In SR, light propagates in a vacuum in a straight line and does not
share the velocity of the source (i.e., additive velocities do not
apply to c regardless of the motion of the source). But clearly it
does share the velocity -- at least, the directional component of the
velocity vector. And the angle of this "straight line" is something
different for every frame.

For example, consider a frame S', which has a pulse-laser at A and a
detector at B, and the path of the light defines a straight line from A
to B. This straight line is at a right angle to an axis we can call
y'. Now, consider a frame S which views S' as moving with a velocity
whose directional component is along the axis y'. From the perspective
of S', who considers his own frame at rest, at time t'1 the laser fires
a pulse at A, which is received by B at time t'2, and B has not moved
between time t'1 and time t'2. However, from the perspective of S, B
*has* moved between the time t1 that the laser fires, and the time t2
that it is detected, and therefore the light travels not from A at time
t1 to where B *is* at time t1, but rather from A at time t1 to where B
*will be* at time t2; and this is not a right-angle to the axis y'.
The only way that the light could take this path is if the light shares
the direction component of the velocity vector of S' -- despite not
sharing the scalar component!

Since the path of the light as assumed by S is longer than the path
assumed by S', then assuming (as both do) that the scalar component of
c is absolute regardless of the velocity of the source, light must take
longer to cover the path assumed by S than to cover the path assumed by
S'. Hence the time light takes to cross this path will be asserted by
S' to have a value less than that asserted by S.

However, each frame's assumptions about the path light takes (and they
are just that, assumptions) have already been incorporated into the
clock synchronization procedures. That is, S', in synchronizing his
clocks, assumes himself at rest; whereas S assumes that the clocks in
S' are in motion; and since light (having an assumed absolute velocity)
is used in SR to conduct the synchronization procedure, S and S' will
have different assumptions about the length of the path light travels
during that synchronization. Thus, it can be seen that the "dilation"
is really an artifact of different assumptions about the length of the
path light takes when S' synchronizes his clocks.

If the principle of the relativity of simultaneity were applied
universally in SR, S would have to conclude that S' mis-synchronized
his clocks, because he incorporated wrong assumptions about the length
of the path that light took from one clock to another during his clock
synchronization procedures. If he did that, the "dilations" would
disappear because they no longer have any mathematical basis. But, in
constrast to every other "observation" by S, in which S is free to deem
his observations correct (even when they disagree with those of S'),
here S, instead of quite properly insisting that S' has
mis-synchronized his clocks, accepts the clock synchronization
procedures of S' as valid!

When I brought this fact out in a previous Usenet post some time ago,
one respondent sneered, "Well, of course S assumes that S' knows how to
properly synchronize his clocks". In fact, however, it isn't the
mechanical prowess of S' that is at issue, but his *assumptions* about
the length of the path taken by light traveling between his clocks
during his synchronization procedure. Why S should be free to insist
on the validity of his own observations with respect to every other
event other than the clock synchronization procedure of S', but not in
the latter case, is a mystery whose answer is not to be found in the
literature of SR.

Mark Adkins

wrote in message
oups.com...
In SR, light propagates in a vacuum in a straight line and does not
share the velocity of the source (i.e., additive velocities do not
apply to c regardless of the motion of the source).

Saying the speed of light is the same is not saying the velocity is the
same. Clearly the light from a source pointing up and a source pointing to
the side will not be the same in any frame.

Bill

But clearly it
does share the velocity -- at least, the directional component of the
velocity vector. And the angle of this "straight line" is something
different for every frame.

For example, consider a frame S', which has a pulse-laser at A and a
detector at B, and the path of the light defines a straight line from A
to B. This straight line is at a right angle to an axis we can call
y'. Now, consider a frame S which views S' as moving with a velocity
whose directional component is along the axis y'. From the perspective
of S', who considers his own frame at rest, at time t'1 the laser fires
a pulse at A, which is received by B at time t'2, and B has not moved
between time t'1 and time t'2. However, from the perspective of S, B
*has* moved between the time t1 that the laser fires, and the time t2
that it is detected, and therefore the light travels not from A at time
t1 to where B *is* at time t1, but rather from A at time t1 to where B
*will be* at time t2; and this is not a right-angle to the axis y'.
The only way that the light could take this path is if the light shares
the direction component of the velocity vector of S' -- despite not
sharing the scalar component!

Since the path of the light as assumed by S is longer than the path
assumed by S', then assuming (as both do) that the scalar component of
c is absolute regardless of the velocity of the source, light must take
longer to cover the path assumed by S than to cover the path assumed by
S'. Hence the time light takes to cross this path will be asserted by
S' to have a value less than that asserted by S.

However, each frame's assumptions about the path light takes (and they
are just that, assumptions) have already been incorporated into the
clock synchronization procedures. That is, S', in synchronizing his
clocks, assumes himself at rest; whereas S assumes that the clocks in
S' are in motion; and since light (having an assumed absolute velocity)
is used in SR to conduct the synchronization procedure, S and S' will
have different assumptions about the length of the path light travels
during that synchronization. Thus, it can be seen that the "dilation"
is really an artifact of different assumptions about the length of the
path light takes when S' synchronizes his clocks.

If the principle of the relativity of simultaneity were applied
universally in SR, S would have to conclude that S' mis-synchronized
his clocks, because he incorporated wrong assumptions about the length
of the path that light took from one clock to another during his clock
synchronization procedures. If he did that, the "dilations" would
disappear because they no longer have any mathematical basis. But, in
constrast to every other "observation" by S, in which S is free to deem
his observations correct (even when they disagree with those of S'),
here S, instead of quite properly insisting that S' has
mis-synchronized his clocks, accepts the clock synchronization
procedures of S' as valid!

When I brought this fact out in a previous Usenet post some time ago,
one respondent sneered, "Well, of course S assumes that S' knows how to
properly synchronize his clocks". In fact, however, it isn't the
mechanical prowess of S' that is at issue, but his *assumptions* about
the length of the path taken by light traveling between his clocks
during his synchronization procedure. Why S should be free to insist
on the validity of his own observations with respect to every other
event other than the clock synchronization procedure of S', but not in
the latter case, is a mystery whose answer is not to be found in the
literature of SR.

Mark Adkins

wrote:
In SR, light propagates in a vacuum in a straight line and does not
share the velocity of the source (i.e., additive velocities do not
apply to c regardless of the motion of the source).

Not quite. The light always propagates with SPEED c in any inertial
frame, but its direction in any frame clearly depends on the orientation
of the source in that frame.


But clearly it
does share the velocity -- at least, the directional component of the
velocity vector. And the angle of this "straight line" is something
different for every frame.

Sure -- because the light source has in general a different orientation
in different frames.

BTW this is true in Newtonian physics for light or any object
with finite speed, such as cannonballs -- drive past a cannon
firing vertically, and in the frame of your car the cannon is
not aimed straight up (where "aimed" is defined by where the
cannonball goes, not necessarily the orientation of the cannon
itself).


Since the path of the light as assumed by S is longer than the path
assumed by S', then assuming (as both do) that the scalar component of
c is absolute regardless of the velocity of the source, light must take
longer to cover the path assumed by S than to cover the path assumed by
S'. Hence the time light takes to cross this path will be asserted by
S' to have a value less than that asserted by S.

Sure.


However, each frame's assumptions about the path light takes (and they
are just that, assumptions)

No, they are MEASUREMENTS. That is, in S' when one measures the distance
from source (at emission time) to detector (at detection time) one gets
a smaller value than when S measures the distance from source (at
emission time) to detector (at detection time). This is just simple
Euclidean geometry plus the fact that in S the source and detector are
moving.


Thus, it can be seen that the "dilation"
is really an artifact of different assumptions about the length of the
path light takes when S' synchronizes his clocks.

With "assumptions" = "measurements" this is sort-of correct; there is
an aditional contibution from "time dilation" (but that, too, is related
to your basic point).


If the principle of the relativity of simultaneity were applied
universally in SR, S would have to conclude that S' mis-synchronized
his clocks,

There is no "principle of the relativity of simultaneity".

S concludes that S' uses a different method to synchronize clocks that
are at rest in S' than S uses for clocks at rest in S. This is
manifestly so, of course.


it isn't the
mechanical prowess of S' that is at issue, but his *assumptions* about
the length of the path taken by light traveling between his clocks
during his synchronization procedure.

No, it is MEASUREMENTS, not assumptions.


Why S should be free to insist
on the validity of his own observations with respect to every other
event other than the clock synchronization procedure of S', but not in
the latter case, is a mystery whose answer is not to be found in the
literature of SR.

Your question does not make sense, once you realize the mistakes pointed
out above. S' uses a different synchronization procedure than S, so of
course S' gets different answers for measurements in which
synchronization is important. Nothing strange or unexpected there....


Tom Roberts

Tom Roberts wrote:
wrote:
In SR, light propagates in a vacuum in a straight line and does not
share the velocity of the source (i.e., additive velocities do not
apply to c regardless of the motion of the source).

Not quite. The light always propagates with SPEED c in any inertial
frame, but its direction in any frame clearly depends on the orientation
of the source in that frame.

I hope you're not suggesting that in one frame the laser is pointed
toward the detector, whereas in another frame the laser is pointing
toward an empty section of space where the detector will be in future,
and that the empty section of space the detector points toward is
different for every such frame.

Because so far as I know, Lorentz transformations may shorten
rectangles but they don't skew them. Either the laser is pointing
toward the detector, in which case it does so in every frame, or else
the laser is pointed into space (but then we have the absurd conclusion
that the angle between laser and detector is different for every
frame).

So, if S assumes that S' is moving, and therefore that the
laser/detector apparatus in S' is moving, then the light must travel
toward where the detector *will be* (according to S, but not according
to S') because light shares the directional component of the velocity
vector of the light source. (But not the scalar component, ha ha!)



But clearly it
does share the velocity -- at least, the directional component of the
velocity vector. And the angle of this "straight line" is something
different for every frame.

Sure -- because the light source has in general a different orientation
in different frames.

BTW this is true in Newtonian physics for light or any object
with finite speed, such as cannonballs -- drive past a cannon
firing vertically, and in the frame of your car the cannon is
not aimed straight up (where "aimed" is defined by where the
cannonball goes, not necessarily the orientation of the cannon
itself).


Yes, but in Newtonian physics velocities are additive and it makes
perfect sense that something sharing the scalar component of a velocity
vector should share the directional component as well. When the scalar
component isn't shared, as in SR, it's rather puzzling that the
directional component is shared.


Since the path of the light as assumed by S is longer than the path
assumed by S', then assuming (as both do) that the scalar component of
c is absolute regardless of the velocity of the source, light must take
longer to cover the path assumed by S than to cover the path assumed by
S'. Hence the time light takes to cross this path will be asserted by
S' to have a value less than that asserted by S.

Sure.


However, each frame's assumptions about the path light takes (and they
are just that, assumptions)

No, they are MEASUREMENTS. That is, in S' when one measures the distance
from source (at emission time) to detector (at detection time) one gets
a smaller value than when S measures the distance from source (at
emission time) to detector (at detection time). This is just simple
Euclidean geometry plus the fact that in S the source and detector are
moving.

The relative motion is observed, but the attribution of that motion to
either of the two frames is an assumption. That is, it is an
*assumption* that frame S' is moving (the assumption of S), and it is
an *assumption* that frame S' is at rest (the assumption of S'). Since
that assumption is, ipso facto, an *assumption* about the distance
light travels between two clocks to be synchronized in S', this results
in different conclusions about the time it takes light to travel this
assumed distance (at an absolute speed of c in all frames).

So, when S' believes that a pair of clocks have been properly
synchronized (i.e., that they simultaneously have the same reading), S
perceives that they have not. Of course, S' has the same perception
about the clocks of S, and therefore when S says that the clocks of S'
do not "simultaneously" possess identical readings, S' is perfectly
within his rights to insist that this is because S has mis-synchronized
*his* clocks. That is to say, simultaneity is relative.

Either a frame is moving, or it is not. If it is moving, then it
should incorporate this assumption (about the distance that light
travels between synchronized clocks) into its calculations and
procedures. If it instead incorporates a distance based on the
assumption that it is at rest, when it is not at rest, then it is in
error and its calculations must involve logically inconsistent
premises. If then, according to S, S' is moving, yet S' assumes itself
at rest and therefore assumes (from the viewpoint of S) an incorrect
distance that light has traveled between clocks that it is
synchronizing, then S must regard these calculations of S' as erroneous
and logically inconsistent. Yet, in SR, absurdly, S accepts them.



Thus, it can be seen that the "dilation"
is really an artifact of different assumptions about the length of the
path light takes when S' synchronizes his clocks.

With "assumptions" = "measurements" this is sort-of correct; there is
an aditional contibution from "time dilation" (but that, too, is related
to your basic point).

Your rephrasings are ignorant. And you're missing my basic point: the
mathematical basis for "time dilation" disappears altogether when the
principle of the relativity of simultaneity is properly (universally)
applied, that is to say, applied to include (rather than exclude as a
special case) the clock synchronization procedure. If simultaneity is
relative in the general case, then it should be also in the specific
case of whether two clocks possess an identical reading simultaneously
(i.e., whether they are properly synchronized); and clearly no two
frames should regard each other's clocks as properly synchronized if
this principle is universally applied. Of course, that immediately and
obviously demonstrates the principle to be ridiculous, which is no
doubt why SR quietly excludes clock synchronization procedures from the
principle of the relativity of simultaneity.



If the principle of the relativity of simultaneity were applied
universally in SR, S would have to conclude that S' mis-synchronized
his clocks,

There is no "principle of the relativity of simultaneity".

There is. See for example, Albert Einstein, "Relativity: The Special
and the General Theory", 1920, Chapter IX. The Relativity of
Simultaneity.


S concludes that S' uses a different method to synchronize clocks that
are at rest in S' than S uses for clocks at rest in S. This is
manifestly so, of course.


it isn't the
mechanical prowess of S' that is at issue, but his *assumptions* about
the length of the path taken by light traveling between his clocks
during his synchronization procedure.

No, it is MEASUREMENTS, not assumptions.

Clearly, whether a frame is "moving" or "at rest" is regarded *by SR
itself* as an assumption; and so, therefore, is the distance that light
is regarded as moving between two clocks in a frame.



Why S should be free to insist
on the validity of his own observations with respect to every other
event other than the clock synchronization procedure of S', but not in
the latter case, is a mystery whose answer is not to be found in the
literature of SR.

Your question does not make sense, once you realize the mistakes pointed
out above. S' uses a different synchronization procedure than S, so of
course S' gets different answers for measurements in which
synchronization is important. Nothing strange or unexpected there....


Tom Roberts

What mistakes?

Mark Adkins

Mark Adkins got to the point:

my basic point: the
mathematical basis for "time dilation" disappears altogether when the
principle of the relativity of simultaneity is properly (universally)
applied, that is to say, applied to include (rather than exclude as a
special case) the clock synchronization procedure.

Say what? Two different frames, say A and B, already have their
own convention to determine simultaneity - that's part of the
definition of an inertial frame in special relativity. Time
dilation is simply the determination by B that A's clock rate,
although lasting exactly one tick per second by A's measurements,
is longer when measured by the clocks in the B frame.

The mathematical basis for time dilation is fairly simple
geometry. In fact, the implications of the underlying geometry
are far more interesting, physically, than all the gee-whiz
stories about twin parodoxes or semantic nonsense about how
clocks are slowed by their velocity. Relativity is fundamentally
about symmetry, and symmetry is described by geometry.


---Tim Shuba---

wrote:
Tom Roberts wrote:
The light always propagates with SPEED c in any inertial
frame, but its direction in any frame clearly depends on the orientation
of the source in that frame.

I hope you're not suggesting that in one frame the laser is pointed
toward the detector, whereas in another frame the laser is pointing
toward an empty section of space where the detector will be in future,
and that the empty section of space the detector points toward is
different for every such frame.

This depends on what you mean by "point". If you mean something like
"the centerline of the laser extended along its length simultaneously",
then yes -- the sticky point is that "simultaneously". If you mean the
actual direction the beam takes, then no.


Either the laser is pointing
toward the detector, in which case it does so in every frame, or else
the laser is pointed into space (but then we have the absurd conclusion
that the angle between laser and detector is different for every
frame).

This does not make sense -- two objects do not determine any sort of
"angle". And look above for the ambiguity in your "pointing".

But if the laser beam hits the detector when viewed from one frame, it
of course does so when viewed from any other frame. Note my phrasing --
objects are not "in" any frame; frames are used for viewing only (i.e.
measuring). Of course objects can be "at rest in" a given frame, but
that is quite different from being "in" the frame (which implies
exclusivity which is not possible).


BTW this is true in Newtonian physics for light or any object
with finite speed, such as cannonballs -- drive past a cannon
firing vertically, and in the frame of your car the cannon is
not aimed straight up (where "aimed" is defined by where the
cannonball goes, not necessarily the orientation of the cannon
itself).

Yes, but in Newtonian physics velocities are additive and it makes
perfect sense that something sharing the scalar component of a velocity
vector should share the directional component as well. When the scalar
component isn't shared, as in SR, it's rather puzzling that the
directional component is shared.

You confuse yourself by attempting to separate "scalar part" from
"directional component". The transforms most naturally relate the
components of _vectors_ (3-vectors in NM, 4-vectors in SR).

BTW in NM, for an object viewed from frame A and from frame B, the two
frames do NOT "share the scalar component" of the object's velocity
(except for certain unusual circumstances):

v . v != (v+u) . (v+u) for 3-velocities u and v.


The relative motion is observed, but the attribution of that motion to
either of the two frames is an assumption. That is, it is an
*assumption* that frame S' is moving (the assumption of S), and it is
an *assumption* that frame S' is at rest (the assumption of S').

No. You are caught up in old-fashioned words. There is no "at rest",
there is only "at rest relative to S" (or S'). There is no "moving",
there is only "moving relative to S" (or S').


Either a frame is moving, or it is not. [...]

That seems to me to be the central part of your error and confusion.
There is no "moving", there is only "moving relative to S" (or S').


Tom Roberts

Tom Roberts wrote:
wrote:
Tom Roberts wrote:
The light always propagates with SPEED c in any inertial
frame, but its direction in any frame clearly depends on the orientation
of the source in that frame.

I hope you're not suggesting that in one frame the laser is pointed
toward the detector, whereas in another frame the laser is pointing
toward an empty section of space where the detector will be in future,
and that the empty section of space the detector points toward is
different for every such frame.

This depends on what you mean by "point". If you mean something like
"the centerline of the laser extended along its length simultaneously",
then yes -- the sticky point is that "simultaneously". If you mean the
actual direction the beam takes, then no.

I didn't say "point", I said pointed.



Either the laser is pointing
toward the detector, in which case it does so in every frame, or else
the laser is pointed into space (but then we have the absurd conclusion
that the angle between laser and detector is different for every
frame).

This does not make sense -- two objects do not determine any sort of
"angle".

It does make sense, nitwit, because I've already explicitly stated that
the angle in question is the angle between the source/detector line and
the direction of motion of S' (according to S). That you are unable to
"comprehend" this obvious relation implicitly without a constant
explicit repetition, demonstrates just how brittle and off-base your
"comprehension" is.


And look above for the ambiguity in your "pointing".

No ambiguity. Either the laser points to the detector or not, as per
my earlier comments. Only a dullard would find this ambiguous enough
to be confusing. Are you sure you aren't an artificial intelligence
program? They seem to have a great deal of trouble interpreting
English, even when perfectly well-formed by human grammatical
standards.


But if the laser beam hits the detector when viewed from one frame, it
of course does so when viewed from any other frame. Note my phrasing --
objects are not "in" any frame; frames are used for viewing only (i.e.
measuring). Of course objects can be "at rest in" a given frame, but
that is quite different from being "in" the frame (which implies
exclusivity which is not possible).


BTW this is true in Newtonian physics for light or any object
with finite speed, such as cannonballs -- drive past a cannon
firing vertically, and in the frame of your car the cannon is
not aimed straight up (where "aimed" is defined by where the
cannonball goes, not necessarily the orientation of the cannon
itself).

Yes, but in Newtonian physics velocities are additive and it makes
perfect sense that something sharing the scalar component of a velocity
vector should share the directional component as well. When the scalar
component isn't shared, as in SR, it's rather puzzling that the
directional component is shared.

You confuse yourself by attempting to separate "scalar part" from
"directional component". The transforms most naturally relate the
components of _vectors_ (3-vectors in NM, 4-vectors in SR).

I don't confuse *myself* about this, you obfuscatory fool.


The relative motion is observed, but the attribution of that motion to
either of the two frames is an assumption. That is, it is an
*assumption* that frame S' is moving (the assumption of S), and it is
an *assumption* that frame S' is at rest (the assumption of S').

No. You are caught up in old-fashioned words. There is no "at rest",
there is only "at rest relative to S" (or S'). There is no "moving",
there is only "moving relative to S" (or S').

Yes. I am not caught up in old-fashioned words. I explicitly said
above that the "movement" of S' is "the assumption of S" and that the
"rest" state of S' is "the assumption of S'". Go back to SR
kindergarten, little boy, if you can't even get this stuff straight.



Either a frame is moving, or it is not. [...]

That seems to me to be the central part of your error and confusion.
There is no "moving", there is only "moving relative to S" (or S').


Tom Roberts

Try reading what I actually wrote, nitwit, instead of pretending that I
wrote something different and then falsely attributing confusion on the
basis of your misrepresentation.

Mark Adkins

wrote in message
oups.com...
|
| Tom Roberts wrote:
| wrote:
| Tom Roberts wrote:
| The light always propagates with SPEED c in any inertial
| frame, but its direction in any frame clearly depends on the
orientation
| of the source in that frame.
|
| I hope you're not suggesting that in one frame the laser is
pointed
| toward the detector, whereas in another frame the laser is
pointing
| toward an empty section of space where the detector will be in
future,
| and that the empty section of space the detector points toward is
| different for every such frame.
|
| This depends on what you mean by "point". If you mean something like
| "the centerline of the laser extended along its length
simultaneously",
| then yes -- the sticky point is that "simultaneously". If you mean
the
| actual direction the beam takes, then no.
|
| I didn't say "point", I said pointed.
|
|
|
| Either the laser is pointing
| toward the detector, in which case it does so in every frame, or
else
| the laser is pointed into space (but then we have the absurd
conclusion
| that the angle between laser and detector is different for every
| frame).
|
| This does not make sense -- two objects do not determine any sort of
| "angle".
|
| It does make sense, nitwit, because I've already explicitly stated
that
| the angle in question is the angle between the source/detector line
and
| the direction of motion of S' (according to S). That you are unable
to
| "comprehend" this obvious relation implicitly without a constant
| explicit repetition, demonstrates just how brittle and off-base your
| "comprehension" is.
|
|
| And look above for the ambiguity in your "pointing".
|
| No ambiguity. Either the laser points to the detector or not, as per
| my earlier comments. Only a dullard would find this ambiguous enough
| to be confusing. Are you sure you aren't an artificial intelligence
| program? They seem to have a great deal of trouble interpreting
| English, even when perfectly well-formed by human grammatical
| standards.
|
|
| But if the laser beam hits the detector when viewed from one frame,
it
| of course does so when viewed from any other frame. Note my
phrasing --
| objects are not "in" any frame; frames are used for viewing only
(i.e.
| measuring). Of course objects can be "at rest in" a given frame, but
| that is quite different from being "in" the frame (which implies
| exclusivity which is not possible).
|
|
| BTW this is true in Newtonian physics for light or any object
| with finite speed, such as cannonballs -- drive past a cannon
| firing vertically, and in the frame of your car the cannon is
| not aimed straight up (where "aimed" is defined by where the
| cannonball goes, not necessarily the orientation of the cannon
| itself).
|
| Yes, but in Newtonian physics velocities are additive and it makes
| perfect sense that something sharing the scalar component of a
velocity
| vector should share the directional component as well. When the
scalar
| component isn't shared, as in SR, it's rather puzzling that the
| directional component is shared.
|
| You confuse yourself by attempting to separate "scalar part" from
| "directional component". The transforms most naturally relate the
| components of _vectors_ (3-vectors in NM, 4-vectors in SR).
|
| I don't confuse *myself* about this, you obfuscatory fool.
|
|
| The relative motion is observed, but the attribution of that
motion to
| either of the two frames is an assumption. That is, it is an
| *assumption* that frame S' is moving (the assumption of S), and it
is
| an *assumption* that frame S' is at rest (the assumption of S').
|
| No. You are caught up in old-fashioned words. There is no "at rest",
| there is only "at rest relative to S" (or S'). There is no "moving",
| there is only "moving relative to S" (or S').
|
| Yes. I am not caught up in old-fashioned words. I explicitly said
| above that the "movement" of S' is "the assumption of S" and that the
| "rest" state of S' is "the assumption of S'". Go back to SR
| kindergarten, little boy, if you can't even get this stuff straight.
|
|
|
| Either a frame is moving, or it is not. [...]
|
| That seems to me to be the central part of your error and confusion.
| There is no "moving", there is only "moving relative to S" (or S').
|
|
| Tom Roberts
|
| Try reading what I actually wrote, nitwit, instead of pretending that
I
| wrote something different and then falsely attributing confusion on
the
| basis of your misrepresentation.
|
| Mark Adkins
|

Roberts read what you wrote? He hasn't in the six years I've been
writing to this newsgroup.
He hasn't even read what Einstein wrote.

[quote]
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.
[end quote]
Ref: http://www.fourmilab.ch/etexts/einstein/specrel/www/


Definitions are assertions, not postulates, and it is from Einstein's
crazy definition that Roberts' crazy assertion "light always propagates
with SPEED c in any inertial frame" is derived.
The cuckoo transforms are derived from

½[tau(0,0,0,t)+tau(0,0,0,t+x'/(c-v)+x'/(c+v))] = tau(x',0,0,t+x'/(c-v))
,

and the ½ is from the crazy definition.

Mathematics is a wonderful tool, you can use to prove a hypothesis
is false. If you find time dilating and lengths contracting, then you
have
a proof reductio-ad-absurdum that Einstein's definition is nonsense.
No need to carry out a physical experiment to see if the absurdity
holds up, but even if you do, Sagnac shows it.

On page http://www.mathpages.com/rr/s2-07/2-07.htm
is a description of the Sagnac effect, and the author of that page
states:
[quote]
A clock attached to the perimeter of the ring would, according to
special relativity, record a lesser time, by the factor
gamma = (1-(v/c)^2)^(1/2), so the Sagnac delay with respect to such
a clock would be [4A\omega/c^2]/(1-(v/c)^2)^(1/2). "
[end quote]

The author has accepted the "Lorentz" (actually Einstein) transforms
at face value instead of deriving them from first principles, a common
error of many.
Sagnac closely resembles Einstein's own thought experiment, in that
it is evaluating the speed and time of flight of the light over a fixed
distance.
Einstein uses reflection to obtain the return (or counterclockwise) ray,
but that is not as important as the values c+v and c-v for the distance
travelled and the resulting times obtained.
In the case of Sagnac, these values apply not to the rotating apparatus
but to the stationary observer, who now simulates Einstein's "moving"
frame, the light's speed being c in the apparatus.
It is as if the apparatus did not rotate and the observer moved around
the circumference.

To see why, we imagine the following:
Ref: http://carouselmagic.com/graphics/lj400.jpg
On the carousel, normally the rider moves with the same angular
velocity as the ride, his relative velocity is zero with respect to the
ride. To model our situation, we need children to walk or run around
the carousel in opposite directions and meet again where they started,
relative to the carousel. Grandpa puts the children on the slowly
turning carousel and off they go in opposite directions, and he waits
to see what happens. The child that moved in the same direction as
the carousel meets grandpa before he meets his sibling, there is a
non-zero angle alpha in the diagram shown at
http://www.mathpages.com/rr/s2-07/2-07.htm
The frequency of the clockwise child, in radians per second or steps
he takes, is different to the frequency of the counterclockwise child,
as seen from where grandpa is standing.
Whether or not we turn the carousel, grandpa could walk around it
to his starting point and obtain the same result.
From the carousel's point of view the speed of the children is c.
From grandpa's point of view the speeds of the children are
c+v and c-v.
The carousel is Einstein's "stationary" frame and grandpa is the
"moving" frame. Einstein uses quotation marks around "stationary"
and "moving" to emphasize the frames are interchangable, he states
[quote]
" In order to render our presentation more precise and to distinguish
this system of co-ordinates verbally from others which will be
introduced hereafter, we call it the "stationary system.''
[end quote]
Ref: http://www.fourmilab.ch/etexts/einstein/specrel/www/

The stationary system is the one in which the speed of light is c.
It is grandpa's watch that must record a lesser time according to
special relativity, not "the clock at the perimeter of the ring" as the
author states, for it is grandpa that perceives c+v and c-v, not the
carousel.

The reason he must do so is Einstein's whimsical definition of time.
[quote]
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.
[end quote]
This definition bears no resemblance to reality or the Sagnac effect,
but it is the heart of special relativity, so I'll proceed.

The transforms Einstein created and unfairly ascribed to Lorentz
were derived from his equation
½[tau(0,0,0,t)+tau(0,0,0,t+x'/(c-v)+x'/(c+v))] = tau(x',0,0,t+x'/(c-v))
where x' is the distance the light travels, here the circumference of
the ring. There is double usage of the term x', it is the distance the
light travels and a coordinate in the "moving" frame.
The remaining parameters for the function tau are y and z, coordinates,
and the time taken by the light to complete a circuit of the ring or
travel
from 0 to x' or the other way or both.
For clarity I shall replace the times x'/(c-v) with the symbol a and
and x'/(c+v) with the symbol b.
The y term can be considered to play a role, since the angle alpha
will produce y = R.cos(alpha), x' = R.sin(alpha), R being the radius
of the ring, R = x'/2\pi.
However, we can ignore y because Einstein later differentiates his
equation by making x' infinitessimally small, and in any event the
coordinate x' is zero even though the distance x' is non-zero, the
light returns to it's starting point in the carousel or ring frame.
It does not quite do so in grandpa's frame, though.
Thus we have Einstein's equation with x' = 0 when used as a
coordinate, and x' =x-vt = the circumference of the ring which is
greater than zero when used as a length. This now gives is
½[tau(0,0,0,t)+tau(0,0,0,t+a+b)] = tau(0,0,0,t+a)***
Now the x', y, and z coordinates are redundant, being zero, leaving
½[tau(t)+tau(t+a+b)] = tau(t+a).
Since tau(t) must equal t, the clock on the carousel being initially
synchronized with grandpa's watch, that too can be disregarded.
The t is redundant, it refers to the time at which the experiment
takes place, leaving
½tau(a+b) = tau(a).
Hence we have divorced length from time by the elimination of
coordinates, taken out the Lorentx contraction and left only
time as the sole parameter to the function tau.
But something is wrong.
In Sagnac, the times a=x'/(c-v) and b=x'/(c+v are not consecutive,
they are concurrent. To make them consecutive, we must ask
grandpa to reverse his direction and walk the opposite way
around the carousel immediately after his first circumnavigation,
or alternatively let grandpa remain and the children to reverse
(or reflect at x') as the carousel slowly turns.
That produces -alpha, and grandpa meets the children at his
original starting location, hence
tau(a+b) = tau(a)+tau(b)
Had grandpa reversed the order of his two excursions we would
have found
½tau(a+b) = tau(b)
We then have two equations for tau,
½tau(a+b) = tau(a) ... 1
½tau(a+b) = tau(b) ... 2
from which is is immediately clear that tau is not a function,
having two different values, unless those values are the same.
Einstein clearly states
[quote]
In the first place it is clear that the equations must be linear on
account of the properties of homogeneity which we attribute
to space and time.
[end quote]
It follows that tau is not a linear function as claimed and Einstein's
definition of time is not satisfied.

Androcles.

footnote:
*** To be pedantic,
½[tau(0,0,0,t)+tau(R.sin(alpha), R.cos(alpha),0,t+a+b)] =
tau(R.sin(alpha), R.cos(alpha),0,t+a)
where R = x'/2\pi, but the coordinates play no significant role in
Sagnac.