Photon Propagation : Straightline or Helix ?

Yes, Yes, Yes.

 

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Google it. What he actually said was “Matter tells space how to curve. Space tells matter how to move.” And that's wrong on multiple counts. A concentration of energy "conditions" the surrounding space making it "neither homogeneous nor isotropic", this being modelled as curved spacetime. Space isn't curved where a gravitational field is. See Baez:

"Similarly, in general relativity gravity is not really a 'force', but just a manifestation of the curvature of spacetime. Note: not the curvature of space, but of spacetime. The distinction is crucial."

As I've said previously, spacetime curvature is the defining feature of a gravitational field, because without it your plot stays flat and level. But light curves because of the local gradient or first deriviative of potential, not the local curvature or second derivative of potential. It's like that tilted board: your marble follows a curved path because the flat board is tilted, it doesn't follow the curvature of the board. In similar vein light doesn't curve "because it follows the curvature of spacetime".

I'm not taking him out of context. He said what he said. And on this matter, I'm right.

 

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Allow me to step in here:

If they're moving horizontally across a gravitational field, the lower photon will curve downwards more than the upper photon. So they won't remain parallel.

Light curves downwards when it moves horizontally across a gravitational field. If it didn't, there wouldn't be any gravity.

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If you have a fast-moving electron instead of a photon moving from left to right, then if you exert an upward force on it that exactly counteracts gravity (which is not a force in the Newtonian sense), it will move in a straight line.

 

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"The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength. They are radical. Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality."
Hermann Minkowski:
On what Wheeler said, I see your correction as rather unecessary pedant, to cover your own many shortcomings..
http://physicalworld.org/restless_universe/html/ru_4_24.html
'Matter tells space how to curve.
Space tells matter how to move.'
Purists might quibble over whether Wheeler should have said 'space-time' rather than 'space', but as a two-line summary of general relativity this is hard to beat.
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Ýou've said many things in your time on this forum, including claiming to have a TOE:
Most take your claims with a grain of salt.

Rubbish. Light/photons certainly do follow geodesic paths in curved spacetime, and to claim it does not is the height of pseudoscience.
In fact light/photons due to their momentum, also create their own spacetime curvature albeit by an infinitesimally tiny amount.

You have certainly taken him out of context on occasions, and on other occasions misinterpreted what he has said and all have been pointed out to you to obviously no avail.

 

That is because both photons are following geodesic paths in curved spacetime. Overall, photons emitted parallel remain parallel due to the fact that we live in a topologically flat universe as per the data from WMAP.

Rubbish...Light has nothing to do with gravity.
Light simply is following geodesic paths in already curved spacetime despite your pretty pictures..

 

Ding Dong continues....

1. somewhere else you claimed that light warps/curves the spacetime...which contradicts above.

2. For that matter each stellar object is following geodesic, so does that mean they have nothing to do with gravity ?

 

This is the biggest problem, a convenient swapping of words, space and spacetime..............

 

Certainly does, albeit very small amount: Think solar sails and momentum.

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And no, it contradicts nothing that I said: My remark which you have taken out of context was in reply to Farsight's speudscientific nonsense.

Mass/energy curves spacetime: voila! Gravity!
OK ding dong?

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Anything more you would like to brush up on?

 

"The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength. They are radical. Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality."
Hermann Minkowski:

 

Actually I wanted to say about instersection of the photons. But still ok.

As per below link, atleast Photons will not loose parallel aspect, due to self gravitation.
http://www.ptep-online.com/index_files/2013/PP-35-L3.PDF

Now the issue is will the photons (initially parallel) on two geodesics (one at r and another at r+dr) outside a spherical symmetry massive source, will they diverge as Farsight is stating, meaning inner geodesic curving more than the outer geodesic ? Intuitively it does not appear so, but then you know the maths.

This one is tricky, but I am inclined to go with you. My argument is that motion/geodesic under multiple source may not be planar, thats the first challenge for it to be called as line. Secondly defining and solving the Geodesic equation for multiple source effect on spacetime, itself is a challenge. The approximation does not guarantee Newtonian simplification too.

You must have responded in hurry here. For non euclidean surface, I feel motion of a particle can be on geodesic even in presence of external force. So it cannot be said that all such loci are non-straightline.

 

You are right here...Minkowski would have said that. But Sir, any chemistry student will tell you that A and B together can make AB (if; some composition), now the properties of AB will not be the same as Properties of A + Properties of B. You can ask your friend Exchemist. This may not be 100% fitting in this case, but the properties of spacetime cannot be said as properties of space ? Do you get it ? For example free space has some properties as permeability and permittivity but spacetime does not have.

So Sir, do not consider the above obiter dictum by Minkowski as gospel truth.......spacetime is not space. Spacetime can have curvature (in mathematical forumulations only) not space. Spacetime can bend (in maths) but not space. Yes, you can have 4D spacetime spatial manifestation mapped in 3D space, but then thats all. Nothing else.

 

Please refain from stating your unevidenced pseudoscience beliefs as facts in the science sections. Experimentation and observation refute your opinion.

 

I could be wrong here, but I'm pretty sure that a particle cannot be on a geodesic in the presence of an external force, by definition. In Newtonian mechanics, a force is defined by how it causes mass to deviate from inertial motion, i.e. accelerate. Similarly, I think a force in GR is defined by how it causes mass/energy to deviate from geodesic motion.

More broadly, this thread is an excellent example of why I think many of the forum members here tend to get misdirected when debating Farsight. What has Farsight talked about over the last two pages? Whether it's correct to understand gravity in terms of geodesics, whether the first-order effects of gravity are better described as "curved" or "tilted" spacetime, and how much flak Minkowski deserves for saying "space" instead of "spacetime". On all three counts, Farsight definitely takes a non-mainstream position, but without any predictive consequence as far as I can tell. If I didn't know any better, I'd say this was a debate over interpretations, where everyone agreed on the physical phenomena and just disagreed about the best framework for thinking about them. Meanwhile, the other thread on the behavior of light -- where Farsight has failed to explain the behavior of two photons on a beamsplitter -- seems to have died with no fanfare. I really believe that any discussion of physics has to be rooted in experimental phenomena, and the only way to pin down Farsight is to focus the conversation on phonemena that his model cannot explain.

 

I must ask you, origin, where in The God's Post #71 did The God "state" anything as "fact"? Unless The God's Post #71 has been edited, the Post does not even contain the word "fact".

Yet, origin, you did not raise your "fact" objection in response to the actual, and clearly Posted, misuse of the word "fact" in Post #65.

 

I'm no expert.
About the use of force in GR...I think you have a choice of models, Force or curved spacetime.
But you don't need a force in the curved spacetime model. See rpenner here...

My bold
I don't think you got that right there fednis.
If both GR 'models', Force or Curved spacetime, are to give the same results, then having a force deviate a particle off its geodesic would not give the same result as the curved spacetime manifold model where the particle is always on its geodesic.

 

,

It was implied, IMO.

I didn't read post #65. I have you, The God and Paddoboy on ignore, since I tire of your bickering at each other, so I usually do not read any of the posts you guys write. I clicked unignore and made a comment which I regret because I am being drawn into your little feud. So back to ignore.

 

Post 65 states the mainstream accepted view and has been reinforced by professional replies via E-Mail.
It is the accepted mainstream theory, not some unsupported mythical fairy story fabricated by unprofessionals.

 

Only if external forces sum to zero will the trajectory of a particle be on a geodesic.
That's a direct translation of the concept of Newton's \(\sum_i \vec{f}_i = m \vec{a}\) into general relativistic terms.

Your source is talking about a universe devoid of all matter, energy and cosmological constant other that two parallel photons. No one who read your post assumed that was the case being considered. I was talking about two photons in our universe.

Here is the paper (ref 1 of your source) from 1931 which supports your claim at the end of §6 and also the end of §9:

Richard C. Tolman, Paul Ehrenfest, and Boris Podolsky. "On the gravitational field produced by light." Physical Review 37 (5) : 602. (March 1, 1931)

In order to reach that conclusion they used approximation techniques to calculate how spacetime curves about beams and pulses of light and then asked about the directional dependence of how that curvature changes the description of speed of light and geodesics of particles. For example in section §7 they show that a pencil of light has twice the gravitational attraction on stationary particles than expected from naively considering \(E=mc^2\) to give the "mass of the photon".

I know the maths are quite rough, but here is a case where an exact solution is known.

If the at the event given by Schwarzschild coordinates \((t,r,\theta,\phi)\) we choose \(T^{\mu} d\lambda\) to be the tangential light-like direction such that:
\(dt = T^{t} d \lambda = d \lambda , \; dr = T^{r} d \lambda = 0, \; d\theta = T^{\theta} d \lambda = \frac{c}{r} \sqrt{1 - \frac{r_s}{r} } d \lambda, \; dr = T^{\phi} d \lambda = 0 \) (here I choose a dimensional \(\lambda\) with units of time)
then it follows that if there are two nearby geodesics separated by infinitesimal bit \(X^{\mu}\) that the geodesics diverge with an acceleration of:
\(R_{\beta \gamma \delta}^{\alpha} T^{\beta} T^{\gamma} X^{\delta} = \frac{ c^2 r_{s} \left(r - r_{s}\right)}{2 r^{4}} \begin{pmatrix} X^{t} - c^{-1} \sqrt{\frac{r^{3}}{r - r_{s}} } X^{\theta} \\ 3 X^{r} \\ c \sqrt{\frac{r - r_{s}}{r^{3}} } X^{t} - X^{\theta} \\ - 3 X^{\phi} \end{pmatrix} \)
which is never zero except when \(X^{\mu} \propto T^{\mu}\), i.e. when the "two infintesimally separated" geodesics are part of the same space-time geodesic (or when \(r_s = 0\) which is flat space-time).

 

Do tell. Maybe you could provide evidence of these "professionals" stating that your claim : "Overall, photons emitted parallel remain parallel due to the fact that we live in a topologically flat universe as per the data from WMAP." is indeed a "fact" - and not just another "paddoboy mythical fairy tail claim of accepted mainstream theory".

Here is a Link to a, more or less, "mainstream" view on the subject : http://map.gsfc.nasa.gov/universe/uni_shape.html
Does it support your "paddoboy mythical fairy tail claim of accepted mainstream theory" or more precisely, as you firmly stated in Post #65, does it back up your claim of a "fact"?

 

...implied...
...on the contrary, origin, it was merely The God's opinion...
...drawn in...
...on the contrary, origin, you inserted yourself...