| Topic: |
Science > Physics |
| User: |
"Peter Christensen" |
| Date: |
29 Apr 2006 05:56:31 AM |
| Object: |
How to 'derive' the LT ? |
I know, that the Lorentz Transform (LT) is introduced by Einstein in
relativity, and that the transformation is obviously invented by Lorentz.
That's not what I mean, when I ask where the transformation is actually
'coming from'. I don't have a copy of the 1905 paper about SR at the moment.
Is it introduced 'just' as a solution to the problems with the light, or is
it possible to get to the Lorentz Transform by a series of arguments. I mean
the physics in Einsteins two postulates and so on. I can't find the answer
in the Physics FAQ, the LT is just presented as a known fact.
I would like to argue, that the transformation between two systems must be
the Lorentz Transform, because of Einsteins postulates and so on. It's
difficult to
explain what I mean in words, without equations and diagrams in this
text-only-format. I've been drawing some diagrams with object paths pictured
in (x,t) and (x',t') diagrams. (like this t' and x' projection on t and x:
http://www.peterchristensen.eu/phys/LT-filer/image009.gif I used here
s=c*t)
I would like to argue, that the angle between x' and x must be the same as
the angle between t and t'. Then I can argue, that t': x=v*t and x': t=x/c.
From this, one can again argue, that t' = gamma*(t-v*x/c^2) and x' =
gamma*(x-v*t) is the solution, where gamma is so far an unknown constant
depending of v.
If L(v) is the matrix for the LT, and L^-1(v) is the transformation back
again to (t,x), then gamma can be determined like this: It's assumed, that
there is no scaling in the transformation, only a rotation. The determinant
of both L(v) and L^-1(v) must therefore be equal to one. From this, gamma(v)
can in both cases be found to be gamma(v)=1/sqrt(1-(v/c)^2)
From assuming that:
1) The angle between x and x' is the same as the angle between t' and t,
where the latter is determined from: tan(phi)=v/c. So that t': x=v*t and
x': t=x/c.
2) The LT is a rotation only. This means, that the determinant for the LT's
is
equal to one, and that gamma(v) can be determined.
It appears, that the LT can be derived from physical arguments, if
these two assumptions can be derived from physical arguments, and the
geometry on these (x,t)-diagrams. Usually the LT is just assumed to be
valid. I don't have any text about relativity, where the LT is derived from
physics and physical assumptions. Why not?
PC
________________
PeCh@MailAPS.org
.
|
|
| User: "Bill Hobba" |
|
| Title: Re: How to 'derive' the LT ? |
29 Apr 2006 06:34:27 PM |
|
|
"Peter Christensen" <PeCh@MailAPS.org> wrote in message
news:44534661$0$15795$14726298@news.sunsite.dk...
I know, that the Lorentz Transform (LT) is introduced by Einstein in
relativity, and that the transformation is obviously invented by Lorentz.
That's not what I mean, when I ask where the transformation is actually
'coming from'. I don't have a copy of the 1905 paper about SR at the
moment.
Is it introduced 'just' as a solution to the problems with the light, or
is
it possible to get to the Lorentz Transform by a series of arguments. I
mean
the physics in Einsteins two postulates and so on. I can't find the answer
in the Physics FAQ, the LT is just presented as a known fact.
I would like to argue, that the transformation between two systems must be
the Lorentz Transform, because of Einsteins postulates and so on. It's
difficult to
explain what I mean in words, without equations and diagrams in this
text-only-format. I've been drawing some diagrams with object paths
pictured
in (x,t) and (x',t') diagrams. (like this t' and x' projection on t and x:
http://www.peterchristensen.eu/phys/LT-filer/image009.gif I used here
s=c*t)
I would like to argue, that the angle between x' and x must be the same as
the angle between t and t'. Then I can argue, that t': x=v*t and x':
t=x/c.
From this, one can again argue, that t' = gamma*(t-v*x/c^2) and x' =
gamma*(x-v*t) is the solution, where gamma is so far an unknown constant
depending of v.
If L(v) is the matrix for the LT, and L^-1(v) is the transformation back
again to (t,x), then gamma can be determined like this: It's assumed, that
there is no scaling in the transformation, only a rotation. The
determinant
of both L(v) and L^-1(v) must therefore be equal to one. From this,
gamma(v)
can in both cases be found to be gamma(v)=1/sqrt(1-(v/c)^2)
From assuming that:
1) The angle between x and x' is the same as the angle between t' and t,
where the latter is determined from: tan(phi)=v/c. So that t': x=v*t and
x': t=x/c.
2) The LT is a rotation only. This means, that the determinant for the
LT's is
equal to one, and that gamma(v) can be determined.
It appears, that the LT can be derived from physical arguments,
It really 'needs' only one postulate - the POR - the speed of light thing
simply fixes a constant that naturally occurs in the theory. Other
'postulates' are strictly speaking required like rulers and clocks have no
memory and inertial frames are isotropic and homogeneous in space and
homogeneous in time (if that was not part of your definition of an inertial
frame to begin with) but it is fairly obvious they are sort of like the
assumption of continuity and differentiability we usually require of most
mathematical models - sure you have to assume them but they are not the key
ones. For three separate derivations see:
http://arxiv.org/abs/physics/0110076,
and ancient, but I still think excellent post by Tom Roberts
http://groups.google.com/groups?hl=en&lr=&c2coff=1&selm=54jfst%24glp%40ssbunews.ih.lucent.com
and chapter 10 of
http://www.courses.fas.harvard.edu/~phys16/Textbook/
It is very interesting to note that the constant c in the lorentz
transformations must be finite if charge is locally conserved - see the
following under charge conservation.
http://www.upscale.utoronto.ca/GeneralInterest/DBailey/SubAtomic/Lectures/LectF13/Lect13.htm
This Hamiltonian can be used to derive the Lorentz force law:
http://galileo.phys.virginia.edu/classes/752.mf1i.spring03/ParticleMagField.htm
But this force law can only result for assuming a finite c:
http://www.cse.secs.oakland.edu/haskell/SpecialRelativity.htm
Thus the laws of QM, charge conservation, and the symmetries of the POR all
work together to pretty much determine the Lorentz transformations - which
his simply another example of at a fundamental level physics seems to be
about symmetries.
Post your email address and I can send you a paper that explains this view
in greater detail.
Thanks
Bill
these two assumptions can be derived from physical arguments, and the
geometry on these (x,t)-diagrams. Usually the LT is just assumed to be
valid. I don't have any text about relativity, where the LT is derived
from physics and physical assumptions. Why not?
PC
________________
PeCh@MailAPS.org
.
|
|
|
| User: "noshellswill" |
|
| Title: Re: How to 'derive' the LT ? |
29 Apr 2006 10:13:26 PM |
|
|
On Sat, 29 Apr 2006 23:34:27 +0000, Bill Hobba wrote:
"Peter Christensen" <PeCh@MailAPS.org> wrote in message
news:44534661$0$15795$14726298@news.sunsite.dk...
I know, that the Lorentz Transform (LT) is introduced by Einstein in
relativity, and that the transformation is obviously invented by Lorentz.
That's not what I mean, when I ask where the transformation is actually
'coming from'. I don't have a copy of the 1905 paper about SR at the
moment.
Is it introduced 'just' as a solution to the problems with the light, or
is
it possible to get to the Lorentz Transform by a series of arguments. I
mean
the physics in Einsteins two postulates and so on. I can't find the answer
in the Physics FAQ, the LT is just presented as a known fact.
I would like to argue, that the transformation between two systems must be
the Lorentz Transform, because of Einsteins postulates and so on. It's
difficult to
explain what I mean in words, without equations and diagrams in this
text-only-format. I've been drawing some diagrams with object paths
pictured
in (x,t) and (x',t') diagrams. (like this t' and x' projection on t and x:
http://www.peterchristensen.eu/phys/LT-filer/image009.gif I used here
s=c*t)
I would like to argue, that the angle between x' and x must be the same as
the angle between t and t'. Then I can argue, that t': x=v*t and x':
t=x/c.
From this, one can again argue, that t' = gamma*(t-v*x/c^2) and x' =
gamma*(x-v*t) is the solution, where gamma is so far an unknown constant
depending of v.
If L(v) is the matrix for the LT, and L^-1(v) is the transformation back
again to (t,x), then gamma can be determined like this: It's assumed, that
there is no scaling in the transformation, only a rotation. The
determinant
of both L(v) and L^-1(v) must therefore be equal to one. From this,
gamma(v)
can in both cases be found to be gamma(v)=1/sqrt(1-(v/c)^2)
From assuming that:
1) The angle between x and x' is the same as the angle between t' and t,
where the latter is determined from: tan(phi)=v/c. So that t': x=v*t and
x': t=x/c.
2) The LT is a rotation only. This means, that the determinant for the
LT's is
equal to one, and that gamma(v) can be determined.
It appears, that the LT can be derived from physical arguments,
It really 'needs' only one postulate - the POR - the speed of light thing
simply fixes a constant that naturally occurs in the theory. Other
'postulates' are strictly speaking required like rulers and clocks have no
memory and inertial frames are isotropic and homogeneous in space and
homogeneous in time (if that was not part of your definition of an inertial
frame to begin with) but it is fairly obvious they are sort of like the
assumption of continuity and differentiability we usually require of most
mathematical models - sure you have to assume them but they are not the key
ones. For three separate derivations see:
http://arxiv.org/abs/physics/0110076,
and ancient, but I still think excellent post by Tom Roberts
http://groups.google.com/groups?hl=en&lr=&c2coff=1&selm=54jfst%24glp%40ssbunews.ih.lucent.com
and chapter 10 of
http://www.courses.fas.harvard.edu/~phys16/Textbook/
It is very interesting to note that the constant c in the lorentz
transformations must be finite if charge is locally conserved - see the
following under charge conservation.
http://www.upscale.utoronto.ca/GeneralInterest/DBailey/SubAtomic/Lectures/LectF13/Lect13.htm
This Hamiltonian can be used to derive the Lorentz force law:
http://galileo.phys.virginia.edu/classes/752.mf1i.spring03/ParticleMagField.htm
But this force law can only result for assuming a finite c:
http://www.cse.secs.oakland.edu/haskell/SpecialRelativity.htm
Thus the laws of QM, charge conservation, and the symmetries of the POR all
work together to pretty much determine the Lorentz transformations - which
his simply another example of at a fundamental level physics seems to be
about symmetries.
Post your email address and I can send you a paper that explains this view
in greater detail.
Thanks
Bill
these two assumptions can be derived from physical arguments, and the
geometry on these (x,t)-diagrams. Usually the LT is just assumed to be
valid. I don't have any text about relativity, where the LT is derived
from physics and physical assumptions. Why not?
PC
________________
PeCh@MailAPS.org
BH:
ohmeohmy .....
Your post reference -- that by T. Roberts deriving the LT -- is IMHO
sufficient to create LT skeptics of most modestly skeptical individuals.
Not to argue the truth of the matter .... rather, Roberts 4 postulates
are on-their-face far from obvious. He say ... believe them. In the same
spirit I might say '... up is special, cause if I fall off a ladder I
hurt' ... or similar foolishness.
Surely referencing a negative experiment, such as Trouton-Noble makes a
stronger case for the required mischief.
nss
*************
.
|
|
|
| User: "Bill Hobba" |
|
| Title: Re: How to 'derive' the LT ? |
29 Apr 2006 11:14:08 PM |
|
|
"noshellswill" <noshellswill@hotmail.com> wrote in message
news:pan.2006.04.30.03.13.24.324697@hotmail.com...
On Sat, 29 Apr 2006 23:34:27 +0000, Bill Hobba wrote:
"Peter Christensen" <PeCh@MailAPS.org> wrote in message
news:44534661$0$15795$14726298@news.sunsite.dk...
I know, that the Lorentz Transform (LT) is introduced by Einstein in
relativity, and that the transformation is obviously invented by
Lorentz.
That's not what I mean, when I ask where the transformation is actually
'coming from'. I don't have a copy of the 1905 paper about SR at the
moment.
Is it introduced 'just' as a solution to the problems with the light, or
is
it possible to get to the Lorentz Transform by a series of arguments. I
mean
the physics in Einsteins two postulates and so on. I can't find the
answer
in the Physics FAQ, the LT is just presented as a known fact.
I would like to argue, that the transformation between two systems must
be
the Lorentz Transform, because of Einsteins postulates and so on. It's
difficult to
explain what I mean in words, without equations and diagrams in this
text-only-format. I've been drawing some diagrams with object paths
pictured
in (x,t) and (x',t') diagrams. (like this t' and x' projection on t and
x:
http://www.peterchristensen.eu/phys/LT-filer/image009.gif I used here
s=c*t)
I would like to argue, that the angle between x' and x must be the same
as
the angle between t and t'. Then I can argue, that t': x=v*t and x':
t=x/c.
From this, one can again argue, that t' = gamma*(t-v*x/c^2) and x' =
gamma*(x-v*t) is the solution, where gamma is so far an unknown constant
depending of v.
If L(v) is the matrix for the LT, and L^-1(v) is the transformation back
again to (t,x), then gamma can be determined like this: It's assumed,
that
there is no scaling in the transformation, only a rotation. The
determinant
of both L(v) and L^-1(v) must therefore be equal to one. From this,
gamma(v)
can in both cases be found to be gamma(v)=1/sqrt(1-(v/c)^2)
From assuming that:
1) The angle between x and x' is the same as the angle between t' and t,
where the latter is determined from: tan(phi)=v/c. So that t': x=v*t and
x': t=x/c.
2) The LT is a rotation only. This means, that the determinant for the
LT's is
equal to one, and that gamma(v) can be determined.
It appears, that the LT can be derived from physical arguments,
It really 'needs' only one postulate - the POR - the speed of light thing
simply fixes a constant that naturally occurs in the theory. Other
'postulates' are strictly speaking required like rulers and clocks have
no
memory and inertial frames are isotropic and homogeneous in space and
homogeneous in time (if that was not part of your definition of an
inertial
frame to begin with) but it is fairly obvious they are sort of like the
assumption of continuity and differentiability we usually require of most
mathematical models - sure you have to assume them but they are not the
key
ones. For three separate derivations see:
http://arxiv.org/abs/physics/0110076,
and ancient, but I still think excellent post by Tom Roberts
http://groups.google.com/groups?hl=en&lr=&c2coff=1&selm=54jfst%24glp%40ssbunews.ih.lucent.com
and chapter 10 of
http://www.courses.fas.harvard.edu/~phys16/Textbook/
It is very interesting to note that the constant c in the lorentz
transformations must be finite if charge is locally conserved - see the
following under charge conservation.
http://www.upscale.utoronto.ca/GeneralInterest/DBailey/SubAtomic/Lectures/LectF13/Lect13.htm
This Hamiltonian can be used to derive the Lorentz force law:
http://galileo.phys.virginia.edu/classes/752.mf1i.spring03/ParticleMagField.htm
But this force law can only result for assuming a finite c:
http://www.cse.secs.oakland.edu/haskell/SpecialRelativity.htm
Thus the laws of QM, charge conservation, and the symmetries of the POR
all
work together to pretty much determine the Lorentz transformations -
which
his simply another example of at a fundamental level physics seems to be
about symmetries.
Post your email address and I can send you a paper that explains this
view
in greater detail.
Thanks
Bill
these two assumptions can be derived from physical arguments, and the
geometry on these (x,t)-diagrams. Usually the LT is just assumed to be
valid. I don't have any text about relativity, where the LT is derived
from physics and physical assumptions. Why not?
PC
________________
PeCh@MailAPS.org
BH:
ohmeohmy .....
Your post reference -- that by T. Roberts deriving the LT -- is IMHO
sufficient to create LT skeptics of most modestly skeptical individuals.
It is rather good and much admired around here.
Not to argue the truth of the matter .... rather, Roberts 4 postulates
are on-their-face far from obvious.
Hmmmmmmm. To me they are all very 'obvious'. But what is obvious to one
may not be to another.
He say ... believe them. In the same
spirit I might say '... up is special, cause if I fall off a ladder I
hurt' ... or similar foolishness.
Surely referencing a negative experiment, such as Trouton-Noble makes a
stronger case for the required mischief.
Physics is an experimental science. Every assumption - it does not matter
how 'obvious' - requires experimental support. So in a sense your view it
is not obvious and my view it is are both redundant - experiment is the
final arbiter. And in its domain of applicability (inertial frames) SR has
yet to find experimental refutation. But I do urge you to think about the
POR - I suspect once you have thought out the issues it too will seem
'obvious'.
Thanks
Bill
nss
*************
.
|
|
|
| User: "brian a m stuckless" |
|
| Title: Re: How to 'derive' the LT ? |
30 Apr 2006 08:00:27 AM |
|
|
$$ Bill Hobba wrote -=-
Physics is an experimental science.
Every assumption - it does not matter how 'obvious' -
requires experimental support.
-=-
And in its domain of applicability (inertial frames)
SR has yet to find experimental refutation.
-=-
Thanks > Bill > > > > > nss > > ************* > > > >
$$ Note "iNERTiAL" means (..is a synonym for), "REST";
$$ And, in a REST FRAME (as SR has distinguished contrary to Newton)
$$ ..of M1, M1 has no THEORETiCAL acceleration towards m1,
$$
$$ ..where (the OPPOSiTE radial vectors of ) m1*v1 = M1*v.
$$
$$ [EVEN THOUGH the THEORETiCAL acceleration M1*v is SMALL].
$$ [EVEN if the EXPERiMENTAL acceleration M1*v, negligible].
$$ The GR-"equations" ARiTHMETiCALLY eliminate Newton's M1*v.
$$ The GR-"equations" *SYSTEMiCALLY* eliminate Newton's M1*v.
$$ <snicker>
$$ This is WHY the *SR* (synonym) "iNERTiAL" replaced "REST".
$$ This is WHY the *SR* (synonym) "iNTRiNSiC" ..means "REST".
$$ Also, OPPOSiTE central RADiAL VECTORs have the SAME sign.
$$ [An OUT-going vector is (+) ..iN-coming vectors are (-)].
$$ Note EQUAL radial vectors areN'T PARALLEL, anyway.
$$ Go-go NETSCAPE news < alt.sci.nanotech >< WHY m1*v1=M1*v >.
.
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| User: "Hexenmeister" |
|
| Title: Re: How to 'derive' the LT ? |
29 Apr 2006 08:24:14 AM |
|
|
"Peter Christensen" <PeCh@MailAPS.org> wrote in message
news:44534661$0$15795$14726298@news.sunsite.dk...
|I know, that the Lorentz Transform (LT) is introduced by Einstein in
| relativity, and that the transformation is obviously invented by Lorentz.
| That's not what I mean, when I ask where the transformation is actually
| 'coming from'. I don't have a copy of the 1905 paper about SR at the
moment.
Not a problem.
For the derivation see a worked example using Einstein's technique,
including diagrams.
http://tinyurl.com/euevp
Androcles
.
|
|
|
|
| User: "Dirk Van de moortel" |
|
| Title: Re: How to 'derive' the LT ? |
29 Apr 2006 07:01:01 AM |
|
|
"Peter Christensen" <PeCh@MailAPS.org> wrote in message news:44534661$0$15795$14726298@news.sunsite.dk...
I know, that the Lorentz Transform (LT) is introduced by Einstein in
relativity, and that the transformation is obviously invented by Lorentz.
That's not what I mean, when I ask where the transformation is actually
'coming from'. I don't have a copy of the 1905 paper about SR at the moment.
You have one now:
http://www.fourmilab.ch/etexts/einstein/specrel/www/
Is it introduced 'just' as a solution to the problems with the light, or is
it possible to get to the Lorentz Transform by a series of arguments. I mean
the physics in Einsteins two postulates and so on. I can't find the answer
in the Physics FAQ, the LT is just presented as a known fact.
Section 14.9 (Appendix I) of
<http://www.courses.fas.harvard.edu/~phys16/Textbook/ch14_appendices.pdf>
combined with section 10.8 of
<http://www.courses.fas.harvard.edu/~phys16/Textbook/ch10.pdf>
Dirk Vdm
.
|
|
|
| User: "Peter Christensen" |
|
| Title: Re: How to 'derive' the LT ? |
08 May 2006 05:05:47 AM |
|
|
"Dirk Van de moortel" <dirkvandemoortel@ThankS-NO-SperM.hotmail.com> skrev i
en meddelelse news:1AI4g.397699$YO.11307163@phobos.telenet-ops.be...
"Peter Christensen" <PeCh@MailAPS.org> wrote in message
news:44534661$0$15795$14726298@news.sunsite.dk...
I know, that the Lorentz Transform (LT) is introduced by Einstein in
relativity, and that the transformation is obviously invented by Lorentz.
That's not what I mean, when I ask where the transformation is actually
'coming from'. I don't have a copy of the 1905 paper about SR at the
moment.
You have one now:
http://www.fourmilab.ch/etexts/einstein/specrel/www/
Now I've read the first half of it, and I noted one thing: Einstein use the
factor phi(v) in fromt of gamma, and then 'shows' that it is simply one. But
from phi(v)*phi(-v)=1 and phi(v)=phi(-v), he can only conclude that phi(v)^2
= 1, which means that phi(v) equals 1 or -1. The physics of this, is just
that a system SigmaŽ can also be defined with the axes x' and t' pointing
the 'other direction' compared with the usual LT. -But Einstein seems to
just frow this detail away, simply by 'forgetting' it...
Is it introduced 'just' as a solution to the problems with the light, or
is
it possible to get to the Lorentz Transform by a series of arguments. I
mean
the physics in Einsteins two postulates and so on. I can't find the
answer
in the Physics FAQ, the LT is just presented as a known fact.
Section 14.9 (Appendix I) of
<http://www.courses.fas.harvard.edu/~phys16/Textbook/ch14_appendices.pdf>
combined with section 10.8 of
<http://www.courses.fas.harvard.edu/~phys16/Textbook/ch10.pdf>
The problem with the x' and s' pointing the 'wrong way' is mentioned here,
and the solution with phi(v)=-1 is neglected.
This textbook looked quite good, and I easily foud it all at
http://www.courses.fas.harvard.edu/~phys16/Textbook/ (recommended).
Thanks to Dirk Vdm for this one...
PC
.
|
|
|
| User: "Dirk Van de moortel" |
|
| Title: Re: How to 'derive' the LT ? |
08 May 2006 11:05:18 AM |
|
|
"Peter Christensen" <PeCh@MailAPS.org> wrote in message news:445f17fa$0$15793$14726298@news.sunsite.dk...
"Dirk Van de moortel" <dirkvandemoortel@ThankS-NO-SperM.hotmail.com> skrev i
en meddelelse news:1AI4g.397699$YO.11307163@phobos.telenet-ops.be...
"Peter Christensen" <PeCh@MailAPS.org> wrote in message
news:44534661$0$15795$14726298@news.sunsite.dk...
I know, that the Lorentz Transform (LT) is introduced by Einstein in
relativity, and that the transformation is obviously invented by Lorentz.
That's not what I mean, when I ask where the transformation is actually
'coming from'. I don't have a copy of the 1905 paper about SR at the
moment.
You have one now:
http://www.fourmilab.ch/etexts/einstein/specrel/www/
Now I've read the first half of it, and I noted one thing: Einstein use the
factor phi(v) in fromt of gamma, and then 'shows' that it is simply one. But
from phi(v)*phi(-v)=1 and phi(v)=phi(-v), he can only conclude that phi(v)^2
= 1, which means that phi(v) equals 1 or -1. The physics of this, is just
that a system SigmaŽ can also be defined with the axes x' and t' pointing
the 'other direction' compared with the usual LT. -But Einstein seems to
just frow this detail away, simply by 'forgetting' it...
Yes, 'forgetting', or just ignoring because of the obvious fact that
the -1 factor would result in times running in different directions:
Suppose you take for instance
t' = - gamma ( t - v x/c^2 )
and consider a clock at rest in the unprimed frame (i.e. a fixed
place with Dx = 0). You would then get
Dt' = - gamma Dt
meaning that the clock runs backwards in the primed frame.
It just amounts to our convention to have our dials run clockwise.
I'd say there's no need to even mention it in this context.
Is it introduced 'just' as a solution to the problems with the light, or
is
it possible to get to the Lorentz Transform by a series of arguments. I
mean
the physics in Einsteins two postulates and so on. I can't find the
answer
in the Physics FAQ, the LT is just presented as a known fact.
Section 14.9 (Appendix I) of
<http://www.courses.fas.harvard.edu/~phys16/Textbook/ch14_appendices.pdf>
combined with section 10.8 of
<http://www.courses.fas.harvard.edu/~phys16/Textbook/ch10.pdf>
The problem with the x' and s' pointing the 'wrong way' is mentioned here,
and the solution with phi(v)=-1 is neglected.
For a similar reason as the one I just outlined.
This textbook looked quite good, and I easily foud it all at
http://www.courses.fas.harvard.edu/~phys16/Textbook/ (recommended).
Yes, *highly* recommended textbook from the very first to the
very last page. Extremely carefully and brilliantly written.
Try the preceding chapters as well!
Dirk Vdm
Thanks to Dirk Vdm for this one...
PC
.
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|
| User: "Peter Christensen" |
|
| Title: Re: How to 'derive' the LT ? |
06 May 2006 04:00:08 AM |
|
|
"Dirk Van de moortel" <dirkvandemoortel@ThankS-NO-SperM.hotmail.com> skrev i
en meddelelse news:1AI4g.397699$YO.11307163@phobos.telenet-ops.be...
"Peter Christensen" <PeCh@MailAPS.org> wrote in message
news:44534661$0$15795$14726298@news.sunsite.dk...
I know, that the Lorentz Transform (LT) is introduced by Einstein in
relativity, and that the transformation is obviously invented by Lorentz.
That's not what I mean, when I ask where the transformation is actually
'coming from'. I don't have a copy of the 1905 paper about SR at the
moment.
You have one now:
http://www.fourmilab.ch/etexts/einstein/specrel/www/
Thanks, i didn't know that it was on the web. I will read this one...
Is it introduced 'just' as a solution to the problems with the light, or
is
it possible to get to the Lorentz Transform by a series of arguments. I
mean
the physics in Einsteins two postulates and so on. I can't find the
answer
in the Physics FAQ, the LT is just presented as a known fact.
Section 14.9 (Appendix I) of
<http://www.courses.fas.harvard.edu/~phys16/Textbook/ch14_appendices.pdf>
combined with section 10.8 of
<http://www.courses.fas.harvard.edu/~phys16/Textbook/ch10.pdf>
Ok, I will spend the day reading phys texts instead of writing to the
physics groups on Usenet. -The worst thing about learning something new, is
that one might feel stupid when looking at ones old postings. But if this is
an indication of learning something new, then it's probably really ok.
PC
_____________________________________________
PeCh@MailAPS.org / Skype: PeterJChristensen
Physical arguments & plain geometry -> LT :
www.PeterChristensen.eu/phys/LT.htm
(Under construction, only constructive comments, please)
.
|
|
|
| User: "Hexenmeister" |
|
| Title: Re: How to 'derive' the LT ? |
06 May 2006 04:39:35 AM |
|
|
"Peter Christensen" <PeCh@MailAPS.org> wrote in message
news:445c6597$0$15787$14726298@news.sunsite.dk...
|
| "Dirk Van de moortel" <dirkvandemoortel@ThankS-NO-SperM.hotmail.com> skrev
i
| en meddelelse news:1AI4g.397699$YO.11307163@phobos.telenet-ops.be...
| >
| > "Peter Christensen" <PeCh@MailAPS.org> wrote in message
| > news:44534661$0$15795$14726298@news.sunsite.dk...
| >> I know, that the Lorentz Transform (LT) is introduced by Einstein in
| >> relativity, and that the transformation is obviously invented by
Lorentz.
| >> That's not what I mean, when I ask where the transformation is actually
| >> 'coming from'. I don't have a copy of the 1905 paper about SR at the
| >> moment.
| >
| > You have one now:
| > http://www.fourmilab.ch/etexts/einstein/specrel/www/
|
| Thanks, i didn't know that it was on the web. I will read this one...
"an observer approaching a source of light with the velocity c,
this source of light must appear of infinite intensity." - IFC Einstein
"Thence we conclude that a balance-clock at the equator must go
more slowly, by a very small amount, than a precisely similar clock
situated at one of the poles under otherwise identical conditions." - IFC
Einstein
"the velocity of light in our theory plays the part, physically, of an
infinitely great velocity."- IFC Einstein
http://www.fourmilab.ch/etexts/einstein/specrel/www/figures/img155.gif
-- IFC Einstein
These are all clues to division by zero and only the clueless would
believe them. Dork is one of the clueless.
The actual zero may be found in
"In agreement with experience we further assume the quantity
http://www.fourmilab.ch/etexts/einstein/specrel/www/figures/img7.gif
to be a universal constant--the velocity of light in empty space."
Notice that the light goes from A to A' (A' = A) in time (t'A-tA), so c =
0/0
and the "constant" velocity c reverses direction.
All quotations are the exact words of First Class Idiot Einstein, from
http://www.fourmilab.ch/etexts/einstein/specrel/www/
Androcles.
.
|
|
|
|
| User: "Euclid Uranium" |
|
| Title: Re: How to 'derive' the LT ? |
10 May 2006 06:04:47 AM |
|
|
"Peter Christensen" <PeCh@MailAPS.org> wrote:
Ok, I will spend the day reading phys texts instead of writing to the
physics groups on Usenet. -The worst thing about learning something new, is
that one might feel stupid when looking at ones old postings. But if this is
an indication of learning something new, then it's probably really ok.
PC
_____________________________________________
If no to p, thus, I have The Landmark river Press IRIN News
Menomonie Dunn County Journal Newburgh Chandler life in The
theoretic formulas of a huff puff of learning aid to Reach mph:
and I'm a full faced with sticks was running water and dx m V
of choice, can make Planck Institut Spatiale IAS, Orsay France
Holos Ukrainy Ukraine the path length unit! Um time and it is
that later she proceeded on usenet, Newsgroup. Those wrong Pd
tried to think material and mass. But they piled on Wednesday,
Journal RSS new Physics that , as around into mid she forges
towards a numerical example (infinite). Lol so to heart bled as
such huge error of it isn't. You went straight line they then
they worked out and then some sort of gravitation The same
position wanders off to Venture: think that support For them
both of gold as far more: than . The image of our description I
would appear in this.
Jake d crire cela sur La Terre. Htm the Faq and improving the
mortgage backed changed that. You backsliding animal accuracy
required r says there's gravity over. Since they see a proxy
in bodies, suffer a small, Trading group is parameters but then
you, whether the doubt; the z independent Colorado Springs
village psychopath.
When you can only if you'll see our support your chosen for
example omnisceince leads to end the talent.
.
|
|
|
|
|
| User: "eleaticus" |
|
| Title: Re: How to 'derive' the LT ? |
29 Apr 2006 02:48:57 PM |
|
|
"Dirk Van de moortel" <dirkvandemoortel@ThankS-NO-SperM.hotmail.com> wrote
in message news:1AI4g.397699$YO.11307163@phobos.telenet-ops.be...
"Peter Christensen" <PeCh@MailAPS.org> wrote in message
news:44534661$0$15795$14726298@news.sunsite.dk...
I know, that the Lorentz Transform (LT) is introduced by Einstein in
relativity, and that the transformation is obviously invented by
Lorentz.
That's not what I mean, when I ask where the transformation is actually
'coming from'. I don't have a copy of the 1905 paper about SR at the
moment.
You have one now:
http://www.fourmilab.ch/etexts/einstein/specrel/www/
ROFFLMFAO! What a complete jackass cretin you are, Dork!
Explain to us the three values of the first argument of Albert's taus.
ROFFLMFAO!
Peter, demand that the idiot, Dork, and his co-cultists explain that first
argument.
eleaticus
ee-lee-AT-i-cus
.
|
|
|
| User: "Dirk Van de moortel" |
|
| Title: Re: How to 'derive' the LT ? |
29 Apr 2006 03:51:08 PM |
|
|
"eleaticus" <eleaticus@bellsouth.net> wrote in message news:nrP4g.22532$MM6.7227@bignews3.bellsouth.net...
"Dirk Van de moortel" <dirkvandemoortel@ThankS-NO-SperM.hotmail.com> wrote
in message news:1AI4g.397699$YO.11307163@phobos.telenet-ops.be...
"Peter Christensen" <PeCh@MailAPS.org> wrote in message
news:44534661$0$15795$14726298@news.sunsite.dk...
I know, that the Lorentz Transform (LT) is introduced by Einstein in
relativity, and that the transformation is obviously invented by
Lorentz.
That's not what I mean, when I ask where the transformation is actually
'coming from'. I don't have a copy of the 1905 paper about SR at the
moment.
You have one now:
http://www.fourmilab.ch/etexts/einstein/specrel/www/
ROFFLMFAO! What a complete jackass cretin you are, Dork!
Explain to us the three values of the first argument of Albert's taus.
ROFFLMFAO!
Peter, demand that the idiot, Dork, and his co-cultists explain that first
argument.
.... and explain the basics of analytic geometry that we got at
the age of 14 to Oren C. Webster aka Eleaticus:
http://users.telenet.be/vdmoortel/dirk/Physics/Fumbles/ImbecilePhysics.html
http://users.telenet.be/vdmoortel/dirk/Physics/Fumbles/Crimes.html
Dirk Vdm
.
|
|
|
| User: "Hexenmeister" |
|
| Title: Re: How to 'derive' the LT ? |
30 Apr 2006 06:24:41 AM |
|
|
"Dirk Van de moortel" <dirkvandemoortel@ThankS-NO-SperM.hotmail.com> wrote
in message news:0lQ4g.398357$rb1.11315252@phobos.telenet-ops.be...
|
| "eleaticus" <eleaticus@bellsouth.net> wrote in message
news:nrP4g.22532$MM6.7227@bignews3.bellsouth.net...
| >
| > "Dirk Van de moortel" <dirkvandemoortel@ThankS-NO-SperM.hotmail.com>
wrote
| > in message news:1AI4g.397699$YO.11307163@phobos.telenet-ops.be...
| > >
| > > "Peter Christensen" <PeCh@MailAPS.org> wrote in message
| > news:44534661$0$15795$14726298@news.sunsite.dk...
| > > > I know, that the Lorentz Transform (LT) is introduced by Einstein in
| > > > relativity, and that the transformation is obviously invented by
| > Lorentz.
| > > > That's not what I mean, when I ask where the transformation is
actually
| > > > 'coming from'. I don't have a copy of the 1905 paper about SR at the
| > moment.
| > >
| > > You have one now:
| > > http://www.fourmilab.ch/etexts/einstein/specrel/www/
| >
| > ROFFLMFAO! What a complete jackass cretin you are, Dork!
| >
| > Explain to us the three values of the first argument of Albert's taus.
| >
| > ROFFLMFAO!
| >
| > Peter, demand that the idiot, Dork, and his co-cultists explain that
first
| > argument.
|
| ... and explain the basics of analytic geometry that we got at
| the age of 14 to Oren C. Webster aka Eleaticus:
|
http://users.telenet.be/vdmoortel/dirk/Physics/Fumbles/ImbecilePhysics.html
| http://users.telenet.be/vdmoortel/dirk/Physics/Fumbles/Crimes.html
|
| Dirk Vdm
and explain the basics of analytic geometry that we got at
the age of 2 to Dirk Van de moortel,
aka Dork Van de merde,
aka Your Basic Moron,
aka local village psychopath:
http://www.androcles01.pwp.blueyonder.co.uk/Dork/classic.htm
http://www.androcles01.pwp.blueyonder.co.uk/Dork/closingspeed.htm
http://www.androcles01.pwp.blueyonder.co.uk/Dork/closingspeed2.htm
http://www.androcles01.pwp.blueyonder.co.uk/Dork/trojan.htm
http://www.androcles01.pwp.blueyonder.co.uk/Dork/human.htm
http://www.androcles01.pwp.blueyonder.co.uk/Dork/zeroone.htm
http://www.androcles01.pwp.blueyonder.co.uk/Dork/falsetrue.htm
http://www.androcles01.pwp.blueyonder.co.uk/Dork/sloppy.htm
http://www.androcles01.pwp.blueyonder.co.uk/Dork/badevents.htm
http://www.androcles01.pwp.blueyonder.co.uk/Dork/inertialacc.htm
http://www.androcles01.pwp.blueyonder.co.uk/Dork/insignificantgravity.htm
http://www.androcles01.pwp.blueyonder.co.uk/Dork/PartialDerivative.htm
http://www.androcles01.pwp.blueyonder.co.uk/Dork/mumble.htm
http://www.androcles01.pwp.blueyonder.co.uk/Dork/stooges.htm
http://www.androcles01.pwp.blueyonder.co.uk/Pigbin/troll.htm
http://www.androcles01.pwp.blueyonder.co.uk/Pigbin/insignificantgravity.htm
http://www.androcles01.pwp.blueyonder.co.uk/Pigbin/cantread.htm
http://www.androcles01.pwp.blueyonder.co.uk/Pigbin/inertialacc.htm
Androcles
.
|
|
|
|
|
|
| User: "Hexenmeister" |
|
| Title: Re: How to 'derive' the LT ? |
29 Apr 2006 10:55:16 AM |
|
|
"Dirk Van de moortel" <dirkvandemoortel@ThankS-NO-SperM.hotmail.com> wrote
in message news:1AI4g.397699$YO.11307163@phobos.telenet-ops.be...
|
| "Peter Christensen" <PeCh@MailAPS.org> wrote in message
news:44534661$0$15795$14726298@news.sunsite.dk...
| > I know, that the Lorentz Transform (LT) is introduced by Einstein in
| > relativity, and that the transformation is obviously invented by
Lorentz.
| > That's not what I mean, when I ask where the transformation is actually
| > 'coming from'. I don't have a copy of the 1905 paper about SR at the
moment.
|
| You have one now:
| http://www.fourmilab.ch/etexts/einstein/specrel/www/
You ought to read it then, instead of babbling about t' and x' as if
you had a clue what your are groaning about, local village psychopath.
Androcles.
.
|
|
|
| User: "Martin Hogbin" |
|
| Title: Re: How to 'derive' the LT ? |
29 Apr 2006 11:48:41 AM |
|
|
"Hexenmeister" <vanquish@broom.Mickey_c> wrote in message news:E%L4g.45245$tc.11043@fe2.news.blueyonder.co.uk...
"Dirk Van de moortel" <dirkvandemoortel@ThankS-NO-SperM.hotmail.com> wrote
in message news:1AI4g.397699$YO.11307163@phobos.telenet-ops.be...
|
| "Peter Christensen" <PeCh@MailAPS.org> wrote in message
news:44534661$0$15795$14726298@news.sunsite.dk...
| > I know, that the Lorentz Transform (LT) is introduced by Einstein in
| > relativity, and that the transformation is obviously invented by
Lorentz.
| > That's not what I mean, when I ask where the transformation is actually
| > 'coming from'. I don't have a copy of the 1905 paper about SR at the
moment.
|
| You have one now:
| http://www.fourmilab.ch/etexts/einstein/specrel/www/
You ought to read it then, instead of babbling about t' and x' as if
you had a clue what your are groaning about, local village psychopath.
Just in case it is not obvious to you, Androcles is one
of the many crackpots on this group. Just ignore him.
Martin Hogbin
.
|
|
|
| User: "Hexenmeister" |
|
| Title: Re: How to 'derive' the LT ? |
29 Apr 2006 02:48:58 PM |
|
|
"Martin Hogbin" <goatREMOVETHIS123@hogbin.org> wrote in message
news:SeydnfQ1FopkBc7ZnZ2dnUVZ8qCdnZ2d@bt.com...
|
| "Hexenmeister" <vanquish@broom.Mickey_c> wrote in message
news:E%L4g.45245$tc.11043@fe2.news.blueyonder.co.uk...
| >
| > "Dirk Van de moortel" <dirkvandemoortel@ThankS-NO-SperM.hotmail.com>
wrote
| > in message news:1AI4g.397699$YO.11307163@phobos.telenet-ops.be...
| > |
| > | "Peter Christensen" <PeCh@MailAPS.org> wrote in message
| > news:44534661$0$15795$14726298@news.sunsite.dk...
| > | > I know, that the Lorentz Transform (LT) is introduced by Einstein in
| > | > relativity, and that the transformation is obviously invented by
| > Lorentz.
| > | > That's not what I mean, when I ask where the transformation is
actually
| > | > 'coming from'. I don't have a copy of the 1905 paper about SR at the
| > moment.
| > |
| > | You have one now:
| > | http://www.fourmilab.ch/etexts/einstein/specrel/www/
| >
| > You ought to read it then, instead of babbling about t' and x' as if
| > you had a clue what your are groaning about, local village psychopath.
|
| Just in case it is not obvious to you, Androcles is one
| of the many crackpots on this group. Just ignore him.
|
| Martin Hogbin
You are jealous because you can't read, Pigbin.
http://www.androcles01.pwp.blueyonder.co.uk/Pigbin/cantread.htm
http://www.androcles01.pwp.blueyonder.co.uk/Pigbin/insignificantgravity.htm
http://www.androcles01.pwp.blueyonder.co.uk/Pigbin/inertialacc.htm
http://www.androcles01.pwp.blueyonder.co.uk/Pigbin/troll.htm
Androcles
.
|
|
|
|
|
| User: "Dirk Van de moortel" |
|
| Title: Re: How to 'derive' the LT ? |
29 Apr 2006 12:47:15 PM |
|
|
"Hexenmeister" <vanquish@broom.Mickey_c> wrote in message news:E%L4g.45245$tc.11043@fe2.news.blueyonder.co.uk...
"Dirk Van de moortel" <dirkvandemoortel@ThankS-NO-SperM.hotmail.com> wrote
in message news:1AI4g.397699$YO.11307163@phobos.telenet-ops.be...
|
| "Peter Christensen" <PeCh@MailAPS.org> wrote in message
news:44534661$0$15795$14726298@news.sunsite.dk...
| > I know, that the Lorentz Transform (LT) is introduced by Einstein in
| > relativity, and that the transformation is obviously invented by
Lorentz.
| > That's not what I mean, when I ask where the transformation is actually
| > 'coming from'. I don't have a copy of the 1905 paper about SR at the
moment.
|
| You have one now:
| http://www.fourmilab.ch/etexts/einstein/specrel/www/
You ought to read it then, instead of babbling about t' and x' as if
you had a clue what your are groaning about, local village psychopath.
You shouldn't have read it.
It drove you insane:
http://users.telenet.be/vdmoortel/dirk/Physics/Fumbles/ClosingSpeed.html
.... which was nice :-)
Dirk Vdm
.
|
|
|
| User: "Hexenmeister" |
|
| Title: Re: How to 'derive' the LT ? |
29 Apr 2006 03:38:31 PM |
|
|
"Dirk Van de moortel" <dirkvandemoortel@ThankS-NO-SperM.hotmail.com> wrote
in message news:DEN4g.398128$_V3.11113511@phobos.telenet-ops.be...
|
| "Hexenmeister" <vanquish@broom.Mickey_c> wrote in message
news:E%L4g.45245$tc.11043@fe2.news.blueyonder.co.uk...
| >
| > "Dirk Van de moortel" <dirkvandemoortel@ThankS-NO-SperM.hotmail.com>
wrote
| > in message news:1AI4g.397699$YO.11307163@phobos.telenet-ops.be...
| > |
| > | "Peter Christensen" <PeCh@MailAPS.org> wrote in message
| > news:44534661$0$15795$14726298@news.sunsite.dk...
| > | > I know, that the Lorentz Transform (LT) is introduced by Einstein in
| > | > relativity, and that the transformation is obviously invented by
| > Lorentz.
| > | > That's not what I mean, when I ask where the transformation is
actually
| > | > 'coming from'. I don't have a copy of the 1905 paper about SR at the
| > moment.
| > |
| > | You have one now:
| > | http://www.fourmilab.ch/etexts/einstein/specrel/www/
| >
| > You ought to read it then, instead of babbling about t' and x' as if
| > you had a clue what your are groaning about, local village psychopath.
|
| You shouldn't have read it.
Why not? I like fiction, and your distortion of it is funny too.
__t'__ -- ahaha... HAHAHAHA... ahaha...
| It drove you insane:
| http://users.telenet.be/vdmoortel/dirk/Physics/Fumbles/ClosingSpeed.html
| ... which was nice :-)
Your insane fumble, local village psychopath.
Spread it around, anyone intelligent will have a good laugh.
"it is MERELY a rate of change of distance."--| Dirk Vdm
That was no Neanderthal gorilla, that was Dork Van de merde the psychopath.
Androcles.
.
|
|
|
|
|
|
|
| User: "Peter Christensen" |
|
| Title: Re: How to 'derive' the LT ? |
07 May 2006 12:20:19 PM |
|
|
From assuming that:
1) The angle between x and x' is the same as the angle between t' and t,
where the latter is determined from: tan(phi)=v/c. So that t': x=v*t and
x': t=x/c.
2) The LT is a rotation only. This means, that the determinant for the
LT's is equal to one, and that gamma(v) can be determined.
It appears, that the LT can be derived from physical arguments, if
these two assumptions can be derived from physical arguments, and the
geometry on these (x,t)-diagrams.
From above, I now think that 1) can be elliminated. Assuming a 'rotation
only', and unit vectors (length 1) for s' and x', should be enough. Please
see www.PeterChristensen.eu/phys/LT-filer/a.gif.
My page about it is still a draft, but if somebody would like to se it, it's
at www.PeterChristensen.eu/phys/LT.htm. (Under construction, only
constructive comments, please.) I think, that we can get all the way to the
LT by physical arguments and some simple geometry. Actually, I think, that a
'rotation only' assumption is also enough to get to the LT. I (now) know
about the LT, that I can also be derived from arguments about linearity and
from arguments about conservation of spacetime intervals (s^2 is the same in
both the (t,x)-system and the (t',x')-system.)
PC
_____________________________________________
PeCh@MailAPS.org / Skype: PeterJChristensen
Physical arguments & plain geometry -> LT :
www.PeterChristensen.eu/phys/LT.htm
(Under construction, only constructive comments, please)
.
|
|
|
| User: "eleaticus" |
|
| Title: Re: How to 'derive' the LT ? |
07 May 2006 06:11:06 PM |
|
|
"Peter Christensen" <PeCh@MailAPS.org> wrote in message
news:445e2c52$0$15792$14726298@news.sunsite.dk...
From assuming that:
1) The angle between x and x' is the same as the angle between t' and t,
where the latter is determined from: tan(phi)=v/c. So that t': x=v*t and
x': t=x/c.
2) The LT is a rotation only. This means, that the determinant for the
LT's is equal to one, and that gamma(v) can be determined.
It appears, that the LT can be derived from physical arguments, if
these two assumptions can be derived from physical arguments, and the
geometry on these (x,t)-diagrams.
From above, I now think that 1) can be elliminated. Assuming a 'rotation
only', and unit vectors (length 1) for s' and x', should be enough. Please
see www.PeterChristensen.eu/phys/LT-filer/a.gif.
My page about it is still a draft, but if somebody would like to se it,
it's
at www.PeterChristensen.eu/phys/LT.htm. (Under construction, only
constructive comments, please.) I think, that we can get all the way to
the
LT by physical arguments and some simple geometry. Actually, I think, that
a
'rotation only' assumption is also enough to get to the LT. I (now) know
about the LT, that I can also be derived from arguments about linearity
and
from arguments about conservation of spacetime intervals (s^2 is the same
in
both the (t,x)-system and the (t',x')-system.)
You don't recognize that your assumptions are inplicit in the conclusions?
You are exercising circular reasoning. It is your conclusion that you use as
premise.
eleaticus
ee-lee-AT-i-cus
PC
_____________________________________________
PeCh@MailAPS.org / Skype: PeterJChristensen
Physical arguments & plain geometry -> LT :
www.PeterChristensen.eu/phys/LT.htm
(Under construction, only constructive comments, please)
.
|
|
|
| User: "Peter Christensen" |
|
| Title: Re: How to 'derive' the LT ? |
08 May 2006 01:20:06 PM |
|
|
"eleaticus" <eleaticus@bellsouth.net> skrev i en meddelelse
news:w8v7g.62445$Jk3.58935@bignews5.bellsouth.net...
"Peter Christensen" <PeCh@MailAPS.org> wrote in message
news:445e2c52$0$15792$14726298@news.sunsite.dk...
From assuming that:
1) The angle between x and x' is the same as the angle between t' and
t,
where the latter is determined from: tan(phi)=v/c. So that t': x=v*t
and
x': t=x/c.
2) The LT is a rotation only. This means, that the determinant for the
LT's is equal to one, and that gamma(v) can be determined.
It appears, that the LT can be derived from physical arguments, if
these two assumptions can be derived from physical arguments, and the
geometry on these (x,t)-diagrams.
From above, I now think that 1) can be elliminated. Assuming a 'rotation
only', and unit vectors (length 1) for s' and x', should be enough.
Please
see www.PeterChristensen.eu/phys/LT-filer/a.gif.
My page about it is still a draft, but if somebody would like to se it,
it's
at www.PeterChristensen.eu/phys/LT.htm. (Under construction, only
constructive comments, please.) I think, that we can get all the way to
the
LT by physical arguments and some simple geometry. Actually, I think,
that
a
'rotation only' assumption is also enough to get to the LT. I (now) know
about the LT, that I can also be derived from arguments about linearity
and
from arguments about conservation of spacetime intervals (s^2 is the same
in
both the (t,x)-system and the (t',x')-system.)
I don't think, that I do this mistake, even though I understand what you
mean. I see, that the LT is often derived as following from eighter the
'linearity of space' or the 'spacetime intervals'. However these assumptions
are not really physical, and I would really like to do without them, if I
should like to argue for the LT in my own way...
You don't recognize that your assumptions are inplicit in the conclusions?
You are exercising circular reasoning. It is your conclusion that you use
as
premise.
As I said, I would like to awoid all 'physical' assumptions, and then argue
for the LT anyway. But I haven't seen a 'derivation' of the LT, that doesn't
depend on eighter the 'linearity of space' or the 'concervation of spacetime
intervals' (s). Even though, I think, that these assumptions are quite
mathematical rather than physical, I don't think that they are wrong just
because of that.
After all, it's called the 'theory of relativity' even these days, when
quite some of the proponents would probably like the 'law of relativity'
better? - Do you understand what I mean by this? -It's just the fact that
the light from a moving object is emitted/absorbed from an object with the
velocity c (compared to an inertial frame), no matter what the velocity of
this object is. Maybe we could also speculate about these things until we
would all be completely insane, without ever reaching a single point of
interest. But if you've ever tried to solve the 'relativity problem' for a
particle in your favorite absolute space, you will at least see that there
is an important problem: Light appears to be emitted/absorbed with the speed
c, no matter what the speed of the inertial frame is.
It's strange, really strange, and we can't solve the problem at all in an
absolute frame. For the frame of interest, the light is emitted with respect
to the frame, rather than the speed of the object. It can really look
strange, I agree. But today we KNOW, that the speed of light can be
measured, compared to all emissions/absorbtions of the relevant object. The
speed of light is simply c, in all known cases. -There is nothing to do
about it, it's just an experimental result: When we take a physical object,
and let it absorb/emit light, it will always happen with the 'speed of
light' c, when seen in the relevant 'inertial frame' of this object. -Maybe
for other frames, things might appear to be different. But our laws of
physics apply in the inertial frame, and not in any other frames, and that's
the point.
I will not try to make a long discussion even longer, so I hope, that you
'c' what I mean... But it's probably just an old discussion going over and
over again...
Einstein knew it, Einstein understood it, and Einstein tried to explain this
to others. -But nobody understood this very charming old fellow,
unfortunately...
eleaticus
ee-lee-AT-i-cus
PC
_____________________________________________
PeCh@MailAPS.org / Skype: PeterJChristensen
Physical arguments & plain geometry -> LT :
www.PeterChristensen.eu/phys/LT.htm
(Under construction, only constructive comments, please)
.
|
|
|
| User: "Timo A. Nieminen" |
|
| Title: Re: How to 'derive' the LT ? |
08 May 2006 03:08:40 PM |
|
|
On Mon, 8 May 2006, Peter Christensen wrote:
"Peter Christensen" <PeCh@MailAPS.org> wrote:
I (now) know
about the LT, that I can also be derived from arguments about linearity
and
from arguments about conservation of spacetime intervals (s^2 is the same
in
both the (t,x)-system and the (t',x')-system.)
I don't think, that I do this mistake, even though I understand what you
mean. I see, that the LT is often derived as following from eighter the
'linearity of space' or the 'spacetime intervals'. However these assumptions
are not really physical, and I would really like to do without them, if I
should like to argue for the LT in my own way...
If we have physical quantities that can be described by 4-vectors, then
the sum of 2 4-vectors
c = a + b
must give the same result in all coordinate systems. That's the physical
argument for linearity of the LT.
The "spacetime interval" assumption can be replaced by further assumptions
about 4-vectors. Basically, that the "angle" between any 2 4-vectors, and
the magnitude of any 4-vector, are independent of the choice of coordinate
system. Easily done by requiring a.b to be independent of choice of
coordinate system.
Both assumptions are made in Newtonian mechanics, with a 3D Euclidean
space, and nobody complains about them there.
--
Timo Nieminen - Home page: http://www.physics.uq.edu.au/people/nieminen/
E-prints: http://eprint.uq.edu.au/view/person/Nieminen,_Timo_A..html
Shrine to Spirits: http://www.users.bigpond.com/timo_nieminen/spirits.html
.
|
|
|
| User: "Hexenmeister" |
|
| Title: Re: How to 'derive' the LT ? |
08 May 2006 10:52:20 PM |
|
|
"Timo A. Nieminen" <timo@physics.uq.edu.au> wrote in message
news:Pine.WNT.4.64.0605090602130.552@serene.st...
| If we have physical quantities that can be described by 4-vectors, then
| the sum of 2 4-vectors
|
| c = a + b
|
| must give the same result in all coordinate systems. That's the physical
| argument for linearity of the LT.
Time is not a vector. That's the physical argument against the linearity of
the LT.
Androcles
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|
| User: "Hexenmeister" |
|
| Title: Re: How to 'derive' the LT ? |
07 May 2006 03:27:26 PM |
|
|
"Peter Christensen" <PeCh@MailAPS.org> wrote in message
news:445e2c52$0$15792$14726298@news.sunsite.dk...
| My page about it is still a draft, but if somebody would like to se it,
it's
| at www.PeterChristensen.eu/phys/LT.htm. (Under construction, only
| constructive comments, please.)
Constructively, get a spelling checker. "Absorption", not absorbtion,
although
it absorbs.
For physics/math content, destruction is all I can offer.
Your page ignores basic principles. Like Einstein, you want to build
castles in the air but have used playing cards. Pull the bottom one out
and the whole house collapses. We don't need an introduction to the LTs,
there are no LTs. You are chasing ghosts.
http://www.androcles01.pwp.blueyonder.co.uk/Smart/Smart.htm
Androcles.
.
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|
| User: "Spoonfed" |
|
| Title: Re: How to 'derive' the LT ? |
07 May 2006 09:31:14 PM |
|
|
Peter Christensen wrote:
From assuming that:
1) The angle between x and x' is the same as the angle between t' and t,
where the latter is determined from: tan(phi)=v/c. So that t': x=v*t and
x': t=x/c.
2) The LT is a rotation only. This means, that the determinant for the
LT's is equal to one, and that gamma(v) can be determined.
It appears, that the LT can be derived from physical arguments, if
these two assumptions can be derived from physical arguments, and the
geometry on these (x,t)-diagrams.
From above, I now think that 1) can be elliminated. Assuming a 'rotation
only', and unit vectors (length 1) for s' and x', should be enough. Please
see www.PeterChristensen.eu/phys/LT-filer/a.gif.
My page about it is still a draft, but if somebody would like to se it, it's
at www.PeterChristensen.eu/phys/LT.htm. (Under construction, only
constructive comments, please.) I think, that we can get all the way to the
LT by physical arguments and some simple geometry. Actually, I think, that a
'rotation only' assumption is also enough to get to the LT. I (now) know
about the LT, that I can also be derived from arguments about linearity and
from arguments about conservation of spacetime intervals (s^2 is the same in
both the (t,x)-system and the (t',x')-system.)
PC
_____________________________________________
PeCh@MailAPS.org / Skype: PeterJChristensen
Physical arguments & plain geometry -> LT :
www.PeterChristensen.eu/phys/LT.htm
(Under construction, only constructive comments, please)
If you're going to stress that it is "Only a rotation" could you at
least say "Only a hyperbolic rotation?" Isn't that the terminology
that made you draw x' and t' perpendicular in the first place? The
idea that LT is "Just a rotation" seems misleading.
Second, in all your diagrams, you have drawn only one ray of light in
one direction. Instead, draw two rays of light going in opposite
directions.
Thirdly, your statement:
1: The angle between x and x' (j) is the same as the angle between
t' and t. It must be like this, if the speed of light from the object
should be equal to c. The knowledge of these angles is enough to argue
for s' = g (s - a*x) and x' = g (x - a*s).
Your main argument here is that it "must be." By drawing the light ray
in the opposite direction, you can SHOW that along that plane of
simultaneity the light rays are equidistant from ray x'. So you could
change that "must be" to an "I have here shown"
Finally, your statement:
2: A rotation is assumed. Just a rotation. This means, that the
transformation does not 'scale' the units on the axes. From this,
it follows, that the determinant for both the LT and LT^-1 should be
equal to 1. Using the expressions from Fig. 9 (below), makes it
possible to derive the factor g. In both cases it gives the result g =
1/sqrt(1-a^2), where a = v/c is used.
It makes me cringe. PLEASE don't say "Just a rotation" This
definition of a rotation is a matrix with determinant 1 may be familiar
to you but in most people's minds, rotations don't distort the object
being rotated. By that definition our affine stretch was a rotation,
the Galilean transformation is a rotation. Once you encompass all
transformations with determinant one into a single category and name
them rotation... Well, let's just put it this way--it's not even
wrong.
If you must use the term rotation, at least say "Just a hyperbolic
rotation." If you're avoiding using that term because it isn't
familiar to laypeople, it will misinform them more to leave it out.
.
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|
| User: "Golden Boar" |
|
| Title: Re: How to 'derive' the LT ? |
29 Apr 2006 07:20:44 PM |
|
|
Peter Christensen wrote:
I know, that the Lorentz Transform (LT) is introduced by Einstein in
relativity, and that the transformation is obviously invented by Lorentz.
That's not what I mean, when I ask where the transformation is actually
'coming from'. I don't have a copy of the 1905 paper about SR at the moment.
Is it introduced 'just' as a solution to the problems with the light, or is
it possible to get to the Lorentz Transform by a series of arguments. I mean
the physics in Einsteins two postulates and so on. I can't find the answer
in the Physics FAQ, the LT is just presented as a known fact.
I would like to argue, that the transformation between two systems must be
the Lorentz Transform, because of Einsteins postulates and so on. It's
difficult to
explain what I mean in words, without equations and diagrams in this
text-only-format. I've been drawing some diagrams with object paths pictured
in (x,t) and (x',t') diagrams. (like this t' and x' projection on t and x:
http://www.peterchristensen.eu/phys/LT-filer/image009.gif I used here
s=c*t)
I would like to argue, that the angle between x' and x must be the same as
the angle between t and t'. Then I can argue, that t': x=v*t and x': t=x/c.
From this, one can again argue, that t' = gamma*(t-v*x/c^2) and x' =
gamma*(x-v*t) is the solution, where gamma is so far an unknown constant
depending of v.
If L(v) is the matrix for the LT, and L^-1(v) is the transformation back
again to (t,x), then gamma can be determined like this: It's assumed, that
there is no scaling in the transformation, only a rotation. The determinant
of both L(v) and L^-1(v) must therefore be equal to one. From this, gamma(v)
can in both cases be found to be gamma(v)=1/sqrt(1-(v/c)^2)
From assuming that:
1) The angle between x and x' is the same as the angle between t' and t,
where the latter is determined from: tan(phi)=v/c. So that t': x=v*t and
x': t=x/c.
2) The LT is a rotation only. This means, that the determinant for the LT's
is
equal to one, and that gamma(v) can be determined.
It appears, that the LT can be derived from physical arguments, if
these two assumptions can be derived from physical arguments, and the
geometry on these (x,t)-diagrams. Usually the LT is just assumed to be
valid. I don't have any text about relativity, where the LT is derived from
physics and physical assumptions. Why not?
PC
________________
PeCh@MailAPS.org
I don't know if this will help, but this is how I derived the Lorentz
factor.
http://groups.google.co.uk/group/sci.physics.particle/browse_frm/thread/5d1072ae0c885b6b/?hl=en#
.
|
|
|
| User: "Hexenmeister" |
|
| Title: Re: How to 'derive' the LT ? |
30 Apr 2006 06:24:41 AM |
|
|
"Golden Boar" <goldenboar@hotmail.com> wrote in message
news:1146356444.710672.6980@j73g2000cwa.googlegroups.com...
|
| Peter Christensen wrote:
| > I know, that the Lorentz Transform (LT) is introduced by Einstein in
| > relativity, and that the transformation is obviously invented by
Lorentz.
| > That's not what I mean, when I ask where the transformation is actually
| > 'coming from'. I don't have a copy of the 1905 paper about SR at the
moment.
[snip]
| I don't know if this will help, but this is how I derived the Lorentz
| factor.
|
|
http://groups.google.co.uk/group/sci.physics.particle/browse_frm/thread/5d1072ae0c885b6b/?hl=en#
derive
One entry found for derive.
Main Entry: derive
Pronunciation: di-'rIv, dE-
Function: verb
Inflected Form(s): de·rived; de·riv·ing
Etymology: Middle English, from Middle French deriver, from Latin
derivare, literally, to draw off (water), from de- + rivus stream -- more at
RUN
transitive senses
1 a : to take, receive, or obtain especially from a specified source b
: to obtain (a chemical substance) actually or theoretically from a parent
substance
2 : INFER, DEDUCE
3 archaic : BRING
4 : to trace the derivation of
intransitive senses : to have or take origin : come as a derivative
http://www.m-w.com/dictionary/derive
How did you INFER, DEDUCE it, Boor?
Here is how it is done:
http://www.androcles01.pwp.blueyonder.co.uk/Smart/Smart.htm
Androcles.
.
|
|
|
|
|
| User: "" |
|
| Title: Re: How to 'derive' the LT ? |
29 Apr 2006 08:00:53 PM |
|
|
Peter Christensen wrote:
I know, that the Lorentz Transform (LT) is introduced by Einstein in
relativity, and that the transformation is obviously invented by Lorentz.
That's not what I mean, when I ask where the transformation is actually
'coming from'. I don't have a copy of the 1905 paper about SR at the moment.
Is it introduced 'just' as a solution to the problems with the light, or is
it possible to get to the Lorentz Transform by a series of arguments. I mean
the physics in Einsteins two postulates and so on. I can't find the answer
in the Physics FAQ, the LT is just presented as a known fact.
I would like to argue, that the transformation between two systems must be
the Lorentz Transform, because of Einsteins postulates and so on. It's
difficult to
explain what I mean in words, without equations and diagrams in this
text-only-format. I've been drawing some diagrams with object paths pictured
in (x,t) and (x',t') diagrams. (like this t' and x' projection on t and x:
http://www.peterchristensen.eu/phys/LT-filer/image009.gif I used here
s=c*t)
I would like to argue, that the angle between x' and x must be the same as
the angle between t and t'. Then I can argue, that t': x=v*t and x': t=x/c.
From this, one can again argue, that t' = gamma*(t-v*x/c^2) and x' =
gamma*(x-v*t) is the solution, where gamma is so far an unknown constant
depending of v.
If L(v) is the matrix for the LT, and L^-1(v) is the transformation back
again to (t,x), then gamma can be determined like this: It's assumed, that
there is no scaling in the transformation, only a rotation. The determinant
of both L(v) and L^-1(v) must therefore be equal to one. From this, gamma(v)
can in both cases be found to be gamma(v)=1/sqrt(1-(v/c)^2)
From assuming that:
1) The angle between x and x' is the same as the angle between t' and t,
where the latter is determined from: tan(phi)=v/c. So that t': x=v*t and
x': t=x/c.
2) The LT is a rotation only. This means, that the determinant for the LT's
is
equal to one, and that gamma(v) can be determined.
It appears, that the LT can be derived from physical arguments, if
these two assumptions can be derived from physical arguments, and the
geometry on these (x,t)-diagrams. Usually the LT is just assumed to be
valid. I don't have any text about relativity, where the LT is derived from
physics and physical assumptions. Why not?
PC
________________
PeCh@MailAPS.org
xxein: Bruce, then Tom, have nut-shelled it pretty close. But there
are still outstanding considerations
Both (and the majority of physics) assume that TWLS = OWLS.
Observation (direct experiment) can only support a TWLS measurement.
It does not consider OWLS. But Lorentz did!
I noticed your use of "angle". The Lorentz transform has no use of
angle as you intend to use it. Angle is a purely mathematical usage -
it is a shortcut math expression - and it has almost no direct bearing
on space and time except for simple momentum (the caveman obvious).
The Lorentz transform is a "SR" scenario. It does not include gravity,
nor did it intend to. It basically ignored any gravity because that
was not its purposeful statement. Besides, Lorentz had no clue as to
what gravity IS - just as we we have no clue now.
If Lorentz had thought a little deeper he could have noticed that
gravity (in the form of circular orbits) provides an extended way of
substantiating OWLS. There are relations that exist that can be
described by velocities (notably the relation between escape velocity
and orbit velocity) that give hint to both gravity and OWLS.
But it seems that the recipe most science-minded people prefer is the
diamond-studded Einsteinian theory of things. No more thinking of
basics --- just make it work according to Einstein. The relationship
between escape velocity and orbit velocity has become a purely
shortened math version that can only support TWLS.
There is nothing wrong with OWLS. Lorentz described it! The math
exists but it has been foreshortened by Einstein and his popular theory
and does not represent it anymore.
*You can look at it this way. I didn't know beans about relativity. I
was interested and read about it. It didn't seem 'kosher'. I read
another book that was not Einsteinian and it made more (physical?)
logical sense.
As I contemplated the second book (as with the Einsteinian one), I had
a choice. Either understand the logic or not. I, like everyone else,
chose to put effort into the Einsteinian (why not!).
OK, I lied. I tried to understand the Einsteinain, first --- and then
I read the other one. One more omission. I knew about Einstein and
didn't comprehend it into logic.
So there I was seeking a logic to this universe. Since Einstein didn't
deliver it, I chose to go along the lines of the 'second' book. From
there, logic made me construct a "SR" that was uniquely different. I
LATER FOUND OUT THAT IT WAS LORENTZIAN.
The point of this is that you can construct the Lorentz transform
completely from logic without Einstein.
From there, questions that remain unanswered, are solved by logical
means instead of mathematical means. The understanding is built upon
logic rather than mathematics. After all, math did not create this
universe. Neither did a logic. But a logic is necessary to make a
mathematical description. Logic comes first.
.
|
|
|
|
| User: "Spoonfed" |
|
| Title: Re: How to 'derive' the LT ? |
30 Apr 2006 09:21:43 AM |
|
|
Peter Christensen wrote:
I would like to argue, that the transformation between two systems must be
the Lorentz Transform, because of Einsteins postulates and so on. It's
difficult to
explain what I mean in words, without equations and diagrams in this
text-only-format. I've been drawing some diagrams with object paths pictured
in (x,t) and (x',t') diagrams. (like this t' and x' projection on t and x:
http://www.peterchristensen.eu/phys/LT-filer/image009.gif I used here
s=c*t)
I would like to argue, that the angle between x' and x must be the same as
the angle between t and t'. Then I can argue, that t': x=v*t and x': t=x/c.
From this, one can again argue, that t' = gamma*(t-v*x/c^2) and x' =
gamma*(x-v*t) is the solution, where gamma is so far an unknown constant
depending of v.
Draw a line back in the direction of -x' and place an event somewhere
along it which produces a light cone.
Draw the light cone as two forty-five degree lines upward.
Note the two locations where s' crosses the light cone are equidistant
from the vector x'. These are simultaneous events in x' frame.
The points on the cone must be equidistant from vector x' at all
"times". (I put times in quotations because at all times, the points
on the cone are equidistant from vector x.)
In order to construct a line such that the the points on the cone are
equidistant from vector x', you can determine with a little bit of
trigonometry that the angle between x' and x must be the same as the
angle between t and t'.
In this construction it is important that the light cone has its origin
along vector x'--i.e. it is a collision event to the observer moving
along x'. Although once you've done this construction and resolved
what happens to this cone, it can be enlightening to use the
transformation to see what happens to noncollision events.
.
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