| Topic: |
Science > Physics |
| User: |
"KaliKinkar" |
| Date: |
12 Jan 2005 09:33:12 AM |
| Object: |
k-calculus |
Can anyone please suggest some good stuff on explaining relativity with
the factor k and Bondi's k-calculus in general.
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| User: "Franz Heymann" |
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| Title: Re: k-calculus |
12 Jan 2005 11:52:08 AM |
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"KaliKinkar" <kalikinkar@gmail.com> wrote in message
news:1105543992.705052.19050@f14g2000cwb.googlegroups.com...
Can anyone please suggest some good stuff on explaining relativity
with
the factor k and Bondi's k-calculus in general.
Read D'Inverno "Introducing Einstein's Relativity"
Franz
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| User: "John Schutkeker" |
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| Title: Re: k-calculus |
18 Feb 2005 05:39:41 PM |
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"KaliKinkar" <kalikinkar@gmail.com> wrote in news:1105543992.705052.19050
@f14g2000cwb.googlegroups.com:
Can anyone please suggest some good stuff on explaining relativity with
the factor k and Bondi's k-calculus in general.
What the hell is k-calculus?
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| User: "Franz Heymann" |
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| Title: Re: k-calculus |
19 Feb 2005 04:38:48 AM |
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"John Schutkeker" <jschutkeker@sbcglobal.net.nospam> wrote in message
news:Xns9601BDDAFC930lkajehoriuasldfjknak@151.164.30.48...
"KaliKinkar" <kalikinkar@gmail.com> wrote in
news:1105543992.705052.19050
@f14g2000cwb.googlegroups.com:
Can anyone please suggest some good stuff on explaining relativity
with
the factor k and Bondi's k-calculus in general.
What the hell is k-calculus?
It has nothing to do with hell. It is a popular method of performing
relativistic calculations.
Read d'Inverno "Intoducing Einstein's Relativity".
--
Franz
"The great tragedy of science -- the slaying of a beautiful hypothesis
by an ugly fact."
T.H. Huxley
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| User: "John Schutkeker" |
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| Title: Re: k-calculus |
21 Feb 2005 04:16:26 PM |
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"Franz Heymann" <notfranz.heymann@btopenworld.com> wrote in news:cv74vn$4e3
$4@titan.btinternet.com:
It has nothing to do with hell.
....silly...
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| User: "Franz Heymann" |
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| Title: Re: k-calculus |
22 Feb 2005 01:00:22 AM |
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"John Schutkeker" <jschutkeker@sbcglobal.net.nospam> wrote in message
news:Xns9604AFB8BD5BClkajehoriuasldfjknak@151.164.30.42...
"Franz Heymann" <notfranz.heymann@btopenworld.com> wrote in
news:cv74vn$4e3
$4@titan.btinternet.com:
It has nothing to do with hell.
...silly...
I'm glad you recognised it as being silly.
--
Franz
"The great tragedy of science -- the slaying of a beautiful hypothesis
by an ugly fact."
T.H. Huxley
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| User: "John Schutkeker" |
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| Title: Re: k-calculus |
19 Feb 2005 03:38:09 PM |
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"Franz Heymann" <notfranz.heymann@btopenworld.com> wrote in news:cv74vn$4e3
$4@titan.btinternet.com:
It has nothing to do with hell. It is a popular method of performing
relativistic calculations.
Read d'Inverno "Intoducing Einstein's Relativity".
What are it's advantages over Lorentz transforms?
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| User: "Franz Heymann" |
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| Title: Re: k-calculus |
20 Feb 2005 01:27:02 AM |
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"John Schutkeker" <jschutkeker@sbcglobal.net.nospam> wrote in message
news:Xns9602A9418F59Clkajehoriuasldfjknak@151.164.30.44...
"Franz Heymann" <notfranz.heymann@btopenworld.com> wrote in
news:cv74vn$4e3
$4@titan.btinternet.com:
It has nothing to do with hell. It is a popular method of
performing
relativistic calculations.
Read d'Inverno "Intoducing Einstein's Relativity".
What are it's advantages over Lorentz transforms?
They are a nice way of implementing Lorentz transforms.
Do your own legwork from here onwards.
--
Franz
"The great tragedy of science -- the slaying of a beautiful hypothesis
by an ugly fact."
T.H. Huxley
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| User: "John Schutkeker" |
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| Title: Re: k-calculus |
21 Feb 2005 04:05:36 PM |
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"Franz Heymann" <notfranz.heymann@btopenworld.com> wrote in news:cv9e46$93o
$3@sparta.btinternet.com:
"John Schutkeker" <jschutkeker@sbcglobal.net.nospam> wrote in message
news:Xns9602A9418F59Clkajehoriuasldfjknak@151.164.30.44...
"Franz Heymann" <notfranz.heymann@btopenworld.com> wrote in
news:cv74vn$4e3
$4@titan.btinternet.com:
It has nothing to do with hell. It is a popular method of
performing
relativistic calculations.
Read d'Inverno "Intoducing Einstein's Relativity".
What are it's advantages over Lorentz transforms?
They are a nice way of implementing Lorentz transforms.
Do your own legwork from here onwards.
Don't mind if I do!
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| User: "George Jones" |
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| Title: Re: k-calculus |
19 Feb 2005 04:24:56 PM |
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John Schutkeker wrote:
"Franz Heymann" <notfranz.heymann@btopenworld.com> wrote in news:cv74vn$4e3
$4@titan.btinternet.com:
It has nothing to do with hell. It is a popular method of performing
relativistic calculations.
Read d'Inverno "Intoducing Einstein's Relativity".
What are it's advantages over Lorentz transforms?
I think Lorentz trnasformations are often presented too early in
introductory books and courses on special relativity.
As for k-calculus, its advantage, like beauty, is in the eye of the
beholder. It is the right thing for some, but not all, teachers,
learners, practitioners, etc, of special realtivity.
k is just the Doppler factor, thought it is not introduced in this way.
One obvious reason that it is useful is that it's useful to probe
spacetime by bouncing light around, as, e.g., Geroch does when defining
distance and time.
An thoughtful introductory book that I think uses k-calculus is Flat
and Curved Space-Times by Ellis (of Hawking and Ellis fame) Williams.
Regards,
George
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| User: "John Schutkeker" |
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| Title: Re: k-calculus |
19 Feb 2005 06:36:23 PM |
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George Jones <george_llew_jones@yahoo.com> wrote in
news:vuOdnYt7I7rnIYrfRVn-2w@look.ca:
k is just the Doppler factor, thought it is not introduced in this way.
You're talking about w = w_0 - k.v . I got that equation under control in
8.03. It was E^2 = m_0*c^4 - c^2*p^2 that stumped me in 8.04. It was so
obviously the right equation, but every time I tried to use it, it blew up
in my face.
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| User: "George Jones" |
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| Title: Re: k-calculus |
19 Feb 2005 07:32:39 PM |
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John Schutkeker wrote:
George Jones <george_llew_jones@yahoo.com> wrote in
news:vuOdnYt7I7rnIYrfRVn-2w@look.ca:
k is just the Doppler factor, thought it is not introduced in this way.
You're talking about w = w_0 - k.v .
Too general.
I got that equation under control in
8.03. It was E^2 = m_0*c^4 - c^2*p^2 that stumped me in 8.04. It was so
obviously the right equation, but every time I tried to use it, it blew up
in my face.
It took me a second to get this. Did you use the notation m_0 for
historical accuracy?
Regards,
George
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| User: "John Schutkeker" |
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| Title: Re: k-calculus |
21 Feb 2005 09:38:53 PM |
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George Jones <george_llew_jones@yahoo.com> wrote in
news:sNednTuJmorldYrfRVn-rg@look.ca:
It was E^2 = m_0^2*c^4 - c^2*p^2 ...
Did you use the notation m_0 for historical accuracy?
I took 8.04 in '81. What are they calling m_0 these days?
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| User: "Franz Heymann" |
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| Title: Re: k-calculus |
22 Feb 2005 01:00:20 AM |
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"John Schutkeker" <jschutkeker@sbcglobal.net.nospam> wrote in message
news:Xns9604E6646DD71lkajehoriuasldfjknak@151.164.30.44...
George Jones <george_llew_jones@yahoo.com> wrote in
news:sNednTuJmorldYrfRVn-rg@look.ca:
It was E^2 = m_0^2*c^4 - c^2*p^2 ...
Did you use the notation m_0 for historical accuracy?
I took 8.04 in '81. What are they calling m_0 these days?
Just plain m
--
Franz
"The great tragedy of science -- the slaying of a beautiful hypothesis
by an ugly fact."
T.H. Huxley
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| User: "George Jones" |
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| Title: Re: k-calculus |
21 Feb 2005 10:40:52 PM |
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John Schutkeker wrote:
George Jones <george_llew_jones@yahoo.com> wrote in
news:sNednTuJmorldYrfRVn-rg@look.ca:
It was E^2 = m_0^2*c^4 - c^2*p^2 ...
Did you use the notation m_0 for historical accuracy?
I took 8.04 in '81. What are they calling m_0 these days?
m. In those days too.
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| User: "Franz Heymann" |
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| Title: Re: k-calculus |
22 Feb 2005 01:00:21 AM |
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"George Jones" <george_llew_jones@yahoo.com> wrote in message
news:YrSdnWn2NLwUKoffRVn-3w@look.ca...
John Schutkeker wrote:
George Jones <george_llew_jones@yahoo.com> wrote in
news:sNednTuJmorldYrfRVn-rg@look.ca:
It was E^2 = m_0^2*c^4 - c^2*p^2 ...
Did you use the notation m_0 for historical accuracy?
I took 8.04 in '81. What are they calling m_0 these days?
m. In those days too.
Many still used m0 in '81.
At least one otherwise excellent book on relativity still did in 1992
The conversion is, regrettably, not yet complete.
--
Franz
"The great tragedy of science -- the slaying of a beautiful hypothesis
by an ugly fact."
T.H. Huxley
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| User: "George Jones" |
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| Title: Re: k-calculus |
22 Feb 2005 06:16:01 AM |
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Franz Heymann wrote:
"George Jones" <george_llew_jones@yahoo.com> wrote in message
news:YrSdnWn2NLwUKoffRVn-3w@look.ca...
John Schutkeker wrote:
George Jones <george_llew_jones@yahoo.com> wrote in
news:sNednTuJmorldYrfRVn-rg@look.ca:
It was E^2 = m_0^2*c^4 - c^2*p^2 ...
Did you use the notation m_0 for historical accuracy?
I took 8.04 in '81. What are they calling m_0 these days?
m. In those days too.
Many still used m0 in '81.
Yes, I know, but the transition was well underway. I think the
introductory but influential special relativity book Spacetime Physics
by Taylor and Wheeler, first published in 1963, may have provided much
of the initial impetus for the transition.
At least one otherwise excellent book on relativity still did in 1992
The conversion is, regrettably, not yet complete.
Just curious, which one - Rindler?
Regards,
George
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| User: "Franz Heymann" |
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| Title: Re: k-calculus |
22 Feb 2005 11:35:14 AM |
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"George Jones" <george_llew_jones@yahoo.com> wrote in message
news:gaCdnTgFuuWrv4bfRVn-tQ@look.ca...
Franz Heymann wrote:
"George Jones" <george_llew_jones@yahoo.com> wrote in message
news:YrSdnWn2NLwUKoffRVn-3w@look.ca...
John Schutkeker wrote:
George Jones <george_llew_jones@yahoo.com> wrote in
news:sNednTuJmorldYrfRVn-rg@look.ca:
It was E^2 = m_0^2*c^4 - c^2*p^2 ...
Did you use the notation m_0 for historical accuracy?
I took 8.04 in '81. What are they calling m_0 these days?
m. In those days too.
Many still used m0 in '81.
Yes, I know, but the transition was well underway. I think the
introductory but influential special relativity book Spacetime
Physics
by Taylor and Wheeler, first published in 1963, may have provided
much
of the initial impetus for the transition.
At least one otherwise excellent book on relativity still did in
1992
The conversion is, regrettably, not yet complete.
Just curious, which one - Rindler?
No. d'Inverno. It is a UK book, so you might not be familiar with it
on that side of the pond.
Apart from that unfortunate lapse, it is a really excellent book.
--
Franz
"The great tragedy of science -- the slaying of a beautiful hypothesis
by an ugly fact."
T.H. Huxley
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| User: "George Jones" |
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| Title: Re: k-calculus |
01 Mar 2005 08:01:54 AM |
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Franz Heymann wrote:
"George Jones" <george_llew_jones@yahoo.com> wrote in message
news:gaCdnTgFuuWrv4bfRVn-tQ@look.ca...
Franz Heymann wrote:
"George Jones" <george_llew_jones@yahoo.com> wrote in message
news:YrSdnWn2NLwUKoffRVn-3w@look.ca...
John Schutkeker wrote:
George Jones <george_llew_jones@yahoo.com> wrote in
news:sNednTuJmorldYrfRVn-rg@look.ca:
It was E^2 = m_0^2*c^4 - c^2*p^2 ...
Did you use the notation m_0 for historical accuracy?
I took 8.04 in '81. What are they calling m_0 these days?
m. In those days too.
Many still used m0 in '81.
Yes, I know, but the transition was well underway. I think the
introductory but influential special relativity book Spacetime
Physics
by Taylor and Wheeler, first published in 1963, may have provided
much
of the initial impetus for the transition.
At least one otherwise excellent book on relativity still did in
1992
The conversion is, regrettably, not yet complete.
Just curious, which one - Rindler?
No. d'Inverno. It is a UK book, so you might not be familiar with it
on that side of the pond.
Apart from that unfortunate lapse, it is a really excellent book.
I very much like d'Inverno, and its on my shelf, but I had forgotten
about its use of m_0.
Regards,
George
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| User: "John Schutkeker" |
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| Title: Re: k-calculus |
24 Feb 2005 08:33:07 AM |
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George Jones <george_llew_jones@yahoo.com> wrote in
news:YrSdnWn2NLwUKoffRVn-3w@look.ca:
John Schutkeker wrote:
George Jones <george_llew_jones@yahoo.com> wrote in
news:sNednTuJmorldYrfRVn-rg@look.ca:
It was E^2 = m_0^2*c^4 + c^2*p^2 ...
Did you use the notation m_0 for historical accuracy?
I took 8.04 in '81. What are they calling m_0 these days?
m. In those days too.
I do recall a bi-stable state involving both symbols. I use m_0 for
clarity, because it tells you that it's the rest mass. It agrees with the
well known E=mc^2, in which m is *not* the rest mass.
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| User: "Franz Heymann" |
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| Title: Re: k-calculus |
25 Feb 2005 04:19:44 AM |
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"John Schutkeker" <jschutkeker@sbcglobal.net.nospam> wrote in message
news:Xns9607612F01D02lkajehoriuasldfjknak@151.164.30.42...
George Jones <george_llew_jones@yahoo.com> wrote in
news:YrSdnWn2NLwUKoffRVn-3w@look.ca:
John Schutkeker wrote:
George Jones <george_llew_jones@yahoo.com> wrote in
news:sNednTuJmorldYrfRVn-rg@look.ca:
It was E^2 = m_0^2*c^4 + c^2*p^2 ...
Did you use the notation m_0 for historical accuracy?
I took 8.04 in '81. What are they calling m_0 these days?
m. In those days too.
I do recall a bi-stable state involving both symbols. I use m_0 for
clarity, because it tells you that it's the rest mass. It agrees
with the
well known E=mc^2, in which m is *not* the rest mass.
It looks as if you are not familiar with Einstein's introduction of
that equation.
If you look it up, you will find that it refers quite specifically to
the *rest mass* of an object.
The subsequent extension is simply a definition of the now out of date
concept of "relativistic mass".
--
Franz
"The great tragedy of science -- the slaying of a beautiful hypothesis
by an ugly fact."
T.H. Huxley
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| User: "Ben Rudiak-Gould" |
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| Title: Re: k-calculus |
24 Feb 2005 04:20:53 PM |
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John Schutkeker wrote:
I use m_0 for clarity, because it tells you that it's the rest mass.
It agrees with the well known E=mc^2, in which m is *not* the rest mass.
This is incorrect. Einstein's original derivation applied to rest mass (more
precisely, to change in rest mass). Relativistic mass is *defined* as energy
divided by c^2, so E=mc^2 does apply to it, but that has no physical
significance.
-- Ben
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| User: "" |
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| Title: Re: k-calculus |
22 Feb 2005 12:51:35 AM |
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In article <Xns9604E6646DD71lkajehoriuasldfjknak@151.164.30.44>, John Schutkeker <jschutkeker@sbcglobal.net.nospam> writes:
George Jones <george_llew_jones@yahoo.com> wrote in
news:sNednTuJmorldYrfRVn-rg@look.ca:
It was E^2 = m_0^2*c^4 - c^2*p^2 ...
Did you use the notation m_0 for historical accuracy?
I took 8.04 in '81. What are they calling m_0 these days?
m
Mati Meron | "When you argue with a fool,
meron@cars.uchicago.edu | chances are he is doing just the same"
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