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Re: alice 'n bob again.. those two..

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  • Charles Goodwin
    I must admit I thought it would be longer. I was under the impression that to get really decent time dilation (e.g. a visit to the galactic core or - for an
    Message 1 of 21 , Jan 31, 2002
      I must admit I thought it would be longer. I was under the impression that to
      get really decent time dilation (e.g. a visit to the galactic core or - for an
      extra couple of years, the furthest visible galaxy - in a human lifetime) you
      needed to accelerate at slightly more than 1g. (Also, of course this is a purely
      academic exercise. Anyone accelerating at 1g and heading towards the galactic
      centre would burn up in the dust clouds between us and there.)

      Charles

      ----- Original Message -----
      From: "Doug Donaghue at 054" <DDonaghue@...>
      To: <Fabric-of-Reality@yahoogroups.com>
      Sent: Friday, February 01, 2002 2:48 AM
      Subject: RE: alice 'n bob again.. those two..


      >
      >
      > > -----Original Message-----
      > > From: Charles Goodwin [mailto:charles@...]
      > > Sent: Tuesday, January 29, 2002 7:49 PM
      > > To: Fabric-of-Reality@yahoogroups.com
      > > Subject: Re: alice 'n bob again.. those two..
      > >
      > >
      > > So what's the answer?! :-)
      > >
      > > Charles
      > >
      >
      > I got 23.4 years of aging for Bob (that's each way, for a total of 46.8
      > years) using:
      >
      > T=(c/a)arccosh((ad/(c^2))+1)
      >
      > where T is the proper time (as measured by Bob in his reference frame), a is
      > acceleration, d is
      > distance and c is 3*10^8. (It also helps to convert 30,000 light years to
      > 2.84*10^20 meters <g>)
      >
      > There is a derivation of this formula in "Gravitation" by Misner, Thorne and
      > Wheeler.
      >
      >
      > Doug
      >
      >
      >
      >
      >
      >
      > Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/
      >
    • Saibal Mitra
      In the old days people could calculate these things using paper and pencil. Here we are in the year 2002 with computers that can perform more computations in a
      Message 2 of 21 , Feb 2, 2002
        In the old days people could calculate these things using paper and pencil.
        Here we are in the year 2002 with computers that can perform more
        computations in a second than one person can perform during his entire life,
        and guess what? We can't compute a simple hyperbolic cosine. I wonder what
        the future will look like once quantum computers have replaced pc's.

        Saibal

        Charles wrote:
        ----- Original Message -----
        From: Charles Goodwin
        To: Fabric-of-Reality@yahoogroups.com
        Sent: Wednesday, January 30, 2002 3:48 AM
        Subject: Re: alice 'n bob again.. those two..


        So what's the answer?! :-)

        Charles

        ----- Original Message -----
        From: "Doug Donaghue at 054" <DDonaghue@...>
        To: <Fabric-of-Reality@yahoogroups.com>
        Sent: Wednesday, January 30, 2002 7:48 AM
        Subject: RE: alice 'n bob again.. those two..


        >
        > Hi again,
        >
        > > calculator on my PC doesn't do hyperbolic cosines so I can't
        > > tell you the
        > > answer...
        > >
        > > Charles
        >
        >
        > I just noticed that the calculator on my PC *does* do hyperbolic
        functions.
        > Put it in scientific mode (click on 'View') and then click the 'Hyp' box
        > just to the right of the 'Inv' box. We're running NT Workstation 4.0
        here.
        >
        >
        > Doug
        >
        >
        >
        >
        >
        >
        > Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/
        >



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      • Doug Donaghue at 054
        Hi, ... In the old days (up until about the 1900 s) the word computer had a very different meaning than it does today. But I still have the Pickett Log
        Message 3 of 21 , Feb 4, 2002
          Hi,

          > -----Original Message-----
          > From: Saibal Mitra [mailto:smitra@...]
          > Sent: Saturday, February 02, 2002 3:24 PM
          > To: Fabric-of-Reality@yahoogroups.com
          > Subject: Re: alice 'n bob again.. those two..
          >
          >
          > In the old days people could calculate these things using
          > paper and pencil.
          > Here we are in the year 2002 with computers that can perform more
          > computations in a second than one person can perform during
          > his entire life,
          > and guess what? We can't compute a simple hyperbolic cosine.
          > I wonder what
          > the future will look like once quantum computers have replaced pc's.


          In the 'old days' (up until about the 1900's) the word 'computer' had a very
          different meaning than it does today. But I still have the Pickett Log Log
          Duplex Decitrig slide rule (12") that I bought in 1960 (for the, then
          princely, sum of $25.00 <g>) and it does hyperbolics just fine.

          OTOH, if you're a *real* purist, use e^u =
          1+u+(u^2/2!)+(u^3/3!)+.....(u^n/n!) and calculate the hyperbolic functions
          as I pointed out earlier.

          It converges fairly quickly (the first 6 or 8 terms are sufficient for 3 or
          4 digits of precision) And, of course, it also works for imaginary or
          complex arguments <g>


          Doug
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