No, certainly not.
It means blurting out without understanding the significance, or following something mindlessly.
Photon Propagation : Straightline or Helix ?
- Thread starter The God
- Start date
No, certainly not.
It means blurting out without understanding the significance, or following something mindlessly.
He along with all others though, are able to see though you.
And all that I have said is pretty well correct I might add.
You need to accept that whatever frame of reference you chose, all objects are trying to follow the straightest path possible, while under the influence of gravity.
It appears exchemist is correct.
As has been told to you a few times now, [parrotised if you wish, but factual none the less] everything will try and move in a straight line, unless acted on by forces, or the curved/warped/twisted nature of spacetime, which we call gravity.
Which part of that do you have a problem with?
So you are talking about gravitational phenomena. Let's talk about helicies. If you have a 3-D Euclidean world then a right helix about the z-axis satisfies equations:
$$ x x' + y y' = 0, x y'' - x'' y = 0, z'' = 0 $$
If we substitute $$x = R \cos ( \theta ) , y = R \sin ( \theta ) $$ we get the simpler form: $$ R R' = 0, 2 R R' \theta' + R^2 \theta'' = 0, z'' = 0$$ or for finite R, $$ R' = 0, \theta'' = 0, z'' = 0$$. But if instead of 3-D Euclidean space, we have a 2-dimensional cylindrical world where $$R = 1$$ then the equation $$\theta'' = 0, z'' = 0$$ is the equation of a straightest possible line in such a cylindrical world. If you slice the cylinder and flatten it out in a way that preserves distances in the sheet, those will be normal straight Euclidean line segments.
We can't flatten out a sphere without distorting distances, but in the limit of a small neighborhood we can flatten out the neighborhood of a great circle and show that it is the straightest possible line.
GR is such a theory that light and satellites and planets trace out the trajectories of the straightest possible lines in complexly curved four-dimensional space-time. So your "observer" is not entitled to describe the motion of the Earth in just any coordinate system and declare the motion is not the straightest possible line. He has to know something about the geometry of the four-dimensional space-time to know what the definition of straight is.
If your observer is intent on applying his own local definition of Cartesian coordinates to describe all that he sees, then the motion of the planets, galaxies and cosmological effects will seem quite weird to him until he discovers General Relativity which is the simplest geometrical theory of curved space-time.
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In GR we don't talk about frame of references, but can talk about local Lorentz frames which are Cartesian coordinate systems built about a time-like geodesic, the space-time trajectory of a body in free-fall. Such coordinates only closely approximate the physics of GR in small neighborhoods where the scale of applicability is a function of how precise you need it to be and how curved space-time is.
Great. You are a devout GR specialist, your posts are meaningful inside the theory, Daecon will now understand what parrotising means by comparing your response with that of Paddoboy.
Your definition of helices is fine, thats basics. But the convoluted (no pun intended) definition of straightline in GR is something absolutely non intuitive.
You are missing the point, motion of a planet is determined by at least three directions....Influence of Sun's gravity (call it first level of curvature), influence of GC gravity (call it second level of curvature, but effective only on a point) and the somewhat complex motion of Galaxy through space (call it third level of curvature).....
The GR does not have exact solution for multiple sources causing curvature, neither it can be superimposed, so which straightline you are talking about for a planet ? The one which appears elliptical if you are on Sun, the one which looks dicey elliptical if you are watching from GC (dicey ? actually entire solar system) ? So please do not make a blanket statement or imply that in the real world all motion of celestial objects are in straightline ? And please observer's observation is not restrained by GR.
I can simulate a helical motion in lab, take an ant on a cylinder with axis in z direction, moving on a circular path on the curved surface of the cylinder in x-y plane, move the cylinder in up direction with some constant velocity, for an outsider observer the motion of ant is helical (this covers your mathematical definition).......The same philosophy and same motion applies to a planet (removing some other unknown complexities).
Oh, I missed that.
What you are implying is that the definition of straightline is GR specific.
Motion of object is certainly helical (or weird as you say)...it is mathematically made to fall in line (again no pun) ?
Yep, accept that correction, thanks rpenner.
Thats not correction, thats fundamentals. Accept the ignorance.
I'm sure Daecon also recognises the credibility of this thread as expressed by others also.
But as I said, and which obviously you ignored....As has been told to you a few times now, [parrotised if you wish, but factual none the less] everything will try and move in a straight line, unless acted on by forces, or the curved/warped/twisted nature of spacetime, which we call gravity.
Which part of that do you have a problem with?
I'm sure also Daecon and others recognise the general futility of this thread, as similar in style and credibility to your other fabricated scenarios and problems with cosmological redshift, gravitational lensing, Schwarzchild radius and compulsory collapses, and others I'm to lazy to mention at this time.
Yes and despite all that fabricated blurting, all bodies are still trying to travel in as straight a line as possible:Let me assure you once again, that all bodies will tend to travel in a straight line unless acted on by a force or under the influence of curved spacetime, which we call gravity.
Again, as others commented on early in the thread, your credibility and sincerity is in question imo.
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I accept the correction as the great man did also, and which distinguishes you from that category obviously. Perhaps you need to accept yours....I can raise most of them to remind you if you like.
https://www.quora.com/If-space-is-c...lines-curve-if-they-were-extended-long-enough
The 'straight' line of common intuition is in fact a special case of a type of curve known as ageodesic. (http://en.wikipedia.org/wiki/Geo...) It is actually geodesics that represent the shortest distance between any two points in a space of a given geometry. The straight line is simply the geodesic for flat Euclidean space. It also has the special property that, for any two points in Euclidean space, the straight line between them is unique; there is only one such line. However, there may be many geodesics between two points in a curved space - even an infinite number, as in the case of the great circles on a sphere connecting the north and south poles.
The concept of geodesics found an important application in Einstein's General Relativity (GR), where they replaced the straight line in Newton's First Law of Motion - 'Any body not being acted upon by an external force remains at rest or in a uniform state of motion in a straight line' - and enabled Einstein to rewrite this as the Law of Geodesic Motion - 'Free-falling objects (i.e. objects not experiencing an external force) move along geodesic paths in curved spacetime.(http://en.wikipedia.org/wiki/Gra...).
The 'straight' line of common intuition is in fact a special case of a type of curve known as ageodesic. (http://en.wikipedia.org/wiki/Geo...) It is actually geodesics that represent the shortest distance between any two points in a space of a given geometry. The straight line is simply the geodesic for flat Euclidean space. It also has the special property that, for any two points in Euclidean space, the straight line between them is unique; there is only one such line. However, there may be many geodesics between two points in a curved space - even an infinite number, as in the case of the great circles on a sphere connecting the north and south poles.
The concept of geodesics found an important application in Einstein's General Relativity (GR), where they replaced the straight line in Newton's First Law of Motion - 'Any body not being acted upon by an external force remains at rest or in a uniform state of motion in a straight line' - and enabled Einstein to rewrite this as the Law of Geodesic Motion - 'Free-falling objects (i.e. objects not experiencing an external force) move along geodesic paths in curved spacetime.(http://en.wikipedia.org/wiki/Gra...).
This force thingie appears to be a news for you...something novel....but this is too basic. Drop this, this is not some great hidden stuff you or origin found out.
Does it?
Yet all the exchanges we have had thus far, it's your own opinion/Interpretation/lack of mainstream knowledge that has been questioned time and time again: Three threads in the fringes, two in pseudoscience and including one in the cesspool attest to that.
But I'll leave you to what you do best.....Further debate with you is not worth the effort, considering your desired intentions.
Thank you !! What a riddance !!
This obviously will end up the way of the other "non issues" fabricated scenarios that have also been put in recent time.
As long as light is traveling through the vacuum of space, in fact as anything is travelling through the vacuum of space, it will continue to move in straight lines. As WMAP determined, our universe/spacetime is overall topologically flat within very tiny error bars, which in effect means that if two rays of light are emitted parallel, they will stay parallel, never diverging or converging: in effect, there is nothing to cause it/them to alter there directions.
Newton’s First Law states that a body will continue moving in a straight line if there are no forces acting upon it.
exchemist
Valued Senior Member
Oh, I totally agree! But also I was the fifth to add to this shemozzle and not until post 17!If you can resist the temptation to respond, it may just possibly go away!
Rpenner,
You know it, that any point motion, however weird can be considered as straightline, its a matter of unfolding the path, the way it is proposed for ant motion on a cylinder curved surface.
You also know it that GR maths does not have easy solution when an object moves under the influence of multiple sources causing distortions. The end result cannot be superimposed due to non-linearity of equations involved. So we take salvage in Numerical methods, which is highly tedious and approximate.
Now the point is
Earth's orbit around Sun can be termed as Geodesic...you can call it straightline...
Our Solar System motion around GC can also be termed as Geodesic....you can call it straightline
(In both these scenarious, first the earth and second the Solar System is to be considered as 'point'...ok granted.
But, the resultant motion of (or resultant locus) of the Earth motion under these two curvatures (by Sun and by GC) cannot be termed as Geodesic....so it is not even straightline in GR ? Choice is yours, you can stick to this...
It is also pertinent to mention that you failed in your argument with farsight about non exitence of SR domain in reality, try applying SR here, if SR is existent.
The relativity guys are baking their cookies and eating that too !! Wow, do you have anything at stake in talking realistically ? You are no Paddoboy lacking in intellectual rigour !! You are know Exchemist or Origin..their past-time is to come on this forum, make some stray comments without contributing anything intellectually worthwhile. Come on, show that there are issues with GR and discuss them. Don't try to push that helical path is a straightline in GR because it is Geodesic, that is for Paddos and ilk.
You know it, that any point motion, however weird can be considered as straightline, its a matter of unfolding the path, the way it is proposed for ant motion on a cylinder curved surface.
You also know it that GR maths does not have easy solution when an object moves under the influence of multiple sources causing distortions. The end result cannot be superimposed due to non-linearity of equations involved. So we take salvage in Numerical methods, which is highly tedious and approximate.
Now the point is
Earth's orbit around Sun can be termed as Geodesic...you can call it straightline...
Our Solar System motion around GC can also be termed as Geodesic....you can call it straightline
(In both these scenarious, first the earth and second the Solar System is to be considered as 'point'...ok granted.
But, the resultant motion of (or resultant locus) of the Earth motion under these two curvatures (by Sun and by GC) cannot be termed as Geodesic....so it is not even straightline in GR ? Choice is yours, you can stick to this...
It is also pertinent to mention that you failed in your argument with farsight about non exitence of SR domain in reality, try applying SR here, if SR is existent.
The relativity guys are baking their cookies and eating that too !! Wow, do you have anything at stake in talking realistically ? You are no Paddoboy lacking in intellectual rigour !! You are know Exchemist or Origin..their past-time is to come on this forum, make some stray comments without contributing anything intellectually worthwhile. Come on, show that there are issues with GR and discuss them. Don't try to push that helical path is a straightline in GR because it is Geodesic, that is for Paddos and ilk.