Geodesics... Light, gravity, black holes

[md65536]

I have a bunch of questions and ideas... please point out any statements that are false.

 

Since reading of the concept in GR that gravitational attraction is a kind of inertia more than a force,

I've been trying to build a conceivable understanding of it.

 

Since then I've tried to "correct" anyone who speaks of light following a curved geodesic as if the light is being affected by gravity, as if gravity is "pulling on the light".

 

I recently read in wikipedia that photons have mass, so does that mean they are affected by gravity? So I'm wrong???

 

But then I read here http://everything2.com/title/Geodesic that geodesics are paths of zero acceleration (in the case of light, this would only be a change of direction). This means light is not "pulled" by gravity, only that its path can be curved by mass.

 

 

So I did some thought experimentation.

 

Suppose you have some photons traveling along a geodesic (which is curved, by a large nearby mass, according to some remote observer).

Suppose you have 2 mirrors at arbitrary positions along the path, which reflect the light back along the same geodesic.

Then the light will continue on that path indefinitely. It will not accelerate towards the gravitational mass.

 

However, I realized the same can be said about a ball or a planet: If it is bounced (perfectly with no energy loss, assume) off a mirror back from the direction it came, it will follow the same path it took to get to the mirror, even though it is being accelerated by gravity. Similarly, in a perfect orbit it will remain on the same path indefinitely. So this thought experiment says nothing about how light and matter are different when it comes to gravity.

 

 

Here now is my speculative explanation of how gravity works without treating anything as a "force":

Suppose again that you have photons traveling a single curved path near a gravitation mass, reflected between 2 mirrors.

Now say that at one of the mirrors, you shift the photons one unit of length toward the gravitational mass as it's being reflected.

It will follow a slightly different geodesic, one which seems "more curved" to a remote observer, because it is closer to the gravitational mass.

So when the photons reach the other mirror, they will be more than 1 unit away from the original geodesic.

Suppose at the second mirror you shift the photons one unit away from the gravitational mass, and then reflect them.

The photons will now follow a geodesic somewhere in between the previous 2 geodesics it had followed.

If you keep repeating this (shifting the photons 1 unit toward the mass at one mirror, and 1 unit away from the mass at the other mirror), then the photons will move toward the gravitational mass, even though no force has acted upon them -- other than the fact that something needs to shift them. But what if they were already shifting like that on their own?...

 

Now instead of mirrors and shifting photons, imagine energy oscillating say in a circular or spherical path.

This is how I imagine for example electrons around an atom.

I assume that all matter can be described as energy (according to e=mc²) -- I saw a posting somewhere here that says that's an incorrect way to view it... is it? --

and that all energy travels at the speed of light,

and also that all traveling energy follows the same geodesics that light does.

 

So if matter is made up of energy oscillating in at least 2 dimensions (one of which is roughly parallel to the direction toward the gravitational mass and one which is roughly perpendicular), then you have energy that is constantly moving in slightly different geodesics, which cause it to move toward the gravitational mass, and as it gains momentum the constant movement toward the mass results in gravitational acceleration.

 

 

Digression: Here is why I think that math is so fundamentally important.

As a crackpot I might say "This completely explains gravity" and end there. That's the extent of my understanding and that's as far as it will ever go.

But a vague idea that shows one mass will move toward another gravitational mass when treated as oscillating energy does not fully explain gravity. Gravity can be described with specific mathematical values, and if my theory can't match them, then my theory does not explain gravity.

 

But another reason that math is important, is that there are lots of different ways to do the math. If I model this oscillating energy idea, there are many variables to work with. Does the size of the oscillation only work with a specific value? Does that correspond to existing measurements of particles? Does it work if the oscillation is treated as completely random in 3 dimensions? Or uniform oscillation in 2 dimensions? Finding ways to make the math work can tell you a LOT about the details of the idea.

 

One day I might try to figure out the math involved with this idea. For now, I can't conceive of the math, and consequently I can't conceive of the possible related ideas that the math might suggest. Without math, all these ideas of how the oscillating energy might be more precisely described, are lost.

 

 

 

Back to the speculation...

 

This idea suggests that "size" is what lets a mass be accelerated in curved spacetime (IE accelerated by gravity).

 

 

So this suggests that a black hole singularity is not affected (accelerated) by gravity. Does this relate to any other existing theories that you know of?

 

I figured this means that singularities, like light, follow geodesics.

A black hole can still be "steered" by external mass, because that external mass can define the curvature of geodesics.

 

So I have this vague idea of 2 black holes on a collision course, would not so much "pull on each other", but rather curve space so that they end up headed straight for each other.

 

 

BUT WAIT, i says to myself...

 

If a black hole can travel along a geodesic, that means that there is a geodesic "pointed away from it."

If that's the case, then light could travel along that geodesic and escape the black hole.

 

This lead to the idea that black holes don't "move through space". Once you have a singularity, it is where it is. It could be treated as an absolute position in space, perhaps??? This doesn't really matter so much, because they can curve space around them, essentially devouring it or something, and 2 black holes can merge by shrinking the space between them to nothing.

 

It's like a fat man at a table, too big to lean over and reach for another helping of turduckpizpizburgon (bacon stuffed in a burger stuffed in a pizza stuffed in another pizza stuffed in a duck stuffed in a turkey and then double deep-fried to perfection), but he can bring the food to him by pulling on the table cloth.

 

 

 

I realize these ideas get confused and convoluted by the end. In the future I might try to explore this properly (with some math and maybe even some research of existing theory, who knows). Does anyone know of some related info or ideas or corrections? Thanks.

Edited January 16, 2011 by md65536

[lemur]

This lead to the idea that black holes don't "move through space". Once you have a singularity, it is where it is. It could be treated as an absolute position in space, perhaps??? This doesn't really matter so much, because they can curve space around them, essentially devouring it or something, and 2 black holes can merge by shrinking the space between them to nothing.

If a large star in a galaxy collapsed into a black hole, why would it suddenly stop moving relative to its gravitational surroundings? I think your "fat man pulling the table cloth" analogy just makes a case for framing all motion relative to a black hole instead of vice versa, but I think that you have the freedom to frame any motion in any frame you want, regardless of whether a black hole is involved or not.

[IM Egdall]

Since reading of the concept in GR that gravitational attraction is a kind of inertia more than a force,

I've been trying to build a conceivable understanding of it.

 

Since then I've tried to "correct" anyone who speaks of light following a curved geodesic as if the light is being affected by gravity, as if gravity is "pulling on the light".

 

I recently read in wikipedia that photons have mass, so does that mean they are affected by gravity? So I'm wrong???

 

But then I read here http://everything2.com/title/Geodesic that geodesics are paths of zero acceleration (in the case of light, this would only be a change of direction). This means light is not "pulled" by gravity, only that its path can be curved by mass.

 

In GR, gravity is spacetime curvature. Take the Earth for example:

- Time warp: The mass/energy of the Earth slows time down. That is time runs slower on the surface of the Earth than it does in outer space where there is no gravity.

- Space warp: The radial distance between two point in space near the surface of the Earth is stretched compared to the distance between these same two points if there was no Earth present.

This combination of time warp and space warp due to the presence of the Earth's mass/energy is called spacetime curvature. It is this spacetime curvature which determines the path of of everything in its neighborhood (such as the Moon around the Earth).

 

Notice I said mass/energy. Both mass and energy warp space and time (produce spacetime curvature). So a photon which is massless but has energy also produces spacetime curvature (gravity).

 

The so-called geodesic is the shortest possible path on a curved surface. Particles with mass and particles with zero mass like photons follow a geodesic path through curved spacetime. See link http://marksmodernphysics.com/ and click on selected animations, "What is a geodesic?" for simple example of a geodesic.

[md65536]

If a large star in a galaxy collapsed into a black hole, why would it suddenly stop moving relative to its gravitational surroundings? I think your "fat man pulling the table cloth" analogy just makes a case for framing all motion relative to a black hole instead of vice versa, but I think that you have the freedom to frame any motion in any frame you want, regardless of whether a black hole is involved or not.

Yes, there's a problem with my reasoning but I'm not sure where. The relativeness of motion would suggest that if a black hole singularity can't move relative to us, then we can't move relative to it. Doesn't make sense.

 

Let me try to rephrase my question.

 

Light cannot escape a black hole because space around it is so severely warped that "straight lines" (geodesics) appear to external observers to curve back toward the black hole.

My conjecture is that black hole singularities would not be affected (accelerated toward) external gravitational masses.

If a singularity does not accelerate, then it should travel in a straight line. The singularity should travel along a geodesic.

 

I guess I'm just confused about how to describe a black hole traveling through space that is so severely curved. It seems to me that the only place a singularity could move to (like its light), is back toward itself.

 

 

Perhaps this is just me confusing relative motion and the "fabric" of spacetime, which to me is just a measurement. Perhaps what I'm saying is nothing more than "an object cannot move to any location relative to itself; it is always stationary relative to itself"... fairly vacuous.

 

 

As an aside...

I think of "gravitons" as an analogy or an effect of measurement rather than a fundamental physical reality, but...

If light cannot escape a black hole, how do gravitons escape it? Wouldn't they travel along the same geodesics?

 

In GR, gravity is spacetime curvature.

 

Isn't gravity an effect of spacetime curvature? It's expressed as a force. Spacetime curvature can't be expressed as a force, can it?

 

 

Particles with mass and particles with zero mass like photons follow a geodesic path through curved spacetime.

Hrm, I don't know where I read about the mass of a photon (somewhere on wikipedia), but I seem to have mixed up mass and maybe "relativistic mass" http://www.weburbia.com/physics/photon_mass.html.

 

 

If a particle with mass is accelerated due to gravity (which is due to to spacetime curvature) then its path isn't a geodesic.

[lemur]

Light cannot escape a black hole because space around it is so severely warped that "straight lines" (geodesics) appear to external observers to curve back toward the black hole.

First of all, in what sense does a geodesic "appear" to be a straight line except in the sense that some object, particle, or light is traveling as an expression of its own momentum without changing course due to force-additions? My understanding of geodesics is that objects/particles can be doing figure-8s but for them it is a straight line because they're not undergoing a change of direction relative to their natural momentum.

 

My conjecture is that black hole singularities would not be affected (accelerated toward) external gravitational masses.

If a singularity does not accelerate, then it should travel in a straight line. The singularity should travel along a geodesic.

Is this because no energy/matter can interact with the BH in a way that produces reaction-force in the black hole? So you're basically saying that nothing can push or pull the BH so how can it move? What about its velocity relative to other things prior to becoming a BH?

 

I guess I'm just confused about how to describe a black hole traveling through space that is so severely curved. It seems to me that the only place a singularity could move to (like its light), is back toward itself.

I view gravity fields as whole entities, so I would think that all the curvature surrounding the BH is part of the black hole, so when it moves all curvature surrounding it moves with it. Likewise, I have the sense that although changes in a gravitational field may move at C, the field itself is a static thing with volume. So I don't think gravity has to 'get' from the singularity to the outskirts of the field, because I just think of the field as existing together with the singularity as part of the same spacetime-unit. That may be flawed but it is what makes sense to me at this moment.

 

Perhaps this is just me confusing relative motion and the "fabric" of spacetime, which to me is just a measurement. Perhaps what I'm saying is nothing more than "an object cannot move to any location relative to itself; it is always stationary relative to itself"... fairly vacuous.

Idk, I think maybe force fields do move relative to themselves when they expand and contract to generate waves. I think they can maybe stretch and compress each other. Maybe I play with magnets too much, but it seems like when you push the repellant poles of two magnets together their fields compress like beach-balls pressing against each other. This analogy works better for magnetic repulsion, because pressure is more tangible when it's positive. Magnetic attraction also seems analogous to pressure but in the sense of being a vacuum, i.e. like moving two vacuum cleaner hoses toward each other while they're sucking?

 

 

 

 

[md65536]

First of all, in what sense does a geodesic "appear" to be a straight line except in the sense that some object, particle, or light is traveling as an expression of its own momentum without changing course due to force-additions? My understanding of geodesics is that objects/particles can be doing figure-8s but for them it is a straight line because they're not undergoing a change of direction relative to their natural momentum.

Yes, that sounds right.

 

A geodesic appears straight from any point on the geodesic, and can appear curved from other locations.

For example, if you were on a rocket heading toward a galaxy whose light is gravitationally lensed on its path to Earth, some remote observer might see that you appear to be curving.

You would observe that you traveled in a straight line the entire trip. The destination galaxy would always appear directly in front of you (you'd never have to turn), and Earth would always appear directly straight behind you.

An observer on Earth who is also on the same geodesic would also observe that you appeared to constantly move straight toward the galaxy.

 

 

Is this because no energy/matter can interact with the BH in a way that produces reaction-force in the black hole? So you're basically saying that nothing can push or pull the BH so how can it move? What about its velocity relative to other things prior to becoming a BH?

No, the conjecture is that energy (or particles) need size in order to be affected by gravity. Basically the energy needs to travel along different geodesics in order to accelerate.

A black hole singularity in particular has no size, so accordingly it would not be affected by gravity (and may or may not be affected by the curvature of space caused by external mass -- this is where I'm confused though).

 

I guess that when a singularity is formed, it basically "escapes" the influence of the universe. I guess it might continue traveling on the course it had when it formed, never accelerating.

 

 

 

 

Now, to throw in even more confusing ideas:

Imagine we consider the known universe to be a black hole according to any external observers.

The conjecture suggests that we inside the black hole would not be influenced gravitationally by anything outside the universe,

however, the "exo-universe" can still be gravitationally affected by our universe (a black hole to them). As for the two interacting, we could receive energy from outside, but no energy could escape our universe (except as Hawking radiation?).

This is a far-fetched conjecture but I think it might be potentially relatable to our current understanding of the universe?

 

 

[lemur]

No, the conjecture is that energy (or particles) need size in order to be affected by gravity. Basically the energy needs to travel along different geodesics in order to accelerate.

A black hole singularity in particular has no size, so accordingly it would not be affected by gravity (and may or may not be affected by the curvature of space caused by external mass -- this is where I'm confused though).

I think I already said this, but I don't see why you would say that a black hole has no size because it's center is defined as a singularity. Why aren't you considering the entirety of the BH's gravitational field as its size?

 

I guess that when a singularity is formed, it basically "escapes" the influence of the universe. I guess it might continue traveling on the course it had when it formed, never accelerating.

I don't see why a BH's gravitational field wouldn't interact with other gravitational fields as it changed position relative to them. If, say, a comet suddenly shrank into a black hole for some reason, it's gravitational field could still interact with the gravitational field of the star it was approaching, no? Wouldn't its geodesic path shift according to the interaction between its own gravitation and that of the star it was approaching? Wouldn't this occur with any two gravitationally significant bodies as they approach each other?

 

Now, to throw in even more confusing ideas:

Imagine we consider the known universe to be a black hole according to any external observers.

The conjecture suggests that we inside the black hole would not be influenced gravitationally by anything outside the universe,

however, the "exo-universe" can still be gravitationally affected by our universe (a black hole to them). As for the two interacting, we could receive energy from outside, but no energy could escape our universe (except as Hawking radiation?).

This is a far-fetched conjecture but I think it might be potentially relatable to our current understanding of the universe?

Imo, if the observed universe was the product of spacetime expansion within a black hole, I would think all incoming matter/energy would be concentrated at the moment of the big bang. I don't see how matter/energy entering a black hole would coincide temporally/spatially with its appearance in the universe within. Where would such matter/energy suddenly appear if it were to enter the universe from outside? All points within the universe are supposedly moving away from the initial moment of the big bang through spacetime expansion. Do you imagine some radiant center of the universe where matter/energy captured outside the universe is consistently emitted into it like a gushing fountain of fresh input?

 

 

[md65536]

I think I already said this, but I don't see why you would say that a black hole has no size because it's center is defined as a singularity. Why aren't you considering the entirety of the BH's gravitational field as its size?

I'm speaking only of the singularity.

Other masses would attract the rest of the black hole due to gravity, but the singularity would be "free" from the influence of even the rest of the black hole.

In a sense, the black hole as a whole would have to go where the singularity goes. The singularity can "pull along" the rest of the BH's matter, but the rest of the BH can't change the velocity of the singularity.

 

Except by modifying geodesics, as you also mention later in your post...

 

 

When I speak of "size" i'm speaking of particles I guess, or more to the point I'm speaking of objects that can be treated as a whole with respect to the conjecture involving oscillating energy. The energy inside a black hole's singularity wouldn't oscillate in the area outside the singularity (I guess???); to the energy inside the singularity, it is confined to a single point. The energy has no size.

 

Similarly, the size of an object like a table wouldn't make a difference, because the energy of its matter oscillates on the size scale of particles, not the table as a whole.

This of course fits reality: Larger objects don't fall faster.

However the conjecture does say that if energy oscillates through a bigger volume, the force of gravity on it will be larger.

This suggests that larger particles have more mass.

This also suggests that particles that are smaller due to length contraction should have less mass -- I think SR claims the opposite will happen?, so that might be proof that this conjecture is wrong?

 

I don't see why a BH's gravitational field wouldn't interact with other gravitational fields as it changed position relative to them. If, say, a comet suddenly shrank into a black hole for some reason, it's gravitational field could still interact with the gravitational field of the star it was approaching, no? Wouldn't its geodesic path shift according to the interaction between its own gravitation and that of the star it was approaching? Wouldn't this occur with any two gravitationally significant bodies as they approach each other?

Yes, if something with zero size follows a geodesic, its path can still be controlled by curving the geodesic. However, even in that case it is not being accelerated... it is just acting on inertia. I don't really know what I'm talking about enough to express it clearly.

 

Imo, if the observed universe was the product of spacetime expansion within a black hole, I would think all incoming matter/energy would be concentrated at the moment of the big bang. I don't see how matter/energy entering a black hole would coincide temporally/spatially with its appearance in the universe within. Where would such matter/energy suddenly appear if it were to enter the universe from outside?

As for location: The holographic principle suggests that every point on a black hole's event horizon maps to every point inside the black hole, and vice versa (someone correct me if that's wrong),

so the energy entering a black hole may appear everywhere within the black hole... perhaps as vacuum energy, or quantum fluctuations or dark energy.

 

As for time: ... Actually I can't conceive of the meaning of time for a singularity that exists for more than an instant as seen from outside the singularity. Perhaps similar to the holographic principle, energy that enters the singularity at any specific time outside the singularity, would map to all time inside the singularity??? I'm completely detached from reality on this idea, now, but I do like the idea that any energy that enters the singularity from outside, at any outside time, could show up inside as energy of the big bang, or in other words as energy that is there for all of known time within the singularity. I don't know though. This is beyond my ability to reason about it. I can't conceive of a mapping from external time to internal time. Time inside or outside of the singularity I would think is "non-existent" or something from the other's perspective.

 

All points within the universe are supposedly moving away from the initial moment of the big bang through spacetime expansion. Do you imagine some radiant center of the universe where matter/energy captured outside the universe is consistently emitted into it like a gushing fountain of fresh input?

 

I prefer to think of it this way: All points in the universe are the location of the big bang. From any point's perspective, from the big bang until now, that point has remained stationary relative to itself. This makes sense when we consider the big bang to start with a singularity; all locations in the universe had the same location at the start. Also, from any point's perspective, the rest of the universe appears to be expanding outward from that point. So I would say that all points in the universe are its "center"??? (or something with the same "feel" as that but expressed more precisely), which at least is compatible with the holographic principle I think.

Edited January 18, 2011 by md65536