In inertial reference frame F0, at x=0 there is a wheel spinning in the y-z plane, and a clock at x=0. Frame F0 observers measure that the wheel is making two revolutions per second. Frame F1 is moving relative to F0 along the x-axis with V = sqrt(3)/2 *c. Frame F1 observers say the F0 clock is running at half the rate of the F1 clocks and the wheel is spinning at one revolution per second. Frame F2 is moving relative to F0 along the x-axis with V = -sqrt(3)/2*c. Frame F2 observers say the F0 clock is running at half the rate of the F2 clocks and the wheel is spinning at one revolution per second.
If F1 and F2 both agree that according to each of their measurements that the wheel in F0 is spinning at one revolution per second according to their respective clocks, why do they say their clocks are not running at the same rate (other than saying that Einstein says you must use light to determine clock rates and distances). Do they simply say, the clocks were not initialized identically in frames F1 and F2, so that's why they appear to be running at the same rate when measuring the rotation rate of the wheel when in reality they are not running at the same rate?
Thanks,
David Seppala
Bastrop tX

On Sunday, July 4, 2021 at 7:07:28 AM UTC-7, sep...@yahoo.com wrote:
> If an inertial reference frame is moving with velocity V parallel to the rest frame of the
> cylinder, can that frame also determine which end of the ribbon was attached to the
> cylinder first?

Of course. In terms of the original system the two cases result in a helix with -1 or +1 turns, and in terms of the moving system this corresponds to 0 or +2 turns. Needless to say, in terms of a system moving in the opposite direction, these would corresponds to -2 or 0 terms. If I was to diagnose your failure to understand these trivial facts, I'd say it's because you have zero grasp of the relativity of simultaneity. Like many clueless newbies, you are aware of time dilation and length contraction, both of which depend only on relative speed, not direction, but your mind is unable to grasp the third element of the relationship between inertia-based coordinate systems, namely, the skew of simultaneity, which is directionally dependent..

You confirm this diagnosis with your next question:

> If F1 and F2 both agree that according to each of their measurements that the wheel in F0 is
> spinning at one revolution per second according to their respective clocks, why do they say
> their clocks are not running at the same rate...?

Again, you are failing to grasp that the skew of simultaneity between systems of inertia-based coordinates is directionally dependent. Remember, these systems of coordinates are defined by the requirement that the equations of mechanics take their simple homogeneous and isotropic form. Since every quantity of energy E has inertia corresponding to E/c^2, it follows that two such systems of coordinates have skewed simultaneities. From this, it is trivial to see that a standard clock at rest is F0 runs slow by the factor sqrt(1-v^2/c^2) in terms of F1 and F2, and also that a clock at rest in either of the latter two systems runs slow by the factor sqrt(1-u^2/c^2) in terms of the other, where u=2v/(1+v^2/c^2).

> Einstein says you must use light to determine clock rates and distances....

That is untrue. [Your brain is filled with misinformation and misunderstandings.] We can define arbitrary coordinate systems in infinitely many ways.. However, the propositions of special relativity are typically expressed in terms of a special class of coordinate systems, namely, systems in terms of which all the equations of physics take their simple homogeneous and isotropic form. Since energy has inertia, it follows that the relationship between any two such systems entails time dilation, length contraction, and the skew of simultaneity.

> Do they simply say, the clocks were not initialized identically in frames F1 and F2...

You haven't included in your scenario more than one clock at rest in any given frame, so the skew of simultaneity is represented only by the coordinate systems themselves. If you posit rows of clocks at rest in each system, with each row synchronized such that mechanical inertia is isotropic in terms of the respective system, then the synchronizations are indeed different, e.g., two events that are simultaneous in terms of one system are not simultaneous in terms of another.

> so that's why they appear to be running at the same rate when measuring the rotation
> rate of the wheel when in reality they are not running at the same rate?

That's completely garbled. The clocks at rest in F1 and F2 are running at the same rate in terms of F0, i.e., they are running slow by the factor sqrt(1-v^2/c^2) in terms of F0, but each of those clocks is running slow by the factor sqrt(1-u^2/c^2) in terms of the system in which the other is at rest. Now do you understand?

On Monday, 5 July 2021 at 20:35:46 UTC+2, Al Coe wrote:

> That is untrue. [Your brain is filled with misinformation and misunderstandings.] We can define arbitrary coordinate systems in infinitely many ways.. However, the propositions of special relativity are typically expressed in terms of a special class of coordinate systems, namely, systems in terms of which all the equations of physics take their simple homogeneous and isotropic form.

Amongst infinitely many possibilities of defining coordinates
we should, of course, choose an impossible one. That's
THE BEST WAY of our beloved Giant Guru.

On 7/5/21 11:55 AM, sepp623@yahoo.com wrote:
> In inertial reference frame F0, at x=0 there is a wheel spinning in
> the y-z plane, and a clock at x=0. Frame F0 observers measure that
> the wheel is making two revolutions per second. Frame F1 is moving
> relative to F0 along the x-axis with V = sqrt(3)/2 *c. Frame F1
> observers say the F0 clock is running at half the rate of the F1
> clocks and the wheel is spinning at one revolution per second. Frame
> F2 is moving relative to F0 along the x-axis with V = -sqrt(3)/2*c.
> Frame F2 observers say the F0 clock is running at half the rate of
> the F2 clocks and the wheel is spinning at one revolution per
> second.

For simplicity in the discussion, let me stipulate that all clocks are
identical and each has an intrinsic tick rate of 1 Hz (i.e. when
measured in its rest frame). Note also that F1 travels at 0.8660 c
relative to F0 (gamma = 2), and at 0.9897 c relative to F2 (gamma = 7).

The wheel is a red herring, and I won't bother to discuss it; I'll
discuss the relationships among the clocks:
* The clock at rest in F0 ticks at 1 Hz measured in F0
* The clock at rest in F0 ticks at 1/2 Hz when measured in F1
* The clock at rest in F0 ticks at 1/2 Hz when measured in F2
* The clock at rest in F1 ticks at 1 Hz measured in F1
* The clock at rest in F1 ticks at 1/2 Hz when measured in F0
* The clock at rest in F1 ticks at 1/7 Hz when measured in F2
* The clock at rest in F2 ticks at 1 Hz measured in F2
* The clock at rest in F2 ticks at 1/2 Hz when measured in F0
* The clock at rest in F2 ticks at 1/7 Hz when measured in F1

Note that I always specified in which frame each measurement is made.

When one says "The clock in F0 ticks at 1 Hz", one did not specify in
which frame the measurement is made. English usage means this is
talking about the clock itself, with nothing else involved, so it is
discussing the clock's INTRINSIC tick rate -- that is inherently
measured in the clock's rest frame. Note, however, in discussions of
relativity it is poor form to rely on this aspect of English prose, and
one should ALWAYS specify in which frame each measurement is made. As I
did above.

> If F1 and F2 both agree that according to each of their measurements
> that the wheel in F0 is spinning at one revolution per second
> according to their respective clocks, why do they say their clocks
> are not running at the same rate

Refer to my previous paragraph. Their clocks ARE ticking at the same
rate, 1 Hz. So your claim here is misstating the situation.

> (other than saying that Einstein says you must use light to determine
> clock rates and distances).

Einstein never said that. Stop making stuff up and pretending it is true.

> Do they simply say, the clocks were not initialized identically in
> frames F1 and F2, so that's why they appear to be running at the
> same rate when measuring the rotation rate of the wheel when in
> reality they are not running at the same rate?

See above. Again you misstate the situation. It is just factually wrong
to think that using a clock in F1 to measure a clock in F0 is measuring
(or "appearing") the tick rate of the clock in F1.

This has nothing whatsoever do to with "initializing" clocks. Rather, it
has to do with the geometrical relationships among these inertial
frames. The clocks are all ticking at the same rate (1 Hz -- see my note
about English usage above), but are measured to have different tick
rates in frames other than their rest frame.

You keep confusing yourself by not ALWAYS specifying in which frame each
measurement is made. Also by using wishy-washy words like "appears".
Modern physics is complicated and subtle; precision in thought and word
is required.

Tom Roberts

On Tuesday, 6 July 2021 at 06:37:21 UTC+2, tjrob137 wrote:
> On 7/5/21 11:55 AM, sep...@yahoo.com wrote:
> > In inertial reference frame F0, at x=0 there is a wheel spinning in
> > the y-z plane, and a clock at x=0. Frame F0 observers measure that
> > the wheel is making two revolutions per second. Frame F1 is moving
> > relative to F0 along the x-axis with V = sqrt(3)/2 *c. Frame F1
> > observers say the F0 clock is running at half the rate of the F1
> > clocks and the wheel is spinning at one revolution per second. Frame
> > F2 is moving relative to F0 along the x-axis with V = -sqrt(3)/2*c.
> > Frame F2 observers say the F0 clock is running at half the rate of
> > the F2 clocks and the wheel is spinning at one revolution per
> > second.
> For simplicity in the discussion, let me stipulate that

That we're all FORCED to THE BEST WAY, which is
the way of Giant Guru and his idiot minions.