On 1/7/23 7:35 PM, RichD wrote:
> Length contraction isn't something that acts on solid objects, it's
> a relationship between coordinate systems in motion.

Yes. RELATIVE motion.

> Given a fan with 4 fan blades. There's a gap between each pair of
> adjacent blades. It begins to rotate.

[I presume the fan has a 4-fold rotational symmetry, so
the blades are identical and equally spaced around the
circumference. If this were not true, the fan would be
unbalanced and not rotate smoothly.]

You must specify HOW it is rotating. As the centers of the blades are
initially 90 degrees apart, we can presume that they remain 90 degrees
apart. That is, the fan retains its 4-fold rotational symmetry while
rotating, so it rotates smoothly; the rotation is coupled equally to
each blade.

> Seen from the inertial frame of the axis, the blades will Lorentz
> contract circumferentially, tangent to the direction of rotation.
> This is measurement only,

Yes.

> we ignore internal stresses due to the centrifuge effect.

OK. That is radial and we are considering the circumference.

> You deny that the gaps will also shrink?

Yes. Because the centers of the blades remain 90 degrees apart. In
circumference, the blades will shrink and the gaps will grow.

Now for something completely different:
> Given two aircraft, flying in line, nose to tail, maintaining
> constant speed and separation. Then they accelerate, in sync,
> maintaining constant separation, in their frame.

You mean constant separation in their SUCCESSIVE inertial rest frames.
This is Born rigid motion, and it requires that the rear plane have
larger proper acceleration than the front plane.

> An earthbound observer sees the ships Lorentz contract. Does he see
> the gap contract?

Yes. This is not at all the same as the fan blades. It is also not the
same as the Bell spaceship paradox.

Tom Roberts

On January 10, Tom Roberts wrote:
>> Length contraction isn't something that acts on solid objects, it's
>> a relationship between coordinate systems in motion.
>
> Yes. RELATIVE motion.
>
>> Given a fan with 4 fan blades. There's a gap between each pair of
>> adjacent blades. It begins to rotate.
>
> [I presume the fan has a 4-fold rotational symmetry, so
> the blades are identical and equally spaced around the
> circumference. ]
> You must specify HOW it is rotating. As the centers of the blades are
> initially 90 degrees apart, we can presume that they remain 90 degrees
> apart. That is, the fan retains its 4-fold rotational symmetry while
> rotating, so it rotates smoothly; the rotation is coupled equally to
> each blade.
>
>> Seen from the inertial frame of the axis, the blades will Lorentz
>> contract circumferentially, tangent to the direction of rotation.
>> This is measurement only,
>
> Yes.
>
>> we ignore internal stresses due to the centrifuge effect.
>
> OK. That is radial and we are considering the circumference.
>
>> You deny that the gaps will also shrink?
>
> Yes. Because the centers of the blades remain 90 degrees apart. In
> circumference, the blades will shrink and the gaps will grow.

Here is your error. You extend Euclidean geometry - specifically the
notion of 90* - beyond its applicable domain.

An angle is defined as the ratio of the circular arc subtended, to its
radius. The arc length depends on the geometry. Euclidean space
is flat; the space of a rotating disc, in relativity, isn't.

You picture the fan blade centers maintaining a constant circumferential
distance, because they're fixed along 90* lines. That picture fails, when
we account for Lorentz length effects. The 90* remains valid close to the
axis, but doesn't imply the Euclidean arc length, far away.

The ENTIRE circumference, at any given radius, contracts. Whether steel
or space, no matter. It's a coordinate effect, not physical.

Another view: draw a circle on the solid disc, at radius r. At rest, its length
is 2πr.

Now set the disc into motion. An observer hovers above the disc,
exactly above the line. He measures its length, the circumference,
as it rotates. Does he see 2πr?

--
Rich

On 1/10/23 5:39 PM, RichD wrote:
> On January 10, Tom Roberts wrote:
>>> Length contraction isn't something that acts on solid objects,
>>> it's a relationship between coordinate systems in motion.
>>
>> Yes. RELATIVE motion.
>>
>>> Given a fan with 4 fan blades. There's a gap between each pair of
>>> adjacent blades. It begins to rotate.
>>
>> [I presume the fan has a 4-fold rotational symmetry, so the blades
>> are identical and equally spaced around the circumference. ] You
>> must specify HOW it is rotating. As the centers of the blades are
>> initially 90 degrees apart, we can presume that they remain 90
>> degrees apart. That is, the fan retains its 4-fold rotational
>> symmetry while rotating, so it rotates smoothly; the rotation is
>> coupled equally to each blade.
>>
>>> Seen from the inertial frame of the axis, the blades will Lorentz
>>> contract circumferentially, tangent to the direction of rotation.
>>> This is measurement only,
>>
>> Yes.
>>
>>> we ignore internal stresses due to the centrifuge effect.
>>
>> OK. That is radial and we are considering the circumference.
>>
>>> You deny that the gaps will also shrink?
>>
>> Yes. Because the centers of the blades remain 90 degrees apart. In
>> circumference, the blades will shrink and the gaps will grow.

I forgot to mention AS MEASURED BY THE INERTIAL FRAME.

In the rotating system the fan blades are unaffected by the rotation.
(We are ignoring radial stresses and strains.)

This is due to the fact that the fan retains its 4-fold rotational
symmetry while rotating -- there are 4 blades equally spaced around the
circle. So the blades shrink and the gaps grow, as seen simultaneously
in the inertial frame of the axis.

> Here is your error.

No, it is YOUR error.

> You extend Euclidean geometry - specifically the notion of 90* -
> beyond its applicable domain.

Hmmm. Go back and READ WHAT I WROTE, without adding your own guesses and
misconceptions.

Specifically: I said "the fan retains its 4-fold rotational symmetry
while rotating", and IT MUST DO SO, as long as "the rotation is coupled
equally to each blade".

> An angle is defined as the ratio of the circular arc subtended, to
> its radius.

Hmmm. That is NOT what I was discussing. I specifically mentioned "the
fan retains its 4-fold rotational symmetry while rotating". The centers
of the blades are separated by 1/4 of the circumference. As we assign
360 degrees to go around the circle, that means the blade centers are 90
degrees apart -- this is so in both the rotating system and the inertial
frame of the axis (measured simultaneously in that frame).

> The arc length depends on the geometry. Euclidean space is flat;
> the space of a rotating disc, in relativity, isn't.

Hmmm. The manifold is flat, but that is a (3+1)-D manifold. If you want
to discuss a 3-D spatial sub-manifold, you must specify how to foliate
spacetime into space and time. You will find that you cannot do that for
the whole disk if you insist the 3-space rotates.

[In cylindrical coordinates (r,phi,z,t), if they rotate
around the z axis r=0, the metric components are not
orthogonal, and you cannot separate space from time
because the (phi,t) component is nonzero.]

> You picture the fan blade centers maintaining a constant
> circumferential distance,

Hmmm. I picture the fan blade centers remaining separated by 1/4 of the
circumference. That does not actually depend on the value of the
circumference, it depends on the fact that this is a circle and there
are 4 blades that are equally spaced around the circle.

> The ENTIRE circumference, at any given radius, contracts.

No. You are confused. In relativity, no moving object ever "contracts"
-- what contracts are MEASUREMENTS BY SOME OTHER INERTIAL FRAME. So if
the inertial frame of the axis measures the fan blades simultaneously in
the frame, the blades will be shorter and the gaps between them will be
larger. That is, the centers of the blades will be the same distance
apart as when the fan is not rotating, but the circumferential length of
each blade is "length contracted" [#].

You are treating the circumference as if it were an object, so let's do
so: Imagine laying N identical short rulers end-to-end around the fan
circumference, rotating with the fan. Start with N=10 and take the limit
N->infinity. Sum up the lengths of those rulers, and you get 2*pi*R
where R is the radius of the circle on which you laid them down. This is
independent of the rotational speed of the fan and rulers, because
"length contraction" does NOT contract any physical object; the inertial
frame of the axis will similarly measure 2*pi*R for that circumference,
using rulers at rest in the frame.

[#] One must be careful when applying "length contraction",
as it is specific to certain physical situations, and is not
general; I state without proof that it applies here.

> Another view: draw a circle on the solid disc, at radius r. At
> rest, its length is 2πr.
>
> Now set the disc into motion.

By "motion" I presume you mean rotation around its center. We must
ignore both radial and circumferential stresses and strains.

> An observer hovers above the disc, exactly above the line. He
> measures its length, the circumference, as it rotates. Does he see
> 2πr?

Yes. Independent of whether he rotates with the disk or remains at rest
in the inertial frame of the axis.

Tom Roberts

On Wednesday, 11 January 2023 at 06:35:00 UTC+1, Tom Roberts wrote:
> On 1/10/23 5:39 PM, RichD wrote:
> > On January 10, Tom Roberts wrote:
> >>> Length contraction isn't something that acts on solid objects,
> >>> it's a relationship between coordinate systems in motion.
> >>
> >> Yes. RELATIVE motion.
> >>
> >>> Given a fan with 4 fan blades. There's a gap between each pair of
> >>> adjacent blades. It begins to rotate.
> >>
> >> [I presume the fan has a 4-fold rotational symmetry, so the blades
> >> are identical and equally spaced around the circumference. ] You
> >> must specify HOW it is rotating. As the centers of the blades are
> >> initially 90 degrees apart, we can presume that they remain 90
> >> degrees apart. That is, the fan retains its 4-fold rotational
> >> symmetry while rotating, so it rotates smoothly; the rotation is
> >> coupled equally to each blade.
> >>
> >>> Seen from the inertial frame of the axis, the blades will Lorentz
> >>> contract circumferentially, tangent to the direction of rotation.
> >>> This is measurement only,
> >>
> >> Yes.
> >>
> >>> we ignore internal stresses due to the centrifuge effect.
> >>
> >> OK. That is radial and we are considering the circumference.
> >>
> >>> You deny that the gaps will also shrink?
> >>
> >> Yes. Because the centers of the blades remain 90 degrees apart. In
> >> circumference, the blades will shrink and the gaps will grow.
> I forgot to mention AS MEASURED BY THE INERTIAL FRAME.

You forgot indeed - as measured by your delusion.

On January 10,  Tom Roberts wrote:
>>>> Length contraction isn't something that acts on solid objects,
>>>> it's a relationship between coordinate systems in motion.
>>>> Given a fan with 4 fan blades. There's a gap between each pair of
> >>> adjacent blades. It begins to rotate.
>
>>> [I presume the fan has a 4-fold rotational symmetry, so the blades
>>> are identical and equally spaced around the circumference. ]
>>> You must specify HOW it is rotating. As the centers of the blades are
>>> initially 90 degrees apart, we can presume that they remain 90
>>> degrees apart. That is, the fan retains its 4-fold rotational
>>> symmetry while rotating, so it rotates smoothly;
>
>>>> Seen from the inertial frame of the axis, the blades will Lorentz
>>>> contract circumferentially, tangent to the direction of rotation.
>>>> This is measurement only,
>
>>> Yes.
> >>
> >>> we ignore internal stresses due to the centrifuge effect.
>
>>> OK. That is radial and we are considering the circumference.
>
>>>> You deny that the gaps will also shrink?
>
>>> Yes. Because the centers of the blades remain 90 degrees apart. In
>>> circumference, the blades will shrink and the gaps will grow.
> I forgot to mention AS MEASURED BY THE INERTIAL FRAME.
> In the rotating system the fan blades are unaffected by the rotation.
> This is due to the fact that the fan retains its 4-fold rotational
> symmetry while rotating --
> So the blades shrink and the gaps grow, as seen simultaneously
> in the inertial frame of the axis.
>
>>  Here is your error.
>> You extend Euclidean geometry - specifically the notion of 90* -
>> beyond its applicable domain.
>
> Hmmm. Go back and READ WHAT I WROTE, without adding your own guesses
> and misconceptions.
> Specifically: I said "the fan retains its 4-fold rotational symmetry
> while rotating", and IT MUST DO SO, as long as "the rotation is coupled
> equally to each blade".

Concur.
Your error is in the assumption that this symmetry enforces a
constant circumferential distance between blade centers.

>> An angle is defined as the ratio of the circular arc subtended, to
>> its radius.
>
> Hmmm. That is NOT what I was discussing. I specifically mentioned "the
> fan retains its 4-fold rotational symmetry while rotating". The centers
> of the blades are separated by 1/4 of the circumference. As we assign
> 360 degrees to go around the circle, that means the blade centers are 90
> degrees apart -- this is so in both the rotating system and the inertial
> frame of the axis (measured simultaneously in that frame).

Your error continues.  1/4 circumference separation, and 90* symmetry
(locally, at the axis) doesn't guarantee a constant circumference, seen
from the inertial frame of the axis, independent of rotational velocity.

To repeat: angles are normally defined in the context of
Euclidean geometry.  In other contexts, we must re-think.
 
In this case, the fact that the blade centers remain aligned
along those lines, doesn't imply they maintain constant
circumferential separation, seen from the external inertial
frame.  That's a non sequitur.

>> The arc length depends on the geometry. Euclidean space is flat;
>> the space of a rotating disc, in relativity, isn't.
>
> Hmmm. The manifold is flat, but that is a (3+1)-D manifold. If you want
> to discuss a 3-D spatial sub-manifold, you must specify how to foliate
> spacetime into space and time. You will find that you cannot do that for
> the whole disk if you insist the 3-space rotates.
> [In cylindrical coordinates (r,phi,z,t), if they rotate
> around the z axis r=0, the metric components are not
> orthogonal, and you cannot separate space from time
> because the (phi,t) component is nonzero.]

OK, that means the circumference is ambiguous, measured
by an observer riding on the disc.

But here we consider measurements from an inertial
frame, outside the disc.  A much simpler proposition.

>> You picture the fan blade centers maintaining a constant
>> circumferential distance,
>
> Hmmm. I picture the fan blade centers remaining separated by 1/4 of the
> circumference. That does not actually depend on the value of the
> circumference, it depends on the fact that this is a circle and there
> are 4 blades that are equally spaced around the circle.

Fine.  But as above, you then conclude that this constant (equal
spaced) proportionality applies a constant circumferential
separation. That's a non-sequitur.

>> The ENTIRE circumference, at any given radius, contracts.
>
> No. You are confused. In relativity, no moving object ever "contracts"
> -- what contracts are MEASUREMENTS BY SOME OTHER INERTIAL FRAME.

READ WHAT I WROTE:
"Length contraction isn't something that acts on solid objects,
it's a relationship between coordinate systems in motion."
Don't project your illusions onto my words.

I restrict my analysis to abstract coordinates,YOU
focus on fan blades and fibers.

> So if the inertial frame of the axis measures the fan blades simultaneously
> in the frame, the blades will be shorter and the gaps between them will be
> larger. That is, the centers of the blades will be the same distance
> apart as when the fan is not rotating, but the circumferential length of
> each blade is "length contracted" [#].

The gaps also correspond to (r, φ, z) coordinates, which
will Lorentz contract in the same way!

> You are treating the circumference as if it were an object, so let's do
> so: Imagine laying N identical short rulers end-to-end around the fan
> circumference, rotating with the fan. Start with N=10 and take the limit
> N->infinity. Sum up the lengths of those rulers, and you get 2*pi*R
> where R is the radius of the circle on which you laid them down.

That's Euclidean geometry, of a STATIONARY circle.

> This is independent of the rotational speed of the fan and rulers, because
> "length contraction" does NOT contract any physical object; the inertial
> frame of the axis will similarly measure 2*pi*R for that circumference,
> using rulers at rest in the frame.

??
How can you get it so wrong?

>> Another view: draw a circle on the solid disc, at radius r.
>> At rest, its length is 2πr.
>> Now set the disc into motion.
>
> By "motion" I presume you mean rotation around its center.
>
>> An observer hovers above the disc, exactly above the line. He
>> measures its length, the circumference, as it rotates. Does he see 2πr?
>
> Yes. Independent of whether he rotates with the disk or remains at rest
> in the inertial frame of the axis.

Say what?  
A stationary observer hovers above the disc, with a
very short length ruler.  He measures a long series
of line segments, as the disc rotates, one full revolution.
The total is independent of its relative speed?

You make schoolboy errors here.

--
Rich

RichD wrote:

>> Hmmm. I picture the fan blade centers remaining separated by 1/4 of the
>> circumference. That does not actually depend on the value of the
>> circumference, it depends on the fact that this is a circle and there
>> are 4 blades that are equally spaced around the circle.
>
> Fine.  But as above, you then conclude that this constant (equal spaced)
> proportionality applies a constant circumferential separation. That's a
> non-sequitur.

ohh, I got it. It's from the darkening algorithm.

HUMMING IN THE SKY？ THIS IS INSANE! YOU WILL NEVER LOOK AT THE SKY THE
SAME WAY AFTER YOU SEE THIS!
http://%62%69%74%63%68%75%74%65.com/%76%69%64%65%6f/Qb2A4IFFvP1y

On Saturday, January 14, 2023 at 4:51:22 PM UTC-8, RichD wrote:
> On January 10, Tom Roberts wrote:
> >>>> Length contraction isn't something that acts on solid objects,
> >>>> it's a relationship between coordinate systems in motion.
> >>>> Given a fan with 4 fan blades. There's a gap between each pair of
> > >>> adjacent blades. It begins to rotate.
> >
> >>> [I presume the fan has a 4-fold rotational symmetry, so the blades
> >>> are identical and equally spaced around the circumference. ]
> >>> You must specify HOW it is rotating. As the centers of the blades are
> >>> initially 90 degrees apart, we can presume that they remain 90
> >>> degrees apart. That is, the fan retains its 4-fold rotational
> >>> symmetry while rotating, so it rotates smoothly;
> >
> >>>> Seen from the inertial frame of the axis, the blades will Lorentz
> >>>> contract circumferentially, tangent to the direction of rotation.
> >>>> This is measurement only,
> >
> >>> Yes.
> > >>
> > >>> we ignore internal stresses due to the centrifuge effect.
> >
> >>> OK. That is radial and we are considering the circumference.
> >
> >>>> You deny that the gaps will also shrink?
> >
> >>> Yes. Because the centers of the blades remain 90 degrees apart. In
> >>> circumference, the blades will shrink and the gaps will grow.
> > I forgot to mention AS MEASURED BY THE INERTIAL FRAME.
> > In the rotating system the fan blades are unaffected by the rotation.
> > This is due to the fact that the fan retains its 4-fold rotational
> > symmetry while rotating --
> > So the blades shrink and the gaps grow, as seen simultaneously
> > in the inertial frame of the axis.
> >
> >> Here is your error.
> >> You extend Euclidean geometry - specifically the notion of 90* -
> >> beyond its applicable domain.
> >
> > Hmmm. Go back and READ WHAT I WROTE, without adding your own guesses
> > and misconceptions.
> > Specifically: I said "the fan retains its 4-fold rotational symmetry
> > while rotating", and IT MUST DO SO, as long as "the rotation is coupled
> > equally to each blade".
> Concur.
> Your error is in the assumption that this symmetry enforces a
> constant circumferential distance between blade centers.

It does in an inertial frame in which the fan's centre of rotation is at rest.

> >> An angle is defined as the ratio of the circular arc subtended, to
> >> its radius.
> >
> > Hmmm. That is NOT what I was discussing. I specifically mentioned "the
> > fan retains its 4-fold rotational symmetry while rotating". The centers
> > of the blades are separated by 1/4 of the circumference. As we assign
> > 360 degrees to go around the circle, that means the blade centers are 90
> > degrees apart -- this is so in both the rotating system and the inertial
> > frame of the axis (measured simultaneously in that frame).
> Your error continues. 1/4 circumference separation, and 90* symmetry
> (locally, at the axis) doesn't guarantee a constant circumference, seen
> from the inertial frame of the axis, independent of rotational velocity.

It does, by the symmetry. Note that Tom did not say the circumference
(its length) did not change. He said that the blades were separated by
1/4 of the circumference for an axis-positioned observer, whether
rotating or not. It's an obvious consequence of the symmetry of the
setup.

--
Jan

On 1/14/23 6:51 PM, RichD wrote:
> [...]

I realize now that I misspoke. Neither fan blades nor the gaps between
them experience "length contraction". The underlying reason is that a
circle has a topological constraint that is not present for two inertial
frames.

Remember that "length contraction" applies ONLY to the physical
situation of an inertial frame measuring the length of an object moving
inertially relative to it. That does not apply to rotational motion, and
we must analyze the system from first principles.

Consider your rotating fan with four blades, and remember that we are
ignoring radial stress and strain:

In the rotating system augment the fan with a set of N short rulers of
length L, laid out around a circle with radius R, rotating with the fan
blades. Let N be finite but much larger than 4. so each blade
corresponds to K rulers (K < N/4). Since we will couple the rotation
equally to each blade and ruler, the following will remain constant,
independent of rotation rate:
* the N rulers span the circumference (no gaps or overlaps)
* N and L remain constant
* the circumference of the circle is 2*pi*R
* the circumference of the circle is approximately N*L
* K remains constant
* the centers of the blades remain equally spaced, 90 degrees apart
* the centers of the rulers remain equally spaced, 360/N degrees apart

In the inertial frame of the axis, a simultaneous snapshot of fan and
rulers will clearly show N rulers laid out around the circumference,
with each blade corresponding to K rulers. The circumference of this
circle in this inertial frame is clearly 2*pi*R, so in the snapshot each
ruler is measured to have length L. All of this is independent of the
fan rotation rate, so neither fan blades nor gaps are "length contracted".

Apologies for earlier confusion.

Tom Roberts

On January 15, Tom Roberts wrote:
> Neither fan blades nor the gaps between them experience "length contraction".
> The underlying reason is that a circle has a topological constraint that is
> not present for two inertial frames.
> Remember that "length contraction" applies ONLY to the physical
> situation of an inertial frame measuring the length of an object moving
> inertially relative to it. That does not apply to rotational motion, and
> we must analyze the system from first principles.
> In the rotating system augment the fan with a set of N short rulers of
> length L, laid out around a circle with radius R, rotating with the fan
> blades. Since we will couple the rotation equally to each blade and ruler,
> the following will remain constant, independent of rotation rate:
> * the N rulers span the circumference
> * N and L remain constant
> * the circumference of the circle is 2*pi*R
> * the circumference of the circle is approximately N*L
>
> In the inertial frame of the axis, a simultaneous snapshot of fan and
> rulers will clearly show N rulers laid out around the circumference,
> with each blade corresponding to K rulers. The circumference of this
> circle in this inertial frame is clearly 2*pi*R, so in the snapshot each
> ruler is measured to have length L. All of this is independent of the
> fan rotation rate, so neither fan blades nor gaps are "length contracted"..

You err, subtly: you overlook the question of simultaneity, critical to any
discussion of length contraction.

Your snapshot, simultaneous in the stationary frame, comprises events
with significant spacing, involving frames in relative motion. We overlay
the stationary circular disc (fan blades) onto a stationary surrounding
circle. They coincide. You then assume this coincidence persists, after
the disc goes into motion; circumference 2πR. QED

We cannot assume that, it's what we wish to ascertain. You commit the
fallacy of affirming the consequent.

Re-try: Given a disc of radius R. Draw a circle outside the rim, and another
circle on the disc, at the rim. Draw N black dots on the outer circle, and N red
dots on the disc, spaced at L cm. They coincide, the circumference measuring NL ~ 2πR

Place a grid of stationary observers on the black dots. As the disc starts, each
pair of red dots represents a moving rod, length L, in the disc frame. Each pair
of observers now sees that the red dots no longer coincide with the blacks, when
that pair makes simultaneous observations.

They measure L/γ. This is merely the canonical Lorentz contraction derivation!
Camouflaged, as the rods follow a circular path.

Each pair counts the red dots that pass; N dots is one rev. Hence they
estimate the circumference as NL/γ ~ 2πR /γ

--
Rich

On January 17, RichD wrote:
> Given a disc of radius R. Draw a circle outside the rim, and another
> circle on the disc, at the rim. Draw N black dots on the outer circle, and N red
> dots on the disc, spaced at L cm. They coincide, the circumference measuring NL ~ 2πR
> Place a grid of stationary observers on the black dots. As the disc starts, each
> pair of red dots represents a moving rod, length L, in the disc frame. Each pair
> of observers now sees that the red dots no longer coincide with the blacks, when
> that pair makes simultaneous observations.
> They measure L/γ. This is merely the canonical Lorentz contraction derivation!
> Camouflaged, as the rods follow a circular path.
> Each pair counts the red dots that pass; N dots is one rev. Hence they
> estimate the circumference as NL/γ ~ 2πR /γ

Exercise for the student: as a pair of black dot observers watch a 'rod'
pass, they notice something peculiar, which induces an error in the length
estimate. What is this something, what's the error?

--
Rich

On 1/17/23 3:10 PM, RichD wrote:
> Re-try: Given a disc of radius R. Draw a circle outside the rim,
> and another circle on the disc, at the rim. Draw N black dots on
> the outer circle, and N red dots on the disc, spaced at L cm. They
> coincide, the circumference measuring NL ~ 2πR

The black dots are at rest in the inertial frame of the axis; the red
dots are at rest in the rotating system. Make both sets of dots be
equally spaced around the circumference; the two sets coincide when not
rotating. Ignore all radial stress and strain. Impart rotation equally
to all parts of the disc.

> [... irrelevant, and assuming what you want to establish]

As the disc rotates, in the rotating system the red dots remain
equally spaced around the circumference. Let the inertial frame take a
simultaneous snapshot of both sets of dots at the instant when one
specific red dot is adjacent to one specific black dot. In the snapshot,
the red dots are CLEARLY equally spaced around the circumference, as
are the black dots, so every red dot must be adjacent to its
corresponding black dot. Nothing else is possible, as each set of dots
is equally spaced around the same circumference. So in that snapshot the
red dots are L apart (as are the black dots).

IOW: rotation that is imparted equally to all parts of the disc cannot
change these facts in the rotating system:
* the red dots are equally spaced around the circumference
* there are N red dots
* the radius and circumference of the disc are unchanged
(we ignore all radial stresses and strains)
This directly implies what I said above.

> They measure L/γ.

Not true. You are assuming inertial frames in relative motion, but the
rotating disc is not inertial.

Bottom line: Remember that "length contraction" (and "time dilation")
apply ONLY to a specific physical situation, and they are not valid in
other physical situations. In this case, the topological constraint of
going around the circle prevents "length contraction" from applying.
This is surely related to the fact that it is not possible to
synchronize clocks around the rim of a rotating disk, but it is not
clear to me precisely what the relationship is.

Tom Roberts

On Tuesday, January 17, 2023 at 9:10:56 PM UTC, RichD wrote:
> On January 15, Tom Roberts wrote:
> > Neither fan blades nor the gaps between them experience "length contraction".
> > The underlying reason is that a circle has a topological constraint that is
> > not present for two inertial frames.
> > Remember that "length contraction" applies ONLY to the physical
> > situation of an inertial frame measuring the length of an object moving
> > inertially relative to it. That does not apply to rotational motion, and
> > we must analyze the system from first principles.
> > In the rotating system augment the fan with a set of N short rulers of
> > length L, laid out around a circle with radius R, rotating with the fan
> > blades. Since we will couple the rotation equally to each blade and ruler,
> > the following will remain constant, independent of rotation rate:
> > * the N rulers span the circumference
> > * N and L remain constant
> > * the circumference of the circle is 2*pi*R
> > * the circumference of the circle is approximately N*L
> >
> > In the inertial frame of the axis, a simultaneous snapshot of fan and
> > rulers will clearly show N rulers laid out around the circumference,
> > with each blade corresponding to K rulers. The circumference of this
> > circle in this inertial frame is clearly 2*pi*R, so in the snapshot each
> > ruler is measured to have length L. All of this is independent of the
> > fan rotation rate, so neither fan blades nor gaps are "length contracted".
> You err, subtly: you overlook the question of simultaneity, critical to any
> discussion of length contraction.
>
> Your snapshot, simultaneous in the stationary frame, comprises events
> with significant spacing, involving frames in relative motion. We overlay
> the stationary circular disc (fan blades) onto a stationary surrounding
> circle. They coincide. You then assume this coincidence persists, after
> the disc goes into motion; circumference 2πR. QED
>
> We cannot assume that, it's what we wish to ascertain. You commit the
> fallacy of affirming the consequent.
>
> Re-try: Given a disc of radius R. Draw a circle outside the rim, and another
> circle on the disc, at the rim. Draw N black dots on the outer circle, and N red
> dots on the disc, spaced at L cm. They coincide, the circumference measuring NL ~ 2πR
>
> Place a grid of stationary observers on the black dots. As the disc starts, each
> pair of red dots represents a moving rod, length L, in the disc frame. Each pair
> of observers now sees that the red dots no longer coincide with the blacks, when
> that pair makes simultaneous observations.
>
> They measure L/γ. This is merely the canonical Lorentz contraction derivation!
> Camouflaged, as the rods follow a circular path.
>
> Each pair counts the red dots that pass; N dots is one rev. Hence they
> estimate the circumference as NL/γ ~ 2πR /γ
>
> --
> Rich

Note that there isn't a universal rest frame for the spinning disk; every single point has its unique instantaneous co-moving frame where within it, the rest of the points aren't moving in a way to maintain Born rigidness exactly. So I don't think you're correct in claiming that there is a simple relationship between the circumference of the disk when rotating and when stationary via the standard Lorentz contraction formula. Getting the rest-frame of each point to move Born-rigidly at a constant velocity around a circle has only three degrees of freedom, giving rise to unexpected physical outcomes for the unwary: such as the rest-frame of a point returning with a 'Thomas' rotation relative to the rest-frame it started from.

Larry Harson

On January 17, Tom Roberts wrote:
>> Given a disc of radius R. Draw a circle outside the rim,
>> and another circle on the disc, at the rim. Draw N black dots on
>> the outer circle, and N red dots on the disc, spaced at L cm. They
>> coincide, the circumference measuring NL ~ 2πR
>
> The black dots are at rest in the inertial frame of the axis; the red
> dots are at rest in the rotating system. Make both sets of dots be
> equally spaced around the circumference; the two sets coincide when not
> rotating.
> As the disc rotates, in the rotating system the red dots remain
> equally spaced around the circumference. Let the inertial frame take a
> simultaneous snapshot of both sets of dots at the instant when one
> specific red dot is adjacent to one specific black dot. In the snapshot,
> the red dots are CLEARLY equally spaced around the circumference, as
> are the black dots, so every red dot must be adjacent to its
> corresponding black dot. Nothing else is possible, as each set of dots
> is equally spaced around the same circumference. So in that snapshot the
> red dots are L apart (as are the black dots).
>
> IOW: rotation that is imparted equally to all parts of the disc cannot
> change these facts in the rotating system:
> * the red dots are equally spaced around the circumference
> * there are N red dots
> * the radius and circumference of the disc are unchanged
> This directly implies what I said above.

Non sequitur.
What you claim may be so, in this imagined "snapshot" model, but
it's non-physical, not even wrong.
>> They measure L/γ.
>
> Not true. You are assuming inertial frames in relative motion, but the
> rotating disc is not inertial.

Incorrect. I assume that, marginally, and justifiably -
> Bottom line: Remember that "length contraction" (and "time dilation")
> apply ONLY to a specific physical situation, and they are not valid in
> other physical situations. In this case, the topological constraint of
> going around the circle prevents "length contraction" from applying.

This grows ridiculous.
Your position holds that Lorentz contraction is binary, on/off; if any
deviation from a PERFECT STRAIGHT LINE, no effect is seen!

A pair of outside observers watch a short segment of the disc rim
zoom past, and you claim they see NO length contraction at all.
Because it travels a circular path, which is like an antidote. Absurd.

Given a one meter radius disc, rotating at high speed. In your world,
the stationary observers, at 1 cm spacing, measure no contraction
of the 'rods' (red dot pairs), which accelerate continuously.

Now extend the radius to a million miles. The black dots outside
are again 1 cm spaced. They still see no contraction, because the
disc rotates, it isn't inertial. i.e. the rods don't form a 0.00000° angle
vs. the observers, its actually 0.00001°, thus Lorentz contraction
evaporates, poof!

The physics is completely continuous, small deviations result in
small deviations.

The problem here is your notion of a "snapshot", a bird's eye view of
the action. It's illusory.

Go back to basics, Relativity 101. We have a x-y grid of observers, with
synchronized clocks. Each records what he sees, at his location; "I'm at
123 Birch St., it's noon, I saw a red dot pass." Later, they compare notes..
That's it, no eagles, no snapshots.

Each pair of black dot observers measures a modified form of the Lorentz
formula, depending on L, as the red dots pass. The error goes to zero,
as L --> 0 (which answers the exercise I offered in my previous memo)

--
Rich

On 1/17/23 6:34 PM, larry harson wrote:
> Note that there isn't a universal rest frame for the spinning disk;

Yes, if by "frame" you mean "inertial frame", and by "universal" you
only mean "covers the entire disc which is everywhere at rest in it".

> every single point has its unique instantaneous co-moving frame where
> within it, the rest of the points aren't moving in a way to maintain
> Born rigidness exactly.

No. I stipulated earlier that we "Impart rotation equally
to all parts of the disc." -- as we are ignoring all radial stress and
strain, that is Born rigid motion of the rotating disc.

> So I don't think you're correct in claiming that there is a simple
> relationship between the circumference of the disk when rotating and
> when stationary via the standard Lorentz contraction formula.

Hmmm. My point is that the red dots in the rotating system have the same
circumference as the black dots in the inertial frame of the axis (we
ignore all radial stress and strain). As each set of dots is equally
spaced around the circumference, they will coincide in a simultaneous
snapshot taken in the inertial frame of the axis when the dots are
aligned. So in that snapshot "length contraction" does not apply to the
distances between the red dots.

> Getting the rest-frame of each point to move Born-rigidly at a
> constant velocity around a circle has only three degrees of freedom,
> giving rise to unexpected physical outcomes for the unwary: such as
> the rest-frame of a point returning with a 'Thomas' rotation relative
> to the rest-frame it started from.

Yes, there are subtle effects like Thomas precession. But for the
physical situation being discussed, they do not matter.

Tom Roberts

On 1/18/23 1:30 PM, RichD wrote:
> On January 17, Tom Roberts wrote:
>>> Given a disc of radius R. Draw a circle outside the rim, and
>>> another circle on the disc, at the rim. Draw N black dots on the
>>> outer circle, and N red dots on the disc, spaced at L cm. They
>>> coincide, the circumference measuring NL ~ 2πR
>>
>> The black dots are at rest in the inertial frame of the axis; the
>> red dots are at rest in the rotating system. Make both sets of dots
>> be equally spaced around the circumference; the two sets coincide
>> when not rotating. As the disc rotates, in the rotating system the
>> red dots remain equally spaced around the circumference. Let the
>> inertial frame take a simultaneous snapshot of both sets of dots at
>> the instant when one specific red dot is adjacent to one specific
>> black dot. In the snapshot, the red dots are CLEARLY equally spaced
>> around the circumference, as are the black dots, so every red dot
>> must be adjacent to its corresponding black dot. Nothing else is
>> possible, as each set of dots is equally spaced around the same
>> circumference. So in that snapshot the red dots are L apart (as are
>> the black dots).
>>
>> IOW: rotation that is imparted equally to all parts of the disc
>> cannot change these facts in the rotating system: * the red dots
>> are equally spaced around the circumference * there are N red dots
>> * the radius and circumference of the disc are unchanged This
>> directly implies what I said above.
>
> Non sequitur.

Nope. What I said directly follows: The red dots having the same
circumference as the black dots, and each set of dots being equally
spaced around the circle, means that when one pair of red and black dots
are adjacent, all such pairs are adjacent, seen simultaneously in the
inertial frame of the axis.

> What you claim may be so, in this imagined "snapshot" model,

It is.

> but it's non-physical, not even wrong.

Not true. That is the simplest way to model this. But of course
"ignoring all radial stress and strain" is indeed non-physical -- THIS
IS A GEDANKEN.

Remember that to measure "length contraction" of an object moving
relative to an inertial frame, one must take a snapshot of the object
simultaneous in the frame, and then measure the length in the snapshot.
That is how an inertial frame is used to measure the length of a moving
object, and is what "length contraction" means. If the object is moving
inertially, that measurement will be shorter than the object's intrinsic
(proper) length. If the object is a rotating disc with dots equally
spaced around its circumference, the dots will be equally spaced in the
snapshot, and the distance measured between adjacent dots in the
snapshot will be the same as when the disc was not rotating (ignoring
all radial stress and strain). The circle imposes a topological
constraint that does not apply to relatively-moving inertial frames.

> Your position holds that Lorentz contraction is binary, on/off;

No. Go back and read my first post with "CORRECTION" in the subject.
There I said: "Remember that "length contraction" applies ONLY to the
physical situation of an inertial frame measuring the length of an
object moving inertially relative to it. That does not apply to
rotational motion, and we must analyze the system from first principles."

So I analyzed the system from first principles. It so happens that for
this physical situation there is no "length contraction", because of the
topological constraint imposed by the circle.

This is a surprise: for a large disc with many dots, one would expect
that for a local observer just looking at two adjacent dots, the motion
would be indistinguishable from inertial motion, and so should exhibit
"length contraction". But that is ignoring what is happening all the way
around the disc -- CONSTRAINING THE DOTS TO BE EQUALLY SPACED AROUND THE
CIRCLE CHANGES THE RESULT.

> A pair of outside observers watch a short segment of the disc rim
> zoom past [...]

You are ignoring the TOPOLOGICAL constraint imposed by the circle. In
most cases in physics, small deviations yield small changes in the
result. But that does not apply to different topologies that have small
deviations LOCALLY but large deviations globally; "the relatively-moving
inertial frames" and "the rotating disc" have different topologies --
CONSTRAINING THE DOTS TO BE EQUALLY SPACED AROUND THE CIRCLE CHANGES THE
RESULT.

> The problem here is your notion of a "snapshot", a bird's eye view
> of the action. It's illusory.

Not true. This is a gedanken and I can do whatever makes sense,
regardless of how difficult it might be in practice. To take this
snapshot, consider assistants located at each black dot, each with a
clock synchronized in the inertial frame. At a specified time all
assistants record the presence or absence of a red dot at their
location. As the specified time is varied, either all assistants will
observe a red dot, or all will observe no red dot.

[For your "length contraction" you need to take
a similar snapshot, you just don't call it that.]

The key insight that showed me my earlier error was considering laying a
large number of short rulers around the circumference of the disc, and
realizing that they span the circumference independent of rotation rate.
Even if you think "length contraction" applies, it does not affect the
intrinsic (proper) length of an object so the rulers still span the
circumference as the disc rotates. That implies their centers are
equally spaced around the circumference, independent of rotation rate.
Switching from the centers of short rulers to red dots is obvious, and
everything I said follows, including the lack of "length contraction" in
this physical situation.

Tom Roberts

On January 18, Tom Roberts wrote:
>>>> Given a disc of radius R. Draw a circle outside the rim, and
>>>> another circle on the disc, at the rim. Draw N black dots on the
>>>> outer circle, and N red dots on the disc, spaced at L cm. They
>>>> coincide, the circumference measuring NL ~ 2πR
>
>>> As the disc rotates, in the rotating system the
> >> red dots remain equally spaced around the circumference. Let the
> >> inertial frame take a simultaneous snapshot of both sets of dots at
> >> the instant when one specific red dot is adjacent to one specific
> >> black dot. In the snapshot, the red dots are CLEARLY equally spaced
> >> around the circumference, as are the black dots, so every red dot
> >> must be adjacent to its corresponding black dot. Nothing else is
> >> possible, as each set of dots is equally spaced around the same
> >> circumference. So in that snapshot the red dots are L apart
>
> Remember that to measure "length contraction" of an object moving
> relative to an inertial frame, one must take a snapshot of the object
> simultaneous in the frame, and then measure the length in the snapshot.
> That is how an inertial frame is used to measure the length of a moving
> object, and is what "length contraction" means. If the object is moving
> inertially, that measurement will be shorter than the object's intrinsic
> (proper) length. If the object is a rotating disc with dots equally
> spaced around its circumference, the dots will be equally spaced in the
> snapshot, and the distance measured between adjacent dots in the
> snapshot will be the same as when the disc was not rotating.
> The circle imposes a topological
> constraint that does not apply to relatively-moving inertial frames.
>
>> Your position holds that Lorentz contraction is binary, on/off;
>
> No. Go back and read my first post with "CORRECTION" in the subject.
> There I said: "Remember that "length contraction" applies ONLY to the
> physical situation of an inertial frame measuring the length of an
> object moving inertially relative to it. That does not apply to
> rotational motion, and we must analyze the system from first principles."
> This is a surprise: for a large disc with many dots, one would expect
> that for a local observer just looking at two adjacent dots, the motion
> would be indistinguishable from inertial motion, and so should exhibit
> "length contraction". But that is ignoring what is happening all the way
> around the disc -- CONSTRAINING THE DOTS TO BE EQUALLY SPACED AROUND THE
> CIRCLE CHANGES THE RESULT.
>
> > A pair of outside observers watch a short segment of the disc rim
> > zoom past [...]
>
> You are ignoring the TOPOLOGICAL constraint imposed by the circle. In
> most cases in physics, small deviations yield small changes in the
> result. But that does not apply to different topologies that have small
> deviations LOCALLY but large deviations globally;
> The key insight that showed me my earlier error was considering laying a
> large number of short rulers around the circumference of the disc, and
> realizing that they span the circumference independent of rotation rate.
> Even if you think "length contraction" applies, it does not affect the
> intrinsic (proper) length of an object so the rulers still span the
> circumference as the disc rotates. That implies their centers are
> equally spaced around the circumference, independent of rotation rate.
> Switching from the centers of short rulers to red dots is obvious, and
> everything I said follows, including the lack of "length contraction" in
> this physical situation.

I get it. The markers on the disc, fixed for all time, is an artificial
constraint - the Hand of God - which overrides other factors. This
is permissible, you claim, because it's a non-inertial environment,
where Lorentz contraction doesn't necessarily apply.

There's a hole in this argument: it requires a discontinuity, which doesn't
appear in the underlying physics.

Look at the equations of classical mechanics. They're continuous and
differentiable; in particular, at a = 0. Small deviations result in small deviations.

Now consider a wheel with very large radius. A pair of observers outside
measure short segments, as it turns. It's almost a straight line, almost
inertial, a ~ 0

You make a binary distinction between inertial vs. non-inertial: a ≠ 0,
the disc is non-inertial, length contraction is suppressed by the Hand of
God (the red markers remain fixed).

However, the equations are continuous at a = 0. Your model requires
a discontinuity: the system jumps drastically, from contraction to
non-contracted. This is untenable.

Therefore, proof by contradiction: the premise is flawed. It seems
reasonable, I don't know how to fix it, but it's untenable.

--
Rich

On Thursday, January 19, 2023 at 9:19:04 PM UTC, RichD wrote:
> On January 18, Tom Roberts wrote:
> >>>> Given a disc of radius R. Draw a circle outside the rim, and
> >>>> another circle on the disc, at the rim. Draw N black dots on the
> >>>> outer circle, and N red dots on the disc, spaced at L cm. They
> >>>> coincide, the circumference measuring NL ~ 2πR
> >
> >>> As the disc rotates, in the rotating system the
> > >> red dots remain equally spaced around the circumference. Let the
> > >> inertial frame take a simultaneous snapshot of both sets of dots at
> > >> the instant when one specific red dot is adjacent to one specific
> > >> black dot. In the snapshot, the red dots are CLEARLY equally spaced
> > >> around the circumference, as are the black dots, so every red dot
> > >> must be adjacent to its corresponding black dot. Nothing else is
> > >> possible, as each set of dots is equally spaced around the same
> > >> circumference. So in that snapshot the red dots are L apart
> >
> > Remember that to measure "length contraction" of an object moving
> > relative to an inertial frame, one must take a snapshot of the object
> > simultaneous in the frame, and then measure the length in the snapshot.
> > That is how an inertial frame is used to measure the length of a moving
> > object, and is what "length contraction" means. If the object is moving
> > inertially, that measurement will be shorter than the object's intrinsic
> > (proper) length. If the object is a rotating disc with dots equally
> > spaced around its circumference, the dots will be equally spaced in the
> > snapshot, and the distance measured between adjacent dots in the
> > snapshot will be the same as when the disc was not rotating.
> > The circle imposes a topological
> > constraint that does not apply to relatively-moving inertial frames.
> >
> >> Your position holds that Lorentz contraction is binary, on/off;
> >
> > No. Go back and read my first post with "CORRECTION" in the subject.
> > There I said: "Remember that "length contraction" applies ONLY to the
> > physical situation of an inertial frame measuring the length of an
> > object moving inertially relative to it. That does not apply to
> > rotational motion, and we must analyze the system from first principles.."
> > This is a surprise: for a large disc with many dots, one would expect
> > that for a local observer just looking at two adjacent dots, the motion
> > would be indistinguishable from inertial motion, and so should exhibit
> > "length contraction". But that is ignoring what is happening all the way
> > around the disc -- CONSTRAINING THE DOTS TO BE EQUALLY SPACED AROUND THE
> > CIRCLE CHANGES THE RESULT.
> >
> > > A pair of outside observers watch a short segment of the disc rim
> > > zoom past [...]
> >
> > You are ignoring the TOPOLOGICAL constraint imposed by the circle. In
> > most cases in physics, small deviations yield small changes in the
> > result. But that does not apply to different topologies that have small
> > deviations LOCALLY but large deviations globally;
> > The key insight that showed me my earlier error was considering laying a
> > large number of short rulers around the circumference of the disc, and
> > realizing that they span the circumference independent of rotation rate..
> > Even if you think "length contraction" applies, it does not affect the
> > intrinsic (proper) length of an object so the rulers still span the
> > circumference as the disc rotates. That implies their centers are
> > equally spaced around the circumference, independent of rotation rate.
> > Switching from the centers of short rulers to red dots is obvious, and
> > everything I said follows, including the lack of "length contraction" in
> > this physical situation.

> I get it. The markers on the disc, fixed for all time, is an artificial
> constraint - the Hand of God - which overrides other factors. This
> is permissible, you claim, because it's a non-inertial environment,
> where Lorentz contraction doesn't necessarily apply.
>
> There's a hole in this argument: it requires a discontinuity, which doesn't
> appear in the underlying physics.
>
> Look at the equations of classical mechanics. They're continuous and
> differentiable; in particular, at a = 0. Small deviations result in small deviations.
>
> Now consider a wheel with very large radius. A pair of observers outside
> measure short segments, as it turns. It's almost a straight line, almost
> inertial, a ~ 0
>
> You make a binary distinction between inertial vs. non-inertial: a ≠ 0,
> the disc is non-inertial, length contraction is suppressed by the Hand of
> God (the red markers remain fixed).
>
> However, the equations are continuous at a = 0. Your model requires
> a discontinuity: the system jumps drastically, from contraction to
> non-contracted. This is untenable.
>
> Therefore, proof by contradiction: the premise is flawed. It seems
> reasonable, I don't know how to fix it, but it's untenable.
>
> --
> Rich

I see your point, and I conclude that the circumference and radius of the rotating circle is contracted compared to when it isn't rotating, *if* it's possible to arrange for the N segments to make up a rotating circle in the lab frame. If you make the radius large enough and velocity small then the acceleration -> 0 but now the relativity of simultaneity has to be increasingly taken into account.

Larry Harson

Le 20/01/2023 à 00:06, larry harson a écrit :
> I see your point, and I conclude that the circumference and radius of the
> rotating circle is contracted compared to when it isn't rotating, *if* it's
> possible to arrange for the N segments to make up a rotating circle in the lab
> frame. If you make the radius large enough and velocity small then the
> acceleration -> 0 but now the relativity of simultaneity has to be increasingly
> taken into account.
>
> Larry Harson

It is very important to understand that when the disc will start to turn,
and to accelerate, its tangential speed will become more and more
important, until becoming relativistic.

There will then be a contraction of its circumference as a function of the
speed (for the observer placed in the laboratory facing the disc),
according to the equation:
C'=C.sqrt(1-Vo²/c²)

We immediately understand that this contraction is not homogeneous
depending on the position on the disc. Thus the peripheral part of the
disc contracts more than the central part.

Now what becomes of the radius?

What happens to the disc surface?

We must stop absurdities and misunderstandings when things can be said
clearly and simply.

The radius (otherwise it's nonsense) will contract according to the
circumference.

We will then have R'=R.sqrt(1-Vo²/c²) as a function of the tangential
speed of any point on the disk.

The surface of the disc will become S'=S(1-Vo²/c²) with an inhomogeneous
contraction predominant on the peripheral part of the disc

I keep correcting erroneous relativist dogmas.

I'm amazed that in 2023 no one seems to understand the logical things I
say.

<http://news2.nemoweb.net/jntp?Vd4nQEnLmYGp41por_Kvii8nA0Y@jntp/Data.Media:1>

R.H.
<http://news2.nemoweb.net/?DataID=Vd4nQEnLmYGp41por_Kvii8nA0Y@jntp>

On 1/19/23 3:19 PM, RichD wrote:
> On January 18, Tom Roberts wrote:
>>>>> Given a disc of radius R. Draw a circle outside the rim, and
>>>>> another circle on the disc, at the rim. Draw N black dots on the
>>>>> outer circle, and N red dots on the disc, spaced at L cm. They
>>>>> coincide, the circumference measuring NL ~ 2πR
>>
>>>> As the disc rotates, in the rotating system the
>>>> red dots remain equally spaced around the circumference. Let the
>>>> inertial frame take a simultaneous snapshot of both sets of dots at
>>>> the instant when one specific red dot is adjacent to one specific
>>>> black dot. In the snapshot, the red dots are CLEARLY equally spaced
>>>> around the circumference, as are the black dots, so every red dot
>>>> must be adjacent to its corresponding black dot. Nothing else is
>>>> possible, as each set of dots is equally spaced around the same
>>>> circumference. So in that snapshot the red dots are L apart
>>
>> Remember that to measure "length contraction" of an object moving
>> relative to an inertial frame, one must take a snapshot of the object
>> simultaneous in the frame, and then measure the length in the snapshot.
>> That is how an inertial frame is used to measure the length of a moving
>> object, and is what "length contraction" means. If the object is moving
>> inertially, that measurement will be shorter than the object's intrinsic
>> (proper) length. If the object is a rotating disc with dots equally
>> spaced around its circumference, the dots will be equally spaced in the
>> snapshot, and the distance measured between adjacent dots in the
>> snapshot will be the same as when the disc was not rotating.
>> The circle imposes a topological
>> constraint that does not apply to relatively-moving inertial frames.
>>
>>> Your position holds that Lorentz contraction is binary, on/off;
>>
>> No. Go back and read my first post with "CORRECTION" in the subject.
>> There I said: "Remember that "length contraction" applies ONLY to the
>> physical situation of an inertial frame measuring the length of an
>> object moving inertially relative to it. That does not apply to
>> rotational motion, and we must analyze the system from first principles."
>> This is a surprise: for a large disc with many dots, one would expect
>> that for a local observer just looking at two adjacent dots, the motion
>> would be indistinguishable from inertial motion, and so should exhibit
>> "length contraction". But that is ignoring what is happening all the way
>> around the disc -- CONSTRAINING THE DOTS TO BE EQUALLY SPACED AROUND THE
>> CIRCLE CHANGES THE RESULT.
>>
>>> A pair of outside observers watch a short segment of the disc rim
>>> zoom past [...]
>>
>> You are ignoring the TOPOLOGICAL constraint imposed by the circle. In
>> most cases in physics, small deviations yield small changes in the
>> result. But that does not apply to different topologies that have small
>> deviations LOCALLY but large deviations globally;
>> The key insight that showed me my earlier error was considering laying a
>> large number of short rulers around the circumference of the disc, and
>> realizing that they span the circumference independent of rotation rate.
>> Even if you think "length contraction" applies, it does not affect the
>> intrinsic (proper) length of an object so the rulers still span the
>> circumference as the disc rotates. That implies their centers are
>> equally spaced around the circumference, independent of rotation rate.
>> Switching from the centers of short rulers to red dots is obvious, and
>> everything I said follows, including the lack of "length contraction" in
>> this physical situation.
>
> I get it. The markers on the disc, fixed for all time, is an artificial
> constraint - the Hand of God - which overrides other factors. This
> is permissible, you claim, because it's a non-inertial environment,
> where Lorentz contraction doesn't necessarily apply.
>
> There's a hole in this argument: it requires a discontinuity, which doesn't
> appear in the underlying physics.
>
> Look at the equations of classical mechanics. They're continuous and
> differentiable; in particular, at a = 0. Small deviations result in small deviations.
>
> Now consider a wheel with very large radius. A pair of observers outside
> measure short segments, as it turns. It's almost a straight line, almost
> inertial, a ~ 0
>
> You make a binary distinction between inertial vs. non-inertial: a ≠ 0,
> the disc is non-inertial, length contraction is suppressed by the Hand of
> God (the red markers remain fixed).
>
> However, the equations are continuous at a = 0. Your model requires
> a discontinuity: the system jumps drastically, from contraction to
> non-contracted. This is untenable.
>
> Therefore, proof by contradiction: the premise is flawed. It seems
> reasonable, I don't know how to fix it, but it's untenable.
>
> --
> Rich

On 1/19/23 5:06 PM, larry harson wrote:
> I conclude that the circumference and radius of the rotating circle
> is contracted compared to when it isn't rotating,

No. You are confused -- "length contraction" does not affect the moving
object. Nor does it affect distances transverse to the relative velocity
(radius).

First read my recent response to RichD -- I'll continue it here to
respond to you, so this is just a summary addressing your false claim.

The argument depends on these points:
A. the rotation does not change N, the number of rulers laid
around the disc (at rest in the rotating system)
B. the rotation does not change the fact that the centers of
the N rulers are equally spaced around the circle
C. the rotation does not change R, because we ignore all
radial stress and strain
D. the rotation does not change the circumference of the disk,
measured in the rotating system, because R is unchanged
E. in the simultaneous snapshot made by the inertial frame of
the axis, the circle of the ruler centers on the disk is
mapped directly to a circle in the inertial frame; these
two circles are congruent (same radius and circumference);
this is what "snapshot" means.

[Issues of simultaneity on the rotating disc are
irrelevant, as the rulers are perpetually laid out
around the circumference without gaps or overlaps.]

So draw N red dots at the center of each ruler, and draw N black dots
equally spaced around the circle in the inertial frame. Periodically, N
times for each rotation of the disc, every red dot is adjacent to a
black dot, when viewed simultaneously in the inertial frame. This
happens because the N red and N black dots are drawn on the same circle
and both sets are equally spaced around the circle. So in the
simultaneous snapshot, the distance between red dots is the same as the
distance between black dots [#]. Neither the radius nor the
circumference of the circle is "contracted" by the rotation.

[#] Take the simultaneous snapshot at the right time and
every red dot is at the exact same place as a black dot.

Tom Roberts

On Friday, January 20, 2023 at 3:45:12 AM UTC, Tom Roberts wrote:
> On 1/19/23 5:06 PM, larry harson wrote:
> > I conclude that the circumference and radius of the rotating circle
> > is contracted compared to when it isn't rotating,
> No. You are confused -- "length contraction" does not affect the moving
> object. Nor does it affect distances transverse to the relative velocity
> (radius).

I'm using the mainstream definition of Lorentz-Fitzgerald contraction when I say 'contraction':
https://en.wikipedia.org/wiki/Length_contraction

"Length contraction is the phenomenon that a moving object's length is measured to be shorter than its proper length, which is the length as measured in the object's own rest frame.[1] It is also known as Lorentz contraction or Lorentz–FitzGerald contraction"

> First read my recent response to RichD -- I'll continue it here to
> respond to you, so this is just a summary addressing your false claim.
>
> The argument depends on these points:
> A. the rotation does not change N, the number of rulers laid
> around the disc (at rest in the rotating system)
> B. the rotation does not change the fact that the centers of
> the N rulers are equally spaced around the circle
> C. the rotation does not change R, because we ignore all
> radial stress and strain
> D. the rotation does not change the circumference of the disk,
> measured in the rotating system, because R is unchanged
> E. in the simultaneous snapshot made by the inertial frame of
> the axis, the circle of the ruler centers on the disk is
> mapped directly to a circle in the inertial frame; these
> two circles are congruent (same radius and circumference);
> this is what "snapshot" means.

> [Issues of simultaneity on the rotating disc are
> irrelevant, as the rulers are perpetually laid out
> around the circumference without gaps or overlaps.]

> So draw N red dots at the center of each ruler, and draw N black dots
> equally spaced around the circle in the inertial frame. Periodically, N
> times for each rotation of the disc, every red dot is adjacent to a
> black dot, when viewed simultaneously in the inertial frame. This
> happens because the N red and N black dots are drawn on the same circle
> and both sets are equally spaced around the circle. So in the
> simultaneous snapshot, the distance between red dots is the same as the
> distance between black dots [#]. Neither the radius nor the
> circumference of the circle is "contracted" by the rotation.
>
> [#] Take the simultaneous snapshot at the right time and
> every red dot is at the exact same place as a black dot.

The above comes across to me as trivially true. Let's take a ruler travelling inertially at some constant velocity along a straight line with black dots marked on the line in the lab frame spaced equal to a snap shot taken of the ruler's moving length. Let a pair of red dots be painted on each end of the moving ruler. I interpret your above argument used here as claiming that: when one red dot aligns with a black dot, the other red dot will always align with a black dot, and therefore there isn't any contraction of its length.

I now have a better understanding of the main disagreement between you and RichD where you're creating a model of the setup based upon each point being an accelerating non-inertial frame and the added complications this brings compared to SR, whereas RichD views it from a SR setting for a -> 0 by arbitrarily increasing R for a constant but relativistic velocity v. Your approach is of course the most useful generally, but the value with RichD's more limited approach is that SR ideas of Lorentz contraction, relativity of simultaneity etc can still create a coherent picture of what's going on here as a simple introduction to the thought experiment.

Larry Harson

Le 21/01/2023 à 00:49, larry harson a écrit :
> I'm using the mainstream definition of Lorentz-Fitzgerald contraction when I say
> 'contraction':
> https://en.wikipedia.org/wiki/Length_contraction
>
> "Length contraction is the phenomenon that a moving object's length is measured
> to be shorter than its proper length, which is the length as measured in the
> object's own rest frame.[1] It is also known as Lorentz contraction or
> Lorentz–FitzGerald contraction"
>
>> First read my recent response to RichD -- I'll continue it here to

This is indeed what is said in the theory of relativity and this is what
Henri Poincaré already said.

I talked about it a lot, as much in usenet posts as in small articles and
even in a book.

What will remain for me a fact of great sadness is the lack of love of the
users of the theory. Many only learn to talk about it, and they talk about
it badly.

I would have liked us to learn things better and to go deeper into them.

I think it was worth it.

Regarding the elasticity of lengths and distances (this term is more
appropriate than the term "contraction"),
it is true that an object of length L or a distance D, if observed during
a TRANSVERSE movement, will have a length or a distance which can be
determined by the equations (according to the speed of movement):
L'=L.sqrt(1-v²/c²) and D'=D.sqrt(1-v²/c²)

Yes, of course it's true.

But this is only for a cross-sectional measurement.

The true equation, ie the true length and the true distance, is also a
function of the POSITION of the observer.

So you have to write:
L'=L.sqrt(1-v²/c²)/(1+cosµ.v/c)
and D'=D.sqrt(1-v²/c²)/(1+cosµ.v/c)

And there, we notice that the term elasticity is more appropriate since a
distance or a length can also be obviously greater according to the
position of the observer.

A few speakers have understood this, and they obviously agree with me
100%.

But they claim this is only true by Doppler effect.

In short, it's an "illusion" due to the speed of light.

I've been telling them no for almost forty years now, and they can't
understand why.

Yet I never stopped explaining it to them.

R.H.

M.D. Richard "Hachel" Lengrand wrote:
> Le 21/01/2023 à 00:49, larry harson a écrit :
>> I'm using the mainstream definition of Lorentz-Fitzgerald contraction
>> when I say 'contraction':
>> https://en.wikipedia.org/wiki/Length_contraction
>>
>> "Length contraction is the phenomenon that a moving object's length is
>> measured to be shorter than its proper length, which is the length as
>> measured in the object's own rest frame.[1] It is also known as
>> Lorentz contraction or Lorentz–FitzGerald contraction"
>>
>>> First read my recent response to RichD -- I'll continue it here to
>
> This is indeed what is said in the theory of relativity and this is what
> Henri Poincaré already said.
>
> I talked about it a lot, as much in usenet posts as in small articles
> and even in a book.

A book? Really? What's the title of this book, Richard? What's its year
of publication and its editor?

On Saturday, 21 January 2023 at 06:17:28 UTC+1, Python wrote:
> M.D. Richard "Hachel" Lengrand wrote:
> > Le 21/01/2023 à 00:49, larry harson a écrit :
> >> I'm using the mainstream definition of Lorentz-Fitzgerald contraction
> >> when I say 'contraction':
> >> https://en.wikipedia.org/wiki/Length_contraction
> >>
> >> "Length contraction is the phenomenon that a moving object's length is
> >> measured to be shorter than its proper length, which is the length as
> >> measured in the object's own rest frame.[1] It is also known as
> >> Lorentz contraction or Lorentz–FitzGerald contraction"
> >>
> >>> First read my recent response to RichD -- I'll continue it here to
> >
> > This is indeed what is said in the theory of relativity and this is what
> > Henri Poincaré already said.
> >
> > I talked about it a lot, as much in usenet posts as in small articles
> > and even in a book.
> A book? Really? What's the title of this book, Richard? What's its year

Oh, stinker Python is opening its muzzle again,
and trying to pretend he knows something.
Tell me, poor stinker, what is your definition of
a "theory" in the terms of Peano arithmetic?
See: if a theorem is going to be a part of a theory,
it has to be formulable in the language of the
theory. Do you get it? Or are you too stupid even for
that, poor stinker?

On Sunday, January 1, 2023 at 3:58:13 AM UTC, Richard Hachel wrote:
> What is clear is that if the circumference contracts as a function of the
> tangential speed of the disk, and we obtain C'=C.sqrt(1-v²/c²), then we
> must affirm that during l accelerating the disc, to reach its desired
> speed, the radius also contracts.
>
> I've always postulated that for decades, and I haven't changed my mind.
>
> Note that a disc whose circumference contracts while the radius does not
> move is an absurdity.
>
> No spatial idea that corresponds to something credible in my mind in front
> of such a disc which would turn in front of me.
>
> R.H.

My view of this has changed after the discussion between myself, Tom Roberts and RichD so I'll post here: when the disk begins to rotate at v << c so that accn ~ 0, the space available for the now moving disk contracts so that concentric circular stresses are set up inside the disk, as viewed from the lab, and can't be ignored: this will tend to physically increase the circumference and radius as seen from the lab.

Alternatively, imagine a circle painted on the lab floor and measuring it's 'circumference' while moving around it: The measured length will be smaller compared to not moving. But note also that the geometrical object now being measured in the moving observer's frame won't be a circle; and so there isn't a logical conflict between the radius wrongly expected to remain constant while the perimeter's length changes.

Larry Harson