> > > > > > If a clock's frequency continuously decreases, it needs winding > > up.
> > > > > > Franz Heymann > > > > > It needs no winding up, let it stop. What I want to know is how do > > we > > > > > express or convey continuously and uniformly decreasing rate of > > > > > counting. Can we know when we reach zero if the rate of counting > > > > > decreases uniformly and continuously? > > > > > Here 'counting' does not divide time into equal intervals and in > > this > > > > > case because there is no linear or angular displacement, time > > appears > > > > > to 'shrink' continuously. How can we canvey rate of shrinkage of > > time?
> > > > I have not a clue as to what you might mean. > > > > I do have a strong suspicion that you don't know either.
> > > > Franz Heymann > > > I know what I mean. Let me make it simpler. A train enteres station at > > > a speed of say, 100miles/hr and brake is applied to it. At the > > > enterence you stand and begin to count the number of compartments as > > > the train begins to decelerate. If the speed of the train was constant > > > the rate of counting of number of compartments would be uniform. That > > > is, the interval of time between any two consecutive numberes would be > > > same. When the train is decelerating the interval of time between 1 > > > and 2 is less than that between 2 and 3 and so on. I call this as as > > > 'continuous decrease in the rate of counting of numbers'. We cannot > > > see both the ends of a period of time. As long as the train is moving > > > counting is possible. When the speed approaches zero and becomes zero > > > there is no way to know at what point of time the train came to a rest > > > because, in L/T, L-->0 and T --->infinity. If we do not have the > > > decelerating object in front of us, there is no way to remember the > > > period of time that was spent without activity between two numbers. No > > > expression can convey decreasing rate of counting, which is same as > > > angular deceleration.
> > Why are you so obseesd with time? > > Why don't you also discuss the possibility that the length of your metre > > stick changes, shrinking continuously?
> > Franz Heymann > Length does shrink or elongate during acceleration. 'Length' of metre > stick does shrink or elongate depending on the environment.
You were talking about a continuing, enduring rate of change, unless I misunderstood you.
> No > experiment within the four walls of a laboratory can prove that > 'dimension' of unit of time can be changed by changing the > environment. If both length and time are assigned similar properties > then mass includes the clock that 'runs slow'.
A clock is what measures time. The concept of a clock running slow in its own frame is nonsense, unless you bought a bum clock.
> We have every reason to > believe that the problem of calculating the internal change is shifted > to the clock.
Sorry, I cannot understand what you mean.
> According to Newton's law, a force of constant magnitude > 'works' with continuously increasing power.
That is gobbledegook.
> Has this possibility been > proved in a laboratory?
The laboratory and gobbledegook don't mix well.
Gopal, you talk so much nonsense that I would rather not continue the discussion.
"Franz Heymann" <Franz.Heym...@btopenworld.com> wrote in message <news:aphgr2$177$3@venus.btinternet.com>... > The phrase "relative velocity" has been bagged for another purpose, so > you should dream up another name. > On second thoughts, don't do that. I think there is already a name for > what you are speaking about. Is it not "closure velocity"?
Right. Mati made same objection. Closure velocity it is. Though I still like "skedaddle", and someday hope to find a use for "scramola". E.g. "Two photons emitted in opposite directions in the lab frame have a skedaddle of 2c".
Also could use impressive name for closure velocity in terms of its transformation properties; not quite a vector, but has definite transfomation laws. "Closure velocity is a bi-axial pseudo-vector", or whatever, would make it sound like a real citizen.
Relative velocity is closure velocity in the rest frame of one of the particles.
>>> In article <2a0cceff.0210260740.1ff51...@posting.google.com>, nullde...@aol.com (Edward Green) writes:
>>> >I've been championing the idea recently "relative velocity" is a >>> >physical object with certain transformation properties, whose >>> >representation in a particular frame is v1 - v2, individual velocities >>> >expressed in that frame.
>>> The name "relative velocity" is taken (as you well know). Use >>> "closing velocity" or "velocity of approach" for the above. We've >>> been over this before, as I'm sure you recall.
>>Yes. Ok ... I wasn't hoping so much to redefine it as to extend the >>domain of definition. But you are right ... better call it something >>else. I kind of like "skedaddle" or "scramola".
>I vote for "skedaddle", it sounds neat.
And, if the experiment goes wrong, the scientists execute a scramola.
In article <apj759$5i...@bob.news.rcn.net>, jmfbah...@aol.com writes: >In article <lAWu9.4$P4.1...@news.uchicago.edu>, > me...@cars3.uchicago.edu wrote: >>In article <2a0cceff.0210271038.b1b6...@posting.google.com>, >nullde...@aol.com (Edward Green) writes: >>>me...@cars3.uchicago.edu wrote in message ><news:TNzu9.73$O4.18932@news.uchicago.edu>... >>>> In article <2a0cceff.0210260740.1ff51...@posting.google.com>, >nullde...@aol.com (Edward Green) writes:
>>>> >I've been championing the idea recently "relative velocity" is a >>>> >physical object with certain transformation properties, whose >>>> >representation in a particular frame is v1 - v2, individual velocities >>>> >expressed in that frame.
>>>> The name "relative velocity" is taken (as you well know). Use >>>> "closing velocity" or "velocity of approach" for the above. We've >>>> been over this before, as I'm sure you recall.
>>>Yes. Ok ... I wasn't hoping so much to redefine it as to extend the >>>domain of definition. But you are right ... better call it something >>>else. I kind of like "skedaddle" or "scramola".
>>I vote for "skedaddle", it sounds neat.
>And, if the experiment goes wrong, the scientists execute a >scramola.
Perfect, now we've use for both terms.
Mati Meron | "When you argue with a fool, me...@cars.uchicago.edu | chances are he is doing just the same"
In <2a0cceff.0210250540.5b665...@posting.google.com>, on 10/25/2002 at 06:40 AM, nullde...@aol.com (Edward Green) said:
>I doubt this. I've seen you make this claim before.
It's standard kinematics in a Minkowski space-time. It's also well supported by experimental data.
>What? Given any "achievable velocities" v1 and v2, the sum is >bounded by 2c. Since the frame in which the sum is 2c - eps is an >inertial frame, that is your bound: v1 + v2 < 2c.
The issue isn't the sum, the issue is the speed of one frame as measured in the other. If v1 < c and v2 < c then that speed is bounded by c, not just by 2c.
>Oh ... you cheated! You used _three_ clocks.
But he didn't cheat enough. Had he used 4 clocks, he could have made it clear that the paradox is symmetrical.
><Sententious conclusion mode>: Indeed, how could it be otherwise? SR >knows nothing of acceleration,
Really? Then what is &x^i/&s along a worldline, where s is the interval? It sure looks like acceleration to me.
>hence any effects of acceleration in SR must merely be an integrated >compounding of many small increments of constant velocity.
What is the trajectory of a charged point-mass in an E-M field? Hint: it doesn't have small increments of constant velocity.
>To deal >with the effects of acceleration per se on matter we need GR.
No. We need GR to deal with accelerated frames of reference, not to deal with acceleration of matter in an inertial frame.
-- Shmuel (Seymour J.) Metz, SysProg and JOAT Atid/2, Team OS/2, Team PL/I
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>(1) mythical prehistory -- need GR to handle accelerated bodies
> (I don't think I ever actually believed this)
>(2) pre-current state -- acceleration in SR can be handled by a >combination of integration (effect of a sequence of instantaneous rest >frames) plus material effects (stress, etc).
>(3) glimmer of nuance --
>I have a momentary doubt that both of these programs correctly applied >are sufficient to completely exhaust any "GR effects" of accelerated >object in flat spacetime.
Okay, you are certainly allowed doubts. But your previous understanding, number (2) is correct.
>Let's look at our friend the Ehrenfest disk again. We proceed in flat >space in an inertial frame of reference, and consider a disk spinning >at steady state, which has already resolved all its inner length >contraction/stress/transient issues.
>Now, on the theme of "kinematics still works as before in fixed >inertial frame", all points at radius r from the axis have >instantaneous speed u = rw, and instantaneous acceleration a = rw^2. >Ok. Now, suppose we choose to fix u, while allowing r to shrink and w >to increase. We see that while u remains fixed, a will scale with >omega.
>Now, lets consider the effect on clocks at this radius. First, during >any small time interval dt in the inertial frame, the clocks are >moving with a given u, hence should appear to be running slower >"special relativistically".
>Agree?
So far.
>Second, because of the increasing acceleration, the stress on the >clocks will increase, which may affect their time keeping ability >purely "mechanically". I.e. (hold your fire, Daryl), they may undergo >physical effects which we would not refer to as "time dilation", but >nonetheless affect the rate at which the clocks run compared to a >unstressed reference.
>Agree?
Yes, that's certainly a possibility. However to actually calculate such an effect, you have to know what kind of clock you're talking about. I don't think there would be any *universal* effect of that type; any effect of acceleration will depend on the type of clock, what it's made of, how big it is, etc.
I think that if we use say radioactive decay as our clock, then the effects of acceleration will be negligible, unless we're talking about really, really, big accelerations.
>So, we have possibly mechanically affected clocks further running at >an apparently aberrant rate, even accounting for the mechanical >effects, via Lorentz transformation.
>I hope you agree so far.
Okay.
>Now, according to the programme "SR contains all effects of >acceleration in flat spacetime", we are apparently finished. There >are no more possible physical effects on the clocks, and hence, first >correcting for mechanical effects of acceleration, we predict any >further disagreement with clocks at rest in the inertial frame >according to the Lorentz transformation.
>Now, have we exhausted the possible effects of acceleration on clocks, >or not? You would claim that we have,
Yes.
>and I hope I have at least >stated your programme fairly and convincingly. I am however not 100% >convinced we have exhausted the physical description. Here's why.
>First, back to pure SR a moment. I claim, though I have not struggled >with this in a while, that _most_ of the effects of SR can be >predicted macroscopically by analyzing the behavior of a flotilla of >space ships which keep themselves in formation by exchanging timed >radar pulses.
Sort of. What you mean is something like this: each spaceship sends light signals to its neighbors, and receives replies. The spaceships then adjust their positions so that the replies from neighbors on either side arrive at the same time. Is that right?
>In a fixed inertial frame, the observer sees the >flotilla is making "mistakes" by ignoring the differing forward, >backward and lateral propogation of light in their own rest frame. >_We_ see the effects of their relative motion past us, but they >blithly ignore it.
>Almost, but not quite "explain" SR, I think.
I think that something like that can be used to justify the Lorentz transformations. However, you need to make physical assumptions about the laws governing motion and forces in order to get that they have the same form in all inertial frames.
>The catch is, in order >to make this picture consistent, we have to reach inside systems on >the ships we have not analyzed, and _postulate_ their adherence to SR. > And I believe, if we then analyzed these smaller systems, we would >find yet smaller systems within 'em which we again had to resort to >postulation on. So we seem to be onto something, but we can't quite >close the loop, and ultimate must adopt the Lorentz invariance of >physics as a postulate, maddeningly hinted at by a kind of infinite >recursion.
>Ok.
Maybe I agree.
>Now, I'm thinking of your nice analysis of gravitational redshift in >terms of the bow and stern of an accelerating space ship, and doppler >effects. Here is a case where we get the gravitational/accelerational >equivalence effects of GR for free from SR. This would tend to >substantiate your claim that all we need is SR to analyze any possible >effect of acceleration in flat space time. But I'm also thinking >about this infinite recursion thing ...
>Proposed moral: there may be acceleration effects on matter, beyond >those predicted macroscopically by a close application of SR to >analyzing the components (like the space ship doppler red shit), and >beyond continuum mechanistic constituent relation effects ... like >stress strain, etc.
Okay, there are two meanings of "there may be acceleration effects...". Do you mean that General Relativity may describe such effects? Or do you mean that there may be such effects that are not captured by General Relativity? The latter is certainly a possibility, and I think it can only be checked by experiment. The former (asking whether GR predicts such things) is a pure mathematical question, and I'm pretty sure that the answer is "no".
>These might correspond to something like "stresses and strain in the >nuclei", below our level of analysis with SR, which would in fact need >the machinery of GR to tease out, albeit we remained in flat >gravitation free space.
No. If you mean additional acceleration-dependent effects predicted by GR, then the answer is no. As I said before, GR is mathematically equivalent to SR in the case of flat spacetime. If spacetime is flat, then GR is nothing more than SR rewritten in coordinate-independent language.
>> No. There is no purely GR-ish effect in flat spacetime.
>Maybe. I only claim, via above analysis, that my doubt is >not-so-stupid, though it may appear tautological that SR is GR in flat >spacetime, so there is nothing more to say. We may lose something in >the simpler machinery.
As I say, it may be that there are acceleration-dependent effects not accounted for by SR---but such effects won't be accounted for by GR, either. It's also possible that for practical reasons the machinery of GR is needed to solve some hairy problem. But the machinery of GR is just the mathematics of curvilinear coordinate systems. I think we can distinguish the theory from the tools necessary to work with the theory. The theory doesn't change just because the problems get harder.
>Consider an Ehrenfest disk again, now masquerading as a centrifuge, >and consider the clocks at r, again. Are you certain we will have >exhausted any effects on these clocks tending to upset their >synchronization with inertial clocks by first considering their speed, >next an mechanical effects of the centrifugal acceleration?
>If we have, then what has happened to the equivalence principle?
The equivalence principle is essentially the claim that any problem in GR with a fixed spacetime metric can be solved by using SR locally.
>These clocks appear to be at the bottom of a gravity well equivalent >wrt a clock on the hub,
What you seem to want to do is to convert the acceleration problem into a gravity problem, and then use GR to solve it. But how do you think that GR solves such problems? It solves them by switching to a free-falling coordinate system and then applying SR. So, using GR can't possibly give you anything new.
>but I don't see any possibility for an >equivalent effect ... we don't have Doppler any more to appeal to, >unless some kind of relativistic transverse Doppler effect?
You don't need Doppler effect for this problem. Clocks that are "higher" in the effective gravitational field are the ones that are closer to the center of the centrifuge. Thus, those clocks are moving slower (since velocity is proportional to the distance from the center). Thus, they will experience less time dilation. So a sort of "gravitational" time-dilation is observed when you compare clocks higher and lower in the effective gravitational field. Work out the numbers, and you will find that the shift is exactly what is predicted by the equivalence principle.
It is kind of strange that the same effect (gravitational time dilation) is sometimes explained by time dilation, and sometimes explained by Doppler shift. But the net effect is the same: clocks lower in a "gravitational field" appear to run slower.
: No. Clock A has always been at rest. Clock B has : always been travelling at speed .866c. Clock C has : always been travelling at speed .866c in the opposite direction.
No, it hasn't. You're not going to win this. You don't have a theory of the beginning of time. Acceleration simply means a change in velocity. It goes WITHOUT saying that you simply don't NEED to stipulate that anything has had a constant velocity since before the big bang. That is just too far back.
: >The fact that it was before you started paying attention to : >the experiment doesn't mean it never happened. : : I set up the conditions, and my conditions say that none of : the three clocks has ever accelerated.
That's just not cosmologically POSSIBLE, Daryl.
: If no clock has accelerated, : it follows that time dilation is not due to acceleration. : I don't know how you can argue that.
Time dilation is due to velocity, but DILATION MEANS A *CHANGE* in the "width" of a time-unit. It means an increase. If you accelerate to a faster speed then time dilates to bigger; if you accelerate to a slower one then it un-dilates to smaller; it is NOT possible for something to be correlated-with-v WITHOUT ALSO being affected by changes-in-v. And here, v is velocity and changes-in-v are accelerations. This is pure semantics. I plead exhaustion.
: >You DON'T GET TO HAVE a "rather than"! Moving clocks DO tick : >slower! : : No, they don't.
You have spent a whole lot of time saying that they do, so don't be trying to deny it now.
: But I already told you how Minkowsky geometry breaks the : symmetry. Minkowsky geometry says that : : T(A,B) + T(B,C) <= T(A,C) : : where T(A,B) is the invariant separation between spacetime : points A and B.
That does NOT break any symmetry. Not that any ever occurred in the first place, in Al's scenario. In the original twin paradox, considering velocity alone, without acceleration, symmetry DOES occur. In all the 3-clock and 4-clock variants that have been talked about since, it doesn't. There is no paradox to resolve. -- --- "It's difficult ... you need to be united to have any strength, but internal issues have to be addressed." --- E. Ray Lewis, on liberalism in America
> In <2a0cceff.0210250540.5b665...@posting.google.com>, on 10/25/2002 > at 06:40 AM, nullde...@aol.com (Edward Green) said:
> >I doubt this. I've seen you make this claim before.
> It's standard kinematics in a Minkowski space-time. It's also well > supported by experimental data.
For a computer guy you seem kind of light on Usenet etiquette.
Rule #1 in Usenet replies: Don't snip so much context the reader has no idea what you are replying to. You may notice that it's been several days since I posted that. You're very flattering, but I don't think many people are given to memorizing my stuff ... including me. Who the hell knows what "this" is now?
Rule #1b: Make sure _you_ understand the context before replying.
By "it" you seem to understand the twin paradox in general. By "this" it would have been evident from context that I understood the claim that the twin paradox can be executed without any accelerated clocks.
In reference to what you thought you were replying to: I have no problem with SR per se and the twin paradox in particular, but I would like to know of any specific experimental test of the twin paradox, as opposed to the structure of SR which supports it. How is the twin paradox _per se_ "well supported by experimental data" -- references.
> >Oh ... you cheated! You used _three_ clocks.
> But he didn't cheat enough. Had he used 4 clocks, he could have made > it clear that the paradox is symmetrical.
No, no, no. The paradox is _not_ symmetrical -- at least by any meaning I understand by "symmetrical". Uncle VitriAl is a horse's ass, but in this case he happens to be a _correct_ horse's ass -- a version of the twin paradox is constructed wherein the difference in proper time along two spacetime trajectories between two events is expected to be observed, but no clock is accelerated.
What Al shows is that the physical effects of acceleration on the clock are irrelevant -- however, the acceleration of one _trajectory_ is indeed relevant, and breaks the symmetry.
> ><Sententious conclusion mode>: Indeed, how could it be otherwise? SR > >knows nothing of acceleration,
> Really? Then what is &x^i/&s along a worldline, where s is the > interval? It sure looks like acceleration to me.
Looks more like velocity to me, but let's not split hairs.
What I meant is that acceleration does not explicitly enter as a term in the Lorentz transformations. This means that an "effect" of acceleration in SR will be the effect of an integration of differential increments with constant velocity. This is what Al's version captures, while excluding a direct "acceleration effect" on the clocks.
Al's version forces us to make the logical distinction between physical acceleration of a clock, and acceleration in the world line -- which in this case is all concentrated in one kink. Al, as is common with brilliant but erractic people -- particularly those possibly suffering from undiagnosed brain lesions -- concocted a brilliant example, but failed to fully analyze its significane: his example splits acceleration of material bodies from acceleration of the trajectory.
> >hence any effects of acceleration in SR must merely be an integrated > >compounding of many small increments of constant velocity.
> What is the trajectory of a charged point-mass in an E-M field? Hint: > it doesn't have small increments of constant velocity.
Um... have you studied calculus? It would seem not. And don't tell me I didn't say "infinitesimal" -- it would be obvious to a person of ordinary skill in the art what I was getting at. You are not trying out for advanced horse's ass placement, are you?
> >To deal > >with the effects of acceleration per se on matter we need GR.
> No. We need GR to deal with accelerated frames of reference, not to > deal with acceleration of matter in an inertial frame.
You are right on this one. I knew that -- I claim -- but that's not what I wrote, so fair is fair. In retrospect I'm wondering if there may not be some more subtle effects of acceleration captured by the machinery of GR, which are lost in translation to SR.
Maybe I am wrong, but at least I'm wrong in a subtle way. ;-)
> >What? Given any "achievable velocities" v1 and v2, the sum is > >bounded by 2c. Since the frame in which the sum is 2c - eps is an > >inertial frame, that is your bound: v1 + v2 < 2c.
> The issue isn't the sum, the issue is the speed of one frame as > measured in the other. If v1 < c and v2 < c then that speed is bounded > by c, not just by 2c.
Nope ... the "issue" here is the sum, because what Al wrote is "the sum". The sum is the sum is the sum ... even in SR. I suppose, if you like, you could say the "relativistic sum". The "relativistic sum" of two velocities is bounded by c, the sum of two velocities is bounded by 2c.
> Shmuel (Seymour J.) Metz, SysProg and JOAT > Atid/2, Team OS/2, Team PL/I
Very impressive, for a programmer. Unfortunately the subject is physics, for which you bat about 1 for 5 on your criticisms. However, you are at least head and shoulders above fellow CS guy George Greene, who dismisses SR as "self-contradictory bullshit". He's probably a crummy programmer too.
Imagine what a reception I would get if I started posting in groups frequented by all your kewl programming friends, jumped in in the middle of a thread and began criticizing without paying attention to context or what was actually written. Consider that I have been polite under the circumstances.
>da...@cogentex.com (Daryl McCullough) writes: > : No. Clock A has always been at rest. Clock B has > : always been travelling at speed .866c. Clock C has > : always been travelling at speed .866c in the opposite direction.
>No, it hasn't.
It's a physics exercise, not a description of an actual situation. It's like when a math problem begins with "If Sally has three apples, and John gives her two more, then how many does she have altogether?" It's completely beside the point to ask "How did Sally get those apples?"
Similarly, it is beside the point to ask how clock B got to travel at .866c. For the purpose of the problem, we can just say that it *is* travelling at that speed.
>Acceleration simply means a change in velocity.
Right, and there is no need for anything to change velocities in order to describe time dilation.
> : I set up the conditions, and my conditions say that none of > : the three clocks has ever accelerated.
>That's just not cosmologically POSSIBLE, Daryl.
That's not true, and it's irrelevant. It's an exercise illustrating how SR works, it's not a description of actual clocks that some astronomer observed travelling near the speed of light through space.
> : If no clock has accelerated, > : it follows that time dilation is not due to acceleration. > : I don't know how you can argue that.
>Time dilation is due to velocity, but DILATION MEANS A *CHANGE* >in the "width" of a time-unit.
I don't care what it means in English. What it means in physics is this: The elapsed time on an ideal clock that travels at speed v is given by
Integral of square-root(1-(v/c)^2) dt
where v and t are measured in any inertial coordinate system.
>It means an increase. If you >accelerate to a faster speed then time dilates to bigger; >if you accelerate to a slower one then it un-dilates to smaller; >it is NOT possible for something to be correlated-with-v >WITHOUT ALSO being affected by changes-in-v.
You are mixing up two different claims: (1) Time dilation does not require acceleration, and (2) Acceleration has no effect on time dilation. The first is true, but the second is false.
> : >You DON'T GET TO HAVE a "rather than"! Moving clocks DO tick > : >slower! > : > : No, they don't.
>You have spent a whole lot of time saying that they do, >so don't be trying to deny it now.
But the point is that the concepts of "moving" and "ticking slower" are relative to a choice of coordinate systems. There is no absolute sense in which one clock is moving and the other is not.
> : But I already told you how Minkowsky geometry breaks the > : symmetry. Minkowsky geometry says that > : > : T(A,B) + T(B,C) <= T(A,C) > : > : where T(A,B) is the invariant separation between spacetime > : points A and B.
>That does NOT break any symmetry.
Yes, it does. One clock travels inertially from event A to event C. (An event is a point in spacetime. To specify an event, you have to give both a location and a time, in some coordinate system.) Its elapsed time is T(A,C). The second clock travels inertially from event A to event B, showing elapsed time T(A,B) and then travels inertially from event B to event C, showing an elapsed time of T(B,C). Its total elapsed time is T(A,B) + T(B,C). Since T(A,C)
>= T(A,B) + T(B,C), the second clock will show the
smallest amount of total elapsed time.
>Not that any ever occurred in the first place, >in Al's scenario. In the original twin paradox, >considering velocity alone, without acceleration, >symmetry DOES occur. In all the 3-clock and 4-clock >variants that have been talked about since, it doesn't. >There is no paradox to resolve.
Right. There are no paradoxes in relativity theory.
In <2a0cceff.0210281526.46a65...@posting.google.com>, on 10/28/2002 at 03:26 PM, nullde...@aol.com (Edward Green) said:
>No, no, no. The paradox is _not_ symmetrical -- at least by any >meaning I understand by "symmetrical".
I can't help the fact that you don't understand simple terms. With 4 clocks and point-of-contact signalling, each observer sees that his measured time is greater than the measured time on a broken trajectory. Thus each observer perceives his clock as running faster than the other's. That's symmetrical.
>What Al shows is that the physical effects of acceleration on the >clock are irrelevant -- however, the acceleration of one >_trajectory_ is indeed relevant, and breaks the symmetry.
No; his thought experiment is intrinsically asymmetrical. Adding a fourth clock restores the symmetry.
>Looks more like velocity to me, but let's not split hairs.
Sorry; typo. I meant &^2xî/&s or &v^i/&s, where s is interval.
>What I meant is that acceleration does not explicitly enter as a >term in the Lorentz transformations.
That's certainly true.
>Um... have you studied calculus?
Better than you, it would seem
>And don't tell me I didn't say "infinitesimal"
Why would I tell you that? I'd be more likely to tell you that you don't understand the difference between an integral and a sum.
>-- it would be obvious to a person of >ordinary skill in the art what I was getting at.
Yes, it would be obvious that you don't understand the concept of a limit. Maybe you should have taken a real Calculus class instead of Calculus for Engineers.
>You are not trying >out for advanced horse's ass placement, are you?
No; I'd stand no chance as long as you were in the running.
>Very impressive, for a programmer. Unfortunately the subject is >physics,
Then stop posting it to sci.math, where you are batting 0 for 5. You might also stop posting to sci.logic, which is even less relevant. For a while I thought that you were AP.
-- Shmuel (Seymour J.) Metz, SysProg and JOAT Atid/2, Team OS/2, Team PL/I
Any unsolicited commercial junk E-mail will be subject to legal action. I reserve the right to publicly post or ridicule any abusive E-mail.
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You generate many slowly moving pion in the lab. You measure their mean lifetime in the lab You generate many fast mesons moving like bats out of hell in the same lab. I have done this with pions having gamma factors of up to 700. You measure their mean lifetime in the lab. The second figure is gamma times larger than the first.
> How is the twin > > paradox _per se_ "well supported by > > experimental data" -- references.
> You generate many slowly moving pion in the lab. You measure their mean > lifetime in the lab > You generate many fast mesons moving like bats out of hell in the same > lab. I have done this with pions having gamma factors of up to 700. > You measure their mean lifetime in the lab. The second figure is gamma > times larger than the first.
I don't doubt that. I was careful to distinguish between experiments which supported the structure of SR in general, from which we deduce the expected behavior of the twins, to experiments which could be mapped directly to the twin paradox. The reason I made this distinction is that the poster I replied to was blithly claiming "it" was "well supported by experimental data" -- it being, in context, the twin paradox. I modestly ask how the twin paradox per se has been subject to direct experimental test.
Your example is to the point, close by, small impact parameter, near kill zone, as it deals with relativistic time dilation. Nonetheless it is not a direct experimental test of the twin paradox set-up, and if one is going to support the sentence "it <antecendent -- the twin paradox> ... well attested ... experimental" ... then I think if one is not talking through one's hat one should have up one's sleeve or possibly secreted in one's trouser legs direct experimental tests of the twin paradox per se, and not its second cousin.
I am especially peeved -- an easy state for me -- because the PP (prior poster) executed a double regression to what he wanted to argue, vs. addressing what I was actually saying -- first, from what in context was clearly Al's specific claim that he could do it without accelerated clock, to any old twin paradox in general, second, from my (alleged) doubt of the any old twin paradox in general, to an implied doubt of relativity in general.
Beauty, huh? I doubt (1) Al's claim he can do twin paradox without acclerated clocks, hence (?) (2) I doubt analysis of twin paradox in general, hence (??) I doubt relativity in general. This is the state the PP wants to achieve, because then he can make vague authoritative pronouncements about "well attested by experiment".
Nothing anybody from the PP to Uncle VitriAl to, yes, e'en you occasionally, likes so much as good SR denier, so one can cite authoritative sounding experiemental evidence. Much simpler than trying to figure out exactly what I was getting at, isn't it.
> > How is the twin > > > paradox _per se_ "well supported by > > > experimental data" -- references.
> > You generate many slowly moving pion in the lab. You measure their mean > > lifetime in the lab > > You generate many fast mesons moving like bats out of hell in the same > > lab. I have done this with pions having gamma factors of up to 700. > > You measure their mean lifetime in the lab. The second figure is gamma > > times larger than the first.
> I don't doubt that. I was careful to distinguish between experiments > which supported the structure of SR in general, from which we deduce > the expected behavior of the twins, to experiments which could be > mapped directly to the twin paradox. The reason I made this > distinction is that the poster I replied to was blithly claiming "it" > was "well supported by experimental data" -- it being, in context, the > twin paradox. I modestly ask how the twin paradox per se has been > subject to direct experimental test.
> Your example is to the point, close by, small impact parameter, near > kill zone, as it deals with relativistic time dilation. Nonetheless > it is not a direct experimental test of the twin paradox set-up, and > if one is going to support the sentence "it <antecendent -- the twin > paradox> ... well attested ... experimental" ... then I think if one > is not talking through one's hat one should have up one's sleeve or > possibly secreted in one's trouser legs direct experimental tests of > the twin paradox per se, and not its second cousin.
This is a direct test of the twins paradox, your objections notwithstanding. Both classes of muon are born and die in the lab. The ones which moved were older when they died..
If you must have an apparently more direct test, there are the clocks flown in aircraft, compared before take-off and landing with an earthbound clock. That type of experiment was later repeated with greater accuracy by comparing an earthbound clock with one flown in a low orbit spacecraft.
> I am especially peeved -- an easy state for me -- because the PP > (prior poster) executed a double regression to what he wanted to > argue, vs. addressing what I was actually saying -- first, from what > in context was clearly Al's specific claim that he could do it without > accelerated clock, to any old twin paradox in general, second, from my > (alleged) doubt of the any old twin paradox in general, to an implied > doubt of relativity in general.
> Beauty, huh? I doubt (1) Al's claim he can do twin paradox without > acclerated clocks, hence (?) (2) I doubt analysis of twin paradox in > general, hence (??) I doubt relativity in general. This is the state > the PP wants to achieve, because then he can make vague authoritative > pronouncements about "well attested by experiment".
> Nothing anybody from the PP to Uncle VitriAl to, yes, e'en you > occasionally, likes so much as good SR denier, so one can cite > authoritative sounding experiemental evidence. Much simpler than > trying to figure out exactly what I was getting at, isn't it.
Well, instead of letting us flounder trying to figure what you were getting at, just tell us.
In <apphal$4m...@helle.btinternet.com>, on 10/30/2002 at 09:01 PM, "Franz Heymann" <Franz.Heym...@btopenworld.com> said:
>> Sorry; typo. I meant &^2x¯/&s or &v^i/&s, where s is interval. >How about fixing your latest typo? Or don't you know any better?
It's not as large a typo as you believe; it looks worse because your news client is ignoring the Content-Type: text/plain; charset=ISO-8859-1 in my article. The difference between what I typed and what I meant to type is one space character. You're so brilliant, you should be able to figure out what happened.
-- Shmuel (Seymour J.) Metz, SysProg and JOAT Atid/2, Team OS/2, Team PL/I
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: What Al shows is that the physical effects of acceleration on the : clock are irrelevant -- however, the acceleration of one _trajectory_ : is indeed relevant, and breaks the symmetry.
This is entirely too charitable. The "trajectory" has "acceleration"?? I've seen actual objects with actual mass accelerate; in SR people can also attribute acceleration to non-inertial *frames*. But to a "trajectory"?? Any frame or object that *follows* that trajectory will have acceleration, yes. In particular, the slips-of-paper with readings-from-no-longer-running- or-extant clocks that Al was positing WILL have acceleration, in his scenario. When the slip is "born" as the clock-it-is-reporting-about "dies", it is moving at the same speed as the dying/source clock. An instant later it is moving the opposite way as a "passenger" on the newborn/newly-running clock that will take it back to where the original event occurred, so that the comparison can occur. So its velocity changed, so it accelerated.
Unless information is being transmitted via light/EMR/photons themselves, it's got to be transmitted via something with rest-mass and that something -- whether it's a clock, a slip, a frame, or anyTHING else, has GOT to BE accelerating in order for the comparison of times along the "different trajectories" to occur. The RELEVANT acceleration is STILL of the PHYSICAL object (or of the clock) emitting the information. It's NOT just PURELY "trajectorial". -- --- "It's difficult ... you need to be united to have any strength, but internal issues have to be addressed." --- E. Ray Lewis, on liberalism in America
George writes: >nullde...@aol.com (Edward Green) writes: > : What Al shows is that the physical effects of acceleration on the > : clock are irrelevant -- however, the acceleration of one _trajectory_ > : is indeed relevant, and breaks the symmetry.
>This is entirely too charitable. >The "trajectory" has "acceleration"??
Yes. If you describe the trajectory as a triple of functions x(t), y(t), z(t)
then the trajectory is unaccelerated if
(d/dt)^2 x = 0 (d/dt)^2 y = 0 (d/dt)^2 z = 0
Otherwise, it is accelerated. Acceleration is a property of a trajectory. The concept of an *object* being accelerated is a derived concept: an object is accelerated if it follows an accelerated trajectory.
>I've seen actual objects with actual mass >accelerate; in SR people can also attribute >acceleration to non-inertial *frames*. >But to a "trajectory"??
What's wrong with that?
>Any frame or object that *follows* that trajectory >will have acceleration, yes. In particular, the >slips-of-paper with readings-from-no-longer-running- >or-extant clocks that Al was positing WILL have >acceleration, in his scenario.
No, those things need not be accelerated. That's the whole point of the three-clock version: absolute no physical object accelerates during the entire thought-experiment. As Ed said, the path from the first clock to the second clock and back to the first is an accelerated path. No physical object follows that path, though.
>When the slip is "born" as the clock-it-is-reporting-about "dies", >it is moving at the same speed as the dying/source >clock. An instant later it is moving the opposite >way as a "passenger" on the newborn/newly-running >clock that will take it back to where the original >event occurred, so that the comparison can occur. >So its velocity changed, so it accelerated.
It isn't necessary that actual physical slips be passed between the clocks. You can use light signals to transfer the times. Light always travels at the same speed.
>Unless information is being transmitted via light/EMR/photons >themselves, it's got to be transmitted via something >with rest-mass and that something -- whether it's a >clock, a slip, a frame, or anyTHING else, has GOT to >BE accelerating in order for the comparison of times >along the "different trajectories" to occur. The RELEVANT >acceleration is STILL of the PHYSICAL object (or of the >clock) emitting the information. It's NOT just PURELY >"trajectorial".
On the contrary, the only relevant acceleration is the acceleration of the trajectory. No physical object needs to accelerate.
> In <apphal$4m...@helle.btinternet.com>, on 10/30/2002 > at 09:01 PM, "Franz Heymann" <Franz.Heym...@btopenworld.com> said:
> >> Sorry; typo. I meant &^2x¯/&s or &v^i/&s, where s is interval.
> >How about fixing your latest typo? Or don't you know any better?
> It's not as large a typo as you believe; it looks worse because your > news client is ignoring the Content-Type: text/plain; > charset=ISO-8859-1 in my article. The difference between what I typed > and what I meant to type is one space character. You're so brilliant, > you should be able to figure out what happened.
I am not vey brilliant. I cannot figure out what happened. All I know is that in your latest line of maths up above here, there are two errors which I hope are only typos.
> > >> Sorry; typo. I meant &^2x¯/&s or &v^i/&s, where s is interval.
> > >How about fixing your latest typo? Or don't you know any better?
> > It's not as large a typo as you believe; it looks worse because your > > news client is ignoring the Content-Type: text/plain; > > charset=ISO-8859-1 in my article.
So that's how it's done. Huh. I was aware empirically that sometimes special characters appeared as gobbledegook, sometimes as special characters.
But you know what? Given the wide variety of newsreaders out there, including those which ignore such frippery, it's best just to use the ascii God gave us (either as an afterthought while having his coffee on the seventh day, or on the tablets).
Please add this to the Usenet etiquette list I started for you.
> > The difference between what I typed > > and what I meant to type is one space character. You're so brilliant, > > you should be able to figure out what happened.
> I am not vey brilliant. I cannot figure out what happened. All I know > is that in your latest line of maths up above here, there are two errors > which I hope > are only typos.
Yes. Well, the tyro has wandered in from some computer group, armed to the teeth with credentials, and expects the same mores to apply -- you didn't realize it was in character set ISO-8859-1 !!??? (Gales of laughter from gallery).
As I said, I am only faithfully reproducing what would happen if I wandered into his homeland and began preaching about assembly code -- toned down by about two orders of magnitude.
"Franz Heymann" <Franz.Heym...@btopenworld.com> wrote in message <news:apqr95$lh$4@sparta.btinternet.com>... > "Edward Green" <nullde...@aol.com> wrote in message > news:2a0cceff.0210301259.78c98b67@posting.google.com... > > "Franz Heymann" <Franz.Heym...@btopenworld.com> wrote in message > <news:apn5i7$1rs$1@knossos.btinternet.com>... > > > You generate many slowly moving pion in the lab. You measure their > mean > > > lifetime in the lab > > > You generate many fast mesons moving like bats out of hell in the > same > > > lab. I have done this with pions having gamma factors of up to 700. > > > You measure their mean lifetime in the lab. The second figure is > gamma > > > times larger than the first.
> > I don't doubt that. I was careful to distinguish between experiments > > which supported the structure of SR in general, from which we deduce > > the expected behavior of the twins, to experiments which could be > > mapped directly to the twin paradox. > This is a direct test of the twins paradox, your objections > notwithstanding. Both classes of muon are born and die in the lab. The > ones which moved were older when they died..
> If you must have an apparently more direct test, there are the clocks > flown in aircraft, compared before take-off and landing with an > earthbound clock.
I accept the latter as a direct test of the twin paradox. It contains the essential element of two clocks meeting at events A and B, one clock having taken a journey, for suitable meaning of "journey".
Mere time dilation doesn't cut it, IMO, as a direct test of the twin paradox. The twin paradox is crafted to show that time dilation, symmetrical at constant relative velocity (the muons don't think too much of _your_ clocks either), can be arranged to give some absolute looking effects. There is no longer anything reciprocal when the clocks are brought together and show different times.
If your muons were to continue living one day, while lab, accelerator, and all the other apparatus you had been using to torment them *poofed* out of existence, they would similarly conclude that _your_ clocks were slow pokes, and that the lab had lived longer than unrelativistic labs were expected to.
The twin paradox is the temporal version of the Ehrenfest disk ... by closing the loop we are forced to concede that reciprocal length and time effects can have absolute consequences -- which we might not have expected.
> > > > You generate many slowly moving pion in the lab. You measure their > > mean > > > > lifetime in the lab > > > > You generate many fast mesons moving like bats out of hell in the > > same > > > > lab. I have done this with pions having gamma factors of up to 700. > > > > You measure their mean lifetime in the lab. The second figure is > > gamma > > > > times larger than the first.
> > > I don't doubt that. I was careful to distinguish between experiments > > > which supported the structure of SR in general, from which we deduce > > > the expected behavior of the twins, to experiments which could be > > > mapped directly to the twin paradox.
> > This is a direct test of the twins paradox, your objections > > notwithstanding. Both classes of muon are born and die in the lab. The > > ones which moved were older when they died..
> > If you must have an apparently more direct test, there are the clocks > > flown in aircraft, compared before take-off and landing with an > > earthbound clock.
> I accept the latter as a direct test of the twin paradox. It contains > the essential element of two clocks meeting at events A and B, one > clock having taken a journey, for suitable meaning of "journey".
> Mere time dilation doesn't cut it, IMO, as a direct test of the twin > paradox. The twin paradox is crafted to show that time dilation, > symmetrical at constant relative velocity (the muons don't think too > much of _your_ clocks either), can be arranged to give some absolute > looking effects. There is no longer anything reciprocal when the > clocks are brought together and show different times.
> If your muons were to continue living one day, while lab, accelerator, > and all the other apparatus you had been using to torment them > *poofed* out of existence, they would similarly conclude that _your_ > clocks were slow pokes, and that the lab had lived longer than > unrelativistic labs were expected to.
> The twin paradox is the temporal version of the Ehrenfest disk ... by > closing the loop we are forced to concede that reciprocal length and > time effects can have absolute consequences -- which we might not have > expected.
In <2a0cceff.0211020753.426e4...@posting.google.com>, on 11/02/2002 at 07:53 AM, nullde...@aol.com (Edward Green) said:
>it's best just to use the ascii God gave us
Nice try, but your explanation is wrong. Better luck next time.
>Yes. Well, the tyro
Wrong again, boy.
>As I said, I am only faithfully reproducing what would happen if I >wandered into his homeland
Are you still laboring under the misapprehension that this tread only exist in sci.physics? You call me a tyro, yet you still don't understand that you are cross-posting to sci.math and sci.logic?
-- Shmuel (Seymour J.) Metz, SysProg and JOAT Atid/2, Team OS/2, Team PL/I
Any unsolicited commercial junk E-mail will be subject to legal action. I reserve the right to publicly post or ridicule any abusive E-mail.
I mangled my E-mail address to foil automated spammers; reply to domain Patriot dot net user shmuel+news to contact me. Do not reply to spamt...@library.lspace.org
In <aps2ku$s7...@venus.btinternet.com>, on 10/31/2002 at 08:09 PM, "Franz Heymann" <Franz.Heym...@btopenworld.com> said:
>I am not vey brilliant. I cannot figure out what happened.
I have my keyboard set to an American Inernational layout; several of the keys are "dead". In particular, if I really want a caret (^), I need to strike the space key; otherwise it is applied as an accent to the next character. Usually that is the behavior that I want, but in this case I wanted ^i, not î.
>All I know >is that in your latest line of maths up above here, there are two >errors
Actually, I see two errors plus a breach of convention.
-- Shmuel (Seymour J.) Metz, SysProg and JOAT Atid/2, Team OS/2, Team PL/I
Any unsolicited commercial junk E-mail will be subject to legal action. I reserve the right to publicly post or ridicule any abusive E-mail.
I mangled my E-mail address to foil automated spammers; reply to domain Patriot dot net user shmuel+news to contact me. Do not reply to spamt...@library.lspace.org
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