Positive energy requires work, negative energy releases work. We get to decide if the electron or its anti-particle the positron has positive or negative energy, but that is an arbitrary decision on our part.
I think it is wrong to think of these variations from average as particles, because one of the properties of particles is that they have defined lifetimes. Virtual particles have bounds on lifetimes depending on how measurements are made. One can never produce a cup of virtual particles, so I think our lingo gets us confused.
This really is a limitation on our knowledge of zero for complex numbers. Unlike the real numbers, complex numbers are not a totally ordered set, so if complex numbers are required to get the interference patterns seen in 2 slit experiments, when we take the road to nowhere (the vacuum), we cannot order the final steps.
The average energy of a vacuum can be zero. The deviation of the average amount of energy cannot be zero. The average is not the deviation from the average. State that clearly, and there is no issue. Blur the line, make BS.
Doug TheStandUpPhysicist.com
ps. There is no need for the Higgs field. When mass gets introduced correctly into a unified field theory, it will break symmetry not spontaneously (ie hyper-convenient, uber-sophisticated BS), but break symmetry in a way directly wired into gravity, which is what mass is all about. One has to connect the graviton to the scalar field so that the equivalence principle works on the quantum level.
Sorry for my apparent lack of precision. I meant it is JUST LIKE EM. So form the 4-current JUST LIKE EM, but put in the invariant mass where you put in the invariant electric charge. These are/. miscommunication issues. I know that vectors can only be subtracted from vectors so the result transforms like a vector.
The J of EM is an electric current density. I want a J that is formed exactly like the J of EM, except where one would put an electric charge q, a Lorentz invariant, I swap in q-G^(1/2) m, also a Lorentz invariant. If both sides of the equation, the source and the fields, are densities, there is no mismatch. There is nothing complicated here, sorry.
I am certain I never discussed a mass-energy density, that is the stuff of a rank-2 tensor.
What is the 4-current used in EM? It is the product of electric charge density and 4-velocity. What is the 4-current used in GEM? The part for EM is exactly the same, and one subtracts from that the square root of Newton's constant G times the product of mass density and 4-velocity. G^(1/2) m has exactly the same units as electric charge. Essentially inertia decreases the effective electrical charge by an unmeasurable amount (electric charge is defined to 10 significant digits, while the mass of an electron in the same units is 16 orders of magnitude smaller).
The proposal MUST use mass if it predicts light will bend 11.5 more microarcseconds around the Sun due to second-order PPN effects than the 10.8 more microarcseconds predicted by GR. Right now we can do light bending measurements to 100 microarcseconds, so three orders of magnitude improvements are required to detect 0.7 microarcsecond difference. The fact that the Sun spins and has a quandrapole moment both make contributions on this order, so it might not be practical.
GR is a rank 2 theory. GR is our best approach to gravity at this time. GR makes predictions. GR has one weakness, quantum. I am researching a different theory. It definitely uses the masses of bodies for doing calculations. The source and the field equations are both vectors, as they must be to have a well-formed equation. The theory can be quantized, because it is in all graduate-level quantum mechanics books under the Gupta/Bleuler quantization method. All I do is alter the interpretation of two of the virtual modes, getting them to do the real work of gravity.
Mass can be part of a scalar, a vector, or a tensor, it happens all the time.
I would disagree. What data we have proves gravity is a metric theory. It cannot show what is the math behind the metric theory. Right now, the only serious player for getting at second order derivatives of a metric that transforms like a tensor is the Riemann curvature tensor. What has been overlooked is the divergence of a covariant derivative transforms like a tensor and has second order derivatives of a metric. Riemann's curvature tensor is the simplest tensor to describe curvature as a tensor. I claim there is a simpler structure that has both second order derivatives of the metric and the potential. You have the freedom to described gravity as a 4-potential effect, a metric effect, or some combination of both. With Newton, its all potential, with GR it is all metric.
I understand the GR is a self-consistent theory, the source is a rank 2 tensor, and the field equations are a rank 2 tensor. To be self-consistent, my source must be a rank 1 tensor like my field equations are a rank 1 tensor. So my work is definitely in direct conflict with GR. Too bad for me, I better keep the day job, which I will, since it is clear you are choosing to define the possibility into oblivion, instead of finding a paper anywhere in the vast literature that directly addresses the issue.
Neither string theory nor loop quantum gravity at this time makes a testable prediction. They are areas of study done by serious people. At this time they CANNOT fail.
In contrast, if you measure the bending of light around the Sun to second order PPN accuracy, GEM theory could be shown to be correct or a failure. If the polarization of a gravity wave is determined, GEM theory could be right or wrong. GEM theory has reached the point of being a testible hypothesis, unlike anything done in string theory or loop quantum gravity.
> If you ditch the stress-energy tensor as source, it's very difficult to convince anyone that the theory you're talking about is "gravity".
I agree, there is a VERY strong bias out there. It is a BLIND SPOT. I referenced the places in the literature you rely upon to dismiss the simplest vector theories for gravity, and they are inadequate. I don't explect you to see or admit a blind spot, because, well, it is a blind spot.
Specifically exercise 7.2. He uses an antisymmetric field strength tensor. MTW is correct, that does not work. That is not what I am trying to do, so the exercise does not apply.
Newton's theory of gravity is the simplest rank 0 field theory that can be made. We know it fails because the speed of light c is not respected. To make Newton's gravity law consistent with special relativity leads right to Einstein's field equations (I think both Feynman and Weinberg showed that, whoever, they were smart). That is the simplest rank 2 field theory to explain gravity. All efforts to quantize the theory have failed to date, and I take that as a message: it cannot be done.
I asked Clifford Will why his review paper did not include the simplest rank 1 field theory possible, which is the focus of my efforts. He repeated a line that I've seen in MTW (beginning of chapter 40 to be specific): gravity must be a metric theory.
You know why he said that? Because he's right: gravity must be a metric theory. For me, it is a question of how to implement a metric theory. Right now, the only way is to use the Riemann curvature tensor, which is composed of the difference between two derivatives of connections and the difference between two products. I try and just use a covariant derivative which is the difference between a standard derivative and a connection. A scalar potential cannot explain the bending of light around the Sun because the g00 term gets smaller than 1, while the g11 term gets larger. A 4-vector potential can do the task. Effectively, by using a 4-potential, I lift potential theory to equal footing with changes in the metric (the connection). It is the ultimate middle ground between a theory which is only about potentials (Newton's rank 0 field theory) and a theory which is only about spacetime geometry (Einstein and Hilbert's rank 2 field theory).
I am aware I should call the proposal a vector field theory. Almost as soon as I say that, the technical folks in the audience say, no cannot be, the graviton must arise from a symmetric rank 2 tensor. That's what is in the action, darn it. The field equations (rank 1) are not the field strength tensor, a reducible asymmetric tensor that splits into the spin 1, rank 2, antisymmetric tensor for EM where like charges repel, and a spin 2, rank 2 , symmetric tensor for gravity.
So I get around the problem cited in MTW by using a different tensor to do the contraction, and am consistent with the use of a symmetric rank 2 field strength tensor required for the graviton.
>I would be very skeptical of any relativistic theory with a source of gravity other than rank-2
Yup, most folks are. Why? Because every reasonable proposal to day uses that. It is also why people think a reasonable theory for gravity should be nonlinear. I had a good discussion with Clifford Will, and that the line he used - not that a linear theory was not possible, but that there has not been a linear theory that is consistent with all experiments to date (light bending around the Sun, the precession of the perihelion of Mercury, tests of the equivalence principle, the strong field tests). I have gotten the light bending right, and the precession of the perihelion was a 4 pager that turned out OK. I feel vary confident that a quadrapole is the lowest order of emission for a gravity wave for my theory, but have not done the nuts and bolts calculation myself (Thorne did it in a related paper).
I hope we agree that sound is a longitudinal wave, and the EM is a transverse wave. The changing pressure in sound is in the direction of the traveling wave. The changing E and B field for light are transverse to the direction the light wave goes.
I'm ready to concede my logic was too simple. Part of the description of the sound field or the E and B fields must include the vectors for those fields. I would have to show that all the vectors that describe gravity all are colinear for the neutrino example. I beleive that to be true, but I did not show that, so you are correct in your critique.
Here is the rank of various parts of the theory.
Rank 0: The Lagrangian
Rank 1: The field equations, the source
Rank 2: The asymmetric field strength tensor.
Exactly the same thing applies for EM. The classical Lagrange density is rank 0. The Maxwell equations can be writen as a rank 1 field theory. The field strength tensor for EM is an antisymmetric rank 2 tensor, F^uv.
Clearly/. is not the best way to communicate physics. I said very clearly, EM waves are transverse, that there is no longitudinal EM wave, yet you appear to think that is what I said.
If you read about the Gupta/Bleuler method for quantizing a 4D wave equation, they talk about 4 modes of emission: 2 transverse, one longitudinal, and one scalar. They are using the word "scalar" to describe the mode of emission, not in reference to tensors. If you are familiar with that approach to quantizing the EM field, it is the scalar mode of emission that would allow negative probabilities. Since that makes no sense, they use a "supplementary condition" to make the longitudinal and scalar modes virtual. What my proposal does is make those modes do the work of gravity, where like charges attract, due to a symmetric field strength tensor of a spin 2 field. EM is the spin 1 antisymmetric field strength tensor where like charges repel.
> SHO does not logically imply longitudinal waves.
I agree with that. Sound happens to be a longitudinal wave. The changes in air pressure occur in the direction it is moving. In my neutrino example, the neutrinos accelerate in the direction they are moving. That is why the neutrino SHO is a longitudinal SHO. This system, the neutrinos moving in a static g field, is a longitudinal wave. I think that is correct at the undergrad level.
No matter how you jiggle an electron, you will never make a longitudinal wave of light, the waves will always be transverse. What I argue is that no matter how one moves masses, it will never be a transverse wave. As Clifford Will wrote in his 100+ page review, if the data comes back to show that the gravity waves caused by the collapse of a dense source is NOT transverse, that would be a big challenge for general relativity. It would also be a piece of data in support of my rank 1 field theory. Fortunately, data will rule the day.
One reason I cut way back on posting to SPR is people decide to toss in negatives, when all I ever care about are the technical issues. I have a Lagrange density, field equations, solutions to the field equations, and experiments like the one discussed in this thread, all plugged through Mathematica. In a measurable way - there are two experiments to test the validity of my proposal, the other being light should bend 0.7 microarcseconds more around the Sun than GR predicts - the GEM theory is a better formed alternative to GR than all of string theory at this time.
The question for me is whether GR is logically consistent on polarization. I know that gravity waves like the ones being hunted for here arise from the "water balloon" kind of motion for an isolated source (a quadrupole moment, no dipoles allowed). And GR predicts that the wave emitted will be transverse.
A simple harmonic oscillator is described by a few things: its period, its wavelength, and its polarization. As you correctly point out, the neutrinos are a different animal from the gravity waves generated by an isolated source, but both have the same cause, gravity. Nature likes to be logically consistent, so the I think the longitudinal SHO for the static gravitational field will also appear as a longitudinal gravity wave for a dynamic gravity field.
If you vibrate an electron back and forth say by heating it up in a light bulb filament, it will emit a photon perpendicular to that motion. EM is a transverse wave every way it is generated, no exceptions. To be logically consistent, I argue that gravity is a scalar or longitudinal wave, no exceptions. My proposal says EM is a transverse, spin 1 field, and gravity is longitudinal/scalar, spin 2 field, both of which travel at the speed of light.
The theory also predicts gravity waves, but the transverse modes of emission for a 4D wave are EM, and the longitudinale and scalar modes are the stuff of gravity. So GEM theory (gravity and EM) predicts that gravity waves will travel at the speed of light, but the polarization will not be transverse like GR predicts.
I think gravity MUST be viewed as a longitudinal wave, not transverse. Here's a thought experiment. You have a cup of neutrinos (see, this is a thought experiment because no such cup can be manufactured). You spill the cup. The neutrinos fall, and when they reach the floor, they keep falling, through the center of the Earth, to the other side, and in about 88 minutes, back to where they started, just to repeat the cycle again. This is a SHO (simple harmonic oscillator), with a period of 88 minutes, and a wavelength of twice the diameter of the Earth. The neutrinos are acceleration in the direction of velocity which is a defining characteristic of a longitudinal wave.
I agree with this, but only because I have a pretty darn elegant Lagrangian. Oh, but it is OBNOXIOUS (and so should be appreciated here at Slashdot). It uses rank 1 field equations, not rank 0 like Newton (wrongo, breaks speed of light rule) nor rank 2 like general relativity (probably wrongo because the field theory cannot be quantized). The antisymmetric field strength tensor of EM is replace by an asymmetric tensor to do both gravity and EM. If you want to check out a technical discussion, it is happening here http://physicsforums.com/showthread.php?t=87097. Yeah, I have more work to do, but you cannot fake elegance, and my proposal is not a "An acceptable 'toy' Lagrangian density function with simple analytical properties is singled out".
I haven't focused on the history since I work on getting quaternions to do things. I am sure it will be an entertaining story. Heaviside kicked Hamilton and Tait's ass. It was a near complete and total victory. The number of nerds that know what a quaternion is is quite low, while scalars and vectors dominate the math landscape. Only rocket scientists and game developers know about them since that is the way to do 3D rotations.
Even though I own the domain name, I try to stay grounded in what they can do, and new directions that can be reached. Nerds had flame wars in the past, they will continue in the future.
"analytic animation" is a riff on analytic geometry: write an equation, get an animation. There is no documentation at this time (my bad again), but the slowly drifting white dot is a function moving at a constant velocity, and all the yellow dots are the sine function of the white dot. Someday it might be cool, but more work is required.
OK. You can say or draw unkind things about our one lord and savior, any physicists you like, but play nicey-nice with the muslims. Of course one could say that my comment about muslims was not genuine, so I should be punished here and now. Oops.
Someday we will have open source software to do analytic animations, and then quaternions may get the respect might deserve (I am an ultra-conservative fringe guy).
Read "Spacetime Physics" by Taylor and Wheeler. It is a well-writen textbook that introduces the notion of the Lorentz invariant interval. It is the old pythagorean theorem with a twist: ds^2 = dx^2 + dy^2 + dz^2 - c^2 dt^2. So this is 4D, where the time part has a minus sign. It is that minus sign that causes all the fun.
There is NO fear of people who get basic definitions wrong. If someone claims 2^3 = 10 because it will make numbers bigger, well, that is not the way 2^3 works (the answer is 8 by the way, since you cannot look in the back of the book). The real book this guy needs to read is "Spacetime Physics" by Taylor and Wheeler.
I KNOW this guy does not understand the work of Wheeler or Feynman, otherwise he would know the definition of the stretch factor gamma. You can challenge the works of these pillars and have a deep respect for what they knew at the time. That's what I do.
doug TheStandUpPhysicist.com (Yup, a unified field theory is there for the download, but just like Nature herself, I don't care if you listen or not.)
The relativistic 4-velocity is not (1, dx/dt, dy/dt, dz/dt) as claimed by the web page author, but it is instead (dt/dgamma, dx/dgamma, dy/dgamma, dz/dgamma), where gamma is definted as the Lorentz invariant interval: gamma^2 = 1/(1 - v.v/c^2). This page gets attention because he bitch-slaps big names, but his basic math claim gets him an F in any undergrad special relativity class.
There is software to look through all the source code a company claims to own, http://blackducksoftware.com./ I'd rather have software do it than have to look by hand.
This is a cool project. It really is stunning: 5 million detailed pictures of the sky! I downloaded an image of the Tarantula nebula just so I could say I have one such image on my machine. In a way, that download does represent how this project is open to the public. Yet I don't think I want to crank through a terabyte of data on my 200mhz Linux box.
It is this level of technical detail available to anyone that makes science such a unique activity.
We don't know how gravity works on a large scale (and physicists don't like to point this out explicitly). Back in the 1960's, Alar Toomre was able to take the profile of light from a spiral galaxy and calculate how fast things were going (it is a tough calculation involving elliptical integrals). He showed two things. First, the velocities of the outer stars should decrease over distance, yet the speed remains constant. Second, a small disturbance along the axis will cause the galaxy to collapse, yet galaxies are stable over billions of years.
Dark matter was invented to get the velocity profile right and make the systems stable. We have a very precise knowledge of what kinds of particles can make up anything (it is called the standard model, built from the groups U(1), SU(2), and SU(3). whatever a group is:-). Yet we cannot decide what the matter used to get correct velocity profiles is at this time. So we don't know what it is made of, and its sole purpose is to cover a math error, an approach which has work in the past, see the history of the neutrino for example.
If we had a stable constant-velocity solution that involves gravity, then there would be no need for dark matter for spiral galaxies. There are other structures that Newton's gravity law fails to explain, but this was the first one noticed.
The big bang has a very similar math problem. Everything is traveling at the same speed, yet there was not enough time to agree to said speed (known as the horizon problem). The solution using the known forces is also mathematically unstable (the flatness problem). It is far worse than balancing a pencil on its tip, requiring some 55 orders of magnitude precision to end up with a Universe 13.7 billion years old. Guth and Linde proposed a way to solve these problems calling it inflation. A period of exponential growth gives everyone the same speed and drives the result to a stable place.
If we had a stable constant-velocity solution that involves gravity, then there would be no need for inflation.
For big systems like spiral galaxies or the big bang, gravity does not work. We do have hyptheses for both problems. Yet both involve types of matter we are still trying to guess. We may be missing something basic, a stable constant-velocity solution that involves gravity. Let's look at gravity again...
F_g = d m V/dtau = m dV/dtau + V dm/dtau
This is the chain rule applied to a relativistic force law. The m dV/dtau is the m A acceleration term that gets all the press. The other term is for constant-velocity. Assume the m A term is zero, solve for the second one, and one has a chance at getting a constant-velocity solution involving gravity. At least that's what I do in my free time.
Slashdot Mirror
Positive energy requires work, negative energy releases work. We get to decide if the electron or its anti-particle the positron has positive or negative energy, but that is an arbitrary decision on our part.
I think it is wrong to think of these variations from average as particles, because one of the properties of particles is that they have defined lifetimes. Virtual particles have bounds on lifetimes depending on how measurements are made. One can never produce a cup of virtual particles, so I think our lingo gets us confused.
This really is a limitation on our knowledge of zero for complex numbers. Unlike the real numbers, complex numbers are not a totally ordered set, so if complex numbers are required to get the interference patterns seen in 2 slit experiments, when we take the road to nowhere (the vacuum), we cannot order the final steps.
doug
The average energy of a vacuum can be zero. The deviation of the average amount of energy cannot be zero. The average is not the deviation from the average. State that clearly, and there is no issue. Blur the line, make BS.
Doug
TheStandUpPhysicist.com
ps. There is no need for the Higgs field. When mass gets introduced correctly into a unified field theory, it will break symmetry not spontaneously (ie hyper-convenient, uber-sophisticated BS), but break symmetry in a way directly wired into gravity, which is what mass is all about. One has to connect the graviton to the scalar field so that the equivalence principle works on the quantum level.
Sorry for my apparent lack of precision. I meant it is JUST LIKE EM. So form the 4-current JUST LIKE EM, but put in the invariant mass where you put in the invariant electric charge. These are /. miscommunication issues. I know that vectors can only be subtracted from vectors so the result transforms like a vector.
The J of EM is an electric current density. I want a J that is formed exactly like the J of EM, except where one would put an electric charge q, a Lorentz invariant, I swap in q-G^(1/2) m, also a Lorentz invariant. If both sides of the equation, the source and the fields, are densities, there is no mismatch. There is nothing complicated here, sorry.
I am certain I never discussed a mass-energy density, that is the stuff of a rank-2 tensor.
What is the 4-current used in EM? It is the product of electric charge density and 4-velocity. What is the 4-current used in GEM? The part for EM is exactly the same, and one subtracts from that the square root of Newton's constant G times the product of mass density and 4-velocity. G^(1/2) m has exactly the same units as electric charge. Essentially inertia decreases the effective electrical charge by an unmeasurable amount (electric charge is defined to 10 significant digits, while the mass of an electron in the same units is 16 orders of magnitude smaller).
The proposal MUST use mass if it predicts light will bend 11.5 more microarcseconds around the Sun due to second-order PPN effects than the 10.8 more microarcseconds predicted by GR. Right now we can do light bending measurements to 100 microarcseconds, so three orders of magnitude improvements are required to detect 0.7 microarcsecond difference. The fact that the Sun spins and has a quandrapole moment both make contributions on this order, so it might not be practical.
GR is a rank 2 theory. GR is our best approach to gravity at this time. GR makes predictions. GR has one weakness, quantum. I am researching a different theory. It definitely uses the masses of bodies for doing calculations. The source and the field equations are both vectors, as they must be to have a well-formed equation. The theory can be quantized, because it is in all graduate-level quantum mechanics books under the Gupta/Bleuler quantization method. All I do is alter the interpretation of two of the virtual modes, getting them to do the real work of gravity.
Mass can be part of a scalar, a vector, or a tensor, it happens all the time.
> It's the definition of what gravity is.
I would disagree. What data we have proves gravity is a metric theory. It cannot show what is the math behind the metric theory. Right now, the only serious player for getting at second order derivatives of a metric that transforms like a tensor is the Riemann curvature tensor. What has been overlooked is the divergence of a covariant derivative transforms like a tensor and has second order derivatives of a metric. Riemann's curvature tensor is the simplest tensor to describe curvature as a tensor. I claim there is a simpler structure that has both second order derivatives of the metric and the potential. You have the freedom to described gravity as a 4-potential effect, a metric effect, or some combination of both. With Newton, its all potential, with GR it is all metric.
I understand the GR is a self-consistent theory, the source is a rank 2 tensor, and the field equations are a rank 2 tensor. To be self-consistent, my source must be a rank 1 tensor like my field equations are a rank 1 tensor. So my work is definitely in direct conflict with GR. Too bad for me, I better keep the day job, which I will, since it is clear you are choosing to define the possibility into oblivion, instead of finding a paper anywhere in the vast literature that directly addresses the issue.
Neither string theory nor loop quantum gravity at this time makes a testable prediction. They are areas of study done by serious people. At this time they CANNOT fail.
In contrast, if you measure the bending of light around the Sun to second order PPN accuracy, GEM theory could be shown to be correct or a failure. If the polarization of a gravity wave is determined, GEM theory could be right or wrong. GEM theory has reached the point of being a testible hypothesis, unlike anything done in string theory or loop quantum gravity.
> If you ditch the stress-energy tensor as source, it's very difficult to convince anyone that the theory you're talking about is "gravity".
I agree, there is a VERY strong bias out there. It is a BLIND SPOT. I referenced the places in the literature you rely upon to dismiss the simplest vector theories for gravity, and they are inadequate. I don't explect you to see or admit a blind spot, because, well, it is a blind spot.
> See MTW (chapter 7)
Specifically exercise 7.2. He uses an antisymmetric field strength tensor. MTW is correct, that does not work. That is not what I am trying to do, so the exercise does not apply.
Newton's theory of gravity is the simplest rank 0 field theory that can be made. We know it fails because the speed of light c is not respected. To make Newton's gravity law consistent with special relativity leads right to Einstein's field equations (I think both Feynman and Weinberg showed that, whoever, they were smart). That is the simplest rank 2 field theory to explain gravity. All efforts to quantize the theory have failed to date, and I take that as a message: it cannot be done.
I asked Clifford Will why his review paper did not include the simplest rank 1 field theory possible, which is the focus of my efforts. He repeated a line that I've seen in MTW (beginning of chapter 40 to be specific): gravity must be a metric theory.
You know why he said that? Because he's right: gravity must be a metric theory. For me, it is a question of how to implement a metric theory. Right now, the only way is to use the Riemann curvature tensor, which is composed of the difference between two derivatives of connections and the difference between two products. I try and just use a covariant derivative which is the difference between a standard derivative and a connection. A scalar potential cannot explain the bending of light around the Sun because the g00 term gets smaller than 1, while the g11 term gets larger. A 4-vector potential can do the task. Effectively, by using a 4-potential, I lift potential theory to equal footing with changes in the metric (the connection). It is the ultimate middle ground between a theory which is only about potentials (Newton's rank 0 field theory) and a theory which is only about spacetime geometry (Einstein and Hilbert's rank 2 field theory).
I am aware I should call the proposal a vector field theory. Almost as soon as I say that, the technical folks in the audience say, no cannot be, the graviton must arise from a symmetric rank 2 tensor. That's what is in the action, darn it. The field equations (rank 1) are not the field strength tensor, a reducible asymmetric tensor that splits into the spin 1, rank 2, antisymmetric tensor for EM where like charges repel, and a spin 2, rank 2 , symmetric tensor for gravity.
So I get around the problem cited in MTW by using a different tensor to do the contraction, and am consistent with the use of a symmetric rank 2 field strength tensor required for the graviton.
>I would be very skeptical of any relativistic theory with a source of gravity other than rank-2
Yup, most folks are. Why? Because every reasonable proposal to day uses that. It is also why people think a reasonable theory for gravity should be nonlinear. I had a good discussion with Clifford Will, and that the line he used - not that a linear theory was not possible, but that there has not been a linear theory that is consistent with all experiments to date (light bending around the Sun, the precession of the perihelion of Mercury, tests of the equivalence principle, the strong field tests). I have gotten the light bending right, and the precession of the perihelion was a 4 pager that turned out OK. I feel vary confident that a quadrapole is the lowest order of emission for a gravity wave for my theory, but have not done the nuts and bolts calculation myself (Thorne did it in a related paper).
I hope we agree that sound is a longitudinal wave, and the EM is a transverse wave. The changing pressure in sound is in the direction of the traveling wave. The changing E and B field for light are transverse to the direction the light wave goes.
I'm ready to concede my logic was too simple. Part of the description of the sound field or the E and B fields must include the vectors for those fields. I would have to show that all the vectors that describe gravity all are colinear for the neutrino example. I beleive that to be true, but I did not show that, so you are correct in your critique.
Here is the rank of various parts of the theory.
Rank 0: The Lagrangian
Rank 1: The field equations, the source
Rank 2: The asymmetric field strength tensor.
Exactly the same thing applies for EM. The classical Lagrange density is rank 0. The Maxwell equations can be writen as a rank 1 field theory. The field strength tensor for EM is an antisymmetric rank 2 tensor, F^uv.
Clearly /. is not the best way to communicate physics. I said very clearly, EM waves are transverse, that there is no longitudinal EM wave, yet you appear to think that is what I said.
If you read about the Gupta/Bleuler method for quantizing a 4D wave equation, they talk about 4 modes of emission: 2 transverse, one longitudinal, and one scalar. They are using the word "scalar" to describe the mode of emission, not in reference to tensors. If you are familiar with that approach to quantizing the EM field, it is the scalar mode of emission that would allow negative probabilities. Since that makes no sense, they use a "supplementary condition" to make the longitudinal and scalar modes virtual. What my proposal does is make those modes do the work of gravity, where like charges attract, due to a symmetric field strength tensor of a spin 2 field. EM is the spin 1 antisymmetric field strength tensor where like charges repel.
> SHO does not logically imply longitudinal waves.
I agree with that. Sound happens to be a longitudinal wave. The changes in air pressure occur in the direction it is moving. In my neutrino example, the neutrinos accelerate in the direction they are moving. That is why the neutrino SHO is a longitudinal SHO. This system, the neutrinos moving in a static g field, is a longitudinal wave. I think that is correct at the undergrad level.
No matter how you jiggle an electron, you will never make a longitudinal wave of light, the waves will always be transverse. What I argue is that no matter how one moves masses, it will never be a transverse wave. As Clifford Will wrote in his 100+ page review, if the data comes back to show that the gravity waves caused by the collapse of a dense source is NOT transverse, that would be a big challenge for general relativity. It would also be a piece of data in support of my rank 1 field theory. Fortunately, data will rule the day.
One reason I cut way back on posting to SPR is people decide to toss in negatives, when all I ever care about are the technical issues. I have a Lagrange density, field equations, solutions to the field equations, and experiments like the one discussed in this thread, all plugged through Mathematica. In a measurable way - there are two experiments to test the validity of my proposal, the other being light should bend 0.7 microarcseconds more around the Sun than GR predicts - the GEM theory is a better formed alternative to GR than all of string theory at this time.
The question for me is whether GR is logically consistent on polarization. I know that gravity waves like the ones being hunted for here arise from the "water balloon" kind of motion for an isolated source (a quadrupole moment, no dipoles allowed). And GR predicts that the wave emitted will be transverse.
A simple harmonic oscillator is described by a few things: its period, its wavelength, and its polarization. As you correctly point out, the neutrinos are a different animal from the gravity waves generated by an isolated source, but both have the same cause, gravity. Nature likes to be logically consistent, so the I think the longitudinal SHO for the static gravitational field will also appear as a longitudinal gravity wave for a dynamic gravity field.
If you vibrate an electron back and forth say by heating it up in a light bulb filament, it will emit a photon perpendicular to that motion. EM is a transverse wave every way it is generated, no exceptions. To be logically consistent, I argue that gravity is a scalar or longitudinal wave, no exceptions. My proposal says EM is a transverse, spin 1 field, and gravity is longitudinal/scalar, spin 2 field, both of which travel at the speed of light.
doug
I've got an alternative, and it does EM too, being discussed here:
http://physicsforums.com/showthread.php?t=87097
The theory also predicts gravity waves, but the transverse modes of emission for a 4D wave are EM, and the longitudinale and scalar modes are the stuff of gravity. So GEM theory (gravity and EM) predicts that gravity waves will travel at the speed of light, but the polarization will not be transverse like GR predicts.
I think gravity MUST be viewed as a longitudinal wave, not transverse. Here's a thought experiment. You have a cup of neutrinos (see, this is a thought experiment because no such cup can be manufactured). You spill the cup. The neutrinos fall, and when they reach the floor, they keep falling, through the center of the Earth, to the other side, and in about 88 minutes, back to where they started, just to repeat the cycle again. This is a SHO (simple harmonic oscillator), with a period of 88 minutes, and a wavelength of twice the diameter of the Earth. The neutrinos are acceleration in the direction of velocity which is a defining characteristic of a longitudinal wave.
doug
TheStandUpPhysicist.com
I agree with this, but only because I have a pretty darn elegant Lagrangian. Oh, but it is OBNOXIOUS (and so should be appreciated here at Slashdot). It uses rank 1 field equations, not rank 0 like Newton (wrongo, breaks speed of light rule) nor rank 2 like general relativity (probably wrongo because the field theory cannot be quantized). The antisymmetric field strength tensor of EM is replace by an asymmetric tensor to do both gravity and EM. If you want to check out a technical discussion, it is happening here
http://physicsforums.com/showthread.php?t=87097. Yeah, I have more work to do, but you cannot fake elegance, and my proposal is not a "An acceptable 'toy' Lagrangian density function with simple analytical properties is singled out".
Later,
doug
TheStandUpPhysicist.com
I haven't focused on the history since I work on getting quaternions to do things. I am sure it will be an entertaining story. Heaviside kicked Hamilton and Tait's ass. It was a near complete and total victory. The number of nerds that know what a quaternion is is quite low, while scalars and vectors dominate the math landscape. Only rocket scientists and game developers know about them since that is the way to do 3D rotations.
Even though I own the domain name, I try to stay grounded in what they can do, and new directions that can be reached. Nerds had flame wars in the past, they will continue in the future.
doug
quaternions.com
TheStandUpPhysicist.com
"analytic animation" is a riff on analytic geometry: write an equation, get an animation. There is no documentation at this time (my bad again), but the slowly drifting white dot is a function moving at a constant velocity, and all the yellow dots are the sine function of the white dot. Someday it might be cool, but more work is required.
Off to make DVD's of the show,
doug
OK. You can say or draw unkind things about our one lord and savior, any physicists you like, but play nicey-nice with the muslims. Of course one could say that my comment about muslims was not genuine, so I should be punished here and now. Oops.
doug
My bad. gamma = dt/dtau, gamma beta = dx/dtau.
Someday we will have open source software to do analytic animations, and then quaternions may get the respect might deserve (I am an ultra-conservative fringe guy).
doug
http://quaternions.sourceforge.net/
Read "Spacetime Physics" by Taylor and Wheeler. It is a well-writen textbook that introduces the notion of the Lorentz invariant interval. It is the old pythagorean theorem with a twist: ds^2 = dx^2 + dy^2 + dz^2 - c^2 dt^2. So this is 4D, where the time part has a minus sign. It is that minus sign that causes all the fun.
doug
TheStandUpPhysicist.com
There is NO fear of people who get basic definitions wrong. If someone claims 2^3 = 10 because it will make numbers bigger, well, that is not the way 2^3 works (the answer is 8 by the way, since you cannot look in the back of the book). The real book this guy needs to read is "Spacetime Physics" by Taylor and Wheeler.
I KNOW this guy does not understand the work of Wheeler or Feynman, otherwise he would know the definition of the stretch factor gamma. You can challenge the works of these pillars and have a deep respect for what they knew at the time. That's what I do.
doug
TheStandUpPhysicist.com
(Yup, a unified field theory is there for the download, but just like Nature herself, I don't care if you listen or not.)
The relativistic 4-velocity is not (1, dx/dt, dy/dt, dz/dt) as claimed by the web page author, but it is instead (dt/dgamma, dx/dgamma, dy/dgamma, dz/dgamma), where gamma is definted as the Lorentz invariant interval: gamma^2 = 1/(1 - v.v/c^2). This page gets attention because he bitch-slaps big names, but his basic math claim gets him an F in any undergrad special relativity class.
doug
TheStandUpPhysicist.com
There is software to look through all the source code a company claims to own, http://blackducksoftware.com./ I'd rather have software do it than have to look by hand.
This is a cool project. It really is stunning: 5 million detailed pictures of the sky! I downloaded an image of the Tarantula nebula just so I could say I have one such image on my machine. In a way, that download does represent how this project is open to the public. Yet I don't think I want to crank through a terabyte of data on my 200mhz Linux box.
It is this level of technical detail available to anyone that makes science such a unique activity.
Hello:
:-). Yet we cannot decide what the matter used to get correct velocity profiles is at this time. So we don't know what it is made of, and its sole purpose is to cover a math error, an approach which has work in the past, see the history of the neutrino for example.
We don't know how gravity works on a large scale (and physicists don't like to point this out explicitly). Back in the 1960's, Alar Toomre was able to take the profile of light from a spiral galaxy and calculate how fast things were going (it is a tough calculation involving elliptical integrals). He showed two things. First, the velocities of the outer stars should decrease over distance, yet the speed remains constant. Second, a small disturbance along the axis will cause the galaxy to collapse, yet galaxies are stable over billions of years.
Dark matter was invented to get the velocity profile right and make the systems stable. We have a very precise knowledge of what kinds of particles can make up anything (it is called the standard model, built from the groups U(1), SU(2), and SU(3). whatever a group is
If we had a stable constant-velocity solution that involves gravity, then there would be no need for dark matter for spiral galaxies. There are other structures that Newton's gravity law fails to explain, but this was the first one noticed.
The big bang has a very similar math problem. Everything is traveling at the same speed, yet there was not enough time to agree to said speed (known as the horizon problem). The solution using the known forces is also mathematically unstable (the flatness problem). It is far worse than balancing a pencil on its tip, requiring some 55 orders of magnitude precision to end up with a Universe 13.7 billion years old. Guth and Linde proposed a way to solve these problems calling it inflation. A period of exponential growth gives everyone the same speed and drives the result to a stable place.
If we had a stable constant-velocity solution that involves gravity, then there would be no need for inflation.
For big systems like spiral galaxies or the big bang, gravity does not work. We do have hyptheses for both problems. Yet both involve types of matter we are still trying to guess. We may be missing something basic, a stable constant-velocity solution that involves gravity. Let's look at gravity again...
F_g = d m V/dtau = m dV/dtau + V dm/dtau
This is the chain rule applied to a relativistic force law. The m dV/dtau is the m A acceleration term that gets all the press. The other term is for constant-velocity. Assume the m A term is zero, solve for the second one, and one has a chance at getting a constant-velocity solution involving gravity. At least that's what I do in my free time.
doug