Ned Heath:
On Wed, 09 Jul 2003 (Bilge) wrote:
That makes the galilean transformations a special case of
the general result.

Galilean transformations do not have finite c, so if your
derivation doesn't rule them out (which it doesn't), you can't
legitimately claim to have derived the finiteness of c.

I already cited a reference written by mathematicians who state
explicitly the equivalence of the affine space for M_c and M_\infty.

[...]

He did NOT select Newtonian mechanics, because he knew it was
not strictly valid.

Einstein could not have made a statement about "inertial frames"
at all without appealing to newtonian mechanics. In fact, special
relativity suffers from the defect of being unable to adequately
define an inertial frame, newton or no newton. If einstein can rely
on classical mechanics to help define the meaning of "inertial",
then it's certain;y reasonable to use the first postulate and
the fact that one cannot turn around in the time direction to rule
out a euclidean metric.

[...]
I did. Infinite `c' doesn't agree with observation.

Of course it doesn't, but particular "observations" are not part
of the principle of relativity. You are not entitled to invoke
observations ("you can't use a marked ruler") when you claim to
be deriving something from the principle of relativity alone.

In a semantics game, I'm entitled to do anything I wish.
And, I can use a marked ruler, since any ruler is marked by
virtue of having endpoints. It sounds like you are trying
to turn special relativity into LET.

[...]
In particular, it states "electrodynamics and optics" in frames
in which "the equations of mechanics hold good". If I wanted to
haggle over semantics, I would have simply said that was enough
to choose a value for `c' as well, since the electrodymanics
at the time, were maxwell's equations.

Bilge, for goodness sakes! That's totally wrong! Einstein
specifically (and famously) AVOIDED basing special relativity
on Maxwell's equations.

I know that quite well. However, since you insist on playing a
game of semantics under the guise of pedantry, I'm going to
simply be pedantic about the wording of the first postulate
stated in the introduction so I can play along.

Your mis-reading of his postulates has already been explained.

I didn't misread anything. I intentionally read what was literally
written for the purpose of responding to your last post, just to
demonstrate that I can play the same game of picking and choosing
the text as I see fit.

[...]
Obviously Newton's equations do NOT hold good in ANY frame,
because if they did, spacetime would have to be Galilean.

Newtonian mechanics can be formulated via a lagrangian and more
generally,

L'[x] = L[x + a] = L[x] + \delta L[x]


\delta L = L[x'] - L[x] = a^{u} dL/dx^{u}

From here it takes just a few more lines to obtain the classical
conservation laws via noether's theorem: energy, momentum and angular
momentum.

So are you going to tell me "mechanics at the time was Newtonian
mechanics, so Einstein could have inferred that spacetime was
Galilean"?

He could have, but his immediate goal was to explain electrodynamics
with a geometric theory. His second postulate is unfortunate in that
he defined the speed of light to be `c' for that reason. The value
of `c' is an experimental issue, not a theoretical issue.

This just further emphasizes how completely you
have failed to understand the foundations of special relativity.

I haven't failed to understand anything in this thread. If I'm
going to play along, I'm going to twist the semantics and make a
game of it, which is different from the one you're playing. I'm
not going to make a serious effort to defend statements you've
misconstrued by shifting the meaning of the question.

"Bill Hobba" wrote in message
...
| Bilge correctly wrote:
| Einstein could not have made a statement about "inertial frames"
| at all without appealing to newtonian mechanics. In fact, special
| relativity suffers from the defect of being unable to adequately
| define an inertial frame, newton or no newton. If einstein can rely
| on classical mechanics to help define the meaning of "inertial",
| then it's certain;y reasonable to use the first postulate and
| the fact that one cannot turn around in the time direction to rule
| out a euclidean metric.
|
| Just so people understand the problem with inertial frames comes when you
| examine then closely - normal simple definitions found in textbooks are ok
| if you don't examine then really carefully. In fact in Lagrangien
mechanics
| you define an inertial reference frame before you introduce any axioms.
| Actually it is also encoded is Newton's first law which should really read
| inertial reference frames exist ie frames in which free particles move
with
| constant velocity. Less someone objects that that is a circular argument
| (ie a free particle is one that has no force acting on it which implies it
| moves at constant velocity) a free particle can be defined as a particle
| that moves as if they were the only thing in an inertial frame. The
| problems with inertial frames comes when you examine closely exactly how
you
| specify a coordinate system and ensure clocks are synchronized. Just a
| question for Bilge though. Exactly how you rigorously define an inertial
| reference frame is not really something I have gone into detail about but
my
| understanding is it can be rigorously defined, it just requires a lot of
| care, or am I wrong?

I like the way Griffiths described an inertial frame in "Introduction to
Electrodynamics".

"To avoid this trap we define an inertial frame formally as one in which
Newton's first law holds. If you want to know whether you're in an inertial
frame, throw some rocks around---if they travel in straight lines at
constant speed, you've got yourself an inertial frame, and any frame moving
at constant velocity with respect to you will be another inertial frame."

I don't see that it has to be any more complicated than this.

FrediFizzx

FrediFizzx wrote:
I like the way Griffiths described an inertial frame in "Introduction to
Electrodynamics".

"To avoid this trap we define an inertial frame formally as one in which
Newton's first law holds. If you want to know whether you're in an
inertial
frame, throw some rocks around---if they travel in straight lines at
constant speed, you've got yourself an inertial frame, and any frame
moving
at constant velocity with respect to you will be another inertial frame."

I don't see that it has to be any more complicated than this.


I like Landaus definition - it is a frame is which space and time are
homogeneous and space is isotropic. It is equivalent to the one above via
the POR (nice little exercise to show this). Problems come when you look at
it really closely. First you must specify a coordinate system. Physically
how do you do this - via rigid rods (SR later shows they do not exist) or
exactly how? Secondly how do we synchronize clocks so we have a universal
time? Using OWLS? Then the speed of light is constant by definition. Take
two clocks at the same point then sync them and slowly move them apart? Are
you sure they will then stay synced? Via two way light speed? Only if your
really sure of the isotropy property. Which then begs the question how do
you show a frame of reference is homogeneous and isotropic? Although I am
no expert he it just seems like a total mine field to me that I just hope
someone has sorted out.

My solution is you accept these things as extra axioms ie you can construct
from stationary rods that are rigid in the classical domain Cartesian
coordinates (guaranteed by Euclidian geometry which you assume valid for
stationary or slow moving lines and points). You also assume you
conceptually have a synced set of stationary clocks at all points. But
physically it still seems a problem.

Thanks
Bill

"Bill Hobba" wrote in message
...
| FrediFizzx wrote:
| I like the way Griffiths described an inertial frame in "Introduction to
| Electrodynamics".
|
| "To avoid this trap we define an inertial frame formally as one in which
| Newton's first law holds. If you want to know whether you're in an
| inertial
| frame, throw some rocks around---if they travel in straight lines at
| constant speed, you've got yourself an inertial frame, and any frame
| moving
| at constant velocity with respect to you will be another inertial
frame."
|
| I don't see that it has to be any more complicated than this.
|
|
| I like Landaus definition - it is a frame is which space and time are
| homogeneous and space is isotropic. It is equivalent to the one above via
| the POR (nice little exercise to show this). Problems come when you look
at
| it really closely. First you must specify a coordinate system.
Physically
| how do you do this - via rigid rods (SR later shows they do not exist) or
| exactly how? Secondly how do we synchronize clocks so we have a universal
| time? Using OWLS? Then the speed of light is constant by definition.
Take
| two clocks at the same point then sync them and slowly move them apart?
Are
| you sure they will then stay synced? Via two way light speed? Only if
your
| really sure of the isotropy property. Which then begs the question how do
| you show a frame of reference is homogeneous and isotropic? Although I am
| no expert he it just seems like a total mine field to me that I just hope
| someone has sorted out.
|
| My solution is you accept these things as extra axioms ie you can
construct
| from stationary rods that are rigid in the classical domain Cartesian
| coordinates (guaranteed by Euclidian geometry which you assume valid for
| stationary or slow moving lines and points). You also assume you
| conceptually have a synced set of stationary clocks at all points. But
| physically it still seems a problem.


OK, I get it. It is a physical measurement problem. How do we go out and
actually measure to see if the thrown rocks do go straight and at a uniform
velocity. Yes, it seems you need to start from Cartesian coordinates and
Euclidian geometry to validate it. Once you are in it, tough to validate.
Hmmm.

FrediFizzx

The answer comes to you shortly after you give up hope of finding it.