# Coordinates, reference frames, and general relativity

64 views

### carlip...@physics.ucdavis.edu

May 9, 2011, 2:52:44 PM5/9/11
to
There's been some confusion here about coordinate systems, reference
frames, general relativity, and geocentrism. Some of the issues are
a bit subtle, so I thought I might try to clarify a little.

*Coordinate systems*: coordinates are human-made labels of points
in space or spacetime. There are a few technical restrictions, but
in general, coordinates are almost completely arbitrary. Points don't
come wearing little name tags; we can call them pretty much what we
want.

Obviously, Nature doesn't care about the choices we make for naming
points. So no real physical process can depend on the choice of
coordinates. The way we *describe* a process may depend on what
coordinates we use for the description, but the actual process cannot.
This is not just true in general relativity; it holds for any sensible
physical theory. (It's possible, for instance, to rewrite ordinary
Newtonian gravity in a way that makes no reference to coordinates;
Cartan did this in 1923.)

Can we make a choice in such a way that the coordinates labeling
the Earth's position don't change in time? Certainly. We can also
make a choice in which the coordinates labeling the Earth and the
coordinates labeling the Moon dance a foxtrot. This means nothing
about the actual motion; it's just a statement about our ability to
choose creative names for points.

(While coordinates don't affect physics, there is a sense in which
physics can affect coordinates. Real physical processes can be easier
to describe in some coordinates than others. If you want to actually
calculate the motion of the planets, you'd be foolish to use anything
other than a barycentric coordinate system. But even this is really a
statement about us -- our ability to do the math -- and not about
Nature.)

*Reference frames*: a reference frame is not just another name for a
coordinate system. A reference frame is a collection of imaginary
observers, spread throughout space and moving along predetermined,
nonintersecting trajectories, each carrying a standard clock. Talking
about a physical process in a particular reference frame means
describing what such a collection of observers would see. This may
be a somewhat anthropomorphic formulation -- another definition
refers to a system of ideal "rods and clocks" -- but the point is that
a reference frame labels what a real, physical observer could actually
observe.

Every reference frame determines a coordinate system. We can simply
label points by the observers at those points. The converse is not
true, though: not every coordinate system determines a reference
frame.

For instance, we can choose coordinates such that the coordinate
values of points on the surface of the Earth are not changing in time.
(The shorthand is that this is a coordinate system in which the Earth
is "not rotating," but keep in mind that this is a statement about the
coordinates, not the Earth.). In such a coordinate system, however,
distant objects will have rapidly changing coordinates ("rotating
around the Earth"). You don't have to go very far -- just as far as
Neptune -- to get to a place where the "coordinate speeds" are faster
than light. Since no physical observer can move faster than light,
such a coordinate system does not determine a reference frame.

In short, coordinates are imaginary; reference frames must be at least
potentially real.

*Causality*: it can sometimes be hard to disentangle real physical
effects from effects of the choice of coordinate. In the early days of
research on gravitational waves, for instance, there were debates
about whether the waves were real or just "coordinate artifacts."

There are some cases, though, in which the distinction is clear.
There's a popular saying (well, popular in certain narrow circles)
that physics propagates at the speed of light, but coordinates can
propagate at the speed of thought.

For coordinates in which the Earth is not rotating, for instance, it
is certainly not true that Neptune is physically moving faster than
light. We can imagine coordinates moving faster than light, but
if we do, can be sure that the coordinate description will give us
artificial results that do not reflect the real physics.

For an Earth-centered coordinate system, in which the Earth is
rotating but not moving around the Sun, the situation is slightly
-- but only slightly -- trickier. We observe aberration of starlight,
a regular change in the direction the light from stars reaches us.
(Simple analogy: if you walk in the rain, the direction the drops
hit you depends on which way you are walking.) In a heliocentric
coordinate system, this variation comes from the orbital motion of
the Earth. In an Earth-centered coordinate system, on the other hand,
the change must instead come from the motion of the stars. (Simple
analogy: you could get the same effect of slanting rain if you were
standing still and the clouds were moving.)

If light traveled at an infinite speed, this would be no problem.
But in fact, light travels at a finite speed. In an Earth-centered
coordinate system, the aberration of light coming from a star 100
light years away would have to reflect the motion of the star 100
years ago; the aberration of light coming from a star 1000 light years
away must reflect the motion of the star 1000 years ago. While one
can choose such a description, it does not reflect the real causality:
there is no physical mechanism by which the motion of the Earth
today can affect the motions of stars in the past. This is especially
true because the Earth's orbit varies; the "cause" of a change in
motion now cannot have the "effect" of changing stars' motions
hundreds or thousands of years ago.

There is an even more dramatic instance of this issue of causality.
The Universe is filled with cosmic microwave background radiation
(CMBR), basically the afterglow from the period just after the Big
Bang when the Universe was very hot and dense. When we observe the
CMBR, we see an annually varying Doppler effect that precisely matches
the Earth's orbital speed and direction. But this radiation has been
traveling freely in space for some 14 billion years. If one tries to
physically explain this Doppler shift an an Earth-centered coordinate
system, one must claim that the 14-billion-year-old plasma in the
very early Universe, ten billion years before the Earth even existed,
somehow exactly anticipated the Earth's orbit, with all its local
variation. Call this what you like, it is not physics.

[By the way: we really know that the CMBR pervades the Universe,
and doesn't just surround the Earth. We can observe its effect in
distant galaxies -- it can produce observable low-energy transitions
among molecular energy levels -- and we can observe the effects of
distant galaxies on the CMBR -- they can cause small but measurable
shifts in its spectrum. Note also that this argument does not rely on
any particular cosmological model: it's enough to know that the CMBR
is reaching us from the very distant Universe, and we can tell that by
the fact that it affects and is affected by distant galaxies.]

*Relative and absolute motion*: There is an old argument over whether
it is sensible to talk about absolute motion at all. The discussion
is commonly expressed in terms of Mach's principle, which says in
some form or another that local properties of matter, such as inertia
and rotation, are determined by distant matter, and are fixed only
relative to a particular distribution of matter in the Universe.

The short answer is simply that we don't know. In particular, the
question of whether general relativity implies/is consistent with
Mach's principle is not settled. The longer answer is that we don't
even know how to formulate the question properly. A 1997 paper by
Bondi and Samuel, for instance, listed ten formulations of Mach's
principle, some of which gave contradictory predictions for certain
experiments.

Note, though, that whether or not some version of Mach's principle
is correct, it makes no sense to claim that *all* relative descriptions
are physically meaningful. One still needs consistency with the
requirement of causality that I described above. In particular:

-- If absolute motion does not exist, then any correct description
must be relative. But this does not mean any relative description
must be correct. A relative description must still not allow events
in the present to affect the past.

-- If there is some absolute description of motion, it, too, must obey
the condition of causality. Again, such a description must not allow
events in the present to affect the past.

In either case, a heliocentric description is very clearly ruled out.

Steve Carlip

### alextangent

May 9, 2011, 3:15:05 PM5/9/11
to

Thanks, that is much appreciated.

Now, can I ask one further favour; rotation. The argument still rages
elsewhere.

### John Harshman

May 9, 2011, 3:18:16 PM5/9/11
to

Nice post, except I think you meant "geocentric" in that last sentence.

Can we rule out as physically meaningless any coordinate system in which
we observe objects (Pluto, say) to be moving faster than light?

### Bruce Stephens

May 9, 2011, 3:22:37 PM5/9/11
to
carlip...@physics.ucdavis.edu writes:

[...]

> In either case, a heliocentric description is very clearly ruled out.

Did you mean geocentric there? (Obviously a description where the Sun
is stationary and at the centre of the universe is also absurd, but one
where the Sun is (approximately) at the centre of the solar system is
fine.)

### Ernest Major

May 9, 2011, 3:29:50 PM5/9/11
to
In message <iq9d5s\$9dl\$1...@speranza.aioe.org>,
carlip...@physics.ucdavis.edu writes

>In either case, a heliocentric description is very clearly ruled out.

While I presume that heliocentric descriptions are ruled out for similar
reasons, was that meant to be geocentric?
--
alias Ernest Major

### Mike Dworetsky

May 9, 2011, 5:33:49 PM5/9/11
to

Excellent! But I think the word you meant in the final sentence was
"geocentric".

--
Mike Dworetsky

### Bill

May 9, 2011, 8:15:44 PM5/9/11
to

Nominated. This is why I like having Pagano around. Every so often he
provokes a post like this one.

### John S. Wilkins

May 9, 2011, 8:47:13 PM5/9/11
to
<carlip...@physics.ucdavis.edu> wrote:

> *Causality*: it can sometimes be hard to disentangle real physical
> effects from effects of the choice of coordinate. In the early days of
> research on gravitational waves, for instance, there were debates
> about whether the waves were real or just "coordinate artifacts."

One can argue that under a four-dimensional view of the universe there
is no causality, just patterns in the spacetime block, regularities in
time and space. A gravity wave would be such a regularity, without the
need to argue that they cause anything, since at the physical level,
nothing causes anything (they just have these regular arrangements and
relationships).

The philosopher of physics who suggested this to me said that meant
"cause" only applies to things like chemistry biology, psychology and
astronomy, not fundamental physics.
--
John S. Wilkins, Associate, Philosophy, University of Sydney
http://evolvingthoughts.net
But al be that he was a philosophre,
Yet hadde he but litel gold in cofre

### Bill

May 9, 2011, 9:13:35 PM5/9/11
to
On May 10, 7:47 am, j...@wilkins.id.au (John S. Wilkins) wrote:

> <carlip-nos...@physics.ucdavis.edu> wrote:
> > *Causality*: it can sometimes be hard to disentangle real physical
> > effects from effects of the choice of coordinate.  In the early days of
> > research on gravitational waves, for instance, there were debates
> > about whether the waves were real or just "coordinate artifacts."
>
> One can argue that under a four-dimensional view of the universe there
> is no causality, just patterns in the spacetime block, regularities in
> time and space. A gravity wave would be such a regularity, without the
> need to argue that they cause anything, since at the physical level,
> nothing causes anything (they just have these regular arrangements and
> relationships).
.
>
> The philosopher of physics who suggested this to me said that meant
> "cause" only applies to things like chemistry biology, psychology and
> astronomy, not fundamental physics.

You mean to say that causation is an emergent property of complex
things like chemicals and organisms which is not present in mere
simple physics? You should tell rnorman about that.

> --
> John S. Wilkins, Associate, Philosophy, University of Sydneyhttp://evolvingthoughts.net

### r norman

May 9, 2011, 9:22:57 PM5/9/11
to
On Mon, 9 May 2011 18:13:35 -0700 (PDT), Bill <broger...@gmail.com>
wrote:

>On May 10, 7:47 am, j...@wilkins.id.au (John S. Wilkins) wrote:
>> <carlip-nos...@physics.ucdavis.edu> wrote:
>> > *Causality*: it can sometimes be hard to disentangle real physical
>> > effects from effects of the choice of coordinate.  In the early days of
>> > research on gravitational waves, for instance, there were debates
>> > about whether the waves were real or just "coordinate artifacts."
>>
>> One can argue that under a four-dimensional view of the universe there
>> is no causality, just patterns in the spacetime block, regularities in
>> time and space. A gravity wave would be such a regularity, without the
>> need to argue that they cause anything, since at the physical level,
>> nothing causes anything (they just have these regular arrangements and
>> relationships).
>.
>>
>> The philosopher of physics who suggested this to me said that meant
>> "cause" only applies to things like chemistry biology, psychology and
>> astronomy, not fundamental physics.
>
>You mean to say that causation is an emergent property of complex
>things like chemicals and organisms which is not present in mere
>simple physics? You should tell rnorman about that.
>

Wilkins has taught me that everything in the universe is necessarily
the mere working out of fundamental physics. If "cause" is not
present there, then it is present nowhere because it cannot "emerge"
from pure nothingness.

He has taught me that what we call "emergence" is merely a
demonstration of our own ignorance. Therefore the notion of causality
must also be a demonstration of our own ignorance. Were there no
humans in the universe, there would be no ignorance, hence no
causality.

Fortunatly, I am a very poor student. He may have taught me all that
but I never learned any of it!

### James Beck

May 9, 2011, 10:12:35 PM5/9/11
to
On Mon, 9 May 2011 17:15:44 -0700 (PDT), Bill <broger...@gmail.com>
wrote:

>On May 10, 1:52 am, carlip-nos...@physics.ucdavis.edu wrote:

Second

### John S. Wilkins

May 9, 2011, 10:16:02 PM5/9/11
to
r norman <r_s_n...@comcast.net> wrote:

I have hopes that you will come to understand it by the end of the
course, however.

### John S. Wilkins

May 9, 2011, 10:15:56 PM5/9/11
to
Bill <broger...@gmail.com> wrote:

> On May 10, 7:47 am, j...@wilkins.id.au (John S. Wilkins) wrote:
> > <carlip-nos...@physics.ucdavis.edu> wrote:
> > > *Causality*: it can sometimes be hard to disentangle real physical
> > > effects from effects of the choice of coordinate. In the early days of
> > > research on gravitational waves, for instance, there were debates
> > > about whether the waves were real or just "coordinate artifacts."
> >
> > One can argue that under a four-dimensional view of the universe there
> > is no causality, just patterns in the spacetime block, regularities in
> > time and space. A gravity wave would be such a regularity, without the
> > need to argue that they cause anything, since at the physical level,
> > nothing causes anything (they just have these regular arrangements and
> > relationships).
> .
> >
> > The philosopher of physics who suggested this to me said that meant
> > "cause" only applies to things like chemistry biology, psychology and
> > astronomy, not fundamental physics.
>
> You mean to say that causation is an emergent property of complex
> things like chemicals and organisms which is not present in mere
> simple physics? You should tell rnorman about that.
>

There are several ways to interpret this. One is that causation is
emergent. Another is that it is an epistemic projection based on our
experience of the world, rather than a fact about the world [the
regularities are, of course, facts about the world]. Of course, under my
interpretation of "emergence" this is the same thing.

### chris thompson

May 9, 2011, 10:24:46 PM5/9/11
to
On May 9, 10:12 pm, James Beck <jdbeck11...@yahoo.com> wrote:
> On Mon, 9 May 2011 17:15:44 -0700 (PDT), Bill <brogers31...@gmail.com>

Thirded

### John S. Wilkins

May 10, 2011, 1:14:29 AM5/10/11
to
chris thompson <chris.li...@gmail.com> wrote:

But it's Carlip: of *course* he's going to write a PotM quality post.
That's unfair to the rest of us.

Fourthed.

### J. J. Lodder

May 10, 2011, 4:02:36 AM5/10/11
to
<carlip...@physics.ucdavis.edu> wrote:

So you would agree I think with my claim
that it doesn't make sense
to refute geocentrism and a non-rotating earth
with the claim that the earth rotates absolutely.
(whatever that may be taken to mean)
One should not try to refute neo-geocentrism
by fleeing into neo-Newtonianism,
by saing that it is obvious that the earth rotates absolutely.
(from coriolis or the like)

It does make sense to say
that permanent non-rotation of the earth is nonsense
because it implies that the whole universe,
down to the big bang, must instantaneously slow down it's rotation
whenever there is an earhquake in Japan,
or when the trees grow in the Northern hemisphere.
Neo-geocentrism has many crazy consequences like this.
(tidal friction brakes the universe, etc.)

Note however that it is not possible
to refute neo-geocentrism this way.
The true believer can always flee into 'goddidit'.
God choreographed all those motions of all those particles
in the whole universe from the big bag up
in precisely such a way that it appears
to an observer on earth as if the earth is rotating.
(to test the faith of the true believer, apparently)
After all, the whole universe is nothing more than a decor
for the uniquely important (christian) events on Earth.

Such a position is very much like omphalism.
(god created the world 6000 years ago,
including all those appearances of a much longer past)

The two even meet, for their are fossils with growth rings
that demonstrate that the universe rotated
much faster in the non-existent geological past.

It is never possible to refute an idiot
who is willing to push his idiocy sufficiently far.
At a certain stage one should simply say that enough is enough,

Jan

### Vend

May 10, 2011, 5:01:53 AM5/10/11
to
On May 10, 2:47 am, j...@wilkins.id.au (John S. Wilkins) wrote:

> <carlip-nos...@physics.ucdavis.edu> wrote:
> > *Causality*: it can sometimes be hard to disentangle real physical
> > effects from effects of the choice of coordinate.  In the early days of
> > research on gravitational waves, for instance, there were debates
> > about whether the waves were real or just "coordinate artifacts."
>
> One can argue that under a four-dimensional view of the universe there
> is no causality, just patterns in the spacetime block, regularities in
> time and space. A gravity wave would be such a regularity, without the
> need to argue that they cause anything, since at the physical level,
> nothing causes anything (they just have these regular arrangements and
> relationships).

I don't think this is correct. The patterns of events in a 4-
dimensional block universe are not arbitrary, they still have to obey
the causality constraint: the events at one point of the spacetime
depend only on the events in its past light-cone.

### alextangent

May 10, 2011, 5:56:04 AM5/10/11
to
On May 10, 9:02 am, nos...@de-ster.demon.nl (J. J. Lodder) wrote:
> <carlip-nos...@physics.ucdavis.edu> wrote:

[carlip bit snipped]

>
> So you would agree I think with my claim
> that it doesn't make sense
> to refute geocentrism and a non-rotating earth
> with the claim that the earth rotates absolutely.
> (whatever that may be taken to mean)
> One should not try to refute neo-geocentrism
> by fleeing into neo-Newtonianism,
> by saing that it is obvious that the earth rotates absolutely.
> (from coriolis or the like)

That doesn't make sense. No "fleeing into neo-Newtoniansim" is
required to measure the bulge of a non-rigid earth, and to provide a
reasonable explanation for said bulge -- that it rotates. Newton
postulated that himself and made a pretty accurate estimate of the
bulge.

The rest is some philosophical discussion where you're confusing
yourself with measuring (or rather, not being able to measure)
rotation in a reference-less non-universe. We don't live in one.

>
> It does make sense to say
> that permanent non-rotation of the earth is nonsense
> because it implies that the whole universe,
> down to the big bang, must instantaneously slow down it's rotation
> whenever there is an earhquake in Japan,
> or when the trees grow in the Northern hemisphere.
> Neo-geocentrism has many crazy consequences like this.
> (tidal friction brakes the universe, etc.)

Agreed.

>
> Note however that it is not possible
> to refute neo-geocentrism this way.

And again, here's you making statements I really can't understand. It
*is* possible to refute; you just did it in the paragraph above. The
rest below is "theology" (your words from a previous post to me). Why
you feel it deserves this many words in reply to this post, when your
previous comments were made with far fewer and confused everyone as a
result, is beyond me.

### J. J. Lodder

May 10, 2011, 6:42:52 AM5/10/11
to

> On May 10, 9:02 am, nos...@de-ster.demon.nl (J. J. Lodder) wrote:
> > <carlip-nos...@physics.ucdavis.edu> wrote:
>
> [carlip bit snipped]
>
> >
> > So you would agree I think with my claim
> > that it doesn't make sense
> > to refute geocentrism and a non-rotating earth
> > with the claim that the earth rotates absolutely.
> > (whatever that may be taken to mean)
> > One should not try to refute neo-geocentrism
> > by fleeing into neo-Newtonianism,
> > by saing that it is obvious that the earth rotates absolutely.
> > (from coriolis or the like)
>
> That doesn't make sense. No "fleeing into neo-Newtoniansim" is
> required to measure the bulge of a non-rigid earth, and to provide a
> reasonable explanation for said bulge -- that it rotates. Newton
> postulated that himself and made a pretty accurate estimate of the
> bulge.
>
> The rest is some philosophical discussion where you're confusing
> yourself with measuring (or rather, not being able to measure)
> rotation in a reference-less non-universe. We don't live in one.

As said many times,
measuring centrifugal and coriolis forces is no problem.
The problem is with the interpretation of those measurements
as proof of -absolute- rotation.
(rather than relative rotation wrt the rest of the universe)
That's what I called neo-Newtonianism.

> > It does make sense to say
> > that permanent non-rotation of the earth is nonsense
> > because it implies that the whole universe,
> > down to the big bang, must instantaneously slow down it's rotation
> > whenever there is an earhquake in Japan,
> > or when the trees grow in the Northern hemisphere.
> > Neo-geocentrism has many crazy consequences like this.
> > (tidal friction brakes the universe, etc.)
>
> Agreed.
>
> >
> > Note however that it is not possible
> > to refute neo-geocentrism this way.
>
> And again, here's you making statements I really can't understand. It
> *is* possible to refute; you just did it in the paragraph above.

To anyone who isn't a complete idiot, yes.
If you want to be an idiot
you can maintain that the earth 'really' doesn't rotate,
just as it 'really' is 6000 years old.

> The
> rest below is "theology" (your words from a previous post to me). Why
> you feel it deserves this many words in reply to this post, when your
> previous comments were made with far fewer and confused everyone as a
> result, is beyond me.

You are not everyone.
And no, this is the first time I mentioned omphalism
and goddidit in this context.

Get used to it: Pagano can't be refuted.
With sufficient idiocy his views can be made unfalsifiable.

All you can do is show that his views are completely crazy,
for they require god to be very hard at work
at all times all over the universe
just to create false impressions in thinking humans.
(so they can be sent to hell for the crime of thinking
rather than having blind faith?)

Scientist should just thrug their shoulders about it,
for it is scientifically irrelevant.
It (like omphalism) is very bad theology though.

Who wants to believe in a lying and deceiving god?

Jan

### J. J. Lodder

May 10, 2011, 7:46:00 AM5/10/11
to
John S. Wilkins <jo...@wilkins.id.au> wrote:

> <carlip...@physics.ucdavis.edu> wrote:
>
> > *Causality*: it can sometimes be hard to disentangle real physical
> > effects from effects of the choice of coordinate. In the early days of
> > research on gravitational waves, for instance, there were debates
> > about whether the waves were real or just "coordinate artifacts."
>
> One can argue that under a four-dimensional view of the universe there
> is no causality, just patterns in the spacetime block, regularities in
> time and space. A gravity wave would be such a regularity, without the
> need to argue that they cause anything, since at the physical level,
> nothing causes anything (they just have these regular arrangements and
> relationships).
>
> The philosopher of physics who suggested this to me said that meant
> "cause" only applies to things like chemistry biology, psychology and
> astronomy, not fundamental physics.

Everything is (fundamental) physics,
even stamp collecting,

Jan

### jillery

May 10, 2011, 9:01:50 AM5/10/11
to
On May 10, 6:42 am, nos...@de-ster.demon.nl (J. J. Lodder) wrote:

It sounds to me almost as if you're saying you don't acknowledge
absolute rotation because Tony is a complete idiot. While I certainly
appreciate the frustration of trying to convince someone who refuses
to even engage, ISTM Tony and his blinkered kin are not the target
audience here. OTOH making statements like "its completely crazy but
philosophically correct", ISTM aids and abets Tony's denials.

> > The
> > rest below is "theology" (your words from a previous post to me). Why
> > you feel it deserves this many words in reply to this post, when your
> > previous comments were made with far fewer and confused everyone as a
> > result, is beyond me.
>
> You are not everyone.
> And no, this is the first time I mentioned omphalism
> and goddidit in this context.
>
> Get used to it: Pagano can't be refuted.
> With sufficient idiocy his views can be made unfalsifiable.
>
> All you can do is show that his views are completely crazy,
> for they require god to be very hard at work
> at all times all over the universe
> just to create false impressions in thinking humans.
> (so they can be sent to hell for the crime of thinking
> rather than having blind faith?)
>
> Scientist should just thrug their shoulders about it,
> for it is scientifically irrelevant.
> It (like omphalism) is very bad theology though.
>
> Who wants to believe in a lying and deceiving god?
>

> Jan- Hide quoted text -
>
> - Show quoted text -- Hide quoted text -
>
> - Show quoted text -

### raven1

May 10, 2011, 10:05:53 AM5/10/11
to
On Mon, 9 May 2011 17:15:44 -0700 (PDT), Bill <broger...@gmail.com>
wrote:

Seconded, although, Carlip's posts are always so well-written and
informative that it's almost a given he'll earn POTM honors for them.

### r norman

May 10, 2011, 10:24:46 AM5/10/11
to
On Tue, 10 May 2011 10:05:53 -0400, raven1
<quotht...@nevermore.com> wrote:

>
>Seconded, although, Carlip's posts are always so well-written and
>informative that it's almost a given he'll earn POTM honors for them.

On behalf of all those (including myself) who have a post nominated
for POTM, I urge that Carlip be declared ineligible for POTM
specifically for that reason.

### TomS

May 10, 2011, 11:50:05 AM5/10/11
to
"On Mon, 09 May 2011 12:18:16 -0700, in article
<IuOdnQS0uvx...@giganews.com>, John Harshman stated..."
[...snip...]

>Can we rule out as physically meaningless any coordinate system in which
>we observe objects (Pluto, say) to be moving faster than light?
>

AIUI, the hypothetical "tachyons" are consistent, moving faster than
light, but they cannot slow down to less than the speed of light.

Also, I have heard from a geocentrist an "explanation" that the objects
that appear to be moving faster than light are actually moving slower
than light, but are imbedded in space which is moving faster than light.
And reference was made to the inflation scenarios of the Big Bang, in
which space expanded faster than light.

Therefore, I amend your question to:

What about objects which cross the speed-of-light barrier? For example,
Neptune, in a geocentric model, at times is moving at a speed less than
the speed of light, and at times is moving faster than light. Likewise
for satellites of Neptune, and interplanetary rockets like Voyager 1.

--
---Tom S.
"... the heavy people know some magic that can make things move and even fly,
but they're not very bright, because they can't survive without their magic
contrivances"
Xixo, in "The Gods Must Be Crazy II"

### Randy C

May 10, 2011, 12:17:38 PM5/10/11
to
> Who wants to believe in a lying and deceiving god?

> Jan

All Biblical creationists.

They also prefer to believe in a God who is cruel and incompetent as
well.

### Ken Aaker

May 10, 2011, 2:53:54 PM5/10/11
to
> There's been some confusion here about coordinate systems, reference
> frames, general relativity, and geocentrism. Some of the issues are
> a bit subtle, so I thought I might try to clarify a little.
>
> *Coordinate systems*: coordinates are human-made labels of points
> in space or spacetime. There are a few technical restrictions, but
> in general, coordinates are almost completely arbitrary. Points don't
> come wearing little name tags; we can call them pretty much what we
> want.
>
> Obviously, Nature doesn't care about the choices we make for naming
> points. So no real physical process can depend on the choice of
> coordinates. The way we *describe* a process may depend on what
> coordinates we use for the description, but the actual process cannot.
> This is not just true in general relativity; it holds for any sensible
> physical theory. (It's possible, for instance, to rewrite ordinary
> Newtonian gravity in a way that makes no reference to coordinates;
> Cartan did this in 1923.)

[snip]

I had a thought the other week that is sort of related to co-ordinate
systems, but I haven't been able to find any information that I can
understand that indicates whether the idea is useful or not.

Is there any way to tell whether the inflation of the cosmos was
caused by space itself expanding or by the "volume" of all the
elementary particles decreasing?

The last bit of the thought was that if the extra dimensions (>4) of
the particles in the universe were to "coil up" and become
unobservable that might allow the elementary particles to become
dramatically smaller.

Ken Aaker

### J. J. Lodder

May 10, 2011, 3:01:53 PM5/10/11
to
jillery <69jp...@gmail.com> wrote:

I'm saying that it is idiotic to try
to counter idiots with outdated science.
(like absolute rotation being 'proved'
by observing Coriolis forces)

Jan

### jillery

May 10, 2011, 3:14:13 PM5/10/11
to
On May 10, 3:01 pm, nos...@de-ster.demon.nl (J. J. Lodder) wrote:
> > absolute rotation because Tony is a complete idiot. While I certainly
> > appreciate the frustration of trying to convince someone who refuses
> > to even engage, ISTM Tony and his blinkered kin are not the target
> > audience here. OTOH making statements like "its completely crazy but
> > philosophically correct", ISTM aids and abets Tony's denials.
>
> I'm saying that it is idiotic to try
> to counter idiots with outdated science.
> (like absolute rotation being 'proved'
> by observing Coriolis forces)

Well, then, I say I almost completely agree with you. I remove your
qualifier and say it's idiotic to try to counter idiots. They have
had much more practice at it. And I'd be happy to end it on that note.

### carlip...@physics.ucdavis.edu

May 10, 2011, 4:14:25 PM5/10/11
to
John Harshman <jhar...@pacbell.net> wrote:
> carlip...@physics.ucdavis.edu wrote:

[...]

> > In either case, a heliocentric description is very clearly ruled out.

> Nice post, except I think you meant "geocentric" in that last sentence.

Oops! Note to self: if you write something after you've put the kids to
bed, proofread carefully the next day.

> Can we rule out as physically meaningless any coordinate system in which
> we observe objects (Pluto, say) to be moving faster than light?

Sort of. I would put it slightly differently. No coordinate system is in
itself physically meaningful, but some can be associated with physically
meaningful reference frames. If you have a coordinate system in which
some observable objects are at rest with respect to the coordinates,
but at the same time physically move faster than light, then that
coordinate system can't be associated with a physically meaningful
reference frame.

This doesn't mean such a coordinate system is useless. If you're looking
at clocks on GPS satellites, for instance, it is sometimes convenient
to use an Earth-centered coordinate system in which the Earth's
coordinates are not rotating. As long as you translate your results
back to real, observable quantities once you're done, and don't get
confused about the difference between coordinate effects and physically
observable effects, there's nothing wrong with that.

The key is that coordinates are tools for calculation, and rarely
anything more; the final results don't -- can't -- depend on your
choice of coordinates. If you look at how JPL computes orbits, for
example, you'll see that they use coordinates as intermediate steps.
But in the end, when they compare with observations, they don't talk
about, for example, "the position of Mercury" -- they talk about "the
time for a radar signal from location X on Earth to reach Mercury
and return, as measured by an atomic clock at rest at location X."

Steve Carlip

### Walter Bushell

May 10, 2011, 4:50:28 PM5/10/11
to
In article <1k11wp1.1byg1ne1rv8ue4N%jo...@wilkins.id.au>,

Oh, by your philosophy, by the time he becomes you. >;)(

--
The Chinese pretend their goods are good and we pretend our money
is good, or is it the reverse?

### Walter Bushell

May 10, 2011, 4:54:13 PM5/10/11
to
In article <1k11wpz.1l9...@de-ster.xs4all.nl>,

Every straight man.

We all worship Aphrodite!
Even though we know she's flighty.

### Earle Jones

May 10, 2011, 5:59:38 PM5/10/11
to
In article
Bill <broger...@gmail.com> wrote:

> On May 10, 1:52 am, carlip-nos...@physics.ucdavis.edu wrote:

[...]

> > -- If there is some absolute description of motion, it, too, must obey
> > the condition of causality.  Again, such a description must not allow
> > events in the present to affect the past.
> >
> > In either case, a heliocentric description is very clearly ruled out.
> >
> > Steve Carlip
>
> Nominated. This is why I like having Pagano around. Every so often he
> provokes a post like this one.

*
Seconded! There's nothing like having a breath of fresh air blown our
way. Thanks Steve!

earle
*

### alextangent

May 10, 2011, 7:03:33 PM5/10/11
to
On May 10, 3:24 pm, r norman <r_s_nor...@comcast.net> wrote:
> On Tue, 10 May 2011 10:05:53 -0400, raven1
>
> <quoththera...@nevermore.com> wrote:
>
> >Seconded, although, Carlip's posts are always so well-written and
> >informative that it's almost a given he'll earn POTM honors for them.
>
> On behalf of all those (including myself) who have a post nominated
> for POTM, I urge that Carlip be declared ineligible for POTM
> specifically for that reason.

Denied. They're JTDG; Just Too Damn Good.

### Bob Casanova

May 10, 2011, 8:15:06 PM5/10/11
to
On Tue, 10 May 2011 15:14:29 +1000, the following appeared
in talk.origins, posted by jo...@wilkins.id.au (John S.
Wilkins):

The universe isn't fair, or Tony would have exploded by now.

>Fourthed.

Fifthed, with the proviso that the error "heliocentric" in
the final sentence is corrected to the obviously intended
"geocentric".
--

Bob C.

"Evidence confirming an observation is
evidence that the observation is wrong."
- McNameless

### John S. Wilkins

May 10, 2011, 9:18:46 PM5/10/11
to
Walter Bushell <pr...@panix.com> wrote:

> In article <1k11wp1.1byg1ne1rv8ue4N%jo...@wilkins.id.au>,
> jo...@wilkins.id.au (John S. Wilkins) wrote:
>
> > r norman <r_s_n...@comcast.net> wrote:
> >

...

> > > Wilkins has taught me that everything in the universe is necessarily
> > > the mere working out of fundamental physics. If "cause" is not
> > > present there, then it is present nowhere because it cannot "emerge"
> > > from pure nothingness.
> > >
> > > He has taught me that what we call "emergence" is merely a
> > > demonstration of our own ignorance. Therefore the notion of causality
> > > must also be a demonstration of our own ignorance. Were there no
> > > humans in the universe, there would be no ignorance, hence no
> > > causality.
> > >
> > > Fortunatly, I am a very poor student. He may have taught me all that
> > > but I never learned any of it!
> >
> > I have hopes that you will come to understand it by the end of the
> > course, however.
>
> Oh, by your philosophy, by the time he becomes you. >;)(

### J. J. Lodder

May 11, 2011, 3:23:36 AM5/11/11
to
Bob Casanova <nos...@buzz.off> wrote:

Well, Tony is A Good Thing, in some sense.
What better anti-propaganda for christianity could you wish?

Great fun BTW, to see protestant fundies
and claiming that the Pope and cardinals
were right after all, and Galileo wrong,

Jan

### John S. Wilkins

May 11, 2011, 4:16:24 AM5/11/11
to
r norman <r_s_n...@comcast.net> wrote:

I gave it up a while back. I haven't had a PotM for ages now...

### Ernest Major

May 11, 2011, 4:53:01 AM5/11/11
to
In message <1k13gfp.jqt...@de-ster.xs4all.nl>, J. J. Lodder
<nos...@de-ster.demon.nl> writes

If you are referring to Tony, he self-identifies as a Catholic. The
question as to whether he is a schismatic has not to the best of my
knowledge been resolved.
>
>Jan
>

--
alias Ernest Major

### Frank J

May 11, 2011, 5:54:29 AM5/11/11
to
> Nominated. This is why I like having Pagano around. Every so often he
> provokes a post like this one.- Hide quoted text -

>
> - Show quoted text -

Thirded (fourthed?)

Thought provoking in itself, and with a bonus of a typo that Pagano
could not resist, setting a new low even for him.

### Bob Casanova

May 11, 2011, 5:01:02 PM5/11/11
to
On Wed, 11 May 2011 09:23:36 +0200, the following appeared
in talk.origins, posted by nos...@de-ster.demon.nl (J. J.
Lodder):

>Bob Casanova <nos...@buzz.off> wrote:
>
>> On Tue, 10 May 2011 15:14:29 +1000, the following appeared
>> in talk.origins, posted by jo...@wilkins.id.au (John S.
>> Wilkins):
>>
>> >chris thompson <chris.li...@gmail.com> wrote:
>> >
>> >> On May 9, 10:12 pm, James Beck <jdbeck11...@yahoo.com> wrote:
>> >> > On Mon, 9 May 2011 17:15:44 -0700 (PDT), Bill <brogers31...@gmail.com>
>> >> > wrote:
>> >> > >Nominated. This is why I like having Pagano around. Every so often he
>> >> > >provokes a post like this one.
>> >> >
>> >> > Second
>> >>
>> >> Thirded
>> >
>> >But it's Carlip: of *course* he's going to write a PotM quality post.
>> >That's unfair to the rest of us.
>>
>> The universe isn't fair, or Tony would have exploded by now.
>
>Well, Tony is A Good Thing, in some sense.
>What better anti-propaganda for christianity could you wish?

Arguably, Ray. Assuming Ray is a Christian, that is; and
assumption which Ray himself seems to deny, at least
implicitly.

>Great fun BTW, to see protestant fundies
>and claiming that the Pope and cardinals
>were right after all, and Galileo wrong,

Isn't it? Seems they prefer the Whore of Rome after all...at
least when the subject isn't evolution.

### Bob Casanova

May 11, 2011, 5:03:22 PM5/11/11
to
On Wed, 11 May 2011 09:53:01 +0100, the following appeared
in talk.origins, posted by Ernest Major
<{\$to\$}@meden.demon.co.uk>:

It has; Tony rejects the public assertions of the Pope,
which IIRC is definitive, and got quite a few people a warm
seat in the town square once upon a time.

### Kent

May 11, 2011, 11:56:48 PM5/11/11
to

It seems to me that if you want the earth stationary at the center of universe you need two assumptions:
1) the law of nature depend on the distance from the center of the universe (in this case the center of the earth). This gets around the problem with objects moving faster than the speed of light.
2) there are forces that depend on the time derivative of the dipole moment of the microwave background

This type of argument is very much in line with Poincare's conventionalism. Or if you prefer, this is Poincare's conventionalism expressed in modern terms.

Now the reason you do not use this frame is because of simplicity. For studies involving planetary or larger scales an earth centric frame is much more complicated to use. On the other hand if you wish to give the directions on how to get to the corner store the geocentric frame is preferred.

### Rolf

May 12, 2011, 6:07:03 AM5/12/11
to
John S. Wilkins wrote:
> chris thompson <chris.li...@gmail.com> wrote:
>
>> On May 9, 10:12 pm, James Beck <jdbeck11...@yahoo.com> wrote:
>>> On Mon, 9 May 2011 17:15:44 -0700 (PDT), Bill
>>> <brogers31...@gmail.com> wrote:
>>>
>>>
>>>
>>>> Nominated. This is why I like having Pagano around. Every so often
>>>> he provokes a post like this one.
>>>
>>> Second
>>
>> Thirded
>
> But it's Carlip: of *course* he's going to write a PotM quality post.
> That's unfair to the rest of us.
>
> Fourthed.

n'thed.

I just love Carlip's style of prose. It speaks to the heart of a
non-scientist.

### Rolf

May 12, 2011, 6:15:57 AM5/12/11
to

Will anyone else besides Tony not assuming it was a typo please confess
here? "Without sincere sorrow and purpose of amendment, confession avails
nothing,"

### Frank J

May 12, 2011, 6:37:40 AM5/12/11
to
> nothing,"-

Not sure what you're asking, but FWIW, I first thought it was a hasty
typo, then briefly wondered if it might have been intentional (as
Lenny would say, it's easy to make Tony howl). But then I remembered
my own hasty typos, such as the embarrassing miscalculation of
aromatic pi electrons (I was thinking C/H ratio in alkanes) in my 2003
"Benzenism" post, and I went back to, and stayed with "probably
unintentional."

### carlip...@physics.ucdavis.edu

May 12, 2011, 1:15:37 PM5/12/11
to

[...]
> Now, can I ask one further favour; rotation. The argument still rages
> elsewhere.

There are at least two distinct issues: can we detect "absolute" rotation
with local measurements, and can we detect rotation if we are allowed
to look at the distant Universe?

For the first question, my answer is, quite firmly, "I don't know." Local
experiments such as the Foucault pendulum or Gravity Probe B, see
effects that are most easily attributed to rotation. But it's an open
question whether general relativistic effects of distant rotating matter
could reproduce the same results.

There are hints in both directions. For instance, in the solution of the
Einstein field equations for an isolated spherical mass in an otherwise
empty universe, we can unambiguously tell whether the mass is rotating.
This can't be an effect of other matter, because in this solution there
is no other matter. On the other hand, if we take this same isolated
spherical mass -- say, nonrotating -- and put it inside a massive rotating
shell, in an otherwise empty universe, we will see effects such as a
Coriolis force that are "induced" from the rotating shell and that mimic
rotation of the mass.

At the very least, the answer depends on the setting (in particular, on
boundary conditions). It remains possible that general relativity is
"Machian" -- unable to locally identify absolute rotation -- if the
Universe is spatially closed. As I said in my previous post, it's not
entirely clear even how to pose the question.

For the second question -- can we detect rotation if we are allowed to
look at the distant Universe? -- the answer is certainly "yes," as long
as we are allowed to assume causality. In particular, changes in local
rotation have identifiable local causes, and these can be attributed
to the distant Universe only if we allow these local causes to act
backwards in time (or if you reject causality altogether).

Steve Carlip

### jillery

May 12, 2011, 1:27:38 PM5/12/11
to
On May 12, 1:15 pm, carlip-nos...@physics.ucdavis.edu wrote:

>
> [...]
>
> > Now, can I ask one further favour; rotation. The argument still rages
> > elsewhere.
>
> There are at least two distinct issues: can we detect "absolute" rotation
> with local measurements, and can we detect rotation if we are allowed
> to look at the distant Universe?
>
> For the first question, my answer is, quite firmly, "I don't know."  Local
> experiments such as the Foucault pendulum or Gravity Probe B, see
> effects that are most easily attributed to rotation.  But it's an open
> question whether general relativistic effects of distant rotating matter
> could reproduce the same results.
>
> There are hints in both directions.  For instance, in the solution of the
> Einstein field equations for an isolated spherical mass in an otherwise
> empty universe, we can unambiguously tell whether the mass is rotating.
> This can't be an effect of other matter, because in this solution there
> is no other matter.  On the other hand, if we take this same isolated
> spherical mass -- say, nonrotating -- and put it inside a massive rotating
> shell, in an otherwise empty universe, we will see effects such as a
> Coriolis force that are "induced" from the rotating shell and that mimic
> rotation of the mass.

I am not disagreeing with you, but I am confused. When you imagine a
non-rotating spherical shell inside a rotating shell, how does the
outside rotating shell "induce" coriolis effects on the non-rotating
inner shell?

### Glenn

May 12, 2011, 3:47:32 PM5/12/11
to
Also, how would this *mimic* rotation of the inner shell, since the
mass is not equivalent.

### alextangent

May 12, 2011, 5:01:42 PM5/12/11
to

I believe it's the Lense–Thirring effect again.
http://philsci-archive.pitt.edu/2681/1/lense.pdf. It's a pretty
approachable paper for the interested layman IMHO. (BTW, Carlip
mentions only a massive shell rotating around a spherical mass.)

### alextangent

May 12, 2011, 5:05:03 PM5/12/11
to
On May 12, 6:15 pm, carlip-nos...@physics.ucdavis.edu wrote:

Thank you.

(It confirms what I suspected was the case; that JJ Lodder had the
wrong end of the stick with reference to an isolated spherical
rotating mass.)

To the POTM voters; can this be included please?

### jillery

May 12, 2011, 7:05:19 PM5/12/11
to
> I believe it's the Lense–Thirring effect again.http://philsci-archive.pitt.edu/2681/1/lense.pdf. It's a pretty

> approachable paper for the interested layman IMHO. (BTW, Carlip
> mentions only a massive shell rotating around a spherical mass.)

The part of Steve's post that I am confused about is this:

"On the other hand, if we take this same isolated
spherical mass -- say, nonrotating -- and put it inside a massive
rotating
shell, in an otherwise empty universe, we will see effects such as a
Coriolis force that are "induced" from the rotating shell and that
mimic
rotation of the mass.

So what do you think I said wrong?

### Mike Dworetsky

May 13, 2011, 2:11:26 AM5/13/11
to

Alex Tangent has requested this be appended to the POTM nominated post. I
second that (he omitted the POTM word in the header so maybe this is the
first).

--
Mike Dworetsky

### Bob Casanova

May 13, 2011, 8:26:52 PM5/13/11
to
On Thu, 12 May 2011 16:05:19 -0700 (PDT), the following
appeared in talk.origins, posted by jillery
<69jp...@gmail.com>:

I'd suggest it was a typo on your part which he only wanted
to clarify; you originally said "When you imagine a
non-rotating spherical SHELL inside a rotating shell..."
rather than Carlip's "When you imagine a non-rotating
spherical MASS inside a rotating shell...". A minor point,
and I believe irrelevant to the physics question at hand; as
I said, a correction of wording only.

### jillery

May 13, 2011, 9:16:13 PM5/13/11
to
On May 13, 8:26 pm, Bob Casanova <nos...@buzz.off> wrote:
> On Thu, 12 May 2011 16:05:19 -0700 (PDT), the following
> appeared in talk.origins, posted by jillery
> <69jpi...@gmail.com>:

Thank you for pointing out my error. So my question wrt physics
stands. Hopefully Steve was not referring to the Lense Thirring
effect, as 39 milliarcseconds of frame-dragging is something I'm hard-
pressed to explain any of the observed effects of Earth's rotation.

### carlip...@physics.ucdavis.edu

May 16, 2011, 3:39:21 PM5/16/11
to
jillery <69jp...@gmail.com> wrote:

[My apologies if I have attributions mixed up -- too many layers for me to
follow...]

> > >> > On May 12, 1:15 pm, carlip-nos...@physics.ucdavis.edu wrote:

[...]

> > >> > > There are hints in both directions. For instance, in the
> > >> > > solution of the Einstein field equations for an isolated
> > >> > > spherical mass in an otherwise empty universe, we can
> > >> > > unambiguously tell whether the mass is rotating. This can't
> > >> > > be an effect of other matter, because in this solution there
> > >> > > is no other matter. On the other hand, if we take this same
> > >> > > isolated spherical mass -- say, nonrotating -- and put it inside
> > >> > > a massive rotating shell, in an otherwise empty universe, we
> > >> > > will see effects such as a Coriolis force that are "induced"
> > >> > > from the rotating shell and that mimic rotation of the mass.

> > >> > I am not disagreeing with you, but I am confused. When you
> > >> > imagine a non-rotating spherical shell inside a rotating shell,
> > >> > how does the outside rotating shell "induce" coriolis effects
> > >> > on the non-rotating inner shell?

The general effect is called "gravitomagnetism." Just as a moving
electric charge produces a magnetic field, a moving mass produces a
gravitomagnetic field. If you look at the mathematics of the Coriolis
force, you'll see that it looks very similar to the math of a charge
moving in a magnetic field.

[...]

> Hopefully Steve was not referring to the Lense Thirring
> effect, as 39 milliarcseconds of frame-dragging is something I'm hard-
> pressed to explain any of the observed effects of Earth's rotation.

The Lense-Thirring effect is a particular cas of gravitomagnetism.
The effect measured by Gravity Probe B is extremely small, but that's
because we're only measuring the effect of the rotation of the Earth,
which by cosmological standards has a tiny mass and a very slow
rotation.

If you imagine the Earth at rest inside a rotating shell of matter, and
calculate the mass of the shell that it would take to induce the observed
Coriolis force, you find that it's roughly the same amount it would take
to "close the Universe," that is, to curl space into a three-dimensional
sphere. This is the right order of magnitude for the actual amount of
matter in the Universe (though I don't know whether "dark energy"
contributes).

Steve Carlip