On 2006-04-01, Spaceman <Realspace@comcast.not> wrote:

"Edwards" <edwards@nouce.trurl.bsd.uchicago.edu> wrote in message
news:slrne2rlhq.qiu.edwards@trurl.bsd.uchicago.edu...

On 2006-03-31, Spaceman <Realspace@comcast.not> wrote:

"Edwards" <edwards@nouce.trurl.bsd.uchicago.edu> wrote in message
news:slrne2osnh.tps.edwards@trurl.bsd.uchicago.edu...

On 2006-03-29, Spaceman <Realspace@comcast.not> wrote:

"Edwards" <edwards@nouce.trurl.bsd.uchicago.edu> wrote in message
news:slrne2m3ic.8l4.edwards@trurl.bsd.uchicago.edu...

On 2006-03-29, Spaceman <Realspace@comcast.not> wrote:

I am talking about adding path distances..
(that is what speed is)

Speed is not "adding path distances".

Yes it is when you timing of such.

I have no idea what you mean by this. In your example above, the
total "path distance" from A to B to C is 2000 km; what are you
claiming is the "speed"?

The speed would be how long it took to travel that path.
hence "distance per time".

Uh, yeah, _per_ _time_. You _can't_ just "add path distances" to come
up with a speed, thanks for clearing that up. (Also note that what
you're describing is the _average_ speed, a quite poor approximation
to the instantaneous speed when acceleration is not zero --
e.g. turning the sharp corner at B in your example above. So the more
"path distances" you add together to come up with a "speed", the
_less_ accurately you're actually measuring the _true_
(i.e. instantaneous) speed of your object.)

accuracy is not what is at question here.

It is if you claim speed has something to do with "adding path
distances", because the _only_ way "adding path distances" can have
anything to do with a "speed" is with _average_ speed, and not
instantaneous ("true") speed.

adding speeds is what is truly at question.

_Combining_ speeds. Whether that ends up being the same as "adding"
speeds is a question of geometry (just like the question of using
sqrt(x^2 + y^2) or x+y).

there is no physical proof that speeds do not add like basic math
would indicate.

Begging the question. "There is no physical proof that distances add
like sqrt(x^2 + y^2) would indicate." Well, duh, you're assuiming the
result by sticking the word "add" in there before you even agree to do
any "physical" observations. Now how speeds _combine_ is a different
question (just as the question of how distances combine in Euclidean
geometry is a different question from just "adding the distances").

such as relative speed of converging objects on a straight road.

It's a _prediction_ of SR that the deviation of the combined velocity
from the "simple addition" of the two velocities in question will not
be measureable (even in principle) for objects moving as slow as
trains or cars.

I asked this in a different post and was ignored: have you ever
actually _done_ any experiments involving objects (electrons, what
have you) for which v/c was _not_ <<1?

I said I can disprove the velocity addition ***** with basic math.
(u + v) does not equal (u + v)/(1 + uv/c2)

Noone claims it does (unless u or v equals zero).

Of course it doesn't, and that is why it is wrong to use
it at all for addition of linear speeds.

Noone uses (u+v)/(1+uv/c^2) for "addition of linear speeds", anymore
than anyone uses the Pythagorean theorem to add distances in the same
direction.

(u+v)/(1+uv/c^2) is used to _combine_ velocities. This combination
turns out to be (experimentally) _indistinguishable_ from the "simple
addition" of the speeds for "slow" moving objects (i.e. v/c << 1, u/c
<< 1). (Analagously: the formula for combining distances oriented at
an angle theta with one another (of which the Pythagorean theorem is a
special case with theta = pi/2) is experimentally indistinguishable
from "simple addition" of the distances when theta is experimentally
indistinguishable from 0.

Why do you "believe" one geometry and not the other? Do you berate
the inhabitants of "spinny ruler land" as stridently as those of your
notional "rubber ruler land"?

No need for any transform ***** and if you used a transform
at all in such a case you would find it would nto match the reality
that is occuring.

For |u| << c and |v| << c, sure.

Nope. for all speeds.

Sorry, that doesn't match the "reality" that is _observed_ to "occur".
_Observation_, remember? The "science of measurement"?

The science of measurement is what you are losing
when you use a transform for such things as converging speeds.

The science of measurement is what you are losing when you insist that
a formula that makes measurably _wrong_ predicition for combining
velocities is nevertheless somehow "right".

u + v never equals (u + v)/(1 + uv/c2)

Noone said it does (unless u or v equals zero). Do you think pointing
out that x+y is not the same as sqrt(x^2 + y^2) disproves the
Pythagorean theorem? The claim you are making about _combination_ of
velocities (under Minokowski geometry) is _exactly the same_.

Excuse me but I don't know why you have brough Pythagorean theorem
into this so much and have not figured out I did not actually
talk about it and simply made one mistake.
Drop the Pythagorean theorem twist, I am not even talking about such.

I will be happy to drop it as soon as you provide a logical argument
for why "u+v never equals (u+v) / (1 + uv/c^2) [except for u=0 or
v=0]" disproves a theorem of Minkowski geometry, but "x+y never equals
sqrt(x^2 + y^2) [except for x=0 or y=0]" does not disprove a theorem
of Euclidean geometry. What's the logical difference between the two
situations?

Yeah, I know, you did homework problems a long time ago in Euclidean
geometry and have arbitrarily put that in your "simple math" bin.
That's not a logical argument because plenty of people have done
enough homework problems in Minkowski geometry to think of _that_ as
simple math. So what's the difference?

therefore it is mathematically wrong accordign to the basic math of
adding distances with a time as the denominator.

That's crap, _individual_ velocities in SR are defined in EXACTLY THE
SAME WAY as in Galilean relativity / Newtonian mechanics, by a
"distance with a time as the denominator".

No,

_Yes_. Give me one citation _anywhere_ to an SR text saying anything
that could _remotely_ be interpreted to contradict the definition of
velocity _in a given frame_ as anything other than dx / dt (where dx
is just a distance _in that frame_ and dt is just a time interval _in
that frame_).

SR states the meter changes length and the second changes rate
the faster you go.

First of all, that is dead wrong. A _given_ observer (at rest in its
inertial frame) will always measure their _own_ meter and second to be
the same, regardless of the motion of other observers. That is the
WHOLE ENTIRE POINT of relativity (SR _or_ Galilean relativity). Look
up proper time, proper length.

Second, that is completely and totally irrelevant to the above
statement regarding the definition of velocity _in a given frame_,
which depends on _nothing_ relevant to _any other frame_. (I.e. it
can be, and indeed is, measured _without_ any reference to Lorentz
transforms, velocity transforms, etc etc).