# What's a graviton?

1. Dec 31, 2012

### Leoragon

I tried looking it up but I can't understand it. Is the graviton some kind of theoretical particle that gives of gravitational waves? I read that it has a 2 spin and is also a boson. And where did this idea originate from?

2. Dec 31, 2012

### K^2

Any linear field can be second-quantized. When you second-quantize a field, you get carrier particles. If you quantize electromagnetic field, you get photons, for example.

Gravity isn't linear, but it is "almost linear" in many situations. Effectively, if you start with Newtonian gravity and add a gravitomagnetic field due to moving masses, similar to how magnetic field arises from moving charges, you can derive linearized gravity, which approximates some of the effects from GR. For example, a gyro in Earth's orbit will precess due to gravitomagnetic interaction with the planet. This effect is predicted both by GR and by linearized gravity, albeit, the magnitudes aren't exactly the same.

Anyways, linearized gravity can be quantized. If you quantize linearized gravity, you end up with a carrier particle called graviton. Unfortunately, the approximations you have to make to arrive at this particle are pretty drastic. There is not yet a known treatment of quantum gravity that produces experimentally verifiable results.

As far as who came up with it, I would point at Feynman. He's basically responsible for QED, and he later studied Quantum Gravity. I don't know if he really was the first one to suggest it, though. Maybe someone will correct me on the historic note.

3. Dec 31, 2012

### Leoragon

a gravitomagnetic field? There's something like that?

4. Dec 31, 2012

### K^2

Yes. If you start with Newtonian gravity, and only correct for Special Relativity, you get a gravitomagnetic effect. Obviously, named so for similarity with magnetic field. The equations for the linearized gravity are identical to Maxwell's Equations. Except instead of ε and μ, you have 1/(4πG) and 4πG/c² respectively. With G being small as it is, that second number is very, very tiny. So the gravitomagnetic effect is rather weak. It takes some rather sensitive equipment in space just to detect that it's there.

Gravitoelectromagnetism.

5. Jan 1, 2013

### andrien

perhaps wheeler.

6. Jan 1, 2013

### DiracPool

What is a linear field? Is there a nonlinear field? If so, what characterizes that? Also, what does it mean to "quantize" a field? Of course, that begs the question, what does it mean to second quantize a field? Forgive my nascentness, but I have never heard of any of these things?

7. Jan 1, 2013

8. Jan 1, 2013

### DiracPool

Ahhh, thanks.

9. Jan 1, 2013

### Leoragon

So basically...

A graviton is the carrier particle of gravity when second quantized?

I still don't get it; I just need a brief explanation

10. Jan 1, 2013

### andrien

electromagnetic interaction can be described as exchange of virtual photon.Similarly one can describe gravitation interaction as being carried by graviton.it is rather very novel way and not much correct.quantization of electromagnetic field is done usually with creation and annihilation operator but quantizing gravity is rather I think very difficult so one can go on with linearized gravity which avoids some complexity.

11. Jan 1, 2013

### Sonderval

Try to get a copy of Feynman's Lectures on Gravitation. The first chapters are really fun - he treats gravity as if it were a so far unknown phenomenon and tries to describe it using QFT. The graviton then emerges quite naturally.

12. Jan 1, 2013

### K^2

(P.S. Note: I am assuming you have at least a basic concept of Lagrangian, Hamiltonian, and Quantum Harmonic Oscillator. If not, this will probably not make a whole lot of sense.)

It might be easier if you forget for a moment about quantum mechanics. Something very similar happens in classical systems. Consider three identical masses m in a row connected by two springs with spring coefficients of k each. They are constrained to move along one dimension for simplicity.

Lets say that positions of the masses are given by $\small y_1$, $\small y_2$, and $\small y_3$. Since center of mass won't accelerate, only two of these are independent if I say that center of mass is at zero. I can then define $\small x_1 = y_2-y_1$ and $\small x_2 = y_3-y_2$, which are spring displacements and can be treated as my actual coordinates. Because CoM isn't moving, $\small \dot{y_1} + \dot{y_2} + \dot{y_3} = 0$. This lets me write down kinetic energy in terms of x coordinates. And all together, this yields the following Lagrangian.

$$L = \frac{1}{3}m (\dot{x_1}^2 + \dot{x_2}^2 + \dot{x_1}\dot{x_2}) - \frac{1}{2}k(x_1^2 + x_2^2)$$

Well, that isn't half as terrible as you might have expected, but notice that if you are to write down equations of motion, the differential equations you get are linked. Equations for $\small x_1$ depend on $\small x_2$ and vice versa.

Can this be helped? Well, yes it can! Lets define $\small q_1 = x_1+x_2$ and $\small q_2 = x_1 - x_2$. This is easily visualized as $\small q_1$ stretching the edge weights apart and $\small q_2$ moving the middle mass in between. Why is this useful? Well, let's re-write the Lagrangian in terms of q variables.

$$L = \frac{1}{4}m \dot{q_1}^2 + \frac{1}{12}m \dot{q_2}^2 - \frac{1}{4}k(q_1^2 + q_2^2)$$

Would you look at that? We no longer have cross-terms. That means we'll have separate equations for $\small q_1$ and $\small q_2$. In other words, these are the natural modes of this problem. Furthermore, each one is just a simple harmonic oscillator. Using the definition of generalized momentum.

$$p_i = \frac{\partial L}{\partial \dot{q_i}}$$

We have $\small p_1 = \frac{m}{2} \dot{q_1}$ and $\small p_2 = \frac{m}{6} \dot{q_2}$. For completion, let us write the Hamiltonian for this system.

$$H = \sum_i p_i \dot{q_i} - L = \frac{p_1^2}{m} + \frac{3p_2^2}{m} + \frac{k}{4}(q_1^2 + q_2^2)$$

Notice that this is just sum of Hamiltonians for two independent oscillators with masses m/2 and m/6 and spring coefficients of k/2.

The most important part of second quantization is done. We have two independent harmonics. But lets imagine now that this is a QM problem. The analysis above still applies with minor editing. You still end up with the same Hamiltonian in diagonalized coordinates. And now we can treat each oscillator as quantum harmonic oscillator. That means you can add to the system energy increments of $\small \hbar \omega_1$ or $\small \hbar \omega_2$ with $\omega_1 = \sqrt{\frac{k}{m}}$ and $\omega_2 = \sqrt{\frac{3k}{m}}$. We have two different modes, and each one can be excited with fixed quanta of energy. Reminds you of anything yet?

If you take a 3D network of masses connected by something that can be approximated as a spring, you end up with a decent model of a solid. That Hamiltonian can be similarly diagonalized, with normal modes forming plain waves. If you further quantize an effective oscillator corresponding to each plain wave, you find that you can add $\small \hbar \omega$ of energy to each such mode! These quanta of energy propagating as plain waves through the solids are the phonons. This is second quantization applied to a very similar problem.

Now you can go to a continuum case. Imagine that instead of masses and springs you have fields. You can write down a Lagrangian density for the field. If it happens to be linear, you can diagonalize it, find normal modes, apply quantum mechanics to the normal modes, and arrive at second-quantized field! Why second quantized? Because diagonalizing to normal modes already quantizes the problem. So the problem is twice quantized. Once into normal modes with discrete energies, and second time into discrete increments of these energies.

Just like normal modes of oscillations in the solid become phonons upon second quantization, the normal modes of electromagnetic field, which also happen to be electromagnetic plain waves, become photons upon second quantization.

There are several really, really exciting things that follow from this. First of all, you can use ladder operators just like you would with harmonic oscillator. These become particle creation/annihilation operators and you can describe your states as operators. Your field is now a bunch of particle states, so you can describe interactions with the same creation/annihilation operators. That lets you use the same formalism for the field theory where now you have interacting fermions. And that can all be summarized with gauge theories... But this is starting to get into more complicated stuff, and you really need a solid grasp of basic QFT formalism to dive deeper into it.
Absolutely. But again, you need to have solid grasp of basic QFT and preferably some QED. Otherwise, it's prohibitively difficult to follow.

13. Jan 1, 2013

### DiracPool

Do you have a link for these? Were they videotaped lectures or archived lecture notes? I'd love to see them. What was the lecture title?

14. Jan 1, 2013

### K^2

Last edited by a moderator: May 6, 2017
15. Jan 1, 2013

### dextercioby

As per Wiki reference http://en.wikipedia.org/wiki/Graviton

Graviton Composition Elementary particle
Statistics Bosonic
Interactions Gravitation
Status theoretical
Symbol G[1]
Antiparticle Self
Theorized 1930s[2]
The name is attributed to Dmitrii Blokhintsev and F. M. Gal'perin in 1934[3]
Discovered hypothetical
Mass 0
Electric charge 0 e
Spin 2

The name would be clear at least. The first to linearize the field equations for gravity was Einstein in 1916, (perhaps = doubt) it was also Einstein who linearized the H-E action, Pauli and Fierz wrote down the action * (which had probably been obtained by Einstein) in 1938 in the HPA article and in 1939 in their PRAS article.

* of a spin 2 classical field.

I have no historical acount for the quantum theory of gravitational waves, either starting with their field equations discovered by Einstein.

16. Jan 1, 2013

### Leoragon

I did not understand a single thing of that..... damn I'm stupid...

17. Jan 2, 2013

### agostino981

I am not an expert in the field, but if you look for a really brief explanation, this is what graviton is:

1. a massless and stable particle, so it has infinite range, just like photon

2. a particle that mediates gravitation

3. a spin 2 particle, as it can be shown that a spin 2 particle gives rise to an interaction identical to gravitation

4. hypothetical, if I recall, there is currently no experiment can prove the existence of graviton.

18. Jan 2, 2013

### Naty1

A graviton is the quantization, that is the localization, of the gravitational field energy or gravitational wave, as the electron is of the electromagnetic field. Nobody knows exactly what any fundamental particle is. It's one view of gravity. General Relativity is another view.

Since everything popped out of a bang, it is believed all particles and fields were once unified, that is, combined in a high energy unstable environment, and via spontaneous symmetry breaking...the movement of the vacuum energy to a more stable and lower energy state where we now exist.... separate pieces emerged, those we now observe around us, particles, waves, energy, time, etc...all APPEAR now as separate entities.

A graviton has not yet been experimentally observed. General relativity does not speak to gravitons; GR is a continuous description of gravity.

Gravity, and hence gravitons, are not part of the 'Standard Model' of particle physics describes subatomic particles via electromagnetic, weak, and strong nuclear interactions. So the Standard Model falls short of being a complete theory of fundamental interactions because is missing gravity.

It has been discovered certain mathematical formalisms seem to match what we observe and have been useful in making predictions of what to look for experimentally.

It turns out that when Gauge fields in a theory are quantized, they describe carriers of the forces in the Standard Model. These quanta of the gauge fields are called gauge bosons, and the theories have been successful field theories explaining the dynamics of elementary particles. But,not so far, gravity.

Eric Verlinde thinks gravity is explained as an entropic force caused by changes in the information associated with the positions of material bodies. A relativistic generalization of the presented arguments directly leads to the Einstein equations.

On the Origin of Gravity
and the Laws of Newton
Erik Verlinde (69 pages)
http://arxiv.org/PS_cache/arxiv/pdf/1001/1001.0785v1.pdf

Don't worry if much of this doesn't make a lot of sense: I could ask a hundred questions about what I just posted and pretty quickly would get to places where 'nobody knows'....

19. Jan 2, 2013

### Leoragon

So what explanation of gravity should I follow? The distortion of space time or this graviton thingy. Or is it that the graviton is the particle that flows to each object that is gravity? Can these two be united? Because if you're just falling in space-time, what's the need of the graviton?

20. Jan 2, 2013

### Naty1

You have to follow the theory that covers the regime you study: GR for large scale, like cosmological predictions; quantum theory, eventually maybe quantum gravity, for the very small. But right now neither GR nor QM cover black hole and big bang singularities.

21. Jan 2, 2013

### Leoragon

So GR for large scales and graviton for small scales?

22. Jan 2, 2013

### dextercioby

The only explanation of gravity to be followed is the one offered by the Theory of General Relativity. There's no final quantum theory of gravity as of yet, so use what we have for sure, just like one is invited to use the Standard Model of Particles and Interactions to explain the other 3 interactions.

23. Jan 3, 2013

### Naty1

Leoragon:

I find answers like post #22 a bit too formulaic....but it's a valid perspective. Let me explain what I was trying to explain.

We are probably past the stage when we should have asked what you mean by 'gravity'. When I suggested quantum mechanics for 'the small', I was referring to things like degenerate matter:

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

Some here might say "that's not gravity' and I'd have to agree....what is going on is not properly described by gravity...so we need something else....The gravitational physics of the large is inadequate at subatomic scales to explain observations we might expect by analogy with large scales.

When the core of a star more than about 1.5 solar masses collapses, as nuclear reactions run out of fuel, Chandrasekhar calculated the large scale effects using GR....
[This is a great story of science, by the way.] But the collapse of some such objects, smaller mass, may later be halted by degenerate electrons. By Pauli Exclusion principle....etc,etc...quantum effects may overwhelm gravitational effects.

Another example might be types of particle production: Horizons are described by GR [I'm not sure if they are also present in relativistic QM.], anyway, it seems that the expansion of geometry itself, especially during early inflation of the universe, can produce matter, as can acceleration, as in the Unruh Effect. But understanding what is going on at the micro scale here not fully explained by GR: it is likely quantum fluctuations in the vacuum become quanta [particles] at super horizon scales. Particle production via changing gravitational fields and expansion is believed a real phenomenon, but understanding it at the micro level seems to require some additional theory.

We can call that 'quantum gravity'.