Please have a critical look at the lines below:
The simplest derivation of the Lorentz transformation simplified: J.M.Levy "A simple derivation of the Lorentz transformation and of the accompanying velocity and acceleration changes," Am.J.Phys 35,615 (2007) arXiv:physics/0603103 revisited.[1]
Levy [1} presents a derivation of the Lorentz transformation (LT) conisdering that it is the simplest one. It is based on the knowledge of the lenght contraction formula
L=L(0)sqrt(1-VxV/cxc) (1)
obtained by considering the light clock from its rest frame and from a reference frame relative to which it moves with constant speed V (L(0) represents the proper lenght of a rod measured measured by an observer relative to whom it is in a state of rest. L representing its distorted length measured by an observer relative to whom it moves with speed V in the direction of the rod.) The derivation is based on the fact that expressing the length of the rod as the sum of the lengths of its components then all the lengths should be measured in the same inertial reference frame.
The single change we make in Levy's approach is to consider that proper length and distorted length are related by
L=f(V)L(0) (2)
where f(V) is an unknown function of the speed of the rod and not of the proper length (to a given rod of proper length L(0) corresponds a single distorted length L.
As in [1] the involved inertial reference frames are K and K' in the standard arrangement. K' moves with speed V in the positive direction of the overlapped OX(O'X') axes. Consider the events M(x,t) detected from K and M'(x',t') detected from K'. The two events take place at the same point in space when the clocks C(x) and C'(x',0) located at that read t and t' respectively. By definition M(x,t) and M'(x',t') represent the same event. All the clocks at rest in K and all the clocks in K' are synchronized following a synchronization procedure proposed by Einstein, respectively.
Consider the relative positions of K and K' as detected from K when the clocks of that frame read t. At that very time the distance between the origins of the frames is Vt, the distance Dx=x-0 being a proper length. The proper length Dx'=x'-0, measured by observers from K is f(V)Dx'=f(V)(x'-0). Adding only lengths measured by observers from K we obtain
Dx=Vt+v(V)dx'. (3)
Considering the relative positions of K and K' as detected from K' when the clocks of that frame read t'. then the distance between the origins O and O' is VDt', Dx'=x-0 is a proper length whereas the length Dx=x-0 measured by observers of K' is f(V)Dx. Adding only lengths measured by observers from K' we obtain
Dx'=f(V)Dx-VDt' (4)
Consider that observers from K and K' measure the speed of a light signal that propagates in the positive direction of the overlapped axes. In accordance with the second postulate they obtain
Dx/Dt=Dx'/Dt'=c (5)
and so we can present (3) as
f(V)cDt'=(c-V)Dt (6)
and (4) as
f(V)cDt=(c+V)Dt'. (7)
Combining (6) and (7) we obtain
f(V)=sqrt(1-VxV/cc) (8)
We have derived so far the Lorentz transformations for the space coordinates of the same event (3)
x'-0=[(x-0)-V(t-0)]/f(V) (9)
and (4)
x-0=[(x'-0)+V(t'-0)]/f(V) (10)
Dividing both sides of (9) and (10) by c and taking into account (5) we obtain the LT for the time coordinates of the same event
t-0=[t'-0)+V(x'-0)/cc]/f(V) (11)
and
t'-0=[(t-0)-V(x-0)/cc]/f(V). (12)
I invite all the participants on the forum to express oppinions about the facts presented above helping to elucidate if the LT could be derived without length contraction or time dilation.
Thanks
I prefer to derive by thought, and then convert the outcome into equations.
That way the understanding comes first.
http://www.outersecrets.com/real/forum_againstum2.htm
But don't forget to get your deriving license first.
That way the understanding comes first.
http://www.outersecrets.com/real/forum_againstum2.htm
But don't forget to get your deriving license first.
Hi Lisa, Farsight (et al?),
Levy's original is here http://arxiv.org/ftp/arxiv/papers/0707/0707.2338.pdf
Can't find the Am.J.Phys physics article .. subscription? Do we need it?
There may be a short delay while I actually read Levy's paper.
Best wishes - C2.
Levy's original is here http://arxiv.org/ftp/arxiv/papers/0707/0707.2338.pdf
Can't find the Am.J.Phys physics article .. subscription? Do we need it?
There may be a short delay while I actually read Levy's paper.
Best wishes - C2.
Hi Liza,
Humble apologies .. that wasn't the link I thought it was (I tried
) Please PM me if I can host a diagram (or whatever) to repair the situation.
Your opening post looks 'stand-alone' .. do we need anything else?
Knowing little myself .. my impression is we are asked whether we can know f(V) without making any further assumptions .. if assumptions required then what/why/how do we assume what we assume?
Best wishes - C2.
Humble apologies .. that wasn't the link I thought it was (I tried
) Please PM me if I can host a diagram (or whatever) to repair the situation. Your opening post looks 'stand-alone' .. do we need anything else?
Knowing little myself .. my impression is we are asked whether we can know f(V) without making any further assumptions .. if assumptions required then what/why/how do we assume what we assume?
Best wishes - C2.
QUOTE (liza+Sep 4 2007, 09:19 AM)
if the LT could be derived without length contraction or time dilation.
It was done 102 years ago by Einstein in his seminal paper. You must have forgotten.
Specifically, Einstein assumed:
A ) The Principle of Relativity -- no result in physics depends on an absolute velocity
B ) Maxwell's equations and astronomical observations agree that a "stationary" observer measures the speed of light from a moving source to be the same as that from a non-moving source, c.
From these two assumptions Einstein (1905a,1905b) derived
1) The Lorentz Transforms, which themselves contain:
1a) Length Contraction
1b) Time Dilation
2) Einsteinian kinematics, where p = m v / sqrt(1 - v^2/c^2), E = m c^2 / sqrt(1 - v^2/c^2
3) The Einstein velocity addition formula
Later (1908) Minkowski showed that algebraically this was the same as saying space and time were not separate things, which is how all physicists work today. Both Length contraction and time dilation arise from treating space and time as separate things with separate meanings, which is the Newtonian and intuitionist view. In Minkowski space-time, these are trivial (boring!) projection effects.
--
If you assume some things that Newton strongly believed
1) The Principle of Relativity 2) The Isotropy of space, 3) Positional invariance in space, 4) Temporal invariance in time, then one number from one measurement from one experiment is enough to believe in time dilation and length contraction even though it's a question about neither length nor time.
Here I do it, using the result of an 1859 measurement:
My post: Newtonian kinematics versus SR was settled in 1859
But according to http://arxiv.org/abs/0708.0929 people have shown this to be true with various degrees of rigor since at least 1910.
W. A. von Ignatowsky, “Einige allgemeine Bemerkungen zum Relativitatsprinzip,” Phys. Z. 11, 972-976 (1910).
A ) The Principle of Relativity -- no result in physics depends on an absolute velocity
B ) Maxwell's equations and astronomical observations agree that a "stationary" observer measures the speed of light from a moving source to be the same as that from a non-moving source, c.
From these two assumptions Einstein (1905a,1905b) derived
1) The Lorentz Transforms, which themselves contain:
1a) Length Contraction
1b) Time Dilation
2) Einsteinian kinematics, where p = m v / sqrt(1 - v^2/c^2), E = m c^2 / sqrt(1 - v^2/c^2
3) The Einstein velocity addition formula
Later (1908) Minkowski showed that algebraically this was the same as saying space and time were not separate things, which is how all physicists work today. Both Length contraction and time dilation arise from treating space and time as separate things with separate meanings, which is the Newtonian and intuitionist view. In Minkowski space-time, these are trivial (boring!) projection effects.
--
If you assume some things that Newton strongly believed
1) The Principle of Relativity 2) The Isotropy of space, 3) Positional invariance in space, 4) Temporal invariance in time, then one number from one measurement from one experiment is enough to believe in time dilation and length contraction even though it's a question about neither length nor time.
Here I do it, using the result of an 1859 measurement:
My post: Newtonian kinematics versus SR was settled in 1859
But according to http://arxiv.org/abs/0708.0929 people have shown this to be true with various degrees of rigor since at least 1910.
W. A. von Ignatowsky, “Einige allgemeine Bemerkungen zum Relativitatsprinzip,” Phys. Z. 11, 972-976 (1910).
rpenner
how could calcule the inverse and direct lorentz transformations.the clocks and ruler by inverse function obtained by dingle would change the time dilatation by the
shrunking of the time and the rulers,would suffer the distension.then the hermitian
matrix multiplied by it inverse,is non-unitary.then the spacetime are ramifications
of disticts spacetime continuos.
then.i think what that there are oppositely,reverse time dilatation and
space contractions is stretched.then the time dilatation is equivalent to the backward in spacetime,as antiparticles,that are two curvatures of spacetime originated by two opposed directions,with changes of velocities,with breaks of symmetries(that are the change of the acceleration direction vector,without altere the magnitude).then the increasement of speeds,does the time,dilate,and
decreasement of the speeds,does stretch the time.then the change of the orientation of opposed directions to motions of the spaceships does cancell the
effect of time dilatation and inversely by consequence the space contraction(that is
the stretched space)
how could calcule the inverse and direct lorentz transformations.the clocks and ruler by inverse function obtained by dingle would change the time dilatation by the
shrunking of the time and the rulers,would suffer the distension.then the hermitian
matrix multiplied by it inverse,is non-unitary.then the spacetime are ramifications
of disticts spacetime continuos.
then.i think what that there are oppositely,reverse time dilatation and
space contractions is stretched.then the time dilatation is equivalent to the backward in spacetime,as antiparticles,that are two curvatures of spacetime originated by two opposed directions,with changes of velocities,with breaks of symmetries(that are the change of the acceleration direction vector,without altere the magnitude).then the increasement of speeds,does the time,dilate,and
decreasement of the speeds,does stretch the time.then the change of the orientation of opposed directions to motions of the spaceships does cancell the
effect of time dilatation and inversely by consequence the space contraction(that is
the stretched space)
Since rpenner provided kindly enough the Einsteinien Kinematics as >
p=mv/sqrt(1 - (v^2/c^2) ), E=Mc^2/sqrt(1 - (v^2/c^2) )
and mentioning the time dilation and Lorentz Contraction, i shall provide the equation for both subjects as >
Length Contraction - l'=l*sqrt(1 - (v^2/c^2) )
and the Time Dilation - t'=t/sqrt(1 - (v^2/c^2) )
NeoNo.1
p=mv/sqrt(1 - (v^2/c^2) ), E=Mc^2/sqrt(1 - (v^2/c^2) )
and mentioning the time dilation and Lorentz Contraction, i shall provide the equation for both subjects as >
Length Contraction - l'=l*sqrt(1 - (v^2/c^2) )
and the Time Dilation - t'=t/sqrt(1 - (v^2/c^2) )
NeoNo.1
QUOTE (Dallas+Sep 5 2007, 08:56 PM)
It was done 102 years ago by Einstein in his seminal paper. You must have forgotten.
The problem is why did Levy repeat the problem?
The problem is why did Levy repeat the problem?
QUOTE (liza+Sep 6 2007, 02:47 AM)
The problem is why did Levy repeat the problem?
Are you sure it was published in Am.J.Phys ? I can see it here : http://arxiv.org/PS_cache/physics/pdf/0606/0606103v4.pdf , in the arxiv.
Either way, it appears to be a crank paper (there are many like this in arxiv), especially when it starts by claiming : "To go straight to the heart of the argument we first derive the Lorentz transforms from length contraction(!)".
As usually, mr. Levy got it backwards (see also rpenner's post), the length contraction is a consequence of the Lorentz transforms, not the other way around.
On further investigation, "dr" Joseph Levy turned up to be a well known loon, with quite a few "papers" published in the loon journal Apeiron. See a sample of his papers here. You can safely ignore his "work".
Are you sure it was published in Am.J.Phys ? I can see it here : http://arxiv.org/PS_cache/physics/pdf/0606/0606103v4.pdf , in the arxiv.
Either way, it appears to be a crank paper (there are many like this in arxiv), especially when it starts by claiming : "To go straight to the heart of the argument we first derive the Lorentz transforms from length contraction(!)".
As usually, mr. Levy got it backwards (see also rpenner's post), the length contraction is a consequence of the Lorentz transforms, not the other way around.
On further investigation, "dr" Joseph Levy turned up to be a well known loon, with quite a few "papers" published in the loon journal Apeiron. See a sample of his papers here. You can safely ignore his "work".
The paper was retitled (to be less boastful) and published.
American Journal of Physics 75, 7 (2007) 615-618
Also, you should always link to arxiv.org like this, not just to the PDF. arxiv lets authors revise their preprints, and in addition to getting the newest version of the paper for free, there is useful meta-data like citation history and raw TeX files.
http://arxiv.org/abs/physics/0606103
http://arxiv.org/abs/physics/0702191
American Journal of Physics 75, 7 (2007) 615-618
Also, you should always link to arxiv.org like this, not just to the PDF. arxiv lets authors revise their preprints, and in addition to getting the newest version of the paper for free, there is useful meta-data like citation history and raw TeX files.
http://arxiv.org/abs/physics/0606103
http://arxiv.org/abs/physics/0702191
QUOTE (rpenner+Sep 5 2007, 09:44 PM)
Specifically, Einstein assumed:
A ) The Principle of Relativity -- no result in physics depends on an absolute velocity
B ) Maxwell's equations and astronomical observations agree that a "stationary" observer measures the speed of light from a moving source to be the same as that from a non-moving source, c.
From these two assumptions Einstein (1905a,1905b) derived
1) The Lorentz Transforms, which themselves contain:
1a) Length Contraction
1b) Time Dilation
2) Einsteinian kinematics, where p = m v / sqrt(1 - v^2/c^2), E = m c^2 / sqrt(1 - v^2/c^2
3) The Einstein velocity addition formula
Later (1908) Minkowski showed that algebraically this was the same as saying space and time were not separate things, which is how all physicists work today. Both Length contraction and time dilation arise from treating space and time as separate things with separate meanings, which is the Newtonian and intuitionist view. In Minkowski space-time, these are trivial (boring!) projection effects.
--
If you assume some things that Newton strongly believed
1) The Principle of Relativity 2) The Isotropy of space, 3) Positional invariance in space, 4) Temporal invariance in time, then one number from one measurement from one experiment is enough to believe in time dilation and length contraction even though it's a question about neither length nor time.
Here I do it, using the result of an 1859 measurement:
My post: Newtonian kinematics versus SR was settled in 1859
But according to http://arxiv.org/abs/0708.0929 people have shown this to be true with various degrees of rigor since at least 1910.
W. A. von Ignatowsky, “Einige allgemeine Bemerkungen zum Relativitatsprinzip,” Phys. Z. 11, 972-976 (1910).
Thanks for your help
Peres starting with the two postulates derive without using the LT the forumulas which account for the rdar echo, doppler effect, time dilation, aberration of light.He considers that using the LT in order to derive them we obscure the ohysics behind them. Using one of the formulas mentioned above, or without using them we can derive the LT. What is wrong in that? De gustibus nihil disputandum. I think it is the learner who should decide.
Asher Peres "Relativistic Telemetry" Am.J.Phys. 56 516 1987
A ) The Principle of Relativity -- no result in physics depends on an absolute velocity
B ) Maxwell's equations and astronomical observations agree that a "stationary" observer measures the speed of light from a moving source to be the same as that from a non-moving source, c.
From these two assumptions Einstein (1905a,1905b) derived
1) The Lorentz Transforms, which themselves contain:
1a) Length Contraction
1b) Time Dilation
2) Einsteinian kinematics, where p = m v / sqrt(1 - v^2/c^2), E = m c^2 / sqrt(1 - v^2/c^2
3) The Einstein velocity addition formula
Later (1908) Minkowski showed that algebraically this was the same as saying space and time were not separate things, which is how all physicists work today. Both Length contraction and time dilation arise from treating space and time as separate things with separate meanings, which is the Newtonian and intuitionist view. In Minkowski space-time, these are trivial (boring!) projection effects.
--
If you assume some things that Newton strongly believed
1) The Principle of Relativity 2) The Isotropy of space, 3) Positional invariance in space, 4) Temporal invariance in time, then one number from one measurement from one experiment is enough to believe in time dilation and length contraction even though it's a question about neither length nor time.
Here I do it, using the result of an 1859 measurement:
My post: Newtonian kinematics versus SR was settled in 1859
But according to http://arxiv.org/abs/0708.0929 people have shown this to be true with various degrees of rigor since at least 1910.
W. A. von Ignatowsky, “Einige allgemeine Bemerkungen zum Relativitatsprinzip,” Phys. Z. 11, 972-976 (1910).
Thanks for your help
Peres starting with the two postulates derive without using the LT the forumulas which account for the rdar echo, doppler effect, time dilation, aberration of light.He considers that using the LT in order to derive them we obscure the ohysics behind them. Using one of the formulas mentioned above, or without using them we can derive the LT. What is wrong in that? De gustibus nihil disputandum. I think it is the learner who should decide.
Asher Peres "Relativistic Telemetry" Am.J.Phys. 56 516 1987
QUOTE (mott.carl+Sep 5 2007, 10:07 PM)
rpenner
how could calcule the inverse and direct lorentz transformations.the clocks and ruler by inverse function obtained by dingle would change the time dilatation by the
shrunking of the time and the rulers,would suffer the distension.then the hermitian
matrix multiplied by it inverse,is non-unitary.then the spacetime are ramifications
of disticts spacetime continuos.
then.i think what that there are oppositely,reverse time dilatation and
space contractions is stretched.then the time dilatation is equivalent to the backward in spacetime,as antiparticles,that are two curvatures of spacetime originated by two opposed directions,with changes of velocities,with breaks of symmetries(that are the change of the acceleration direction vector,without altere the magnitude).then the increasement of speeds,does the time,dilate,and
decreasement of the speeds,does stretch the time.then the change of the orientation of opposed directions to motions of the spaceships does cancell the
effect of time dilatation and inversely by consequence the space contraction(that is
the stretched space)
Thanks for your help.
Conider the Lorentz transformations ready derived and present them as
xsqrt(1-VV/cc)=Vt'+x'
x'sqrt(1-VV/cc)=x-Vt
you obtain directly the results obtained by Levy, adding only lengths measured by observers of the same reference frame.
What I did is to show that it is not necessary to know start from the beginning if dilation or contraction takes place.
Is there something wrong in that?
how could calcule the inverse and direct lorentz transformations.the clocks and ruler by inverse function obtained by dingle would change the time dilatation by the
shrunking of the time and the rulers,would suffer the distension.then the hermitian
matrix multiplied by it inverse,is non-unitary.then the spacetime are ramifications
of disticts spacetime continuos.
then.i think what that there are oppositely,reverse time dilatation and
space contractions is stretched.then the time dilatation is equivalent to the backward in spacetime,as antiparticles,that are two curvatures of spacetime originated by two opposed directions,with changes of velocities,with breaks of symmetries(that are the change of the acceleration direction vector,without altere the magnitude).then the increasement of speeds,does the time,dilate,and
decreasement of the speeds,does stretch the time.then the change of the orientation of opposed directions to motions of the spaceships does cancell the
effect of time dilatation and inversely by consequence the space contraction(that is
the stretched space)
Thanks for your help.
Conider the Lorentz transformations ready derived and present them as
xsqrt(1-VV/cc)=Vt'+x'
x'sqrt(1-VV/cc)=x-Vt
you obtain directly the results obtained by Levy, adding only lengths measured by observers of the same reference frame.
What I did is to show that it is not necessary to know start from the beginning if dilation or contraction takes place.
Is there something wrong in that?
QUOTE (rpenner+Sep 6 2007, 06:26 AM)
The paper was retitled (to be less boastful) and published.
American Journal of Physics 75, 7 (2007) 615-618
Also, you should always link to arxiv.org like this, not just to the PDF. arxiv lets authors revise their preprints, and in addition to getting the newest version of the paper for free, there is useful meta-data like citation history and raw TeX files.
http://arxiv.org/abs/physics/0606103
http://arxiv.org/abs/physics/0702191
Thank you,
Am.J.Phys publishes a lot of garbage (no original research). They reached a new low with the Levy paper.
American Journal of Physics 75, 7 (2007) 615-618
Also, you should always link to arxiv.org like this, not just to the PDF. arxiv lets authors revise their preprints, and in addition to getting the newest version of the paper for free, there is useful meta-data like citation history and raw TeX files.
http://arxiv.org/abs/physics/0606103
http://arxiv.org/abs/physics/0702191
Thank you,
Am.J.Phys publishes a lot of garbage (no original research). They reached a new low with the Levy paper.
the proper time u',perceived by observer in spaceships with high speed,is equivalent to the proper timw u'* is seen as the clock be anticlock with the
time backward in time,but in higher dimensions there is the lose of spinors of
left-right handed;so exist not causal relations between the that called of "past" and"future".the reverse lorentz transformations couple to the antichrous lorentz
transformations does spacetime be dilatated or extended,depemdending whether
the intrinsic and extrinsic spacetime curves,are respectively hyperbolics and
elliptics.there a cancel the other.then spacetime are only variations depending
of the reference frames,if is going forward in time( increasing the speed of spaceships,advancing,and other when the spaceships is returning to the rest frame.then there is several pathways,going forward and coming backward,in the
geometric line;hyperbolic and other;elliptic.
time backward in time,but in higher dimensions there is the lose of spinors of
left-right handed;so exist not causal relations between the that called of "past" and"future".the reverse lorentz transformations couple to the antichrous lorentz
transformations does spacetime be dilatated or extended,depemdending whether
the intrinsic and extrinsic spacetime curves,are respectively hyperbolics and
elliptics.there a cancel the other.then spacetime are only variations depending
of the reference frames,if is going forward in time( increasing the speed of spaceships,advancing,and other when the spaceships is returning to the rest frame.then there is several pathways,going forward and coming backward,in the
geometric line;hyperbolic and other;elliptic.
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