| Topic: |
Science > Physics |
| User: |
"" |
| Date: |
18 Mar 2007 10:09:18 PM |
| Object: |
Relativity Question |
I've probably got something basically wrong with the General
Relativity ideas, as they lead me to a contradiction. for example, I
understood that it states that any coordinates system is legitimate,
i.e. any observer can decide he's the center of the universe and
measure all particles' locations and velocities relative to himself -
even observers who have relative acceleration (contrary to Special
Relativity). So let's assume we on earth decide that the sun revolves
around us - but that can be refuted, as Kepler's third law states that
the retio T^2/R^3 of the orbit depends on the mass of the orbited
body, and of course this ratio is the same whether looking from the
sun or from the earth. So it can be prooved that we revolve around the
sun and not vice versa (Relativity doesn't change Kepler's law so
much, does it?).
Another Relativity question I came upon years ago, and I'm sure
bothers a lot: if I have two static charges, say at coordinates
(0,0,0) and (0,1,0), I have an electric force. Now assume another
ovserver who moves at a constant velocity (in the x axis) - he'll see
these two charges as moving, adding a magnetic force, resulting in a
different total force (and a different acceleration of the charges,
which can be measured). That's because the electric force is the same
(as the observer's velocity doesn't change the charges nor their
distance, as it's on the x axis) and the magnetic force depends on its
own velocity relative to the charges. In Classic Physics we could
solve this by assuming an absolute space, but of course in Special
Relativity this is unacceptable (and the observer's velocity can be
non-relativistic, so the answer isn't here).
Any one can help me with these? thanks a lot in advance.
.
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| User: "Ben Rudiak-Gould" |
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| Title: Re: Relativity Question |
19 Mar 2007 10:27:56 AM |
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wrote:
I've probably got something basically wrong with the General
Relativity ideas, as they lead me to a contradiction. for example, I
understood that it states that any coordinates system is legitimate,
This is really a content-free statement by itself; it's like saying that the
laws of physics are independent of which units you use (feet versus meters).
You /can/ say that an object dropped near the earth's surface has fallen a
distance of 16 t^2 after time t, which is true in imperial units but not in
metric; but if you follow the rules for keeping track of units, any physical
law you write down will automatically work in any units. It's the same with
coordinates, except that the rules aren't usually taught and used until the
graduate level.
What makes general relativity special (no pun intended) is that the
mathematical machinery you need for keeping track of coordinates is the same
machinery you need for keeping track of the gravitational field. This is
sometimes true in Newtonian gravity: if your coordinate system is
accelerating but not rotating, you can say that the fictitious force is
actually a gravitational force arising from a uniform gravitational
potential gradient through the system. This doesn't work for rotating
coordinates, though, because there's a velocity-dependent force in that
case. In general relativity, it works in the rotating case and in all other
cases. But the gravitational field is more general than that -- it also
includes field configurations that can't arise from any change of
coordinates, and these can be described in a coordinate-independent absolute
way. Einstein was very keen on the fictitious-force side of general
relativity in the early days, but the modern perspective is that the
important part of the theory is that part that doesn't depend on your choice
of coordinates. So a modern physicist would say that, yes, the earth really
is circling the sun and not the other way around, based on the absolute
curvature of spacetime. Einstein would probably have said that you can just
as well say the sun is circling the earth, but to make that work you have to
introduce extra gravitational effects of unclear meaning and origin (they're
coordinate-dependent and don't arise from the presence of matter).
Another Relativity question I came upon years ago, and I'm sure
bothers a lot: if I have two static charges, say at coordinates
(0,0,0) and (0,1,0), I have an electric force. Now assume another
ovserver who moves at a constant velocity (in the x axis) - he'll see
these two charges as moving, adding a magnetic force, resulting in a
different total force (and a different acceleration of the charges,
which can be measured).
Yes, the total force is different by a factor of sqrt(1 - (v/c)^2), which is
the time dilation factor. So the magnetic field is necessary for consistency
with special relativity. In fact you can derive all of the properties of the
magnetic field this way, by starting with the static electric field and then
considering what extra forces are needed to make it consistent.
-- Ben
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| User: "" |
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| Title: Re: Relativity Question |
21 Mar 2007 07:31:35 PM |
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On Mar 19, 5:27 pm, Ben Rudiak-Gould <br276delet...@cam.ac.uk> wrote:
.... So a modern physicist would say that, yes, the earth really
is circling the sun and not the other way around, based on the absolute
curvature of spacetime. Einstein would probably have said that you can just
as well say the sun is circling the earth, but to make that work you have to
introduce extra gravitational effects of unclear meaning and origin (they're
coordinate-dependent and don't arise from the presence of matter).
Okay, that's vagually what I wanted to say: From the so-called
Einstein point of view, you'd have to add a gravity field to make the
sun look like it rotates the earth. If I got it correctly, this field
would be centered at the earth and would mimick a sun-massed body,
thus making the sun rotate with the correct T^2/R^3 ratio. But we on
earth don't actually feel such a field (we're not attracted to the
earth so strongly). What did I get incorrect this time?
AnotherRelativityquestionI came upon years ago, and I'm sure
bothers a lot: if I have two static charges, say at coordinates
(0,0,0) and (0,1,0), I have an electric force. Now assume another
ovserver who moves at a constant velocity (in the x axis) - he'll see
these two charges as moving, adding a magnetic force, resulting in a
different total force (and a different acceleration of the charges,
which can be measured).
Yes, the total force is different by a factor of sqrt(1 - (v/c)^2), which is
the time dilation factor. So the magnetic field is necessary for consistency
with specialrelativity. In fact you can derive all of the properties of the
magnetic field this way, by starting with the static electric field and then
considering what extra forces are needed to make it consistent.
Oh, no. If v is small enough, your sqrt would be negligible, while
the magnetic force isn't. So let's look at an even better example:
assume an infinite wire along the x-axis along which a current I
flows, and a (stationary) charge at (0,1,0). It would feel no force,
as the wire is electrically neutral (no electric force) and the charge
is stationary (no magnetic one). Now consider an abserver which moves
at speed v in the x direction - he'll see the charge moving, meaning a
magnetic force will be present and the charge would acceletate in the
y axis, while no such acceleration was in the former force-free
coordinates system (the moving observer would see no static electric
field to start with. Also assume v is non-relativistic). What did I
get wrong THIS time? it's a nice paradox I have here.
Thanks a lot for your previous answer.
-- Ben
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| User: "Sam Wormley" |
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| Title: Re: Relativity Question |
18 Mar 2007 11:19:19 PM |
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wrote:
I've probably got something basically wrong with the General
Relativity ideas, as they lead me to a contradiction. for example, I
understood that it states that any coordinates system is legitimate,
i.e. any observer can decide he's the center of the universe and
measure all particles' locations and velocities relative to himself -
even observers who have relative acceleration (contrary to Special
Relativity). So let's assume we on earth decide that the sun revolves
around us - but that can be refuted, as Kepler's third law states that
the retio T^2/R^3 of the orbit depends on the mass of the orbited
body, and of course this ratio is the same whether looking from the
sun or from the earth. So it can be prooved that we revolve around the
sun and not vice versa (Relativity doesn't change Kepler's law so
much, does it?).
Another Relativity question I came upon years ago, and I'm sure
bothers a lot: if I have two static charges, say at coordinates
(0,0,0) and (0,1,0), I have an electric force. Now assume another
ovserver who moves at a constant velocity (in the x axis) - he'll see
these two charges as moving, adding a magnetic force, resulting in a
different total force (and a different acceleration of the charges,
which can be measured). That's because the electric force is the same
(as the observer's velocity doesn't change the charges nor their
distance, as it's on the x axis) and the magnetic force depends on its
own velocity relative to the charges. In Classic Physics we could
solve this by assuming an absolute space, but of course in Special
Relativity this is unacceptable (and the observer's velocity can be
non-relativistic, so the answer isn't here).
Any one can help me with these? thanks a lot in advance.
These questions aren't particularly related to relativity, but more
good old Newtonian Mechanics.
When wo bodies (say the sun and the earth) orbit each other, they
are in Keplerian orbit around there common center of mass (baricenter)
o aberration of starlight - is sufficient evidence the earth orbits
the sun
http://scienceworld.wolfram.com/physics/StellarAberration.html
o Foucault pendulum - is sufficient evidence the earth spins on
is axis
http://scienceworld.wolfram.com/physics/FoucaultPendulum.html
o observation of the planetary orbits and using Kepler's third law
on couls estimate the mass of the sun... similarly one can estimate
the mass of the earth by observing earth satellites.
Orbital velocity = (GM/r)^0.5 and one can solve for M assuming the
mass of the orbiting object, m << M, the mass of the object being
orbited.
Also look at these:
No Center
http://www.astro.ucla.edu/~wright/nocenter.html
http://www.astro.ucla.edu/~wright/infpoint.html
Also see Ned Wright's Cosmology Tutorial
http://www.astro.ucla.edu/~wright/cosmolog.htm
http://www.astro.ucla.edu/~wright/cosmology_faq.html
WMAP: Foundations of the Big Bang theory
http://map.gsfc.nasa.gov/m_uni.html
WMAP: Tests of Big Bang Cosmology
http://map.gsfc.nasa.gov/m_uni/uni_101bbtest.html
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