According to Yukawa theory, long range force carrier particle have zero mass.but how does it have spin 2?
Since we do not yet have a quantum theory of gravity, this question can not be answered in a satisfactory way. What may be of some value is this: Linearized GR, that was studied by Einstein in 1918 (and is treated in text books on GR), agrees with the Pauli-Fierz spin-2 theory in flat space-time of 1939, in connection with their important studies of higher spin equations (spin-statistics, etc). This (approximate) theory allows one to compute, for example the decay rate of the d-state of a hydrogen atom with the emission of a graviton. The lifetime for this decay is, by the way, about 10^32 years (hard to test!). (This was sometimes a student problem in my courses on quantum field theory. The calculation is very close to that for photon emission.) Beyond first order perturbation theory, there are fundamental conceptual problem, as some people realized already shortly after 1930. String people can tell you, of course, much more, but on that I am not competent.
worth to have a look at the attached link... gravitons knocking at your door.
http://phys.org/news/2016-01-gravitational-rumors-ripple-science-world.html
Gravitons are spin-2 particles because These force carrieres (assuming that These exist) are Tensor bosons; they are described by a Tensor of 2nd rank. A scalar is a Tensor of 0th rank and therefore a scalar field particle is a spin-0-particle, a vector is Tensor of 1st rank and if a particle is a vector boson, it is a spin-1-particle.
Hence, Gravitons are Tensors of 2nd rank and therefore spin-2-particles.
Graviyions are spin-2 particles also ferminionic and bosonic descriptions are possible..
Since we do not yet have a quantum theory of gravity, this question can not be answered in a satisfactory way. What may be of some value is this: Linearized GR, that was studied by Einstein in 1918 (and is treated in text books on GR), agrees with the Pauli-Fierz spin-2 theory in flat space-time of 1939, in connection with their important studies of higher spin equations (spin-statistics, etc). This (approximate) theory allows one to compute, for example the decay rate of the d-state of a hydrogen atom with the emission of a graviton. The lifetime for this decay is, by the way, about 10^32 years (hard to test!). (This was sometimes a student problem in my courses on quantum field theory. The calculation is very close to that for photon emission.) Beyond first order perturbation theory, there are fundamental conceptual problem, as some people realized already shortly after 1930. String people can tell you, of course, much more, but on that I am not competent.
Nobody "knows" that graviton has spin 2. Simply since nobody knows if gravitons really exist. I don't think so.
Quantum gravity is easily explainable through space's quanta, by hypothesizing their absorption effected by fermions. With a lot of glad consequences that solve many other issues.
They say "spin 2" because of the mathematics. It's a theoretical need. Nothing more. At the moment we only observed spin 1 bosons, and the spin 0 Higgs boson.
Article A superfluid Theory of Everything? [outdated version]
Every boson that we know of (except the Hicks boson) interacts with fermions in 2 ways : on the kinetic part of any fermion (its spinor), through a momentum, on one hand, and on the charged part of the fermion (each boson corresponds to a field force and acts on particles carrying the same kind of charge) on the other hand. Because the kinetic part of a fermion is linked to its mass, and so to its gravitational charge, if gravitons follow the same picture, they would act 2 fold on the kinetic part. This action would be represented by an order 2 tensor in the Lie algebra of the Spin group (where the spin is valued). Labeling this spin as "2" would not have the same meaning as for the other spin (it does not refer to a class of representation of the Spin group). A bit of computation, speculative, shows that actually the only sensible value for the graviton would be as a multiple of the Casimir element (which is an order 2 tensor).
graviton must be boson, for obvious reasons.
next, it should be massless, so spin zero is excluded.
spin 1 is akward, because we have already photon,
next choice is: SPIN 2(!)
Resume: that's theoretical physics today!
If we assume that the neutrino is massless, why not could it be the graviton?
@ Esa: The "fermions" are the fields (=matter), the bosons make the "force".
@Anton
1) why do you say that spin zero is excluded for massless bosons if Higgs boson is zero spin and has a mass of 126 GeV/c^2 (that is "much" more than the up / down quarks which form fermions) ?
2) why spin 1 can only pertain to photon if we also have gluon and Z & W bosons which are spin 1 ?
3) the fermions are the fields? So Earth (composed of fermions) "is" its gravitational field ? Or a proton "is" its static electric field ? On the contrary, we know that a static electric field (such as that of an electron or proton) is constituted by virtual photons, which are emitted and reabsorbed by the particle. That's the official point of view. Okay, electromagnetic energy is a part of the mass of a charged particle but not all. Bosons are rather the force carriers which constitute the field.
And about gravity we don't know yet whether these carriers really exist and how this force works as far as its quantum aspect is concerned.
@Esa
the nobel prize 2015 states that neutrinos have a mass. They can't be the gravitons! I'm convinced gravity is driven by space quanta's dynamics.
Carissimo, Higgs bosons have no mass at all! This Higgs reaction, whatever this is, takes place at 126GeV, that is what CERN claims. The Higgs Lagrangian has a positive quadratic mass term (=no mass!) and a quartic, again no mass, and an arbitrary "vacuum expectation value" whatever this is, but never a "mass".
Photon goes with its 4-potential, with additional gauge terms, so far ok, a Lorentz 4-vector. gluon is a tensor product SO(3,1)xSU(3), and makes selfcouplings, ... forget it. "graviton" should be a nice 2 spin field, with gauging, like photons.
Earth consists of ATOMS, always composed components, nuclear matter is not understood till today.
there is nothing "emitted" or "absorbed", Schrödinger/Dirac Coulomb problem works in all details,
Neutrino mass is matter of believe.
Actually I have a general answer for all bosons (meaning "carriers" of force fields). In the gauge theories (which are the basis of QTF) the force fields are represented by connections. These connections are usually assumed to be smooth, but if they have discontinuous derivatives, the result can be represented as a particle which follows the lines of propagation of the field, and as a "potential" with support these lines. Moreover they behave in a lagrangian (from a mathematical point of view) as individual particles so there is no need for the Higgs boson. The theory can be done for any force field, and is consistent with the usual physical phenomena, and even explains the Planck's law. The difficulty is that we know little about the weak and strong force fields, and even the gravitational field (see my book Mathematics in Physics on this site for more).
@Anton,
write to the guys of standard model and to CERN and pretend they change things by stating that Higgs boson can't have a mass. You speak of the lagrangian... maybe it indicates zero energy?
Higgs field is a scalar field, it contains energy. And you know that E=mc^2 , thus, what has energy has a mass!
One could say "then also a photon has a mass?" The answer is "yes", you can calculate photon's momentum as p = h / lambda (photon has a momentum since it is also a particle, not only a wave) but it has no "rest mass"...this is a different issue.
- Atoms consist of fermions (and so the Earth!). And a charged fermion "is not" its static electric field. So you're wrong if you say "matter is the field". And you contradict yourself if you state "matter is not understood" ...but you explain it as a field! Is it understood or not? Is it its field or not only?
Finally, write to the Nobel committee and say they must revoke the Nobel prize because, as you say, neutrinos' mass is a matter of believe.
Discussions here are precious, useful and consistent. They should remain so.
I said: NUCLEAR matter is not understood!
there are lots of lousy Nobel prices!
Since E=mc^2 holds hence any discontinuities in the Lagrangean of stcok exchange for application, has to have a zero mass in the equilibrium ground state in space and time, as both Professors Schober and Dutailly seem to state, so fermions and bosons behave similarly in an equilibrium of the pricexquantity system which is that they contract to their ground state for a next round of perturbation and factorisation following the Arrow of Time. There is nothing wrong in testing gravity by using Newtonian Calculus with Leibnitz factorisation potentials. Earl Prof. (University Institute Chair) Dr.(D.Phil.) SKM QC EPS Fellow (Indirect) MES MRES MAICTE
Anton: The "fermions" are the fields (=matter), the bosons make the "force".
You think the mass indicates no matter?
I think the matter field is the same as the gravity field and the fermion-like vacuum energy, maybe the same basis as behind the neutrinos, seems to be quite a good candidate to form that field.
Besides, the gravity is no force.
To Esakki,
to come back to your question. The label 1/2, 1, 2,... attached to a spin refers to a class of representation of the group Spin(3). When the label is an integer it means that the spin is symmetric with respect to the group SO(3) : the particle shows a physical symmetry (one can say that it looks the same under a rotation with axis the velocity of the particle). It works well for fermions, to which is attached a spinor, representing its kinematic part, defined in a representation of the Clifford algebra. For bosons it is a bit more complicated. Let us say that it is usually considered that a boson is symmetric with respect to a spatial rotation with axis its velocity, whence a spin 1. But a spin 2 has no real correspondance for a graviton, which is assumed to be represented by an order 2 tensor. Thus the 2 has not the same meaning as for a composite particle.
Anton: since Newton gravity is force!!! ma = F
Sorry, it's force no more since SEP revealed and not falsified.
Dear Jean Claude
You are on the right track, but not fully. Within Special Relativity, the description of arbitrary spin is completely clarified since a long time. Below I quote from the introduction of my article "Unitary Representations of the inhomogeneous Lorentz group and their Significance in Quantum Physics'' (arXive: 0809.4942, published in the Springer "Handbook of Spacetime'', edited by A. Ashtekar and V. Vesslin, p.265-278):
Minkowski's great discovery of the spacetime structure behind Einstein's special theory of relativity (SR) had an enormous impact on much of twentieth century physics. The symmetry requirement of physical theories with respect to the automorphism group of Minkowski spacetime -- the inhomogeneous Lorentz or Poincar\'{e} group -- is particularly constraining in the domain of relativistic quantum theory and led to profound insights. Among the most outstanding early contributions are Wigner's great papers on relativistic invariance \cite{W1}. His description of the (projective) irreducible representations of the inhomogeneous Lorentz group, that classified single particle states in terms of mass and spin, has later been taken up on the mathematical side by George Mackey, ....
Sorry Norbert,
First I disagree with the use of the Poincarré's group, and the well known Wingner's demonstration. The Poincarré group involves displacement, this is the semi product of the group of rotations (which by the way should be Spin(3,1)) and the translations. Of course the translation of the origin of the frame has nothing to do in the matter, and is meaningless in General Relativity. We need only the Spin group, and a representation on a complex vector space to get the spinors, and the straight solution is to look for a representation of the Clifford algebra. This way we have a consistent representation of spinors, in GR, and it is easy to retrivieve the usual : antiparticles and spin. And indeed the Poincarré group has 10 degrees of freedom, and it is obvious that the motion of a body does not need more than 6 degrees of freedom.
Second about the spin. There is a first "spin", (spin up or down) which has nothing to do with QM, it is just the choice of a direction with respect to velocity of the particle (the scalars +1 and -1 are elements of the spin group). The second is related to the invariance of the spinor with respect to SO(3). With QM in a system where the state of the particle is stationary, its spin is quantized and its value can be labeled by one of the unitary representations of Spin(3). Whence the label.
Third about the projective representations. They are a nuisance, and as soon as possible one gets rid of them. Actually they have no meaning, they are not needed in QM. Their introduction has a meaning only to represent the state of a particle with the EM field (which was the usual occurence when it was invented) : the EM goes with U(1) and the natural representation of the state of a particle is then the tensorial product of a spinor and an element of U(1).
You can find all this, and more, in my book on this site (Mathematics in Physics v4) but of course not on arXiv or Springler : as far as I know they accept only theories which have been certified by the Academy since 50 years century at least. And anyway my book is free.
Einstein Gravitation theory vs. Ferent Gravitation theory!!!
Columbia University in New York City is hosting a "major" event the morning of Thursday February 11, 2016!
Einstein Gravitation theory: the speed of the gravitons = 3 × 10^8 m/s
Ferent Gravitation theory: the speed of the gravitons = 1.001762 × 10^17 m/s
Einstein Gravitation theory: LIGO has two L-shaped detectors that are run and monitored by a collaboration of more than 1,000 researchers from 15 nations, budget: millions of dollars.
Ferent Gravitation theory: 1 independent researcher - Adrian Ferent, budget 0$.
Einstein Gravitation theory: Gravitation is a distortion of space-time.
Ferent Gravitation theory: Gravitation is a force mediated by gravitons.
What do you think, Gravitation is a distortion or a force?
Who do you think is right Einstein or Ferent?
http://www.techinsider.io/gravitational-wave-nature-ligo-february-11-2016-2
https://www.researchgate.net/publication/287331589_Ferent_Gravitation_theory
@ Esa:
Anton: since Newton gravity is force!!! ma = F
Sorry, it's force no more since SEP revealed and not falsified.
more sorry, F = ma is tru forever.
next, what is SEP?
@ jean claude Dutailly: you can't ignore translation because of homogeneous space time.
To Anton,
The space time is not homogeneous ! First in SR because there is a privileged direction (time), second in GR because of the metric which has not the same value everywhere. When you transport a frame from one point to another the path that you use matters.
Anyway the translation in the Poincaré group is the translation of the origin of the coordinates. But what matters is the motion (rotational or translational) of a body with respect to a local frame (that is where it is), not the motion with respect to some observer who would be far away.
to jean claude: it's enough that it is locally Poincare. Next we embed ISO(3,1) into a higher group like SO(3,2) or SO(4,2) and trade translational space time (of course!) into global isotropy.
"But what matters is the motion (rotational or translational) of a body with respect to a local frame" Never, the body is fixed, I do the motion!
Dear Prof. Sorli,
I think String Theoretic Econophysically speaking, please refer to my papers on Haag's Theorem on my RG page, Prof. Higgs and Prof. Englert by their findings had shown that the Goldstone Theorem, and I am no expert on this like Prof. Higgs or Englert, or youngsters like Prof. T. Saini who try to search for mass, forecasts that the lower bound on particle mass is zero by which we can never verify the Laws of Conservation of Energy for e.g., can be evaded by considering the conversion of energy to mass in fields of Bosons taking place because of its overlap with the Higgs field which consists of Higgs Bosons. Correct me if I am wrong. No one had shown this before other than by Higgs-Englert duo. Their experiments at CERN also showed this. Prof. Venetiano and I have also shown, let's say implied, that String Theoretically the Higgs field fails the test of infinite dimensions, unless Strings of particles in the field are differentiable in the Dirichlet sense. So the HIggs mechanism is an experimentally observed mechanism definitely. Earl Prof. (Sir Ashutosh Mukherjee University Institute Chair) Dr. (D.Phil.)SKIM QC EPS Fellow (Indirect) MES MRES MAICTE
Dear Esakki!
Graviton and Quarks have the same source: convincing theoretical arguments. But they are used as a basis for following theories. Both of them are not proven. At this point all science is speculative.
If the graviton would exist, there must be also a "coulombtron" as reason for the electrostatic force. Furthermore all the invented particles (e.g. Graviton and Quarks) should have it's own special and different particle matter. And what's about "dark matter"?
Gravity waves and gravitons are very different things. Thought experiment: If suddenly the sun would disappears it's gravitational field would also disappear. We would observe a gravity wave. In universe mostly in the centre of galaxies sometimes happens processes in which great amounts of mass are be converted to energy. It's always observed by humans but the event was very fare away. The dinosaur were able to observe such a event in our galaxy. We have not a chance too.
Regards
Hans
Hi, Hans-G., "Coulombtron" (very nice!) exists! It is the zero component of the current jµ.
A better thought experiment. A positronium vanishes: (q+,q-;2hn), so the 2 electronic masses 2m vanish together with their gravitational field. Assume this positronium was in an orbit around the earth: Now the earth moves a bit in the former center of gravity?
Hi Anton!
You said: "It is the zero component of the current jµ."
In my opiniom a particle is a real object resp. an object of the objective reality. Not a mathematical term or equation. Furthermore I'm not sure what you mean with "the former center of gravity"?
Regards! Hans
Thank you for all your valid answers.(Particularly, Prof.Andrew) I did PhD in Maths. If I want to do research on Quantum Gravity. What should I do?.
I think it is because the field is a second rank tensor, the metric tensor itself. In perturbative quantum gravity, the peturbation from the flat metric is considered as classical field the excitation of which are the gravitons.
Just as a vector field (massless) is spin one, the second rank tensor field is spin two.
The gravitational field (GF) of Moon and Sun makes (approximatively) 2 high tides per day. Thus tide is a quadrupolar deformation of the ocean. This is related to the fact that GF has "spin" S=2, whether or not it is quantified. It derives from a potential tensor h_{mu,nu}. A rotation of angle pi does not change the sign of its space components h_{i,j} (i and j equal 1, 2 or 3).
By contrast :
The electromagnetic field (EMF) has "spin" S=1, whether or not it is quantified. It derives from a potential vector A_{mu}. A rotation of angle pi reverses the sign of its space components A_i (i equal 1, 2 or 3). The field of a nearby ion makes a dipolar deformation of an atom (Stark effect).
The quantas of EMF and GF (photon and graviton) have spin (intrinsic angular momenta) respectively S= h/(2 pi) and S=2 * h/(2 pi).
Generalisation : For a field of spin S, a rotation of angle pi/S reverses the sign of its space components. If the gravitational field had spin 3 we would have 3 tides per day...
Xavier Artru
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