Is gravitation faster than light?

[CarstenDierks]

As far as I read, gravitation or better: gravitational waves expand with c.

However, particles like photons which are moving along with c are subject to the curvature of space. Regarding a black hole, light cannot escape with c but gravitation can.

Is gravitation thus faster than c?

Carsten

[dextercioby]

As far as I read, gravitation or better: gravitational waves expand with c.

However, particels like photons wich are moving along with c are subject to the curvature of space. Regarding a blackhole, light cannot escape with c but gravitation can.

Is gravitation thus faster than c?

Carsten


The short answer is:NO.What do you mean,"gravitation can (escape a blackhole)"...???Gravitation IS a black hole (too)...A singularity in the gravitational field,that is...If u want to,a particular solution to the Einstein equations...

Daniel.

[Hurkyl]

The gravitational field outside the black hole is already there; it doesn't need to "escape".

Of course, anything that happens inside the black hole cannot propagate to the outside... so any gravitational waves that are inside the hole never make it out.

The same, incidentally, is true of the electromagnetic field of the hole.

[Problem+Solve=Reason]

Hasn't science, so far, proven it be impossible to move faster than c?

------ Life is a Problem... SOLVE IT!!!!

[CarstenDierks]

Hi Problem+Solve,

Hasn't science, so far, proven it be impossible to move faster than c?
Not quite. Theoretical physics do not rule out speeds faster than c (see also: Dirac theory). Mass cannot move as fast or faster than c.

Particles faster than c are called tachyons. However, no one has found tachyons so far.

Of course, anything that happens inside the black hole cannot propagate to the outside... so any gravitational waves that are inside the hole never make it out.
Hm, Hurkyl, is it really true that gravitational waves cannot leave a black hole?

Changes in a gravitational field are supposed to be "communicated" by gravitational waves. If gravitational waves (which have not been detected so far) were not able to leave a black hole, nothing outside a black hole would notice changes in the gravitation of the black hole.

Since black holes of different masses are observable, are we not able to conduct that they can send out gravitational waves with this information?

Otherwise, black holes should all show the same mass (= gravitation): the mass which is necessary to initially form a black hole. Afterwards, information on the increase of its mass would not be able to be "communicated" outside the black hole...

Moreover, would there be only a 0-or-1 approach to the escape of gravitational waves from a black hole? A gradual influence on the gravitational waves seems more likely, since gravitational fields and the curvature of space also gradually influence c.

So far I read that the existing theories of gravitation (including SRT, GRT) and EM show explanatory gaps in situations of singularity (big bang, black holes). Is this one of the gaps or which are they?

Carsten

[Problem+Solve=Reason]

Alright, thank you.... Do you know a good referece page on the Dirac Theory? I understand the basics of it, but want to know more. Again, thankyou...

---- Life is a Problem.... SOLVE IT!!!!!

[CarstenDierks]

Alright, thank you.... Do you know a good referece page on the Dirac Theory?

Well, I do not know the profound reference pages but here are some links:

A simple introduction:
http://encyclopedia.thefreedictionary.com/Tachyon

A simple introduction into the equation:
http://www.iscmns.org/iccf11/ppt/FilippovDtachyon.pdf

Not bad at all:
http://www.cbloom.com/physics/2d_dirac.html

More detailed, with coupling of branes:
http://www.iop.org/EJ/abstract/1126-6708/2001/02/002
http://citebase.eprints.org/cgi-bin/citations?id=oai:arXiv.org:hep-th/0003122

Have fun reading!

Carsten

[Hurkyl]

Hm, Hurkyl, is it really true that gravitational waves cannot leave a black hole?

In GR, I'm quite sure -- otherwise we'd be able to get information from inside the black hole.

The resolution is this: the increase of mass doesn't occur inside the hole -- it occurs on its boundary as massive objects fall from the outside to the inside.

[CarstenDierks]

The resolution is this: the increase of mass doesn't occur inside the hole -- it occurs on its boundary as massive objects fall from the outside to the inside.
That is a good point!

The boundary must be the Schwarzschild radius, right?

[Hurkyl]

The boundary is the event horizon. It doesn't have to be spherical... (but maybe it quickly changes into a spherical shape? I don't recall for sure)

[CarstenDierks]

As far as I know the Schwarzschild radius is the event horizon since the escape speed at this point becomes c.

[caribou]

Something I realized a day or two back is that in the sum-over-histories version of quantum theory, if a particle is near a black hole then some of the paths being summed up must cross over the event horizon and come back out again! :biggrin:

These are obviously faster-than-light histories which form part of the sum-over-histories that result in the light-speed-or-less particles that make up the universe.

I knew there were faster-than-light histories but this crossing over the event horizon was just an amusing thing I realized. Thought I'd mention it. :smile:

[CarstenDierks]

Thanks, Caribou, that is another interesting point. Maybe the particle will not be able to escape the black hole once it has passed the Schwarzschild radius - even if its probability inside the radius was just a fraction above zero. If it interacts with the black hole inside the radius its probability becoms 100% (like interaction with a measuring device).


But still my initial question remains. Maybe I should state it differently:

In the theory of gravitational waves: Are these waves influenced by relativity and the curvature of space (as photons and other particles are) or not?

If yes, I would consider it paradox because gravitation would influence itself.

If no, I would consider time dilation, lenght contraction and the like to behave differently with gravitational waves as they behave with other particles like photons. (But this would also imply that c is not the proper speed for gravitational waves.)

Does anybody know the answer?

Carsten

[caribou]

I just looked up Jim Hartle's book on gravity and noticed something about a definition.

Gravitational waves are "ripples in spacetime curvature" caused by "any mass in nonspherical, nonlinear motion". But a mass in spherical and/or linear motion must still affect other masses.

So I assume this means gravitational waves and gravitons are different things, with the former emitted in many situations and being made up of the latter.

I think gravitational waves from a black hole are like ripples when a stone is moved back and forth in water. The stone doesn't really change in any significant way.

Gravitons would be smeared out quantum particles with wave properties that can make up these ripples when they occur. So a graviton is a gravitational wave in a different sense.

My guess is that with gravitons we'd be talking about them in smeared out orbits outside and inside the black hole's horizon with them being in increasing and increasing numbers closer to the center. And this is where the gravity comes from, with these orbiting gravitons affecting the paths of other gravitons and anything else.

A black hole is a big cloud of gravitions going out from the singularity to the event horizon and beyond? And something which disturbs a black hole causes a whole lot of gravitons to be knocked out of orbit and form a gravitational wave?

I'm speculating well beyond my own level of knowledge now. :bugeye: :biggrin:

[selfAdjoint]

If you accept a graviton theory of gravity, a gravity wave would be a coherent stream of gravitons, i.e. their wave functions would be in macroscopic synch.

[Leo32]

As far as I read, gravitation or better: gravitational waves expand with c.

However, particles like photons which are moving along with c are subject to the curvature of space. Regarding a black hole, light cannot escape with c but gravitation can.

Is gravitation thus faster than c?

Carsten

According to the GRT, curvature is gravity and vice versa.
Gravitational waves should not be imagined like electro magnetic waves, but rather as curvature ripples which move across the 4 dimensional space.

As such, gravity does not escape from a black hole. It is created by the black hole, in this sense that the black hole curves the space around it.

Greetz,
Leo

[CarstenDierks]

Thank you caribou, selfAdjoint and Leo!

But I believe I still do not have an answer to my question. I am sorry for bugging you, but maybe I have missed the clue.

Let me put the question differently:

If we think of gravitons instead of gravitational waves, do they move with the speed of c?

And are they influenced by relativity as well as the curvature of space?

Example: Are gravitons from a mass m deflected if they pass nearby the space curvature of another mass M?

Carsten

[MiGUi]

As far as I remember, fields are considered to be established when you do a problem. They travel at the speed of light, so if you don't have mass or charge in the infinite, then the fields in the infinite are zero always.

[DB]

Leo said it well, As such, gravity does not escape from a black hole. It is created by the black hole, in this sense that the black hole curves the space around it.
Light cannot escape a black hole because the force of gravity i.e gravitons, are forcing it them back. Gravity is the black hole (though the singularity is mass).

When we say gravity waves travel at c, a good example of this is such: If the sun were to disapear right now, it would take ~8mins for earth's orbit to be affected (aswell for us to see it). So picture a wave through 4 dimensional spacetime traveling at c. So if a black hole was to disapear, let's say a black hole powering a galaxie, the gravitons would travel at c, so each star would lose its orbit at different moments.

[CarstenDierks]

Hi DB,

that is correct. By theory, the observer on such a star (or an observer orbiting it) should notice ("watch") the black hole vanish at the same time his star loses the orbit around it.

As such, gravity does not escape from a black hole. It is created by the black hole, in this sense that the black hole curves the space around it.

Also correct. But are gravitons or gravitational waves the same as curvature of space? The curvature itself is static in the sense of resting in space. The wave (or gravitons) propagate with a speed (c?). So it must be two different effects even if they have the same origin.

But this would imply, that

a) gravitons are either able to propagate at a higher escape speed from the black hole than photons. (However it would mean our observer´s star would lose orbit before the observer notices the black hole vanish.)

or

b) gravitons propagate at c but we do not know how they escape a black hole. (And does the relativity of c apply to gravitons as well: speed, time, length contraction?)


I do not want to be impolite. My insisting on this point might seem like it but it is truly not and I sure do not want it to look like it. I am just a little curious.


Of course, anything that happens inside the black hole cannot propagate to the outside... so any gravitational waves that are inside the hole never make it out.
Hurkyl, is this an accepted theory or rather a personal assumption?

If gravitons or gravitational waves occur from the boundary of a black hole (Schwarzschild radius), why wouldn´t photons do the same? But wouldn´t we see a white hole instead of a black one?


Your curious

Carsten

[Problem+Solve=Reason]

Hurkyl, is this an accepted theory or rather a personal assumption?

If gravitons or gravitational waves occur from the boundary of a black hole (Schwarzschild radius), why wouldn´t photons do the same? But wouldn´t we see a white hole instead of a black one?


Your curious

Carsten

Are you purposing that photons would originate from the boundary of the black hole, and then be sucked into the middle therefor making the black hole bright? Plus, I am wondering if the Schwarzschild Radius is the same thing as an event horizon. I am currently reading up on Schwarzschild Radius and should know more soon...
Also, why would gravitons have to escape the black hole when EVERTHING is being sucked into it. Wouldn't the photons and gravitons be travaling "side by side" at the same rate of speed, going towards the black hole. I'm not sure where im going with that one but hopefully ill find something interesting when I get where im going. :yuck: :grumpy:

---- Life is a Problem... SOLVE IT!!!!

[CarstenDierks]

Are you purposing that photons would originate from the boundary of the black hole, and then be sucked into the middle therefor making the black hole bright?
Hi Problem+Solve,
No, I was referring to an earlier post by Hurkyl (#8). His suggestion was that gravitons might originate from the boundaries to be able to escape the black hole.

So my reasoning was: Why should the same not apply for photons?

Or the other way around: Black holes are black because they do not emit photons at their boundary. So why should they emit gravitons at that point when capturing additonal mass without emitting photons at the same time?

Carsten

[DB]

But are gravitons or gravitational waves the same as curvature of space?

A gravitational wave is packets of gravitons, so we consider gravitational waves to be made up of gravitons. When a star is born, it's mass and density will curve space, by doing so it automatically sends gravitational waves traveling at c. Like throwing a rock in a pond, the second the rock hits the water it "curves' the body of water, with ripples traveling at a certain speed.

But this would imply, that

a) gravitons are either able to propagate at a higher escape speed from the black hole than photons. (However it would mean our observer´s star would lose orbit before the observer notices the black hole vanish.)

or

b) gravitons propagate at c but we do not know how they escape a black hole. (And does the relativity of c apply to gravitons as well: speed, time, length contraction?)


Remeber that a graviton is a very hypothetical particle, it is used mainly in string theory, helping to intertwine both quantum mechanics and relativity.
Gravitons have rest mass zero just as photons, so we now know that they will travel at c and can have similar properties.So don't get confused that gravitons are escaping a black hole, they dont need to, they are lost in space. What I mean is, that when a black hole is created it sends gravitational waves (gravitons) outward, through space, "forever". So it doesn't need to escape a black hole, the creation of a black hole itself sends them outward. You might ask then what is keeping photons from escaping if gravitons are gone. Spacetime curvature.

I've explained this in a different thread

A common anology of spacetime fabric is "space foam" (like those beds where you can leave a hand print) a rubberish fabric. If you were to place a bowling ball in the center of space foam is would sink, curving the fabric along it's circumference. Now if you took a ball with exactly the same mass but with 1/10th the circumference and radius it will sink to the same depth that the bowling ball did and curve the space foam around its circumference. But since the circumference is much smaller, it would lead to a greater curvature of space foam. It would look like a hole. I think you can picture it. So knowing this situation, general relativity tells us that: the greater the curvature of spacetime, the strong the gravitational force. So if we took a marble and placed it on the space foam for both situations (very important that we don't place it with a force or initial velocity because it would fall into "orbit" for a bit) Here's what would happen:

The bowling ball: the marble would roll towards the center of the bowling ball at a moderate accelerated speed.

The denser bowling ball of same mass: the marble would actually roll slower towards the "event horizon" of the hole, though once it passed it, it would fall towards the ball at much faster accelerated speed than our other situation.

Edit: I realize now surface area might be better to say than circumference.


I found this too: http://www.bun.kyoto-u.ac.jp/~suchii/embed.diag2.jpg
So mathematically Einstein proved (in short) that a photon in a black hole cannot escape because the hole is to deep. Though spacetime curvature doesn't exist as an example of a space fabric situation, it is just a way we use to see what going on, math is the true way of understanding gravity.


[QUOTE]If gravitons or gravitational waves occur from the boundary of a black hole (Schwarzschild radius), why wouldn´t photons do the same? But wouldn´t we see a white hole instead of a black one?[QUOTE]

A bondary of a black hole is the event horizon. Any photon (anything) passed the event horizon can shine to it's hearts content. Pass the event horizon black holes aren't so bad, they power our galaxies, they are key to life. Also whites holes have not been proven to exist, and are very complicated phenomena, breaking laws of thermodynamics.

If you have anymore questions or I didn't cover what you want to know just ask. :biggrin:

[DB]

Plus, I am wondering if the Schwarzschild Radius is the same thing as an event horizon. I am currently reading up on Schwarzschild Radius and should know more soon...

Picture a cone with the base upward. The tip of the cone is the singularity, the circumference of the circular base is the event horizon, the radius of that base is simply the schwarzschild radius. :wink:

[Hurkyl]

No, I was referring to an earlier post by Hurkyl (#8). His suggestion was that gravitons might originate from the boundaries to be able to escape the black hole.

I said nothing about gravitons! Nor about photons! GR is a classical theory, which appears to be inconsistent with current methods of quantization. Similarly, the EM field that one could describe in GR is a classical field, not a quantum field. AFAIK, any talk about photons in GR is really speculative -- "Once we get these things united, things probably should behave like this..."


Or the other way around: Black holes are black because they do not emit photons at their boundary.

No, they're called black because light cannot escape from the inside.

[CarstenDierks]

If you accept a graviton theory of gravity, a gravity wave would be a coherent stream of gravitons, i.e. their wave functions would be in macroscopic synch.
Of course we cannot say for sure if graviton particles exist. For string theory and quantum mechanics it would be very important, as I understand.

But can you (or anybody else) tell me, whether in theory gravitational waves (= gravitons) and the curvature of space (= gravitation, gravitational force) are equal?

Carsten

[CarstenDierks]

Hi DB,

thanks for the substantial explanations. That helps already to increase my understanding.

If you have anymore questions or I didn't cover what you want to know just ask.
I would like to, if I may.

I am still a little confused when relating all facts.

For me it is difficult to understand why gravitational waves (gravitons) should propagate through spacetime with c and, thus, cause space curvature (if I have understood that correctly).

Difficult because of the following:

(1) If gravitons (gravitational waves) are not at rest in a gravitational field, this would imply to me that mass needs to constantly emit gravitational waves (gravitons) to "replace" those which are "gone".

(2) If mass curves spacetime: Is the curvature once "engraved" in spacetime and "rests" there until a new gravitational wave "updates the information"?

Or:
(3) Is the curvature of spacetime just "newly" evoked by every ripple of a gravitational wave passing by?

(4) Do gravitational waves interfere with each other? Probably yes because gravitational forces and the curvature of space of two objects do add up.

Arising questions:

(5) Is it allowed to conclude out of (4) and (1) that the path of gravitons is not straight but also influenced by the curvature of spacetime (of other objects)? Meaning: Gravitons (gravitational waves) have to travel along our (curved) cosmos as it exists?

(6) Out of (4): What about gravitational forces of 2 objects of identical mass on a 3rd object right in-between the two? Is the gravitational force for the 3rd object zero? But is spacetime not curved at that point due to the sum of the curvature of the first two objects?

(7) Out of (6): So are gravitons (gravitational waves) and the curvature of spacetime really equal?

(8) Out of (2): Is this true for black holes? Do they curve spacetime and the curvature "rests" there because the gravitons (gravitational waves) cannot escape from inside of the black hole? Is the gravitational field of black holes never "updated" by gravitons (gravitational waves)?

(9) Out of (1), (3), (4), (7) and (8): How can black holes capture gravitons (gravitational waves) inside the Schwarzschild radius and, at the same time, emit gravitons (gravitational waves) to curve space and exert gravitational force?

(10) Out of (9): How does quantum and/or string theory explain the speed and escape speed of gravitons (gravitational waves)?


I hope I was able to put everything into the context as it currently occurs to me - and to show where my gaps in understand (relating) it are situated.

Carsten

[Louis Cypher]

Vey interesting but arent you forgetting that the graviton has never been detected so all of this is just conjecture, personally I think gravity has no force carrier and we have allready unified all the forces; gravity is an effect of mass, there is no mediator, thus it can escape a black hole, as we know even photons probably have mass, all be it extremely small, so gravitons ought not to be able to escape from a black hole either.

Thus my point mass is caused by the atoms themselves not by any mediating force carrier.

[CarstenDierks]

Thus my point mass is caused by the atoms themselves not by any mediating force carrier.
Hm. How should one mass particle get the information where the second mass particle is located at? And how is the (gravitational) force enacted which attracts both particles?

Since a theory on gravitational waves and gravitons does exist, it should also provide answers to the questions I am still having. That is what I am looking for.

Carsten

[DB]

I'm not an expert, but I'll try to anwser your questions with my best knowledge of general relativity. I hope you like reading...


For me it is difficult to understand why gravitational waves (gravitons) should propagate through spacetime with c and, thus, cause space curvature (if I have understood that correctly).

Yup your're gettin it. I guess you could say that gravitational waves cause space curvature, though you could say vice versa, and aswell that gravitational waves are space curvature. They propagate at c because they have rest mass zero as does a photon.


Difficult because of the following:

(1) If gravitons (gravitational waves) are not at rest in a gravitational field, this would imply to me that mass needs to constantly emit gravitational waves (gravitons) to "replace" those which are "gone".

Not exactly so. First let's consider gravitational waves as a force through spacetime. Let's almost forget about graviton particles for they are very hypothetical and are just what make up the gravitational wave. So we don't say gravitation is emited, it's exerted. We know that when space is curved by mass, it will "deforme" all of space, most anologically spacetime fabric.
Like the rock in the pond, when we throw the rock in, ripples will not be continuesly exerted forever, but the ripples that were exerted along the body of water will continue traveling as so until they barely have a wavelenght (or are slowed or stoped by more ripples of another force). Once the rock has hit bottom, it's deformation towards the body of water is finished. Now the water will adapt to have this new rock in its pond. Translation::tongue2: the second a star is formed in space it deformes (curves) spacetime fabric, and by doing so it effects spacetime by sending gravitational waves along space forever. Once the star is formed and balanced in space, it's job is done, and space has adapted to the deformation of this new star. So the star is the rock, the gravitational waves are the ripples and spacetime fabric is the water. So gravitational waves are not constantly emited, it happens once and travels as a wave at the speed of light. Those which are "gone" have already done their job of curving space. They will keeping doing their job forever, but always at further and futher parts of the cosmos. It is now space curvature (created by the wave) to do it's job of creating and exerting gravity. (Think of gravitational waves through the water anology, but don't think of it as what gravity is, because you can't sink to the bottom of spacetime. The bowling ball anology is good for gravity.)


(2) If mass curves spacetime: Is the curvature once "engraved" in spacetime and "rests" there until a new gravitational wave "updates the information"?

Yes. Engraved is a great word. But the altering of a star's gravitational field is usually very minimal because stars are far away from eachother, so there is minimal effect. But it happens and I will give an example soon.


Or:
(3) Is the curvature of spacetime just "newly" evoked by every ripple of a gravitational wave passing by?

Ill say no, but I don't exactly understand the question. Once a gravitational wave has passed a certain spot, that spot is officially considered effected by the mass that sent the wave off. The only way that the certain spot can be effected again by the same mass is if the mass or density were to change (of the mass) or if the mass would disapear, "taking it's wave back". What I mean by this is that if the object were to disapear it would send of a wave that would un-deforme space.
And remember that all this doesn't happen at once, the waves have a finite speed "c", and each spot is affected at different times.


(4) Do gravitational waves interfere with each other? Probably yes because gravitational forces and the curvature of space of two objects do add up.

Right. Right. Here's what I said I would get to. In our solar system, planet's orbits are elliptical, they are eccentric. There are debatable reasons for why, some say it's because planets don't orbit the sun, they orbit the common center of mass between the sun and that planet, some say that other gravitational force of other planets effect orbits, mostly Jupiter. And Jupiter is a great example for more understanding. Because it's so big it has a much stronger force of gravity i.e it curves spacetime more. (this is why it has 63 moons and probably more. More objects are likely to fall in orbit around Jupiter because of its strong gravitational force.) So now picture the sun sending a gravitational wave and Jupiter doing the same. The sun and Jupiter (in astronomical terms) are very close to eachother. So the two waves sent of by each mass will clash together. Once the clash is finished with, spacetime has adapted to the deformation. It's engraved. :wink: Now in the middle of this weird deformation of space (between the sun and Jupiter), we've got planets. The sun obviously has a stronger gravitational force, so the planets orbit the sun, but they are still effected by Jupiter's gravity. Making their orbits eccentric. (This is not completely proven, but today it is said that Jupiter probably has an effect in our solar system.) (And aswell, planet's past Jupiter still feel the effect of both the sun's and Jupiter's gravity) So yes. Gravitational waves interfere with each other.

*The reason planets orbit is around bigger mass is because they start off with velocity.Iif we were to slightly place a planet in space near a star in would be forced towards the star at an accelerated speed (dependant on the mass). "In would fall down the slope". In a black hole, "it would fall into the hole and be stuck".


Arising questions:

(5) Is it allowed to conclude out of (4) and (1) that the path of gravitons is not straight but also influenced by the curvature of spacetime (of other objects)? Meaning: Gravitons (gravitational waves) have to travel along our (curved) cosmos as it exists?

Ya, because all large object's are symmetric. They are all completly 3-Dimensional, and will exert gravitational waves (gravitons) in every direction of the cosmos.


(6) Out of (4): What about gravitational forces of 2 objects of identical mass on a 3rd object right in-between the two? Is the gravitational force for the 3rd object zero? But is spacetime not curved at that point due to the sum of the curvature of the first two objects?

Let's make sure that the objects have the same density also.
This is a complicated question and is being studied today by trying to understand what's going on in binary star systems and star clusters. But I'll say this, because the question is answerable. As long as the objects are sperated by inches, centimeters, millimeters, they will both exerted the same gravitational wave (because they are the same mass and density). But when these waves "clash" together they will have a different overall curvature of space. Possible equal to the sum of each of their gravitational forces, but not exactly sure. But if we put an object in the middle I'm stumped. One would have to study the motion of this 3rd object alot to understand what kind of pattern (orbit) it would follow, and why is that so. It's being studied as we speak. There are alot of experts on this site that might have a basic answer, but it is a complicated matter.


(7) Out of (6): So are gravitons (gravitational waves) and the curvature of spacetime really equal?

Let's put it this way. Gravitational waves (gravitons) curve spacetime at equal magnitudes.


(8) Out of (2): Is this true for black holes? Do they curve spacetime and the curvature "rests" there because the gravitons (gravitational waves) cannot escape from inside of the black hole? Is the gravitational field of black holes never "updated" by gravitons (gravitational waves)?

None of this happens. The curve rests with every object in space wherther it's a black hole or pluto. The same as any object in space, once it's there, it's there with the speed of light, then it's engraved in space. Your question does makes sense though. But the let's say a black hole gained mass. The second it did so it would curve space more, in all directions. The reason the gravitational waves can "escape" the "hole" (the strong force of gravity) is because they travel along space curvature itself. Gravitons aren't exerted by the mass, they are exerted by the change in mass. Gravitons don't come out of the singularity of a black hole. They come from around.

One slight change is space curvature will effect the next and so on. So picture a gravitational wave in a black hole, it will travel in all directions around the singularity. This wave will curve this spot, that spot will curve the spot right after it and so on. It's one big wave. Not a particle. (String theory is the real use of the graviton.) So as one spot in space is affected (more curved), at the speed of light the next will be affected (curved). Leading to a spacetime wave climbing up the hole, climbing up the space fabric. The spacetime (gravitational) wave created the curve in the first place. You can't say that once the hole has changed (is deformed) the hole itself won't let it. It's already been changed. (The change is due to the change in mass)


(9) Out of (1), (3), (4), (7) and (8): How can black holes capture gravitons (gravitational waves) inside the Schwarzschild radius and, at the same time, emit gravitons (gravitational waves) to curve space and exert gravitational force?

Think I covered this. I also think you mean the event horizon not the Schwarzschild radius, which is where nothing can escape. Gravitational waves (packets of gravitons) don't have to escape the event horizon, "they go around it". In other words they travel along the curve of a black hole as a wave. They are what put the event horizon there in the first place.


(10) Out of (9): How does quantum and/or string theory explain the speed and escape speed of gravitons (gravitational waves)?

The speed of a graviton is that of light: "c". Quantum and string theory, uses the graviton's properties and finds that they match those to supersymmetric strings. Example: they both have spin-2. The graviton is a way to incorperated gravity into particle physics and string theory.

Carsten I think your questions are very valid and I understand their meaning. I hope I was able to cover them, and it is a difficult task to both ask, answer and understand what is going on in spacetime curvature of a black hole. Hope I helped :smile:

[DB]

as we know even photons probably have mass, all be it extremely small.

Photons have zero rest mass. They do however, have relavitistic mass equal to:

M_{relavitistic. photon}=\frac{hv}{c^2}

[benpadiah]

it occurs to me that possibly the force-carrying particle of gravity itself might be the tachyon.

-ben

[DB]

I did not know that, though if this were completely true it would highly effect string theory.

P.S. Carsten, if you didn't know the tachyon is a particle said to travel faster than light. But it hasn't been proven yet.

[DB]

it occurs to me that possibly the force-carrying particle of gravity itself might be the tachyon.

-ben

http://en.wikipedia.org/wiki/Tachyon

Here it doesn't say anything about tachyons making up gravitational waves or tachyons carrying any force of gravity.

[benpadiah]

and we all know that if it doesn't say it in a book, or at least on the internet, than it cannot be possible.

-ben

[SimonA]

There is no "force-carrying particle of gravity". Gravity is the result of the impact various forms of stable vortices (particles) make on what is eroneously called "the vacuum". Any vortex will move towards a region where it is more free to rotate. Thus space-time seems warped by mass, and it is, and it is in terms of QM but in QM the fact the level of the "vacuum" is shifted by the action of the vortec of the particle itself is glossed over. Einstein's left side of his equation is spot on. His right side is right as well but just needs updating. The big "G" needs to be rephrased so that it includes the ZPF. Well thats the first step. Then next is to add in the extra dimesnions...

[DB]

Exactly.
I think tachyons have really nothing to do with gravity.

[Schneibster]

As far as I know the Schwarzschild radius is the event horizon since the escape speed at this point becomes c.The Schwarzchild radius is the radius at which the density of an object would be sufficient for that object to establish an event horizon and become a black hole. Every object has a Schwarzchild radius. The Schwarzchild radius always describes a sphere. However, not every object is dense enough to be a black hole. In a non-rotating black hole, you are correct, and the Schwarzchild radius is identical to the event horizon.

However, in a rotating black hole, the event horizon is distorted into a spheroid by an effect called frame dragging; this effect is one of the few predictions of the General Theory of Relativity that has not been confirmed. Recent experiments using Earth-orbiting satellites appear to show frame dragging is a reality; but the certainty is not yet high enough to declare this as a fact. Assuming that this is true, then there could be a region of a rotating black hole (near the equator) where the Schwarzchild radius would be inside the edge of the event horizon; the event horizon would then project out past the Schwarzchild radius. Surrounding this area would be an area where frame dragging would take place, and that frame dragging would be in excess of the speed of light outward from the Schwarzchild radius (not the event horizon!) to the same distance as that radius. Within this area of frame dragging, very close to the event horizon but still outside it, is an area called the ergosphere. No object in the ergosphere can avoid rotating with the hole; to do so, it would have to travel faster than the speed of light. At the edge of the ergosphere, an object must travel at the speed of light to avoid rotating with the hole. Matter inside the ergosphere but outside the event horizon can theoretically eventually escape from the black hole; anything that enters the event horizon can never leave.

Kerr's solutions to GRT that describe the rotating black hole have some other very peculiar effects, particularly on the singularity, which becomes a ring, and also the possibility of a so-called "naked singularity;" this (http://www.astronomical.org/astbook/blkhole.html) has more information.

[CarstenDierks]

Hi DB,

First of all: Thank you very much for your great explanations! That clarifies a lot!

I have still some comments on it. Also some questions remain or are newly evoked. I hope I may ask them.

I'm not an expert, but I'll try to anwser your questions with my best knowledge of general relativity. I hope you like reading...
Yes, I definitely enjoyed it!

(Think of gravitational waves through the water anology, but don't think of it as what gravity is, because you can't sink to the bottom of spacetime. The bowling ball anology is good for gravity.)
Plus: After the stone has sunk to the bottom, the water surface is flat again. This is what distracted me. So: space stays curved after the wave.

Ill say no, but I don't exactly understand the question.
Well it was either (2) or (3). So if we consider (2: space stays curved) as correct, (3: after a ripple has curved space it flattens again) is incorrect.

So now picture the sun sending a gravitational wave and Jupiter doing the same. The sun and Jupiter (in astronomical terms) are very close to eachother. So the two waves sent of by each mass will clash together. Once the clash is finished with, spacetime has adapted to the deformation. It's engraved.
The picture is good. Moreover, the curvature stays not fixed since Jupiter orbits the sun. Jupiter sends out gravitational waves all the time due to its acceleration. As far as I read, accelerated mass sends out gravitational waves. So Jupiter can (has to) update his gravitational field (or: space dent) all the time.

But if we put an object in the middle I'm stumped. One would have to study the motion of this 3rd object alot to understand what kind of pattern (orbit) it would follow, and why is that so. It's being studied as we speak. There are alot of experts on this site that might have a basic answer, but it is a complicated matter.
I believe we have to distinguish between two different effects:
(a) The gravitational forces of both masses exhibit field vectors of opposite directions. Thus, right in-between them the sum of the vectors equals zero.
(b) In terms of space curvature, we have a small "hill" in-between the dents of both masses. The top of the hill constitutes a point of instable balance. If the particle rests right at this point, it will stay. One small move of the particle to either side will lead to gravitational attraction by one of the masses.

However, this indicates to me, that curvature of spacetime and gravitational waves (gravitons) are not equal.

Textbooks say: Space curvature is gravitation. But I ask: Does curved space provide for vector directions?

A gravitational wave or a graviton propagates with a vector direction. A curved space (which rests) apparently not. Or am I wrong?

Let's put it this way. Gravitational waves (gravitons) curve spacetime at equal magnitudes.
Yes, the first is action and the second is reaction.

The reason the gravitational waves can "escape" the "hole" (the strong force of gravity) is because they travel along space curvature itself. ...Leading to a spacetime wave climbing up the hole, climbing up the space fabric. ...
Still escaping and climbing with the speed of c?

I also think you mean the event horizon not the Schwarzschild radius, which is where nothing can escape. Gravitational waves (packets of gravitons) don't have to escape the event horizon, "they go around it".
Well, I read the event horizon is the Schwarzschild radius. Of course, a radius and a horizon are different things: the horizon is located at that radius. Or do you have different definitions of Schwarzschild radius and event horizon?

Well, I am afraid, I am coming up with more questions than answers.

Carsten

[DB]

Plus: After the stone has sunk to the bottom, the water surface is flat again. This is what distracted me. So: space stays curved after the wave.Yup, stays curved.

The picture is good. Moreover, the curvature stays not fixed since Jupiter orbits the sun. Jupiter sends out gravitational waves all the time due to its acceleration. As far as I read, accelerated mass sends out gravitational waves. So Jupiter can (has to) update his gravitational field (or: space dent) all the time.
Yes, it orbits, but as it keeps around the same radial distanse (elliptical) its curvature of space remains proportional as it orbits. Is Jupiter really accelerating? I didn't know this.

I believe we have to distinguish between two different effects:
(a) The gravitational forces of both masses exhibit field vectors of opposite directions. Thus, right in-between them the sum of the vectors equals zero.
(b) In terms of space curvature, we have a small "hill" in-between the dents of both masses. The top of the hill constitutes a point of instable balance. If the particle rests right at this point, it will stay. One small move of the particle to either side will lead to gravitational attraction by one of the masses.
Perfect! It makes sense! I'm sorry, I had thought that it would be more complicated but your description totally gives me a visual. Thanks. (but I still do assume in star clusters its more complicated)

However, this indicates to me, that curvature of spacetime and gravitational waves (gravitons) are not equal.
Could you elaborate more on this please? I think you have a point but I can't understand it.

Textbooks say: Space curvature is gravitation. But I ask: Does curved space provide for vector directions?
It provides for the vector directions of gravitational waves, created by mass; curving space sending of its waves in every direction of spacetime.

A gravitational wave or a graviton propagates with a vector direction. A curved space (which rests) apparently not. Or am I wrong?
You're right.

Still escaping and climbing with the speed of c?
Yup. Climbing up spactime, up the curve that the mass created.

Well, I read the event horizon is the Schwarzschild radius. Of course, a radius and a horizon are different things: the horizon is located at that radius. Or do you have different definitions of Schwarzschild radius and event horizon?

Picture a cone with the base upward. The tip of the cone is the singularity, the circumference of the circular base is the event horizon, the radius of that base is simply the schwarzschild radius. :wink:

:smile:

[DB]

We're learning from eachother. :wink:
This is why I love physicsforums.

[Schneibster]

Hi Carsten, I'd like to give you a slightly different viewpoint on the answers to some of your questions that may help you understand better. As DB said, I hope you like reading!
For me it is difficult to understand why gravitational waves (gravitons) should propagate through spacetime with c and, thus, cause space curvature (if I have understood that correctly). This is the first part of the problem right here. Gravity can propagate in waves, but the normal everyday gravity that we deal with does not. It is merely a distortion of spacetime.

Think of an electron. There it sits. It has an electric charge, which distorts space all around it; we call this distortion the "electric field." Its nature is described by Maxwell's equations. But do you see any waves coming from it? No, you do not. If you did, then it would be emitting energy- and a motionless electron has no energy to emit, so that would violate mass-energy conservation.

That field, in quantum mechanical terms, is a field of virtual photons. These virtual photons are emitted and reabsorbed by the vacuum surrounding the electron so quickly that their presence is not in violation of the conservation law, because of uncertainty. Remember, though, that these are virtual photons, not real ones.

OK, so now we move the electron around some way. In fact, we oscillate it. Now it has some energy; and it emits that energy- as photons! And these are not virtual photons- they are real, and they go shooting off into space. In fact, if we get a whole bunch of electrons to do this together, inside of a wire, we can make radio waves. And in fact, that is exactly how a radio works- and it makes electromagnetic energy, which is photons.

So now you can see the difference between an electric field and an electric wave. The first is virtual photons; the second is real photons.

In the same way, a planet or star creates a distortion of space around it; but instead of being the space of electrical fields, this is the space of gravity fields. And that space, instead of being a separate entity from our normal spacetime like the space of electromagnetic fields, is our normal spacetime. So there are a few things that are a little different because of that. But the principle remains the same.

Now you can see that gravity waves are a different thing from the gravity field; and you can also see that the gravity field is only virtual gravitons (yes, yes, I know, we haven't proven they exist yet... I'm getting there), but the gravity waves are real gravitons. They make up gravity radiation.

So now your question is, "what is the speed of gravity waves?" And the answer is, "the speed of light." And your next question (and it is a different one!) is, "what is the speed of propagation of gravity?" And the answer is the same.

Now, all we have right now to describe gravity is the equivalent of Maxwell's equations, called the General Theory of Relativity, but for gravity instead of for electromagnetism and light. This theory talks about a lot of other things than gravity, because gravity warps spacetime, and GRT tells all about spacetime; but among the things we get from GRT is the field equations for the gravity force, and for gravity radiation.

We have QED (quantum electrodynamics) for our quantum theory of light and electromagnetism; and we even have a quantum field theory to describe electromagnetism and light. But we have neither a quantum theory nor a quantum field theory for gravity. Every time we try to make one, we run up against infinities in all the equations. There's some really crucial concept we just don't understand yet.

But that doesn't mean we don't understand gravity; we have field equations for it. We just don't understand quantum gravity. Keep in mind that all of electronics up until a very short time ago were all based completely on Maxwell's Equations; we never needed QED to design electrical circuits. Just recently, we started doing things sophisticated enough that the field equations aren't enough; but we still don't do very many things like that, and mostly we still just use the field equations. There are actually electrical engineers who are having problems because they have to learn quantum mechanics- QED, specifically- and they have only ever needed Maxwell's equations all their lives!

(1) If gravitons (gravitational waves) are not at rest in a gravitational field, this would imply to me that mass needs to constantly emit gravitational waves (gravitons) to "replace" those which are "gone".No. They are virtual gravitons. They are emitted and reabsorbed by the vacuum, because it is under stress from the presence of the mass. Just as it is under stress from the presence of an electric charge and emits and reabsorbs virtual photons.

(2) If mass curves spacetime: Is the curvature once "engraved" in spacetime and "rests" there until a new gravitational wave "updates the information"? The curvature changes as the object moves, but the change reaches out across the curvature at the speed of light. So there is a lag at the outside reaches of the gravity field. But remember, the waves are created by oscillation; simple movement doesn't distort things enough to create gravity waves.

Or:
(3) Is the curvature of spacetime just "newly" evoked by every ripple of a gravitational wave passing by?I assume this is obvious from the above.

(4) Do gravitational waves interfere with each other? Probably yes because gravitational forces and the curvature of space of two objects do add up.Yes, of course they would. But remember that you would have to either reflect them from something, or you would have to have two sources of waves; simple gravity fields aren't enough to create waves, you have to have oscillation.

(5) Is it allowed to conclude out of (4) and (1) that the path of gravitons is not straight but also influenced by the curvature of spacetime (of other objects)? Meaning: Gravitons (gravitational waves) have to travel along our (curved) cosmos as it exists?Yes, that is correct.

(6) Out of (4): What about gravitational forces of 2 objects of identical mass on a 3rd object right in-between the two? Is the gravitational force for the 3rd object zero? But is spacetime not curved at that point due to the sum of the curvature of the first two objects?There will be an area where the curvature of space-time forms a "lane" directly between the two massive objects. Any object along that lane, and equidistant from the two massive objects, would feel no net force. But don't be fooled by your physics book's picture of a "rubber sheet" with the two massive objects making "dimples" that both attract the object between; this is in four dimensional spacetime, so it is just a matter of the forces balancing.

Keep in mind as well that such an object would still be subject to tidal forces, unless it were of zero thickness. So it's really best to say it feels no net attractive force, because it does feel a tidal force that is the sum of the two tidal forces, rather than their difference (I'll leave it to you to figure out why; it will give you confidence in dealing with such situations).

(7) Out of (6): So are gravitons (gravitational waves) and the curvature of spacetime really equal?No. Real gravitons are a sign of gravitational waves; virtual gravitons are a sign of a gravitational field.

(8) Out of (2): Is this true for black holes? Do they curve spacetime and the curvature "rests" there because the gravitons (gravitational waves) cannot escape from inside of the black hole? Is the gravitational field of black holes never "updated" by gravitons (gravitational waves)?Yes, this is also true of black holes. The gravitational field does not emanate from inside the hole, nor do the virtual gravitons; the field is the consequence of the mass, not the product of the mass, although you will come across books by some rather famous people who have forgotten this. Similarly, the virtual gravitons are not emitted by the hole; they are produced by the vacuum as a result of the stress placed on it by the warping that is the consequence of the mass, they are not produced by the hole. For the rest, including the lag, everything stays pretty much the same. I did another post in which I described frame dragging, and there are some consequences that you should think about of that that I did not detail in that post. Can you see what they might be?

(9) Out of (1), (3), (4), (7) and (8): How can black holes capture gravitons (gravitational waves) inside the Schwarzschild radius and, at the same time, emit gravitons (gravitational waves) to curve space and exert gravitational force?It is two different things. Remember, it is not the singularity that emits the virtual gravitons; it is the vacuum that does it. That should clarify this point for you. In field terms, the curvature of spacetime is controlled by the mass inside it; there is no reason why that curvature should not continue right on through the event horizon, although we cannot look inside the event horizon to see that it is so.

It is probable (I have not seen it mentioned anywhere) that any gravity waves that might be emitted by the singularity would not be able to exit the event horizon, because gravitational radiation could not make it past it any more than light could.

(10) Out of (9): How does quantum and/or string theory explain the speed and escape speed of gravitons (gravitational waves)?I think the above is sufficient; remember that there is no viable quantum theory of gravity, and that string theory cannot currently provide specific equations that describe this state of affairs. I'd stick with the field equations that we have that we know work; they are our best source of knowledge at this time.


I hope I was able to put everything into the context as it currently occurs to me - and to show where my gaps in understand (relating) it are situated.

CarstenWell, I hope that helped!

DB, I also hope I didn't irritate you- my intent was not to replace or refute what you were saying, it was to add my own perspective, which seems different from yours, though not in opposition to it. I expect to learn a thing or two from reading your responses.

[DB]

No problem Schneibster. No irritation here. I learned alot from your post. I think you say it perfect:

"the virtual gravitons are not emitted by the hole; they are produced by the vacuum as a result of the stress placed on it by the warping that is the consequence of the mass"

This is a great definition of the creation of gravitational waves or virtual gravitons. "Stress placed on a vacuum by mass."

[benpadiah]

I think tachyons have really nothing to do with gravity.

I'll remember you said that.

-ben

[CarstenDierks]

Hi Schneibster,

Thank you very much. I really enjoyed reading and understanding. I was just a little busy during the past days so I have just currently found some time to respond. I am sorry for being a little overdue…

Keep in mind as well that such an object would still be subject to tidal forces, unless it were of zero thickness. So it's really best to say it feels no net attractive force, because it does feel a tidal force that is the sum of the two tidal forces, rather than their difference (I'll leave it to you to figure out why; it will give you confidence in dealing with such situations).
I assume you mean the tidal force at both sides of the object. Either side is closer to one of the masses and, thus, its particles feel a greater attraction to one of them like tidal waves on earth caused by the moon.

Of course, if it was just one quantum particle right in the middle of the two masses, it would not be exposed to tidal forces but “feel” zero gravity.

No. Real gravitons are a sign of gravitational waves; virtual gravitons are a sign of a gravitational field.
When examining real gravitons and virtual gravitons, what is the difference of their properties as a quantum particle?

I did another post in which I described frame dragging, and there are some consequences that you should think about of that that I did not detail in that post. Can you see what they might be?
Where did you post it? Do you indicate time dilation and length contraction associated with frame dragging? Would this weaken the gravitational field?

I think the above is sufficient; remember that there is no viable quantum theory of gravity, and that string theory cannot currently provide specific equations that describe this state of affairs. I'd stick with the field equations that we have that we know work; they are our best source of knowledge at this time.
OK. But what needs to be done, which gravitational problems have to be solved in string theory?

Well, I hope that helped!
Yes, indeed!

I still have some other small questions which I will include in the next post.

Thanks a lot,

Carsten

[CarstenDierks]

Hi Schneibster,

Here are the other small questions. I hope I will not bother you too much with them:

But we have neither a quantum theory nor a quantum field theory for gravity. Every time we try to make one, we run up against infinities in all the equations.
Which are they in detail? Or at least the most important ones?


Just recently, we started doing things sophisticated enough that the field equations aren't enough; but we still don't do very many things like that, and mostly we still just use the field equations.
What are these sophisticated things?


But remember, the waves are created by oscillation; simple movement doesn't distort things enough to create gravity waves.
By oscillation you mean something like an orbit around a sun? Or what would it be exactly? When mass moves through space, does it not need to send out gravitational waves to “update” space curvature around it? Eventually it has moved and so has the gravitational “information carved into space” around it.


There will be an area where the curvature of space-time forms a "lane" directly between the two massive objects. Any object along that lane, and equidistant from the two massive objects, would feel no net force.
With these “lanes” you mean geodetic lines?


In field terms, the curvature of spacetime is controlled by the mass inside it; there is no reason why that curvature should not continue right on through the event horizon, although we cannot look inside the event horizon to see that it is so.
Of course, we do not know for sure if gravity in the singularity behaves totally alike as in our “normal” cosmos, right? Especially, if temperatures rise to extreme heights…

What happens physically, if real gravitons of a gravitational wave are kept inside a black hole? Will they come across the same point in space more than once? Will they thus curve space stronger? Will they accumulate behind the event horizon? Will they fall back into singularity? Will the gravitational waves interfere with each other?

I know, I am still curious…

Carsten

[Schneibster]

Hi Schneibster,

Thank you very much. I really enjoyed reading and understanding. I was just a little busy during the past days so I have just currently found some time to respond. I am sorry for being a little overdue…Sure! I'm glad it helped you understand.


I assume you mean the tidal force at both sides of the object. Either side is closer to one of the masses and, thus, its particles feel a greater attraction to one of them like tidal waves on earth caused by the moon.The tidal force is felt all through an object, and it tends to pull the object apart. The tidal force near a neutron star or black hole would kill you; and it would do so farther away if you had your feet toward the center of mass and your head away than if you lay prone with your back or your chest pointing toward the center of mass. This is because the difference in pull increases with the distance between the far and near sides of the object feeling the tides. The reason for the tidal force is because the force of gravity decreases as the square of the distance; thus, the far side is pulled with less force than the near side, and the difference between the pulls is the tidal force.

Consider carefully that since the tidal force is attempting to pull the object apart, while the gravity on an object between two others might cancel, the tidal forces would add!

Of course, if it was just one quantum particle right in the middle of the two masses, it would not be exposed to tidal forces but “feel” zero gravity.If the point-particle physics theories are correct, then yes, that is correct- but if string physics is correct, then there might be a slight tidal force, because strings are not zero size.

When examining real gravitons and virtual gravitons, what is the difference of their properties as a quantum particle?If gravitons even exist, you mean? ;)

There is no difference in their properties; but of course there is a difference in their behavior, and that difference is that a real particle travels long-distance through space, whereas the virtual particle is very limited in how far it can travel because it must disappear before uncertainty time runs out. Remember that energy (and therefore mass, by E=mc^2) and time are conjugate under uncertainty.

Where did you post it? In this thread; here (http://physicsforums.com/showpost.php?p=427412&postcount=38).

Do you indicate time dilation and length contraction associated with frame dragging? Would this weaken the gravitational field?Frame dragging doesn't result in time dilation and length contraction, except as the standard result of the perception of velocity on the part of the object accelerated by the frame dragging by an observer to whom it is in relative motion. Frame dragging doesn't weaken gravity; it is an effect of the gravity of a rotating mass.

OK. But what needs to be done, which gravitational problems have to be solved in string theory?String physics incorporates a quantum theory of gravity; unfortunately, no one knows what the exact equations that describe a theory of physics that makes contact with our real-world observations are. Only the approximate equations are known, and none of them yield enough detail to allow the precise correct equations to be determined so that experiments can be run to see if they agree with reality or not. You should read Brian Greene's The Elegant Universe for more information.

Because string physics cannot be confirmed at the current time, I usually prefer to call it "string physics," since it is not yet a formal theory.

I still have some other small questions which I will include in the next post.

Thanks a lot,

CarstenSure, go ahead.

[Schneibster]

Which are they in detail? Or at least the most important ones?We get infinite probabilities for the equations that describe the interaction of the graviton with other particles. Probabilities run from zero to one; we don't know what a probability of two means, much less a probability of infinity.

What are these sophisticated things?Semiconductors. Most EEs use approximations of their behavior. It is rare in an engineering setting to need to know more than that; but if you have to, then the quantum properties of the materials become important. A good example would be gallium arsenide laser diodes.

The first approximation of a silicon junction between P-type and N-type materials is 0.7V. Thus, when you need to know the "on" voltage across the base-to-emitter junction of an NPN transistor, in the first approximation where the current is minimal, you can just use 0.7V there. To get the precise value, you must either measure the transistor on a curve tracer, or you must have a reliable figure for the DC amplification factor, called "DC beta," from the manufacturer. The accuracy of the figures from the manufacturer is generally limited, and they give a range that may be orders of magnitude. However, in most situations, particularly in troubleshooting, this level of approximation is sufficient.

By oscillation you mean something like an orbit around a sun? Or what would it be exactly? When mass moves through space, does it not need to send out gravitational waves to “update” space curvature around it? Eventually it has moved and so has the gravitational “information carved into space” around it.Oscillation in general is a complex phenomenon. I would envision a star or planet suspended in a rigid motionless frame by springs, bouncing back and forth; this is of course impossible in real life, but analogous situations can occur, for instance if two massive objects are orbiting one another and the orbit is unstable and the objects are getting closer and closer. Astronomers believe that they will be able to detect gravitational radiation from stars falling into supermassive black holes believed to be at the centers of many galaxies using a project called LIGO that is currently being built in the northwestern US. They also believe they will be able to detect something much more rare: the merging of two black holes, or two neutron stars, or a neutron star and a black hole. They expect to be able to find out some really interesting details about gravity from this information.

The variations in the gravity field caused by linear motion will of course result in a continuous "update" of the gravity field of an object, but they do not create "waves" of gravity. To create a wave from any motion requires an oscillation; this is a general fact of physics, not limited to gravity fields but also true (as my example showed) of the electromagnetic field. You cannot use the analogy of water waves, like from the prow of a boat, which is what it sounds like you are trying to do; water waves are transverse waves, but light and gravity waves are longitudinal, and furthermore while water presents resistance to the movement of objects, space does not.

With these “lanes” you mean geodetic lines?Actually, I was thinking in terms of the exact analogy I told you not to use; a rubber sheet. :eek: If two bowling balls were put on the sheet, there would be a "groove" running between them. This is what I meant by a "lane."

Of course, we do not know for sure if gravity in the singularity behaves totally alike as in our “normal” cosmos, right? Especially, if temperatures rise to extreme heights…...and that is because we do not have a quantum theory of gravity! But even without it, we know that the strength of the field at any point is dependent on the size of each mass that affects that point and its distance from that point; if any of the masses is moving, then it also depends on the state of motion. This is independent of whether the mass is a black hole, or a regular star, or a planet, or whatnot. It is also independent of temperature, at least as far as we know; and in fact, we know that it is independent of temperature to at least 10 million degrees Kelvin, because we have a pretty thorough understanding of our Sun.

What happens physically, if real gravitons of a gravitational wave are kept inside a black hole? Will they come across the same point in space more than once? Will they thus curve space stronger? Will they accumulate behind the event horizon? Will they fall back into singularity? Will the gravitational waves interfere with each other?

I know, I am still curious…

CarstenHee hee, nobody knows the answers to any of these questions. Remember Hawking: "A black hole has no hair."

[Caroline Thompson]

... The variations in the gravity field caused by linear motion will of course result in a continuous "update" of the gravity field of an object, but they do not create "waves" of gravity ... But suppose gravity is itself caused by waves? Since it is generally admitted that we have no satisfactory theory as to the cause of gravity, perhaps my own model deserves consideration. It is possibly similar in effect to string theory, but involves no "gravitons", whether real or virtual, only waves, which are being produced and absorbed all the time by all condensed matter. Under my "Phi-Wave Aether" model, gravity is of the same nature as all other forces: they all travel at speed c as waves in the aether, the differences between them being due to different degrees of coherence and different higher-level periodic patterns superposed on very high frequency longitudinal waves. The "fields" are themselves formed by waves, and are all constantly updated, whether or not the sources are moving.

Just a thought ...

I haven't tried to incorporate black holes into the theory, but if I'm right there is no avoiding propagation at speed c.

Caroline
http://freespace.virgin.net/ch.thompson1/

[DB]

Actually, I was thinking in terms of the exact analogy I told you not to use
How come we shouldn't use the bowling ball analogy?

[Schneibster]

Caroline, all waves have energy, and take energy to make; they are all made by oscillation. They dissipate this energy into the environment continuously. Fields, on the other hand, represent static energy; there is a difference in the energy of the vacuum with the field and without the field; but fields do not disspate energy. It doesn't matter whether you are talking classically or in QM terms. Thus, your idea would violate mass/energy conservation.

[Schneibster]

DB, the bowling ball/rubber sheet analogy is in two dimensions bent in a third; but the reality is four dimensions on a manifold. Thus, if you use only the analogy, it will break down and give you wrong understanding sometimes.

[Nereid]

But suppose gravity is itself caused by waves? Since it is generally admitted that we have no satisfactory theory as to the cause of gravity, perhaps my own model deserves consideration. It is possibly similar in effect to string theory, but involves no "gravitons", whether real or virtual, only waves, which are being produced and absorbed all the time by all condensed matter. Under my "Phi-Wave Aether" model, gravity is of the same nature as all other forces: they all travel at speed c as waves in the aether, the differences between them being due to different degrees of coherence and different higher-level periodic patterns superposed on very high frequency longitudinal waves. The "fields" are themselves formed by waves, and are all constantly updated, whether or not the sources are moving.

Just a thought ...

I haven't tried to incorporate black holes into the theory, but if I'm right there is no avoiding propagation at speed c.

Caroline
http://freespace.virgin.net/ch.thompson1/In a few words - if that's possible - how does your idea differ from GR?

[Nereid]

To clarify something that's been rather, shall we say, elided in many posts in this thread.

'Gravitational radiation' aka 'gravitational waves' are a direct consequence of GR; to the extent that no good observational or experimental data to date is inconsistent with GR, so we can expect that these are 'real'.

'Gravitons' are NOT part of GR; they require some 'quantum' theory compatible with GR. To date, AFAIK, there is NO observational data that even hints at what form a quantised form of GR should take (so theorists can - and do - imagine anything they like!).

Re black holes: there is very good observational data consistent with the existence of stellar mass (and above, to billion sol) BHs; the extent to which these 'behave' like GR, QM, of Nereid's pet ideas is entirely unconstrained by good observational data (at this time).

[JesseM]

The variations in the gravity field caused by linear motion will of course result in a continuous "update" of the gravity field of an object, but they do not create "waves" of gravity. To create a wave from any motion requires an oscillation; this is a general fact of physics, not limited to gravity fields but also true (as my example showed) of the electromagnetic field. You cannot use the analogy of water waves, like from the prow of a boat, which is what it sounds like you are trying to do; water waves are transverse waves, but light and gravity waves are longitudinal, and furthermore while water presents resistance to the movement of objects, space does not. In electromagnetism, it is acceleration of charges which causes electromagnetic waves, it doesn't necessarily have to be oscillation. For a charge moving at constant velocity, other charges will act as though they are always attracted to its current position with no light-delay; if the charge accelerates, though, other charges will continue to be attracted to a "linear extrapolation" of the charge's position (where it would have been if it had not accelerated) until an electromagnetic wave travelling at the speed of light reaches them.

For gravity, it's a bit more complicated, Steve Carlip says here (http://groups-beta.google.com/group/sci.physics.relativity/browse_frm/thread/946490070d3e6653/7c7dcedb66266948) that it depends on the quadrupole term in a multipole expansion rather than the dipole term as in electromagnetism, so gravity can "anticipate" the orbits of planets as well as linear motion--see this page (http://math.ucr.edu/home/baez/physics/Relativity/GR/grav_speed.html) for more info: In general relativity, on the other hand, gravity propagates at the speed of light; that is, the motion of a massive object creates a distortion in the curvature of spacetime that moves outward at light speed. This might seem to contradict the Solar System observations described above, but remember that general relativity is conceptually very different from Newtonian gravity, so a direct comparison is not so simple. Strictly speaking, gravity is not a "force" in general relativity, and a description in terms of speed and direction can be tricky. For weak fields, though, one can describe the theory in a sort of Newtonian language. In that case, one finds that the "force" in GR is not quite central--it does not point directly towards the source of the gravitational field--and that it depends on velocity as well as position. The net result is that the effect of propagation delay is almost exactly cancelled, and general relativity very nearly reproduces the Newtonian result.

This cancellation may seem less strange if one notes that a similar effect occurs in electromagnetism. If a charged particle is moving at a constant velocity, it exerts a force that points toward its present position, not its retarded position, even though electromagnetic interactions certainly move at the speed of light. Here, as in general relativity, subtleties in the nature of the interaction "conspire" to disguise the effect of propagation delay. It should be emphasized that in both electromagnetism and general relativity, this effect is not put in ad hoc but comes out of the equations. Also, the cancellation is nearly exact only for constant velocities. If a charged particle or a gravitating mass suddenly accelerates, the change in the electric or gravitational field propagates outward at the speed of light.

Since this point can be confusing, it's worth exploring a little further, in a slightly more technical manner. Consider two bodies--call them A and B--held in orbit by either electrical or gravitational attraction. As long as the force on A points directly towards B and vice versa, a stable orbit is possible. If the force on A points instead towards the retarded (propagation-time-delayed) position of B, on the other hand, the effect is to add a new component of force in the direction of A's motion, causing instability of the orbit. This instability, in turn, leads to a change in the mechanical angular momentum of the A-B system. But total angular momentum is conserved, so this change can only occur if some of the angular momentum of the A-B system is carried away by electromagnetic or gravitational radiation.

Now, in electrodynamics, a charge moving at a constant velocity does not radiate. (Technically, the lowest order radiation is dipole radiation, which depends on the acceleration.) So, to the extent that A's motion can be approximated as motion at a constant velocity, A cannot lose angular momentum. For the theory to be consistent, there must therefore be compensating terms that partially cancel the instability of the orbit caused by retardation. This is exactly what happens; a calculation shows that the force on A points not towards B's retarded position, but towards B's "linearly extrapolated" retarded position. Similarly, in general relativity, a mass moving at a constant acceleration does not radiate (the lowest order radiation is quadrupole), so for consistency, an even more complete cancellation of the effect of retardation must occur. This is exactly what one finds when one solves the equations of motion in general relativity. What happens physically, if real gravitons of a gravitational wave are kept inside a black hole? Will they come across the same point in space more than once? Will they thus curve space stronger? Will they accumulate behind the event horizon? Will they fall back into singularity? Will the gravitational waves interfere with each other?

I know, I am still curious…

Carsten Hee hee, nobody knows the answers to any of these questions. Remember Hawking: "A black hole has no hair." Actually it was Wheeler (http://www.usd.edu/phys/courses/phys300/gallery/clark/wheeler.html) who coined that phrase. And Steve Carlip addresses these questions here (http://www.faqs.org/faqs/astronomy/faq/part4/section-11.html), both in the case of classical gravitational waves and gravitons: D.09 How can gravity escape from a black hole?

In a classical point of view, this question is based on an incorrect
picture of gravity. Gravity is just the manifestation of spacetime
curvature, and a black hole is just a certain very steep puckering
that captures anything that comes too closely. Ripples in the
curvature travel along in small undulatory packs (radiation---see
D.05), but these are an optional addition to the gravitation that is
already around. In particular, black holes don't need to radiate to
have the fields that they do. Once formed, they and their gravity
just are.

In a quantum point of view, though, it's a good question. We don't
yet have a good quantum theory of gravity, and it's risky to predict
what such a theory will look like. But we do have a good theory of
quantum electrodynamics, so let's ask the same question for a charged
black hole: how can a such an object attract or repel other charged
objects if photons can't escape from the event horizon?

The key point is that electromagnetic interactions (and gravity, if
quantum gravity ends up looking like quantum electrodynamics) are
mediated by the exchange of *virtual* particles. This allows a
standard loophole: virtual particles can pretty much "do" whatever they
like, including travelling faster than light, so long as they disappear
before they violate the Heisenberg uncertainty principle.

The black hole event horizon is where normal matter (and forces) must
exceed the speed of light in order to escape, and thus are trapped.
The horizon is meaningless to a virtual particle with enough speed.
In particular, a charged black hole is a source of virtual photons
that can then do their usual virtual business with the rest of the
universe. Once again, we don't know for sure that quantum gravity
will have a description in terms of gravitons, but if it does, the
same loophole will apply---gravitational attraction will be mediated
by virtual gravitons, which are free to ignore a black hole event
horizon.

See R Feynman QED (Princeton, ???) for the best nontechnical account
of how virtual photon exchange manifests itself as long range
electrical forces.

[Schneibster]

Thanks for the detailed clarifications, Jesse.

[Caroline Thompson]

In a few words - if that's possible - how does your idea differ from GR?
(a) It is not mathematical, only intuitive.
(b) It provides an idea for actual cause for gravity.
(c) It quite unashamedly assumes an aether, not just letting one creep in by the back door.

Of couse it is not much use as a "theory" because of its lack of equations, but it does make a few qualitative predictions. For more see my web site. I have been cautioned not to try and introduce personal theories on this forum, otherwise I'd say more here.

Caroline
http://freespace.virgin.net/ch.thompson1/

[Nereid]

In a few words - if that's possible - how does your idea differ from GR?(a) It is not mathematical, only intuitive.
(b) It provides an idea for actual cause for gravity.
(c) It quite unashamedly assumes an aether, not just letting one creep in by the back door.

Of couse it is not much use as a "theory" because of its lack of equations, but it does make a few qualitative predictions. For more see my web site. I have been cautioned not to try and introduce personal theories on this forum, otherwise I'd say more here. Thanks.

I think you started posting here after the big discussion we had on the extent to which we would encourage, support, or even allow qualitative personal ideas in the 'science' parts of PF (the Theory Development section used to be one of the most active parts of PF!). Never mind; the decision was to strongly discourage these, unless they are 'nearly ready for prime time' (e.g. been accepted for publication in a peer-reviewed journal).

On the other hand, critiques of 'mainstream' physics - especially in the form of penetrating questions and showing (apparent) internal and external inconsistencies - is very much to be encouraged! :smile:

[CarstenDierks]

Well, thank you all for your posts!

I will no be able to answer quickly to all of them, but here is the most important one for me:

Once again, we don't know for sure that quantum gravity
will have a description in terms of gravitons, but if it does, the
same loophole will apply---gravitational attraction will be mediated
by virtual gravitons, which are free to ignore a black hole event
horizon.

See R Feynman QED (Princeton, ???) for the best nontechnical account
of how virtual photon exchange manifests itself as long range
electrical forces.

So this leads back to post # 1:

At least virtual gravitons are able to move faster than c to escape the event horizon.

Is this also true for virtual photons in an EM field?

That implies, that information can leave a black hole, correct?

Carsten

[JesseM]

Well, thank you all for your posts!

I will no be able to answer quickly to all of them, but here is the most important one for me:



So this leads back to post # 1:

At least virtual gravitons are able to move faster than c to escape the event horizon.

Is this also true for virtual photons in an EM field? Yes, that page I quoted said that in terms of the "virtual particle" picture, a charged black hole's electromagnetic attraction would be explained in terms of virtual photons escaping the event horizon. That implies, that information can leave a black hole, correct?

Carsten No, FTL virtual particles apparently don't imply FTL information transfer. This is discussed in this FAQ on virtual particles (http://math.ucr.edu/home/baez/physics/Quantum/virtual_particles.html): Do they go faster than light? Do virtual particles contradict relativity or causality?

In section 2, the virtual photon's plane wave is seemingly created everywhere in space at once, and destroyed all at once. Therefore, the interaction can happen no matter how far the interacting particles are from each other. Quantum field theory is supposed to properly apply special relativity to quantum mechanics. Yet here we have something that, at least at first glance, isn't supposed to be possible in special relativity: the virtual photon can go from one interacting particle to the other faster than light! It turns out, if we sum up all possible momenta, that the amplitude for transmission drops as the virtual particle's final position gets further and further outside the light cone, but that's small consolation. This "superluminal" propagation had better not transmit any information if we are to retain the principle of causality.

I'll give a plausibility argument that it doesn't in the context of a thought experiment. Let's try to send information faster than light with a virtual particle.

Suppose that you and I make repeated measurements of a quantum field at distant locations. The electromagnetic field is sort of a complicated thing, so I'll use the example of a field with just one component, and call it F. To make things even simpler, we'll assume that there are no "charged" sources of the F field or real F particles initially. This means that our F measurements should fluctuate quantum- mechanically around an average value of zero. You measure F (really, an average value of F over some small region) at one place, and I measure it a little while later at a place far away. We do this over and over, and wait a long time between the repetitions, just to be safe.



.
.
.
------X
------
X------


^ time
------X me |
------ |
you X------ ---> space


After a large number of repeated field measurements we compare notes. We discover that our results are not independent; the F values are correlated with each other-- even though each individual set of measurements just fluctuates around zero, the fluctuations are not completely independent. This is because of the propagation of virtual quanta of the F field, represented by the diagonal lines. It happens even if the virtual particle has to go faster than light.

However, this correlation transmits no information. Neither of us has any control over the results we get, and each set of results looks completely random until we compare notes (this is just like the resolution of the famous EPR "paradox").

You can do things to fields other than measure them. Might you still be able to send a signal? Suppose that you attempt, by some series of actions, to send information to me by means of the virtual particle. If we look at this from the perspective of someone moving to the right at a high enough speed, special relativity says that in that reference frame, the effect is going the other way:


.
.
.

X------
------
------X



you X------ ^ time
------ |
------X me |
---> space


Now it seems as if I'm affecting what happens to you rather than the other way around. (If the quanta of the F field are not the same as their antiparticles, then the transmission of a virtual F particle from you to me now looks like the transmission of its antiparticle from me to you.) If all this is to fit properly into special relativity, then it shouldn't matter which of these processes "really" happened; the two descriptions should be equally valid.

We know that all of this was derived from quantum mechanics, using perturbation theory. In quantum mechanics, the future quantum state of a system can be derived by applying the rules for time evolution to its present quantum state. No measurement I make when I "receive" the particle can tell me whether you've "sent" it or not, because in one frame that hasn't happened yet! Since my present state must be derivable from past events, if I have your message, I must have gotten it by other means. The virtual particle didn't "transmit" any information that I didn't have already; it is useless as a means of faster-than-light communication.

The order of events does not vary in different frames if the transmission is at the speed of light or slower. Then, the use of virtual particles as a communication channel is completely consistent with quantum mechanics and relativity. That's fortunate: since all particle interactions occur over a finite time interval, in a sense all particles are virtual to some extent. It should also be noted that I have seem a number of physicists argue that we shouldn't really think of virtual particles as real physical entities at all--they are just graphic representations of terms in a perturbation series, and thus have no more physical reality than terms in a Taylor series used to approximate the value of some physical function (the electromagnetic field, perhaps) near some point. Arnold Neumaier's physics FAQ (http://www.mat.univie.ac.at/~neum/physics-faq.txt) discusses this argument in detail: -----------------------------------------------
3b. How meaningful are single Feynman diagrams?
-----------------------------------------------

The standard model is a theory defined in terms of a Lagrangian.
To get computable output, Feynman graph techniques are used.
But individual Feynman graphs are meaningless (often infinite);
only the sum of all terms of a given order can be given - after
a process called renormalization - a well-defined (finite) meaning.
This is well-known; so no-one treats the Feynman graphs as real.
What is taken as real is the final outcome of the calculations,
which can be compared with measurements.

-------------------------------------
3c. How real are 'virtual particles'?
-------------------------------------

All language is only an approximation to reality, which simply is.
But to do science we need to classify the aspects of reality
that appear to have more permanence, and consider them as real.
Nevertheless, all concepts, including 'real' have a fuzziness
about them, unless they are phrased in terms of rigorous mathematical
models (in which case they don't apply to reality itself but only to
a model of reality).

In the informal way I use the notion, 'real' in theoretical physics
means a concept or object that
- is independent of the computational scheme used to
extract information from a theory,
- has a reasonably well-defined and consistent formal basis
- does not give rise to misleading intuition.
This does not give a clear definition of real, of course.
But it makes for example charge distributions, inputs and outputs of
(theoretical models of) scattering experiments, and quarks something
real, while making bare particles and virtual particles artifacts of
perturbation theory.

Quarks must be considered real because one cannot dispense with them
in any coherent explanation of high energy physics.

Virtual particles must not be considered real since they arise only in
a particular approach to high energy physics - perturbation theory
before renormalization - that does not even survive the modifications
needed to remove the infinities. Moreover, the virtual particle content
of a real state depends so much on the details of the computational
scheme (canonical or light front quantization, standard or
renormalization group enhances perturbation theory, etc.) that
calling virtual particles real would produce a very weird picture of
reality.

...

The figurative virtual objects in QFT are there only because of the
well-known limitations of the foundations of QFT. In a nonperturbative
setting they wouldn't occur at all. This can be seen by comparing with
QM. One could also do nonrelativistic QM with virtual objects but
no one does so (except sometimes in motivations for QFT),
because it does not add value to a well-understood theory.

Virtual particles are an artifact of perturbation theory that
give an intuitive (but if taken too far, misleading) interpretation
for Feynman diagrams. More precisely, a virtual photon, say,
is an internal photon line in one of the Feynman diagrams. But there
is nothing real associated with it. Detectable photons are always
real, 'dressed' photons.

Virtual particles, and the Feynman diagrams they appear in,
are just a visual tool of keeping track of the different terms
in a formal expansion of scattering amplitudes into multi-dimensional
integrals involving multiple propaators - the momenta of the virtual
particles represent the integration variables.
They have no meaning at all outside these integrals.
They get out of mathematical existence once one changes the
formula for computing a scattering amplitude.

Therefore virtual particles are essentially analogous to virtual
integers k obtained by computing
log(1-x) = sum_k x^k/k
by expansion into a Taylor series. Since we can compute the
logarithm in many other ways, it is ridiculous to attach to
k any intrinsic meaning. But ...

... in QFT, we have no good ways to compute scattering amplitudes
without at least some form of expansion (unless we only use the
lowest order of some approximation method), which makes
virtual particles look a little more real. But the analogy
to the Taylor series shows that it's best not to look at them
that way. (For a very informal view of QED in terms of clouds of
virtual particles see
http://groups.google.com/groups?sel...%40univie.ac.at
and the later mails in this thread.)

A sign of the irreality of virtual particles is the fact that
when one does partial resummations of diagrams (which is essential for
renormalization), many of the virtual particles disappear.
A fully nonperturbative theory would sum everything, and no virtual
particles would be present anymore. Thus virtual particles are
entirely a consequence of looking at QFT in a perturbative way
rather than nonperturbatively.

[Caroline Thompson]

Caroline, all waves have energy, and take energy to make; they are all made by oscillation. They dissipate this energy into the environment continuously. Fields, on the other hand, represent static energy; there is a difference in the energy of the vacuum with the field and without the field; but fields do not disspate energy. It doesn't matter whether you are talking classically or in QM terms. Thus, your idea would violate mass/energy conservation.The waves from which forces are formed are the self-same waves in the aether that, when carrying a different modulation, form radiation. Radiation is, I understand, a wave that does not dissipate in a vacuum. I don't see the problem.

Incidentally, surely light does dissipate just a tiny bit, otherwise the night sky would be bright (Olbers' paradox)? What experimental evidence do we have that forces don't dissipate similarly over similar distances? In my Phi-Wave-Aether theory, the high-level patterns get smudged out so that radiation and the forces lose their effectiveness. The net intensity of the phi-waves, though, almost certainly stays the same. On the scale of the whole universe, there is conservation of "phi-energy".

Caroline
http://freespace.virgin.net/ch.thompson1/

[Schneibster]

The waves from which forces are formed are the self-same waves in the aether that, when carrying a different modulation, form radiation. Forces aren't formed from waves. A force is the action of a field; and a field is apparently a basic entity (I had thought until very recently that fields were "made up" of virtual particles, but it turns out that this is merely a convenient way of representing fields that gives some correct results in regard to certain mensurables if not pushed too far. In fact, the virtual particles have no real existence, and cannot be relied upon as anything but a mathematical contrivance that allows some, but not all, of the properties of the field to be described. Apparently, fields and dimensions are the fundamental entities making up our universe; and if string physics turns out to be correct, it may turn out that the fields are all due to the distortion of dimensions, so dimensions may turn out to be the single fundamental entity).

(Even more interestingly, it appears that while a field is not made up of anything, a wave can be considered to be made up of something, specifically quanta; and these quanta reveal their presence by the contrafactuality of the "violet catastrope," and by the reality of the photoelectric effect, at least in the case of the quanta of the electromagnetic interaction. I have still not finished considering the implications of this with regard to the field, nor the implications with regard to string physics.)

A wave is not a field, but the variation of a field. In order for a field to vary, the source of the field must accelerate (not merely move, but accelerate). In the absence of acceleration, there is no wave. In the absence of expenditure of energy, there is no acceleration. Thus, for a wave to be formed, an object that is the source of a field must accelerate; and for an object to do this in the absence of a source of energy is, as I said, a violation of the conservation of mass/energy.

Radiation is, I understand, a wave that does not dissipate in a vacuum. I don't see the problem.Then you do not know the difference between a wave and a field. See above. Radiation is a wave made up of the variation of the field of the vacuum, which is all fields at their minimum potential in the absence of any field associated with an object, and that minimum potential plus the potential of the object's field in the presence of a field associated with an object.

Incidentally, surely light does dissipate just a tiny bit, otherwise the night sky would be bright (Olbers' paradox)? That would violate the conservation of mass/energy as well. Light is energy in one of its forms, specifically the variation of the electromagnetic field of the vacuum. As I previously stated, that variation is caused by the acceleration of some object, and acceleration is a phenomenon that implies the application of a force, which requires energy.

In regard to Olbers' paradox, there are several different possible solutions, and the most widely accepted one is that the universe is not infinite in time. This solution has the advantage over your proposed solution that it does not contradict well-known experimental results.

What experimental evidence do we have that forces don't dissipate similarly over similar distances? The evidence of the conservation of mass/energy. No experiment has ever been observed that violates this law; the discoverer of such an experiment would be sure to report it and accept their inevitable Nobel Prize.

Brightness observations on stars conform to the inverse-square law, which is the result of the geometry of spacetime. These brightness observations are consistent for particular types of stars, and the distance to the stars is established using simple geometric techniques (see Hipparcos and Tycho data, which establish the distances to millions of stars geometrically with error bars indicating accuracies better than ten significant figures). If the electromagnetic force were to dissipate over distance, we would observe that stars of a given type that were further away would be uniformly less bright than stars of the same type that were closer, and we do not observe this. The Herzsprung-Russell diagram is proof of this fact.

Rotation observations of the planets in the Solar System would be affected by any dissipation of gravity over distance, requiring an ever-increasing correction for each planet successively further from the Sun; this correction is not observed.

Therefore, the electromagnetic and gravity fields are not affected by any "dissipation" of their strength over spatial distances, and there is observational evidence to supplement laboratory experiment evidence that this is true.

In my Phi-Wave-Aether theory, the high-level patterns get smudged out so that radiation and the forces lose their effectiveness. The net intensity of the phi-waves, though, almost certainly stays the same. On the scale of the whole universe, there is conservation of "phi-energy".I'm sorry, I have not studied your proposal enough to comment on it.

[CarstenDierks]

Hi Schneibster,

May I still continue to “bug you” with a couple of questions? :smile:

Forces aren't formed from waves. A force is the action of a field; and a field is apparently a basic entity

If a gravitational wave curves space and space curvature is a gravitational field, isn´t a gravitational field a gravitational force? Thus the wave would have formed the force…

Radiation is a wave made up of the variation of the field of the vacuum, which is all fields at their minimum potential in the absence of any field associated with an object, and that minimum potential plus the potential of the object's field in the presence of a field associated with an object.
Hm, that was a little complicated. I must admit I did not fully understand it.

In regard to Olbers' paradox, there are several different possible solutions, and the most widely accepted one is that the universe is not infinite in time.

Yes. And there is dark matter absorbing light. And moreover, the universe might not be infinite in space.

Carsten

[Nereid]

If a gravitational wave curves space and space curvature is a gravitational field, isn´t a gravitational field a gravitational force? Thus the wave would have formed the force…A gravitational wave does indeed 'create it's own gravity', but it is extraordinarily weak.
Yes. And there is dark matter absorbing light. And moreover, the universe might not be infinite in space.Just to nitpick one thing ... 'dark matter' (as in non-baryonic matter) does not absorb photons; what does absorb photons is 'dark baryonic matter', e.g. dust. However, in equilibrium, all such baryonic absorbers also emit photons (e.g. light is absorbed, heating the dust, so it emits more in the IR/microwave region).

There have been several good discussions on gravitation and its speed in the Special & General Relativity section of PF; do readers feel this thread should be moved there (it'd get the attention of folk who are very familiar with GR).

[CarstenDierks]

Hi Nereid,

Thanks for the details!

There have been several good discussions on gravitation and its speed in the Special & General Relativity section of PF; do readers feel this thread should be moved there (it'd get the attention of folk who are very familiar with GR).
Maybe we should move on with the discussion involving those guys. Would you move this thread there or would we start a new thread in that section? How would it work?

Carsten

[Caroline Thompson]

Forces aren't formed from waves. A force is the action of a field; and a field is apparently a basic entity .... I know this is what is generally thought, but I think it is holding back understanding. The assumption that there are no underlying waves -- that the field is an intrisically static phenomenon -- held back Einstein and Lorentz, preventing them from seeing how to link macroscopic forces with "quantum-level" ones.

At the quantum level, we know that everything is constantly changing. We know that "interference" phenomena are important. To me, this implies that at that level there are high-frequency waves, underlying all the forces and causing everything that we see.

I'm sorry, I have not studied your proposal enough to comment on it.I've afraid I have not time now to read all your comments, but perhaps in any event it would be more profitable to discuss my hypothesis after reading one of my papers, e.g.:

"The Phi-Wave Aether: a Wave Theory of Everything", http://freespace.virgin.net/ch.thompson1/Essays/PWA.2colApeiron.pdf or html version: http://freespace.virgin.net/ch.thompson1/Essays/PWA.Apeiron.htm

Cheers
Caroline

[CarstenDierks]

I know this is what is generally thought, but I think it is holding back understanding. The assumption that there are no underlying waves -- that the field is an intrisically static phenomenon -- held back Einstein and Lorentz, preventing them from seeing how to link macroscopic forces with "quantum-level" ones.

At the quantum level, we know that everything is constantly changing. We know that "interference" phenomena are important. To me, this implies that at that level there are high-frequency waves, underlying all the forces and causing everything that we see.

Dear Caroline,

with all respect to your theory, but first of all, I would like to understand how science explains our universe. And secondly I would like to understand where it still has frontiers in explaining it.

Can you help us/me in the questions of this thread? But I would like to hear no speculations at this time but only the widely accepted theories. Everything else is confusing at this point.

I am very open to new ideas, but let us first understand the facts. And afterwards, I am happy to open a new thread on speculations.

Best regards,
Carsten

[Jio Moonshadow]

The short answer is:NO.What do you mean,"gravitation can (escape a blackhole)"...???Gravitation IS a black hole (too)...A singularity in the gravitational field,that is...If u want to,a particular solution to the Einstein equations...

Daniel.

Modestly, a black hole is not formed or comprised of any gravitational force. I've copyright on my first book on a logical examination of the universe. Quantum mechanics to black holes and antimatter. a black hole i call FSA, force to siphon acceleration. To have a gravitational force there must be a great density of reactions for short. After the supernova explodes the gravitational force is dispersed. Also, planetary and nova gravitational force is faster than light.

[Schneibster]

Hi Schneibster,

May I still continue to “bug you” with a couple of questions? :smile: Of course, and I will explain the answers as best I can. :wink:

If a gravitational wave curves space and space curvature is a gravitational field, isn´t a gravitational field a gravitational force? Well, the gravitational field is the amount of gravitational force that an object at each different point within the field would experience. So the field can vary from one point to another, and the value it varies to at a particular point is the magnitude of the force at that point.

Thus the wave would have formed the force…No. The curvature of space itself can either be smooth and continuous, which is the presence of a gravitational field, or it can have waves in it, which is the presence of gravitational radiation. Even being smooth, it can still have dips in it; those dips are gravity wells, places where as you get closer and closer to a certain point, the force gets stronger and stronger. But they are smooth, with no waves. Waves are only created when an object accelerates.

Radiation is a wave made up of the variation of the field of the vacuum, which is all fields at their minimum potential in the absence of any field associated with an object, and that minimum potential plus the potential of the object's field in the presence of a field associated with an object.Hm, that was a little complicated. I must admit I did not fully understand it. OK, we were talking about how fields manifest themselves.

All around our planet is the vacuum. Move far enough away from suns, and planets, and everything else, and it's pretty empty. There isn't much in it. What a field is, is some kind of warping or curving of that flat, empty vacuum. Warp it this way, you get gravity; warp it that way, you get an electric field. It doesn't really matter whether you're out in space or on the surface of the earth; that vacuum field exists everywhere, and it has all the warpings of all the different fields in it; each field that is actually present in a particular part of the vacuum will have its own field strength in it, and fields that are not present will have field strengths too, but they will be zero. It is easier to think of the simple case out in the middle of space first, then about the possible complications.

Now, these warpings or curvatures are continuous; they aren't periodical in space, like a water wave is periodical. There aren't peaks and troughs; there are just levels of strength in this particular... direction (although it isn't any direction you can imagine) that aren't zero, or aren't as close to zero as they could be. And they vary from one little piece of vacuum to the next only the tiniest bit. And as you move closer to the origin of the field, that energy level gets higher and higher from one little piece of the vacuum to the next. That is a field. (That is actually a spherical field; there are other types, but they are not relevant to this discussion.)

Now, let's suppose that instead of being smooth, there are waves in this field. That is, instead of increasing smoothly as you get closer to a source, they increase to a peak, and then decline to a trough, and then increase and decline again, over and over. This is different from the smooth increase. And this is the difference between a field, and a wave.

In regard to Olbers' paradox, there are several different possible solutions, and the most widely accepted one is that the universe is not infinite in time.Yes. And there is dark matter absorbing light. And moreover, the universe might not be infinite in space.Well, now, there's no proof one way or the other on whether the universe is finite or infinite in space; but there is more evidence that it is infinite than there is that it is finite, although that evidence is not as compelling as the evidence for the universe's finity in time.

On the other hand, the statement that there is dark matter absorbing light has no supporting evidence at all, and a considerable amount of controverting evidence; as a result, I cannot concur with your statement.

[Jio Moonshadow]

The universe does have walls or dropoff points. Simple example, if the universe is a vacuum or an area of CNP constant negative pressure, or the darkness or nothing visually percieved. At a point the pressure becomes of such a great negative pressure qualities that atomic operations would not be allowed, or universe wall. CNP respectively -17,-18,-19to the 3rd or actual pressure and not molecular compression. A black hole or force to siphon is formed when the nova explodes and create a weakness -15to the third of the surrounding environment. A universe of a greater negative pressure -27to the 3rd also a vacuum forces a siphon on our universe. The Logic of Negativity copyright 2004. Logical examination of the universe tying all sciences to single science. PHYSICS.

It may be percieved that gravity is responsible for a black hole, thats only because any gravitational force remaining is trapped and cannot escape. Along with a substance in chemistry that was deemed missing.

Anthony Giguere 1979

[JesseM]

Waves are only created when an object accelerates. Since gravitational waves depend on the quadrupole moment, constant acceleration won't produce them, only a changing acceleration will produce them. Electromagnetic waves depend on the dipole moment, so any change in velocity of a charge (acceleration) will produce electromagnetic waves. All around our planet is the vacuum. Move far enough away from suns, and planets, and everything else, and it's pretty empty. There isn't much in it. What a field is, is some kind of warping or curving of that flat, empty vacuum. Warp it this way, you get gravity; warp it that way, you get an electric field. Classical fields like electromagnetism are not traditionally understood in terms of changing the curvature of space, they're just force vectors attached to every point in ordinary flat space. Are you thinking of the Kaluza-Klein (http://en.wikipedia.org/wiki/Kaluza-Klein_theory) theory of electromagnetism? Now, these warpings or curvatures are continuous; they aren't periodical in space, like a water wave is periodical. There aren't peaks and troughs; there are just levels of strength in this particular... direction (although it isn't any direction you can imagine) that aren't zero, or aren't as close to zero as they could be. I'm not sure if there's actually a way to get curvature of spacetime to correspond to the idea of a force pulling in a particular direction--as I understand it, GR is really a fundamentally different picture of gravity, one that doesn't involve "forces" at all. Those schematic diagrams where they show gravity wells as depressions in a rubber sheet are a bit misleading, it's not like there's anything pulling "down" on objects as they move along the sheet, you could just as easily represent gravity wells as humps rather than depressions--the idea is that objects moving in the absence of other forces always follow a "geodesic" path, which on a curved 2D surface would mean the path with the shortest distance (like a segment of a 'great circle' on a globe), but in curved spacetime means the path with the greatest proper time (this is explained a little on this page (http://www.lns.cornell.edu/spr/2004-04/msg0060035.html)).

[Nereid]

Per CarstenDierks' request (which I am fully in accord with), we're now in SR & GR.

To the regular contributors to this thread: I think you'll now find that most of your questions and issues will be at least grounded in the modern understanding of GR ...

[pervect]

I'm not sure if there's actually a way to get curvature of spacetime to correspond to the idea of a force pulling in a particular direction--as I understand it, GR is really a fundamentally different picture of gravity, one that doesn't involve "forces" at all.


Under the proper circumstances, the curvature of spacetime does reduce rigorously to the idea of a force. Very strong fields or very high velocities prevent this approximation from working rigorously, however.

To give the gory details, the geodesic deviation equation gives the equation of a path that a freely falling particle of negligible mass will take. This is


\frac{d^2 x^a}{d \tau^2} + \Gamma^a{}_{bc} \frac{dx^b}{d \tau}\frac{dx^c}{d \tau} = 0


When spatial curvature is negligible, on can apprxomiate this as


\frac{d^2 x^a}{d \tau^2} + c^2 \Gamma^a{}_{00} + 2 c \Gamma^a{}_{0b} \frac{d x^b}{d \tau} = 0


This throws out all the space-space curvature terms.

This means that the geodesic path of a particle acts just as if it experienced a pair of forces on it - a velocity independent force due to the \mbox{\Gamma^0{}_{00}} term plus a velocity dependent force due to the second term. The first term, which is Newtonian gravity, can be considered to be analogous to the Columb force on a charge. The second term can be considered to be analogous to the magnetic force on a moving charge.

The anaology between weak-field gravitation an electromagnetism is sufficiently good that one can write a variant of Maxwell's equations for the two "force" components.

A good reference for this, if one can get a hold of it, is "Analogy between general relativity and electromagnetism for slowly moving particles in weak gravitational fields" by Harris. Thanks to Pete for pointing this paper out to me, even if he DID lose his copy :-).

To skip around a bit and address some of the questions that other posters made after skim-reading this thread

In standard general relativity gravity propagates at exactly 'c', the speed of light.

It's worthwhile checking out the sci.physics.faq How does gravity get out of a black hole (http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/black_gravity.html)

Note that neither light nor gravity waves can escape from a black hole, but both the electrostatic columb force of a charged black hole and the gravitational force of a massive black hole can escape. This has nothing whatsoever to do with the speed of gravity, though, as can be seen from the fact that the columb force also escapes a charged black hole. Note also that the only information that escapes from a black hole is it's charge (which generates the columb force of a charged black hole), and its mass (which generates the gravitational force).

[CarstenDierks]

Hi Nereid,

Thank you for moving. I hope we can get some additional interesting input in this group.


Schneibster and all others:

Thank you for the answers. I am still keeping up reading and looking up some papers on virtual particles, fields and the like.

However, before moving on, I have still a problem with some statements in prior post that seem contradictory to me.

So I would like to clarify some questions first:

(1) Gravitation curves spacetime.

(2) The curvature of spacetime (associated with gravitation) is only evoked by gravitational waves. A gravitational wave can constitute, aggravate, impair or erase the curvature.

(3) Every change in the extent of the curvature has to be evoked by a gravitational wave.

(4) If mass particles move, the curvature moves with them.

(5) Gravitational waves are only evoked if mass is in accelerated motion.
or:
(6) Gravitational waves are only evoked by changes in the acceleration of mass?

(7) Out of (2), (3), (4), (5) and (6): How does the curved spacetime of an object in linear motion move along with the object (since no gravitational waves are send out to "update" the "curvature information")?

I hope someone knows is a simple solution to this. Schneibster, do you?

Carsten

[JesseM]

(1) Gravitation curves spacetime. You might also say that mass/energy curves spacetime, and that what we call "gravitation" is really just an effect of the fact that all objects follow geodesic paths through curved spacetime (a geodesic is the closest thing to a 'straight line' in curved space or curved spacetime, like how the shortest distance between two points on a sphere is determined by the great circle (http://mathworld.wolfram.com/GreatCircle.html) which passes through both points). As pervect explained above, in certain limits these geodesic paths will look just like the paths you'd get if you imagine gravity as a force pulling on objects in flat spacetime. (2) The curvature of spacetime (associated with gravitation) is only evoked by gravitational waves. A gravitational wave can constitute, aggravate, impair or erase the curvature. What do you mean by "only evoked by"? Spacetime can be curved by systems which are not generating any gravitational waves. (3) Every change in the extent of the curvature has to be evoked by a gravitational wave. No. It's easier to think about this in analogy with electromagnetism--any acceleration of a charge will produce electromagnetic waves, but a charge moving at constant velocity will not. For a charge moving at constant velocity, the electromagnetic field is changing--other charges will act as though they are always attracted to the current position of the moving charge. This does not imply the force is acting faster than light though, it's more as if the the electromagnetic field can "extrapolate" the position of a charge moving at constant velocity, so if the charge suddenly accelerates, other charges will continue to act as if they are attracted to the position the charge would have been if it had continued to move at constant velocity, until they recieve an "update" in the form of an electromagnetic wave travelling at the speed of light, which was generated by the original acceleration.

In a similar way, the curvature of spacetime can apparently "extrapolate" constant acceleration (including 0 acceleration, or movement at constant velocity)--it is only when there is a change in the rate of acceleration that gravitational waves are generated. (4) If mass particles move, the curvature moves with them. Yes, at least locally. (5) Gravitational waves are only evoked if mass is in accelerated motion.
or:
(6) Gravitational waves are only evoked by changes in the acceleration of mass? #6. (7) Out of (2), (3), (4), (5) and (6): How does the curved spacetime of an object in linear motion move along with the object (since no gravitational waves are send out to "update" the "curvature information")? Again, you can think of it as a sort of "extrapolation". Presumably you could prove this by looking at solutions to the equations of GR involving masses moving at constant velocity (or at constant acceleration).

[pervect]

So I would like to clarify some questions first:

(1) Gravitation curves spacetime.


Yes. Or, alternatively, gravitation is curved space-time.


(2) The curvature of spacetime (associated with gravitation) is only evoked by gravitational waves. A gravitational wave can constitute, aggravate, impair or erase the curvature.

(3) Every change in the extent of the curvature has to be evoked by a gravitational wave.


No, to both of the above. Gravitational waves are important only under the most extreme conditions. Gravity can, and does exist as a curvature of space-time without the existence of gravitational waves.

Think of electrostatics. A pair of unlike charges attract each other. It is not necessary for an actual electromagnetic wave to exist for like charges to attract. Do not confuse actual electromagnetic waves with 'virtual" particles or waves.

[pervect]

Gravity & Electromagnetism - a comparison, and a perspective of "how gravity propagates".

Let's start with electromagnetism. There are a couple of ways to describe the electromagnetic field, but one of the simplest is in terms of the electric and magnetic fields. The electromagnetic field at any point in space-time has six components - 3 components of the electric field, and 3 components of the magnetic field. The fields arise ultimately from charges and the motion of charges. It takes 4 variables at any point in space-time to describe the charge and the motion of charge (current) there.

These six components of the electromagnetic field must satisfy a set of linear differential equations called Maxwell's equations that describe how the field variables interact with each other and with charges. The wave-like properties of light, the fact that light always travels at a speed less than or equal to c (exactly equal to c in empty space, lower in regions where there is matter), and the fact that any general changes in the electromagnetic field propagates at a speed less than 'c' are all determined by the nature of these linear differential equations.

Now, let's look at gravity. Instead of 6 variables to describe the electromagnetic field, one has 20 indpendent quantities which make up the Riemann curvature tensor, which describes the curvature of space-time at a individual point. Alternatley, one can describe space-time and it's local curvature by the 10 independent components of the metric tensor. The metric tensor is probably a little easier to grasp than the Riemann curvature tensor - it describes how one computes the distance between any two points. The 10 components of the metric tensor entirely determine all 20 components of the Riemann curvature tensor. This happens because the 20 components of the Riemann curvature tensor satisfy a set of differential equations known as the Bianchi iidentity.

There's more that can be said to make the Riemann tensor a bit more intuitive, but unfortunately this post is already getting to be a bit on the long side, so I'll leave this material out.

The source of the gravitational field is not charge, but energy - any sort of non-gravitational energy. Usually, though, the energy in the rest mass of matter dominates all other forms of energy. The description of the energy distribution in GR is given via the stress-energy tensor, which requires 10 variables at any point in space time - quite a bit more than the 4 that it took for electromagnetic theory.

Einsteins' equation, which describes gravity, is a NONLINEAR differential equation which relates the 20 components of the Riemann curvature tensor to the 10 components of the stress energy tensor at any point in space time. This is very similar to the way that Maxwell's equations relate the 6 electric and magnetic field comonents to the 4 components of charge and current at any poitn in space-time.

The non-linearity is an important difference between Einstein's equation and Maxwell's equation that makes gravity a lot harder. However, because these differential equations form a "quasi-linear, diagonal, second-order hyperbolic system" (whew!) it turns out that the solution of these differential equations locally exhibit much of the same "wave-like" properties that the solutions of Maxwell's equations do - specifically, changes in the field configuration always propagate at a speed slower than some value, 'c'.

[add]
http://www.physlink.com/Education/AskExperts/ae98.cfm
was a useful web source/refrerence for some (not all) of the points above.

[yogi]

Field vs Wave - some previous commentors have asserted authoritatively that waves, unlike static fields, must dissipate energy. Faraday first envisioned EM waves as fields that detached themselves - as such the wave retains its field energy as it propagates through a perfect medium - there is nothing inconsistent with the notion of a wave, wavelet, photon, or a deBroglie matter wave being able to communicate its intrinsic conservative field energy into some form of force.. e.g., in the case gravity - perhaps a pressure wave. If I recall, Caroline is a advocate and contributor to the inflow theory of gravity which depends upon a real aether.

Almost every force I can think of is somehow connected to a dynamic - motion of something, as Dirac once commented when faced with having to describe the vector potential in free space.

[pervect]

Field vs Wave - some previous commentors have asserted authoritatively that waves, unlike static fields, must dissipate energy.


I must have missed that part. Standard theory does not predict that electromagnetic waves in a vacuum lose energy, for instance - though they can and do "spread out", so their energy also spreads out over a larger volume. It sounds to me like it is being proposed that the energy in the waves is disappearing somehow, which doesn't sound like a very promising theory as it violates the conservation of energy in a major way.


Faraday first envisioned EM waves as fields that detached themselves - as such the wave retains its field energy as it propagates through a perfect medium - there is nothing inconsistent with the notion of a wave, wavelet, photon, or a deBroglie matter wave being able to communicate its intrinsic conservative field energy into some form of force.. e.g., in the case gravity - perhaps a pressure wave. If I recall, Caroline is a advocate and contributor to the inflow theory of gravity which depends upon a real aether.


If we have a positive charge and a negative charge sitting there in free space, attracting each other, but held back so that they are not accelerating, it is not standard to say that there are "waves" involved in the attraction. There are no actual light waves that can be detected in such a case (as with a camera, a radio receiver, or some other instrument that detects electromagnetic radiation).

There are some ways of looking at this attraction that involve "virtual particles", but it's not very much used for actual calculations. Hence my note about not confusing "real" waves with "virtual" ones.

The same applies to gravity. A pair of masses just sitting there attracting each other are not going to be emitting actual gravity waves, of the sort that could be detected with a gravity wave detector (LIGO, or one of its successors).

Onto the next point I want to talk about - differential equations.

The usual notion of physics relies heavily on differeintial equations. I hope this isn't scaring anybody, differential equations are sometimes as simple as

f = ma

This is a differential equation, because the accleration is the second derivative of the position. Usually the force is a function of position, and because of Newton's law above, the acceleration is proportional to the force. This means the second derivative of the position is a function of the position. Thus we have - a differential equation. Newton's laws are just differential equations.

Newton's laws are differential equations, and so are Maxwell's equations, Just about all of physics is differential equations. General relativity is not any different, in spite of the fact that it deals with some unusual notions like curved space-time. When you get behind curved space-time to the math that describes it, you see differential equations, just like the rest of physics. For instance, we say that mass in general relativity travels along a geodesic, which is a litle more general than saying that it experiences a force. How do we describe a geodesic? You guessed it (I hope!) - we describe a geodesic with a differential equations.

[yogi]

pervect - Good post re differential equations. I was referring to post #51 - I think I know what the author of it is trying to say - but as worded it implies that the EM wave is losing energy to the environment - that may happen with ocean waves where a close look reveals only an up and down motion of the particles in a friction medium. Of course if you look even closer, you will get your face wet.

[Garth]

Standard theory does not predict that electromagnetic waves in a vacuum lose energy, for instance - though they can and do "spread out", so their energy also spreads out over a larger volume. It sounds to me like it is being proposed that the energy in the waves is disappearing somehow, which doesn't sound like a very promising theory as it violates the conservation of energy in a major way.

But in the standard theory do not photons lose energy with cosmological/gravitational red shift?

That theory, GR, conserves energy-momentum, i.e. particle 'rest' masses rather than energy.

If we treat the electromagnetic waves as quanta, individual photons, then the photons from a distant galaxy or quasar are emitted at one frequency \nu with energy E = h\nu and are received much later in cosmological time with a smaller frequency and presumably a smaller energy. They have travelled across space-time, in zero proper time, with no forces acting on them and no work done on or by them, so where has their energy gone?



Garth

[pervect]

But in the standard theory do not photons lose energy with cosmological/gravitational red shift?


GR does, of course, have its own issues with energy conservation, which you and I have talked about quite a bit.

For those who came in late and are still with us, the sci.physics.faq

Is energy conserved in General Relativity (http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html)

is a good reference to the issue of energy conservation in GR.

However, there are several extremely important concepts of energy conservation that GR does have that the theory being prposed seems to lack.

The first concept that GR has is the concept that the divergence of the stress energy tensor is zero. This is called by many the "local conservation of energy", though this terminology seems to confuse mathemeticans. (See Wald pg 286 for an example of this usage). This is the differential form of the energy conservation law as described by the sci.physics.faq reference.

The second concept of energy conservation in GR applies only in asymptotically flat space times, and on the cosmological scale space-time in the actual universe isn't asymptotically flat, so this notion doesn't apply.

A third notion of energy conservation requires static spacetiems, and also doesn't apply.

However, the proposed theory of light in free space losing energy "just because" doesn't seem to have any notion whatsoever of energy conservation in any sense whatsoever - a serious lack, IMO.

[Garth]

However, the proposed theory of light in free space losing energy "just because" doesn't seem to have any notion whatsoever of energy conservation in any sense whatsoever - a serious lack, IMO.
A serious lack IMHO as well!

Consider model GR universe filled with a photon gas - the CMB - with no matter at all, i.e. the completely radiation dominated universe. The energy of each photon decreases inversely proportionally to the scale factor of the universe:-
For each photon:-

As lambdap = lambdap0R(t)/R0

Ep = h.nup = h.c/lambdap = Ep0.R0/R(t).

But if photon number is conserved then the total energy contained in the photon gas decreases inversely with R(t).

Where has the energy gone? A standard answer might: be into the energy absorbed by the expansion of the universe; but how?

Each photon is travelling along a null geodesic with no forces acting on it and no work done on or by it, so what is the mechanism by which it exchanges energy with the gravitational field? Does not the exchange of energy require a mediating force and would not such a force acting on the photon be a violation of the equivalence principle?

Just a thought or two.

Garth

[pervect]

A serious lack IMHO as well!

Consider model GR universe filled with a photon gas - the CMB - with no matter at all, i.e. the completely radiation dominated universe. The energy of each photon decreases inversely proportionally to the scale factor of the universe:-
For each photon:-

As lambdap = lambdap0R(t)/R0

Ep = h.nup = h.c/lambdap = Ep0.R0/R(t).

But if photon number is conserved then the total energy contained in the photon gas decreases inversely with R(t).

Where has the energy gone? A standard answer might: be into the energy absorbed by the expansion of the universe; but how?

Each photon is travelling along a null geodesic with no forces acting on it and no work done on or by it, so what is the mechanism by which it exchanges energy with the gravitational field? Does not the exchange of energy require a mediating force and would not such a force acting on the photon be a violation of the equivalence principle?

Just a thought or two.

Garth


Yes, this is a rather disturbing notion. On the other hand, if you take a little tiny cube of flat space-time, the rate of change of energy stored in the cube is still equal to the net inflow or outflow of energy through the faces of the cube - the differential conservation law tells us this. And you can always find a coordinate system where the space-time is flat. (Or you can use the more general form of the theorem where one uses the covariant derivative and not even need the notion of flat space time to make the same point, i.e.)

\nabla^a T_{a0} = 0

rather than taking the divergence of the stress energy tensor in a locally flat coordinate system.

Note that one can replace the zero with an arbitrary index - the zero index makes statements about energy conservation, a non-zero index makes statements about momentum conservation.

So this form of the conservation law is saying that yes, the energy density at any point in space-time is going down, but it's going down because energy is flowing out of the cube as the universe expands. This is not too surprising, if we have a fixed volume cube, and the universe expands, and the energy distribution is isotropic, that the energy has to be flowing out of the cube to fill all of space as the universe expands, and the energy density in a cube of fixed volume is going down as time goes down.

I'm not sure exactly how to reconcile these two points of view at this moment. I'm a bit suspicious of the assumption that the photon number is constant, but I'm not totally convinced this is the real explanation yet.

[add]
I think there's a much better explanation. The energy is going into "the gravitational field". The gravitational self energy is higher when the universe is smaller than when it is larger. This gravitational self-energy doesn't show up in the differential conservation law, it only shows up in finite volumes as discussed in the physics FAQ. I don't think there is anyway to make this idea rigorous, though, unless I'm wrong about not finding any timelike Killing vectors in the flat FRW spacetime. Without asymptotic flatness or a timelike Killing vector, there's no way that I know of to rigorously define the energy in the gravitational field.

[yogi]

Maybe not the G field as such - but if the universe is under tension, expansion will increase the stress energy - the loss of energy in the photon gas may correspond to the energy gained by the spatial volume.

[pervect]

I've been reading up on this point a little more.

It looks like that during the matter dominated phase, when the pressure of the universe is nearly zero, (density of mass energy) * (volume) remains essentially constant. But it's definitely not a standard idea to interpret this number as the "mass of the universe". Basically the FRW universe just doesn't fit any of the standard conditions in GR where an energy can be defined over a finite volume (asymptotic flatness, or staticity). Note that the differential energy consevation law still works without a hitch, though.

When the pressure isn't zero (this happens when there is a gravitationally significant amount of radiation), the above function isn't constant.

If we let PV = (density of mass energy) * (volume)

then d(PV)/dt = -(pressure) d (volume)

MTW, pg 705 is the reference for the above.

So what we have in the matter dominated era is the universe expanding, and the energy density per unit volume going down, to maintain a constant product. However, we resist calling this constant product the total energy of the universe.

In the case where radiation is present, the universe does sort of "cool off" as it expands, a lot like any expanding gas.

[Chronos]

Only problem with that is the universe was not matter dominated in the early inflationary phase, it was radiation dominated.

[pervect]

Only problem with that is the universe was not matter dominated in the early inflationary phase, it was radiation dominated.

I'm not sure what problem you are referring to Chronos. If your problem is that PV is not constant during the early radiation phase, I agree. Further reading gives the result that (pressure)*(volume)*(4/3) is a constant during the early radiation dominated phase, when we make the plausible assumption that all pressure is due to radiation.

This, then, is a good reason not to regard PV as the "mass of the universe". (I already mentioned that this wasn't a good idea, but it probably isn't a bad idea to make this point more explicit).

I've gotten off track, and fumbled around a bit (it was educational) - but where I started was with the issue of how to reconcile cosmological energy loss with the differential conservation law. The fact that the energy lost is proportional to the volume is sufficient to allow the reconcilliation. As we take the limit to zero volume, the energy loss goes to zero, so there is no conflict with the differential conservation law.

This also means that if we take a small enough piece of space-time, the energy loss can be neglected. In the current epoch of the universe, because the radiation pressure is so low, a "small enough" piece of space-time is quite large even on a cosmological scale. On a human scale, the volume required for cosmological energy loss is enormous. This means that our everyday expeiences and experimental results that show energy being conserved are not impacted by the cosmological issues - the cosmological issues are real, but don't have any impact on experiments carried out on a human timescale.

[Garth]

This also means that if we take a small enough piece of space-time, the energy loss can be neglected Are you happy with that? It seems that anything can be neglected if you make it small enough, however it is the whole universe that we are supposed to be dealing with here!

Adding pressure does not resolve the energy problem, it deepens it; a Friedmann dust universe does preserve mass-energy - because density ~ R-3, however pressure makes the expansion, counter intuitively, harder and slows it down as it adds another form of energy to the system. The density now decreases faster and mass is absorbed by the cosmic expansion, density ~ R-(3 + a), and M = density x volume; but by what mechanism? Do atoms or dust particles simply disappear into the 'aether'?

Garth

[pervect]

Are you happy with that? It seems that anything can be neglected if you make it small enough, however it is the whole universe that we are supposed to be dealing with here!

Adding pressure does not resolve the energy problem, it deepens it; a Friedmann dust universe does preserve mass-energy - because density ~ R-3, however pressure makes the expansion, counter intuitively, harder and slows it down as it adds another form of energy to the system. The density now decreases faster and mass is absorbed by the cosmic expansion, density ~ R-(3 + a), and M = density x volume; but by what mechanism? Do atoms or dust particles simply disappear into the 'aether'?

Garth

Well, I'm not exactly "happy" with that, but the universe isn't constrained to operate in a manner that pleases me :-). There are certain aspects of quantum mechanics that disturb me more than the energy problem, actually. Like particles passing through both slits in a two-slit experiment and interfering with themselves, for example.

It's possible that there is some sort of missing "scalar field", or as in your SCC theory, or some other sort of non-scalar field that accounts for the "missing" energy - but we don't have any evidence for such a thing, yet. It's certainly worth looking for.

It's also possible that energy conservation is only approximate. We've seen a lot of other symmetries in physics that broke down under extreme enough conditions. The universe did have to get created somehow, after all - and if energy is conserved, we either have to believe that the energy of the universe is zero, or that energy conservation can be violated somehow or other.

It is somewhat useful to be able to put some sort of bounds on how much energy is being "lost", though, though of course the answer is coordinate system dependent,

[yogi]

Some interesting relationships are arrived it by considering inflation to be an on going phenomena - the universe then is in a state of increasing negative pressure - energy is continually added in the form of spatial stress - the total energy is proportional to the surface area of the Hubble Sphere, the density is proportional to 1/R, there is no singularity at the beginning, the total energy (negative potential plus stress) is always zero ...