Photon Propagation : Straightline or Helix ?

I ask you the exact same-- so please enlighten me.

 

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As origin told you earlier in this thread, everything tends to travel in a straight line unless acted on by a force [Newtonian] or follows geodesics in curved spacetime caused by other mass. [GR]

As already warned, your obtuseness and continuing efforts to move the goal posts whenever you are caught out, is still prevalent.
Let me state it again, If the Sun were magically removed, [say by your mythical magical spaghetti monster] the Earth would continue to travel on a tangent.
If that doesn't make sense, and I'm being too hard on you, the definition of a tangent and accompanying diagram follows......
https://en.wikipedia.org/wiki/Tangent
In geometry, the tangent line(or simply tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point.

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Tangent to a curve. The red line is tangential to the curve at the point marked by a red dot.

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Tangent plane to a sphere
In geometry, the tangent line

 

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Yet measurements and data continue to show that spacetime is warped, curved, twisted and waved in the presence of mass: Think GP-B and aLIGO.
Einstein and GR are more confirmed then ever before.
https://einstein.stanford.edu/content/relativity/q411.html

 

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Yet I think it is more helpful to address first principles and make progress than to quote exotica and claim this has somehow addressed the unnaddressed first principles.

 

More of the usual....nonsense!
Obviously you do not know what a geodesic is!
[And btw, that is all everyone is trying to tell you]

http://www.dictionary.com/browse/geodesic
Also, geodesical. pertaining to the geometry of curved surfaces, inwhich geodesic lines take the place of the straight lines of planegeometry.

https://en.wikipedia.org/wiki/Geodesic
In differential geometry, a geodesic (/ˌdʒiːəˈdɛsɪk, ˌdʒiːoʊ-, -ˈdiː-, -zɪk/[1][2]) is a generalization of the notion of a "straight line" to "curved spaces". The term "geodesic" comes from geodesy, the science of measuring the size and shape of Earth; in the original sense, a geodesic was the shortest route between two points on the Earth's surface, namely, asegment of a great circle.

http://mathworld.wolfram.com/Geodesic.html
A geodesic is a locally length-minimizing curve. Equivalently, it is a path that a particle which is not accelerating would follow. In the plane, the geodesics are straight lines. On the sphere, the geodesics are great circles (like the equator). The geodesics in a space depend on the Riemannian metric, which affects the notions of distance and acceleration.

In summing and as origin informed you way back in post 2 or 3, when you started this new crusade, all bodies, including light tend to travel in straight lines, and the shortest possible distance between two points which is known as geodesics.

It's incredible how severe afflictions of delusions of grandeur can blind someone to their total lack of credibility, in their own mind.

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If I may offer some advice:
You have started many threads here, all with apparent ulterior motives in trying in some form or other, to invalidate all of mainstream cosmology.
Your continued failure with all these evangelisitc missions you undertake, has seen you sink to the lowest levels of ignorance of mainstream cosmology, evident by the fact that of your totally baseless claims that GP-B and aLIGO were fraudulent results.
Not much more can really be said, except probably that delusions of grandeur and having a false impression of one's own importance, is a treatable condition.
The point i'm making is that everyone is aware of that and are laughing behind your back, while you continually try and salvage some credibility.
I'm a big softy at heart and can see the hole you are digging for yourself, and sincerely ask you to step back and see what you are doing to yourself.
It isn't nice.

 

What exotica?
The two experiments mentioned [and there are many more] simply confirm that GR is as near certain in applicability as anyone could wish for.
We have two theories of gravity that serve us well and address "first principles"
They are Newtonian: Masses attract each other with a force that varies as the inverse square of the distance between them.
GR: A more accurate precise application that masses simply curves or warps the otherwise flat fabric of spacetime.

 

Oh ! So now you know about tangent. Good, keep it up. Very soon you will know about 'normal' also..

 

I wish to change the definition of straightline in general.....

The basis for this change :

1. In flatspace time a particle can travel in Euclidean straightline even when acceleration is non zero.
2. The motion of stellar objects is free space is quite curvy, even though there is no external force on them, they just follow the spacetime warping. Under the circumstances calling this motion as straightline is intuitively bad.

Revised Definition of straightline..

1. The least path as traverseable by the light between two points shall be termed as straightline.

For example, in flat spacetime, the least path between pts A and points B shall be Euclidean straightline, as the light can traverse that.

In curved spacetime, light cannot traverse the Euclidean least path between point A and Point B, it has to take a domed shape to cover the distance between A and B, thus this curved line (null geodesic between these two points) shall be termed as straightline. Any line having larger curvature shall be an arc, and any line having lesser curvature shall be non existent (non traverseable even by the light).

This is much better, as calling the wavy orbit of moon around sun as straightline (due to absence of force) is not done...

 

Paddoboy,

Let us see how you answer this..

The Earth moves in curved path, caused due to warping of spacetime around Sun ?

So if we leave the frame dragging apart (which can be settled with Gravitomagnetic concept also), then what was the need to carry out GP-B....Look at the motion of Earth and Moon, and voila you can say spacetime is curved without the presence of any force. GR is established ? Why, GP-B, Paddoboy ? Do you know ? Thats why don't bring these exotica, there is no consensus on GP-B and now on aLIGO.....Because space aorund you is not curved, you can give any property to spacetime, whatever you want, who cares ?

 

Name the degree and I have !
Did I ask you whats yours ?
You have to demonstrate something first to be brought in that category, you have not yet.

 

This is not done.

You made an assertion that

"Einstein says point B actually is in a straight line in spacetime coordinates."

So farsight is right in asking you when and where Einstein said that ? Onus is on you to establish that first.

 

You seem rather excited?

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Didn't any of your many imaginary Phd's cover tangents?

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Obviously those Phd's also fail in this area:
It's worth noting my friend, that the way you continue to try and denigrate science, from the comfort of your chair at home on a remote science forum, is also the way of a lot of God bothering nuts and YEC's.

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Check out how easy it is for the professionals such as Neil De-Grasse Tyson and Richard Dawkins to put them in their places.
You seem to be heading that way.
In answering your question though precision experiments such as GP-B and aLIGO will continue as science never gives up trying and will keep probing further and further to find any limitations on theories such as GR, as near certain as it is.
The LHC is another. I read somewhere that the next stage will be at full capacity and they expect to find further indications of the Higgs and perhaps even more, just as aLIGO was expected to confirm gravitational waves which it of course did and in the process also BH's.
The advanced LISA is another long awaited for experiment that will make more observations and the JWST when launched is expected to reveal even more data re the early universe/spacetime.
Who cares?

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Real scientists, cosmologists, physicists etc care: That's what the scientific method and peer review is all about.

 

I don't think you are referring to anything that could be observed by measuring the photons that are emitted from the earth and moon as they rotate and travel to an observer. You may be thinking of a model animation that displays the relative positions of the earth and the moon as the moon rotates around the earth and the earth rotates around the sun (and the sun rotates around the galactic center).

The issue is similar to the animation based on the redshift distances calculated from the HST UDF images, the velocity of the frame of reference of the 'observer' is not something that can possibly exist in our universe [if you know what I mean].

 

I understand GR. You don't. And you can't find Einstein saying point B actually is in a straight line in spacetime coordinates because he didn't. Your Nerf gun bullet in your vertical carriage doesn't travel in a straight line.

 

ahh-- are you diverting now?--

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i already know the answer, your formal education is simply google , wiki, and YT university, along with nothing more.

 

In section 2, equation 1 of Einstein's 1914 “The Formal Foundation to Relativity” he defines a straight line.
In equation 2a, he introduces the metric used in General Relativity. And then he says equations 1 and 2a “determine the motion of a material point in a gravitational field”.
Later, in section 7 he returns to this topic and derives, from equation 1 and equation 2a, equation 23b in terms of definitions 24 and 24a which (barring notation changes over the past 100 years) is exactly the geodesic line that has been the topic of this thread.

This is pretty basic stuff.

Photon Propagation : Straightline or Helix ?, post 25
Photon Propagation : Straightline or Helix ?, post 41

 

wiki, google and YT do not offer degrees

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(shrugs)

 

No you don't. You may or may not know all of Einstein speeches and what he wrote, but that is irrelvent if you cannot work out problems in GR. You may know that integration is the area under a curve but if you can't actually integrate an equation then you do not know calculus.

You just don't seem to understand that the crux of GR is in the math and discussions about the math can only be approximations and analogies.

 

if the trajectory was broken-up in increments, those increments would measure to be straight lines. the more you break them up, the more that these straight lines show.

 

Since it's in general true of all smooth lines that you can break them up into approximately straight lines, we still need an actual definition of straight line. Einstein gives us one directly from late 19th-century geometry of curved manifolds.

Let's look at polar coordinates in a 2-D plane. Here the line element is \(ds^2 = dr^2 + r^2 d\theta^2\)
So the metric components are: \(g_{rr} = 1, g_{r\theta} = g_{\theta r} = 0, g_{\theta\theta} = r^2\). Since it is diagonal, this saves us lots of effort.
So the inverse metric has: \(g^{rr} = 1, g^{r\theta} = g^{\theta r} = 0, g^{\theta\theta} = r^{-2}\).
So the derivatives with respect to \(r\) are: \(\partial_{r} g_{rr} = 0, \partial_{r} g_{r\theta} = \partial_{r} g_{\theta r} = 0, \partial_{r} g_{\theta\theta} = 2r\)
And the derivatives with respect to \(\theta\) are: \(\partial_{\theta} g_{rr} = 0, \partial_{\theta} g_{r\theta} = \partial_{\theta} g_{\theta r} = 0, \partial_{\theta} g_{\theta\theta} = 0\)
So we have:
\(\Gamma_{r r}^{r} = 0 \)
\(\Gamma_{\theta r}^{r} = 0 \)
\(\Gamma_{r r}^{\theta} = 0 \)
\(\Gamma_{\theta r}^{\theta} = \frac{1}{2} \left( g^{\theta \theta} \left( \frac{ \partial g_{\theta\theta} }{ \partial r } \right) \right) = \frac{1}{2} r^{-2} (2r) = r^{-1} \)
\(\Gamma_{r \theta}^{r} = 0 \)
\(\Gamma_{\theta\theta}^{r} = \frac{1}{2} \left( g^{r r} \left( - \frac{ \partial g_{\theta\theta} }{ \partial r } \right) \right) = \frac{1}{2}(- 2 r) = -r \)
\(\Gamma_{r\theta}^{\theta} = \frac{1}{2} \left( g^{\theta \theta} \left( \frac{ \partial g_{\theta\theta} }{ \partial r } \right) \right) = \frac{1}{2} r^{-2} (2r) = r^{-1}\)
\(\Gamma_{\theta\theta}^{\theta} = 0 \)

Which means the definition of a straight line is:
\( r'' - r (\theta')^2 = 0, \theta'' + 2 r^{-1} r' \theta' = 0\)

Solutions of the form: \(r = r_0 \sqrt{1 + k^2 \lambda^2} , \; \theta = \theta_0 + \tan^{-1} k \lambda \) work, because:
\(r' = \frac{ r_0 k^2 \lambda}{ \sqrt{1 + k^2 \lambda^2} }, \; r'' = \frac{ r_0 k^2 }{ \left(1 + k^2 \lambda^2 \right)^{\frac{3}{2}} } \)
\(\theta' = \frac{k}{1 + k^2 \lambda^2}, \; \theta'' = - \frac{2 k^3 \lambda}{ \left(1 + k^2 \lambda^2 \right)^2 } \)

That's how you get from the metric to straight lines.

Since \(ds^2 = dr^2 + r^2 d\theta^2\) we can compute:
\((s')^2 = (r')^2 + r^2 (\theta')^2 = r_0^2 k^2 \) which is constant. This property in GR means light-like geodesics stay light-like and similarly for space-like and time-like geodesics, which reinforces how GR and geometry go hand-in-hand.