Photons VS.Higgs-boson particle

What i meant to say is that: Isnt 'curvature of spacetime' and 'curvature of photon' around the Moon should be same as per GR ?

 

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Yes... I think.

 

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'Curvature of spacetime' depends on mass or mass-density and it does not depend upon the shape of the mass.


'Curvature of photon' will depend on shape of the mass.


So, I think these two curvatures may not be same all the time.

 

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1) Is incorrect. The curvature of spacetime is the same as gravity. The shape of an object does affect the shape of its gravitational field and thus the curvature of spacetime. Even variations in the density of an object changes its gravitational field and the associated curvature of spacetime.

I remember somewhere reading about an attempt to develope field equations that could accurately describe the complex gravitational field of irregularly shaped asteroids.

2) Photons follow the curvature of spacetime.., pretty much period. There may be some of debate on this but the divergence of the path of a photon from the curvature of spacetime is likely so small, that it would be unmeasureable for any gravitationally significant object we are able to observe.

3) That makes #3 false. At least to within the limits of our ability to detect and observe the world, in ways that would reveal the curvature of spacetime and the path of photons.

 

Right.

If two objects of equal mass but different shape free-falls under the same gravity, will their acceleration differe due to their shapes?

I am talking about the total mass of a body, be it asteroid or planet or some other mass.

Do you think frame-dragging has no effect at all to bend spacetime or to bend a photon particle?

If frame-dragging has a effect in bending a photon particle, then #3 may not be false.

 

Within the context of flat space/spacetime — and SR or classical everyday conditions, one would expect there to be no difference. In practice, in the curved space/spacetime of complex gravitational fields and where multiple fields may be involved, as in the solar sytem and many planets, as an irregularly shaped gravitational mass rotates the shape of the field will have an effect that will vary with that rotation... This is not associated with frame dragging. Instead it is associated with the irregular shape of the field itself.

Most of the time when modeling gravity and gravitational fields a uniform shape and density are used.., because it is almost impossible to account for variations in mass density, when not all of the information is available and the mass density and center of mass, changes over time for most real gravitational systems.

When you qualify the conditions to ideal conditions like; total mass or a uniform shape or mass density, shape then has no effect.., because it is not an idealized situation.

The question was about the shape of an object affecting a gravitational field, and YES it does.., and no in most cases it is not taken into consideration.., because the idealized sphere of uniform mass density and total mass.., and Newtonian formulas are accurate enough to put a sattelite on Mars. Remembering that all along the journey there are key locations where corrections are made to the trajectory.... And that within the context of those good enogh calculations made using Newton's formulas there is no curvature of space or frame dragging...

You keep going back to this.... Yes frame dragging is one small piece of the whole picture when you are considering the curvature of space. But to keep it in persecutive. The attractive force associated with the curvature of space/spacetime would be measured in hundreds of miles during the same time frame that frame dragging would be measured in fractions of an arc second. (The earth has a circumference of approximately 24,000 miles. That makes one arcsecond, \((1/3600\) of a degree), on the surface of the earth, about 0.02 miles — \(24000/360/3600\) — circumference/degrees/arcseconds. Everything rounded.)

Hansda, it is far easier to conceive of frame dragging in a classical Newtonian way, though it is not Newtonian, than the curvature of space associated with gravity as an attractive force. That said they are both aspects of a gravitational field which emerge from Einstein's field equations.

I believe it is better to think of the two as different perspectives or views of the same thing. They are both aspects of the same curvature. It is likely that "seeing" them as separate, is an artifact of how we conceptualized curvature.

It is kind of like an object can have both a length and a width, both are integral aspects of the object, but we "see" and measure them separately.

The curvature of space/spacetime has both a component we associate with an attractive force and a component of rotation we call frame dragging. We separate them in measurement, but they are not really separate things... BUT the rotation or frame dragging part is a very small fraction of the total, when compared with the attractive part.

Note: I keep using Newtonian concepts or descriptions like attraction, because they accurately describe these things locally and there is no clear and easy way to describe curvature similarly, in lay oriented terms.

 

Suppose there is a mass which is very irregularly shaped. Its surface is rough and full of many curvatures. Gravitational force will work through every part of the surface of this mass.


Will the curvature of spacetime around this mass follow its curvature of surface ?


Even if the spacetime follows the curvature of surface of the mass, will the particle photon also also follow the same curvature of surface of the mass?

 

Yes.

However, the affect that the shape of the mass has on the shape of the gravitational field, will also depend on the total mass involved and the distance from the center of mass.

As you increase the distance from the object's center of mass the shape of the field becomes less important. Take a large asteroid that has an irregular shape. A small object passing very close may be affected by the irregular shape of the asteroid and the corresponding irregular shape of its gravitational field.

However, take the same asteroid and its interaction with the sun's gravitational field. In this case the asteroid's shape will have no measurable effect. The interaction occurs at a scale where the irregular shape has no significance.

Yes. However, once again the curvature will only be significant close to the mass. As the distance from the center of mass is increased the irregular shape of the gravitational field will become less defined.

Even the Earth's gravitational field is not uniform. http://en.wikipedia.org/wiki/Geoid#Spherical_harmonics_representation, you can see from the illustration in this link that the irregular shape of the Earth's gravitational field would only be significant very close to the surface. Even then the Earth's field is not strong enough for us to measure any associated gravitational lensing.

Yes. And once again, the curvature and resulting gravitational lensing would be significant and detectable/measurable, only where the gravitational field is strong...

We could not measure gravitational lensing associated with an irregularly shape asteroid... And most, if not all, objects that are massive enough that we can measure gravitational lensing are also so massive that they are essentially spherical.

A mass which is small enough to have an irregular shape, would not be associated with a significant curvature of space. It would no result in a strong field.

 

I think perhaps, gravitational lensing is the only case where particle photon follows gravity or GR.


There are other phenomena of photon which do not follow GR or gravity. These phenomena of photon can be considered as Reflection, Refraction, Diffraction and Optical Vortex. These phenomena of photon do not follow GR or gravity.

 

All of the above are things that we observe locally, in an observationally flat space/spacetime. That does not mean that any local curvature of space/spacetime does not affect them. It just means that any curvature is observationally and measureably insignificant... Too small to see or measure.

And yes those things are not caused by the curvature of space/spacetime. Note, I am not entirely familiar with the details of optical vortexes, so separating this phenomena from curvature, is an assumption on my part. The rest are the result of the direct interaction between light and mediums other than the vacuum, or the curvature of space/spacetime.

 

'Curvature of spacetime' may be too small to see or measure but Reflection, Refraction, Diffraction of photon can be seen/observed. So here Particle Photon does not follow spacetime.

So, your statement #3 in post #64 is not correct.

Optical Vortex may depend upon spacetime but they are not due to gravity.

 

The two are not mutually exclusive. In classical terms reflection, refraction and diffraction are not the result of spacetime curvature, that does not mean that a photon that is, say reflected off of a mirror is not also affected by the local curvature of space.., even when that curvature is so small it is undetectable.

Wrong! In that post your comment #1 suggested that cuvature was the result of total mass only and not by shape, and your comment #2 that it was shape that affects curvature. Your #3 stated that the two were different. My response was that you were wrong. The curvature of space/spacetime can be measured in different ways. That does not make the different measurements, measurements of different things...

Just because we measure the length and width of an object as two different measurements, does not mean they are not measurements of the same object. The same is true for curvature... And if you re-read my whole post you will see that is what I was attempting to explain.

As I said, I am not entirely familiar with the details of "optical vortex", that said.., spacetime or the curvature of spacetime and gravity are the same thing. So if "optical vortex" involves one it involves the other... And I am not claiming any such relationship exists, I don't know enough about the issue of an optical votes to say. What I am saying is that you cannot separate curvature of spacetime from gravity. They are the same thing.

Since this discussion has involved curvature throughout, if your intent is to limit some statement to a flat space/spacetime and SR, you must say so explicitly.

 

What i am saying is that 'curvature of photon' always may not follow 'curvature of spacetime'.

Spacetime does not undergo Reflection, Refraction or Diffraction. Spacetime undergoes gravitational lensing. So, as far as gravitational lensing is concerned particle photon follows spacetime but in the cases of Reflection, Refraction and Diffraction particle photon does not follow spacetime.


Optical vortex though involves spacetime but it is due frame-dragging effect and not due gravity. See this link http://phys.org/news/2011-04-physicists-visualize-warped-space.html .

 

Any answer to the issue you raise here requires bridging the gap between GR and QM. It would seem that in theory any unification of the two would have to explain how curvature emerges from the quantum state and thus how reflection and curvature are associated. No one has any good answers for this right now, so it becomes highly specualtive to try defining these relationships from a lay oriented perspective, which is where this disscussion is.

The above link is to an article addressing a theoretical application involving black holes. As far as I can tell there is no empirical evidense presented. And I still have no real fundamental understanding of the underlying mechanisms of an "optical vortex".., so am making no comment on whether the curvature of space in any form, is or is not involved. I just don't know.

If our other assumptions are accurate, it suggests that they are related or connected in some way, but the answer to that lies somewhere in the future, it would seem.

 

In gravitational lensing, optics follow gravity.

In Reflection, Refraction and Diffraction optics does not follow gravity.

As far as optics is concerned bending of photon is due change in its speed. In the case of Gravitational Lensing also velocity of photon may be changing locally to cause its bending.

For optical vortex you can see the following links: http://arxiv.org/abs/1112.3414 , http://en.wikipedia.org/wiki/Optical_vortex .