OPTICS and GRAVITY

Yes I know that, see above where I said things get more complicated when you start talking about two planets. We had a conversation about this with RJ a while back.

I don't misunderstand them. But you can look back at your post #90 where you said "how can you possibly object to anyone using space and spacetime interchangeably" . And then you can look at my post #93 where I higlighted "Note: not the curvature of space, but of spacetime. The distinction is crucial.". And you can eat humble pie over your horrendous misunderstanding of that.

 

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Ah, we're getting the old Your post will not be visible until a moderator has approved it for posting again. How quaint.

 

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Natural path of light is along a geodesic. If a mass m free falls, it will also travel along the geodesic. If another mass M is placed nearby so as to cause gravitational lensing, it will curve the geodesic. So, both light and the mass m will follow this curvature of geodesic. If mass m is gravitationally significant it will bend further towards mass M. If mass m is gravitationally insignificant it will just follow the curvature of geodesic like light.

See these links http://ajp.aapt.org/resource/1/ajpias/v48/i1/p72_s1?isAuthorized=no and http://www.iisc.ernet.in/currsci/apr102005/1155.pdf .

A quote from the abstract of the second link is as follows, " For material particles, the ‘particle’ part dominates, and for relativistic quantum particles, the deflection approaches that for light."

 

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Shine a light beam across the room you're in. It looks like it's straight, but actually it's a little bit curved, a geodesic. Now throw a ball across the room. Does it travel along that geodesic? No.

That ball is gravitationally insignificant.

I'll take a look. But meanwhile note that if you threw an electron across the room at the same speed as the ball, it would follow the same path as the ball, not the light beam. If however you fired the electron at 99% of the speed of light, its path would more resemble that of the light beam.

Edit: it looks good. Note that Unnikrishnan refers repeatedly to the wave nature of matter, which I referred to in my post #111. For matter just sitting there or moving very slowly only the 2GM/c²R term applies. For light it's 4GM/c²R. If however you move the matter very fast, it tends towards 4GM/c²R. Try drawing a horizontal line to represent a light beam, and a square to represent matter at rest. Then for fast-moving matter draw a parallelogram. For even-faster-moving matter draw a more-tilted parallelogram, and note that in extremis it starts resembling the horizontal line. Things aren't quite as simple as that in reality, but I think it gets it across pretty well.

 

I said, "if a mass m free falls". I wanted to mean if the mass m is in a region where there is no gravitational field. The mass m will move/fall freely and follow its initial velocity along the geodesic.

If the ball is affected by gravity, it becomes gravitationally significant. A free particle is gravitationally insignificant. An infinitesimal mass is gravitationally insignificant.

If electron is considered as a free particle, it will move at a constant velocity and remain unaffected by gravity.

Considering particle Neutrino, which has a non-zero mass but is gravitationally insignificant, what do you think its curvature would be in gravitational lensing? 2M/R or 4M/R?



Note: If deflection of a massive particle becomes less than that of a photon particle in a gravitational field; the massive particle has to travel faster than light. See http://adsabs.harvard.edu/abs/1974NCimL..11..459S and http://arxiv.org/abs/1110.1223 .

 

It will go in a straight line.

And yet it follows a curved path in a gravitational field. Despite this it is gravitationally insignificant.

No. An electron will fall down. So will a proton. So will a neutron. And a collection of electrons protons and neutrons called a ball will fall down too.

The latter. It moves at a speed that is so close to c that we cannot distinguish its speed from c.

A massive particle can't travel faster than light, end of story. I'll look at your links and get back to you.

First link: forget tachyons, they are hypothetical.
Second link: ditto.

 

I am not sure that if you are excluding the influence of a gravitational field, you would still refer to the path of any object as following a geodesic... In the absence of a gravitational field you are in essence limiting the conditions to those consistent with the flat space-time of SR.., and objects moving in straight lines, rather than following some intrinsic curvature of space-time.

However, setting that aside, there is a more significant difference between how a photon moves through space/space-time and how a massive particle (which would include the electron) or object would move through the same space/space-time. The significant difference being, the essentially external force or influence, the inertial resistance the involved mass generates on any change in the particle's/object's motion.

While a photon does have momentum, it does not appear to be subject to the laws of inertia, and thus follows the curvature of space-time, with a constant velocity of c.

In the case of massive particles/objects, all forces acting on the particle/object must be considered, including the inertia associated with its mass. Where a massive particle/object is freely falling in a gravitational field, under most circumstances we could assume that it follows a geodesic defined by the gravitational field and associated curvature of space-time. However, should the massive particle/object have any velocity originating from, other than its interaction with the involved gravitational field, its inertial resistance to any change in it state of motion, would have to be considered as representing an external force. The path of the particle/object through space-time would then be defined by a combination of the geometry of space, or the curvature of the space-time, through which it travels and the inertia associated with its inherent velocity, or any velocity associated with an external force, past or present.

In practice things would be far more complex. It would be difficult to find any region of space where there was one gravitational field. And locally, as in our solar system or galaxy, it would be difficult to find any location where the influence of many gravitational fields were not changing constantly, as the dynamics of the involved inertial system changes. Planets, stars and solar systems, all orbit the systems they are a part of. Constantly changing the gravitational dynamics.

 

Tachyons may be hypothetical but the point which can be noted from those two papers is that, deflection of a particle in a gravitational field is dependant upon its speed. This is a inverse relationship. Higher the speed, lower is the deflection angle and lower the speed, higher is the deflection angle.

You rightly pointed out that a massive particle can not exceed the speed of light. So, a massive particle also can not deflect less than the deflection of a photon particle in a gravitational field.

 

Your above statements are true for a gravitationally significant mass, which can free-fall under the effect of gravity.


An infinitesimal mass which does not contribute significantly in the gravitational field, will not free-fall under the effect of gravity and will travel along the geodesic following the curvature of space/spacetime.

 

Hansda, any particle with rest mass that can be set at rest within a gravity well, will free fall into the gravity well.

This has been proven with a mass as small as an atom and experiments have been conducted with neutrons. The margin of error for the neutrons was too large for the results to be conclusive. There comes a point where experiment must await better methods and technology.

There is no reason to believe that any particle or object which has mass will not be equally influenced by a gravitational field.

In my previous post I did mention, that for any mass which has velocity, not derived from an interaction with the gravitational field it is moving through, its inertia associated with that velocity would affect the extent that its path is affected by the gravitational field and associated curvature of space-time.

 

OnlyMe: I've come to the conclusion that hansda is determined to believe what he wants to believe, regardless of anything we tell him or refer to.
hansda: I can't help you further I'm afraid.

 

I sometimes agree, but am not as certain. Hansda's understanding has evolved some over the course of several threads dealing with this issue, or related issues.

Space-time curvature is a difficult concept to get a firm grasp on, without some understanding of the abstract geometry. I think that a significant part of the confussion is that, he continues to try and build a classical conceptual geometry, to describe what is happening.

To be honest it is as difficult to describe what is happening, in classical terms, as it is to understand it in classical terms. Bridging that gap without moving off and into the mathematical models, is the challenge.., for anyone attempting to describe the conceptual model of space-time, in a lay oriented manner.

 

I think you have not read the wiki article, which i linked in post #117, where infinitesimal mass is explained as: "The Schwarzschild geodesics pertain only to the motion of particles of infinitesimal mass m, i.e., particles that do not themselves contribute to the gravitational field.

Do read this site http://en.wikipedia.org/wiki/Schwarzschild_geodesics. (I am linking once again).

 

Gravitational lensing is a 3D physical phenomena, though its mathematics are in 4D.

 

A particle is gravitationally significant if it is affected by gravitational field and either accelerates or decelerates in the gravitational field. This particle will follow Einsteins Equivalence Principle.

However if a massive particle(like Neutrino) travels at a constant speed in the gravitational field, it can be said that; this particle is gravitationally insignificant. Does particle Neutrino follow Einsteins Equivalence Principle?

 

I think at some time in the past rpenner answered the first part of your question about the neutrino. It, (the neutrino) is affected by gravity. It does not travel at the speed of light, but so close that the difference is not measurable. (If it was not rpenner, I am sure it has been addressed. You have raised the issue of the neutrino several times.)

The velocity of a neutrino is not constant in a gravitational filed. It is just so close to c, that any variation is unmeasurable.

The problem in "seeing" that in most circumstances, is its mass is extremely small and its velocity is very near that of light. The extremely small mass of the neutrino leads to an extremely small inertia.., together with its near c velocity, its path through curved space-time will be very similar to that of light.., as close as any massive particle can get.

The second part of your question, "Does particle Neutrino follow Einsteins Equivalence Principle?", would only make sense if you were able to measure a neutrino accelerating. The principle of equivalence is about the equivalence of uniform acceleration and an equivalent stationary location in a gravitational field. The principle of equivalence can only be examined where some measureable uniform acceleration exists.

 

Let us consider that, particle Neutrino is affected by gravity and it has a near light speed. What would be its curvature in a gravitational field, where gravitational lensing is hapenning? Exactly that of photon or 'slightly more' or 'slightly less'?

I think this bending for particle Neutrino will be 'slightly more' than that of particle photon, because particle Neutrino has mass and it is affected by gravity.

It can be said that as the mass of the particle increases, its bending will increase and vice-versa.

 

Beginning with the word, " Let us consider...", is like saying let us guess about this...

Data obtained from the 1987A super nova event supports conclusions that over a distance of some 168,000 LY the velocity and path through space-time of the neutrino, is indistinguishable from that of light... Note, it does not prove that the neutrino travels at the speed of light, or that it travels an identical path through space-time, it just supports the fact that even over the distance involved, the difference is less than the uncertainty involved in measurement.

Theoretically it would seem that the mass and inertia of the neutrino would have, an impact on how closely its path through spacetime, is to that of a photon.., but the evidence so far, is that any difference is beyond our ability to measure. The theory here is based on an understanding of how the inertia of more massive objects influences their interaction with gravity and the curvature of space-time, not on any data directly associated with the neutrino.

Think about it. It is easier for us to detect and measure photons — light, than it is to detect and measure neutrinos.

It would not be the mass of an object alone that influences how the curvature of space-time affects its path. Two objects of different masses and the same velocity, would be affected in the same manner. Two objects of different velocities would be affected differently. It is the inertia relative to mass, that is important rather than mass as an absolute value.

 

Consider an hypothetical particle of mass m and travelling at the velocity of c. What would be its curvature in gravitational lensing? Same as photon or slightly more?

My understanding is that bending of such particle will be slightly more than that of particle photon though its speed is c, because of its mass m and gravitational effect.

What you think?

 

Your hypothetical includes insufficient information...

If a mass of 100 kilos traveling at c past the earth, the Earth's gravitational field would have little affect, just as it would have little affect on the path of light or a neutrino. Let it pass near a neutron star or black hole and things would likely turnout different.