I can't do this justice tonight, but here are a couple of comments.

I'm just including the few bits that I'm answering in this post. If
time allows I may respond to other bits in the future.


On Wed, 27 Jul 2005 22:54:21 +0000, Androcles wrote:


"sal" wrote in message
news | On Tue, 26 Jul 2005 02:31:38 +0000, Androcles wrote:
|
[ ... ]
|
| This is semantic logic-chopping, really. Relative velocity,
| closing velocity -- either one works for me. Either way, it's the
| time derivative of a length, rather than the time derivative of
| the location of an object, and as such it's not a "velocity" at
| all in the sense that it doesn't tell you how fast something's
| going.

Can't agree. It isn't possible to state how fast anything is going
without a reference (usually implied) as to what that speed is
relative too.

To measure the velocity of an object you need to know the time and
location of two points on its path, in some particular frame of
reference. One point won't do, because you need to evaluate a
derivative in the "real world" and that always takes two points (plus
the assumption that the object's motion is uniform).

Like, say, you might find that at time 1 its X coordinate is 3, at
time 2 its X coordinate is 16, and its Y and Z coordinates are fixed
at zero. From that you'd conclude that it's traveling at

(16 - 3)/(2 - 1) = 13

If c=1, then it's moving at 13C. (Give it a ticket; it's breaking the
rules.)

You can use scope probes and rulers, or synchronized clocks, or
whatever you want to get your two readings. But you can't get away
from the fact that you need two readings.

The velocity is then whatever you measured, as viewed by any observer
who is at rest with respect to the "particular frame of reference".

And you can't get away from the fact that the "vacuum" isn't anywhere
in particular, doesn't have a particular time attached to it, and can
never provide you with the events you need to determine how fast it's
going.

Relative speed (or closing speed or whatever you care to call it),
viewed from a particular frame of reference, can be obtained by plain
old vector addition, or by explicitly subtracting the positions and
then differentiating, which will give the same result.

Speed that _would_ _be_ measured by an observer in some other FoR must
be found using composition of velocities, of course.


| If two cars collide head-on, each going 60 MPH (which is legal
| again in this country), then as viewed by an observer by the side
| of the road each car had speed = 60 MPH (and velocity = +/- 60
| depending on the direction, if we use the convention that speed =
| abs(velocity)). The "closing speed" or "relative speed" or
| whatever you want to call it is 120 MPH, but it's not the velocity
| of any object, as viewed by our roadside observer, because it's
| not the derivative of a position.

You display the same confusion that put Galileo under house arrest.

I thought they arrested him for not giving God proper credit in his
papers.

Why do people think the Earth is the absolute frame of reference
against which this 60 MPH is to be measured? The car is travelling
around the Sun, a distance of approximately 93,000,000 * 2*pi miles,
in one year. In the frame of the fixed stars your 60 mph is a
relative speed. The Earth moves. ALL speeds are relative. No
exceptions. You've adopted what Einstein called the "customary
view". His magnet and conductor are hurtling around the solar system
too, at 0.0001c in the "empty space". That should make it quite
possible to detect relativistic effects easily, if there were any.
Radio transmission to spacecraft near Saturn, relative to the
spacecraft, are sent at between 0.9999c and 1.0001c in empty space.

In the FoR of an observer on Earth, you mean, right?

In the craft's FoR it would seem different.

Either way we'd need somebody out in space with a clock to tell us
when the signal passed him by in order to confirm the velocity, of
course. Otherwise it's just my-theory-against-yours. You can't
determine a velocity with just one point.


[ ... snip (but I read it first...)... ]


| | Does an electron falling toward the Earth radiate?
|
| I think it's called Cherenkov radiation, but you only get it in
| a medium.
|
| No, Cherenkov radiation is what you get when a charged particle
| travels faster than SoL in a medium. Has nothing to do with
| acceleration (save that it's accompanied by rather rapid
| deceleration).

No, No, NO!
Cherenkov radiation is what you get when a charged particle travels
faster than SoL in a medium.

Do you always agree by saying "No"? It must drive your wife crazy.

Yup.

Perhaps she's used to it...

Nope.


[ ... ]

| No, I have no shrine to Einstein, I'm not even on a first name
| basis with him. I have to dig out one of his books every once in
| a while to answer some post of yours, but I don't spend nearly as
| much time following him as you do, I suspect... :-)
|

What was all that stuff you wrote about on Sagnac, then? It's not
even a moving vacuum fibre...

It's 'cause I got in an embarrassing corner over in fr.sci.physique in
an argument over contraction on a rotating disk, and someone claimed
the Sagnac effect proved his point. I went and thought about it and
came up with what I felt was a nice way of looking at it. I put that
into a web page. That's it.

If you want to know about the experiments that have been done and what
devices are available, google it, or look in an encyclopedia.
Britannica has something on it, for instance. I'm not signing up to
do your research for you.


| I enjoy the math.

Do you? Cool! What is the fewest number of colours needed for a map,
no
two countries with the same colour to share a border, all countries to
share a border with another, 1) on a plane sheet of paper, (4
colours)

And on a torus it's ... um ... at least 5, for sure, 'cause I can
think of an example that needs 5. But is it exactly 5, or is it 6?
Not sure, my visualization the 6-color example has lost its vertical
hold and I'm not sure if it's correct.


2) on a Mobius strip,

Don't know. (Do you?) Certainly at least 4 because that can be done
with a "local" example that works on anything 2-dimensional. But is
it more than 4? Hmmm...

3) on a Klein bottle,

Ouch! Don't know, and can't even picture it.

4) on a sphere ?

Four again. Puncture the sphere, and it's isomorphic to the plane.
Puncture it in the middle of one country and you're done -- any
example requiring more than 4 colors would map 1:1 onto the plane,
where we know it's only 4.


Assume the surface is transparent, same colour shows through the other
side.

That makes a difference to the Mobius strip and the Klein bottle, but
not to the plane, sphere, or torus.


| I'm also getting a kick out of reading Stephen Hawking's "Une
| Brève Histoire du Temps" which I picked up used for a couple
| bucks. It's a very light read but it's fun. It's more of a
| history-of-science book than a science book, which I suppose
| should have been apparent from the title.

Yeah... I read the English translation many years ago. Hawking's
haughty first wife didn't like me much, she thought he shouldn't
have a beer. Can't think why she brought him into a bar...

Seriously??

I can believe she didn't think he should drink. Can't do his CNS any
good.


I'd have to have Coca Cola with bourbon.

UGH

[ ... ]

| The force on a charged particle is
|
| F = q(E + VxB)

Forces only exist between TWO bodies. F = GMm/r^2. When the
irresistable force meets the immovable object, the other object
moves. Do a push up. You move, not the floor. There is something
missing in your equation, the implied immovable object.

The observer who measures the field is the one whose observation of
the particle provides the V in the equation.

There isn't anything to push "against" in the Lorentz force law.


| (unless I've flipped the sign). Of course, q is the amount of
| charge, V is the velocity of the charge, E and B are as usual,'x'
| is the cross product. But the "velocity" of the _field_ is not
| present in the formula.

Correct. we don't employ the velocity of the plane with the TV with
the electron beam inside the vacuum, it is implied that the motion
of the electron is relative to the tube and so is the force, F=
MA+ma. M is so huge it has neglible acceleration, A = 0, so we write
F = ma, forgetting the recoil. This forgetfulness is what makes
acceleration absolute. Momentum is conserved, AND it is ALWAYS zero.

Earth is treated as an infinite momentum source/sink, of course.

I still think acceleration is absolute.

[ ... ]

| You can't have vortices in the vacuum, or so most people believe.
|
| QED.

Now you are bringing belief into it.

Someplace I ran across a variant on Ritz-Fox that claimed vortices in
the vacuum normalized the velocity of light, providing a finite
extinction length even in "vacuum". But I couldn't find the reference
again later so I couldn't quote it.

Too bad.

[ ... ]

| | How do you handle the Sagnac effect in emission theory?
|
| Emission theory is only about light in EMPTY space.
|
| I thought you'd said previously that in a physical medium such as
| air or glass, light travels at SoL in the air or glass, relative
| to that object. At least, that's what you said when we were
| arguing about redshifts and spectroscopes, a long time back. Are
| you disavowing that now?

I think I said at a speed characteristic of the medium. You'll need
to quote me to get a brandy back, IF I mislead you
unintentionally. I don't recall the exact phrase I used. c/n
relative to the medium is what I mean today and meant then.

That's what I thought.

In that case, wouldn't a fixed observer watching a rotating fiber
optic ring, where the ring's tangential velocity is V, see the light
traveling around it one way at

U+ = c/n + V

and the other way at

U- = c/n - V

??

Sure looks like it to me.

And that leads very easily to the conclusion that there is no Sagnac
effect.


| It doesn't help, anyway. The Sagnac effect works just fine using
| _evacuated_ tubes, too. (You know, tubes filled with empty space,
| which you just said emission theory _is_ about.)

Emission theory is what Einstein used to derive his cuckoo
transforms before he added his own definition of time. Sagnac has
air on the OUTSIDE, dragging the light on the inside. You are seeing
conservation of momentum, nothing more.

Say that again? You'll need to spell that out because I didn't get it.

The version with evacuated tubes emits the light in vacuum, and
reflects it off of mirrors in vacuum.

The version with a fiber optic ring emits the light directly into the
fiber, and the whole lot goes around together.

| Sagnac space isn't empty.
|
| The experiment's been done both ways: empty space and non-empty
| space. The result is much the same: the time to go around the
| ring is different one way than the other way, when the ring is
| rotating. It's quite strange.

You are back to a universal frame, then.

That's one way to explain it. But then you run into trouble with
MMX.


--
Nospam becomes physicsinsights to fix the email

"sal" wrote in message
news |I can't do this justice tonight, but here are a couple of comments.
|
| I'm just including the few bits that I'm answering in this post. If
| time allows I may respond to other bits in the future.

yeah, yeah... You'll never keep up with me.
|
|
| On Wed, 27 Jul 2005 22:54:21 +0000, Androcles wrote:
|
|
| "sal" wrote in message
| news | | On Tue, 26 Jul 2005 02:31:38 +0000, Androcles wrote:
| |
| [ ... ]
| |
| | This is semantic logic-chopping, really. Relative velocity,
| | closing velocity -- either one works for me. Either way, it's the
| | time derivative of a length, rather than the time derivative of
| | the location of an object, and as such it's not a "velocity" at
| | all in the sense that it doesn't tell you how fast something's
| | going.
|
| Can't agree. It isn't possible to state how fast anything is going
| without a reference (usually implied) as to what that speed is
| relative too.
|
| To measure the velocity of an object you need to know the time and
| location of two points on its path, in some particular frame of
| reference. One point won't do, because you need to evaluate a
| derivative in the "real world" and that always takes two points (plus
| the assumption that the object's motion is uniform).

If you know the length of a boxcar, you can count them at a railroad
crossing and know the length of the train. When the locomotive passes,
look at your watch, and when the last car passes, look at your watch
again.
The speed of the train at 8:50 am on a Monday morning in the summer
of 2000 at Leetsdale, Pa. was 11 mph. I know, I was there waiting to go
to work, it was hot in the car and I had nothing to do but wait,
sweltering.
The train was 0.9 miles long and took 4 minutes and 54 seconds,
which is forever when waiting at a RR crossing, low on gas and the sun
blazing down.


|
| Like, say, you might find that at time 1 its X coordinate is 3, at
| time 2 its X coordinate is 16, and its Y and Z coordinates are fixed
| at zero. From that you'd conclude that it's traveling at
|
| (16 - 3)/(2 - 1) = 13
|
| If c=1, then it's moving at 13C. (Give it a ticket; it's breaking the
| rules.)
|
| You can use scope probes and rulers, or synchronized clocks, or
| whatever you want to get your two readings. But you can't get away
| from the fact that you need two readings.
|
| The velocity is then whatever you measured, as viewed by any observer
| who is at rest with respect to the "particular frame of reference".
|
| And you can't get away from the fact that the "vacuum" isn't anywhere
| in particular, doesn't have a particular time attached to it, and can
| never provide you with the events you need to determine how fast it's
| going.
|
| Relative speed (or closing speed or whatever you care to call it),
| viewed from a particular frame of reference, can be obtained by plain
| old vector addition, or by explicitly subtracting the positions and
| then differentiating, which will give the same result.
|
| Speed that _would_ _be_ measured by an observer in some other FoR must
| be found using composition of velocities, of course.

"Of course" nothing, absolute nonsense.

|
|
| | If two cars collide head-on, each going 60 MPH (which is legal
| | again in this country), then as viewed by an observer by the side
| | of the road each car had speed = 60 MPH (and velocity = +/- 60
| | depending on the direction, if we use the convention that speed =
| | abs(velocity)). The "closing speed" or "relative speed" or
| | whatever you want to call it is 120 MPH, but it's not the velocity
| | of any object, as viewed by our roadside observer, because it's
| | not the derivative of a position.
|
| You display the same confusion that put Galileo under house arrest.
|
| I thought they arrested him for not giving God proper credit in his
| papers.
|
| Why do people think the Earth is the absolute frame of reference
| against which this 60 MPH is to be measured? The car is travelling
| around the Sun, a distance of approximately 93,000,000 * 2*pi miles,
| in one year. In the frame of the fixed stars your 60 mph is a
| relative speed. The Earth moves. ALL speeds are relative. No
| exceptions. You've adopted what Einstein called the "customary
| view". His magnet and conductor are hurtling around the solar system
| too, at 0.0001c in the "empty space". That should make it quite
| possible to detect relativistic effects easily, if there were any.
| Radio transmission to spacecraft near Saturn, relative to the
| spacecraft, are sent at between 0.9999c and 1.0001c in empty space.
|
| In the FoR of an observer on Earth, you mean, right?

NO I DON'T! I mean in the FoR of the empty space, the same
empty space that Einstein says the velocity of light is c in.
If you want something as an anchor, in the frame of reference
of an observer on Mars as the signal hurtles past.


| In the craft's FoR it would seem different.

Of course it would. Earth is approaching Saturn at 0.0001c
a little over once a year, the signal leaves Earth at c and hits
the spacecraft at 1.0001c, then six months later at 0.9999c.



|
| Either way we'd need somebody out in space with a clock to tell us
| when the signal passed him by in order to confirm the velocity, of
| course. Otherwise it's just my-theory-against-yours. You can't
| determine a velocity with just one point.

Easily done. Have the spacecraft time-stamp a bounced signal,
we don't need a person.

|
| [ ... snip (but I read it first...)... ]

So you agreed with it, or you would have said something.

|
|
| | | Does an electron falling toward the Earth radiate?
| |
| | I think it's called Cherenkov radiation, but you only get it in
| | a medium.
| |
| | No, Cherenkov radiation is what you get when a charged particle
| | travels faster than SoL in a medium. Has nothing to do with
| | acceleration (save that it's accompanied by rather rapid
| | deceleration).
|
| No, No, NO!
| Cherenkov radiation is what you get when a charged particle travels
| faster than SoL in a medium.
|
| Do you always agree by saying "No"? It must drive your wife crazy.
|
| Yup.
|
| Perhaps she's used to it...
|
| Nope.
|
|
| [ ... ]
|
| | No, I have no shrine to Einstein, I'm not even on a first name
| | basis with him. I have to dig out one of his books every once in
| | a while to answer some post of yours, but I don't spend nearly as
| | much time following him as you do, I suspect... :-)
| |
|
| What was all that stuff you wrote about on Sagnac, then? It's not
| even a moving vacuum fibre...
|
| It's 'cause I got in an embarrassing corner over in fr.sci.physique in
| an argument over contraction on a rotating disk, and someone claimed
| the Sagnac effect proved his point. I went and thought about it and
| came up with what I felt was a nice way of looking at it. I put that
| into a web page. That's it.

Waste of time, especially for someone that claims to be short of it.
|
| If you want to know about the experiments that have been done and what
| devices are available, google it, or look in an encyclopedia.
| Britannica has something on it, for instance. I'm not signing up to
| do your research for you.

According to Lorentz, the ring becomes elliptical as it is compressed
by aether, the Earth hurling through space, but the circumference
will not change.
According to Einstein, the circumference will change when you turn
the light on.
" It is at once apparent that this result still holds good if the clock
moves
from A to B in any polygonal line, and also when the points A and B
coincide."
Both were crazy.

|
|
| | I enjoy the math.
|
| Do you? Cool! What is the fewest number of colours needed for a map,
| no
| two countries with the same colour to share a border, all countries
to
| share a border with another, 1) on a plane sheet of paper, (4
| colours)
|
| And on a torus it's ... um ... at least 5, for sure, 'cause I can
| think of an example that needs 5. But is it exactly 5, or is it 6?
| Not sure, my visualization the 6-color example has lost its vertical
| hold and I'm not sure if it's correct.
|
|
| 2) on a Mobius strip,
|
| Don't know. (Do you?) Certainly at least 4 because that can be done
| with a "local" example that works on anything 2-dimensional. But is
| it more than 4? Hmmm...


Six, but I don't have the proof to hand.


|
| 3) on a Klein bottle,
|
| Ouch! Don't know, and can't even picture it.


(fixed font)
Connect the edges as shown, A to B, B to B.

__________
| open |
| |
| |
open open plain plane
| |
| |
|___open__|


___A__B__
| |
| |
| |
open open Moebius strip
| |
| |
|__B__A__|


___A__B__
| |
c c
| |
v v torus
| |
D D
|__A__B__|

___A___
/ \
| |
| |
A A sphere
| |
| |
\____A___/


___A__B__
| |
C C
| |
v v Klein bottle
| |
D D
|__B__A__|




|
| 4) on a sphere ?
|
| Four again. Puncture the sphere, and it's isomorphic to the plane.

Correct.

| Puncture it in the middle of one country and you're done -- any
| example requiring more than 4 colors would map 1:1 onto the plane,
| where we know it's only 4.
|
|
| Assume the surface is transparent, same colour shows through the
other
| side.
|
| That makes a difference to the Mobius strip and the Klein bottle, but
| not to the plane, sphere, or torus.
|
|
| | I'm also getting a kick out of reading Stephen Hawking's "Une
| | Brève Histoire du Temps" which I picked up used for a couple
| | bucks. It's a very light read but it's fun. It's more of a
| | history-of-science book than a science book, which I suppose
| | should have been apparent from the title.
|
| Yeah... I read the English translation many years ago. Hawking's
| haughty first wife didn't like me much, she thought he shouldn't
| have a beer. Can't think why she brought him into a bar...
|
| Seriously??

Yeah, Sussex U at Brighton, many years ago. I was reading QM.
Hawking was on a gurney, his wife pushed him around. He could speak
normally then. I had no idea who he was, but he came up to our group
and started chatting physics so I offered to buy him a beer, I needed a
refill anyway.
His wife said to me "Don't you know who this is?" with her snooty nose
in the air, and I replied "Nope".
She says "He's Steven Hawking!" and pushed him away.
I'd have bought her one too. Oh well...
Britain is still very much a class-conscious society, I'm
still 1,243,676th in line for the throne.
No, wait... my neighbour George passed away, aged 84, make that
1,243,675th.


|
| I can believe she didn't think he should drink. Can't do his CNS any
| good.
|
|
| I'd have to have Coca Cola with bourbon.
|
| UGH
|
I thought that might make you cringe.

| [ ... ]
|
| | The force on a charged particle is
| |
| | F = q(E + VxB)
|
| Forces only exist between TWO bodies. F = GMm/r^2. When the
| irresistable force meets the immovable object, the other object
| moves. Do a push up. You move, not the floor. There is something
| missing in your equation, the implied immovable object.
|
| The observer who measures the field is the one whose observation of
| the particle provides the V in the equation.
|
| There isn't anything to push "against" in the Lorentz force law.

You mean the TV doesn't go backwards in the FoR of the electron?
I thought it did until the electron hit the tube face and knocked
it forward again, conserving momentum.



|
|
| | (unless I've flipped the sign). Of course, q is the amount of
| | charge, V is the velocity of the charge, E and B are as usual,'x'
| | is the cross product. But the "velocity" of the _field_ is not
| | present in the formula.
|
| Correct. we don't employ the velocity of the plane with the TV with
| the electron beam inside the vacuum, it is implied that the motion
| of the electron is relative to the tube and so is the force, F=
| MA+ma. M is so huge it has neglible acceleration, A = 0, so we write
| F = ma, forgetting the recoil. This forgetfulness is what makes
| acceleration absolute. Momentum is conserved, AND it is ALWAYS zero.
|
| Earth is treated as an infinite momentum source/sink, of course.
|
| I still think acceleration is absolute.

Well, you would. You have an absolute frame of reference for it to be
absolute in, the empty space c is constant and absolute in.
Einstein has relative time and absolute space, Newton has absolute
time and relative space.




|
| [ ... ]
|
| | You can't have vortices in the vacuum, or so most people believe.
| |
| | QED.
|
| Now you are bringing belief into it.
|
| Someplace I ran across a variant on Ritz-Fox that claimed vortices in
| the vacuum normalized the velocity of light, providing a finite
| extinction length even in "vacuum". But I couldn't find the reference
| again later so I couldn't quote it.
|
| Too bad.

No great loss to me.

| [ ... ]
|
| | | How do you handle the Sagnac effect in emission theory?
| |
| | Emission theory is only about light in EMPTY space.
| |
| | I thought you'd said previously that in a physical medium such as
| | air or glass, light travels at SoL in the air or glass, relative
| | to that object. At least, that's what you said when we were
| | arguing about redshifts and spectroscopes, a long time back. Are
| | you disavowing that now?
|
| I think I said at a speed characteristic of the medium. You'll need
| to quote me to get a brandy back, IF I mislead you
| unintentionally. I don't recall the exact phrase I used. c/n
| relative to the medium is what I mean today and meant then.
|
| That's what I thought.
|
| In that case, wouldn't a fixed observer watching a rotating fiber
| optic ring, where the ring's tangential velocity is V, see the light
| traveling around it one way at
|
| U+ = c/n + V
|
| and the other way at
|
| U- = c/n - V
|
| ??

Yep. I'm no aetherialist or relativist, so what I do is open out
the fibre into a straight line and inject light into both ends
simultaneously. In Sagnac we truly have simultaneity, of course.
Now to an observer moving relatively to the fibre, the speed
of light is c+v one way and c-v the other.
Now we are back to the train experiment, light leaves at 0 and 80
It travels the full length of the train (or fibre) in 4 seconds one
way and 16 seconds the other, bounces at each end.

Fibre moving left to right.
Light starting from the left.
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))
½[tau(0,0,0,0)+tau(0,0,0,20)] = tau(32,0,0,16).

Light starting from the right:
½[tau(x',0,0,t)+tau(x',0,0,t+x'/(c-v)+x'/(c+v))] = tau(0,0,0,t+x'/(c+v))
½[tau(32,0,0,0)+tau(32,0,0,20)] = tau(0,0,0,4).

Solve tau.


| Sure looks like it to me.
|
| And that leads very easily to the conclusion that there is no Sagnac
| effect.
|
It leads to making nonsense out of your relativity.

|
| | It doesn't help, anyway. The Sagnac effect works just fine using
| | _evacuated_ tubes, too. (You know, tubes filled with empty space,
| | which you just said emission theory _is_ about.)
|
| Emission theory is what Einstein used to derive his cuckoo
| transforms before he added his own definition of time. Sagnac has
| air on the OUTSIDE, dragging the light on the inside. You are seeing
| conservation of momentum, nothing more.
|
| Say that again? You'll need to spell that out because I didn't get
it.

Ok...
Part one:
Emission theory is what Einstein used to derive his cuckoo
transforms before he added his own definition of time.
You can see that it takes 4 seconds to travel the length of a 32 unit
cable one way and 16 seconds the other.
Part two:
A magnet doesn't have to touch a conductor to induce a current, right?
The field passes through the conductor.
Light is electromagnet in its form, and the magnetic field of the light
will interact with air outside the fibre.


| The version with evacuated tubes emits the light in vacuum, and
| reflects it off of mirrors in vacuum.

In a G-field. Near other fixed objects.
Now, you might think I'm floundering here. You'd be right, I am.
What is DO know is that relativity is stupid and there is research
needed, which isn't going to happen all the time you relativists
claim to have all the answers. I don't have all the answers, I only
know you've got the wrong one.
|
| The version with a fiber optic ring emits the light directly into the
| fiber, and the whole lot goes around together.
|
| | Sagnac space isn't empty.
| |
| | The experiment's been done both ways: empty space and non-empty
| | space. The result is much the same: the time to go around the
| | ring is different one way than the other way, when the ring is
| | rotating. It's quite strange.
|
| You are back to a universal frame, then.
|
| That's one way to explain it. But then you run into trouble with
| MMX.

You were in trouble the moment you accepted the cuckoo transforms,
because tau(x',y,z,t) isn't tau(x,y,z,t).
Tau is a transform from the train to the train, not the track to the
train.

Androcles.


|

Androcles wrote:
snip
|
| Ouch! Don't know, and can't even picture it.


(fixed font)
Connect the edges as shown, A to B, B to B.

__________
| open |
| |
| |
open open plain plane
| |
| |
|___open__|


___A__B__
| |
| |
| |
open open Moebius strip
| |
| |
|__B__A__|


___A__B__
| |
c c
| |
v v torus
| |
D D
|__A__B__|

___A___
/ \
| |
| |
A A sphere
| |
| |
\____A___/


___A__B__
| |
C C
| |
v v Klein bottle
| |
D D
|__B__A__|




snip

You were in trouble the moment you accepted the cuckoo transforms,
because tau(x',y,z,t) isn't tau(x,y,z,t).
Tau is a transform from the train to the train, not the track to the
train.

Androcles.


Marvelous geometry!
Now if interchanging time and space only worked
as well as the appropriate application of Coulomb's
Law we could really dazzle 'em with magic tricks. ;-)

Sue...
http://scienceworld.wolfram.com/phys...ulombsLaw.html
http://scienceworld.wolfram.com/phys...lombForce.html



|

"Sue..." wrote in message
oups.com...
|
| Androcles wrote:
| snip
| |
| | Ouch! Don't know, and can't even picture it.
|
|
| (fixed font)
| Connect the edges as shown, A to B, B to B.
|
| __________
| | open |
| | |
| | |
| open open plain plane
| | |
| | |
| |___open__|
|
|
| ___A__B__
| | |
| | |
| | |
| open open Moebius strip
| | |
| | |
| |__B__A__|
|
|
| ___A__B__
| | |
| c c
| | |
| v v torus
| | |
| D D
| |__A__B__|
|
| ___A___
| / \
| | |
| | |
| A A sphere
| | |
| | |
| \____A___/
|
|
| ___A__B__
| | |
| C C
| | |
| v v Klein bottle
| | |
| D D
| |__B__A__|
|
|
|
|
| snip
|
| You were in trouble the moment you accepted the cuckoo transforms,
| because tau(x',y,z,t) isn't tau(x,y,z,t).
| Tau is a transform from the train to the train, not the track to the
| train.
|
| Androcles.
|
|
| Marvelous geometry!

Err... topology.

Chewing gum or modelling clay doesn't have much geometry.
You can stretch the surfaces, shrink them, bend them, puncture
them, but they have to remain surfaces.
Can you puncture a torus and turn it inside out?
Theoretically you can, you've opened an edge of
___A__B__
| |
c c
| |
v v torus
| |
D D
|__A__B__|

so its a pipe, a cylinder.

Get an old car tyre inner tube and try it.


| Now if interchanging time and space only worked
| as well as the appropriate application of Coulomb's
| Law we could really dazzle 'em with magic tricks. ;-)
|
| Sue...
| http://scienceworld.wolfram.com/phys...ulombsLaw.html
| http://scienceworld.wolfram.com/phys...lombForce.html

I've told you before, you can't have mu0, epsilon0.
You can have mu1, mu2, mu3, mu(n), but no mu0.
Now be a good girl and play with the safe toys you've been
given, mu0 and epsilon0 are locked away in the cupboard
where you can't reach them, along with the speed of sound
in a vacuum and the volume of a gas at absolute zero.
Now now, stop pouting, I mean what I say. You can't have
mu0 or epsilon0 to play with, there's aether in them and its
dangerous for little girls.
Here's a black hole instead. See if you can find the bright
green flying elephant's egg at the bottom.
Androcles.