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Nov 12, 2022, 4:48:56 PM11/12/22

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Neptune is about 30 astronomical units (au) from Earth.

If I look at the planet Neptune from Earth, I am not looking at a

stationary object.

In my reference, Neptune makes a full 360-degree turn in 24 hours.

I was curious to check at what speed Neptune is moving with respect to

my terrestrial frame of reference from which I am observing it and I

have discovered that, incredibly, Neptune (with respect to me) is

moving faster than the speed of light and exactly at 327,000 km per

second.

Obviously I am wrong in my calculations which are these.

The space traveled by Neptune is a circumference that has its center in

the Earth and a radius of 30 au.

Thus, the circumference traveled (in my reference) by Neptune in the 24

hours is 2*pi*r*30=2*3.14*30=188.4 au long.

In one hour Neptune travels 188.4/24=7.85 au.

In one minute Neptune travels 7.85/60=0.13 au.

In a second Neptune travels 0.13/60=0.00218 au.

Since an au corresponds to approximately 150,000,000 km, Neptune

travels 0.00218*150,000.00=327,000 km per second, with respect to me.

Can you tell me where is the conceptual or calculation error?

[[Mod. note -- I see no conceptual or calculation error here.

As a quick sanity check, https://en.wikipedia.org/wiki/Neptune

gives the radius of Neptune's orbit about the sun as 4.5e9 km,

so the apparent speed in the rotating-with-the-Earth reference frame

is 2*pi*4.5e9 km / (24*3600 s) = 330,000 km/s.

So, relative to your rotating-with-the-Earth reference frame, Neptune

is moving a bit faster than the speed of light.

There's no contradiction with relativity here -- this is just a

(non-inertial) *coordinate* speed; there's no *physical object* in

whose inertial reference frame another *physical object* is moving

faster than the speed of light.

In fact, we can carry your argument much farther: instead of considering

a reference frame attached to the Earth (rotating about once per 24 hours),

[Actually, you probably want the siderial rotation period,

once per 23 hours 56 minutes.]

let's consider a reference frame attached to the rotor of an ultracentifuge

(sitting in a lab on the Earth's surface) rotating at 60,000 rpm = 1000 Hz.

Relative to that (rapidly-rotating) reference frame, an object (stationary

on the Earth's surface) about 50 km away would be moving slightly faster

than the speed of light.

Nature doesn't know about coordinates (which are solely a human construct),

so (as a famous relativist once said in a slightly different context)

coordinates can change "at the speed of thought".

-- jt]]

If I look at the planet Neptune from Earth, I am not looking at a

stationary object.

In my reference, Neptune makes a full 360-degree turn in 24 hours.

I was curious to check at what speed Neptune is moving with respect to

my terrestrial frame of reference from which I am observing it and I

have discovered that, incredibly, Neptune (with respect to me) is

moving faster than the speed of light and exactly at 327,000 km per

second.

Obviously I am wrong in my calculations which are these.

The space traveled by Neptune is a circumference that has its center in

the Earth and a radius of 30 au.

Thus, the circumference traveled (in my reference) by Neptune in the 24

hours is 2*pi*r*30=2*3.14*30=188.4 au long.

In one hour Neptune travels 188.4/24=7.85 au.

In one minute Neptune travels 7.85/60=0.13 au.

In a second Neptune travels 0.13/60=0.00218 au.

Since an au corresponds to approximately 150,000,000 km, Neptune

travels 0.00218*150,000.00=327,000 km per second, with respect to me.

Can you tell me where is the conceptual or calculation error?

[[Mod. note -- I see no conceptual or calculation error here.

As a quick sanity check, https://en.wikipedia.org/wiki/Neptune

gives the radius of Neptune's orbit about the sun as 4.5e9 km,

so the apparent speed in the rotating-with-the-Earth reference frame

is 2*pi*4.5e9 km / (24*3600 s) = 330,000 km/s.

So, relative to your rotating-with-the-Earth reference frame, Neptune

is moving a bit faster than the speed of light.

There's no contradiction with relativity here -- this is just a

(non-inertial) *coordinate* speed; there's no *physical object* in

whose inertial reference frame another *physical object* is moving

faster than the speed of light.

In fact, we can carry your argument much farther: instead of considering

a reference frame attached to the Earth (rotating about once per 24 hours),

[Actually, you probably want the siderial rotation period,

once per 23 hours 56 minutes.]

let's consider a reference frame attached to the rotor of an ultracentifuge

(sitting in a lab on the Earth's surface) rotating at 60,000 rpm = 1000 Hz.

Relative to that (rapidly-rotating) reference frame, an object (stationary

on the Earth's surface) about 50 km away would be moving slightly faster

than the speed of light.

Nature doesn't know about coordinates (which are solely a human construct),

so (as a famous relativist once said in a slightly different context)

coordinates can change "at the speed of thought".

-- jt]]

Nov 15, 2022, 3:46:02 AM11/15/22

to

uigi Fortunati sabato 12/11/2022 alle ore 06:48:52 ha scritto:

> Neptune is about 30 astronomical units (au) from Earth.

>

> If I look at the planet Neptune from Earth, I am not looking at a stationary object.

>

> In my reference, Neptune makes a full 360-degree turn in 24 hours.

>

> I was curious to check at what speed Neptune is moving with respect to my terrestrial frame of reference from which I am observing it and I have discovered that, incredibly, Neptune (with respect to me) is moving faster than the speed of light and exactly at 327,000 km per second.

>

> Obviously I am wrong in my calculations which are these.

>

> The space traveled by Neptune is a circumference that has its center in the Earth and a radius of 30 au.

>

> Thus, the circumference traveled (in my reference) by Neptune in the 24 hours is 2*pi*r*30=2*3.14*30=188.4 au long.

>

> In one hour Neptune travels 188.4/24=7.85 au.

>

> In one minute Neptune travels 7.85/60=0.13 au.

>

> In a second Neptune travels 0.13/60=0.00218 au.

>

> Since an au corresponds to approximately 150,000,000 km, Neptune travels 0.00218*150,000.00=327,000 km per second, with respect to me.

>

> Can you tell me where is the conceptual or calculation error?

>

> [[Mod. note -- I see no conceptual or calculation error here.

Okay.
> Neptune is about 30 astronomical units (au) from Earth.

>

> If I look at the planet Neptune from Earth, I am not looking at a stationary object.

>

> In my reference, Neptune makes a full 360-degree turn in 24 hours.

>

> I was curious to check at what speed Neptune is moving with respect to my terrestrial frame of reference from which I am observing it and I have discovered that, incredibly, Neptune (with respect to me) is moving faster than the speed of light and exactly at 327,000 km per second.

>

> Obviously I am wrong in my calculations which are these.

>

> The space traveled by Neptune is a circumference that has its center in the Earth and a radius of 30 au.

>

> Thus, the circumference traveled (in my reference) by Neptune in the 24 hours is 2*pi*r*30=2*3.14*30=188.4 au long.

>

> In one hour Neptune travels 188.4/24=7.85 au.

>

> In one minute Neptune travels 7.85/60=0.13 au.

>

> In a second Neptune travels 0.13/60=0.00218 au.

>

> Since an au corresponds to approximately 150,000,000 km, Neptune travels 0.00218*150,000.00=327,000 km per second, with respect to me.

>

> Can you tell me where is the conceptual or calculation error?

>

> [[Mod. note -- I see no conceptual or calculation error here.

In my animation

https://www.geogebra.org/m/sn4eav7h

I have highlighted on the left the point of view of the reference of the

fixed stars where Neptune is (almost) stationary and the Earth rotates

on itself by 360° in 24 hours.

And on the right, the point of view of the terrestrial reference where

the Earth stands still and Neptune rotates 360° around the Earth in 24

hours.

Speed is relative and, therefore, from our point of view, we are

observing a body moving at relativistic speed (with respect to us) and

it is a condition that affects all planets and all stars eternally

moving at different speeds.

Some speeds (indeed most of them) are not such that they can be

considered negligible compared to the speed of light.

So, my question is this: Why with our telescopes do we always (and only)

see perfectly spherical celestial bodies and have we never seen one

contracted in the direction of motion like the one at the top right of

my animation?

Nov 15, 2022, 7:17:26 AM11/15/22

to

In article <tkvd81$aqr$1...@gioia.aioe.org>, Luigi Fortunati

relativistic speeds:

A. Lampa, _Z. f. Physik_, 27, 138, 1924.

J. Terrell, _Phys. Rev._, 116, 1041, 1959.

R. Penrose, _Proc. Camb. Phil. Soc._, 55, 137, 1959.

I can turn around in a second but the relative motion of the Moon, much

faster than the speed of light, doesn't correspond to the notion of

relative motion normally discussed in SR.

<fortuna...@gmail.com> writes:

> So, my question is this: Why with our telescopes do we always (and only)

> see perfectly spherical celestial bodies and have we never seen one

> contracted in the direction of motion like the one at the top right of

> my animation?

It is a misconception that spheres look contracted when moving at
> So, my question is this: Why with our telescopes do we always (and only)

> see perfectly spherical celestial bodies and have we never seen one

> contracted in the direction of motion like the one at the top right of

> my animation?

relativistic speeds:

A. Lampa, _Z. f. Physik_, 27, 138, 1924.

J. Terrell, _Phys. Rev._, 116, 1041, 1959.

R. Penrose, _Proc. Camb. Phil. Soc._, 55, 137, 1959.

I can turn around in a second but the relative motion of the Moon, much

faster than the speed of light, doesn't correspond to the notion of

relative motion normally discussed in SR.

Nov 16, 2022, 12:28:21 PM11/16/22

to

Phillip Helbigundress to reply martedě 15/11/2022 alle ore 13:17:21 ha

scritto:

In my animation

https://www.geogebra.org/m/pxcxznqz

I added a light clock on Neptune, where the photon (in the reference of

the inhabitant of neptune) moves vertically (up and down) along the red

line.

Instead, for the terrestrial observer, the same photon follows a zigzag

path.

Thus, Neptune's space *must* be contracted (in the direction of motion)

for the terrestrial observer.

This is the correct notion of relative motion normally discussed in SR.

scritto:

https://www.geogebra.org/m/pxcxznqz

I added a light clock on Neptune, where the photon (in the reference of

the inhabitant of neptune) moves vertically (up and down) along the red

line.

Instead, for the terrestrial observer, the same photon follows a zigzag

path.

Thus, Neptune's space *must* be contracted (in the direction of motion)

for the terrestrial observer.

This is the correct notion of relative motion normally discussed in SR.

Nov 17, 2022, 4:04:47 AM11/17/22

to

Phillip Helbig wrote:

>> It is a misconception that spheres look contracted when moving at

>> relativistic speeds:

>>

>> A. Lampa, _Z. f. Physik_, 27, 138, 1924.

>> J. Terrell, _Phys. Rev._, 116, 1041, 1959.

>> R. Penrose, _Proc. Camb. Phil. Soc._, 55, 137, 1959.

>>

>> I can turn around in a second but the relative motion of the Moon, much

>> faster than the speed of light, doesn't correspond to the notion of

>> relative motion normally discussed in SR.

Luigi Fortunati <fortuna...@gmail.com> wrote:
>> It is a misconception that spheres look contracted when moving at

>> relativistic speeds:

>>

>> A. Lampa, _Z. f. Physik_, 27, 138, 1924.

>> J. Terrell, _Phys. Rev._, 116, 1041, 1959.

>> R. Penrose, _Proc. Camb. Phil. Soc._, 55, 137, 1959.

>>

>> I can turn around in a second but the relative motion of the Moon, much

>> faster than the speed of light, doesn't correspond to the notion of

>> relative motion normally discussed in SR.

[[question about an apparent paradox involving special relativity

and a rotating reference frame]]

I think the underlying cause of Luigi's apparent paradox may be that

special relativity implicitly assues that the geometry of space is

Euclidean... but the geometry of a rotating reference frame is non-Euclidean.

(The non-Euclidean nature of rotating reference frames results in things

like the Sagnac effect, the Ehrenfest paradox, etc.)

There are interesting and relevant discussions in

https://en.wikipedia.org/wiki/Sagnac_effect

https://en.wikipedia.org/wiki/Ehrenfest_paradox

https://en.wikipedia.org/wiki/Born_coordinates

--

-- "Jonathan Thornburg [remove -color to reply]" <dr.j.th...@gmail-pink.com>

currently on the west coast of Canada

"!07/11 PDP a ni deppart m'I !pleH" -- slashdot.org page footer, 2022-10-16

"eHpl !'I mrtpaep dnia P PD1 /107" -- slightly more plausible message

given PDP-11 little-endian byte order

Nov 17, 2022, 4:53:46 PM11/17/22

to

I wrote:

> Luigi Fortunati <fortuna...@gmail.com> wrote:

> [[question about an apparent paradox involving special relativity

> and a rotating reference frame]]

>

> I think the underlying cause of Luigi's apparent paradox may be that

> special relativity implicitly assues that the geometry of space is

> Euclidean... but the geometry of a rotating reference frame is non-Euclidean.

> (The non-Euclidean nature of rotating reference frames results in things

> like the Sagnac effect, the Ehrenfest paradox, etc.)

>

> There are interesting and relevant discussions in

> https://en.wikipedia.org/wiki/Sagnac_effect

> https://en.wikipedia.org/wiki/Ehrenfest_paradox

> https://en.wikipedia.org/wiki/Born_coordinates

Two other excellent discussions which directly address the complexities
> Luigi Fortunati <fortuna...@gmail.com> wrote:

> [[question about an apparent paradox involving special relativity

> and a rotating reference frame]]

>

> I think the underlying cause of Luigi's apparent paradox may be that

> special relativity implicitly assues that the geometry of space is

> Euclidean... but the geometry of a rotating reference frame is non-Euclidean.

> (The non-Euclidean nature of rotating reference frames results in things

> like the Sagnac effect, the Ehrenfest paradox, etc.)

>

> There are interesting and relevant discussions in

> https://en.wikipedia.org/wiki/Sagnac_effect

> https://en.wikipedia.org/wiki/Ehrenfest_paradox

> https://en.wikipedia.org/wiki/Born_coordinates

of rotating reference frames in relativity are physics FAQ entries:

https://math.ucr.edu/home/baez/physics/Relativity/SR/rotatingCoordinates.html

https://math.ucr.edu/home/baez/physics/Relativity/SR/rigid_disk.html

ciao,

Nov 17, 2022, 4:54:16 PM11/17/22

to

inertial reference frame. SR only applies in inertial frames.

Velocities in a rotating frame are not real and you can't use SR with

these coordinates.

Rich L.

Nov 17, 2022, 4:54:46 PM11/17/22

to

I wrote:

> Luigi Fortunati <fortuna...@gmail.com> wrote:

> [[question about an apparent paradox involving special relativity

> and a rotating reference frame]]

>

> I think the underlying cause of Luigi's apparent paradox may be that

> special relativity implicitly assues that the geometry of space is

> Euclidean... but the geometry of a rotating reference frame is non-Euclidean.

>

> Luigi Fortunati <fortuna...@gmail.com> wrote:

> [[question about an apparent paradox involving special relativity

> and a rotating reference frame]]

>

> I think the underlying cause of Luigi's apparent paradox may be that

> special relativity implicitly assues that the geometry of space is

> Euclidean... but the geometry of a rotating reference frame is non-Euclidean.

>

> There are interesting and relevant discussions in

> [[references]]
On further thought, I think the questions Luigi raised don't actually

involve the rotating-coordinate issues discussed in those references.

Instead, Luigi's questions are "just" about what we see if we observe

something (Neptune) in a reference frame which is moving *faster*

than the speed of light.

As Phillip Helbig noted, it's easy to see observationally that the
answer is "nothing special" -- if you spin your body around at an

angular frequency of faster than about 1 revolution per 8 seconds,

your body reference frame will have the Moon moving faster than the

speed of light, and empirically the Moon looks pretty ordinary

when you do this.

Nov 18, 2022, 9:14:13 PM11/18/22

to

On 11/17/22 3:54 PM, Richard Livingston wrote:

> [...] the rotating coordinate frame is not an inertial reference

> frame.

True.

A minor point: in SR all possible frames are inertial, because "frame"

implies the coordinate axes are mutually orthogonal, and that only

happens for Minkowski coordinates at rest in an inertial frame. Rotating

and otherwise-accelerated coordinates do not have mutually orthogonal

coordinate axes.

> SR only applies in inertial frames.

False. SR applies in any coordinates if the physical situation is within

its domain of applicability. That domain is restricted to flat manifolds

with the topology of R^4, which means that gravitation is absent (or at

least negligible).

Note, however, that standard presentations of SR give equations only in

inertial coordinates (within its domain). To determine what equations

apply in rotating or otherwise-accelerated coordinates, one starts with

the usual equations in inertial coordinates and applies the appropriate

coordinate transform to the desired coordinates.

> Velocities in a rotating frame are not real and you can't use SR

> with these coordinates.

That is merely repeating the above mistake.

Tom Roberts

> [...] the rotating coordinate frame is not an inertial reference

> frame.

True.

A minor point: in SR all possible frames are inertial, because "frame"

implies the coordinate axes are mutually orthogonal, and that only

happens for Minkowski coordinates at rest in an inertial frame. Rotating

and otherwise-accelerated coordinates do not have mutually orthogonal

coordinate axes.

> SR only applies in inertial frames.

its domain of applicability. That domain is restricted to flat manifolds

with the topology of R^4, which means that gravitation is absent (or at

least negligible).

Note, however, that standard presentations of SR give equations only in

inertial coordinates (within its domain). To determine what equations

apply in rotating or otherwise-accelerated coordinates, one starts with

the usual equations in inertial coordinates and applies the appropriate

coordinate transform to the desired coordinates.

> Velocities in a rotating frame are not real and you can't use SR

> with these coordinates.

Tom Roberts

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