| Topic: |
Science > Physics |
| User: |
"gsax" |
| Date: |
16 Jul 2005 04:38:01 AM |
| Object: |
Inertial frames of reference |
Hi
I am confused about "Inertial Frames of Reference" (IFR)..
While I was studying Special Theory of Relativity (STR), I understood
that an IFR is any frame that is moving with a uniform speed...
When I looked up General theory of Relativity (GTR), they say that any
frame of reference in Free Fall, is an IFR....
How come ? Since during free fall the frame is accelerating....so how
come it is an IFR..
Also coould someone please give me a real world example of an IFR?
thanks
Gsax
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| User: "Martin Hogbin" |
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| Title: Re: Inertial frames of reference |
16 Jul 2005 06:26:06 AM |
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"gsax" <gaurav_iitg@yahoo.com> wrote in message news:1121506681.598677.43510@f14g2000cwb.googlegroups.com...
Hi
I am confused about "Inertial Frames of Reference" (IFR)..
While I was studying Special Theory of Relativity (STR), I understood
that an IFR is any frame that is moving with a uniform speed...
When I looked up General theory of Relativity (GTR), they say that any
frame of reference in Free Fall, is an IFR....
How come ? Since during free fall the frame is accelerating....so how
come it is an IFR..
Also coould someone please give me a real world example of an IFR?
You have come across one of the important differences between SR
and GR. In SR all inertial frames are infinite in extent and in uniform
translatory (non-rotating) motion with respect to one another.
In GR inertial frames exist only locally and are free-fall frames.
Many modern SR text books use the GR definition of an inertial
frame. If you have no large masses to produce gravitation then
all non-rotating free-fall frames will be in uniform motion with respect
to one another.
An example of an inertial frame in both SR and GR would be a
non-rotating inertial frame in deep space and well away from
large masses.
Martin Hogbin
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| User: "" |
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| Title: Re: Inertial frames of reference |
16 Jul 2005 05:06:38 AM |
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To Gsax
You are not confused but I assure you that those who attempt to give
you the stamp of authority answer will be confused and all the bluffing
and blustering in the world can't hide their confusion.
Relativity is just an irritating extension and expansion of Newtonian
framehopping,whereas Newton just took a small step in invoking an
erroneous geocentric/heliocentric orbital equivalency,the early 20th
century concept took this all the way to homocentricity.
Newton's outlook is based on Flamsteed's rotation of the Earth to the
fixed stars in 23 hours 56 min 04 sec and relativists just change
this to rotation of the Earth to inertial space thereby setting up the
idea of observer with choices he does not have.
Rather than go down the road where these guys will ***** you to
death,why not just enjoy the faster Earth moving in an inner orbital
circuit overtaking the outer planets of Jupiter and Saturn which inturn
infers heliocentricity,in other words enjoying clestial motions on its
own terms ratther than being caught up in empirical jargon.
http://www.opencourse.info/astronomy/introduction/05.motion_planets/jupiter_saturn_retro.gif
Maybe even enjoy Galileo's explanation for the footage of the motion
of Saturn and Jupiter against the Earth's motion.
[Here Salviati explains Jupiter's motion, then follows with:]
Now what is said here of Jupiter is to be understood of Saturn and Mars
also. In Saturn these retrogressions are somewhat more frequent than in
Jupiter, because its motion is slower than Jupiter's, so that the Earth
overtakes it in a shorter time. In Mars they are rarer, its motion
being faster than that of Jupiter, so that the Earth spends more time
in catching up with it. Next, as to Venus and Mercury, whose circles
are included within that of the Earth, stoppings and retrograde motions
appear in them also, due not to any motion that really exists in them,
but to the annual motion of the Earth. This is acutely demonstrated by
Copernicus . . .
You see, gentlemen, with what ease and simplicity the annual motion --
if made by the Earth -- lends itself to supplying reasons for the
apparent anomalies which are observed in the movements of the five
planets. . . . It removes them all and reduces these movements to
equable and regular motions; and it was Nicholas Copernicus who first
clarified for us the reasons for this marvelous effect." 1632, Dialogue
Concerning the Two Chief World Systems
Then again,you will probably miss the magnificent point of Copernican
heliocentricity in infering an orbital center from the motions of the
Earth.
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| User: "Sam Wormley" |
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| Title: Re: Inertial frames of reference |
16 Jul 2005 07:20:07 AM |
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wrote:
To Gsax
You are not confused but I assure you that those who attempt to give
you the stamp of authority answer will be confused and all the bluffing
and blustering in the world can't hide their confusion.
Martin Hogbin gave a good answer.
+------------+ +---------------------------------------------+
| PLEASE | | BEST TO IGNORE ATTENTION SEEKING TROLLS |
| DO NOT | | LIKE KELLEHER -- THEY DRY |
| FEED | | UP AND BLOW AWAY WITHOUT FEEDBACK |
| DA | | |
| TROLLS | | http://www.angelfire.com/space/usenet/ |
+------------+ +---------------------------------------------+
| | | | | |
| | | | | |
| | | | | |
| | | | | |
| | | | | |
`\ '/ / ' / `\ '/ / ' / `\ '/ / ' /
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| User: "Too Many Kooks Spoil the Brothel" |
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| Title: Re: Inertial frames of reference |
16 Jul 2005 06:20:58 AM |
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gsax wrote:
Hi
I am confused about "Inertial Frames of Reference" (IFR)..
While I was studying Special Theory of Relativity (STR), I understood
that an IFR is any frame that is moving with a uniform speed...
When I looked up General theory of Relativity (GTR), they say that any
frame of reference in Free Fall, is an IFR....
How come ? Since during free fall the frame is accelerating....so how
come it is an IFR..
Also coould someone please give me a real world example of an IFR?
thanks
Gsax
In GR, you're accelerating when you're standing still. On the surface
of a planet (which most of us have done from time to time).
In the Equivalence Principle, free fall is (locally) the equivalent of
an inertial frame. Standin' on a planet is the equivalent of uniform
acceleration.
This simple insight gave Einstein the key to extending relativity
theory to explain gravity, and predict new phenomena ...
Come to think of it, the ONLY real-world examples of inertial frames
are freely-falling frames.
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| User: "vic" |
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| Title: Re: Inertial frames of reference |
17 Jul 2005 04:47:38 PM |
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Too Many Kooks Spoil the Brothel wrote:
gsax wrote:
Hi
I am confused about "Inertial Frames of Reference" (IFR)..
While I was studying Special Theory of Relativity (STR), I understood
that an IFR is any frame that is moving with a uniform speed...
When I looked up General theory of Relativity (GTR), they say that any
frame of reference in Free Fall, is an IFR....
How come ? Since during free fall the frame is accelerating....so how
come it is an IFR..
Also coould someone please give me a real world example of an IFR?
thanks
Gsax
In GR, you're accelerating when you're standing still. On the surface
of a planet (which most of us have done from time to time).
In the Equivalence Principle, free fall is (locally) the equivalent of
an inertial frame. Standin' on a planet is the equivalent of uniform
acceleration.
This simple insight gave Einstein the key to extending relativity
theory to explain gravity, and predict new phenomena ...
Come to think of it, the ONLY real-world examples of inertial frames
are freely-falling frames.
"freely-falling frames". !!?? you are a fokin fruitcake
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| User: "N:dlzc D:aol T:com \dlzc\ N: dlzc1 D:cox" |
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| Title: Re: Inertial frames of reference |
17 Jul 2005 06:10:16 PM |
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Dear vic:
"vic" <je93je@tokyo.com> wrote in message
news:1121636858.781817.259440@g14g2000cwa.googlegroups.com...
Too Many Kooks Spoil the Brothel wrote:
....
Come to think of it, the ONLY real-world
examples of inertial frames are freely-falling
frames.
"freely-falling frames". !!?? you are a fokin fruitcake
To translate out of GRese, this means "frames in orbit". If that
helps.
David A. Smith
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| User: "Too Many Kooks Spoil the Brothel" |
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| Title: Re: Inertial frames of reference |
21 Jul 2005 05:30:50 AM |
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vic wrote:
Too Many Kooks Spoil the Brothel wrote:
gsax wrote:
Hi
I am confused about "Inertial Frames of Reference" (IFR)..
While I was studying Special Theory of Relativity (STR), I understood
that an IFR is any frame that is moving with a uniform speed...
When I looked up General theory of Relativity (GTR), they say that any
frame of reference in Free Fall, is an IFR....
How come ? Since during free fall the frame is accelerating....so how
come it is an IFR..
Also coould someone please give me a real world example of an IFR?
thanks
Gsax
In GR, you're accelerating when you're standing still. On the surface
of a planet (which most of us have done from time to time).
In the Equivalence Principle, free fall is (locally) the equivalent of
an inertial frame. Standin' on a planet is the equivalent of uniform
acceleration.
This simple insight gave Einstein the key to extending relativity
theory to explain gravity, and predict new phenomena ...
Come to think of it, the ONLY real-world examples of inertial frames
are freely-falling frames.
"freely-falling frames". !!?? you are a fokin fruitcake
I TRIED fokin one once, but I ain't never been one!
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| User: "Ben Rudiak-Gould" |
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| Title: Re: Inertial frames of reference |
16 Jul 2005 01:29:21 PM |
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gsax wrote:
I am confused about "Inertial Frames of Reference" (IFR)..
While I was studying Special Theory of Relativity (STR), I understood
that an IFR is any frame that is moving with a uniform speed...
When I looked up General theory of Relativity (GTR), they say that any
frame of reference in Free Fall, is an IFR....
Operationally, an inertial frame is one defined by a collection of
accelerometers (attached to the clocks) which all read "0".
The point of the GTR approach is that if you're in free-fall, the
accelerometers, no matter what their physical design, will all read zero
(approximately, or exactly in an appropriate limit). This is because gravity
accelerates everything equally. So even though you're "really" accelerating,
there's no way to tell that you are. This is a lot like not being able to
tell that you're "really" moving with respect to the aether: why not try
formulating a theory without the extraneous concept? That was the idea that
originally led Einstein to GTR (and the one he famously called "the happiest
thought of my life").
-- Ben
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| User: "Tom Roberts" |
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| Title: Re: Inertial frames of reference |
17 Jul 2005 08:10:52 PM |
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gsax wrote:
I am confused about "Inertial Frames of Reference" (IFR)..
While I was studying Special Theory of Relativity (STR), I understood
that an IFR is any frame that is moving with a uniform speed...
That is not sufficient to define an IFR in SR -- speed relative to what?
The usual definition in SR is that an inertial frame is one in which
Newton's laws hold good to first order in v/c for the speed v of any
object of interest. In particular, his first law implies that any free
object moves in a uniform straight line relative to any inertial frame.
When I looked up General theory of Relativity (GTR), they say that any
frame of reference in Free Fall, is an IFR....
In GR there are no IFRs in the sense of SR. In SR each IFR extends to
infinity in all directions (including time). In GR that is not possible.
In actuality, a SMALL frame of reference in freefall is APPROXIMATELY
inertial in GR. Here "small" and the accuracy of the approximation
depend on both the size of the region in which the frame is to be used,
and on the curvature of spacetime throughout that region. The smaller
the frame, and the weaker the curvature in its region, the more accurate
this approximation.
On the surface of the earth, for instance, assuming the surface is
inertial is a terrible assumption for tracking a thrown baseball; but it
is quite accurate for describing the elementary particle collisions in a
high-energy accelerator. The main difference is in the duration of the
observation -- for the baseball several seconds, for the particles
several nanoseconds.
Exercise: using a Newtonian approximation, how far does a
truly-inertial frame fall during a particle measurement
that lasts 20 nanoseconds? How far does it fall for a
baseball measurement lasting 3 seconds? In both cases start
with a frame at rest relative to the measurement.
Hint: use the formula h = 1/2 g t^2, with g = 9.8 m/sec^2.
How come ? Since during free fall the frame is accelerating....so how
come it is an IFR..
"Acceleration" has several meanings in GR. You are thinking of
"coordinate acceleration", which is the only meaning the word has in SR.
You are implicitly thinking that the local rest frame of that baseball
is accelerating relative to the surface of the earth -- and it is. But
the coordinates of that surface frame are themselves being accelerated,
not the baseball (ignoring air resistance).
In GR, gravitation is not a force, it is a geometrical property of the
manifold. The best generalization in GR of "acceleration" in SR is the
4-acceleration in GR. For an object in freefall (e.g. that baseball
without air), the 4-acceleration is zero; for an object at rest on the
surface of the earth its 4-acceleration is nonzero (it points UP, and is
due to the force of contact with the surface).
So in GR the baseball frame is "not accelerating" (i.e. has zero
4-acceleration), while the earth surface frame is "accelerating" (has
nonzero 4-acceleration).
Also coould someone please give me a real world example of an IFR?
Consider the space station: inside it one can construct Cartesian
coordinates, and to high accuracy free objects move in uniform straight
lines inside its walls. This is not perfect, however, and is not truly
"zero gravity", it is properly called microgravity (measurements of
acceleration due to gravity are indeed about a million times smaller
than on the surface of the earth -- unobservably small for thrown
objects but accessible to careful measurements).
Just think about it: all free objects in the station are
actually orbiting the earth with the station, and therefore
follow elliptical paths with the earth at one focus. Ditto
for the station's center-of-gravity. So a baseball above the
stations c-o-g is on a slightly different ellipse than the
c-o-g itself. But both ellipses have sizes that are thousands
of kilometers long, and the interior of the station restricts
you to measuring only a few meters of their paths; without
extremely good measurements you cannot distinguish the
difference, and the path of the baseball looks like a uniform
straight line, even for quite slow throws that on earth would
appear to be simply dropped. If you could measure the
baseball's path with a precision far better than is practical
you could detect it is not really a straight line.
[Note in practice the air inside the space station is quite
important; I'm ignoring it here.]
But it need not be so exotic: when you jump off a high diving platform,
except for air resistance you are in freefall, and therefore are at rest
in a locally-inertial frame. [But again, the air is rather important --
c.f. skydiving which is just a much higher platform.]
Tom Roberts tjroberts@lucent.com
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| User: "Schoenfeld" |
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| Title: Re: Inertial frames of reference |
18 Jul 2005 12:07:48 AM |
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Tom Roberts wrote:
[snip]
zeta function, rather.
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| User: "Schoenfeld" |
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| Title: Re: Inertial frames of reference |
18 Jul 2005 11:06:12 AM |
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Schoenfeld wrote:
Tom Roberts wrote:
[snip]
zeta function, rather.
This was a correction to a previous reply, which google groups failed
to post.
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