Once Again: Relativity for Thought Experiments
Daryl McCullough
experiments involving relativity, we can describe the
claims of SR as the following:
There exists a coordinate system such that, as measured
using that coordinate system,
1. Light travels as constant velocity, with magnitude c, in any
direction.
2. A standard clock will show an elapsed time T that satisfies
dT/dt = square-root(1-(v/c)^2).
3. A standard measuring rod, with equilibrium length L when
at rest, will have equilibrium length L square-root(1-(v/c)^2)
when traveling at speed v in a direction parallel to its length.
4. A standard measuring rod, with equilibrium length L when
at rest, will also have equilibrium length L when traveling
at speed v in a direction perpendicular to its length.
5. An object in freefall (no external forces acting on it)
will travel with constant velocity with magnitude less than c.
Theorem: If (x,y,z,t) is a coordinate system satisfying 1-5,
and (x',y',z',t') is a second coordinate system related to the
first through some combination of
rotations, translations, or Lorentz transformations,
then the second coordinate system will also satisfy 1-5.
For those who believe that relativity is paradoxical
or inconsistent, could you please show how claims 1-5
lead to a contradiction?
--
Daryl McCullough
Ithaca, NY
Edward Green
wrote:
Obviously I don't believe your axioms lead to a contradiction, but I
have a comment. For me, the major open issue in SR is whether it is
inevitable or accidental. In either case we would like to produce a
more detailed microscopic understanding which elucidated its status.
In case it is accidental we of course expect it eventually to fail
_even at a point_, since there are no perfect coincidences in nature.
That it has not yet failed to so many 9's of accuracy is not
conclusive evidence that it will never fail, because there is a lot of
room between here and infinity (in the energy scale, for example).
Thank you for your detailed analysis of the Christoffel symbols, BTW.
All I can say it that I have printed them out for study on a rainy
day. Whether it will ever rain that hard is an open question. Wait...
that sounded pejorative: I didn't mean to; the pejoration is entirely
on my part -- I recognize my limitations. At this point in my life
grokking the Christoffel symbols may be right up there with learning
Latin as things I am likely to have left undone. There is remarkably
little explanatory material on the web about them, BTW.
Daryl McCullough
>Obviously I don't believe your axioms lead to a contradiction, but I
>have a comment. For me, the major open issue in SR is whether it is
>inevitable or accidental. In either case we would like to produce a
>more detailed microscopic understanding which elucidated its status.
Yes, it is certainly possible that SR may someday be viewed as
some kind of effective theory which breaks down in the very small.
If that's what the anti-SR crowd were saying, I don't think there
would be much disagreement.
But most of the anti-SR crowd is saying that it is inconsistent,
which is a mathematical, rather than empirical claim. And one that
is easily proved to be false (to the extent that anything can
be proved with certainty).
Sue...
> experiments involving relativity, we can describe the
> claims of SR as the following:
>
> There exists a coordinate system such that, as measured
> using that coordinate system,
>
> 1. Light travels as constant velocity, with magnitude c, in any
> direction.
Ahhh... No. That is how folks think they have violated
light-0speed with near-field measurements. The formal
statement leaves no room for that interpretation.
[1]<< the four-dimensional space-time continuum of the
theory of relativity, in its most essential formal
properties, shows a pronounced relationship to the
three-dimensional continuum of Euclidean geometrical space.
In order to give due prominence to this relationship,
however, we must replace the usual time co-ordinate t by
an imaginary magnitude
sqrt(-1)
ct proportional to it. Under these conditions, the
natural laws satisfying the demands of the (special)
theory of relativity assume mathematical forms, in which
the time co-ordinate plays exactly the same rôle as
the three space co-ordinates. >>
http://www.bartleby.com/173/17.html
>
> 2. A standard clock will show an elapsed time T that satisfies
> dT/dt = square-root(1-(v/c)^2).
No... A "co-ordinate clock" might show that.
http://en.wikipedia.org/wiki/Einstein_synchronisation
http://en.wikipedia.org/wiki/Coordinate_time
>
> 3. A standard measuring rod, with equilibrium length L when
> at rest, will have equilibrium length L square-root(1-(v/c)^2)
> when traveling at speed v in a direction parallel to its length.
That is Lorentz ether theory, not relativity.
http://en.wikipedia.org/wiki/Lorentz_ether_theory
>
> 4. A standard measuring rod, with equilibrium length L when
> at rest, will also have equilibrium length L when traveling
> at speed v in a direction perpendicular to its length.
>
> 5. An object in freefall (no external forces acting on it)
> will travel with constant velocity with magnitude less than c.
http://en.wikipedia.org/wiki/Equivalence_principle#The_weak_equivalence_principle
>
> Theorem: If (x,y,z,t) is a coordinate system satisfying 1-5,
> and (x',y',z',t') is a second coordinate system related to the
> first through some combination of
> rotations, translations, or Lorentz transformations,
> then the second coordinate system will also satisfy 1-5.
>
> For those who believe that relativity is paradoxical
> or inconsistent, could you please show how claims 1-5
> lead to a contradiction?
1-5 doesn't seem to have much relation to relativity
so it is moot.
Sue...
The future of science
>
>
>
> > 3. A standard measuring rod, with equilibrium length L when
> > at rest, will have equilibrium length L square-root(1-(v/c)^2)
> > when traveling at speed v in a direction parallel to its length.
>
>
>
>
> > 4. A standard measuring rod, with equilibrium length L when
> > at rest, will also have equilibrium length L when traveling
> > at speed v in a direction perpendicular to its length.
>
> > 5. An object in freefall (no external forces acting on it)
> > will travel with constant velocity with magnitude less than c.
>
>
>
>
> > Theorem: If (x,y,z,t) is a coordinate system satisfying 1-5,
> > and (x',y',z',t') is a second coordinate system related to the
> > first through some combination of
> > rotations, translations, or Lorentz transformations,
> > then the second coordinate system will also satisfy 1-5.
>
> > For those who believe that relativity is paradoxical
> > or inconsistent, could you please show how claims 1-5
> > lead to a contradiction?
>
> 1-5 doesn't seem to have much relation to relativity
> so it is moot.
>
> Sue...
>
>
>
>
>
> > --
> > Daryl McCullough
>
> - Show quoted text -
Accelerate and things around you apprear to move around you in the
opposite direction.
That is the appearence of relativity. Einstein never qualified that it
was an oppposite
or that in the distance it appears to slow.
Mitch Raemsch
Unified_Perspective
wrote:
First inconsistency:
Postulate 2 seems mathematically inconsistent.
In both ordinary and tensor calculus, T the total time interval is
considered to be the summation of d(t)the infinitesimally small time
intervals.
This makes the relation d(T)/dt problematic. If d(T) is equal to dt
then you have 1= square-root(1-(v/c)^2)which is only true for v=0.
If d(T) which you specify is the elapse time is not equal to the sum
of its derivatives dt you are not using calculus, or you are not using
it properly.
Second inconsistency:
Postulate 4 is only consistent with an observer traveling with the rod
and Postulate 3 is only consistent with the experience of an observer
at rest in relation to the moving rod.
If no reference frame for the observer is specified, which is the case
in your posting, then Postulate 3 and Postulate 4 are directly
contradictory.
The first inconsistency first appears in Einstein's 1905 paper, the
last three paragraphs of section 4 and comprises no more than a minor
flaw in an otherwise stellar work.
The second inconsistency, the failure to specify the observers frame
of reference and to differentiate between the proper length L (the
moving observer) and the apparent length L' (the resting observer) is
a very common fault, which in this case seems to lie with you, as you
are representing this information to be consistent with Einstein's
theories, which I do not find to be the case, his work I find
generally quite careful and consistent regarding which frame of
reference is being considered.
Daryl McCullough
>
>On Feb 25, 11:57=A0am, stevendaryl3...@yahoo.com (Daryl McCullough)
>First inconsistency:
>
>Postulate 2 seems mathematically inconsistent.
>
>In both ordinary and tensor calculus, T the total time interval is
>considered to be the summation of d(t)the infinitesimally small time
>intervals.
dt is not the derivative of T, it's the derivative of t.
t is a time coordinate. T is the elapsed time on a clock.
They aren't the same thing, except in the case in which the
clock has speed 0.
The future of science
wrote:
>
> - Show quoted text -
Those caluclus symbols don't give the full perspective.
There is no acceleration or speeding up that reaches C by rate or goes
above.
The calculus for acceleration obeys weight limit laws.
The change of speed limit is the same as the speed limit in the
universe
that Einstein brought.
MItch Raemsch
Daryl McCullough
>
>On Feb 25, 11:57=A0am, stevendaryl3...@yahoo.com (Daryl McCullough)
>Second inconsistency:
>
>Postulate 4 is only consistent with an observer traveling with the rod
That comment doesn't make any sense to me.
>and Postulate 3 is only consistent with the experience of an observer
>at rest in relation to the moving rod.
And neither does that.
>If no reference frame for the observer is specified,
All the measurements 1-5 are with respect to a specific coordinate
system. Didn't you see the preface: "There exists a coordinate system
such that, as measured using that coordinate system"
Lengths are measured relative to a coordinate system.
Velocities are measured relative to a coordinate system.
Clock rates are measured relative to a coordinate system.
Koobee Wublee
> There exists a coordinate system such that, as measured
> using that coordinate system,
>
> 1. Light travels as constant velocity, with magnitude c, in any
> direction.
This was first proposed by Voigt in 1887. <shrug>
> 2. A standard clock will show an elapsed time T that satisfies
> dT/dt = square-root(1-(v/c)^2).
Let’s not confuse Doppler effect with time dilation. <shrug>
> 3. A standard measuring rod, with equilibrium length L when
> at rest, will have equilibrium length L square-root(1-(v/c)^2)
> when traveling at speed v in a direction parallel to its length.
>
> 4. A standard measuring rod, with equilibrium length L when
> at rest, will also have equilibrium length L when traveling
> at speed v in a direction perpendicular to its length.
FitzGerald-Lorentz speculation. <shrug>
> 5. An object in freefall (no external forces acting on it)
> will travel with constant velocity
That is called the conservation of momentum. <shrug>
> with magnitude less than c.
Speed limit to c is a consequence of all the infinite transforms that
satisfy the null results of the MMX but not satisfy the principle of
relativity including Larmor’s transform that gives rise to the Lorentz
transform from a mathematical mistake made by Poincare. <shrug>
> Theorem: If (x,y,z,t) is a coordinate system satisfying 1-5,
> and (x',y',z',t') is a second coordinate system related to the
> first through some combination of
> rotations, translations, or Lorentz transformations,
> then the second coordinate system will also satisfy 1-5.
Yes, and this is exactly where the paradox manifests itself. <shrug>
> For those who believe that relativity is paradoxical
> or inconsistent, could you please show how claims 1-5
> lead to a contradiction?
You are still shrouded in mysticism. Concentrate on the symmetry in
which the paradox lies within. <shrug>
rasterspace
the wavefront has a speed, but no (directed) velocity.
how about the simple phrase, brought out
in discussing Einstein's "photon" neologism
for a quantum of light-energy with an old theoretical physics prof,
"relativity of vacuum?"
her's Atlas and Bucky shugging mightily at you!
> > 1. Light travels as constant velocity, with magnitude c, in any
> > direction.
> You are still shrouded in mysticism. Concentrate on the symmetry in
Mathal
wrote:
> For the purposes of discussing the various thought
> experiments involving relativity, we can describe the
> claims of SR as the following:
>
> There exists a coordinate system such that, as measured
> using that coordinate system,
>
> 1. Light travels as constant velocity, with magnitude c, in any
> direction.
>
> 2. A standard clock will show an elapsed time T that satisfies
> dT/dt = square-root(1-(v/c)^2).
>
> 3. A standard measuring rod, with equilibrium length L when
> at rest, will have equilibrium length L square-root(1-(v/c)^2)
> when traveling at speed v in a direction parallel to its length.
>
> 4. A standard measuring rod, with equilibrium length L when
> at rest, will also have equilibrium length L when traveling
> at speed v in a direction perpendicular to its length.
>
> 5. An object in freefall (no external forces acting on it)
> will travel with constant velocity with magnitude less than c.
I'd avoid the word 'freefall' - too many misleading connotations.
The crux of the matter is here though. No object with 'mass' can
travel at the speed of light. TRUE
There is anywhere in this universe a place where there are no external
forces acting upon any object with mass. FALSE
Even multiple galaxies rotate around common centers. You can't isolate
SR from the effects of mass- it is an 'effect' of mass, separate and
distinct from GR.
Mathal
The future of science
It is appearence science but there is real motion created by
acceleration.
When you begin to move things around you appear to move in the
opposite direction.
In the distance it gets slower.
Relativity reduces to the last thing Einstein said: Closing velocity
Which is C-v, C+v
Each frame has speed through distance in space. But there is no
absolute rest so thing are already moving together in multiple
motions.
Combined motion's that are not relativistic is the answer and of
course that means what Einstein was considered greatest for was
not his greatest.
MItch Raemsch
> In either case we would like to produce a
> more detailed microscopic understanding which elucidated its status.
> In case it is accidental we of course expect it eventually to fail
> _even at a point_, since there are no perfect coincidences in nature.
> That it has not yet failed to so many 9's of accuracy is not
> conclusive evidence that it will never fail, because there is a lot of
> room between here and infinity (in the energy scale, for example).
>
> Thank you for your detailed analysis of the Christoffel symbols, BTW.
> All I can say it that I have printed them out for study on a rainy
> day. Whether it will ever rain that hard is an open question. Wait...
> that sounded pejorative: I didn't mean to; the pejoration is entirely
> on my part -- I recognize my limitations. At this point in my life
> grokking the Christoffel symbols may be right up there with learning
> Latin as things I am likely to have left undone. There is remarkably
> little explanatory material on the web about them, BTW.- Hide quoted text -
Tom Roberts
> I'd avoid the word 'freefall' - too many misleading connotations.
But being free of all forces is essential to the argument. It requires a lab in
freefall to remove the first-order effects of gravity (which manifest themselves
as forces between objects inside and the lab floor).
[Higher-order effects of gravity cannot be removed by any means,
but can be made arbitrarily small by making the lab small enough
and/or by moving it to a region where the gravitation (metric)
is sufficiently uniform.]
Another approach is to perform the experiment very quickly -- in the LHC
experiments, each event has a duration less than ~100 ns, and during such a
short time period the difference between the lab frame and a freely falling
locally inertial frame is FAR below their measurement resolutions. So they can
(and DO!) analyze each event using SR, neglecting gravity.
> There is anywhere in this universe a place where there are no external
> forces acting upon any object with mass. FALSE
> Even multiple galaxies rotate around common centers.
Physics is a quantitative science, and effects which are too small to measure
can be neglected. There most definitely are places where the effects of
gravitation and other masses are negligible:
A) inside the International Space Station, the effects of earth's gravity are
about a million times smaller than on the surface, and for many/most experiments
that is indeed negligible. The KEY point is that the ISS is in freefall, while a
lab on earth's surface is not. In particular, the altitude of the ISS has
nothing to do with it (altitude << earth's radius), except that it needs to be
far enough above the atmosphere to orbit in freefall [%].
B) the LHC experimental halls are places where gravity can be neglected for the
events of interest.
C) any table-top optical experiment is a place where gravity can be neglected
for measurements of light.
D) etc....
[%] A major component of the "gravity" inside the ISS is due to
drag from the earth's remaining atmosphere. The satellite carrying
Gravity Probe B was designed to eliminate that, too.
> You can't isolate
> SR from the effects of mass- it is an 'effect' of mass, separate and
> distinct from GR.
SR cannot handle anything related to gravitation or a non-zero curvature of the
metric. In neither SR nor GR does gravitation affect the mass of an object --
mass it intrinsic to objects.
In practice, for non-gravitational experiments one uses GR to compute the
effects of gravitation on a given configuration, and uses that to design the
experiment [#] so they can be neglected and SR used in the analysis (which makes
it VASTLY simpler). If one cannot make the effects of gravitation be negligible,
then one must include them in the analysis; for non-gravitational experiments
this is EXTREMELY rare.
[#] In most cases this just means supporting all components
against the earth's gravity, which is just common sense.
Tom Roberts
Daryl McCullough
>
>On Feb 25, 7:57=A0am, stevendaryl3...@yahoo.com (Daryl McCullough)
>wrote:
>> For the purposes of discussing the various thought
>> experiments involving relativity, we can describe the
>> claims of SR as the following:
>>
>> There exists a coordinate system such that, as measured
>> using that coordinate system,
>>
>> 1. Light travels as constant velocity, with magnitude c, in any
>> direction.
>>
>> 2. A standard clock will show an elapsed time T that satisfies
>> dT/dt = square-root(1-(v/c)^2).
>>
>> 3. A standard measuring rod, with equilibrium length L when
>> at rest, will have equilibrium length L square-root(1-(v/c)^2)
>> when traveling at speed v in a direction parallel to its length.
>>
>> 4. A standard measuring rod, with equilibrium length L when
>> at rest, will also have equilibrium length L when traveling
>> at speed v in a direction perpendicular to its length.
>>
>> 5. An object in freefall (no external forces acting on it)
>> will travel with constant velocity with magnitude less than c.
>
>I'd avoid the word 'freefall' - too many misleading connotations.
>The crux of the matter is here though. No object with 'mass' can
>travel at the speed of light. TRUE
>There is anywhere in this universe a place where there are no external
>forces acting upon any object with mass. FALSE
That's a complete irrelevancy. The point is to try to
understand the implications of the theory of special relativity.
Making an idealization of "no external forces" is exactly like
problems in Newtonian physics in which one ignores friction, or
ignores air resistance. It's not that there is no friction, or
that there is no air resistance, but such forces complicate the
calculation of the consequences of Newton's laws. Once someone
understands the simplified versions, one can then ask how complications
such as friction, air resistance, gravity, etc. affects the answer.
In exploring whether SR is *consistent* or not, there is no
need to take into account any such complications.
Tom Roberts
> Mathal says...
>> [...]
>
> That's a complete irrelevancy. The point is to try to
> understand the implications of the theory of special relativity.
> Making an idealization of "no external forces" is exactly like
> problems in Newtonian physics in which one ignores friction, or
> ignores air resistance. It's not that there is no friction, or
> that there is no air resistance, but such forces complicate the
> calculation of the consequences of Newton's laws. Once someone
> understands the simplified versions, one can then ask how complications
> such as friction, air resistance, gravity, etc. affects the answer.
>
> In exploring whether SR is *consistent* or not, there is no
> need to take into account any such complications.
Good point, complimentary to mine (in another post).
Tom Roberts
Mathal
wrote:
I agree with you completely, there is no need to explore this
complication, in that it doesn't affect the outcome that SR is a
completely consistent model.
My interest has always been and will continue to be the underlying
'structure' (for lack of a better word) of this universe.
Mathal
Inertial
news:ee78d2a5-31df-4830...@q2g2000pre.googlegroups.com...
>
>On Feb 25, 10:57 am, stevendaryl3...@yahoo.com (Daryl McCullough)
>wrote:
>> For the purposes of discussing the various thought
>> experiments involving relativity, we can describe the
>> claims of SR as the following:
>>
>> There exists a coordinate system such that, as measured
>> using that coordinate system,
>>
>> 1. Light travels as constant velocity, with magnitude c, in any
>> direction.
>
>Ahhh... No. That is how folks think they have violated
>light-0speed with near-field measurements.
Utter nonsense
> The formal
>statement leaves no room for that interpretation.
[snip copy-paste quote mining that is irrelevant to whatever point Sue
thinks she was making, because she has no understanding at all of the quotes
she pastes or the threads to which she replies]
>> 2. A standard clock will show an elapsed time T that satisfies
>> dT/dt = square-root(1-(v/c)^2).
>
>No... A "co-ordinate clock" might show that.
Bahahaha .. a 'co-ordinate clock' .. now she makes up her own nonsense terms
because she doesn't understand physics
[snip links that are irrelevant to whatever point Sue thinks she was making,
because she has no understanding at all of the quotes she pastes or the
threads to which she replies]
>> 3. A standard measuring rod, with equilibrium length L when
>> at rest, will have equilibrium length L square-root(1-(v/c)^2)
>> when traveling at speed v in a direction parallel to its length.
>
>That is Lorentz ether theory, not relativity.
It is both .. but Sue has no idea what either theory actually says.
[snip links that are irrelevant to whatever point Sue thinks she was making,
because she has no understanding at all of the quotes she pastes or the
threads to which she replies]
>> 4. A standard measuring rod, with equilibrium length L when
>> at rest, will also have equilibrium length L when traveling
>> at speed v in a direction perpendicular to its length.
>>
>> 5. An object in freefall (no external forces acting on it)
>> will travel with constant velocity with magnitude less than c.
[snip links that are irrelevant to whatever point Sue thinks she was making,
because she has no understanding at all of the quotes she pastes or the
threads to which she replies]
>> Theorem: If (x,y,z,t) is a coordinate system satisfying 1-5,
>> and (x',y',z',t') is a second coordinate system related to the
>> first through some combination of
>> rotations, translations, or Lorentz transformations,
>> then the second coordinate system will also satisfy 1-5.
>>
>> For those who believe that relativity is paradoxical
>> or inconsistent, could you please show how claims 1-5
>> lead to a contradiction?
>
>1-5 doesn't seem to have much relation to relativity
>so it is moot.
You don't have an relevance to anything. Everything you post is moot. Once
again you prove yourself a moron, pretending to be knowledgeable, and are
determined to advertise the fact to those of us who actually DO understand.
Daryl McCullough
>
>On Feb 25, 7:57 am, Daryl McCullough wrote:
>
>> There exists a coordinate system such that, as measured
>> using that coordinate system,
>>
>> 1. Light travels as constant velocity, with magnitude c, in any
>> direction.
>
>This was first proposed by Voigt in 1887.
That's irrelevant. The question for this thread is:
Are assumptions 1-5 consistent? Mathematically consistent?
Yes, or no?
>> 2. A standard clock will show an elapsed time T that satisfies
>> dT/dt = square-root(1-(v/c)^2).
>
>Let's not confuse Doppler effect with time dilation.
Well, what I wrote is definitely not the Doppler effect,
but what you call it is irrelevant.
>> 3. A standard measuring rod, with equilibrium length L when
>> at rest, will have equilibrium length L square-root(1-(v/c)^2)
>> when traveling at speed v in a direction parallel to its length.
>>
>> 4. A standard measuring rod, with equilibrium length L when
>> at rest, will also have equilibrium length L when traveling
>> at speed v in a direction perpendicular to its length.
>
>FitzGerald-Lorentz speculation.
That's completely irrelevant. This thread is purely about the
question: Are assumptions 1-5 mathematically inconsistent? Yes, or no?
>> 5. An object in freefall (no external forces acting on it)
>> will travel with constant velocity
>
>That is called the conservation of momentum.
So?
>> with magnitude less than c.
>
>Speed limit to c is a consequence of all the infinite transforms that
>satisfy the null results of the MMX but not satisfy the principle of
>relativity including Larmor=92s transform that gives rise to the Lorentz
>transform from a mathematical mistake made by Poincare. <shrug>
>
>> Theorem: If (x,y,z,t) is a coordinate system satisfying 1-5,
>> and (x',y',z',t') is a second coordinate system related to the
>> first through some combination of
>> rotations, translations, or Lorentz transformations,
>> then the second coordinate system will also satisfy 1-5.
>
>Yes, and this is exactly where the paradox manifests itself.
Then show how assumptions 1-5 lead to a contradiction. The
short answer is: they don't. They *PROVABLY* do not. If you
think otherwise, then give a mathematical derivation that
only uses assumptions 1-5.
Daryl McCullough
>
>On Feb 25, 10:57=A0am, stevendaryl3...@yahoo.com (Daryl McCullough)
>wrote:
>> For the purposes of discussing the various thought
>> experiments involving relativity, we can describe the
>> claims of SR as the following:
>>
>> There exists a coordinate system such that, as measured
>> using that coordinate system,
>>
>> 1. Light travels as constant velocity, with magnitude c, in any
>> direction.
>
>Ahhh... No. That is how folks think they have violated
>light-0speed with near-field measurements. The formal
>statement leaves no room for that interpretation.
The point of this thread is to discuss whether assumptions
1-5 are mathematically consistent. That's a logical/mathematical
question, not affected by experimental results.
Once there is agreement as to the consistency of those assumptions,
*THEN* you can bring up the issue of whether they are in agreement
with experiment.
If you want to go into experimental evidence right away, I will
take that as agreement that there is no mathematical problem with
the assumptions, that they are mathematically consistent. Are you
agreeable to that?
Once again, the assumptions:
There exists a coordinate system such that, as measured
using that coordinate system,
1. Light travels as constant velocity, with magnitude c, in any
direction.
2. A standard clock will show an elapsed time T that satisfies
dT/dt = square-root(1-(v/c)^2).
3. A standard measuring rod, with equilibrium length L when
at rest, will have equilibrium length L square-root(1-(v/c)^2)
when traveling at speed v in a direction parallel to its length.
4. A standard measuring rod, with equilibrium length L when
at rest, will also have equilibrium length L when traveling
at speed v in a direction perpendicular to its length.
5. An object in freefall (no external forces acting on it)
will travel with constant velocity with magnitude less than c.
--
Daryl McCullough
Ithaca, NY
Sue...
wrote:
> Sue... says...
>
>
>
>
>
> >On Feb 25, 10:57=A0am, stevendaryl3...@yahoo.com (Daryl McCullough)
> >wrote:
> >> For the purposes of discussing the various thought
> >> experiments involving relativity, we can describe the
> >> claims of SR as the following:
>
> >> There exists a coordinate system such that, as measured
> >> using that coordinate system,
>
> >> 1. Light travels as constant velocity, with magnitude c, in any
> >> direction.
>
> >Ahhh... No. That is how folks think they have violated
> >light-0speed with near-field measurements. The formal
> >statement leaves no room for that interpretation.
>
> The point of this thread is to discuss whether assumptions
> 1-5 are mathematically consistent. That's a logical/mathematical
> question, not affected by experimental results.
You include three hypothetical processes in your
statements.
Without considering possible mechanisms, the rod knows it speed
on the coordinate system and distorts its shape
accordingly.
You are also describing a clock that knows its speed
on the coordinate system and slows in rate with
increasing speed, relative to the coordinate system.
If the temporal axis is orthogonal to the three
spatial axes, the clock and rods can never be in
conflict.
What is it you are trying to tell us about
light propagation or free falling masses with
your hypothetical clocks and rods?
Such objects violate the principle of relativity
but if they existed, what would you demonstrate
with them?
Sue...
<<In 1907 Einstein criticized the "ad hoc" character
of Lorentz's contraction hypothesis in his theory of
electrons, because according to him it was only
invented to rescue the hypothesis of an immobile
ether. Einstein thought it necessary to replace
Lorentz's theory of electrons by assuming that
Lorentz's "local time" can simply be called "time",
and he stated that the immobile ether as the theoretical
fundament of electrodynamics was unsatisfactory>>
http://en.wikipedia.org/wiki/Lorentz_ether_theory
Daryl McCullough
>
>On Feb 28, 9:25=A0am, stevendaryl3...@yahoo.com (Daryl McCullough)
>wrote:
>> The point of this thread is to discuss whether assumptions
>> 1-5 are mathematically consistent. That's a logical/mathematical
>> question, not affected by experimental results.
>
>You include three hypothetical processes in your
>statements.
>
>Without considering possible mechanisms, the rod knows it speed
>on the coordinate system and distorts its shape
>accordingly.
Once again, the question is: are assumptions 1-5 mathematically
inconsistent, or not? The mechanism is irrelevant at this stage.
>Such objects violate the principle of relativity
That's false. If assumptions 1-5 hold in one inertial coordinate system,
then they hold in every other inertial coordinate system related to the
first through a Lorentz transformation, rotation or translation.
So does the fact that your objections have nothing to do with
the consistency of 1-5 mean that you agree that the assumptions
are mathematically consistent?
Sue...
wrote:
> Sue... says...
>
>
>
> >On Feb 28, 9:25=A0am, stevendaryl3...@yahoo.com (Daryl McCullough)
> >wrote:
> >> The point of this thread is to discuss whether assumptions
> >> 1-5 are mathematically consistent. That's a logical/mathematical
> >> question, not affected by experimental results.
>
> >You include three hypothetical processes in your
> >statements.
>
> >Without considering possible mechanisms, the rod knows it speed
> >on the coordinate system and distorts its shape
> >accordingly.
>
> Once again, the question is: are assumptions 1-5 mathematically
> inconsistent, or not? The mechanism is irrelevant at this stage.
>
> >Such objects violate the principle of relativity
>
> That's false. If assumptions 1-5 hold in one inertial coordinate system,
> then they hold in every other inertial coordinate system related to the
> first through a Lorentz transformation, rotation or translation.
But they don't hold true. Objects don't change
shape in inertial motion. It they did, aeroplanes
would not need pitot tubes.
"What is an Inertial Coordinate System?"
http://www.mathpages.com/home/kmath386/kmath386.htm
>
> So does the fact that your objections have nothing to do with
> the consistency of 1-5 mean that you agree that the assumptions
> are mathematically consistent?
No... You haven't eliminated the ambiguous assumptions
of physical phenomena that accompany terms like
"light" and "inertia" to claim mathematical consistency.
<<The weakness of the principle of inertia lies in this,
that it involves an argument in a circle:a mass moves
without acceleration if it is sufficiently far from
other bodies; we know that it is sufficiently
far from other bodies only by the fact that it moves
without acceleration.>> --A.Einstein
http://www.mathpages.com/rr/s4-07/4-07.htm
Sue...
Daryl McCullough
>stevendaryl3...@yahoo.com (Daryl McCullough) wrote:
>>> Such objects violate the principle of relativity
>>
>> That's false. If assumptions 1-5 hold in one inertial coordinate system,
>> then they hold in every other inertial coordinate system related to the
>> first through a Lorentz transformation, rotation or translation.
>
>But they don't hold true. Objects don't change
>shape in inertial motion. It they did, aeroplanes
>would not need pitot tubes.
Whatever. Right now, I don't care what you believe.
I'm trying to establish two things: (1) The rules 1-5
are mathematically consistent, and (2) If the rules
hold in one inertial coordinate system, then they
hold in any other inertial coordinate system related
to the first through Lorentz transformations, rotations
or translations.
Speculation about mechanisms is not relevant to these
points. If you agree on the two points, then you can
then go on to say that you object to SR for whatever
other philosophical reasons, or empirical reasons, you
like. But at least we can get past these objections
to SR from the point of view of consistency.
Koobee Wublee
> That's completely irrelevant. This thread is purely about the
> question: Are assumptions 1-5 mathematically inconsistent? Yes, or no?
After laying down all these rules, to claim all transformation, that
still follow these rules, are still valid is just stupid. Here is an
example.
Eric and Daryl both went to the local sporting goods store and each
bought a defective pair of binoculars. The distortion is in the
horizontal direction where all observations through such a pair of
binoculars would yield a person to be much fatter than in real life.
Now, Eric and Daryl observe each other through their binoculars and
would comment on how chubby the other one is. At this state, all the
transformations are within the rules laid out, but when Eric and Daryl
meet, they then realize their binoculars are indeed defective.
Gee! Yours truly just cannot believe anyone would bring this up to
justify this moron’s belief. Well, that is not surprising for someone
who has a history of manually designing voodoo mathematics to justify
his believe.
<shame> <shame> <shame>
** FAITH IS THEORY
** LYING IS TEACHING
** NITWIT IS GENIUS
** OCCULT IS SCIENCE
** PARADOX IS KOSHER
** BULLSHIT IS TRUTH
** BELIEVING IS LEARNING
** IGNORANCE IS KNOWLEDGE
** MYSTICISM IS WISDOM
** CONJECTURE IS REALITY
** PLAGIARISM IS CREATIVITY
** MATHEMAGICS IS MATHEMATICS
Daryl McCullough
>
>On Feb 28, 6:19 am, Daryl McCullough wrote:
>
>> That's completely irrelevant. This thread is purely about the
>> question: Are assumptions 1-5 mathematically inconsistent? Yes, or no?
>
>After laying down all these rules, to claim all transformation, that
>still follow these rules, are still valid is just stupid.
Whatever. The question is whether rules 1-5 are mathematically consistent.
Do you agree that they are, or not?
Daryl McCullough
For reference, the rules:
There exists a coordinate system such that, as measured
using that coordinate system,
1. Light travels as constant velocity, with magnitude c, in any
direction.
2. A standard clock will show an elapsed time T that satisfies
dT/dt = square-root(1-(v/c)^2).
3. A standard measuring rod, with equilibrium length L when
at rest, will have equilibrium length L square-root(1-(v/c)^2)
when traveling at speed v in a direction parallel to its length.
4. A standard measuring rod, with equilibrium length L when
at rest, will also have equilibrium length L when traveling
at speed v in a direction perpendicular to its length.
5. An object in freefall (no external forces acting on it)
will travel with constant velocity with magnitude less than c.
Theorem(proof left as an exercise): If (x,y,z,t) is a coordinate system
satisfying 1-5, and (x',y',z',t') is a second coordinate system
related to the first through some combination of
rotations, translations, or Lorentz transformations,
then the second coordinate system will also satisfy 1-5.
--
Daryl McCullough
Ithaca, NY
Sue...
wrote:
> Sue... says...
>
> >stevendaryl3...@yahoo.com (Daryl McCullough) wrote:
> >>> Such objects violate the principle of relativity
>
> >> That's false. If assumptions 1-5 hold in one inertial coordinate system,
> >> then they hold in every other inertial coordinate system related to the
> >> first through a Lorentz transformation, rotation or translation.
>
> >But they don't hold true. Objects don't change
> >shape in inertial motion. It they did, aeroplanes
> >would not need pitot tubes.
>
> Whatever. Right now, I don't care what you believe.
> I'm trying to establish two things:
> (1) The rules 1-5 are mathematically consistent, and
Try writing them in mathematical terms. Remove
the references to light and inertia.
> (2) If the rules hold in one inertial coordinate system, then they
> hold in any other inertial coordinate system related
> to the first through Lorentz transformations, rotations
> or translations.
Not all inertial coordinate systems have the
same specification so it is unlikely.
If you want to restrict the specification, Fitzpatrick,
is a good example:
http://farside.ph.utexas.edu/teaching/em/lectures/node109.html
To repeat the why:
"What is an Inertial Coordinate System?"
http://www.mathpages.com/home/kmath386/kmath386.htm
>
> Speculation about mechanisms is not relevant to these
> points. If you agree on the two points, then you can
> then go on to say that you object to SR for whatever
> other philosophical reasons, or empirical reasons, you
> like. But at least we can get past these objections
> to SR from the point of view of consistency.
To show mathematical consistency you should remove references
to inertia and light, for which you have no physical
description.
If you want to dispel objections to relativity, it might
be easier if you don't confuse it with Lorentz ether
theory.
http://en.wikipedia.org/wiki/Lorentz_ether_theory#Later_activity_and_Current_Status
Sue...
Prai Jei
continuum:
> In article <ikh4p...@drn.newsguy.com>, Daryl McCullough says...
>>Whatever. The question is whether rules 1-5 are mathematically consistent.
>>Do you agree that they are, or not?
>
> For reference, the rules:
>
> There exists a coordinate system such that, as measured
> using that coordinate system,
>
> { & mucel mo vpon þis wyse ]
You may as well not bother. You'll never shut these antirelativists up no
matter how much maths you throw at them. Meanwhile, they can never offer
anything concrete in return.
(I'm OK with it all though.)
--
ξ:) Proud to be curly
Interchange the alphabetic letter groups to reply
Androcles
"Prai Jei" <pvstownse...@ntlworld.com> wrote in message
news:ikh6gt$n37$1...@news.eternal-september.org...
| Daryl McCullough set the following eddies spiralling through the
space-time
| continuum:
|
| > In article <ikh4p...@drn.newsguy.com>, Daryl McCullough says...
| >>Whatever. The question is whether rules 1-5 are mathematically
consistent.
| >>Do you agree that they are, or not?
| >
| > For reference, the rules:
| >
| > There exists a coordinate system such that, as measured
| > using that coordinate system,
| >
| > { & mucel mo vpon þis wyse ]
|
| You may as well not bother. You'll never shut these antirelativists up no
| matter how much maths you throw at them. Meanwhile, they can never offer
| anything concrete in return.
|
| (I'm OK with it all though.)
You may as well not bother. You'll never shut these relativists up no
matter how much maths you throw at them. Meanwhile, they can never offer
anything concrete in return.
"Let there be given a stationary rigid rod; and let its length be L as
measured by a measuring-rod which is also stationary. We now imagine
the axis of the rod lying along the axis of x of the stationary system of
co-ordinates, and that a uniform motion of parallel translation with
velocity v along the axis of x in the direction of increasing x is then
imparted to the rod. We now inquire as to the length of the moving rod" --
Einstein
"The length to be discovered by the operation (b) we will call ``the length
of the (moving) rod in the stationary system.''"-- Einstein
"This we shall determine on the basis of our two principles, and we shall
find that it differs from L." -- Einstein.
AND THE ANSWER IS...
"xi = (x-vt)/sqrt(1 - v^2/c^2)" -- Einstein.
Yep, xi differs from L, Greek letters differ from Roman letters.
In agreement with experience we further assume the deranged babbling
incompetent cretin couldn't answer his own inquiry, he was too stupid
to realise xi is greater than L when he wrote 'for v=c all moving
objects--viewed from the "stationary'' system--shrivel up into plane
figures', whereas his own equation shows they stretch to infinity...
sqrt(1-c^2/c^2) = 0.
"But the ray moves relatively to the initial point of k, when measured in
the stationary system, with the velocity c-v" - Einstein
"the velocity of light in our theory plays the part, physically, of an
infinitely great velocity" - Einstein.
"In agreement with experience we further assume the quantity
2AB/(t'A -tA) = c to be a universal constant--the velocity of light in
empty space." -- Einstein
He was right. The distance from A to A divided by the time it takes
to get there is undefined. Anyone that divides by zero is a lunatic.
You are ok with it all, though, you fucking idiot.
Daryl McCullough
>
>On Feb 28, 3:37=A0pm, stevendaryl3...@yahoo.com (Daryl McCullough)
>wrote:
>> Whatever. Right now, I don't care what you believe.
>
>> I'm trying to establish two things:
>
>> (1) The rules 1-5 are mathematically consistent, and
>
>Try writing them in mathematical terms. Remove
>the references to light and inertia.
I don't see the point of that, at all. It's hard for me to imagine
someone who would be capable of understanding such a
formalization who would need it to formalized to that extent.
The most rigorous formalization of what I said is in terms
of differential geometry. Anyone capable of understanding
differential geometry would know that SR is mathematically
consistent.
So your answer is: you can't understand what the rules mean,
and so have no idea whether they are consistent or not. Fine.
>> (2) If the rules hold in one inertial coordinate system, then they
>> hold in any other inertial coordinate system related
>> to the first through Lorentz transformations, rotations
>> or translations.
>
>Not all inertial coordinate systems have the
>same specification so it is unlikely.
What I said is provably true.
beth howland
considering that SR is habitually shown
on the x-axis?... well, except when
they go on to a phase-space diagram with "t is the scalar."
Daryl McCullough
No, they are related, but different.
The relativistic Doppler shift for frequencies is
square-root((1-(v/c))/(1+(v/c))
where v is the relative speed between sender and receiver.
The time dilation factor is square-root(1-(v/c)^2)
beth howland
to justify the asymmetry of the accelerated astronaut,
compared to teh stay-at-home, when they both see ... oops.
Daryl McCullough
beth howland says...
>
>that is really going to throw him for loop. it is a kind of hard,
>to justify the asymmetry of the accelerated astronaut,
>compared to teh stay-at-home, when they both see ... oops.
Doppler shift is one way to keep track of the relative ages of
the two twins in a "twin paradox".
Suppose that one twin jets off at 0.866c for 1000 seconds
(as measured by someone on Earth), turns around and
comes back at the same speed.
To keep track of the relative aging, let's assume
that both the traveling twin and the stay-at-home
twin send a light pulse once per hour.
The Doppler shift formula tells us that for the outward
journey, the signals will arrive at a rate of
square-root((1-v/c)/(1+v/c)) per second, which is about
0.27 signals per second.
For the return journey, the Doppler shift formula
is the same, but with the sign of v flipped:
square-root((1+v/c)/(1-v/c)) per second, which is about
3.73 signals per second.
Okay, here's where the asymmetry comes in: the traveling
twin observes signals from the other
twin at the rate of .27 per second for half
the time, and 3.73 per second for half the time. So on the
average, he receives 2 signals, for each 1 signal
that he sends. So in total, the traveling twin sends out
only half as many signals as he receives.
What about the stay-at-home twin? Well, he also sees
signals at the rate of 0.27 per second for part of the
time, and at the rate of 3.73 per second for part of the
time. But the amount of time seeing the lower rate
is longer than the amount of time seeing the higher
rate. If the traveling twin turns around at time 1000,
then at that time, the traveling twin is a distance of
866 light-seconds away. The image of his turning around
will take another 866 seconds to reach the stay-at-home
twin. The higher rate will not be visible until after
this point.
So the stay-at-home twin sees the lower rate of 0.27
per second for 1866 seconds, for a total of 500 signals,
and the lower rate of 3.73 per second for the last 134
seconds, for a total of 500 more signals. So in total,
the stay-at-home twin sends out 2000 signals, and
receives 1000.
From the point of view of either twin, the traveling
twin only sends out half as many signals as the stay-at-home
twin.
Koobee Wublee
wrote:
> beth howland says...
>> that is really going to throw him for loop. it is a kind of hard,
>> to justify the asymmetry of the accelerated astronaut,
>> compared to teh stay-at-home, when they both see ... oops.
>
> Doppler shift is one way to keep track of the relative ages of
> the two twins in a "twin paradox".
So, you are confused Doppler effect from time dilation. <shrug>
> The Doppler shift formula tells us that for the outward
> journey, the signals will arrive at a rate of
> square-root((1-v/c)/(1+v/c)) per second, which is about
> 0.27 signals per second.
Doppler shift is always the observed speed of the signal divided by
the wavelength. In air, the speed of sound goes by (c +/- v) while
the wavelength is invariant, and that is the classical Doppler
effect. In relativity, the speed is always c. So, the relativistic
Doppler effect only depends on how the wavelength is transformed. So,
how exactly is the wavelength transformed in SR? You want to prepare
a bag before you puke. <shrug>
Supposed in these two twins taking videos of themselves. The
bandwidth of the video is f1. With a simple mixing of carrier
frequency of f0, what are the results in frequency bands? When the
mixed signal is received by the other twin, what is the Doppler shift
of the entire frequency band? When the receiving twin adjusts for the
Doppler shift by mixing the received signal with a frequency
appropriately shifted in accounting for the Doppler shift, what is the
result bandwidth of the original video signal?
> ...
You have shown deeply in your heart that you would rather abandoning
logic and science than embracing the nonsense of SR in which you have
zealously BELIEVE IN so. You have been shown that all your voodoo
math is garbage justifying your religion. <shrug>
Koobee Wublee
> Koobee Wublee says...
>> After laying down all these rules, to claim all transformation, that
>> still follow these rules, are still valid is just stupid.
>
> Whatever. The question is whether rules 1-5 are mathematically consistent.
> Do you agree that they are, or not?
No, you have been told that they are not mathematically consistent.
They manifest paradoxes which are forbidden in real life. <shrug>
Oh, you probably want to know where the inconsistencies occur. Well,
that is in the twin’s paradox, the Doppler shift, and others. The
Lorentz transform is just bad. Yours truly has also gone out of His
way to show where and how the Lorentz transform gone bad, and that was
never addressed and met with dumbfounded silence from the self-styled
physicists. <shrug>
Without addressing the fault of the path leading to the Lorentz
transform, talking about the faults of the Lorentz transform is rather
unethical against what science stands for. <shrug>
Sue...
wrote:
> Sue... says...
>
>
>
> >On Feb 28, 3:37=A0pm, stevendaryl3...@yahoo.com (Daryl McCullough)
> >wrote:
> >> Whatever. Right now, I don't care what you believe.
>
> >> I'm trying to establish two things:
>
> >> (1) The rules 1-5 are mathematically consistent, and
>
------------
> >Try writing them in mathematical terms. Remove
> >the references to light and inertia.
-------------
>
> I don't see the point of that, at all. It's hard for me to imagine
> someone who would be capable of understanding such a
> formalization who would need it to formalized to that extent.
<<Because of their use of natural language, the standards
of rigour for informal proofs will depend on the audience
of the proof. In order to be considered a proof, however,
the argument must be rigorous enough; a vague or
incomplete argument is not a proof.>>
http://en.wikipedia.org/wiki/Mathematical_proof
>
> The most rigorous formalization of what I said is in terms
> of differential geometry. Anyone capable of understanding
> differential geometry would know that SR is mathematically
> consistent.
>
> So your answer is: you can't understand what the rules mean,
> and so have no idea whether they are consistent or not. Fine.
Attempts to channel the words of another don't strengthen
your association with the scientific community but followers
of the occult love it. So do expound on you special abilities
for entertainment if nothing else. :-))
>
> >> (2) If the rules hold in one inertial coordinate system, then they
> >> hold in any other inertial coordinate system related
> >> to the first through Lorentz transformations, rotations
> >> or translations.
>
> >Not all inertial coordinate systems have the
> >same specification so it is unlikely.
>
> What I said is provably true.
<<What we do expect is that any physically
significant interrelation between physical quantities
(i.e., position, velocity, etc.) which appears to hold
in the coordinate system of the first experimentalist
will also appear to hold in the coordinate system of
the second experimentalist. We usually refer to such
interrelationships as laws of physics. So, what we are
really saying is that the laws of physics do not depend
on our choice of coordinate system. In particular, if a
law of physics is true in one coordinate system then it
is automatically true in every other coordinate system,
subject to the proviso that both coordinate systems are
inertial. >>
http://farside.ph.utexas.edu/teaching/em/lectures/node112.html
Your 1) is not physically significant because light
has no mass.
Your 2) and 3) are not physically significant because
they are physically absurd and coordinate dependent.
http://en.wikipedia.org/wiki/Noether%27s_theorem#Applications
That leaves only universality of free fall, your 5)
as any indicator that inertia can be tested on a
given coordinate system.
<< All test particles at the alike spacetime
point in a given gravitational field will
undergo the same acceleration, independent
of their properties, including their rest mass.
The principle does not apply to physical bodies, which
experience tidal forces, or heavy point masses, whose
presence changes the gravitational field around them.
This form of the equivalence principle is closest to
Einstein's original statement: in fact, his statements
imply this one.
Active, passive, and inertial masses... >>
http://en.wikipedia.org/wiki/Universality_of_free_fall#The_weak_equivalence_principle
See also:
<<...we can account for the ever decreasing acceleration
of a particle subject to a constant force [see Eq. (1542)]
by supposing that the inertial mass of the particle
increases with its velocity according to the rule
(1546). Henceforth, $m_0$ is termed the rest mass,
and $m$ the inertial mass. >>
http://farside.ph.utexas.edu/teaching/em/lectures/node126.html
Your 1-5 is devoid of any device, mathematically or physically
that can exchange mass for energy with the ether it assumes.
That is the essence of inertial effects.
So you and Hendrik Lorentz have really pulled a rabbit
out of the hat in less that 150 years. :-))
http://en.wikipedia.org/wiki/Lorentz_ether_theory#Later_activity_and_Current_Status
I'll await your rigorous maths 'till I change my
opinion that you are pulling something other than
a rabbit from some place other than a hat.
Sue...
Daryl McCullough
>
>On Feb 28, 1:41 pm, Daryl McCullough wrote:
>> Koobee Wublee says...
>
>>> After laying down all these rules, to claim all transformation, that
>>> still follow these rules, are still valid is just stupid.
>>
>.
>> Do you agree that they are, or not?
>
>No, you have been told that they are not mathematically consistent.
Well, that is false. They are provably consistent.
Daryl McCullough
>
>On Feb 28, 7:29 pm, stevendaryl3...@yahoo.com (Daryl McCullough)
>wrote:
>> beth howland says...
>
>>> that is really going to throw him for loop. it is a kind of hard,
>>> to justify the asymmetry of the accelerated astronaut,
>>> compared to teh stay-at-home, when they both see ... oops.
>>
>> Doppler shift is one way to keep track of the relative ages of
>> the two twins in a "twin paradox".
>
>So, you are confused Doppler effect from time dilation.
No, they are different effects, but the Doppler shift formula can
be used to keep track of the difference in ages of two twins.
If two twins depart and return, and each twin sends out a
signal once per second (as measured by his own clock), then
the age of each twin (in seconds) will be equal to the number
of signals received by the other twin. If you know the rate
of the receiving of the signals at various times
(which is given by the relativistic Doppler shift formula) then
it is a simple calculation to figure out the number of signals
received.
Daryl McCullough
Nothing, really. I asked whether several straight-forward
assumptions were consistent, and she gives me various quotes
that she found in various places.
"Light has no mass"
"Your 2) and 3) are not physically significant"
Those statements have *NOTHING* to do with this thread. The
question is about the consistency of the assumptions, not the
true nature of light, not the physical significance of this or
that, not the mechanisms that underlie relativity, etc.
At this stage, we're simply talking about the consistency
of the assumptions. If you have nothing to say on that matter,
then I will take that as an indication that, as far as you
know, they are consistent.
Once again, the assumptions:
There exists a coordinate system such that, as measured in that
coordinate system,
1. Light travels as constant velocity, with magnitude c, in any
direction.
2. A standard clock will show an elapsed time T that satisfies
dT/dt = square-root(1-(v/c)^2).
3. A standard measuring rod, with equilibrium length L when
at rest, will have equilibrium length L square-root(1-(v/c)^2)
when traveling at speed v in a direction parallel to its length.
4. A standard measuring rod, with equilibrium length L when
at rest, will also have equilibrium length L when traveling
at speed v in a direction perpendicular to its length.
5. An object in freefall (no external forces acting on it)
will travel with constant velocity with magnitude less than c.
Theorem: If (x,y,z,t) is a coordinate system satisfying 1-5,
and (x',y',z',t') is a second coordinate system related to the
first through some combination of
rotations, translations, or Lorentz transformations,
then the second coordinate system will also satisfy 1-5.
--
Daryl McCullough
Ithaca, NY
Daryl McCullough
><<Because of their use of natural language, the standards
>of rigour for informal proofs will depend on the audience
>of the proof. In order to be considered a proof, however,
>the argument must be rigorous enough; a vague or
>incomplete argument is not a proof.>>
>http://en.wikipedia.org/wiki/Mathematical_proof
That's really the point of this thread; the people who
claim that relativity is inconsistent are incapable of
giving a proof in that sense. They are basically mathematically
illiterate. That's the reason that I would prefer to stick
to the intuitive concepts that I gave, because a more formal
mathematical presentation would be completely lost on the
intended audience.
Daryl McCullough
>your association with the scientific community but followers
>of the occult love it.
You are bizarre, Sue.
Sue...
> Sue... says...
>
> Nothing, really. I asked whether several straight-forward
> assumptions were consistent, and she gives me various quotes
> that she found in various places.
>
> "Light has no mass"
> "Your 2) and 3) are not physically significant"
>
> Those statements have *NOTHING* to do with this thread. The
> question is about the consistency of the assumptions, not the
> true nature of light, not the physical significance of this or
> that, not the mechanisms that underlie relativity, etc.
>
> At this stage, we're simply talking about the consistency
> of the assumptions. If you have nothing to say on that matter,
> then I will take that as an indication that, as far as you
> know, they are consistent.
Without any way to apply mathematical rigour to undefined
terms, it is indeed safe to say your statements are as
consistent as the life-line on my palm is consistent
with a circular arc.
http://www.palmistrylines.com/
>
> Once again, the assumptions:
>
> There exists a coordinate system such that, as measured in that
> coordinate system,
>
> 1. Light travels as constant velocity, with magnitude c, in any
> direction.
>
> 2. A standard clock will show an elapsed time T that satisfies
> dT/dt = square-root(1-(v/c)^2).
>
> 3. A standard measuring rod, with equilibrium length L when
> at rest, will have equilibrium length L square-root(1-(v/c)^2)
> when traveling at speed v in a direction parallel to its length.
>
> 4. A standard measuring rod, with equilibrium length L when
> at rest, will also have equilibrium length L when traveling
> at speed v in a direction perpendicular to its length.
>
> 5. An object in freefall (no external forces acting on it)
> will travel with constant velocity with magnitude less than c.
>
> Theorem: If (x,y,z,t) is a coordinate system satisfying 1-5,
> and (x',y',z',t') is a second coordinate system related to the
> first through some combination of
> rotations, translations, or Lorentz transformations,
> then the second coordinate system will also satisfy 1-5.
http://en.wikipedia.org/wiki/Garbage_In,_Garbage_Out
Sue...
Sue...
You have a twin with the same mass and charge
as an electron that we can try that with?
<<a 45 GeV electron accelerated by the Large
Electron-Positron Collider (LEP) at Cern in 1989 would
have had a Lorentz factor γ of about 88,000 (90 GeV
divided by the electron rest mass of 511 keV). Its
coordinate speed v would have been about sixty four
trillionths shy of lightspeed c at 1 lightsecond per
map second.>>
http://en.wikipedia.org/wiki/Proper_velocity
See also:
http://en.wikipedia.org/wiki/Lorentz_force
Sue...
Daryl McCullough
Okay, Sue. I will take that as an indication that you have nothing
to say on the topic of this thread.
Daryl McCullough
>
>On Mar 1, 6:01=C2=A0am, stevendaryl3...@yahoo.com (Daryl McCullough) wrote:
>> Koobee Wublee says...
>>
>>
>>
>> >On Feb 28, 7:29 pm, stevendaryl3...@yahoo.com (Daryl McCullough)
>> >wrote:
>> >> beth howland says...
>>
>d,
>> >>> to justify the asymmetry of the accelerated astronaut,
>> >>> compared to teh stay-at-home, when they both see ... oops.
>>
>> >> Doppler shift is one way to keep track of the relative ages of
>> >> the two twins in a "twin paradox".
>>
>> >So, you are confused Doppler effect from time dilation.
>>
>> No, they are different effects, but the Doppler shift formula can
>> be used to keep track of the difference in ages of two twins.
>> If two twins depart and return, and each twin sends out a
>> signal once per second (as measured by his own clock), then
>> the age of each twin (in seconds) will be equal to the number
>> of signals received by the other twin. If you know the rate
>> of the receiving of the signals at various times
>> (which is given by the relativistic Doppler shift formula) then
>> it is a simple calculation to figure out the number of signals
>> received.
>
>You have a twin with the same mass and charge
>as an electron that we can try that with?
Sue, I really do not remember a single time in which
I read a meaningful response from you.
Daryl McCullough
>Sue, I really do not remember a single time in which
>I read a meaningful response from you.
I wonder if you are like that in person. I imagine someone
saying to you: What miserable weather we've been having lately,
and you respond:
http://en.wikipedia.org/wiki/Weather
"Weather is the state of the atmosphere, to the degree that it is hot
or cold, wet or dry, calm or stormy, clear or cloudy.[1] Most weather phenomena
occur in the troposphere,[2][3] just below the stratosphere. Weather refers,
generally, to day-to-day temperature and precipitation activity, whereas climate
is the term for the average atmospheric conditions over longer periods of
time.[4] When used without qualification, "weather" is understood to be the
weather of Earth."
Sue...
> Sue... says...
>
> ><<Because of their use of natural language, the standards
> >of rigour for informal proofs will depend on the audience
> >of the proof. In order to be considered a proof, however,
> >the argument must be rigorous enough; a vague or
> >incomplete argument is not a proof.>>
> >http://en.wikipedia.org/wiki/Mathematical_proof
>
> That's really the point of this thread; the people who
> claim that relativity is inconsistent are incapable of
> giving a proof in that sense.
Maybe "the people" are claiming your Lorentz ether
theory is inconsistent with relativity and your
knee jerk defence blinds you from considering
that very real possibility.
<<Poincaré noticed in 1905 that Lorentz's theory of
1904 was not perfectly "Lorentz invariant" in a few
equations such as Lorentz's expression for current density
(it was admitted by Lorentz in 1921 that these were defects).>>
http://en.wikipedia.org/wiki/Lorentz_ether_theory
> They are basically mathematically
> illiterate. That's the reason that I would prefer to stick
> to the intuitive concepts that I gave, because a more formal
> mathematical presentation would be completely lost on the
> intended audience.
You are posting to the wrong forum if your intended
audience is "mathematical illiterates".
<<Models, in both science and mathematics, need to be
internally consistent and also ought to be falsifiable
(capable of disproof).>>
http://en.wikipedia.org/wiki/Scientific_method#Relationship_with_mathematics
Perhaps your offering of self consistency might garner
some praise in this areana:
http://en.wikipedia.org/wiki/Poetry
Sue...
Daryl McCullough
>
>On Mar 1, 6:30=A0am, stevendaryl3...@yahoo.com (Daryl McCullough) wrote:
>> Sue... says...
>>
>> ><<Because of their use of natural language, the standards
>> >of rigour for informal proofs will depend on the audience
>> >of the proof. In order to be considered a proof, however,
>> >the argument must be rigorous enough; a vague or
>> >incomplete argument is not a proof.>>
>> >http://en.wikipedia.org/wiki/Mathematical_proof
>>
>> That's really the point of this thread; the people who
>> claim that relativity is inconsistent are incapable of
>> giving a proof in that sense.
>
>Maybe "the people" are claiming your Lorentz ether
I didn't say anything about an ether. Your response has
nothing to do with what I said.
Daryl McCullough
>You are posting to the wrong forum if your intended
>audience is "mathematical illiterates".
My intended audience is the people who believe that SR
is inconsistent. The term "mathematically illiterate"
is certainly applicable to everyone in that group.
Sue...
The names you use are inconsequential. Can you
show how your statements 1-5 differ from Lorentz
ether theory?
http://en.wikipedia.org/wiki/Lorentz_ether_theory
The slowing clocks and distorting measuring rods are
at odds with Einstein's relativity which states:
<< All inertial frames are totally equivalent
for the performance of all physical experiments.
In other words, it is impossible to perform a physical
experiment which differentiates in any fundamental sense
between different inertial frames. By definition, Newton's
laws of motion take the same form in all inertial frames.
Einstein generalized[1] this result in his special theory of
relativity by asserting that all laws of physics take the
same form in all inertial frames. >>
http://farside.ph.utexas.edu/teaching/em/lectures/node108.html
[1]<< the four-dimensional space-time continuum of the
theory of relativity, in its most essential formal
properties, shows a pronounced relationship to the
three-dimensional continuum of Euclidean geometrical space.
In order to give due prominence to this relationship,
however, we must replace the usual time co-ordinate t by
an imaginary magnitude
sqrt(-1)
ct proportional to it. Under these conditions, the
natural laws satisfying the demands of the (special)
theory of relativity assume mathematical forms, in which
the time co-ordinate plays exactly the same rôle as
the three space co-ordinates. >>
http://www.bartleby.com/173/17.html
<< where epsilon_0 and mu_0 are physical constants which
can be evaluated by performing two simple experiments
which involve measuring the force of attraction between
two fixed charges and two fixed parallel current carrying
wires. According to the relativity principle, these experiments
must yield the same values for epsilon_0 and mu_0 in all
inertial frames. Thus, the speed of light must be the
same in all inertial frames. >>
http://farside.ph.utexas.edu/teaching/em/lectures/node108.html
Sue...
Androcles
"Sue..." <suzyse...@yahoo.com.au> wrote in message
news:e3738201-1e8f-4862...@u24g2000prn.googlegroups.com...
Sue...
====================================
"It seems that Light is propagated in time, spending in its passage from
the sun to us about seven Minutes of time:" -- DEFIN. II of Opticks Or,
A Treatise of the Reflections, Refractions, Inflections and Colours of
Light - Sir Isaac Newton.
"the velocity of light in our theory plays the part, physically, of an
infinitely great velocity" --§ 4. Physical Meaning of the Equations
Obtained in Respect to Moving Rigid Bodies and Moving Clocks
-- ON THE ELECTRODYNAMICS OF MOVING BODIES By A. Einstein
Mouth McCullough is as mathematically illiterate as Einstein was.
He imagines speed is measured as "The Hobbit, or There and Back Again."
http://www.fourmilab.ch/etexts/einstein/specrel/www/figures/img7.gif
tB is undefined.
Daryl McCullough
>> I didn't say anything about an ether. Your response has
>> nothing to do with what I said.
>
>The names you use are inconsequential. Can you
>show how your statements 1-5 differ from Lorentz
>ether theory?
The issue for this thread is: are the assumptions consistent? Yes or no?
Sue...
The are not. They suffer the same flaws as
Lorentz ether theory.
http://en.wikipedia.org/wiki/Lorentz_ether_theory
Can you show how your statements 1-5 differ from Lorentz
ether theory?
sqrt(-1)
Sue...
- Hide quoted text -
Daryl McCullough
>e:
>> >> I didn't say anything about an ether. Your response has
>> >> nothing to do with what I said.
>>
>> >The names you use are inconsequential. Can you
>> >show how your statements 1-5 differ from Lorentz
>> >ether theory?
>>
>> The issue for this thread is: are the assumptions consistent? Yes or no?
>
>The are not.
That is wrong. They are perfectly consistent. This
is easily seen by the following "model" of the assumptions:
Consider a train moving on railroad tracks.
The train measures the passage of time by
a "light clock" oriented perpendicular to
the path of the train. One unit of time is
the time required for a light pulse to travel
from a mirror positioned above one track to
a mirror positioned on the other track and
back again. (We assume that the paths of the
light pulses can be continually adjusted, by
auxiliary mirrors, so that the pulses always
go between the two mirrors following an acceleration.)
We model a "standard rod of proper length L" as
a pair of parallel mirrors with adjustable distance
between them. The mirrors are adjusted so that
the time required for a light pulse to travel
from one mirror to the other and back is
2L/c, as measured using the standard light
clock described above.
With a tiny bit of algebra, you can show that
as measured by the rest frame of the rails,
if we assume that light has speed c in all
direction, then if the train is set in motion
at speed v, then
(1) The rate of the light clock will go down,
by a factor of square-root(1-(v/c)^2).
(2) The length of a standard rod of proper length
L on the train that is oriented perpendicular to the
direction of motion will have length L as measured in the rest
frame of the rails.
(3) The length of a standard rod of proper length
L on the train that is oriented parallel to the
direction of motion will have length L square-root(1-(v/c)^2)
as measured in the rest frame of the rails.
This shows that if it is possible to have a signal
with constant speed in any direction in any single
reference frame, then it is possible to satisfy my
assumptions 1-5.
Sue...
Even Newton knew such a device was physically
absurd. Did your intended audience die in
the 15th or 16th century?
Do you have names for the angels that position
the mirrors?
Try this because the angels probably have a union
contract that will bust your budget:
"A practical derivation of the Lorentz factor"
http://meshula.net/wordpress/?p=222
>
> We model a "standard rod of proper length L" as
> a pair of parallel mirrors with adjustable distance
> between them. The mirrors are adjusted so that
> the time required for a light pulse to travel
> from one mirror to the other and back is
> 2L/c, as measured using the standard light
> clock described above.
>
> With a tiny bit of algebra, you can show that
> as measured by the rest frame of the rails,
> if we assume that light has speed c in all
> direction, then if the train is set in motion
> at speed v, then
>
> (1) The rate of the light clock will go down,
> by a factor of square-root(1-(v/c)^2).
Some recent linear Sagnac experiments will give you
an idea what really happens but "A practical derivation
of the Lorentz factor" above, is close to the mark.
>
> (2) The length of a standard rod of proper length
> L on the train that is oriented perpendicular to the
> direction of motion will have length L as measured in the rest
> frame of the rails.
>
> (3) The length of a standard rod of proper length
> L on the train that is oriented parallel to the
> direction of motion will have length L square-root(1-(v/c)^2)
> as measured in the rest frame of the rails.
>
> This shows that if it is possible to have a signal
> with constant speed in any direction in any single
> reference frame, then it is possible to satisfy my
> assumptions 1-5.
That isn't relativity and it isn't true in the near-field.
If you believe it is, you should be supporting the near-field FTL
claims that crop up about monthly. I saw one in the past
week. So hop in there and offer your support to the
poster that doesn't know relativity from LET.
If you want to say something about light, try this:
<< where epsilon_0 and mu_0 are physical constants which
can be evaluated by performing two simple experiments
which involve measuring the force of attraction between
two fixed charges and two fixed parallel current carrying
wires. According to the relativity principle, these experiments
must yield the same values for epsilon_0 and mu_0 in all
inertial frames. Thus, the speed of light must be the
same in all inertial frames. >>
http://farside.ph.utexas.edu/teaching/em/lectures/node108.html
Sue...
>
Daryl McCullough
>> This shows that if it is possible to have a signal
>> with constant speed in any direction in any single
>> reference frame, then it is possible to satisfy my
>> assumptions 1-5.
>
>That isn't relativity and it isn't true in the near-field.
Why is it that you can't seem to make a relevant response?
My point was to show that my assumptions 1-5 are mathematically
consistent. Do you agree that they are? If not, then show the
inconsistency.
"Near-field" is *COMPLETELY* irrelevant. What I describe is
a *MODEL* not a theory. It's a way to show that a set of assumptions
is consistent by exhibiting a logically system (however unrealistic)
that satisfies those assumptions.
Sue...
> Sue... says...
>
>
>
> >On Mar 1, 8:20=A0am, stevendaryl3...@yahoo.com (Daryl McCullough) wrote:
> >> This shows that if it is possible to have a signal
> >> with constant speed in any direction in any single
> >> reference frame, then it is possible to satisfy my
> >> assumptions 1-5.
>
> >That isn't relativity and it isn't true in the near-field.
>
> Why is it that you can't seem to make a relevant response?
> My point was to show that my assumptions 1-5 are mathematically
> consistent. Do you agree that they are? If not, then show the
> inconsistency.
I think Einstein and Minkowski showed that they are inconsistent
somewhere anound 1918 so I will leave it to you to show
their errors.
Again... Your have not distinguished you assumptions
from the theory they appear in:
http://en.wikipedia.org/wiki/Lorentz_ether_theory
>
> "Near-field" is *COMPLETELY* irrelevant. What I describe is
> a *MODEL* not a theory. It's a way to show that a set of assumptions
> is consistent by exhibiting a logically system (however unrealistic)
> that satisfies those assumptions.
What good is that?
1/1 = 1
is logical and consistent.
With a logical and consistent statement in hand, can
you now reveal all the mysteries of light and inertia
to the world?
Sue...
Daryl McCullough
>> Why is it that you can't seem to make a relevant response?
>> My point was to show that my assumptions 1-5 are mathematically
>> consistent. Do you agree that they are? If not, then show the
>> inconsistency.
>
>I think Einstein and Minkowski showed that they are inconsistent
>somewhere anound 1918
No, they didn't. You are very confused.
Okay, Sue. It's clear that you have nothing intelligent to say on
this topic.
Daryl McCullough
>> "Near-field" is *COMPLETELY* irrelevant. What I describe is
>> a *MODEL* not a theory. It's a way to show that a set of assumptions
>> is consistent by exhibiting a logically system (however unrealistic)
>> that satisfies those assumptions.
>
>What good is that?
If (for the purpose of the various thought experiments) SR is
mathematically equivalent to a set of provably consistent assumptions,
then it follows that attempts to derive a contradiction from the
"twin paradox" or the various other paradoxes is doomed to failure.
That is the case.
Sue...
wrote:
That seems to leave you in disagreement about a few points.
<< Einstein's relativity principle states that:
All inertial frames are totally equivalent
for the performance of all physical experiments.
In other words, it is impossible to perform a physical
experiment which differentiates in any fundamental sense
between different inertial frames. By definition, Newton's
laws of motion take the same form in all inertial frames.
Einstein generalized[1] this result in his special theory of
relativity by asserting that all laws of physics take the
same form in all inertial frames. >>
http://farside.ph.utexas.edu/teaching/em/lectures/node108.html
[1]<< the four-dimensional space-time continuum of the
theory of relativity, in its most essential formal
properties, shows a pronounced relationship to the
three-dimensional continuum of Euclidean geometrical space.
In order to give due prominence to this relationship,
however, we must replace the usual time co-ordinate t by
an imaginary magnitude
sqrt(-1)
ct proportional to it. Under these conditions, the
natural laws satisfying the demands of the (special)
theory of relativity assume mathematical forms, in which
the time co-ordinate plays exactly the same rôle as
the three space co-ordinates. >>
http://www.bartleby.com/173/17.html
<< where epsilon_0 and mu_0 are physical constants which
can be evaluated by performing two simple experiments
which involve measuring the force of attraction between
two fixed charges and two fixed parallel current carrying
wires. According to the relativity principle, these experiments
must yield the same values for epsilon_0 and mu_0 in all
inertial frames. Thus, the speed of light must be the
same in all inertial frames. >>
http://farside.ph.utexas.edu/teaching/em/lectures/node108.html
Too bad you were not born a few centuries earlier.
You would have found a bit more support for your
notions.
<< Subsequent to the advent of special relativity, only
a small number of individuals have advocated the
Lorentzian approach to physics. Many of these, such as
Herbert E. Ives (who, along with G. R. Stilwell, performed
the first experimental confirmation of time dilation) have
been motivated by the belief that special relativity is
logically inconsistent, and so some other conceptual framework
is needed to reconcile the relativistic phenomena. For
example, Ives wrote "The 'principle' of the constancy
of the velocity of light is not merely 'ununderstandable',
it is not supported by 'objective matters of fact'; it
is untenable..."[C 8]. However, the logical consistency
of special relativity (as well as its empirical success)
is well established, so the views of such individuals are
considered unfounded within the mainstream scientific
community. >>
http://en.wikipedia.org/wiki/Lorentz_ether_theory
Sue...
Daryl McCullough
>On Mar 1, 10:43=A0am, stevendaryl3...@yahoo.com (Daryl McCullough)
>wrote:
>That seems to leave you in disagreement about a few points.
>
>
><< Einstein's relativity principle states that:
>
> All inertial frames are totally equivalent
> for the performance of all physical experiments.
And that is satisfied by the fact that assumptions 1-5, if
they hold in one coordinate system, will hold in every other
coordinate system related to the first through rotations,
translations and Lorentz transformations.
At the level of the thought experiments used for discussing
the consistency of SR, my assumptions 1-5 give a consistent,
description of the "laws of physics" that are true in every
inertial frame.
Sue...
wrote:
> Sue... says...
>
> >On Mar 1, 10:43=A0am, stevendaryl3...@yahoo.com (Daryl McCullough)
> >wrote:
> >That seems to leave you in disagreement about a few points.
>
> ><< Einstein's relativity principle states that:
>
> > All inertial frames are totally equivalent
> > for the performance of all physical experiments.
>
> And that is satisfied by the fact that assumptions 1-5, if
> they hold in one coordinate system, will hold in every other
> coordinate system related to the first through rotations,
> translations and Lorentz transformations.
But they dont hold true. That is why Minkowski put
time on an orthogonal axis.
>
> At the level of the thought experiments used for discussing
> the consistency of SR, my assumptions 1-5 give a consistent,
> description of the "laws of physics" that are true in every
> inertial frame.
Your 1-5 makes no mention of tensors or complex numbers.
You are juist kidding yourself if you think you are making
any statements about Einstein and Minkowksi's theory without
a method to describe an axis, orthogonal to the three spatial
axes.
Dropping terms like "inertial" into your statements is not sufficient
to include relativity in your Lorentzian statemens.
<<Today the "special theory" exists only, aside from its historical
importance, as a convenient set of widely applicable formulas for
important limiting cases of the general theory, but the
epistemological
foundation of those formulas must be sought in the context of the
==> general theory. <==
>>
http://www.mathpages.com/rr/s4-07/4-07.htm
Have you heard of:
Tensors? Imaginaries? Reals?
You have an example that corrects the deficiency but
I assume ignorance is bliss for you.
<<In special relativity, the laws of physics are only required
to exhibit tensor behaviour under transformations between different
inertial frames: i.e., translations, rotations, and Lorentz
transformations. >>
<< In general relativity, the laws of physics are required to
exhibit tensor behaviour under all non- singular coordinate
transformations. >>
http://farside.ph.utexas.edu/teaching/em/lectures/node112.html
So you are like the teenager that gets high smoking oregano
rather than admit his pot supplier pulled a trick.
Enjoy your delusions.
Sue...
Daryl McCullough
>
>On Mar 1, 11:12=A0am, stevendaryl3...@yahoo.com (Daryl McCullough)
>wrote:
>> Sue... says...
>> ><< Einstein's relativity principle states that:
>>
>> > All inertial frames are totally equivalent
>> > for the performance of all physical experiments.
>
>> And that is satisfied by the fact that assumptions 1-5, if
>> they hold in one coordinate system, will hold in every other
>> coordinate system related to the first through rotations,
>> translations and Lorentz transformations.
>
>But they don't hold true. That is why Minkowski put
>time on an orthogonal axis.
That's a complete non-sequitur. As I have told you several times,
the point of this thread is to investigate the CONSISTENCY of the
assumptions that are used in SR thought experiments, not their
truth.
The assumptions 1-5 are consistent, they satisfy the principle of
relativity, and they are sufficient to compute the outcomes of most
thought experiments involving Special Relativity.
Sue...
For the class of thought experiments where mirrors are
fortuitously adjusted by angels, who could argue otherwise.
Sue...
Daryl McCullough
>
>On Mar 1, 12:31=A0pm, stevendaryl3...@yahoo.com (Daryl McCullough)
>wrote:
>> The assumptions 1-5 are consistent, they satisfy the principle of
>> relativity, and they are sufficient to compute the outcomes of most
>> thought experiments involving Special Relativity.
>
>For the class of thought experiments where mirrors are
>fortuitously adjusted by angels, who could argue otherwise.
Whatever. The point is that there is nothing *inconsistent* about
the predictions of SR.
Koobee Wublee
> Koobee Wublee says...
> >No, you have been told that they are not mathematically consistent.
>
> Well, that is false.
That is because you don’t understand the basics. <shrug>
> They are provably consistent.
The twin’s paradox is a paradox that manifests directly out of the
Lorentz transform. Your denial does not resolve it. It just shows how
ignorant you are. It is just a matter of time that the next
generations of physicists will be laughing at you. <shrug>
Other than the twin’s paradox, there are more paradoxes from SR. One
example is the energy transformation predicts a contradictory result
from the transformation of time under SR. <shrug>
Koobee Wublee
> Koobee Wublee says...
> >So, you are confused Doppler effect from time dilation.
>
> No, they are different effects, but the Doppler shift formula can
> be used to keep track of the difference in ages of two twins.
This is just not true. <shrug>
Let’s look at the Galilean transform where
** dt’ = dt
Instead of SR’s
** dt’ = (dt – [v] * d[s] / c^2) / sqrt(1 – v^2 / c^2)
Where
** [v], [s] = vectors of velocity and position
** * = dot product
Under your voodoo math, the Galilean transform does not yield any
Doppler shift, but that is a direct contradiction to any observation.
The gross inconsistency does not seem to bother you. So, what do you
plead?
The only lame excuse that yours truly can think of that you could come
up with is that the Galilean transform is wrong. Are you claiming
just that? <shrug>
> If two twins depart and return, and each twin sends out a
> signal once per second (as measured by his own clock), then
> the age of each twin (in seconds) will be equal to the number
> of signals received by the other twin. If you know the rate
> of the receiving of the signals at various times
> (which is given by the relativistic Doppler shift formula) then
> it is a simple calculation to figure out the number of signals
> received.
This is not true. You are grossly confused the Doppler effect from
time dilation. Yours truly has given you a simple direction that you
can find what amounts to the Doppler effect and what amounts to time
dilation, and it looks like you have no intellectual capacity to
understand that simple concept. Oh, well. It is very difficult to
discuss anything logical with an idiot. <shrug>
Daryl McCullough
>
>On Mar 1, 3:01 am, Daryl McCullough wrote:
>> Koobee Wublee says...
>
>> >So, you are confused Doppler effect from time dilation.
>>
>> No, they are different effects, but the Doppler shift formula can
>> be used to keep track of the difference in ages of two twins.
>
>This is just not true.
It certainly is. Suppose you have two people, Ann and Bob who
synchronize their watches to t=0 when they are together. Then
they depart, each promising to send a light signal once per second
(according to his or her watch). At some later time, they reunite
and compare watches.
Then, when they get back together the following will be true:
1. The number of signals from Ann received by Bob will be equal
to the time on Bob's watch, in seconds. Call that number t_bob.
2. The number of signals from Bob received by Ann will be equal
to the time on Ann's watch, in seconds. Call that number t_ann.
Now, let N_bob(t) be the cumulative number of signals received
by Ann from Bob up to time t. Then the rate R_bob(t)
defined by d/dt N_bob(t) is the rate, according to Ann's watch,
that Ann receives signals from Bob at time t.
So we have:
t_bob
= N_bob(t_ann)
= Integral of (d/dt N_bob(t)) dt
= Integral of R_bob(t) dt
where R_bob(t) is the measured rate for signals received by
Ann at time t.
Now, how do you compute R_bob(t)? The short answer is the
relativistic Doppler shift formula:
R_bob(t) = square-root((1-v/c)/(1+v/c))
where v is the relative speed between Ann and Bob. But
if Ann and/or Bob is *changing* velocity, then which value
of v do you use?
The answer is a little bit complicated. Let e_1 be the event
at which Ann's watch shows time t. At that time, Ann just
received some signal from Bob. Let e_2 be the event at which
Bob *sent* that signal. (Since signals take time to propagate,
e_2 will be earlier than e_1.) Then the correct relative velocity
v to use is the relative velocity between Ann at event e_1 and
Bob at event e_2.
If you do that correctly, you will find that the Doppler
shift calculation for the elapsed time on Ann and Bob's
watches when they get back together is exactly the same
as the relativistic time dilation prediction, as computed
in any inertial frame.
Daryl McCullough
>
>On Mar 1, 2:57 am, Daryl McCullough wrote:
>> Koobee Wublee says...
>
>> >No, you have been told that they are not mathematically consistent.
>>
>> Well, that is false.
>
>That is because you don't understand the basics.
The basics as you understand it are inconsistent. So your understanding
is clearly not worth very much. It isn't worth anyone's while to learn
an inconsistent theory.
So there are two slightly different versions of SR being discussed;
an inconsistent version, which is the version that you, Ken Seto,
and various others insist that people get right, and a perfectly
consistent version, which is the version that I (and basically every
other physicist) uses.
Don't you agree that it's weird that you insist that people use the
inconsistent version of SR, and that you have no interest in learning
the consistent version? Why do you dwell on an inconsistent theory?
Why do you have no interest in the consistent variant of that theory?
It's very bizarre.
marcus_b
> On Feb 25, 7:57 am, Daryl McCullough wrote:
>
> > There exists a coordinate system such that, as measured
> > using that coordinate system,
>
> > 1. Light travels as constant velocity, with magnitude c, in any
> > direction.
>
> This was first proposed by Voigt in 1887. <shrug>
>
Hmm, same year as Michelson-Morley. <grimace>
Of course what Einstein noticed was that the constancy of speed of
light was
implied by Maxwell's laws. What was the title of his paper?
<belch>
> > 2. A standard clock will show an elapsed time T that satisfies
> > dT/dt = square-root(1-(v/c)^2).
>
> Let’s not confuse Doppler effect with time dilation. <shrug>
>
Right, let's not. <burp> Why should we? Einstein didn't.
> > 3. A standard measuring rod, with equilibrium length L when
> > at rest, will have equilibrium length L square-root(1-(v/c)^2)
> > when traveling at speed v in a direction parallel to its length.
>
> > 4. A standard measuring rod, with equilibrium length L when
> > at rest, will also have equilibrium length L when traveling
> > at speed v in a direction perpendicular to its length.
>
> FitzGerald-Lorentz speculation. <shrug>
>
> > 5. An object in freefall (no external forces acting on it)
> > will travel with constant velocity
>
> That is called the conservation of momentum. <shrug>
>
Assuming its mass doesn't change ... and who's doing the
measurement? <cough>
> > with magnitude less than c.
>
> Speed limit to c is a consequence of all the infinite transforms that
> satisfy the null results of the MMX but not satisfy the principle of
> relativity including Larmor’s transform that gives rise to the Lorentz
> transform from a mathematical mistake made by Poincare. <shrug>
>
What exactly was Poicare's mistake? Reference?
> > Theorem: If (x,y,z,t) is a coordinate system satisfying 1-5,
> > and (x',y',z',t') is a second coordinate system related to the
> > first through some combination of
> > rotations, translations, or Lorentz transformations,
> > then the second coordinate system will also satisfy 1-5.
>
> Yes, and this is exactly where the paradox manifests itself. <shrug>
>
There is no paradox.
> > For those who believe that relativity is paradoxical
> > or inconsistent, could you please show how claims 1-5
> > lead to a contradiction?
>
> You are still shrouded in mysticism. Concentrate on the symmetry in
> which the paradox lies within. <shrug>
An ungrammatical non-answer duly noted. <spasm>
Marcus.
rasterspace
• In 1906, Norwegian explorer Ronald Amundsen and six crew
members sailed the Northwest Passage from east to west,
becoming the first to completely traverse the passage.
• In 1940, and again in 1944, a group of Canadians, led by
Royal Canadian Mounted Police officer Henry Larsen, traversed the
Northwest Passage.
These three expeditions occurred in periods when the Arctic was
warmer than to- day. These warm periods were caused by natural
cycles and occurred before the so-called increase in man-made CO2.
Library of Canada, 1908.
When one looks at the climate, there has to be a sense of the history
of science and exploration. To this end, one must look at all
available sources of data. When looking at the Arctic, researchers
must consult old ship logs and logbooks for companies like the
Hudson Bay Company, which give a valuable picture of the past.
The Hudson Bay Company’s logs document that over the 19th
Century, part of the Northwest Passage was navigable, if ships
stayed below certain latitudes. These data fill out the picture
for the period before 1979, which is the point when satellites
were launched to monitor the sea surface temperature, and
pressure at sea surface and sea bottom.
This year’s Arctic Sea ice melt was the largest since the start of
the use of satellites to monitor the Arctic.
rasterspace
what is wrong with the Lorentz transform. now, if
you can do that without invoking Minkowski's silly phasespace slogans,
you'll get a bonus point.
Koobee Wublee
> On Feb 25, 11:54 pm, Koobee Wublee wrote:
> > This was first proposed by Voigt in 1887. <shrug>
>
> Hmm, same year as Michelson-Morley. <grimace>
That is correct. However, Voigt was not referring to the MMX of
1887. Voigt proposed the constancy in the speed of light based on
Michelson’s solo 1881 experiment which also showed null results.
<shrug>
> Of course what Einstein noticed was that the constancy of speed of
> light was implied by Maxwell's laws.
That is nonsense. The constancy in the speed of light predicted by
Maxwell’s equations is only valid against the stationary background of
the Aether. This is within the same concept of the speed of sound
within the medium of propagation. You really need to get the basics
straight. <shrug>
> What was the title of his paper? <belch>
Oh, that is the piece of toilet paper that you use to wipe away from
your face of the fermented diarrhea of Einstein the nitwit, the
plagiarist, and the liar. How does it take like that gives you a
satisfying belch? <shrug>
> > Let’s not confuse Doppler effect with time dilation. <shrug>
>
> Right, let's not. <burp> Why should we? Einstein didn't.
The nitwit did. So have done the rest of self-styled physicist in the
past 100 years. <shrug>
> > That is called the conservation of momentum. <shrug>
>
> Assuming its mass doesn't change ... and who's doing the
> measurement? <cough>
Observed mass is observed dependent, and rest mass is dependent on the
curvature in spacetime according to proper interpretation of GR.
<shrug>
> > Speed limit to c is a consequence of all the infinite transforms that
> > satisfy the null results of the MMX but not satisfy the principle of
> > relativity including Larmor’s transform that gives rise to the Lorentz
> > transform from a mathematical mistake made by Poincare. <shrug>
>
> What exactly was Poicare's mistake? Reference?
All transforms relate two observers’ observations on the same observed
target. Larmor’s original version of the Lorentz transform must
reference back to the stationary background of the Aether. Thus, to
relate the observations of two such observers, you need two such
transforms where each relates to the absolute frame of reference
first. Through how each observer relates to the absolute frame of
reference, you can then formulate how the two observers’ observations
are related. However, the way this transform was written allowing the
two observers to travel in parallel against the stationary background
of the Aether, it allows the absolute frame of reference to be dropped
from subsequent calculations. Thus, in this special case, the
relationship between the observations of these two observers do not
involve the stationary background of the Aether. However, this is not
the case in general, and this is where Poincare’s mistake lies in.
<shrug>
Einstein the nitwit had nothing to do with this mistake. Einstein the
plagiarist was merely plagiarizing Poincare’s works. Einstein the
liar was not happy the way he had fudged the Lorentz transform. So,
in his book, the nitwit, the plagiarist, and the liar did attempt to
re-derive the Lorentz transform from equations equating zero with
zero, and voila, the Lorentz transform was created from absolute
nonsense. <shrug>
> > You are still shrouded in mysticism. Concentrate on the symmetry in
> > which the paradox lies within. <shrug>
>
> An ungrammatical non-answer duly noted. <spasm>
Excuse me. Care to correct my grammar? If not, get lost.
Koobee Wublee
> So your understanding
> is clearly not worth very much. It isn't worth anyone's while to learn
> an inconsistent theory.
The discussion is about nonsense of SR and GR. Yours truly has not
brought out any new conjectures. So, please stop tossing crap around
to justify your religious belief. <shrug>
By the way, you have not answered the following question.
We have a pair of preachers, Eric and Daryl. Eric stays at home while
Daryl travels at speed of (c / 2) away from Eric. Both Eric and Daryl
start to make movies about each self. Each movie within its each
frame of reference has a video bandwidth of 10MHz. Each then mixes
the video with a 100MHz carrier frequency and transmits the mixed
signal to towards each other.
What frequency should each use to demodulate the received signal?
After decoding the received signal, what is the bandwidth of the
demodulated video signal?
Hint:
If you are weak in RF, the mixing a signal with bandwidth of f2 with a
carrier frequency of f1 will result in two bands centered around f1.
The upper band goes from f1 to (f1 + f2) while the lower band resides
from f1 to (f1 – f2). This falls in the same math that multiplies two
sine (or cosine) waves with different frequencies.
Further application:
You can then use the same method to see the nonsense of the GPS-GR
relationship. <shrug>
Koobee Wublee
tear your nonsense apart? That is:
You have arrived at a relative Doppler shift out of the Lorentz
transform. Using the same method, what is the Doppler shift for the
Galilean transform?
This is a simple and fair question. So, why are you avoiding the
question? Do you not understand what Galilean transform is?
<shrug>
Don Stockbauer
Why all this effort being spent on relativity when cybernetics is much
more important, since it is the science of creating huge artificial
brains????
<meta-shrug>
Daryl McCullough
>
>On Mar 2, 4:31 am, Daryl McCullough wrote:
>
>> So your understanding
>> is clearly not worth very much. It isn't worth anyone's while to learn
>> an inconsistent theory.
>
>The discussion is about nonsense of SR and GR.
But my point is that unless you are dealing with SR *as* it is
understood by physicists today, talking about it is completely
irrelevant. Which is the case.
In particular, your understanding of the application of SR
to the twin paradox is not used by any physicist. What people
who ACTUALLY work with SR would say about it is this: To compute
the elapsed time on any traveling clock, you use the following
formula:
T = integral of square-root(1-(v/c)^2) dt
where v and t are measured in any *single* inertial cartesian
coordinate system. This is consistent (it gives the same
result using any inertial coordinate system) and it satisfies
the principle of relativity (the integral has the same form
in every inertial coordinate system).
The way that you use SR to compute the results of the twin
paradox are indeed inconsistent, but that is because you don't
actually know the theory of SR (as it is understood by physicists).
Daryl McCullough
>
>Why don=92t you address what I have pointed out first before we go on to
>tear your nonsense apart? That is:
>
>You have arrived at a relative Doppler shift out of the Lorentz
>transform.
That's not completely true. The relativistic Doppler shift formula
takes into account two different things: (1) relativity, and (2)
propagation delay for light signals.
>Using the same method, what is the Doppler shift for the
>Galilean transform?
Part of the derivation works exactly the same whether you are
using Galilean relativity or Special relativity. So let me give
a derivation for this initial part, and then show how Galilean
versus Special relativity affects the answer.
Suppose that there is a frame F in which light travels at speed
c in all directions, as measured in that frame. Let there be
two observers, A and B. A is at rest in frame F, and B is
traveling at constant velocity v relative to frame F, away from A.
In the following, all coordinates are assumed to be in the
coordinate system of A.
Assume that at regular intervals, A sends a light signal toward B,
and at regular intervals, B sends a light signal toward A.
Let T_AS be the time between signals, as sent by A.
Let T_BS be the time between signals, as sent by B.
Let T_BR be the time between signals, as received by B.
Let T_AR be the time between signals, as received by A.
Now let's calculate the relationships between these 4 numbers.
Let e_0 be the event at which A and B are initially together.
Its coordinates, will be assumed to be (x=0, t=0).
Let e_1 be the event at which A sends out his first signal.
Its coordinates will be (x=0, t=T_AS).
Let e_2 be the event at which B sends out his first signal.
Its coordinates will be (x=v T_BS, t=T_BS)
Let e_3 be the event at which B receives the first signal
from A. Its coordinates will be (x=v T_BR, t= T_BR)
Let e_4 be the event at which A receives the first signal
from B. Its coordinates will be (x=0, t=T_AR)
Since a light signal travels from event e_1 to the event
e_3, it must be that
|x_3 - x_1| = c (t_3 - t_1)
So
v T_BR = c (T_BR - T_AS)
(1) T_BR = 1/(1-v/c) T_AS
Since a light signal travels from event e_2 to the event
e_4, it must be that
|x_4 - x_2| = c (t_4 - t_2)
So
v T_BS = c (T_AR - T_BS)
(2) T_AR = (1+v/c) T_BS
So equation (1) says that the delay between signals arriving at B
is greater than the delay between signals sent by A by a factor of
1/(1-v/c).
Equation (2) says that the delay between signals arriving at A
is greater than the delay between signals sent by B by a factor
of (1+v/c).
Note that these delay formulas are slightly different. The delay
received by the stationary observer, A, is not the same as the
delay received by the moving observer, B.
Also note: everything done so far is EXACTLY the same, whether
we are using Galilean relativity or Special Relativity.
Now, we're not quite to the Doppler shift formula yet. Everything
so far was done in the coordinate system of A. What we really want
to know is the ratios T_BR'/T_AS and T_AR/T_BS' where T_BR' is the
time between signals received by B as measured in the
coordinate system of B, and T_BS' is the time between signals
sent by B as measured in the coordinate system of B.
There are two different answers, depending on whether we assume
Galilean relativity or Special relativity.
For Galilean relativity:
The relationship between t' and t is simple:
t' = t
So for this case, we have:
(3) T_BR'/T_AS = T_BR/T_AS = 1/(1-v/c)
(4) T_AR/T_BS' = T_AR/T_BS = 1+v/c
For Special relativity:
The relationship between t' and t is more complicated:
t' = gamma (t - v/c^2 x)
T_BR' = gamma (T_BR - v/c^2 x_BR)
Where x_BR is the x-location of B when he receives the first
signal. Since B is traveling at speed v, x_BR = v T_BR. So
we have:
T_BR' = gamma (T_BR - v/c^2 * v T_BR)
= gamma (1-(v/c)^2) T_BR
= 1/gamma T_BR
where I used 1/gamma^2 = (1-(v/c)^2).
Using equation (1) gives:
T_BR' = 1/gamma T_BR = 1/gamma 1/(1-v/c) T_AS
Now, 1/gamma = square-root(1-(v/c)^2)
= square-root(1-v/c) square-root(1+v/c)
So the equation for T_BR' simplifies to
T_BR' = square-root((1+v/c)/(1-v/c)) T_AS
So:
(5) T_BR'/T_AS = square-root((1+v/c)/(1-v/c))
Similarly,
T_BS' = 1/gamma T_BS
From equation (2), we have:
T_BS = 1/(1+v/c) T_AR, so:
T_BS' = 1/gamma * 1/(1+v/c) T_AR
Once again using 1/gamma = square-root(1-v/c) square-root(1+v/c),
this simplifies to:
T_BS' = square-root((1-v/c)/(1+v/c)) T_AR
So:
(6) T_AR/T_BS' = square-root((1+v/c)/(1-v/c))
Note that equations (5) and (6) give the same
relationship between receiving times and sending
times, regardless of whether A or B is sending.
So we can see that using Galilean relativity, we get (equations
(3) and (4)) that there is a difference between the case in which
the sender is at rest, and the case in which the receiver is at
rest. Using Special Relativity, we get (equations (5) and (6))
that there is *NO* difference in the two cases.
So according to Galilean relativity, careful measurement of the Doppler
effect would allow someone to detect the "rest frame of the medium", the
frame in which light has speed c in all directions. According to
Special Relativity, the Doppler effect gives no preference to one frame
over another.
marcus_b
> On Mar 2, 7:36 am, marcus_b wrote:
>
> > On Feb 25, 11:54 pm, Koobee Wublee wrote:
> > > This was first proposed by Voigt in 1887. <shrug>
>
> > Hmm, same year as Michelson-Morley. <grimace>
>
> That is correct. However, Voigt was not referring to the MMX of
> 1887. Voigt proposed the constancy in the speed of light based on
> Michelson’s solo 1881 experiment which also showed null results.
> <shrug>
>
Much the same.
> > Of course what Einstein noticed was that the constancy of speed of
> > light was implied by Maxwell's laws.
>
> That is nonsense. The constancy in the speed of light predicted by
> Maxwell’s equations is only valid against the stationary background of
> the Aether.
Even though no assumption of an aether is required to derive the
speed of EM radiation from Maxwell's laws ...
> This is within the same concept of the speed of sound
See above.
> within the medium of propagation. You really need to get the basics
> straight. <shrug>
>
So you think there is an aether.
What's with all this shrugging?
> > What was the title of his paper? <belch>
>
> Oh, that is the piece of toilet paper that you use to wipe away from
> your face of the fermented diarrhea of Einstein the nitwit, the
> plagiarist, and the liar. How does it take like that gives you a
> satisfying belch? <shrug>
>
Gratuitous, obscene, and unjustified. And what do you mean by
"How does it take" ? And was your shrug satisfying, or just a tic?
And the reference? Where did Poincare make this mistake (in) ?
> Einstein the nitwit had nothing to do with this mistake. Einstein the
> plagiarist was merely plagiarizing Poincare’s works. Einstein the
> liar was not happy the way he had fudged the Lorentz transform. So,
> in his book, the nitwit, the plagiarist, and the liar did attempt to
> re-derive the Lorentz transform from equations equating zero with
> zero, and voila, the Lorentz transform was created from absolute
> nonsense. <shrug>
>
> > > You are still shrouded in mysticism. Concentrate on the symmetry in
> > > which the paradox lies within. <shrug>
>
> > An ungrammatical non-answer duly noted. <spasm>
>
> Excuse me. Care to correct my grammar? If not, get lost.
in ... within. A little redundant. And not the last time,
either. <twitch>
Just curious to see your reaction to the following. Two travelers,
Anne and Bill, are simultaneously next to each other at time t = 0 by
both their clocks. Bill accelerates quickly to 1/2 c in a straight
line away
from Anne. He sends back a signal periodically. The signal includes
the time that his clock is registering. After 1 year, he stops and
abruptly turns around, now travelling at 1/2 c back toward Anne. At
exactly the time he stops, he sends a signal to Anne, saying, "I am
turning around now. The time on my clock is XXX.XXX". Anne, who
buys into SR, receives this signal quite some time later. She says
to herself, "Hmm. According to my clock and calculations based on
his speed, he stopped and turned around at YYY.YYY. Further, if
I compute what his clock should have said when he stopped, I get
ZZZ.ZZZ."
So. By your reckoning, what are XXX.XXX, YYY.YYY, and ZZZ.ZZZ?
Marcus.
rasterspace
Koobee Wublee
> On Mar 2, 2:33 pm, Koobee Wublee wrote:
> > That is correct. However, Voigt was not referring to the MMX of
> > 1887. Voigt proposed the constancy in the speed of light based on
> > Michelson’s solo 1881 experiment which also showed null results.
> > <shrug>
>
> Much the same.
Hmmm... What is your point, again? <shrug>
> > That is nonsense. The constancy in the speed of light predicted by
> > Maxwell’s equations is only valid against the stationary background of
> > the Aether.
>
> Even though no assumption of an aether is required to derive the
> speed of EM radiation from Maxwell's laws ...
This statement is grossly mistaken. Apparently, you don’t understand
the Maxwell’s equations. The Aether is denied by the self-styled
physicists only after applying the Lorentz transformation of the
coordinate system instead of the good old Galilean. <shrug>
> > This is within the same concept of the speed of sound
>
> See above.
Still does not compute. What is your point, again? For your
information, sound remains medium dependent regardless if the Lorentz
transform is applied or not. <shrug>
> > within the medium of propagation. You really need to get the basics
> > straight. <shrug>
>
> So you think there is an aether.
The null results of the MMX actually point towards the existence of
the Aether. <shrug>
> What's with all this shrugging?
Ask professor Roberts. He was shrugging for 20 years before yours
truly out-shrugged him. <shrug>
> > Oh, that is the piece of toilet paper that you use to wipe away from
> > your face of the fermented diarrhea of Einstein the nitwit, the
> > plagiarist, and the liar. How does it take like that gives you a
> > satisfying belch? <shrug>
>
> Gratuitous, obscene, and unjustified. And what do you mean by
> "How does it take" ? And was your shrug satisfying, or just a tic?
Hmmm... Yours truly does not remember now. It is obviously a typo
--- a very unimportant typo in fact. Thus, yours truly is not going
to lose any sleep over it. <shrug>
> > All transforms relate two observers’ observations on the same observed
> > target. Larmor’s original version of the Lorentz transform must
> > reference back to the stationary background of the Aether. Thus, to
> > relate the observations of two such observers, you need two such
> > transforms where each relates to the absolute frame of reference
> > first. Through how each observer relates to the absolute frame of
> > reference, you can then formulate how the two observers’ observations
> > are related. However, the way this transform was written allowing the
> > two observers to travel in parallel against the stationary background
> > of the Aether, it allows the absolute frame of reference to be dropped
> > from subsequent calculations. Thus, in this special case, the
> > relationship between the observations of these two observers do not
> > involve the stationary background of the Aether. However, this is not
> > the case in general, and this is where Poincare’s mistake lies in.
> > <shrug>
>
> And the reference? Where did Poincare make this mistake (in) ?
Well, that is the point. It looks like yours truly is the first to
point that one. One day, yours truly will publish that result.
<shrug>
> > Einstein the nitwit had nothing to do with this mistake. Einstein the
> > plagiarist was merely plagiarizing Poincare’s works. Einstein the
> > liar was not happy the way he had fudged the Lorentz transform. So,
> > in his book, the nitwit, the plagiarist, and the liar did attempt to
> > re-derive the Lorentz transform from equations equating zero with
> > zero, and voila, the Lorentz transform was created from absolute
> > nonsense. <shrug>
>
> > Excuse me. Care to correct my grammar? If not, get lost.
>
> in ... within. A little redundant. And not the last time,
> either. <twitch>
Oh? Still does not compute. It does not matter. Once again, yours
truly is not going to lose any sleep over mis-spelling or grammatical
errors. You have to get over that. <shrug>
> Just curious to see your reaction to the following. Two travelers,
> Anne and Bill, are simultaneously next to each other at time t = 0 by
> both their clocks. Bill accelerates quickly to 1/2 c in a straight
> line away
> from Anne. He sends back a signal periodically. The signal includes
> the time that his clock is registering. After 1 year, he stops and
> abruptly turns around, now travelling at 1/2 c back toward Anne. At
> exactly the time he stops, he sends a signal to Anne, saying, "I am
> turning around now. The time on my clock is XXX.XXX". Anne, who
> buys into SR, receives this signal quite some time later. She says
> to herself, "Hmm. According to my clock and calculations based on
> his speed, he stopped and turned around at YYY.YYY. Further, if
> I compute what his clock should have said when he stopped, I get
> ZZZ.ZZZ."
>
> So. By your reckoning, what are XXX.XXX, YYY.YYY, and ZZZ.ZZZ?
Assuming SR hold throughout,
** XXX.XXX = 1 year, since you have specified as Bill’s time
In reality, according to SR’s relative simultaneity, there are no
coherent answers to YYY.YY and ZZZ.ZZ. However, that is not what you
are expecting, is it? So, the mystified version has 1 year in Bill’s
time translates to 1.15 years in Ann’s time at c / 2. Ann received
Bill’s turn around signal 2.31 years (Ann’s time) after Bill left.
Thus,
** YYY.YYY = 1.15 years
** ZZZ.ZZZ = 1 year
The reverse is true. That is where the paradox resides. <shrug>
Koobee Wublee
again.
Koobee Wublee
The equation above is fine if the Galilean transform satisfies the
null results of the MMX modeling light as waves. Since it does not,
you must use the ballistic theory of light for the Galilean
transform. In which case, correcting what you have above, it becomes
the following.
** |x_3 - x_1| = (c + v) (t_3 - t_1)
> So
>
> v T_BR = c (T_BR - T_AS)
>
> (1) T_BR = 1/(1-v/c) T_AS
Corrected, the above equation should read:
** T_BR = (1 + v / c) T_AS
> Since a light signal travels from event e_2 to the event
> e_4, it must be that
> |x_4 - x_2| = c (t_4 - t_2)
>
> So
>
> v T_BS = c (T_AR - T_BS)
>
> (2) T_AR = (1+v/c) T_BS
Same here.
> So equation (1) says that the delay between signals arriving at B
> is greater than the delay between signals sent by A by a factor of
> 1/(1-v/c).
>
> Equation (2) says that the delay between signals arriving at A
> is greater than the delay between signals sent by B by a factor
> of (1+v/c).
So, there is another way deriving the classical Doppler effect other
than (speed / wavelength). Holding the wavelength invariant yields
the same results. <shrug>
> Note that these delay formulas are slightly different. The delay
> received by the stationary observer, A, is not the same as the
> delay received by the moving observer, B.
>
> Also note: everything done so far is EXACTLY the same, whether
> we are using Galilean relativity or Special Relativity.
>
> Now, we're not quite to the Doppler shift formula yet. Everything
> so far was done in the coordinate system of A. What we really want
> to know is the ratios T_BR'/T_AS and T_AR/T_BS' where T_BR' is the
> time between signals received by B as measured in the
> coordinate system of B, and T_BS' is the time between signals
> sent by B as measured in the coordinate system of B.
>
> There are two different answers, depending on whether we assume
> Galilean relativity or Special relativity.
>
> For Galilean relativity:
>
> The relationship between t' and t is simple:
>
> t' = t
>
> So for this case, we have:
>
> (3) T_BR'/T_AS = T_BR/T_AS = 1/(1-v/c)
> (4) T_AR/T_BS' = T_AR/T_BS = 1+v/c
>
> For Special relativity:
>
> The relationship between t' and t is more complicated:
>
> t' = gamma (t - v/c^2 x)
>
> T_BR' = gamma (T_BR - v/c^2 x_BR)
Let’s see. Both the Galilean and the Lorentz transforms involve two
observers and one observed. The transform then relates how the
observation of the observed by one observer is related to the
observation of the same observed by the other observer. So, in the
case of the Lorentz transform described below,
** dt’ = (dt – v dx / c^2) / sqrt(1 – v^2 / c^2)
** dx’ = (dx – v dt) / sqrt(1 – v^2 / c^2)
** dy’ = dy
** dz’ = dz
The primed observer uses (x’, y’, z’, t’) to observe the observed, and
the unprimed observer uses (x, y, z, t) to observe the same observed.
In doing so, the speed between the primed and the unprimed observer is
v.
So, in our application,
** (dx/dt)^2 + (dy/dt)^2 + (dz/dt)^2 = c^2
Since the observed is light itself. <shrug>
> Where x_BR is the x-location of B when he receives the first
> signal. Since B is traveling at speed v, x_BR = v T_BR. So
Thus, x_BR is not v T_BR.
Say dy’ = dy = dz’ = dz = 0. The velocity transformation of the
Lorentz transform becomes the following familiar quantity.
** dx’/dt’ = (dx/dt – v) / (1 – v dx/dt / c^2)
Your claim will result in the following.
** dx’/dt’ = (v – v) / (1 – v^2 / c^2) = 0
Since according to you
** dx/dt = v
Your mathemagic trick is called. Do you want to try again or behave
like a punk stomping his feet and maintaining the mathemagics you have
conjured up is indeed sound mathematics according to the Lorentz
transform? The choice is yours. <shrug>
Eric Gisse
> Why do you keep avoiding the question?
It is so cute when you pretend you are interested in honest discourse.
[snip rest]
Daryl McCullough
>
>On Mar 2, 1:48 pm, Daryl McCullough wrote:
>
>> Part of the derivation works exactly the same whether you are
>> using Galilean relativity or Special relativity. So let me give
>> a derivation for this initial part, and then show how Galilean
>> versus Special relativity affects the answer.
>>
>> Suppose that there is a frame F in which light travels at speed
>> c in all directions, as measured in that frame. Let there be
>> two observers, A and B. A is at rest in frame F, and B is
>> traveling at constant velocity v relative to frame F, away from A.
>>
>> In the following, all coordinates are assumed to be in the
>> coordinate system of A.
>>
>> Assume that at regular intervals, A sends a light signal toward B,
>> and at regular intervals, B sends a light signal toward A.
>> Let T_AS be the time between signals, as sent by A.
>> Let T_BS be the time between signals, as sent by B.
>> Let T_BR be the time between signals, as received by B.
>> Let T_AR be the time between signals, as received by A.
>>
>> Now let's calculate the relationships between these 4 numbers.
>>
>> Let e_0 be the event at which A and B are initially together.
>>
>> Let e_1 be the event at which A sends out his first signal.
>> Its coordinates will be (x=0, t=T_AS).
>>
>> Let e_2 be the event at which B sends out his first signal.
>>
>> Let e_3 be the event at which B receives the first signal
>> from A. Its coordinates will be (x=v T_BR, t= T_BR)
>>
>> Let e_4 be the event at which A receives the first signal
>> from B. Its coordinates will be (x=0, t=T_AR)
>>
>> Since a light signal travels from event e_1 to the event
>> e_3, it must be that
>> |x_3 - x_1| = c (t_3 - t_1)
>
>The equation above is fine if the Galilean transform satisfies the
>null results of the MMX modeling light as waves.
The above derivation *only* assumes that light has speed
c in the coordinate system in which A is at rest. That's
the only assumption being made.
>** |x_3 - x_1| = (c + v) (t_3 - t_1)
That isn't correct. The dependence on v is *already*
included in the fact that x_3 = v T_BR.
Let's go through a simple example. Suppose that
B is traveling at 1/2 the speed of light, and
that T_AS is 1 second.
So at t=0, A is at x=0, B is at x=0.
At t=1, A sends out a light signal. B is at x=1/2 light-second.
At t=2, the light signal is at x=1 light-second, and so is B.
My formula said:
x_3 - x_1 = c (t_3 - t_1)
x_3 in this case is the value of x when the light signal
reaches B. That is 1 light-second.
x_1 in this case is the value of x when the light signal
is sent from A, which is 0.
t_3 is the time at which the light signal reaches B. That
is 2.
t_1 is the time at which the light signal is sent from A.
That is 1.
So my formula says:
(1 - 0) = c (2 - 1)
which is true.
Eric Gisse
> Koobee Wublee says...
>
[...]
Yeah like I haven't tried that with him before. It won't take long for
you to remember he's a moron.
rasterspace
the results of Michelson-Morley experiment were not, quite "null,"
and several scientists improved this observation,
such as D.C.Miller.
Sue...
<<...(5.10) is exactly the longitudinal Doppler effect (3.10) .
The final crucial step is
substituting them altogether to Eq. (5.6) to see if it is valid.
Then it turns to be just right-- - both sides have the same value
m'_o c^2 as shown in (5.7).
All four equations match perfectly, the proof is finished. It means
the validity of Eqs. (5.1) with (5.2) as well as the basic postulate
of
SR-----the principle of relativity does hold for two inertial frames.
>>
"de’ Broglie’s paradox, relativistic Doppler effect, and the
derivation of mass-energy relation in special relativity"
--Guang-jiong Ni a)
http://cdsweb.cern.ch/record/788100/files/0408047.pdf
Sue...
Daryl McCullough
Sue, if you have nothing to say, don't post. I know that adopting
that rule would eliminate nearly all of your posts, but I think that
it would improve your signal to noise ratio tremendously.
Googling for quotes doesn't really add anything to the discussion.
Everyone has access to Google, they can Google for quotes on their
own. What Google can't do, and neither can you, it seems, is to
take into account the meaning of what is being discussed and offer
comments that relate to what others have said. That human element
is what makes it a discussion. Try to be human, rather than an
Eliza program.
Koobee Wublee
> Sue, if you have nothing to say, don't post. I know that adopting
> that rule would eliminate nearly all of your posts, but I think that
> it would improve your signal to noise ratio tremendously.
It is OK for someone to post invalid mathematics if the poster
gracefully accepts the blame. After all, nobody is perfect. Everyone
makes mistakes. Thus, it is appreciated if Daryl, who consistently
defecates his voodoo mathematics all over these newsgroups to justify
his own religious belief and fails to concede just that as mathemagics
after a serious discussion, would refrain from that. Without Daryl’s
voodoo mathematics, the signal to noise of this group would also
improve by quite a few dBs. <shrug>
marcus_b
That's not what I asked. I said by YOUR reckoning. I don't think
you assume SR.
> ** XXX.XXX = 1 year, since you have specified as Bill’s time
>
> In reality, according to SR’s relative simultaneity, there are no
> coherent answers to YYY.YY and ZZZ.ZZ. However, that is not what you
> are expecting, is it?
I expected you would answer the question with your own presumably
coherent answers, not what you think SR would say.
> So, the mystified version has 1 year in Bill’s
> time translates to 1.15 years in Ann’s time at c / 2. Ann received
> Bill’s turn around signal 2.31 years (Ann’s time) after Bill left.
> Thus,
>
> ** YYY.YYY = 1.15 years
> ** ZZZ.ZZZ = 1 year
>
> The reverse is true.
Not in SR. Ann and Bill are not symmetric.
> That is where the paradox resides. <shrug>
What are ***your own*** answers?
Marcus.
Edward Green
Do tell more.
Eric Gisse
He is either lying or stupid. The MMX was null within error, Dayton
Miller's technique and analysis has repeatedly been shown to be
flawed, and experiment has repeatedly shown such that Michelson type
interferometer experiments end up nulling out.
There is nothing new here - just another idiot.
Tom Roberts
Miller was a prisoner of his time, and did not know about digital signal
processing or modern error analysis. The two combine to show that his
conclusions were wrong and that his data show no SIGNIFICANT variation with
orientation. While HE could not know this, we can.
See my discussion here:
http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html#Experiments_not_consistent_with_SR
Or my paper here: http://www.arxiv.org/abs/physics/0608238
Tom Roberts
Alfonso
> For the purposes of discussing the various thought
> experiments involving relativity, we can describe the
> claims of SR as the following:
>
> There exists a coordinate system such that, as measured
> using that coordinate system,
>
> 1. Light travels as constant velocity, with magnitude c, in any
> direction.
>
> dT/dt = square-root(1-(v/c)^2).
>
> at rest, will have equilibrium length L square-root(1-(v/c)^2)
> when traveling at speed v in a direction parallel to its length.
>
> 4. A standard measuring rod, with equilibrium length L when
> at rest, will also have equilibrium length L when traveling
> at speed v in a direction perpendicular to its length.
>
>
> Theorem: If (x,y,z,t) is a coordinate system satisfying 1-5,
> and (x',y',z',t') is a second coordinate system related to the
> first through some combination of
> rotations, translations, or Lorentz transformations,
> then the second coordinate system will also satisfy 1-5.
>
> or inconsistent, could you please show how claims 1-5
> lead to a contradiction?
The assumption that the same light at the same point in space shall have
the same speed relative to two observers in relative motion is a totally
irrational assumption. It brings into question what we mean by speed and
its acceptance plunged physics into mysticism.
As Essen pointed out Science requires units of measurement in order to
carry out experiment. Measurement theory - one of Essen's fields of
expertise - requires that one's fundamental units are chosen with great
care to avoid duplication. We chose to define fundamental units of
distance and time and in so doing defining them as universal constants.
Units are the only thing you can *define* as constant. Einstein broke a
fundamental law of measurement theory. He defined a speed as a constant,
(speed is a derived unit) thus duplicating units. What he did was create
a new set of units whereby length and time, instead of being universal
constants are allowed to vary so as to make the speed of light (when
measured by these new units = c). While such a bizarre system of units
may be made to work i.e. not lead to mathematical contradiction, there
is really no point in doing so.
Dono.
> While such a bizarre system of units
> may be made to work i.e. not lead to mathematical contradiction, there
> is really no point in doing so.
He did it in order to confuse the idiots.
Androcles
"Alfonso" <Alf...@duffadd.com> wrote in message
news:ArydnfQbSshdnOjQ...@bt.com...
that Virgin Mary was not a virgin.
"A standard clock will show an elapsed time T that satisfies dT/dt =
clock exist it would not be standard.
Predictions of relativity.
"In agreement with experience we further assume the quantity
2AB/(t'A-tA) = c to be a universal constant--the velocity of
light in empty space." --Einstein
In agreement with bullshit:
"the velocity of light in our theory plays the part, physically,
of an infinitely great velocity" -- Einstein.
"We establish by definition that "the ``time'' required by light
to travel from A to B equals the ``time'' it requires to travel
from B to A."-- Einstein.
"In accordance with definition the two clocks synchronize if
tB-tA = t'A-tB", but tB-tA is 1/2(t'A-tA).
Hence tB-tA plays the part, physically, of half an infinitesimally
small duration of time.
Clock A can see the Earth and Earth can see clock A; no matter
how far apart they are they are synchronized, the light signals
between them play the part, physically, of taking half of an
infinitesimally small duration of time, which plays the part,
physically, of zero.
In agreement with experience:
Clock A reads 6:00 am at dawn, it's a perfect clock.
In agreement with experience:
Clock B reads 12:00 pm at noon, it's a perfect clock.
In agreement with bullshit:
"if one of two synchronous clocks at A is moved in a closed curve
with constant velocity until it returns to A, the journey lasting
t seconds, then by the clock which has remained at rest the travelled
clock on its arrival at A will be 1/2 tv^2/c^2 second slow."- Einstein.
In agreement with Einstein's assumption:
Clock A meets clock B at A and is 6 hours slow. Both clocks
synchronize with Earth, because "in accordance with definition
the two clocks synchronize if 0 = 0"-- Einstein.
In disagreement with the Principle of Simultaneity (A meets B when B
meets A):
Clock A meets clock B at dawn and clock B sees clock A arrive at noon.
In agreement with experience:
The dork Einstein plays the part, physically, of a deranged lying cretin.
Eric Gisse
People who say that invariably - for *some* reason - also *just
happen* to not understand the theory they are calling 'mysticism'. I'm
sure it is coincidence rather than a case of cause and effect.
Personally I find it odd how SR can be regarded as 'mysticism' when it
is carefully explained in as many textbooks as you are willing to
read. I resolve that little paradox by realizing that the only people
who call it 'mysticism' are the ones who just don't get it. I am yet
to see an example of a person who both understands relativity and
calls it 'mysticism'.
>
> As Essen pointed out Science requires units of measurement in order to
> carry out experiment. Measurement theory - one of Essen's fields of
> expertise - requires that one's fundamental units are chosen with great
> care to avoid duplication. We chose to define fundamental units of
> distance and time and in so doing defining them as universal constants.
> Units are the only thing you can *define* as constant. Einstein broke a
> fundamental law of measurement theory. He defined a speed as a constant,
> (speed is a derived unit) thus duplicating units. What he did was create
> a new set of units whereby length and time, instead of being universal
> constants are allowed to vary so as to make the speed of light (when
> measured by these new units = c). While such a bizarre system of units
> may be made to work i.e. not lead to mathematical contradiction, there
> is really no point in doing so.
Since units are a local concept, how do you imagine you use units to
make anything constant? An example, please.