualified one, because it applies to only a certain type of "observer," to wit: "an ideally knowledgeable
observer."

aintnuthin said...

Therefore, what might, on the surface, appear to be an observation (measurement) could in fact just be the equivalent of a mere "appearance" if it is made by one who is less than "ideally knowledgeable."

In our case, Jill could make an accurate measurement which is NOT an "observation" by Hogg's definition. Any "measurement" she made which she believed indicated that Jack's clock was running slower than hers would have to be based on less than "ideal knowledge" because any such appearance is not of a "real effect." The fact of the matter is that her clock is running slower than Jack's, not the other way around. Furthermore, to the extent assumes she is stationary, she cannot be "ideally informed," since she is in fact moving.

Any attempt by Fowler to legitimatize her erroneous conclusions must therefore reduce to an attempt to make "mere appearance" seem "real" and to make what is mere "seeing" into an "observation" (which it aint).

That's one reason why I asked you why you are working so hard to "prove" that a false conclusion by Jill (that the time in Jack's frame was 6.4 seconds rather than 10) was a legitimate "observation." It can't be. It is not made by an "ideally knowledgeable" observer. Her conclusions are those of an "observer" who is fundamentally mistaken about her own state of motion.

aintnuthin said...

I don't think you are capable of accurately and consistently separating "real" from "apparent" effects, because you don't appear to even think in those terms. For you, there are no "real" effects. All is mere appearance. All subjective sensations are "real" for you because they "really occur." You don't appear to even think in terms which presuppose an "objective reality." This was, of course, the mathguy's main beef against Dingle (who, by the way, changed his view when he matured, intellectually speaking, just as Einstien did).

You may pay lip service to the notion of an objective reality, but your thought patterns indicate otherwise. An underlying presumption that subjective phenomena are indicative of what you call "objective" reality and/or that "objective reality" does not exist seems to emerge in your claims. Many people think the same way. When that is their tacit assumption they can't really even think in terms of an objective reality.

aintnuthin said...

Hogg, by the way, appears to be fully aware of where his distinction between "real" and "apparent" effects could ultimately lead.

He says, for example:

"By symmetry, E must also measure D's speed to be u with respect O@(to E's rest frame. If this is not obvious to you, notice that there is no absolute difference between D and E. If they did not measure the same speed, which one of them would measure a higher speed? In order for one to measure a higher speed, one of them would have to be in a special or "preferred" frame; the principle of relativity precludes this."

Here he stops short of an "objective" point of view on the grounds that "the principle of relativity precludes this." That merely states that he is "respecting" the PR.

Elsewhere he says that: "When D is not moving with respect to E the
wristwatch and light-clock tick at the same rate, but when D is moving at high speed, they tick at different rates because, by supposition, one is time-dilated and the other is not."

Here he acknowledges the fact that the dogma of "mutual reciprocity" can't be literally true. Only ONE watch can be time dilated, not both. He goes on to say:

"D could use the relative tick rates of the watch and clock to determine his speed, and thereby violate the principle of relativity."

What does this mean? Putting it in the context of Jack and Jill I take it to mean this: Jill could acknowledge that her clock records 8 while Jack's records 10 (this would be the difference in the "relative tick rates") and thereby determine her speed relative to Jack (which is .6c, not zero, as she claims). But she can't do that because it is forbidden. To do so would be to "violate the principle of relativity."

So, here we are...First he acknowledges that time dilation is not mutually reciprocal. That implies a way to determine which one is really moving. Logically speaking, it would be an effective way of determining one's relative speed. But such logic is forbidden because that would undermine the principal of relativity.

Of course he does not, at any point, ever suggest rejecting the principle of relativity as a way of carrying his preference for measuring "real" effects to it's logical conclusion. He can't. He's there to teach SR, not question it.

One Brow said...

J said...
Physicists typically prove time dilation at very high velocities, don't they, OB??

As clocks have become more accurate, the speed have decreased. A decade or two ago they did exeriments in airplanes.

And use the LT, which are not exactly algebra but calculus (the old delta notation in Einstein's own book on SR and GR, and space and time collapsed via Minkowski) ...

You only need calculus in situations when one or more objects are constantly accelerating (such as in orbit).

Gold nuclei in an accelerator, etc. At even high speeds (supersonic jets) it is negligible--few nanoseconds.

OK. Why does that matter?

At 60% C...still negligible, wouldn't it be--though the different frames of references has been demonstrated empirically (ie the clocks in planes--no shit you probably say): either way, if the LT are not used, then's it's still the Gallilean-Newtonian tran..

However, the Galileo-Newton translations give the wrong answers, as is wrong outside the error bars. At 60% of c, it's hugely wrong.

So Jill (and Jack) needs to ramp her ride near to C, IMHE--tho another issue (yll probably scoff) presents itself.. would human vision/eyes even function near C? Not very well, if at all.

Why would that be an issue?