Gravitron Size Estimate and Higgs Boson Explained

[woodysooner]

What is the estimate of the gravitron size and can someone explain why it must be spin 2

also what is the higgs boson

it is expected to be massive, electrically neutral, and spinless.

why.

Cheers
Woody

 

[jtolliver]

can someone explain why [the graviton] must be spin 2

The spin has to do with how it transforms under the lorentz group. Since gravity requires at least a tensor of the second rank to describe it the graviton must be spin 2.

also what is the higgs boson

it is expected to be massive, electrically neutral, and spinless.

why.

The higgs boson is the particle that gives mass to other particles. It is spinless because mass is a scalar. The fact that it is electrically neutral is what separates electromagnetism from the weak force, by not giving a mass to the photon.
The higgs field has a potential of the form $\lambda^2 (\phi ^* \phi - m^2)^2$ where $\phi$ is the higgs field. The potential possesses a phase symmetry and is minimized when $\phi = m e^{i \theta}$. However only one of those is the vacuum, so the phase symmetry is spontaneously broken, and the vacuum state is taken to be $\phi = m$. When dealing with low-energy states it is convenient to redefine the field as $\phi ' = \phi - m$. When expressed in terms of $\phi'$ and terms higher order than quadratic are dropped the potential is $4 m^2 \lambda^2 Re(\phi')^2$, which is just the mass term for a particle with mass $2m\lambda$, so the higgs boson is massive. If it were electrically charged with charge q, then near the vacuum it would give the photon a mass of 2mq.

 

[woodysooner]

If it's so large why can we not see it?
When you say large is that like grain of sand or light year lenths?

 

[Nereid]

If it's so large why can we not see it?
When you say large is that like grain of sand or light year lenths?

I don't think jtolliver mentioned anything about the (hypothetical) graviton's physical size. The physical 'size' of a particle such as an electron or graviton isn't all that meaningful, unless clearly defined. For example, there is something called 'cross section', which if you've never heard of the idea, you might think is some kind of area ... which it is, but then you quickly learn that the 'cross sections' of some particles vary with 'energy', and with the type of interaction ('collision').

Maybe you could never 'see' a graviton because the graviton-photon interaction has a 'zero cross section'?

 

[woodysooner]

interesting.. but how could we detect them. or can we never.

 

[humanino]

There are current experiments aiming at detecting gravitational waves. None of them has so far obtained convincing result. This is because those wave are so incredibly weak ! A truck driving within a mile would typically produce a noise above the level of the gravitational wave signal.

So imagine how far we are from detecting a quantum of those waves ! We can hope to detect them not from cosmological waves, but from elementary process in accelerators. If someone finds corrections to some quantity due to graviton scatteting, we could hope to make a precise measurement in agreement with the corrections. That is the only way I see we could make it.

The Higgs boson will soon be observed in Geneva. This is an optimistic opinion, but still, the status is very different for this boson.

 

[woodysooner]

Geneva as in CERN right? what are they doing to observe it, like what are they smashing or watching??

if gravity is that weak how could we ever observe it, by what means are physicists using?

thanx for helping

 

[woodysooner]

oh by the way I was going to ask: Why so optimistic, is mainstream thinking it's close or is this just a gut feeling cause higgs boson just adds up and makes sense. Didn't Hawking say, he didn't think it would be found for there was no such thing. I hope they find it because its abstractly elegant.

 

[humanino]

About the Higgs boson at CERN :
http://www.exploratorium.edu/origins/cern/ideas/higgs.html
Those guys are actually smashing heavy ions (such as lead Pb) and/or protons at very high energy. Some reactions they are looking for can be seen here :
http://www.quark.lu.se/~atlas/thesis/egede/thesis-node10.html#fig:HiggsProduction
As for the discovery of Higgs boson : it almost already took place ! They saw several events (maybe hundred), and the probability that they are wrong must be less than 1%. So Hawking is 99% wrong on that point. Hawking is very often wrong nowadays (^_^)

Again : this is very different for the graviton ! The graviton is NOT supposed to give mass to particles. It is the particle associated to the metric field, that is the geometry of spacetime. We are far from seeing it.

 

[woodysooner]

that was some neat stuff not that I understood half of that picture on the second link but thanks a lot.

Yeah the more and more i read on hawking the more i see kinda his arrogance towards other's ideas or at least in some instances.

But for all his lil nuances his mind makes up for it.

you say we are far from the gravitron

Why is that.

 

[woodysooner]

oh, and what is the metric field... sorry if I am lil dumb in this. is that something to do with tensors or at least i always think i see that in discussions on tensors.

still not sure what a tensor is, went to john baez's site(absolutely kewl) to learn more bout einsteins equation and tensors, but still not getting it so if you or anyone can give me an idea it would be appreciated greatly.

 

[Nereid]

you say we are far from the gravitron

Why is that.

First, unlike the Higgs, or even the supersymmetric sparticles, the theoretical status of the graviton is far from assured - gravity (per GR) doesn't have the same kind of structure as the three other forces.

The earlier post by humanino sums up the observational challenges, assuming a decent theoretical basis can be found.

 

[woodysooner]

could it be assumed that gravity is just to weak and not a force, just a result of gr's bending of space causing things to fall towards it, and in that respect we have already solved the puzzle connecting the other three forces into one.

and if anyone can look at my post before this and tried to help me out.

thanx nereid.

 

[humanino]

oh, and what is the metric field... sorry if I am lil dumb in this. is that something to do with tensors or at least i always think i see that in discussions on tensors.

still not sure what a tensor is, went to john baez's site(absolutely kewl) to learn more bout einsteins equation and tensors, but still not getting it so if you or anyone can give me an idea it would be appreciated greatly.

A tensor is not such a mysterious thing. Consider a vector : it is quantity that carry one indice : in the usual 3-dim space, the indice runs over x, y and z. Denote $$V_i$$ the vector. The vectorial nature can be expressed by the fact that when one changes the basis in space, the new value of the coordinate of the vector are determined by a linear combination of the old values :
$$V_{j(new)} = \sum_i O_{i,j} V_{i(old)}$$
Here, $$O_{i,j}$$ is a matrix related to the change of basis.

Now a tensor carries several indices : for example with two indices, one gets
$$T_{k,l} = O_{i,k} O_{l,j} T_{i,j}$$
with an implicit sum over i and j

This is one way to define tensor : through their transformation law. One can also use other equivalent definitions, depending on what feature one wants to inlight. The definition given here is not very geometric for instance.

The metric tensor allows one to compute infinitesimal length in spacetime. The length of the very small intervall with coordinates $$V_i$$ is given by :
$$\textquotedblright length\textquotedblright = \sqrt{ g_{i,j} V_i V_j }$$
between quotes because this is not the usual euclidian length.

In flat spacetime, one can find a basis in which the metric is diagonal and given by :
$$\textquotedblright length\textquotedblright = \sqrt{ t^2 -x^2-y^2-z^2 }$$
Diagonal means that there is no such term as $$x\times y$$ for instance.
You see that it vanishes along a path taken by light rays. Maybe now you could say "the metric field is a rank two tensor". It is symmetric. (Is it obvious ?) This in turn implies that the graviton has spin 2.

 

[woodysooner]

I don't know what I don't grasp that, I have worked with vectors for years, but thanks though.

 

[humanino]

You can recursively define a tensor of rank n+1 as a linear form on the tensors of rank n !

I'm sorry woodysooner, I did my best. Maybe you can find a good book, such as Hofstadter's "Geometry, particles and fields" (world scientific) (This reference might be unaccurate, let me know if you want me to check it ! It is written by a high-school teacher, but also deals with advanced concepts. I love this book.)

 

[woodysooner]

oh i wasn't blaming you for my lack of understanding at all I am greatful that you helped, ill just keep chuggin I'll figger it out then when i do i'll come back read your post and be like whoa that was good lol.

 

[gjconely]

Measuring

I am just curious on measuring of the gravitron wave. I did a search on google and the first site I came to was about the Ligo facility, which was about the only article I could find on this. I wonder if this could be better measured from a satellite and if so if they have tried or plan to. I doubt it however

 

[Norman]

I am just curious on measuring of the gravitron wave. I did a search on google and the first site I came to was about the Ligo facility, which was about the only article I could find on this. I wonder if this could be better measured from a satellite and if so if they have tried or plan to. I doubt it however

Check out http://lisa.nasa.gov"

 

[Schrodinger's Dog]

About the Higgs boson at CERN :
http://www.exploratorium.edu/origins/cern/ideas/higgs.html
Those guys are actually smashing heavy ions (such as lead Pb) and/or protons at very high energy. Some reactions they are looking for can be seen here :
http://www.quark.lu.se/~atlas/thesis/egede/thesis-node10.html#fig:HiggsProduction
As for the discovery of Higgs boson : it almost already took place ! They saw several events (maybe hundred), and the probability that they are wrong must be less than 1%. So Hawking is 99% wrong on that point. Hawking is very often wrong nowadays (^_^)

Again : this is very different for the graviton ! The graviton is NOT supposed to give mass to particles. It is the particle associated to the metric field, that is the geometry of spacetime. We are far from seeing it.

that was some neat stuff not that I understood half of that picture on the second link but thanks a lot.

Yeah the more and more i read on hawking the more i see kinda his arrogance towards other's ideas or at least in some instances.

But for all his lil nuances his mind makes up for it.

you say we are far from the gravitron

Why is that.

Very interested in those pictures so I'm going to make a stab at decoding them, if someone could tell me where my assumptions are wrong

$$\bar{t}$$

$$\bar{q}$$

$$q$$

$$t$$

assuming are top quarks and quarks? And the bars above are the antimatter versions, g are gluons.

$$H_0$$

I assume is the Higgs.

OK so far easy to follow the Feynman diagrams, but:-

The bottom graph I'm guessing is the collision energies themselves with the Pb being something to do with the lead ions mentioned before. Showing that between certain ranges, the energy produced gives all of the reactions in the diagrams above. This describes in what eV range those values for the Higgs boson are found I guess? Showing where certain reactions dominate.I'd be grateful if someone could clarify exactly what the graph shows, or any errors in assumption.

 

[humanino]

The bottom graphs shows the production rate of Higgs' boson, for several production mechanism as indicated by the diagrams, as a function of the Higgs mass. I think you follow the diagrams correctly, and also understood the bottom graph, but might be a little confused. There is no lead involved on this graph, if I understood correctly this is only for proton-proton collision.

The rate is given at the LHC energy (14 TeV indicated), and integrated over all other variables (my guess !) such as angles, or partons energies.

Depending on the Higgs mass, such or such process (diagram, production mechanism) dominates.

By the way, notice that the scale is logarithmical, and that the diagram for $$q\bar{q}\rightarrow H^{0}Z$$ is not given.

 

[Schrodinger's Dog]

The bottom graphs shows the production rate of Higgs' boson, for several production mechanism as indicated by the diagrams, as a function of the Higgs mass. I think you follow the diagrams correctly, and also understood the bottom graph, but might be a little confused. There is no lead involved on this graph, if I understood correctly this is only for proton-proton collision.

The rate is given at the LHC energy (14 TeV indicated), and integrated over all other variables (my guess !) such as angles, or partons energies.

Depending on the Higgs mass, such or such process (diagram, production mechanism) dominates.

By the way, notice that the scale is logarithmical, and that the diagram for $$q\bar{q}\rightarrow H^{0}Z$$ is not given.

Ah that's much clearer, thanks a bunch.

 

[Gib Z]

Don't worry I've worked with vectors too, and from what i know his last expression for length should have been all plus signs in stead of negatives.

 

[Gib Z]

Crap I was replying to the first pages last comment, which i thought was the last comment >.< now I look, it was 3 years ago...

 

[cristo]

Don't worry I've worked with vectors too, and from what i know his last expression for length should have been all plus signs in stead of negatives.

The 'length' should not have all positive signs. Note that humanino uses the term 'length' and explains that this is not the usual euclidean length. In euclidean space, the line element is $ds^2=dx^2+dy^2+dz^2$. However, here we are not in Euclidean space, but are in Minkowski spacetime, where the line element is given by $ds^2=dt^2-dx^2-dy^2-dz^2$. This is where the -ve signs in the length come from.

 

[Gib Z]

eep..i remember reading that somewhere, too bad i didnt remember that lol. ty cristo

 

[Mentz114]

Woody,
I assume you mean 'graviton'. The gravitron is actually a machine for making gravity.