Some troubling assumptions of SR

On 11 Feb 2007 19:07:56 -0800, (Daryl
McCullough) wrote:

Lester Zick says...

Einstein's postulate of an isotropically
constant relative c requires a variably dependent spatial geometry.

No, it doesn't.

It doesn't? Then how exactly is Einstein's postulate of isotropically
constant relative c supposed to be realized? I mean given FLT how does
Eintein get around the problem of different relative c's? Just saying
it doesn't require variably dependent spatial geometries or
anisometries doesn't show us how Einstein otherwise did the trick.

There is no special mystery about this. It's in the source document.
In order to comply with FLT and his postulate of an isotropically
constant relative c, spatial geometry in the direction of v must be
contracted by a second order function of v.

You are confused. Time dilation and length contraction are
effects involving transformations between two different
inertial coordinate systems. Look at the analogous transformation
in Euclidean coordinates. You have one coordinate system with
coordinates x and y. In another coordinate system rotated relative
to the first, the coordinates are x' and y' related to x and y
through

I have no idea what you're talking about here with "rotated"
coordinate systems. The problem started out with relative motion
studies akin to Michelson-Morley. Einstein maintained c would be
isotropically constant for all relative motion experiments. There is
no rotation or involvement "between two different coordinate systems".
There is only the one MM experimental coordinate system and the
difficulty is to explain the null results of relative motion
experiments of that class in the context of Fitzgerald-Lorentz
Transforms. And spatial geometric contraction is the technique
Einstein used to explain isotropically constant relative c and the
null results of MM in one experimental coordinate system. So why you
bring secondary coordinates systems into the problem is a mystery.

x' = x cos(theta) + y sin(theta)
y' = y cos(theta) - x sin(theta)

To see the analogy with the Lorentz transformations more clearly,
let's introduce a parameter m = tan(theta). This is the "slope"
of the x' axis measured relative to the x axis. In terms of m,
we have

x' = 1/square-root(1+m^2) (x + m y)
y' = 1/square-root(1+m^2) (y - m x)

Would you say that in the rotated coordinate system,
that the x' axis is "contracted" by an amount related
to the slope m? No, not at all. Rotating a coordinate
system by a slope m doesn't cause it to contract any
more than moving it at speed v does in Special Relativity.

Then perhaps you can explain Einstein's resolution of isotropically
constant relative c for relative motion experiments such as MM without
secondary coordinate systems or "rotated" coordinate systems.

You seem very confused.

Perhaps, just not as confused as yourself, Daryl.

I'm confused about a good many things, but Special
Relativity is not one of them. On this particular
subject, you don't know what you are talking about
and I do. I'm sure there is a topic where you know
what you are talking about, but physics apparently
is not one of them.

Very good. You "know" I don't know what I'm talking about only because
you don't talk about what I'm talking about. You know
what's puzzling in all this is that I take the trouble to post a very
specific line of reasoning to show exactly what I'm talking about and
you don't even have the courtesy to reply to it. You just delete my
line of reasoning and proclaim I'm wrong and you're right.

My line of reasoning is only directed at one thing: isotropically
constant relative c postulated by Einstein and the resolution of
relative motion experiments such as MM in one frame of reference
in that context. And to do that we don't require secondary frames of
reference or rotations etc. We only need to examine Einstein's own
claims regarding second order velocity dependent spatial contraction
and anisometries and not what you imagine he might otherwise
have meant.

~v~~

Dirk Van de moortel wrote:
"David Marcus" wrote in message ...
Dirk Van de moortel wrote:
"Daryl McCullough" wrote in message ...
Dirk Van de moortel says...

Daryl, you are talking technically to a troll.
That does not work :-)

I thought that the terminology "troll" meant someone who made
intentionally provocative posts just to get a rise out of people.

It is my experience that this is exactly what he is doing.
On top of that he tries to make you believe that he is just
confused - by stressing that you are just confused :-)

Can you give some evidence for this? I haven't seen any such evidence on
sci.math.

Meanwhile you have your evidence :-)

Are you just saying that he is trying to be provocative or do you also
think that he really knows when he says something incorrect?

--
David Marcus

On Feb 12, 4:54 pm, Lester Zick wrote:
On 11 Feb 2007 19:07:56 -0800, (Daryl

McCullough) wrote:
Lester Zick says...

Einstein's postulate of an isotropically
constant relative c requires a variably dependent spatial geometry.

No, it doesn't.

It doesn't? Then how exactly is Einstein's postulate of isotropically
constant relative c supposed to be realized? I mean given FLT

Fermat's Last Theorem?

how does
Eintein get around the problem of different relative c's?

WHAT different relative c's? What on earth makes you think there are
different relative c's? There AREN'T.

Just saying
it doesn't require variably dependent spatial geometries or
anisometries doesn't show us how Einstein otherwise did the trick.

But it HAS been explained to you, Lester. You just mumble some
gobbledygook that red-shifting and blue-shifting are inconsistent with
it, when they are nothing of the kind.

If you have a star with respect to which you are at rest, the light
coming from that star has *measured* speed c. If you then accelerate
to a nonzero speed with respect to the same star and repeat the light
speed measurement, you'll find that the *measured* value is *still* c.
There is no difference in relative c's.

There is also absolutely no inconsistency with this result and any
other experimental result you can obtain by measurement.

PD

Lester Zick says...

Given three bodies A, B, and C with A and B
stationary with respect to one another and C in motion with respect to
A and B are A and B in the same SR frame of reference with each other
and is C in the same or different SR frame of reference?

As I understand the phrase "reference frame", it doesn't make
sense to ask whether an object is *in* a reference frame, it only
makes sense to ask whether an object is *at rest* relative to a
reference frame. Maybe some people use the phrase "in reference
frame F" to mean "at rest relative to reference frame F", but I
think that's a confusing way to say things.

People talk about A's reference frame or C's reference frame,
but all that "A's reference frame" means is "the frame in which
A is at rest". C is "in" A's frame, but it isn't at *rest* in
A's frame.

To my way of thinking A and B are in a common SR frame of reference
and C is in a different frame of reference because C is at a different
velocity from A and B and second order relative velocity determines a
frame of reference in SR.

As I said, I think it's clearer to just say "A and B are at rest relative
one reference frame, and C is in motion relative to that frame."

And if second order relative velocity doesn't
determine a frame of reference in SR

How could it? Velocity is relative to a frame. Every object has
velocity 0 in its own rest frame.

then how does the square root of
1-vv/cc apply to a frame of reference in SR to determine contraction
and provide for an isotropically constant relative c and explain null
results of relative motion experiments such as Michelson-Morley?

The assumption from which the null result of the Michelson-Morley
experiment follows is this:

(1) The laws of physics have the same form when expressed in any inertial
coordinate system.

(2) Inertial coordinate systems are related by the Lorentz transformations
(actually, the Poincare transformations, which include Lorentz transformations,
rotations, and translations).

The parameter v appearing in the Lorentz transformations is the
velocity of one frame relative to another frame.

--
Daryl McCullough
Ithaca, NY

On Mon, 12 Feb 2007 00:30:48 -0000, "George Dishman"
wrote:


"Lester Zick" wrote in message
.. .
On Sun, 11 Feb 2007 13:02:55 -0000, "George Dishman"
wrote:
"Lester Zick" wrote in message
...
On Sat, 10 Feb 2007 20:52:38 -0000, "George Dishman"
wrote:
"Lester Zick" wrote in message
om...
On Sat, 10 Feb 2007 12:05:22 -0000, "George Dishman"
wrote:
...
The same is true in Newtonian physics, the kinetic
energy of an object is zero in its rest frame
and the value diffes from frame to frame regardless
of what theory you use.

Nonsense, George. There is only one frame of reference in Newtonian
physics, ...

You really need to find out what a frame is, Lester.

I may not know what a frame is, ..

Perhaps. First I should apologise for my terse response but
when you say "Nonsense" to something that is perfectly true,
it isn't helping Jim to learn these basics.

Consider two objects A and B moving apart with no forces
acting on either. That is they are moving under their own
inertia.

- A B -

As Daryl said, frames are subtly distinct from coordinate
systems but we can make an arbitrary choice of using
rectilinear coordinates with the object at the origin
(rather than say polar) and use that as an example.

Suppose we measure distances from A. We could set up a
grid of lines 1m apart with A at the origin:

-1 0 1 2 3 4 5 6

| | | | | | | |
2 -+--+--+--+--+--+--+--+-
| | | | | | | |
1 -+--+--+--+--+--+--+--+-
| | | | | | | |
0 -+--A--+--+--+--B--+--+-
| | | | | | | |
-1 -+--+--+--+--+--+--+--+-
| | | | | | | |


You can define the location of B using those coordinates
and then taking the time derivative of those gives you
the velocity of B "in the rest frame of A". Call that V.

You can do the same the other way round, fix the origin
as object B:

-5 -4 -3 -2 -1 0 1 2

| | | | | | | |
2 -+--+--+--+--+--+--+--+-
| | | | | | | |
1 -+--+--+--+--+--+--+--+-
| | | | | | | |
0 -+--A--+--+--+--B--+--+-
| | | | | | | |
-1 -+--+--+--+--+--+--+--+-
| | | | | | | |

Now B's velocity is obviously zero by definition and we
expect the velocity of A to be -V in the frame of B. That
is true in both classical theory and SR.

Going back to some comments in earlier threads, note that
both frames extend to infinity in all directions hence
overlap everywhere, and the origin of B's frame is moving
at velocity V in A's coordinates.

Notice that I have chosen to defined both grids as being
equally spaced with 1m separation. Of course we are really
talking about measurements using the metre as a basic unit
but either way, distances in the x and y directions are
using equal units so the frames are "isometric" as I think
you are using the term. Again, that is true in both
classical theory and SR.

Where the theories differ is the equations used to work
out the coordinates of an object, or more accurately an
event, in one frame given the coordinates of the same event
in the other frame. That's where the Galilean and Lorentz
transforms come in.

George, what makes you think you can lay out an isometric coordinate
system and then just say the equations used to work with coordinates
are different in different systems ..

I can say it because those are the facts Lester, you
seem to have some unusual misconceptions about SR.

Okay, George, we've been over most of this material before but now you
claim that equations defined in terms of isometric spatial coordinates
work just swell in anisometric spatial coordinates and because of that
my understandings of anisometric geometries in SR are misconceptions.
Just swell.

.. when the very basis of equations is
the metric system used and the whole point of anisometry in SR is that
coordinate systems or spatial metrics are velocity dependent and not
isometric or MM should work?

The MMx does work lester. It is not the coordinate systems
themselves that change but the relationships between them.

Last time I checked, George, MM yields null results and doesn't work
just swell and you can change all the relationships you want but it
still doesn't work and won't work and that failure to work was exactly
what Einstein attempted to explain with his isotropically constant
relative c postulate in every single SR frame of reference which he
justified by hypothesizing a velocity dependent spatial contraction as
a function of 1-vv/cc.

Take two points P and Q a distance D apart both at rest in
frame "A". Let a photon move from P to Q in time t=D/c. Now
translate the event coordinates of emission at P and
reception at Q into frame "B" and calculate the speed. If
you use the Galilean Transforms, the answer is c-V but if
you use the Lorentz Transforms the answer is c.

If you lay out an MMx in the "A" frame with a null result
and then transform the coordinates of the events to the
"B" frame using the Lorentz Transforms, you will find the
result is also a null, just as is found in real life.

And this is what you mean when you say "MMx does work . . ."? George,
I really think you better get a new definition for the term "works"

All you've shown is a Euclidean-Galilean-Cartesian-Newtonian frame of
reference for both A and B that applies isometrically throughout space
and I agree.

1) The spatial part is Euclidean.

2) I choose Cartesian for simplicity but I could equally
well have used Polar coordinates, and as Daryl says the
coordinate system is not fundamental to the definition
anyway.

3) It is not specified whether it is Galilean or Lorentzian,
the frames are the same in both. If you translate between
the frame using the Galilean Transforms, you get the
Newtonian view and if you translate with the Lorentz
Transforms you get SR.

What you haven't shown however is Einstein's SR anisometry

That's because there is no "anisometry" in SR, that is your
misconception. Try the test I suggested above, work out the
event coordinates of an MMX and apply the Lorentz Transforms
and you will find it works just fine.

Yeah, George, I'm beginning to think you've gone right around the
twist here. FLT specifies a variable anisotropic relative c. Einstein
says there is a constant isotropic relative c despite FLT. And now you
say that Einstein never suggested a second order velocity dependent
spatial anisometry to resolve that conflict? So what exactly is the
functional dependence in 1-vv/cc supposed to resolve? What is v if not
velocity? And what is contraction supposed to resolve if not the
contradiction between FLT and Einstein's postulate?

which describes the variable spatial metric needed to make a constant
relative isotropic c both for A and B when their velocities differ.

And if A and B traverse space at different v's and light for both A
and B is assumed to traverse space independently of A and B then those
velocity dependent second order anisometric spatial metrics in SR
conflict. There simply is no way around it that I can see. And if I
say it rather abruptly I apologize but we've been over and over the
point and you just refuse to take it.

I too will be blunt then, the reason nobody is taking your
point is because your understanding of SR is flawed and the
point is simply wrong.

Thanks for the explanation, George.

Frames in SR are exactly the same as
those in Newtonian physics, it is the Transforms that convert
event coordinates between frames that differ.

Then back to the original point I made and please explain Einstein's
postulate of isotropically constant relative c he used to explain why
FLT didn't work in just one frame of reference. Just saying FLT
converts event coordinates between frames doesn't explain why they
don't work and produce null results in any one MM frame.

So if Jim or whoever asked the
question is going to learn what's right instead of what's wrong he
might just as well start right here.

Indeed, he can learn that your statement:

Nonsense, George. There is only one frame of reference in Newtonian
physics, ...

was wrong. You can now see that we have laid out two different
frames regardless of whether we are discussing Newtonian physics
or SR. At least that is one point that has been cleared up.

George, you're a pompous ass. But then you're British. You say things
without any justification whatsoever and expect others to agree that
clears things up. Stiff upper lip, what, and God Save the Queen.

FLT predicted an anisotropic relative c which should have been
detected by MM in its reference frame but wasn't. Even if you include
a rest frame of reference you wind up subtracting zero from v. Big
deal.That still leaves v and still leaves one reference frame to which
FLT applies and an anisotropic relative c which MM should have
detected but didn't and in which Einstein's postulate of an isotropic
relative c was explained by an anisotropic second order velocity
dependent anisometric contraction which you prefer to pretend isn't
there. You're just guessing and I'm tired of listening to nonsense.

~v~~

On 12 Feb 2007 15:27:31 -0800, (Daryl
McCullough) wrote:

Lester Zick says...

Given three bodies A, B, and C with A and B
stationary with respect to one another and C in motion with respect to
A and B are A and B in the same SR frame of reference with each other
and is C in the same or different SR frame of reference?

As I understand the phrase "reference frame", it doesn't make
sense to ask whether an object is *in* a reference frame, it only
makes sense to ask whether an object is *at rest* relative to a
reference frame.

A distinction without a difference as far as I can tell. If I say a
given object is "in a reference frame" as far as I'm concerned that
just means it's a rest in that frame and if it isn't in that reference
frame it's in motion with respect to objects in that reference frame.

Maybe some people use the phrase "in reference
frame F" to mean "at rest relative to reference frame F", but I
think that's a confusing way to say things.

People talk about A's reference frame or C's reference frame,
but all that "A's reference frame" means is "the frame in which
A is at rest". C is "in" A's frame, but it isn't at *rest* in
A's frame.

Sure but that means objects at rest share one set of characteristics
and those not at rest don't share the same set of characteristics and
the determinate of which characteristics one set shares and another
doesn't in the context of SR is constant velocity.

To my way of thinking A and B are in a common SR frame of reference
and C is in a different frame of reference because C is at a different
velocity from A and B and second order relative velocity determines a
frame of reference in SR.

As I said, I think it's clearer to just say "A and B are at rest relative
one reference frame, and C is in motion relative to that frame."

Personally I don't see it makes any kind of critical difference.

And if second order relative velocity doesn't
determine a frame of reference in SR

How could it? Velocity is relative to a frame. Every object has
velocity 0 in its own rest frame.

But not relative to other rest frames including any possible absolute
rest frame which is exactly what MM was designed to detect but didn't.
FLT explained those experimental expectations in terms of anisotropic
second order velocity dependence for an experimental platform relative
to space in general and Einstein's postulate of isotropically constant
relative velocity uses a second order velocity dependent function in
1-vv/cc to explain why relative motion experiments such as MM fail.
And that requires a hypothetical anisometric spatial contraction.

then how does the square root of
1-vv/cc apply to a frame of reference in SR to determine contraction
and provide for an isotropically constant relative c and explain null
results of relative motion experiments such as Michelson-Morley?

The assumption from which the null result of the Michelson-Morley
experiment follows is this:

(1) The laws of physics have the same form when expressed in any inertial
coordinate system.

(2) Inertial coordinate systems are related by the Lorentz transformations
(actually, the Poincare transformations, which include Lorentz transformations,
rotations, and translations).

The parameter v appearing in the Lorentz transformations is the
velocity of one frame relative to another frame.

I agree except that the design objective of MM was to detect motion of
the experimental platform through space in absolute terms predicted by
FLT. In other words the rest frame in such a case was thought to be
space in general. And the failure of relative motion studies such as
MM was hypothetically explained in terms of Einstein's postulate of
isotropically constant relative c which he justified in contrast to
predictions of FLT by means of a second order velocity dependent
anisometric spatial contraction.

~v~~

Lester Zick wrote:
[...]
And of course you're not a troll because you tow the party line.
[...]

Lester, watch your spelling. It's TOE the line. As in putting your feet
as close to the lines as possible. As in lining up on the parade ground.
IOW, to align yourself with the party line, which is what you intend by
using this cliche.

Yeah, yeah, I know a bunch of semi-literates, AKA sports writers,
started writing the cliche as if it were about hauling on something or
other, but they're wrong.

Lester Zick says...

(Daryl McCullough) wrote:

Look at the analogous transformation
in Euclidean coordinates. You have one coordinate system with
coordinates x and y. In another coordinate system rotated relative
to the first, the coordinates are x' and y' related to x and y
through

I have no idea what you're talking about here with "rotated"
coordinate systems.

I'm trying to get you to see the analogy between
a rotation of coordinates in Euclidean geometry
and a Lorentz transformation in Special Relativity.

Rotation:

x -- x cos(theta) + y sin(theta)
y -- y cos(theta) - x sin(theta)

Lorentz transformation:

x -- x cosh(theta) + t sinh(theta)
t -- t cosh(theta) + x sinh(theta)

In the case of a rotation, the parameter theta has the
meaning that tan(theta) = slope of new x-axis relative to old x-axis.
In the case of a Lorentz transformation, the parameter theta
has the meaning that tanh(theta) = the velocity of the origin of the
new coordinate system relative to the old coordinate system.

A Lorentz transformation doesn't involve "contraction" any
more than a regular rotation does.

Then perhaps you can explain Einstein's resolution of isotropically
constant relative c for relative motion experiments such as MM without
secondary coordinate systems or "rotated" coordinate systems.

The *problem* to be explained is "How can light have speed c in
all reference frames?" The hypothesis that all laws of physics
are invariant under Lorentz transformations explains that result.

--
Daryl McCullough
Ithaca, NY

Lester Zick says...
(Daryl McCullough) wrote:

As I understand the phrase "reference frame", it doesn't make
sense to ask whether an object is *in* a reference frame, it only
makes sense to ask whether an object is *at rest* relative to a
reference frame.

A distinction without a difference as far as I can tell.

Then please use my terminology, if it doesn't make any
difference to you.

FLT explained those experimental expectations in terms of anisotropic
second order velocity dependence for an experimental platform relative
to space in general and Einstein's postulate of isotropically constant
relative velocity uses a second order velocity dependent function in
1-vv/cc to explain why relative motion experiments such as MM fail.
And that requires a hypothetical anisometric spatial contraction.

No, it doesn't. What it requires is that

1. The distance between two events, as measured in one frame,
is different from the distance between the same events, as measured
in another frame.

2. The time between two events, as measured in one frame,
is different from the time between the same events, as measured
in another frame.

It does *not* require that anything is physically contracted.

--
Daryl McCullough
Ithaca, NY

On Feb 12, 6:15 pm, Lester Zick wrote:
On 12 Feb 2007 15:27:31 -0800, (Daryl

McCullough) wrote:
Lester Zick says...

Given three bodies A, B, and C with A and B
stationary with respect to one another and C in motion with respect to
A and B are A and B in the same SR frame of reference with each other
and is C in the same or different SR frame of reference?

As I understand the phrase "reference frame", it doesn't make
sense to ask whether an object is *in* a reference frame, it only
makes sense to ask whether an object is *at rest* relative to a
reference frame.

A distinction without a difference as far as I can tell. If I say a
given object is "in a reference frame" as far as I'm concerned that
just means it's a rest in that frame and if it isn't in that reference
frame it's in motion with respect to objects in that reference frame.


And by your definition, no object could then be measured to be moving
in any particular reference frame, because (by definition) it isn't in
that frame.

PD