- 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/

> - 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/

>

Yahoo! Groups Sponsor

Your use of Yahoo! Groups is subject to the Yahoo! Terms of Service. - Hi,

> -----Original Message-----

In the 'old days' (up until about the 1900's) the word 'computer' had a very

> 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.

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