On October 10, Stan Fultoni wrote:
>> > We are describing the situation in terms of two systems of
>> > inertial coordinates, one in which the wall is at rest, and one in
>> > which the bolt is not moving axially. The wall is not spinning in
>> > terms of either of these inertial coordinate systems, and the bolt
>> > is spinning in terms of both (at different rates).
>
>> It's natural to also use the rotating bolt as a frame.
>
> No, see above. A rotating system of coordinates is not an inertial coordinate
> system, and is not related to inertial coordinate systems by Lorentz transformations.
I see.
So, according to law, an observer, who isn't an inertial coordinate
system, is not permitted to make timing measurements. If he
does, his papers must be burned.
>> The cosmos sees the earth spin, and move linearly through
>> space. We watch the cosmos revolve around us. We aren't
>> inertial.
>
> No, the surface of the spinning earth is not moving inertially, and a
> coordinate system in which the earth is not rotating is not an inertial
> coordinate system.
> Therefore, no earthbound astronomer can measure the rate at which
> the sky appears to revolve around us.
We have a difference of opinion.
The earth, like the stud, rotates and moves linearly. You claim
that neither can time the revolutions that it sees; of the sky,
or the threaded housing.
I claim that we can measure the sidereal day, and an
astronomer riding the bolt can do likewise, even though non-inertial.
I have centuries of astronomy to support my position.
>>> We place a mark on some point of the bolt, the period of spin is time
>>> between when that mark is on top.
>
>> The problem here is that the bolt doesn't make a full turn, due
>> to differing clock rates.
>
> The bolt makes a full turn during the time in which it makes a full turn,
> in any specified system of coordinates.
You define a full turn as: a full turn.
Informative indeed.
>> You have to sort out all these issues...
>
> There are no unsorted issued here.
Let's see... you define a turn of the bolt as transit of
a point on the bolt, from "the top" to "the top" (of the shaft).
And time that, to define the period.
As explained previously - and you admit - a corresponding
adjacent point on the bolt will not turn 360*, during that revolution.
Because it "untwists"; your phrase, remember? (and I agree)
Conventionally, a full turn (revolution) of a rotating object is
defined as a 360* turn. But that is not the case here... per
your definition.
Recapping your logic: the time of a full turn is the time of
a full turn... except when it isn't.
> You're just deeply confused... about many things, apparently.
We'll leave that judgement to the judges.
>> Do the bolt and housing threads grind, due to length contraction?
>
> No, this was explained to you in detail previously, both at the low level in
> terms of the effects of length contraction, time dilation, and skew of simultaneity
> on the length, pitch, spin rate, and thread spacing,
Litany of relativistic properties is not an explanation.
Assertion is not explanation.
You need to show mathematical relationships between these
properties, step by logical step, leading to a conclusion.
a/k/a proof
> and also at the high level in terms of the one-to-one linear mapping.
ah yes, the high level one-to-one mapping explanation...
let's review that gem of crystal clear reasoning:
"... consider that everything has been arranged so that in terms
of S [the wall] the spinning and translating bolt just glides through.
Now, if we transform the coordinates of every particle of the bolt and the wall
using the Lorentz tranformation to the coordinates S', noting that the
transformation is linear and one-to-one, any x,y,z,t maps to a unique x',y',z',t',
so if there is no collision when decribed in terms of the former, there is no
collision in terms of the latter"
Let's restart... given a bolt and matching tapped hole, which flows
smoothly at low speed.
We ask: does it still flow without crashing, at high speed?
Your high level response:
"If it glides smoothly at low speed, then various observers,
in various states of motion, will also see it glide through".
Profound, truly.
Now please, try to focus, engage the full power of your neural net:
the question is not:
"If a bolt operates smoothly at low speed, will others see it
the same way?"
The question is:
"If a bolt operates smoothly at low speed, will it continue to do so,
when accelerated to high speed?"
That is the question.
Observers zooming around, watching the action, with their
coordinates and transformations, have NO MATERIAL
IMPACT ON THE PHYSICAL REALITY!
sheesh!
`> in the rest system of the wall, the bolt threads are "untwisted" due to
> the skew of simultaneity,
Right.
As mentioned above, the bolt doesn't turn 360* in one rev. (per your
definition); i.e. it's untwisted
> so the axial distance between them is greater, but the length contraction
> accounts for them remaining matched with the spacing of the grooves,
Assertion is not derivation.
You have not shown that these effects cancel.
> and the spin rate is slowed to match the axial speed.
You're confused. The spin rate (seen by the wall) isn't
slowed by that mechanism.
It's slowed because the bolt exemplifies the twins paradox:
on each turn, its wristwatch shows a shorter time than the
wall's watch. The wall appears to turn faster.
The relationship between spin rate and linear speed is a tautology:
v = (pitch spacing / rev) * (rev / sec)
The linear speed is stipulated, in this example.
The pitch spacing is modulated by length contraction,
but also by the "untwisting", alluded above, due to the
modulated spin rate.
The question, again: does this resultant pitch spacing still
match the wall channel spacing?
You have not shown this.
Spare me your confident assertions.
> Is there something about this you don't understand?
--
Rich