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Androcles wrote:





Do me a favour.
Einstein wrote

"light is always propagated in empty space with a definite
velocity c which is independent of the state of motion of the
emitting body"
Reference :
http://www.fourmilab.ch/etexts/einstein/specrel/www/

Then he wrote:
"But the ray moves relatively to the initial point of k, when
measured in the stationary system, with the velocity c-v, so
that x'/(c-v) = t."






I don't know what the context of this is. I assume he's not
talking about how fast the light is moving in a given frame,
but
rather how fast the light is moving away from some other
object,
as seen not in the object's own frame but in a frame where the
object itself is moving at velocity v. In this case, although
light will still travel at c in this frame, the distance
between
the light ray and the object moving at velocity v will be seen
to
grow at the rate (c-v) in this frame. In the object's own
frame,
though, the distance between itself and the light ray would
grow
at the rate c, as relativity predicts.





You didn't reply to this part of my post--can you provide me
with
the context of that statement by Einstein?




I've given you the reference.




Ah, I didn't notice that you were quoting from a website, sorry.
But
that's a pretty long article, which section did you get the quote
involving the equation x'/(c-v) = t from?



Section 3. It wouldn't refer to it as an "article" though. It's the
original
paper that Einstein wrote in 1905 creating special relativity.



I see my interpretation was correct, then. He is saying that you
have
two reference frames, K and k, and that in K's reference frame, the
distance between the origin of k and a ray of light is growing at
the
rate (c-v).



For some duration of time.
For another duration of time the rate is v+c.
These durations are not equal.
Time is not a vector, it has no additive inverse.






This does not mean that the ray of light is moving at velocity (c-v)
in k's reference frame; in both K and k, the light is moving at
velocity c.




I don't believe in magic. If c = c+v and c = c-v, then v = 0.


Nowhere has anyone said that c = c-v.

Really? Tell all those that claim c is invariant that they are not to
say it,
then.



Rather, the idea here is that if
you measure the speed that the distance between k and the light ray is
growing using K's rulers and clocks, it is growing at the rate (c-v);
but if you measure the speed that the distance between k and the light
ray is growing using k's rulers and clocks, it is growing at the rate
c.

Yeah. I know. Stupidity is rife around here.


Since K and k use different rulers and clocks, then *if* you believe
that rulers shrink and clocks dilate, it shouldn't be so surprising
that
K's rulers and clocks will give a different answer than k's rulers and
clocks.

As I said, I don't believe in magic.


I know you don't actually believe that, but the point is that
advocates of relativity do, so clearly they are not saying anything so
silly as c = c-v, rather they are saying:
speed measured by K's rulers and clocks = c-v
speed measured by k's rulers and clocks = c

Show me the evidence.


If V = (c+v)/(1+v/c) then use that to derive the LTs.
If the system of equations is linear as Einstein claims, it shoud be
no trouble.


Where are you getting V = (c+v)/(1+v/c)? That's not an equation I can
remember seeing.

§ 5. The Composition of Velocities
http://www.fourmilab.ch/etexts/einstein/specrel/www/

You don't know very much about relativity, do you?
Why are you talking to me as if you did?




You are one of those that starts at the Lorentz
Transforms, proceeds to lecture on what you imagine I'm not aware
of, then conclude you are right.




You didn't really read my post, so how do you know this?



I didn't read it in depth, no. I quickly glanced down and saw some
equations I recognised as wasn't prepared to comment on, since they
cannot be derived in any sensible manner.



They can be derived from the fact that all the fundamental laws of
physics display the property of "Lorentz invariance".



Bull****.




This is a mathematical property which can be verified simply by
examining the equations. Do you understand what it means to say a
given equation shows Lorentz invariance? If not, I can go into more
detail.



Go on then, explain circularity .... err .... Lorentz invariance to
me.


Well, first I'll describe Galilei invariance since it's mathematically
a
bit simpler, then I'll explain Lorentz invariance. Here are the
Galilei
transformations for transforming between inertial reference frames in
Newtonian physics:

x'=x - vt
y'=y
z'=z
t'=t

x=x' + vt'
y=y'
z=z'
t=t'

To say a certain physical equation is "Galilei-invariant" just means
the
form of the equation is unchanged if you make these substitutions. For
example, suppose at time t you have a mass m1 at position (x1, y1, z1)
and another mass m2 at position (x2, y2, z2) in your reference frame.
Then the Newtonian equation for the gravitational force between them
would be:

F = Gm1m2/[(x1 - x2)^2 + (y1 - y2)^2 + (z1 - z2)^2]

Now, suppose we want to transform into a new coordinate system moving
at
velocity v with respect to the first one. In this coordinate system,
at
time t' the mass m1 has coordinates (x1', y1', z1') and the mass m2
has
coordinates (x2', y2', z2'). Using the Galilei transformations, we can
figure how the force would look in this new coordinate system, by
substituting in x1 = x1' + vt', x2 = x2' + vt', y1 = y1', y2 = y2',
and
so forth. With these substitutions, the above equation becomes:

F = Gm1m2/[(x1' + vt' - (x2' + vt'))^2 + (y1' - y2')^2 + (z1' -
z2')^2]

and you can see that this simplifies to:

F = Gm1m2/[(x1' - x2')^2 + (y1' - y2')^2 + (z1' - z2')^2]

In other words, the equation has exactly the same form in both
coordinate systems. This is what it means to be "Galilei invariant".
More generally, if you have *any* physical equation which computes
some
quantity (say, force) as a function of various space and time
coordinates, like f(x,y,z,t) [of course it may have more than one of
each coordinate, like the x1 and x2 above, and it may be a function of
additional variables as well, like m1 and m2 above] then for this
equation to be "Galilei invariant", it must satisfy:
f(x'+vt,y',z',t') = f(x',y',z',t')

Oh, that's an easy one.
v = 0.



From this, it's pretty simple to see what it must mean for a given
physical equation to be "Lorentz invariant" as well. Here are the
Lorentz transformation equations:

x'=gamma(x - vt)

Don't you mean xi = gamma.x' ?
Einstein uses x' = x-vt. See, you've called the Galilean Transform
x' = x-vt, which is correct. The Lorentz is the Galilean * gamma.





y'=y
z'=z
t'=gamma(t - vx/c^2)
Oops. You did it again. be careful with those primes.

*tau* =gamma(t - vx/c^2)

Another easy one.
v = x/t, by definition, so

tau = (t- vt * v /c^2) * gamma.
tau = t (1-v^2/c^2) * gamma.
= t * sqrt(1-v^2/c^2)
So the simpler form is
xi = x' * gamma
tau = t / gamma.

The speed of the "stationary" frame as measured from the "moving" frame
is then

upsilon = xi/tau

Prove |upsilon| = |v| (to preseve symmetry).


x=gamma(x' + vt')
y=y'
z=z'
t=gamma(t' + vx'/c^2)

where gamma = 1/squareroot(1-v^2/c^2)

So, if you have some physical equation f(x,y,z,t), then for it to be
"Lorentz-invariant" it just must have the following property:

f(gamma(x'+vt'),y',z',gamma(t'+vx'/c^2)) = f(x',y',z',t')

This is just a mathematical property of a given equation or set of
equations, it is just a matter of calculation to check if the equation
satisfies it (the equation for Newtonian gravity would not have this
property, so it would not be Lorentz-invariant).

Thank goodness for that. You are mixing greek notation with prime
notation,
that can only confuse you (and me). Be consistent. I have no idea what
you
mean by vt', or x'.



And it is a fact that
Maxwell's laws do have this property of Lorentz-invariance, as do all
the most fundamental laws currently known (such as the laws of quantum
field theory).


Maxwell's equations are based on aether. There is no aether.
I'll accept Einstein's opener.
"It is known that Maxwell's electrodynamics--as usually understood
at the present time--when applied to moving bodies, leads to asymmetries
which do not appear to be inherent in the phenomena. "
Nice "facts" you present.



However, if it is true that all the fundamental laws of nature obey
Lorentz invariance,
it must be true that if different observers in motion with relation
to one another all use the same procedure to define the coordinates
of
events in their frame--building a network of rulers and clocks which
are at rest with respect to themselves, and synchronizing the clocks
using the assumption that light moves at the same speed in all
directions in their frame--



It seemeth impossible for it to be, for if I walk away from a candle
set
by the wall and you walk toward the same candle, we then have some
motion between us. If we then divide that motion equally between us,
and
impart it to the candle such that it appeareth to be at rest upon the
floor upon which we walk, how then doth the light divide it's motion
between us, that we may both observe it to be the same?

Because you and I use different rulers and clocks to measure this
motion.

I've only got one ruler and one clock, there are two light sources, one
I walk toward and the other I walk away from.

Even if we lived in a Newtonian universe where rulers and
clocks
wouldn't *naturally* appear to shrink and slow down, suppose I bought
you some phony gag rulers and clocks from the novelty shop, with the
markings on the rulers too short by a factor of squareroot(1-v^2/c^2),
and each tick of the clock longer then it should be by a factor of
1/squareroot(1-v^2/c^2). Suppose I also made different clocks of yours
be out-of-sync, by using the (false, in a Newtonian universe)
assumption
that a beam of light emitted from the midpoint of two clocks (by a
source at rest relative to me, if you believe light's velocity depends
on the source velocity, although in classical E&M it should actually
depend on the rest frame of the aether) should strike both clocks at
the
same time, even if one clock is moving towards the point the light was
emitted and one is moving away from it.

If you are moving away from me at velocity v, and you are using these
gag rulers and clocks (which have been synchronized using this
incorrect
procedure, in the Newtonian universe we're living in) to measure
things,
do you agree that *as measured by your incorrect rulers and clocks*,
then if I measure the light to be moving at c, you will also measure
it
to be moving at c? Do you agree that if I want to find some equations
to
transform between my correct measurements and your incorrect
measurements, the correct equations will be the Lorentz transformation
equations?

I don't use gag rules and clocks, I have only one rule and one clock.
I approach one source of light as I recede from the other.
You are not involved.

S1-----------------------------me-----------S2
|------------------L1---------------L2-----|

I walk toward S1. I walk away from S2.
Prove that my watch runs at a different rate for S1 than for S2 so that
I get one speed of light from both sources. I love magic, show me some.
But always remember, I know it is magic. All I have to do is figure out
how the trick is done.



then the Lorentz transformation equations will indeed be the correct
way to transform measurements made with one set of rulers and clocks
into measurements made with another set.



I do not see any justification for magic or incorrect assumption.


This is not an assumption, it's just a logical consequence of the idea
that all the fundamental equations of physics exhibit the mathematical
property of "Lorentz invariance" which I described above. You may not
believe that in our final Theory of Everything, the fundamental laws
really *will* all be Lorentz-invariant ones, but do you agree that
*if*
all the fundamental laws were Lorentz-invariant, then if different
observers all used the same procedure to measure distance and time
(excluding procedures that rely on external reference points--imagine
each observer must construct his measuring system in a windowless box,
with no knowledge of how fast the box is moving in relation to the
rest
of the universe), that necessarily implies that the correct way to
transform between different observers' coordinate systems will be the
Lorentz transformation?


Get to the math, start proving. All your words are meaningless attempts
at persuasion, as were Einstein's. You are wasting your time using them
on me. I'm not giving up the PoR in favour of Lorentz invariance.







From your comments I gather you probably believe that existing laws
are not really fundamental, and that when we find the real
fundamental
laws they will not be Lorentz-invariant...



Quite so, the Lorentz Transforms do not exist.


They are just equations for transforming one set of coordinates to
another, so I don't see how they could fail to "exist".

Because time is not a vector.
When you can rotate an apple into an orange or travel back in time,
Harry Potter will have a unicorn hair core to his magic wand.
Harry Potter's wand exists as fiction only, as do the Lorentz
Transforms.
Fiction can be written in mathematics just as in literature, and you are
discussing fiction.


The empirical
question is whether they would correctly transform between different
observers' measurements on rulers and clocks, but even in a Newtonian
universe where they wouldn't do so if each observer designs his
network
of rulers and clocks in a "natural" way, it would still be possible to
artificially create distorted rulers and clocks such that they would
correctly transform between the normal set and the distorted one, as I
described above in my "novelty shop scenario".


Get to the math, start proving. All your words are meaningless attempts
at persuasion, as were Einstein's. You are wasting your time using them
on me. I'm not giving up the PoR in favour of Lorentz invariance.






but would you at least agree that *if* the fundamental laws are
Lorentz-invariant, then the Lorentz transformation will be the
correct
way to transform between measurements on different observers' rulers
and clocks?



If you can use
1/2[tau(0,0,0,t)+tau(0,0,0,t+x'/V+x'/V)] = tau(x',0,0,t+x'/V)
since "the velocity of light c cannot be altered by composition with
a
velocity less than that of light. For this case we obtain V =
(c+w)/(1+w/c) = c."
to derive the Lorentz Transforms, I'll take another look.

Go ahead. I'm amenable to reason.
Explain to me how the two velocities of light, c-v and c+v, measured
over a single distance, are really only one, c.


Is this equation from section 3 of that Einstein paper? I didn't see
it
there, and I need to know the context before I can answer this
question.

No, section 5. Come back when you've read all of it.
[remainder snipped, too many errors already].
Androcles.

Androcles wrote:

"Jesse Mazer" wrote in message
...


Androcles wrote:



"Jesse Mazer" wrote in message
...




Androcles wrote:





"Jesse Mazer" wrote in message
...





Androcles wrote:






"Jesse Mazer" wrote in message
...






Androcles wrote:







"Jesse Mazer" wrote in message
. ..







Androcles wrote:








"Jesse Mazer" wrote in message
. ..








Androcles wrote:







Do me a favour.
Einstein wrote

"light is always propagated in empty space with a definite
velocity c which is independent of the state of motion of the
emitting body"
Reference :
http://www.fourmilab.ch/etexts/einstein/specrel/www/

Then he wrote:
"But the ray moves relatively to the initial point of k, when
measured in the stationary system, with the velocity c-v, so
that x'/(c-v) = t."








I don't know what the context of this is. I assume he's not
talking about how fast the light is moving in a given frame,
but
rather how fast the light is moving away from some other
object,
as seen not in the object's own frame but in a frame where the
object itself is moving at velocity v. In this case, although
light will still travel at c in this frame, the distance
between
the light ray and the object moving at velocity v will be seen
to
grow at the rate (c-v) in this frame. In the object's own
frame,
though, the distance between itself and the light ray would
grow
at the rate c, as relativity predicts.







You didn't reply to this part of my post--can you provide me
with
the context of that statement by Einstein?






I've given you the reference.






Ah, I didn't notice that you were quoting from a website, sorry.
But
that's a pretty long article, which section did you get the quote
involving the equation x'/(c-v) = t from?





Section 3. It wouldn't refer to it as an "article" though. It's the
original
paper that Einstein wrote in 1905 creating special relativity.





I see my interpretation was correct, then. He is saying that you
have
two reference frames, K and k, and that in K's reference frame, the
distance between the origin of k and a ray of light is growing at
the
rate (c-v).




For some duration of time.
For another duration of time the rate is v+c.
These durations are not equal.
Time is not a vector, it has no additive inverse.








This does not mean that the ray of light is moving at velocity (c-v)
in k's reference frame; in both K and k, the light is moving at
velocity c.




I don't believe in magic. If c = c+v and c = c-v, then v = 0.



Nowhere has anyone said that c = c-v.



Really? Tell all those that claim c is invariant that they are not to
say it,
then.


The claim that c is invariant does not imply that c = c-v. Like I said,
no one says that c = c-v, so I don't need to tell anyone not to say it.






Rather, the idea here is that if
you measure the speed that the distance between k and the light ray is
growing using K's rulers and clocks, it is growing at the rate (c-v);
but if you measure the speed that the distance between k and the light
ray is growing using k's rulers and clocks, it is growing at the rate
c.



Yeah. I know. Stupidity is rife around here.




Since K and k use different rulers and clocks, then *if* you believe
that rulers shrink and clocks dilate, it shouldn't be so surprising
that
K's rulers and clocks will give a different answer than k's rulers and
clocks.



As I said, I don't believe in magic.


I wasn't asking if you believe that rulers and clocks actually change
this way, I'm just saying that *if* they change this way, different
reference frames will get different measurements. Are you saying it is
logically impossible that rulers could shrink and clocks could slow down
depending on their velocity?

Note, again, that if all the laws of physics are Lorentz-invariant, then
all physical rulers *must* shrink and all physical rulers must slow down.





I know you don't actually believe that, but the point is that
advocates of relativity do, so clearly they are not saying anything so
silly as c = c-v, rather they are saying:
speed measured by K's rulers and clocks = c-v
speed measured by k's rulers and clocks = c



Show me the evidence.


The evidence of what? The evidence that rulers and clocks actually do
change in this way? Or are you just asking me to prove that *if* we
assume they change in this way, then it is possible to prove that K's
rulers and clocks will measure the distance expanding at c-v, while k's
rulers and clocks will measure the distance expanding at c?





If V = (c+v)/(1+v/c) then use that to derive the LTs.
If the system of equations is linear as Einstein claims, it shoud be
no trouble.



Where are you getting V = (c+v)/(1+v/c)? That's not an equation I can
remember seeing.



§ 5. The Composition of Velocities
http://www.fourmilab.ch/etexts/einstein/specrel/www/

You don't know very much about relativity, do you?
Why are you talking to me as if you did?


The law of composition of velocities given in section 5 is V =
(v+w)/(1+v*w/c^2). If you plug in w=c, then you'll get the equation you
posted above, but why would you expect me to recognize a specific case
of a general equation for velocity composition, when you provided no
context whatsoever? Relativity textbooks will all present the general
case, but Einstein only mentioned the specific case as an aside, for the
purposes of proving that if something moves c in one frame then it must
move c in every other (since (v + c)/(1 + v/c) = c, by simple algebra).

So, are you just asking me to derive the Lorentz transformation from the
fact that if something moves at c in one frame, it must move at c in
every other?








You are one of those that starts at the Lorentz
Transforms, proceeds to lecture on what you imagine I'm not aware
of, then conclude you are right.






You didn't really read my post, so how do you know this?





I didn't read it in depth, no. I quickly glanced down and saw some
equations I recognised as wasn't prepared to comment on, since they
cannot be derived in any sensible manner.





They can be derived from the fact that all the fundamental laws of
physics display the property of "Lorentz invariance".




Bull****.






This is a mathematical property which can be verified simply by
examining the equations. Do you understand what it means to say a
given equation shows Lorentz invariance? If not, I can go into more
detail.




Go on then, explain circularity .... err .... Lorentz invariance to
me.



Well, first I'll describe Galilei invariance since it's mathematically
a
bit simpler, then I'll explain Lorentz invariance. Here are the
Galilei
transformations for transforming between inertial reference frames in
Newtonian physics:

x'=x - vt
y'=y
z'=z
t'=t

x=x' + vt'
y=y'
z=z'
t=t'

To say a certain physical equation is "Galilei-invariant" just means
the
form of the equation is unchanged if you make these substitutions. For
example, suppose at time t you have a mass m1 at position (x1, y1, z1)
and another mass m2 at position (x2, y2, z2) in your reference frame.
Then the Newtonian equation for the gravitational force between them
would be:

F = Gm1m2/[(x1 - x2)^2 + (y1 - y2)^2 + (z1 - z2)^2]

Now, suppose we want to transform into a new coordinate system moving
at
velocity v with respect to the first one. In this coordinate system,
at
time t' the mass m1 has coordinates (x1', y1', z1') and the mass m2
has
coordinates (x2', y2', z2'). Using the Galilei transformations, we can
figure how the force would look in this new coordinate system, by
substituting in x1 = x1' + vt', x2 = x2' + vt', y1 = y1', y2 = y2',
and
so forth. With these substitutions, the above equation becomes:

F = Gm1m2/[(x1' + vt' - (x2' + vt'))^2 + (y1' - y2')^2 + (z1' -
z2')^2]

and you can see that this simplifies to:

F = Gm1m2/[(x1' - x2')^2 + (y1' - y2')^2 + (z1' - z2')^2]

In other words, the equation has exactly the same form in both
coordinate systems. This is what it means to be "Galilei invariant".
More generally, if you have *any* physical equation which computes
some
quantity (say, force) as a function of various space and time
coordinates, like f(x,y,z,t) [of course it may have more than one of
each coordinate, like the x1 and x2 above, and it may be a function of
additional variables as well, like m1 and m2 above] then for this
equation to be "Galilei invariant", it must satisfy:
f(x'+vt,y',z',t') = f(x',y',z',t')



Oh, that's an easy one.
v = 0.


You misunderstand, the idea is for a law to be Galilei invariant, it
must satisfy f(x'+vt, y', z', t') = f(x', y', z', t') for *all* possible
values of v. It's not too hard to see that this would be true for the
equation for the Newtonian gravitational force I provided above.






From this, it's pretty simple to see what it must mean for a given
physical equation to be "Lorentz invariant" as well. Here are the
Lorentz transformation equations:

x'=gamma(x - vt)



Don't you mean xi = gamma.x' ?


No, the equation above comes from my relativity textbook. I don't know
what the notation "xi" represents in this context.

Einstein uses x' = x-vt. See, you've called the Galilean Transform
x' = x-vt, which is correct. The Lorentz is the Galilean * gamma.


For transforming x to x', it is just the Galilean * gamma, but not for
transforming t to t'.









y'=y
z'=z
t'=gamma(t - vx/c^2)


Oops. You did it again. be careful with those primes.

*tau* =gamma(t - vx/c^2)


No, I meant to write t'. If one frame S uses coordinates (x,y,z,t) and a
different frame S' uses coordinates (x',y',z',t'), and S sees the origin
of S' moving at velocity v along the x-axis, then the Lorentz
transformation says that t' = gamma*(t - vx/c^2). Perhaps Einstein used
different notation in his paper, but using the notation I have
specified, this would be the correct equation.





Another easy one.
v = x/t, by definition, so

tau = (t- vt * v /c^2) * gamma.
tau = t (1-v^2/c^2) * gamma.
= t * sqrt(1-v^2/c^2)
So the simpler form is
xi = x' * gamma
tau = t / gamma.

The speed of the "stationary" frame as measured from the "moving" frame
is then

upsilon = xi/tau

Prove |upsilon| = |v| (to preseve symmetry).


I don't know what tau and xi and x' mean in your notation. But in the
notation I have described, my equations are correct (and they are
written that way in my relativity textbook).




x=gamma(x' + vt')
y=y'
z=z'
t=gamma(t' + vx'/c^2)

where gamma = 1/squareroot(1-v^2/c^2)

So, if you have some physical equation f(x,y,z,t), then for it to be
"Lorentz-invariant" it just must have the following property:

f(gamma(x'+vt'),y',z',gamma(t'+vx'/c^2)) = f(x',y',z',t')

This is just a mathematical property of a given equation or set of
equations, it is just a matter of calculation to check if the equation
satisfies it (the equation for Newtonian gravity would not have this
property, so it would not be Lorentz-invariant).



Thank goodness for that. You are mixing greek notation with prime
notation,
that can only confuse you (and me). Be consistent. I have no idea what
you
mean by vt', or x'.


See above, I'm not using any "greek notation" at all, and I'm just
saying using primed vs. unprimed to distinguish the coordinates of the
two different frames (they aren't supposed to represent derivatives, if
that's what's confusing you). Now that you see my notation, do you agree
that the property of "Lorentz-invariance" is a purely mathematical one
that can be checked just by looking at the equations for a given law of
physics?






And it is a fact that
Maxwell's laws do have this property of Lorentz-invariance, as do all
the most fundamental laws currently known (such as the laws of quantum
field theory).




Maxwell's equations are based on aether. There is no aether.


Maxwell used a model involving the aether, but Maxwell's equations are
just mathematical formulas which allow you to calculate the dynamical
behavior of a system of charges over time, you are not required to
believe anything about *why* the equations have the particular form they do.

I'll accept Einstein's opener.
"It is known that Maxwell's electrodynamics--as usually understood
at the present time--when applied to moving bodies, leads to asymmetries
which do not appear to be inherent in the phenomena. "
Nice "facts" you present.


The statement "Maxwell's laws are Lorentz-invariant" is a purely
mathematical one, it could be checked by a mathematician who had no idea
what the physical significance of the laws was, just like the statement
"Newtonian gravity is Galilei-invariant" (which I demonstrated earlier).
So, denying that Maxwell's laws are Lorentz-invariant is like denying
that pi is irrational--mathematically wrong, plain and simple,
regardless of what the laws of physics are like.

As for Einstein's statement, when he said "as usually understood at the
present time", he was referring to the idea that Maxwell's equations
would only be exactly correct in the rest frame of the aether, and that
in other frames you'd have to modify them using a Galilei
transformation. But since the equations are Lorentz-invariant, if you
use a Lorentz transformation to translate between different frames
instead of a Galilei transformation, then Maxwell's equations will be
correct in *every* reference frame.







However, if it is true that all the fundamental laws of nature obey
Lorentz invariance,
it must be true that if different observers in motion with relation
to one another all use the same procedure to define the coordinates
of
events in their frame--building a network of rulers and clocks which
are at rest with respect to themselves, and synchronizing the clocks
using the assumption that light moves at the same speed in all
directions in their frame--




It seemeth impossible for it to be, for if I walk away from a candle
set
by the wall and you walk toward the same candle, we then have some
motion between us. If we then divide that motion equally between us,
and
impart it to the candle such that it appeareth to be at rest upon the
floor upon which we walk, how then doth the light divide it's motion
between us, that we may both observe it to be the same?



Because you and I use different rulers and clocks to measure this
motion.



I've only got one ruler and one clock, there are two light sources, one
I walk toward and the other I walk away from.


If you've only got one ruler and one clock, then you aren't measuring
things according to the physical setup that is used in deriving the
Lorentz transformation. Relativity just says that *if* each observer
measures the coordinates of events using a network of rulers and clocks
at rest relative to himself (with the clocks synchronized using
light-signals), with each event's position determined by the markings on
a ruler right next to the event, and each event's time determined by the
reading on a clock right next to the event, *then* the Lorentz
transformation will give the correct method of translating one
observer's coordinates to another observer's coordinates.

If you think this if-then statement is incorrect, you must believe that
even *if* you each observer assigns coordinates to events using the
setup of rulers and clocks described by Einstein, the Lorentz
transformation will not be the correct way to translate between
different coordinate systems. If you think that the if-then is correct,
but just don't believe that the setup of rulers and clocks described by
Einstein is the best way to assign coordinates to events, then you
aren't really disagreeing with the Lorentz transformation, since the
Lorentz transformation is only talking about what happens *if* each
observer assigns coordinates to events in this way.


Even if we lived in a Newtonian universe where rulers and


clocks
wouldn't *naturally* appear to shrink and slow down, suppose I bought
you some phony gag rulers and clocks from the novelty shop, with the
markings on the rulers too short by a factor of squareroot(1-v^2/c^2),
and each tick of the clock longer then it should be by a factor of
1/squareroot(1-v^2/c^2). Suppose I also made different clocks of yours
be out-of-sync, by using the (false, in a Newtonian universe)
assumption
that a beam of light emitted from the midpoint of two clocks (by a
source at rest relative to me, if you believe light's velocity depends
on the source velocity, although in classical E&M it should actually
depend on the rest frame of the aether) should strike both clocks at
the
same time, even if one clock is moving towards the point the light was
emitted and one is moving away from it.

If you are moving away from me at velocity v, and you are using these
gag rulers and clocks (which have been synchronized using this
incorrect
procedure, in the Newtonian universe we're living in) to measure
things,
do you agree that *as measured by your incorrect rulers and clocks*,
then if I measure the light to be moving at c, you will also measure
it
to be moving at c? Do you agree that if I want to find some equations
to
transform between my correct measurements and your incorrect
measurements, the correct equations will be the Lorentz transformation
equations?



I don't use gag rules and clocks, I have only one rule and one clock.


But you claimed earlier that the Lorentz transformation was "illogical".
If you agree that using gag rulers and clocks like the ones I described,
the Lorentz transformation would accurately tranform between different
observer's measurements in a purely Newtonian universe, then obviously
there is no logical contradiction in the Lorentz transformation.


I approach one source of light as I recede from the other.
You are not involved.

S1-----------------------------me-----------S2
|------------------L1---------------L2-----|

I walk toward S1. I walk away from S2.
Prove that my watch runs at a different rate for S1 than for S2 so that
I get one speed of light from both sources. I love magic, show me some.
But always remember, I know it is magic. All I have to do is figure out
how the trick is done.


Can I assume in my proof that all the fundamental laws of physics,
including those that govern your ruler, your clock, and the light, have
the mathematical property of Lorentz-invariance?







then the Lorentz transformation equations will indeed be the correct
way to transform measurements made with one set of rulers and clocks
into measurements made with another set.




I do not see any justification for magic or incorrect assumption.



This is not an assumption, it's just a logical consequence of the idea
that all the fundamental equations of physics exhibit the mathematical
property of "Lorentz invariance" which I described above. You may not
believe that in our final Theory of Everything, the fundamental laws
really *will* all be Lorentz-invariant ones, but do you agree that
*if*
all the fundamental laws were Lorentz-invariant, then if different
observers all used the same procedure to measure distance and time
(excluding procedures that rely on external reference points--imagine
each observer must construct his measuring system in a windowless box,
with no knowledge of how fast the box is moving in relation to the
rest
of the universe), that necessarily implies that the correct way to
transform between different observers' coordinate systems will be the
Lorentz transformation?




Get to the math, start proving. All your words are meaningless attempts
at persuasion, as were Einstein's. You are wasting your time using them
on me. I'm not giving up the PoR in favour of Lorentz invariance.


Do you understand that "Lorentz invariance" is a purely mathematical
property of a given set of equations, that doesn't assume anything about
the physical meaning of these equations? Do you agree that all the
fundamental equations of physics which physicists know at present have
this property of Lorentz invariance?

And what is it you want me to prove, exactly? My statement above was
that *if* all the fundamental laws have this property of
Lorentz-invariance, and *if* different observers all use the same
procedure to construct a coordinate system for themselves, *then* it is
guaranteed that the Lorentz transformation will accurately translate
between different observer's coordinates. So naturally, to prove an
if-then statement, you must assume for the sake of the argument that the
"if" part is true, and then show that the "then" part follows as a
logical consequence. So am I allowed to assume for the sake of the
argument that all the fundamental laws of nature have the property of
Lorentz-invariance? If not, please specify what you are asking me to prove.










From your comments I gather you probably believe that existing laws


are not really fundamental, and that when we find the real
fundamental
laws they will not be Lorentz-invariant...




Quite so, the Lorentz Transforms do not exist.



They are just equations for transforming one set of coordinates to
another, so I don't see how they could fail to "exist".



Because time is not a vector.


No, time is not assumed to be a vector in relativity. Each observer
assigns a given event a time-coordinate t simply by looking at the
reading on a clock next to the event, with the clock being part of a
large network of clocks which are all at rest relative to the observer
and which have been synchronized using light-signals. The Lorentz
transformation just tells you how one observer's time-coordinate will
relate to some other observer's time-coordinate, assuming they assign
time-coordinates in this way.



The empirical
question is whether they would correctly transform between different
observers' measurements on rulers and clocks, but even in a Newtonian
universe where they wouldn't do so if each observer designs his
network
of rulers and clocks in a "natural" way, it would still be possible to
artificially create distorted rulers and clocks such that they would
correctly transform between the normal set and the distorted one, as I
described above in my "novelty shop scenario".




Get to the math, start proving. All your words are meaningless attempts
at persuasion, as were Einstein's. You are wasting your time using them
on me. I'm not giving up the PoR in favour of Lorentz invariance.


Again, what are you asking me to prove here? If you like, I can prove
that in a Newtonian universe where rulers and clocks don't "naturally"
change as they move, then if an observer moving at velocity v uses some
novelty-shop rulers and clocks, where the rulers have been shrunk by
squareroot(1 - v^2/c^2) and the ticks of the clock are slowed down by a
factor of 1/squareroot(1 - v^2/c^2), and if this observer also
incorrectly "synchronizes" these clocks by assuming light moves at c in
all directions relative to himself (when really, in this Newtonian
universe, light moves at c+v in one direction relative to him and c-v in
the opposite direction), then the formula for translating between my
correct network of rulers and synchronized clocks and his incorrect
network will be the Lorentz transformation.

But if this isn't the sort of thing you want me to prove, please specify
what you are asking for here.










but would you at least agree that *if* the fundamental laws are
Lorentz-invariant, then the Lorentz transformation will be the
correct
way to transform between measurements on different observers' rulers
and clocks?




If you can use
1/2[tau(0,0,0,t)+tau(0,0,0,t+x'/V+x'/V)] = tau(x',0,0,t+x'/V)
since "the velocity of light c cannot be altered by composition with
a
velocity less than that of light. For this case we obtain V =
(c+w)/(1+w/c) = c."
to derive the Lorentz Transforms, I'll take another look.

Go ahead. I'm amenable to reason.
Explain to me how the two velocities of light, c-v and c+v, measured
over a single distance, are really only one, c.



Is this equation from section 3 of that Einstein paper? I didn't see
it
there, and I need to know the context before I can answer this
question.



No, section 5. Come back when you've read all of it.
[remainder snipped, too many errors already].
Androcles.


The paper just goes over results I am already familiar with using
different notation, so I don't think it's necessary for me to read the
whole thing. If you want to cite equations from the paper, please just
mention which section you got them from.

Jesse

"Jesse Mazer" wrote in message
...

I wasn't asking if you believe that rulers and clocks actually change
this way, I'm just saying that *if* they change this way, different
reference frames will get different measurements.

If pigs could fly they'd be pigeons.


Are you saying it is logically impossible that rulers could shrink and
clocks could slow down depending on their velocity?

Yes.


Note, again, that if all the laws of physics are Lorentz-invariant,
then all physical rulers *must* shrink and all physical rulers must
slow down.

Which is logically impossible. So forget Lorentz invariance, it is
sci-fi.

Show me the evidence.


The evidence of what?

Rulers shrinking.



The evidence that rulers and clocks actually do change in this way?

Yes. Show me the evidence.


Or are you just asking me to prove that *if* we assume they change in
this way, then it is possible to prove that K's rulers and clocks will
measure the distance expanding at c-v, while k's rulers and clocks
will measure the distance expanding at c?

Couldn't care less what you "if" about. Show me the evidence.







If V = (c+v)/(1+v/c) then use that to derive the LTs.
If the system of equations is linear as Einstein claims, it shoud be
no trouble.


Where are you getting V = (c+v)/(1+v/c)? That's not an equation I can
remember seeing.


§ 5. The Composition of Velocities
http://www.fourmilab.ch/etexts/einstein/specrel/www/

You don't know very much about relativity, do you?
Why are you talking to me as if you did?


The law of composition of velocities given in section 5 is V =
(v+w)/(1+v*w/c^2). If you plug in w=c, then you'll get the equation
you posted above, but why would you expect me to recognize a specific
case of a general equation for velocity composition, when you provided
no context whatsoever?
I quoted verbatim.
I'm not going to continue a conversation with somebody that challenges
my integrity when I quote Einstein.

Androcles.

Androcles wrote:

"Jesse Mazer" wrote in message
...



I wasn't asking if you believe that rulers and clocks actually change
this way, I'm just saying that *if* they change this way, different
reference frames will get different measurements.



If pigs could fly they'd be pigeons.




Are you saying it is logically impossible that rulers could shrink and
clocks could slow down depending on their velocity?



Yes.


That's absurd, I don't think you understand the meaning of "logically
impossible". "Logically impossible" has nothing to do with real-world
plausibility--for example, it is logically possible that the world is
flat, or that tomorrow the sun will vanish (of course, I don't see why
the assumption of shrinking rulers and slowing clocks would be as
implausible as these examples, but never mind that now). To show that
something is logically impossible you must show that it leads to a
logical contradiction--if you assume it is true, that assumption can be
used to prove that it is false. Can you do this with the assumption that
rulers contract and clocks slow down?




Show me the evidence.



The evidence of what?



Rulers shrinking.


In a general sense, the evidence for shrinking rulers is just the
evidence that all the fundamental laws of nature are described by
equations which have the mathematical property of Lorentz-invariance.
Again, if all the fundamental laws are Lorentz-invariant, then rulers
*must* shrink and clocks *must* slow down in this manner.

Measuring a moving extended object travelling at relativistic speeds at
an exact instant in time (in your own frame) is rather difficult, of
course, so I'm not sure if there's any more specific evidence for
Lorentz contraction. There is certainly plenty of experimental evidence
for time dilation, though. I already mentioned experiments with particle
decay times extending as they move at relativistic speeds; another
example would be experiments where one of a pair of synchronized atomic
clocks is placed onboard the space shuttle, then when it returns to
earth the clock that rode on the shuttle will be a few microseconds
behind the earthbound clock, by just the factor that is predicted by
relativity.










If V = (c+v)/(1+v/c) then use that to derive the LTs.
If the system of equations is linear as Einstein claims, it shoud be
no trouble.




Where are you getting V = (c+v)/(1+v/c)? That's not an equation I can
remember seeing.



§ 5. The Composition of Velocities
http://www.fourmilab.ch/etexts/einstein/specrel/www/

You don't know very much about relativity, do you?
Why are you talking to me as if you did?



The law of composition of velocities given in section 5 is V =
(v+w)/(1+v*w/c^2). If you plug in w=c, then you'll get the equation
you posted above, but why would you expect me to recognize a specific
case of a general equation for velocity composition, when you provided
no context whatsoever?


I quoted verbatim.
I'm not going to continue a conversation with somebody that challenges
my integrity when I quote Einstein.

Androcles.







Nowhere in the above paragraph did I "challenge your integrity". I was
responding to your own challenge to my knowledge of relativity (your
comment 'You don't know very much about relativity, do you?') based on
the fact that I did not immediately recognize the equation V =
(c+v)/(1+v/c); I was just pointing out that this is not considered an
important relativistic equation, it would only appear as an intermediate
step in a proof that when you plug w=c into the law of composition of
velocities, V = (v+w)/(1+v*w/c^2), you will get V = c.

So again, what did you mean when you asked me to derive the LTs from V =
(c+v)/(1+v/c)? Again, if you are just asking me to derive the LTs from
the assumption that light travels at c in all frames, then I'd be happy
to do so.

Jesse

"Androcles" wrote in message
k...

[snip]

Which is logically impossible. So forget Lorentz invariance, it is
sci-fi.

I see you have never tried to see if Maxwell's equations obey Lorentz
or Galilean invariance.
Have a shot at it if you want to give yourself an unpleasant surprise.

Since in reality you are to stupid to do that, read a thin undergrad
book by Turner, "Relativity Physics". Page 26 - 28 shows neatly that
Maxwell's equations are *not* invariant with respect to the Galilean
transformation. Pages 105 - 106 show that they are in fact Lorentz
invariant.

I bet a penny to a pound that you will not understand the derivations,
in view of your proven track record vis-s-vis algebraic ignorance.
Nevertleless. let us know how you get on with it.

Franz



[snip]

Franz Heymann wrote:

"Androcles" wrote in message
. uk...

[snip]



Which is logically impossible. So forget Lorentz invariance, it is
sci-fi.



I see you have never tried to see if Maxwell's equations obey Lorentz
or Galilean invariance.
Have a shot at it if you want to give yourself an unpleasant surprise.


Of course, before Einstein physicists didn't think Maxwell's laws would
be correct in every observer's reference frame--they thought they would
only hold exactly in the rest frame of the aether. They would have
believed that to state the laws of electromagnetism in a way that would
hold in all frames, you'd have to replace every x in Maxwell's laws with
(x - v*t), where v represents the observer's velocity relative to the
rest frame of the aether...any derivatives of x would have to be
replaced in the same way, like replacing dx/dt with (dx/dt - v). This
would give a new set of electromagnetic laws which would be
Galilei-invariant, and which would reduce to Maxwell's laws in the case
where v=0.

But a prediction of this Galilei-invariant analogue of Maxwell's laws
would be that for an observer in motion relative to the aether, light
will be observed to move at different speeds in different directions,
relative to himself. Unfortunately this was not supported by the
Michelson-Morley experiment. Androcles proposes to explain this negative
result with the suggestion that the velocity of light depends on the
velocity of the source, but this would be false according to both
Maxwell's laws *and* the modified Galilei-invariant analogue of
Maxwell's laws (which says that light waves, like sound waves, always
travel at the same speed in the rest frame of the aether/air, regardless
of the velocity of their source). So unless he can find a theory that
gives correct predictions for all the various experiments in classical
electromagnetism, and yet does not have the feature that the velocity of
light is independent of the source velocity, then his ideas wouldn't
even have seemed plausible to a physicist in a time before the theory of
relativity had been published (but after the Michelson-Morley experiment
had been done).

Jesse

"Jesse Mazer" wrote in message
...

Of course, before Einstein physicists didn't think Maxwell's laws
would be correct in every observer's reference frame--they thought
they would only hold exactly in the rest frame of the aether. They
would have believed that to state the laws of electromagnetism in a
way that would hold in all frames, you'd have to replace every x in
Maxwell's laws with (x - v*t), where v represents the observer's
velocity relative to the rest frame of the aether...any derivatives of
x would have to be replaced in the same way, like replacing dx/dt with
(dx/dt - v). This would give a new set of electromagnetic laws which
would be Galilei-invariant, and which would reduce to Maxwell's laws
in the case where v=0.

But a prediction of this Galilei-invariant analogue of Maxwell's laws
would be that for an observer in motion relative to the aether, light
will be observed to move at different speeds in different directions,
relative to himself. Unfortunately this was not supported by the
Michelson-Morley experiment.

The speed of light in diamond, water, air, any transparent medium is
constant with respect to the medium. MMX fails to support aether.
In MMX, the medium is air. It is as simple as that.


Androcles proposes to explain this negative result with the suggestion
that the velocity of light depends on the velocity of the source,
Since source, medium and detector are all relatively at rest, MMX
disposes of the aether only.
1) speed of light relative to source.
2) speed of light relative to medium.
3) speed of light relative to detector.


MMX satisfies all three.
SR fails to satisfy MMX, however.

but this would be false according to both Maxwell's laws *and* the
modified Galilei-invariant analogue of Maxwell's laws (which says that
light waves, like sound waves, always travel at the same speed in the
rest frame of the aether/air,

Forget aether, it doesn't exist. Air does, though. So does water.
A stick passing through the air-water interface appears bent.
That is empirical evidence that the speed of light is medium dependent.



regardless of the velocity of their source).

Source dependency only applies in the absence of a medium. There is
no aether.


So unless he can find a theory that gives correct predictions for all
the various experiments in classical electromagnetism, and yet does
not have the feature that the velocity of light is independent of the
source velocity, then his ideas wouldn't even have seemed plausible to
a physicist in a time before the theory of relativity had been
published (but after the Michelson-Morley experiment had been done).

Nobody has a computer then. Today we can calculate what the result
would be if a bullet stream from a moving machine gun moving in an
elliptical
orbit that obeyed Kepler's laws were to arrive at any distance.
The intensity of arriving bullets (grey line) looks like this.


http://www.androc1es.pwp.blueyonder....r/V1493Aql.JPG

If you examine the image closely, you'll see a crossover where the
faster bullets
has caught up with and passed the slower bullets.
That is a simple distance / time plot, distance vertical and time
horizontal.
What you would see is a sudden increase in the rate of arrival of
bullets,
then a second maximum, eventually tailing off.
A star in elliptical orbit would do the same thing.
Androcles.

On Tue, 11 Jan 2005, Androcles wrote:

The speed of light in diamond, water, air, any transparent medium is
constant with respect to the medium.

Loosely phrased, and wrong. The phase speed of light of a given frequency
in diamond, water, air, any stationary medium, is constant with respect to
the stationary medium.

--
Timo Nieminen - Home page: http://www.physics.uq.edu.au/people/nieminen/
Shrine to Spirits: http://www.users.bigpond.com/timo_nieminen/spirits.html

"Timo Nieminen" wrote in message
news:Pine.LNX.4.50.0501111102040.1887-100000@localhost...
On Tue, 11 Jan 2005, Androcles wrote:

The speed of light in diamond, water, air, any transparent medium is
constant with respect to the medium.

Loosely phrased, and wrong. The phase speed of light of a given
frequency
in diamond, water, air, any stationary medium, is constant with
respect to
the stationary medium.

--
Timo Nieminen - Home page:
http://www.physics.uq.edu.au/people/nieminen/
Shrine to Spirits:
http://www.users.bigpond.com/timo_nieminen/spirits.html

Good enough to explain MMX.
Androcles.

On Tue, 11 Jan 2005, Androcles wrote:

"Timo Nieminen" wrote:
On Tue, 11 Jan 2005, Androcles wrote:

The speed of light in diamond, water, air, any transparent medium is
constant with respect to the medium.

Loosely phrased, and wrong. The phase speed of light of a given
frequency
in diamond, water, air, any stationary medium, is constant with
respect to
the stationary medium.

Good enough to explain MMX.

So is SR, so is a fully-dragged Galilean ether, so is a Lorentz
ruler-shrinking clock-slowing ether, and so is just about any emission
theory.

Ordinarily, it would be somewhat pedantic point, but empirical
observations of the speed of light in a moving medium were historically
important, and continue to be theoretically important, in chosing which of
the above explanations of MMX could be correct. In the context of using an
emission theory to explain MMX, it's a worthwhile point.

--
Timo Nieminen - Home page: http://www.physics.uq.edu.au/people/nieminen/
Shrine to Spirits: http://www.users.bigpond.com/timo_nieminen/spirits.html