(May 4, 2015 at 6:44 am)Rhondazvous Wrote: The story line is that the guy made the daylight last longer by praying for the sun and the moon to stand still. This gives credence to the idea that the sun and moon revolve around the Earth, which is exactly how the cosmos would look to an Earth-bound naked eye.  The deity had a perfect opportunity to demonstrate his divine omniscience and he blew it.

The church has known for over 500 years that the biblical creation story bears not the slightest resemblance to the universe we live in. Yet, the Christian lie persists because there are too many people making too much money to let it die.

I have already come to terms with the fact that even if science ever finds a way to undisputedly prove that god does not exist, people everywhere will still follow religion and make excuses. I can see it now…between the outright denials and the claims that god is simply testing us.

(May 3, 2015 at 6:16 pm)Alex K Wrote:

(May 3, 2015 at 5:46 pm)IATIA Wrote: Just call me "No one".  The sun cannot stand still.

Wait, aren't we talking earth standing still here? 

Of course, but consider to whom I am responding.

(May 3, 2015 at 9:36 pm)Rhondazvous Wrote: I find that people who don't believe the Bible know a lot more about it and about Christian history than those who do believe it.

I would refine your statement by dividing the believers into two groups: the "thinking" and the "ignorant." You can see the handiwork of the "ignorant" on Conservapedia. For a glimpse at how the "thinking" view things, see The New Oxford Annotated Bible, Augmented 3rd ed., Oxford U. Press, 2007. While mostly Christians, the editors don't have to buy a literal Moses authorship of the Pentateuch and they well realize that Joshua and his motionless sun & mood are a legend. They provide notes on the structure and redaction of biblical texts, and how the texts fit in with the Hebrew culture as far as this can be known.

(May 3, 2015 at 10:14 pm)Jenny A Wrote:

(May 3, 2015 at 8:18 pm)Jörmungandr Wrote: Actually, if you rotate the rest of the solar system around the earth's axis of rotation, it could be made to appear as if the sun stood still without stopping the rotation of the earth.

...the solar system would have to travel awful fast to make the trip.  [T]hat would have the sun traveling at a little over 3% of the speed of light.  Should the sun travel around us, we'd fall in.

This gets into the complicated issue of reference frames. In physics all motion is relative, so it doesn't matter whether you think of a rotating earth in a stationary reference frame or a stationary earth in a rotating reference frame. In either of these frames the relative speed of sun and earth is simply the 30 km/sec we expect from the earth's orbital situation. The only thing that's going 3% of the speed of light is the imaginary axes of the rotating frame at that distance. If you extend them out far enough, they appear to go faster than light in violation of Einstein's Special Relativity.

James Callaghan explains in The Geometry of Spacetime: An Introduction to Special & General Relativity (Springer, 2000,  §4.1, pp. 152-153): There are equations that convert coordinates between the stationary and rotating frames. Rulers measuring length in the transverse direction are foreshortened by a Lorentz transformation when converting. This eliminates the huge apparent speeds.

As far as the orbital motion goes, again it doesn't matter which body moves around which: it's relative motion that counts, and  earth is in free fall in either case. The orbit is a conic section, for earth a nearly circular ellipse. As long as we have that 30 km/sec transverse component, we don't fall straight into the sun.

Feel free to correct me on any of these matters if I'm wrong; I'm not expert at this stuff.  

(May 4, 2015 at 2:11 am)Alex K Wrote: I think we should all agree that I am not a cutting edge lactating bull sitter...

Lacerating? Or milk?  

Other News: Now that the banno button has been pushed, the thread and its slavery will die. However we do have our own forms of exploiting human labor which have replaced slavery. We buy computers assembled by workers in poor countries who make $1 an hour and get no healthcare. While people in an employment relationship are technically free to go, in practice they may find it difficult to do so as they are dependent on steady wages and cognizant that any who quit jobs or complain about working conditions won't get the good references they need. I agree we've progressed beyond slavery, but that has little to do with our high and mighty morals showing up much better than those of ancient peoples. We have an industrial economy that obviates the need for slave labor, and the development of this economy, not compassion, was what led to slavery's abolition.

(May 4, 2015 at 11:17 am)Hatshepsut Wrote:

(May 3, 2015 at 10:14 pm)Jenny A Wrote: ...the solar system would have to travel awful fast to make the trip.  [T]hat would have the sun traveling at a little over 3% of the speed of light.  Should the sun travel around us, we'd fall in.

This gets into the complicated issue of reference frames. In physics all motion is relative, so it doesn't matter whether you think of a rotating earth in a stationary reference frame or a stationary earth in a rotating reference frame. In either of these frames the relative speed of sun and earth is simply the 30 km/sec we expect from the earth's orbital situation. The only thing that's going 3% of the speed of light is the imaginary axes of the rotating frame at that distance. If you extend them out far enough, they appear to go faster than light in violation of Einstein's Special Relativity.

James Callaghan explains in The Geometry of Spacetime: An Introduction to Special & General Relativity (Springer, 2000,  §4.1, pp. 152-153): There are equations that convert coordinates between the stationary and rotating frames. Rulers measuring length in the transverse direction are foreshortened by a Lorentz transformation when converting. This eliminates the huge apparent speeds.

As far as the orbital motion goes, again it doesn't matter which body moves around which: it's relative motion that counts, and  earth is in free fall in either case. The orbit is a conic section, for earth a nearly circular ellipse. As long as we have that 30 km/sec transverse component, we don't fall straight into the sun.

Feel free to correct me on any of these matters if I'm wrong; I'm not expert at this stuff.  

Yes, what you say sounds all correct (although I didn't check the numbers), and the question what it means to be stationary is really subtle in General Relativity. One can indeed easily go to a spacetime-dependent reference frame in which the earth is fixed at a certain coordinate position while the sun rotates around it. This is allowed in GR because it is set up to be completely coordinate-choice independent by design.
If you make this coordinate change, the transformation of the metric tensor into the geostationary rotating reference frame causes the introduction of large nonvanishing Christoffel connections which introduce "gravitational forces" pulling the entire universe towards the earth such that it rotates around earth once every 24 hours. This metric grows without bounds as one goes further and further away from the solar system. At the end of the day, the coordinate system which is special from a purely mathematical perspective is the one where the metric does not diverge as one goes away from earth, and this is more or less the same as a Newtonian inertial frame where the Galaxy is unaccelerated and slowly rotates.

One can do the analogous thing in Newtonian physics and choose a rotating reference frame. The only difference to GR is that one has to live with a change of the mathematical laws, in the form of new coriolis and centrifugal forces. In this case, we have a unique notion which systems are special, namely those in which the newtonian laws have the simplest form and all pseudo forces vanish. The eerie aspect of GR is, as I said, that it is not immediately obvious from the equations which frame is "correct". Einstein fought a lot with the problem of coordinate invariance exactly 100 years ago, and he was afraid that his theory didn't make any predictions because of the huge freedom (His "hole problem"). Fortunately, he figured out how to extract physical information despite the coordinate freedom.

Quote:

(May 4, 2015 at 2:11 am)Alex K Wrote: I think we should all agree that I am not a cutting edge lactating bull sitter...

Lacerating? Or milk?  

You underestimate my potential for bad and/or nonsensical jokes.

(May 4, 2015 at 11:40 am)Alex K Wrote: .... and the question what it means to be stationary is really subtle in General Relativity. One can indeed easily go to a spacetime-dependent reference frame in which the earth is fixed at a certain coordinate position while the sun rotates around it. This is allowed in GR because it is set up to be completely coordinate-choice independent by design.

If you make this coordinate change, the transformation of the metric tensor into the geostationary rotating reference frame causes the introduction of large nonvanishing Christoffel connections which introduce "gravitational forces" pulling the entire universe towards the earth such that it rotates around earth once every 24 hours...

Fortunately the chapter of Callaghan's book I consulted is only SR, not GR. I don't know differential geometry or tensor calculus and thus cannot read GR with understanding. I can barely do the SR chapters for that matter, which are written mostly at an introductory calculus level. What baffles me a little is that you can do a rotating reference frame in SR even though SR doesn't allow any problems that involve accelerated motion or gravity. I take that's because the problem was just kinematic, without involving mass or force.

I would recommend Callaghan, though. His writing style is clear, with lengthy explanations to aid in understanding and more steps shown in the math than usual for this kind of book.

(May 4, 2015 at 1:45 pm)Hatshepsut Wrote:

(May 4, 2015 at 11:40 am)Alex K Wrote: .... and the question what it means to be stationary is really subtle in General Relativity. One can indeed easily go to a spacetime-dependent reference frame in which the earth is fixed at a certain coordinate position while the sun rotates around it. This is allowed in GR because it is set up to be completely coordinate-choice independent by design.

If you make this coordinate change, the transformation of the metric tensor into the geostationary rotating reference frame causes the introduction of large nonvanishing Christoffel connections which introduce "gravitational forces" pulling the entire universe towards the earth such that it rotates around earth once every 24 hours...

Fortunately the chapter of Callaghan's book I consulted is only SR, not GR. I don't know differential geometry or tensor calculus and thus cannot read GR with understanding. I can barely do the SR chapters for that matter, which are written mostly at an introductory calculus level. What baffles me a little is that you can do a rotating reference frame in SR even though SR doesn't allow any problems that involve accelerated motion or gravity. I take that's because the problem was just kinematic, without involving mass or force.

I would recommend Callaghan, though. His writing style is clear, with lengthy explanations to aid in understanding and more steps shown in the math than usual for this kind of book.

You can do a rotating reference frame in SR, but you have to introduce some of the differential geometry machinery of GR in order to pull it off correctly. The difference between SR and GR is then that there is no true spatial curvature and you start out with a minkowskian metric where the line element is simply ds^2 = dt^2 - dx^2 - dy^2 - dz^2. But when you go to a moving frame from there, you have to transform the metric to something more complicated and use riemannian geometry even if it's just SR. Otherwise I wouldn't know how one would correctly take the new coordinates into account.

Quote:We buy computers assembled by workers in poor countries who make $1 an hour and get no healthcare.

Yeah...what the republicunts and their rich leash holders want for the USA.

(May 4, 2015 at 2:11 am)Alex K Wrote: I think we should all agree that I am not a cutting edge lactating bull sitter. But I have other qualities.

Although you may have other qualities, I do not agree that you are not a cutting edge lactating bull sitter.  I have not seen any proof of this!  Do you expect us to just take your word for it?

(May 4, 2015 at 7:55 pm)Pyrrho Wrote:

(May 4, 2015 at 2:11 am)Alex K Wrote: I think we should all agree that I am not a cutting edge lactating bull sitter. But I have other qualities.

Although you may have other qualities, I do not agree that you are not a cutting edge lactating bull sitter.  I have not seen any proof of this!  Do you expect us to just take your word for it?

He's actually  putting a ledge in for a dull splitter.

(May 4, 2015 at 5:29 pm)Alex K Wrote: ...use riemannian geometry even  if it's just SR. Otherwise I wouldn't know how one would correctly take the new coordinates into account.

I dare not clog the forum. Callaghan considers a special case. The non-rotating frame is presumed inertial. The two observers coincide in space and have no linear motion relative to one another. The rotation is uniform about the x-axis. The only world line tracked belongs to a point that remains stationary in the rotating frame. In this case, Callaghan just applied the classical rotation matrix to change the two space coordinates and a separate equation, T(t) = t * sqrt(1 - w^2*r^2/c^2) to find the proper time T on the world line, which is a helix in the non-rotating frame. It was simple because the point's radial distance r, common to both observers, and the  rotating frame's angular rate w are constant. I can see this won't work if the point begins moving about. But I admit I'm in pretty heavy seas with this kind of stuff.  

Nonetheless, though the point is stationary in the rotating frame, it's clock is slower relative to both observers the greater r is. Callagan also noted that the rotating frame has a boundary: it only covers events inside the cylinder of radius c/w centered on the x-axis. I agree it's a non-interesting situation: all this to describe a stationary dot as seen by two people, one of whom is dizzy!