| Topic: |
Science > Physics |
| User: |
"Fred Chen" |
| Date: |
27 Mar 2005 02:05:42 AM |
| Object: |
How inertial to be an inertial reference frame? |
I was always uneasy about the definition a la Mach of an inertial
reference frame as "not accelerating with reference to the distant
stars".
Clearly we know that astronomical objects do not fit in inertial
reference frames even with respect to one another. The Earth rotates on
its axis as it orbits around the Sun, the Sun orbits the Milky Way
center, etc. Yet we have no qualms applying inertial reference frame
special relativity treatments to objects in these frames.
All objects on Earth are automatically in a rotating (hence
accelerating) reference frame.
Perhaps then there is no pure absolute definition of "inertial
reference frame", but merely a practical concept. Still not that
reassuring.
Fred
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| User: "Bilge" |
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| Title: Re: How inertial to be an inertial reference frame? |
27 Mar 2005 05:17:32 AM |
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Fred Chen:
I was always uneasy about the definition a la Mach of an inertial
reference frame as "not accelerating with reference to the distant
stars".
Clearly we know that astronomical objects do not fit in inertial
reference frames even with respect to one another. The Earth rotates on
its axis as it orbits around the Sun, the Sun orbits the Milky Way
center, etc. Yet we have no qualms applying inertial reference frame
special relativity treatments to objects in these frames.
All objects on Earth are automatically in a rotating (hence
accelerating) reference frame.
Perhaps then there is no pure absolute definition of "inertial
reference frame", but merely a practical concept. Still not that
reassuring.
In general relativity, there are no inertial frames, so inertial
frames only exist to the extent that such an approximation is useful.
Such approximations are often useful and hold very well for quite
large accelerations if one treats an accelerated object as instantan-
eously inertial at every point along its world line.
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| User: "Bill Hobba" |
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| Title: Re: How inertial to be an inertial reference frame? |
27 Mar 2005 06:28:25 AM |
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"Fred Chen" <flipsu5@comcast.net> wrote in message
news:1111910742.861412.112060@l41g2000cwc.googlegroups.com...
I was always uneasy about the definition a la Mach of an inertial
reference frame as "not accelerating with reference to the distant
stars".
Clearly we know that astronomical objects do not fit in inertial
reference frames even with respect to one another. The Earth rotates on
its axis as it orbits around the Sun, the Sun orbits the Milky Way
center, etc. Yet we have no qualms applying inertial reference frame
special relativity treatments to objects in these frames.
All objects on Earth are automatically in a rotating (hence
accelerating) reference frame.
Perhaps then there is no pure absolute definition of "inertial
reference frame", but merely a practical concept. Still not that
reassuring.
I like the definition by Landau in Mechanics. It is a frame that is
homogeneous in space and time an isotropic in space. That puts the emphasis
where I believe it really belongs - on the symmetry properties of such a
frame.
Thanks
Bill
Fred
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| User: "Ben Bean" |
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| Title: Re: How inertial to be an inertial reference frame? |
27 Mar 2005 09:32:58 PM |
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"Fred Chen" <flipsu5@comcast.net> wrote in message
news:1111910742.861412.112060@l41g2000cwc.googlegroups.com...
I was always uneasy about the definition a la Mach of an inertial
reference frame as "not accelerating with reference to the distant
stars".
[...]
Perhaps then there is no pure absolute definition of "inertial
reference frame", but merely a practical concept. Still not that
reassuring.
Fred
I agree with you 100% Fred on that last thought. Clearly, there are no true
inertial frames actually found in Nature... it is a hypothetical concept
only, an imaginary vantage which is not acted upon by *any* external forces
whatsoever. Yet gravity is everywhere, so alas.
But because the math of Relativity is so mild in the less extreme venues, we
do wind up using approximations and treating them as if they deviate
negligibly from actual inertial frames.
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| User: "Tom Roberts" |
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| Title: Re: How inertial to be an inertial reference frame? |
27 Mar 2005 10:21:36 PM |
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Fred Chen wrote:
I was always uneasy about the definition a la Mach of an inertial
reference frame as "not accelerating with reference to the distant
stars".
As with most statements attributed to Mach, that is too nebulous for any
real use. In particular, there _are_ no "fixed stars" (a phrase commonly
used in this context). And the "distant stars" do not form a "reference
system" in any recognizable sense (they move with respect to each
other). Moreover, the visible "distant stars" are mostly in our own
galaxy, which is known to be rotating....
Moreover, since 1915 or so we have a clear and obvious way out of your
dilemma -- use GR, in which "inertial reference frame" is reduced to
only local usage and meaning. It is quite clear that there is no such
thing as an "inertial frame which covers the universe", and the approach
of GR fits well with such observations.
Clearly we know that astronomical objects do not fit in inertial
reference frames even with respect to one another. The Earth rotates on
its axis as it orbits around the Sun, the Sun orbits the Milky Way
center, etc. Yet we have no qualms applying inertial reference frame
special relativity treatments to objects in these frames.
This is, of course, an APPROXIMATION. For instance, in most tabletop
optical experiments performed in a laboratory on earth, one can analyze
the system using SR, because during the transit time of the light beams
the non-inertial motions of the lab are negligible. [some systems, like
fiber-optic gyroscopes, must be analyzed taking into account the
rotation of the earth.]
All objects on Earth are automatically in a rotating (hence
accelerating) reference frame.
Yes. And if they are at rest on the surface they are also accelerating
upward relative to any locally-inertial frame (in the GR sense). But
still, for many experiments (e.g. tabletop optics, high-energy particle
collisions, ...) the "lab frame" is so accurately inertial that using SR
is no problem.
Perhaps then there is no pure absolute definition of "inertial
reference frame", but merely a practical concept. Still not that
reassuring.
In the light of GR this is the best one can hope for. Live with it.
Nature has no need for human "reassurance"....
Tom Roberts tjoberts@lucent.com
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| User: "Ben Rudiak-Gould" |
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| Title: Re: How inertial to be an inertial reference frame? |
30 Mar 2005 07:43:06 AM |
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Fred Chen wrote:
Perhaps then there is no pure absolute definition of "inertial
reference frame", but merely a practical concept. Still not that
reassuring.
Well, it's both. There's a theoretical notion of inertial frame which is
precise and exact, and an empirical notion which is imprecise and
provisional. The theory is supposed to approximate the reality, but often it
feels like it's the other way around...
-- Ben
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| User: "Tom Roberts" |
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| Title: Re: How inertial to be an inertial reference frame? |
30 Mar 2005 07:03:42 PM |
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Ben Rudiak-Gould wrote:
There's a theoretical notion of inertial frame which is
precise and exact,
Nope. The inability to define such a global inertial frame was one of
the primary reasons Einstein embarked on the path from SR to GR.
There are frames (coordinates) that are _approximately_ inertial in a
local region....
and an empirical notion which is imprecise and
provisional. The theory is supposed to approximate the reality, but
often it feels like it's the other way around...
Theories are "pure" but the real world always has warts. From a
theoretical standpoint, this is at base the difference between equations
of motion and initial conditions....
Tom Roberts tjroberts@lucent.com
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| User: "Nick" |
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| Title: Re: How inertial to be an inertial reference frame? |
27 Mar 2005 02:07:46 AM |
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Not accelerating except in gravity.
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| User: "Fred Chen" |
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| Title: Re: How inertial to be an inertial reference frame? |
27 Mar 2005 02:34:24 AM |
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Nick wrote:
Not accelerating except in gravity.
Could this be an explanation:
http://www.seop.leeds.ac.uk/entries/spacetime-iframes/
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| User: "Nick" |
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| Title: Re: How inertial to be an inertial reference frame? |
27 Mar 2005 02:43:54 AM |
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I think weightless frames are inertial. So nonuniform
motion in freefall qualifies. Thats all I can tell you Fred.
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