Understanding Spin-2 Bosons & Graviton Theory of Gravity

[bbbl67]

I'm somewhat familiar with the General Relativity description of gravity, at least conceptually. So I thought I'd ask about the graviton theory of gravity. Specifically, I've read elsewhere that a graviton must be a Spin-2 boson. Okay, given that as it may, how does a spin-2 boson differ from a spin-1 or spin-0 boson? What is the difference in behaviour between these three types of bosons? Also, all of the familiar force carrier bosons, like the photon, the gluon, the W & Z bosons are spin 1, while the Higgs boson is spin-0, I gather. So what is it that makes the photon, gluon, and W & Z similar to each other, while being different from the Higgs, and how are they all different from the graviton?

Also do any of the graviton theories come close to reproducing General Relativity? Somewhere I read that graviton theory so far only reproduces Newtonian Gravity, rather than GR?

 

[dextercioby]

While this is the proper place to ask all these questions, I'm afraid clear answers don't really exist. Or if they do, they are not clear to me. There's no valid (=renormalizabile like QCD) graviton theory, unless there's no cross interaction between gravitons, hence no curvature or... gravity. In other words, the only theory which makes sense is either the quantized linear gravity, or an effective field description of gravity. The latter is reviewed here: http://arxiv.org/abs/gr-qc/9512024

 

[bbbl67]

Okay, I understand, no real theory of gravitons vs. gravity yet. So what exactly is linearized gravity? A linear approximation of General Relativity?

So what about the other part of the question, the differences between boson spins?

 

[DelcrossA]

My understanding of it is that the graviton is said to have be spin-2 because it is described as a rank-2 tensor field. More specifically, the polarization tensor for a graviton is given by the direct product of two polarization vectors (the ones used to describe a photon field).
$$R^\mu_\nu \ R^\rho_\sigma \ \epsilon^\nu_{\pm} \ \epsilon^\sigma_{\pm}$$

Note: the +- denotes the helicity of the particle. So the total product with will be changed by a net phase of ##\pm2\theta## (##\theta## is the rotation angle about the chosen axis that the R operators rotate about) so that it transforms as if it had a helicity of +-2. Meaning,
$$\epsilon^\nu_{\pm} \ \epsilon^\sigma_{\pm}=\epsilon^{\nu\sigma}_{2\pm}$$

 

[bbbl67]

My understanding of it is that the graviton is said to have be spin-2 because it is described as a rank-2 tensor field. More specifically, the polarization tensor for a graviton is given by the direct product of two polarization vectors (the ones used to describe a photon field).
$$R^\mu_\nu \ R^\rho_\sigma \ \epsilon^\nu_{\pm} \ \epsilon^\sigma_{\pm}$$

Note: the +- denotes the helicity of the particle. So the total product with will be changed by a net phase of ##\pm2\theta## (##\theta## is the rotation angle about the chosen axis that the R operators rotate about) so that it transforms as if it had a helicity of +-2. Meaning,
$$\epsilon^\nu_{\pm} \ \epsilon^\sigma_{\pm}=\epsilon^{\nu\sigma}_{2\pm}$$

No idea what those equations mean, whatsoever.

Let's go about this in a different direction. Does the graviton hypothesis imply that gravity is an energy field again, like under Newton. Because under Einstein, it became a negative energy field.

 

[Nugatory]

Does the graviton hypothesis imply that gravity is an energy field again, like under Newton.

Quantum field theories are even more alien to classical mechanics than general relativity - the Newtonian notion of position and thus of force as something that affects the second derivative of that position doesn't appear.

 

[bbbl67]

Quantum field theories are even more alien to classical mechanics than general relativity - the Newtonian notion of position and thus of force as something that affects the second derivative of that position doesn't appear.

Okay, but doesn't the idea of a quantum particle, the graviton in this case, imply that it's a particle of energy?

 

[Nugatory]

Okay, but doesn't the idea of a quantum particle, the graviton in this case, imply that it's a particle of energy?

No. It is "a quantized excitation of a quantum field" - and if you think this is less than helpful when you want a math-free intuitive picture of what's going on, I agree with you.

 

[jtbell]

a particle of energy

Energy is not a substance, or "stuff"; it's a property of something.

 

[bbbl67]

Energy is not a substance, or "stuff"; it's a property of something.

Leon Lederman in his book Beyond The God Particle, considers energy to be stuff, while mass is just a property of that stuff.

Also this video from PBS Spacetime also considers energy to be stuff, while mass is just a property of the energy. That conclusion starts at 7:48 of the video.

 

[Nugatory]

Leon Lederman in his book Beyond The God Particle, considers energy to be stuff, while mass is just a property of that stuff.

Also this video from PBS Spacetime also considers energy to be stuff, while mass is just a property of the energy. That conclusion starts at 7:48 of the video.

Those are both popularizations, and neither is an acceptable source under the PhysicsForums rules.

There's nothing wrong with popularizations as long as you understand their limitations... But one of those limitations is that they oversimplify in many ways. "Energy is stuff" and "mass is just a property of the energy" are statements so vague as to be lacking in any meaning unless backed up with some serious mathematical rigor.

 

[bbbl67]

Those are both popularizations, and neither is an acceptable source under the PhysicsForums rules.

There's nothing wrong with popularizations as long as you understand their limitations... But one of those limitations is that they oversimplify in many ways. "Energy is stuff" and "mass is just a property of the energy" are statements so vague as to be lacking in any meaning unless backed up with some serious mathematical rigor.

Well, both were done by well-respected physicists. If you consider energy to be a property of stuff, then what do you consider "stuff" to be?

 

[Feeble Wonk]

Well, both were done by well-respected physicists. If you consider energy to be a property of stuff, then what do you consider "stuff" to be?

Ahhh... the question of ontological reality. It seems like a reasonable question to me. [emoji848]

...aaaaand now the thread closes.

 

[Nugatory]

Well, both were done by well-respected physicists.

Many excellent popularizations (and some rather bad ones too) are done by well-respected physicists. This is a good thing, because too few people have the opportunity to learn enough math to take on the real thing - but when you read them you have to remember that you're not taking on the real thing.

If you consider energy to be a property of stuff, then what do you consider "stuff" to be?

That question is too imprecise to answer - there's just no way to attach a rigorous meaning to the phrase "energy is a property of 'stuff'" so no way to consider it true or false. However, we've drifted far from your original question about spins... For that, I am aware of no answer that is both the real deal and less technical than http://arxiv.org/abs/hep-ph/9405255

 

[atyy]

Okay, I understand, no real theory of gravitons vs. gravity yet. So what exactly is linearized gravity? A linear approximation of General Relativity?

The paper that dextercioby refers to by Donoghue says that gravitons = classical GR + small quantum corrections. So there is a good theory of quantum gravity (including most of the nonlinear part of GR, using gravitons) in the same sense that we have a good theory of quantum electromagnetism (using photons and electrons, as worked out by Tomonaga, Feynman, Schwinger and others).

The quantum gravity theory does not include full GR, in the sense that it does not include spacetime very near black hole or big bang singularities. However, that is the part of GR that we do not trust - in part because the quantum theory fails, so the basic answer is that we do have a good theory of quantum gravity that reproduces the successful parts of classical GR.

 

[bbbl67]

The quantum gravity theory does not include full GR, in the sense that it does not include spacetime very near black hole or big bang singularities. However, that is the part of GR that we do not trust - in part because the quantum theory fails, so the basic answer is that we do have a good theory of quantum gravity that reproduces the successful parts of classical GR.

But doesn't GR work fabulously up until the event horizon of a black hole? It's only when you get past the event horizon towards the center of the BH that we have idea about. Since you said that linear gravity doesn't "include spacetime very near a black hole"? Or do you mean very near a black hole singularity?

 

[haael]

Physicists will rot in hell for making simple things sound hard.

We have different kinds of fields.
The simplest is the scalar field (aka spin 0), where each point is assigned a scalar. Example: pressure or temperature.
Then we can have vector fields (aka spin 1), where each point has an associated vector. Example: wind.
We can also have fields where each point is assigned a matrix. These are called tensor field. Sometimes with restrictions, i.e. it has to be symmetric. We call them also spin-2 fields.

What kind of field is gravity, according to GR? It's literally the field of deformation. What kind of field is it? It's a symmetric tensor field. (Try Wikipedia: deformation tensor.)

The statement "graviton has to have spin 2" means really: "Gravity is deformation of spacetime, deformation is a tensor field and graviton is the quantum of that field."

In quantum mechanics we don't really have scalars, vectors and tensors, but their quantized relatives: quantum scalars, quantum vectors and quantum tensors, but you don't have to care about that right now.

 

[bbbl67]

Physicists will rot in hell for making simple things sound hard.

Amen! ;-)

 

[atyy]

But doesn't GR work fabulously up until the event horizon of a black hole? It's only when you get past the event horizon towards the center of the BH that we have idea about. Since you said that linear gravity doesn't "include spacetime very near a black hole"? Or do you mean very near a black hole singularity?

No, I was not talking about linear gravity. The graviton theory includes nonlinearities. Your quote of my post is not correct.

 

[nikkkom]

No idea what those equations mean, whatsoever.
Let's go about this in a different direction.

You ask for answers, but when they are given to you, you don't like them. That's unproductive.

The answer to "why graviton must be a spin-2 particle" is mathematical: only spin-2 particles will result, in classical limit, in a force which looks like GR. If you don't understand the math which shows this, it is your problem, not math's. BTW, this particular math is slightly above my head too, but I don't go down the road "I don't understand it, so I'll demand a different explanation". There is no non-mathematical explanation to it.

 

[Khashishi]

Then we can have vector fields (aka spin 1), where each point has an associated vector. Example: wind.
We can also have fields where each point is assigned a matrix. These are called tensor field. Sometimes with restrictions, i.e. it has to be symmetric. We call them also spin-2 fields.

Now wait a minute. The electromagnetic field is a rank 2 antisymmetric tensor field, but the photon is spin 1. Now, the electromagnetic field is typically broken down into two 3-element "vector" fields, but they certainly aren't valid rank 1 tensors.

 

[haael]

Tensor fields may be broken down into vector or scalar fields and lower rank fields may be combined into higher rank fields. Some of these constructions work only in certain number of dimensions. Some of these constructions have deep physical significance too.

 

[bbbl67]

We have different kinds of fields.
The simplest is the scalar field (aka spin 0), where each point is assigned a scalar. Example: pressure or temperature.
Then we can have vector fields (aka spin 1), where each point has an associated vector. Example: wind.
We can also have fields where each point is assigned a matrix. These are called tensor field. Sometimes with restrictions, i.e. it has to be symmetric. We call them also spin-2 fields.

What kind of field is gravity, according to GR? It's literally the field of deformation. What kind of field is it? It's a symmetric tensor field. (Try Wikipedia: deformation tensor.)

Very nice explanation. So spin number corresponds to scalars, vectors, and tensors. So how would one interpret a Spin-1/2 particle? Would such a particle have the properties of both a scalar (spin-0), and a vector (spin-1), i.e. something that can sit still in space and something that can also move through it?

 

[bbbl67]

You ask for answers, but when they are given to you, you don't like them. That's unproductive.

The answer to "why graviton must be a spin-2 particle" is mathematical: only spin-2 particles will result, in classical limit, in a force which looks like GR. If you don't understand the math which shows this, it is your problem, not math's. BTW, this particular math is slightly above my head too, but I don't go down the road "I don't understand it, so I'll demand a different explanation". There is no non-mathematical explanation to it.

They just presented that with a bunch of equations and they expected that I'd automatically understand what those equations meant. That's no explanation at all! Subsequent to that other people have come up with a lot of great explanations of what it means, physical explanations.

This question was marked with an "Intermediate" ranking, not an "Advanced" ranking, so if I got equations, I'd want explanations of what those equations meant.

 

[bbbl67]

Tensor fields may be broken down into vector or scalar fields and lower rank fields may be combined into higher rank fields. Some of these constructions work only in certain number of dimensions. Some of these constructions have deep physical significance too.

So what you're saying is that in the case of an electromagnetic field, even though it's a Tensor field (just like gravity), and the carrier of the electromagnetic field is a spin-1 vector particle, the photon, the tensor can be broken down into sub-vectors? If that's the case, then why can't a hypothetical graviton also be a spin-1 vector particle?

 

[haael]

So what you're saying is that in the case of an electromagnetic field, even though it's a Tensor field (just like gravity), and the carrier of the electromagnetic field is a spin-1 vector particle, the photon, the tensor can be broken down into sub-vectors?

Electromagnetic field 4-potential is a 4-dimensional vector. It may be split into a scalar (electric potential) and a 3-vector (magnetic potential). This is Newtonian approximation of relativity. These values may be used to derive electric field 3-vector and magnetic field 3-pseudovector. This works only in 3 dimensions.

4-potential may also be taken exterior derivative and we get electromagnetic tensor.

If that's the case, then why can't a hypothetical graviton also be a spin-1 vector particle?

Yes it can! In 5 dimensions. It's called Kaluza-Klein theory.

The full rank-2 5-tensor of KK may be split into 4-tensor, 4-vector and a scalar. The 4-tensor gives rise to the usual gravity in 4 dimensions. The 4-vector gives force identical to electromagnetism in 4 dimensions. The scalar is a field describing variation in speed of propagation of electromagnetism that doesn't have equivalent in usual 4-dimensional GR.
If you manage to quantize these fields, you will get a graviton, a photon (in this context sometimes called graviphoton) and a particle called a dilaton. Fundamentally, they are all modes of 5-dimensional graviton.

You can derive almost any object from almost everything, but only certain constructions bear physical sense.

 

[bbbl67]

Yes it can! In 5 dimensions. It's called Kaluza-Klein theory.

The full rank-2 5-tensor of KK may be split into 4-tensor, 4-vector and a scalar. The 4-tensor gives rise to the usual gravity in 4 dimensions. The 4-vector gives force identical to electromagnetism in 4 dimensions. The scalar is a field describing variation in speed of propagation of electromagnetism that doesn't have equivalent in usual 4-dimensional GR.
If you manage to quantize these fields, you will get a graviton, a photon (in this context sometimes called graviphoton) and a particle called a dilaton. Fundamentally, they are all modes of 5-dimensional graviton.

You can derive almost any object from almost everything, but only certain constructions bear physical sense.

This KK theory was the precursor to Superstring Theory wasn't it? So would something similar be possible under 10 or 11 dimensional Superstring?

As for KK theory, are you saying that under this theory, electromagnetism and gravity are related to each other? Much like we found out that Electromagnetism and Weak are related to each other?

 

[haushofer]

The funny thing is that string theory already contains different p-forms (extensions of the vector potential A) before compactification. So you don't need to perform a KK-reduction on the metric; that would be a double strike.

The problem with KK-theory is that you need to keep the 5th dimension small, which is not trivial in GR; spacetime is dynamical. This is known as the problem of moduli-stabilization, and string theory also suffers from it. Afaik, this is one reason why people have abandoned KK-theory as unification.

 

[nikkkom]

So how would one interpret a Spin-1/2 particle? Would such a particle have the properties of both a scalar (spin-0), and a vector (spin-1), i.e. something that can sit still in space and something that can also move through it?

No. Spin-1/2 particle is not a mix of a scalar and a vector. (It's more like square root of a vector). Scalar particles don't only stand still.

 

[nikkkom]

This KK theory was the precursor to Superstring Theory wasn't it?

No. Superstring theory is a sypersymmetric extension of string theory.

As for KK theory, are you saying that under this theory, electromagnetism and gravity are related to each other?

Yes. 5-dimensional Lorentz group of rotations splits into 4-dimensional Lorentz group and 1-dimensional group of rotations on the remaining compactified dimension. 1-dimensional rotations are isomorphic to U(1) group, which is a gauge group of electromagnetism. Therefore it will look exactly like electromagnetism.

 

[thierrykauf]

The electromagnetic field is an antisymmetric rank two tensor field therefore (not but) it is a vector field. Just count the number of components. Antisymmetric means its diagonal is zero. There remains one triangular block which has 3 + 2 + 1 = 6 independent components. These are the electric field and magnetic field vector.
Gravity is a symmetric rank two tensor, it's diagonal is not zero. It therefore has 6 (upper triangular block) + 4 (diagonal) = 10 independent components (the metric tensor). A spin n field has (n(
The solutions to Einstein's equations are NOT waves in general (no pun) since these are non-linear equations. But if you neglect nonlinear terms you can obtain wave-like solutions, those were detected recently. Nonlinear in this context means the graviton creates and is subject to gravitational attraction. That makes gravity similar to a non-Abelian gauge interaction such as QCD. In contrast EM is an Abelian gauge theory because the photon has no charge and therefore cannot interact with the electrons that produced it.

 

[vanhees71]

Of course, photons interact with electrons. That's how we detect them all the time.

Also your counting is misleading since both the photon and the graviton are massless fields and thus they have only two physical polarization states (except for scalar fields which have of course only 1).