Groups > sci.physics.relativity > #615372

Re: Reconciling the Time Dilation and Relativistic Doppler

Newsgroups	sci.physics.relativity
Date	2023-07-15 06:21 -0700
References	(17 earlier) <7f37ea5c-96c4-4d0a-9179-25eb2b7b7686n@googlegroups.com> <4ef3c3c9-91e7-43a8-8d7a-2357679d3dfcn@googlegroups.com> <eda7168a-c986-4a5b-ab02-b1129908ebabn@googlegroups.com> <3a55b4be-779a-49c3-93fb-363d4f882896n@googlegroups.com> <e84cdabe-9834-4e0c-a34c-9be8c21f0f9cn@googlegroups.com>
Message-ID	<8e3430fa-4374-4cdb-bd3f-e2f0ec3f2bcbn@googlegroups.com> (permalink)
Subject	Re: Reconciling the Time Dilation and Relativistic Doppler
From	patdolan <patdolan@comcast.net>

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On Friday, July 14, 2023 at 8:02:45 PM UTC-7, patdolan wrote:
> On Friday, July 14, 2023 at 7:50:45 PM UTC-7, patdolan wrote: 
> > On Friday, July 14, 2023 at 7:15:45 PM UTC-7, Bill wrote: 
> > > On Friday, July 14, 2023 at 7:43:21 AM UTC-7, patdolan wrote: 
> > > > > Again, mindlessly trying to transpose the earth and the rocket (the most common newbie mistake of all) is not valid, because, as explained to you before, the earth is at rest in a single system of inertial coordinates S for the entire scenario, whereas the rocket is at rest first in terms of one such system S' and then in terms of another such system S", and this has the physical implications that have been patiently explained to you. 
> > > > 
> > > > [Okay, I see my mistake now, so I'm finally ready to actually read the explanation. Unfortunaterly, I can't figure out how to scroll up to read the explanations you kindly provided, so could you please] Explain them again.[?] 
> > > 
> > > Sure, using the relativistic Doppler formula, the total elapsed proper time on earth seen by the rocket is T*sqrt[(1-v)/(1+v)] + T*sqrt[(1-v)/(1+v)], which equals 2Tg, where T is half the total elapsed proper round-trip time of the rocket. Of course, the total elapsed proper time of the rocket seen by the earth is T' (1+v)sqrt[(1-v)/(1+v)] + T' (1-v)sqrt[(1+v)/(1-v)], which equals 2T'/g, where T' is half the total elapsed proper time of the earth. Both of these signify that T' = Tg. 
> > > 
> > > Now, in terms of the earth's standard inertial coordinates S, with the departure event "e0" at x=0,t=0, the rocket's turn-around event "e1" is at x=Tvg, t=Tg, and the reunion event "e2" is at x=0, t=2Tg. The earth event "e3" that is simultaneous in terms of the outbound system S' with "e1" is at x=0, t=Tg(1-v), and the earth event "e4" that is simultaneous in terms of the inbound system S" with "e1" is at x=0, t=Tg(1+v). So, the total elapsed earth time from e0 to e2 is T/g + 2Tgv^2 + T/g, which equals 2Tg, in agreement with the Doppler observation. 
> > > > The point under discussion now is exactly how does acceleration, in and 
> > > > of itself, save the twins paradox. 
> > > 
> > > Save the paradox? Do you mean how does the dynamical asymmetry resolve the alleged paradox? That was explained in the preceding paragraphs (and in the previous post, and the one before that, and...) Again, the classical newbie "paradox" is based on the assumption of symmetry, so when the dynamical asymmetry is pointed out, the paradox evaporates. It's like this: Newbie says the conditions are symmetrical but the results are asymmetrical -- paradox! (Or at least a violation of Leibniz's principle of sufficient reason!) The adult points out that the conditions are not symmetrical, and the asymmetry of the results is systematically related to the asymmetry in the conditions. End of "paradox". 
> > > 
> > > PD+50IQ wrote: 
> > > > Well, okay, so there is no paradox, and all of special relativity, including all the relativistic effects that Newbie finds so baffling, follow unavoidably from the local Lorentz invariance of all physical laws. But can you tell me if there is some simple way of knowing the elapsed proper time along any arbitrary path, regardless of whether it is accelerating or not? 
> > > 
> > > Sure, in terms of ANY standard system of inertial coordinates x,t, the elapsed proper time along a given timelike path in flat spacetime between two events is simply the integral of sqrt(dt^2 - dx^2) along the path. In curved spacetime it is the integral of sqrt[g_mn dx^m dx^n]. 
> > So..uhm...I just see a repetition of the rocket-out-turn-around-back version. You you please address the other version wherein the earth travels out and back? Surely your last paragraph is not meant as an analysis of the latter, wherein you a wave a magic wand over these situation while chanting the incantation "not symmetrical"
> Justify this expression T' (1+v)sqrt[(1-v)/(1+v)] + T' (1-v)sqrt[(1+v)/(1-v)] 

Derive the expression T' (1+v)sqrt[(1-v)/(1+v)] + T' (1-v)sqrt[(1+v)/(1-v)] from the Lorentz transforms.
> 
> Why isn't it Tsqrt[(1-v)/(1+v)] + T[(1+v)/(1-v)] instead?

Thread

Reconciling the Time Dilation and Relativistic Doppler patdolan <patdolan@comcast.net> - 2023-07-11 09:14 -0700
  Re: Reconciling the Time Dilation and Relativistic Doppler Tom Roberts <tjoberts137@sbcglobal.net> - 2023-07-11 13:19 -0500
    Re: Reconciling the Time Dilation and Relativistic Doppler patdolan <patdolan@comcast.net> - 2023-07-11 12:19 -0700
      Re: Reconciling the Time Dilation and Relativistic Doppler whodat <whodaat@void.nowgre.com> - 2023-07-11 14:31 -0500
        Re: Reconciling the Time Dilation and Relativistic Doppler patdolan <patdolan@comcast.net> - 2023-07-11 12:55 -0700
          Re: Reconciling the Time Dilation and Relativistic Doppler whodat <whodaat@void.nowgre.com> - 2023-07-11 16:03 -0500
          Re: Reconciling the Time Dilation and Relativistic Doppler Athel Cornish-Bowden <athel.cb@gmail.com> - 2023-07-12 09:41 +0200
            Re: Reconciling the Time Dilation and Relativistic Doppler Maciej Wozniak <maluwozniak@gmail.com> - 2023-07-12 00:53 -0700
            Re: Reconciling the Time Dilation and Relativistic Doppler Prokaryotic Capase Homolog <prokaryotic.caspase.homolog@gmail.com> - 2023-07-12 02:28 -0700
              Re: Reconciling the Time Dilation and Relativistic Doppler Maciej Wozniak <maluwozniak@gmail.com> - 2023-07-12 02:38 -0700
              Re: Reconciling the Time Dilation and Relativistic Doppler Athel Cornish-Bowden <athel.cb@gmail.com> - 2023-07-12 12:12 +0200
      Re: Reconciling the Time Dilation and Relativistic Doppler Sylvia Else <sylvia@email.invalid> - 2023-07-12 17:00 +1000
        Re: Reconciling the Time Dilation and Relativistic Doppler patdolan <patdolan@comcast.net> - 2023-07-12 00:13 -0700
          Re: Reconciling the Time Dilation and Relativistic Doppler Sylvia Else <sylvia@email.invalid> - 2023-07-12 22:11 +1000
            Re: Reconciling the Time Dilation and Relativistic Doppler Maciej Wozniak <maluwozniak@gmail.com> - 2023-07-12 05:16 -0700
            Re: Reconciling the Time Dilation and Relativistic Doppler patdolan <patdolan@comcast.net> - 2023-07-12 08:50 -0700
              Re: Reconciling the Time Dilation and Relativistic Doppler Bill <davos2329@gmail.com> - 2023-07-12 16:44 -0700
                Re: Reconciling the Time Dilation and Relativistic Doppler patdolan <patdolan@comcast.net> - 2023-07-12 17:08 -0700
                Re: Reconciling the Time Dilation and Relativistic Doppler Bill <davos2329@gmail.com> - 2023-07-12 17:55 -0700
                Re: Reconciling the Time Dilation and Relativistic Doppler Bill <davos2329@gmail.com> - 2023-07-12 18:00 -0700
                Re: Reconciling the Time Dilation and Relativistic Doppler patdolan <patdolan@comcast.net> - 2023-07-12 18:05 -0700
                Re: Reconciling the Time Dilation and Relativistic Doppler patdolan <patdolan@comcast.net> - 2023-07-12 18:17 -0700
                Re: Reconciling the Time Dilation and Relativistic Doppler Bill <davos2329@gmail.com> - 2023-07-12 18:21 -0700
                Re: Reconciling the Time Dilation and Relativistic Doppler patdolan <patdolan@comcast.net> - 2023-07-12 21:11 -0700
                Re: Reconciling the Time Dilation and Relativistic Doppler Bill <davos2329@gmail.com> - 2023-07-12 22:01 -0700
                Re: Reconciling the Time Dilation and Relativistic Doppler Bill <davos2329@gmail.com> - 2023-07-12 22:11 -0700
                Re: Reconciling the Time Dilation and Relativistic Doppler patdolan <patdolan@comcast.net> - 2023-07-12 23:17 -0700
                Re: Reconciling the Time Dilation and Relativistic Doppler Bill <davos2329@gmail.com> - 2023-07-13 00:03 -0700
                Re: Reconciling the Time Dilation and Relativistic Doppler patdolan <patdolan@comcast.net> - 2023-07-13 09:50 -0700
                Re: Reconciling the Time Dilation and Relativistic Doppler Bill <davos2329@gmail.com> - 2023-07-13 11:46 -0700
                Re: Reconciling the Time Dilation and Relativistic Doppler patdolan <patdolan@comcast.net> - 2023-07-13 12:20 -0700
                Re: Reconciling the Time Dilation and Relativistic Doppler rotchm <rotchm@gmail.com> - 2023-07-13 14:39 -0700
                Re: Reconciling the Time Dilation and Relativistic Doppler patdolan <patdolan@comcast.net> - 2023-07-13 15:41 -0700
                Re: Reconciling the Time Dilation and Relativistic Doppler Bill <davos2329@gmail.com> - 2023-07-13 16:53 -0700
                Re: Reconciling the Time Dilation and Relativistic Doppler patdolan <patdolan@comcast.net> - 2023-07-13 17:35 -0700
                Re: Reconciling the Time Dilation and Relativistic Doppler Bill <davos2329@gmail.com> - 2023-07-13 17:49 -0700
                Re: Reconciling the Time Dilation and Relativistic Doppler patdolan <patdolan@comcast.net> - 2023-07-13 17:53 -0700
                Re: Reconciling the Time Dilation and Relativistic Doppler Bill <davos2329@gmail.com> - 2023-07-13 18:30 -0700
                Re: Reconciling the Time Dilation and Relativistic Doppler patdolan <patdolan@comcast.net> - 2023-07-13 18:33 -0700
                Re: Reconciling the Time Dilation and Relativistic Doppler Bill <davos2329@gmail.com> - 2023-07-13 22:32 -0700
                Re: Reconciling the Time Dilation and Relativistic Doppler rotchm <rotchm@gmail.com> - 2023-07-13 19:28 -0700
                Re: Reconciling the Time Dilation and Relativistic Doppler patdolan <patdolan@comcast.net> - 2023-07-13 19:38 -0700
                Re: Reconciling the Time Dilation and Relativistic Doppler Prokaryotic Capase Homolog <prokaryotic.caspase.homolog@gmail.com> - 2023-07-13 19:58 -0700
                Re: Reconciling the Time Dilation and Relativistic Doppler patdolan <patdolan@comcast.net> - 2023-07-14 02:50 -0700
                Re: Reconciling the Time Dilation and Relativistic Doppler rotchm <rotchm@gmail.com> - 2023-07-14 04:45 -0700
                Re: Reconciling the Time Dilation and Relativistic Doppler Maciej Wozniak <maluwozniak@gmail.com> - 2023-07-14 05:08 -0700
                Re: Reconciling the Time Dilation and Relativistic Doppler Volney <volney@invalid.invalid> - 2023-07-14 14:22 -0400
                Re: Reconciling the Time Dilation and Relativistic Doppler patdolan <patdolan@comcast.net> - 2023-07-14 11:26 -0700
                Re: Reconciling the Time Dilation and Relativistic Doppler Volney <volney@invalid.invalid> - 2023-07-14 18:21 -0400
                Re: Reconciling the Time Dilation and Relativistic Doppler patdolan <patdolan@comcast.net> - 2023-07-14 16:28 -0700
                Re: Reconciling the Time Dilation and Relativistic Doppler Volney <volney@invalid.invalid> - 2023-07-15 19:48 -0400
                Re: Reconciling the Time Dilation and Relativistic Doppler patdolan <patdolan@comcast.net> - 2023-07-15 16:54 -0700
                Re: Reconciling the Time Dilation and Relativistic Doppler Bill <davos2329@gmail.com> - 2023-07-16 08:34 -0700
                Re: Reconciling the Time Dilation and Relativistic Doppler Bill <davos2329@gmail.com> - 2023-07-16 08:42 -0700
                Re: Reconciling the Time Dilation and Relativistic Doppler patdolan <patdolan@comcast.net> - 2023-07-16 16:08 -0700
                Re: Reconciling the Time Dilation and Relativistic Doppler Bill <davos2329@gmail.com> - 2023-07-16 16:49 -0700
                Re: Reconciling the Time Dilation and Relativistic Doppler patdolan <patdolan@comcast.net> - 2023-07-16 22:17 -0700
                Re: Reconciling the Time Dilation and Relativistic Doppler Bill <davos2329@gmail.com> - 2023-07-17 00:15 -0700
                Re: Reconciling the Time Dilation and Relativistic Doppler Volney <volney@invalid.invalid> - 2023-07-17 01:44 -0400
                Re: Reconciling the Time Dilation and Relativistic Doppler patdolan <patdolan@comcast.net> - 2023-07-16 22:57 -0700
                Re: Reconciling the Time Dilation and Relativistic Doppler Volney <volney@invalid.invalid> - 2023-07-17 02:50 -0400
                Re: Reconciling the Time Dilation and Relativistic Doppler Mitchell Demas <letl@alliecim.he> - 2023-07-17 09:28 +0000
                Re: Reconciling the Time Dilation and Relativistic Doppler Maciej Wozniak <maluwozniak@gmail.com> - 2023-07-17 00:08 -0700
                Re: Reconciling the Time Dilation and Relativistic Doppler Newton Patselas <nale@lsawttnp.no> - 2023-07-17 09:54 +0000
                Re: Reconciling the Time Dilation and Relativistic Doppler Maciej Wozniak <maluwozniak@gmail.com> - 2023-07-16 10:05 -0700
                Re: Reconciling the Time Dilation and Relativistic Doppler Maciej Wozniak <maluwozniak@gmail.com> - 2023-07-14 11:30 -0700
                Re: Reconciling the Time Dilation and Relativistic Doppler Bill <davos2329@gmail.com> - 2023-07-14 06:32 -0700
                Re: Reconciling the Time Dilation and Relativistic Doppler patdolan <patdolan@comcast.net> - 2023-07-14 07:43 -0700
                Re: Reconciling the Time Dilation and Relativistic Doppler rotchm <rotchm@gmail.com> - 2023-07-14 09:39 -0700
                Re: Reconciling the Time Dilation and Relativistic Doppler patdolan <patdolan@comcast.net> - 2023-07-14 09:48 -0700
                Re: Reconciling the Time Dilation and Relativistic Doppler patdolan <patdolan@comcast.net> - 2023-07-14 10:56 -0700
                Re: Reconciling the Time Dilation and Relativistic Doppler Bill <davos2329@gmail.com> - 2023-07-14 19:15 -0700
                Re: Reconciling the Time Dilation and Relativistic Doppler patdolan <patdolan@comcast.net> - 2023-07-14 19:50 -0700
                Re: Reconciling the Time Dilation and Relativistic Doppler patdolan <patdolan@comcast.net> - 2023-07-14 20:02 -0700
                Re: Reconciling the Time Dilation and Relativistic Doppler Bill <davos2329@gmail.com> - 2023-07-14 23:35 -0700
                Re: Reconciling the Time Dilation and Relativistic Doppler Maciej Wozniak <maluwozniak@gmail.com> - 2023-07-14 23:50 -0700
                Re: Reconciling the Time Dilation and Relativistic Doppler patdolan <patdolan@comcast.net> - 2023-07-15 06:21 -0700
                Re: Reconciling the Time Dilation and Relativistic Doppler Bill <davos2329@gmail.com> - 2023-07-15 16:50 -0700
              Re: Reconciling the Time Dilation and Relativistic Doppler Sylvia Else <sylvia@email.invalid> - 2023-07-13 13:18 +1000
                Re: Reconciling the Time Dilation and Relativistic Doppler patdolan <patdolan@comcast.net> - 2023-07-12 20:55 -0700
                Re: Reconciling the Time Dilation and Relativistic Doppler Sylvia Else <sylvia@email.invalid> - 2023-07-13 14:03 +1000
                Re: Reconciling the Time Dilation and Relativistic Doppler patdolan <patdolan@comcast.net> - 2023-07-12 21:08 -0700
                Re: Reconciling the Time Dilation and Relativistic Doppler Sylvia Else <sylvia@email.invalid> - 2023-07-13 14:34 +1000
                Re: Reconciling the Time Dilation and Relativistic Doppler patdolan <patdolan@comcast.net> - 2023-07-12 21:36 -0700
                Re: Reconciling the Time Dilation and Relativistic Doppler whodat <whodaat@void.nowgre.com> - 2023-07-13 00:48 -0500
                Re: Reconciling the Time Dilation and Relativistic Doppler whodat <whodaat@void.nowgre.com> - 2023-07-13 00:47 -0500
          Re: Reconciling the Time Dilation and Relativistic Doppler Teofilo Totolos <tltt@tooioltt.lo> - 2023-07-12 13:58 +0000
    Re: Reconciling the Time Dilation and Relativistic Doppler patdolan <patdolan@comcast.net> - 2023-07-11 14:29 -0700
      Re: Reconciling the Time Dilation and Relativistic Doppler "Dono." <eggy20011951@gmail.com> - 2023-07-11 19:04 -0700
        Re: Reconciling the Time Dilation and Relativistic Doppler patdolan <patdolan@comcast.net> - 2023-07-11 19:09 -0700
      Re: Reconciling the Time Dilation and Relativistic Doppler rotchm <rotchm@gmail.com> - 2023-07-11 21:19 -0700
      Re: Reconciling the Time Dilation and Relativistic Doppler rotchm <rotchm@gmail.com> - 2023-07-11 21:23 -0700
        Re: Reconciling the Time Dilation and Relativistic Doppler Maciej Wozniak <maluwozniak@gmail.com> - 2023-07-11 22:20 -0700
        Re: Reconciling the Time Dilation and Relativistic Doppler patdolan <patdolan@comcast.net> - 2023-07-11 22:58 -0700
          Re: Reconciling the Time Dilation and Relativistic Doppler patdolan <patdolan@comcast.net> - 2023-07-11 23:10 -0700
          Re: Reconciling the Time Dilation and Relativistic Doppler Sylvia Else <sylvia@email.invalid> - 2023-07-12 20:37 +1000
          Re: Reconciling the Time Dilation and Relativistic Doppler rotchm <rotchm@gmail.com> - 2023-07-12 04:32 -0700
            Re: Reconciling the Time Dilation and Relativistic Doppler Maciej Wozniak <maluwozniak@gmail.com> - 2023-07-12 04:39 -0700
          Re: Reconciling the Time Dilation and Relativistic Doppler Richard Hachel <r.hachel@frite.fr> - 2023-07-12 11:37 +0000
        Re: Reconciling the Time Dilation and Relativistic Doppler rotchm <rotchm@gmail.com> - 2023-07-12 06:01 -0700
  Re: Reconciling the Time Dilation and Relativistic Doppler Jack Liu <liuedy@gmail.com> - 2023-07-13 02:42 -0700

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