Is gravitation faster than light?

[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 that's the first step. Then next is to add in the extra dimensions...

 

[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 Schwarzschild 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 Schwarzschild radius. The Schwarzschild 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 Schwarzschild 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 Schwarzschild radius would be inside the edge of the event horizon; the event horizon would then project out past the Schwarzschild 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 Schwarzschild 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 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 each other. 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 a lot to understand what kind of pattern (orbit) it would follow, and why is that so. It's being studied as we speak. There are a lot 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.

 

[DB]

We're learning from each other.
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.

Carsten

Well, 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 a lot 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.

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,

Carsten

Sure, 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. 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…

Carsten

Hee 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]

Gravitons, gravitational waves, and so on ...

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 traveling at the speed of light reaches them.

For gravity, it's a bit more complicated, Steve Carlip says here 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 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 http://www.usd.edu/phys/courses/phys300/gallery/clark/wheeler.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 traveling 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!

 

[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:

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. [URL='https://www.physicsforums.com/insights/author/a-neumaier/']Arnold Neumaier's physics FAQ[/url] 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...@univie.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.