Higgs Boson, String Theory and Gravity

[matthias31415]

Hi everybody,

let's assume the Higg's boson exists. If I understand String theory correctly (and I understand very little of it), then Higg's particle - just as any other particle - can be expressed as a particular vibration state of a string.

If I understand Higg's theory correctly, then Higg's particle is the only particle to induce spacetime curvature itself. All other mass does so by invoking Higg's particles.

Now, my question is: how can I understand that one particular vibrational state (and that particular one ONLY) alters spacetime geometry? Sounds weird. Do I simply have to accept this or is there more to Higgs/String theory?

thanks in advance
-matthias 31415

 

[jtbell]

If I understand Higg's theory correctly, then Higg's particle is the only particle to induce spacetime curvature itself. All other mass does so by invoking Higg's particles.

No. The Higgs is a part of the standard model of elementary particle physics, which has nothing to say about gravity.

 

[atyy]

The word "mass" refers to different things in particle physics and gravity.

"Mass" in particle physics is "rest mass" or "invariant mass". In particle physics, every particle is a wave. The invariant mass of a particle refers to how the particle's frequency changes with its wavelength.

"Mass" in gravity refers to "gravitational mass" which in particle physics is called "energy". A particle with zero invariant mass still has energy, and so has gravitational mass, and can bend and be bent by spacetime.

A third thing which can bend spacetime is spacetime itself, although that has neither invariant mass nor energy (at least not localizable energy). This is because the equation governing spacetime's interaction with itself is nonlinear.

 

[Demystifier]

Now, my question is: how can I understand that one particular vibrational state (and that particular one ONLY) alters spacetime geometry? Sounds weird. Do I simply have to accept this or is there more to Higgs/String theory?

As others told you, Higgs is not the particle responsible for spacetime geometry. Instead, it is the graviton. But graviton is also nothing but a particular vibrational state of a closed string, so your question sustains.

A partial answer is that one graviton does not make spacetime geometry. But a whole bunch of gravitons in a special state (so-called coherent state) does.

 

[matthias31415]

Thanks for all you explanations! Now...

jtbell, I've heard over and over that Higgs would be the very particle "borrowing" mass to others. I think what you said is related to atyy's comment, that mass in particle physics is not the same as gravitational mass.

atyy, is this true? I am already trying not to mix rest mass with relativistic mass. Now you tell me that gravitational mass is yet another type of mass? It seems pretty mean of physicists to use one single term for three different entities ;-). Seriously, I always thought invariant mass to be the "source" of gravity. The mass of protons, neutrons and electrons make up the mass of an atom. The mass of all atoms on Earth make up the mass of the earth. The mass of the Earth attracts the moon, which is just another way of saying that it bends space-time. Where's the split between invariant mass (that of protons and so forth) and the gravitational mass responsible for space-time curvature? Furthermore, I do not understand your statement "The invariant mass of a particle refers to how the particle's frequency changes with its wavelength." Isn't frequency and wavelength simply connected via the equation c = f x lambda?

Demystifier, can you further explain this mystery to me? If one special vibrational state of a closed string can bend space-time, why can't other vibrational states do the same? What is so special about the graviton-vibration? Do I have to accept this in terms of a law of nature or does string theory provide sort of a mechanism that would explain this a little bit deeper? An analogy: if only one particular vibrational state of the vocal cord of a soprano is able to break window glass, no one would postulate a window-breaking-particle that by fundamental law of nature corresponds to this very frequency...

 

[fzero]

The term "mass" really isn't being used for different things, but rather one must respect the particular physical framework in order to deduce what it means.

When we can neglect general relativity, then the energy of a system is defined as the conserved quantity associated with time-translation invariance. In flat space, translations in time are (almost) always symmetries of the field theories that describe elementary particles. If translations in space are also symmetries, then we can also define momentum. The mass of a system can then be defined as the value of the energy when the total momentum is zero. To be precise, this is the "inertial" mass of the system.

For an elementary particle, the mass can be identified as a parameter in the equation of motion for the corresponding quantum field. It is this parameter that is directly related to the Higgs mechanism in the Standard Model. For a composite system, the energy of the system involves not only the masses of the elementary constituents, but also the potential energy of the configuration. For example, the ground state of the hydrogen atom has a binding energy of -13.6 eV, so the mass of the hydrogen atom is

$$ m_H = m_p + m_e - 13.6~\mathrm{eV}/c^2,$$

i.e., a bit less than the sum of the masses of its parts.

Now, when we refer to gravitational mass, we're usually talking about the Newtownian limit of general relativity. In this case, the notion that the gravitational and inertial masses are identical is part of the collection of ideas known as the equivalence principle. There is no proof of the equivalence principle in general, but the Standard Model of particle physics is consistent with it.

In general relativity proper, it is not just mass that acts as a source for gravity, but all forms of energy. In fact, the relevant object that appears in the Einstein field equations of GR is the stress-energy tensor. The stress-energy tensor is just a fancy way of expressing the conserved quantities associated with translations in time and space, which I said earlier were just the energy and and momentum. Note that having gravity couple to the energy is actually required from the observation that the mass of a bound state also involves a contribution from the potential energy of the system. It would not be consistent (in the Newtonian limit) for gravity to ignore this contribution.

Now, in a field theory describing elementary particles, like the Standard Model, or even some sort of string theory, every particle in the theory (not just the graviton) contributes to the stress tensor. So every particle, massive or massless, is a source for gravity and therefore spacetime curvature. It is therefore not true that only the graviton is responsible for geometry: any matter will curve the geometry around it.

The graviton is special, since it represents a localized excitation of the metric field. In fact, this manifests itself in the requirement that every other field must have a nonzero coupling to the graviton field. This is different from the other fundamental interactions, where an elementary particle must have a corresponding nonzero charge to participate in the interaction. For example, electrons and quarks are electrically charged, so they can participate in electromagnetic interactions involving photons. However, particles like neutrinos and the Higgs particle are electrically neutral, so they don't directly interact with photons.

Gravity and gravitons are different, since every particle has a nonzero gravitational charge corresponding to its energy. In a certain sense, this coupling to the graviton is one way to represent precisely how a given particle influences the geometry around it.

 

[atyy]

Furthermore, I do not understand your statement "The invariant mass of a particle refers to how the particle's frequency changes with its wavelength." Isn't frequency and wavelength simply connected via the equation c = f x lambda?

fzero says it more precisely that the invariant mass is a parameter in the equations of motion. However, a simple way to think about it is that for a free particle, E²=p²c²+m²c⁴, and with the de Broglie relations that energy is related to frequency, and momentum related to wavelength, this becomes a relation bewteen wavelength and frequency. The phase velocity of a wave would still be v=fλ, but now v is not the special relativistic constant c, and changes with frequency, referred to as "velocity dispersion".

Where's the split between invariant mass (that of protons and so forth) and the gravitational mass responsible for space-time curvature?

For fields, there is a generalization of the energy to something called the stress-energy tensor, which is the source of gravity in general relativity. A particle with invariant mass has energy, but a particle with zero invariant mass also has energy and is therefore able to bend spacetime.

 

[Demystifier]

Demystifier, can you further explain this mystery to me? If one special vibrational state of a closed string can bend space-time, why can't other vibrational states do the same? What is so special about the graviton-vibration? Do I have to accept this in terms of a law of nature or does string theory provide sort of a mechanism that would explain this a little bit deeper? An analogy: if only one particular vibrational state of the vocal cord of a soprano is able to break window glass, no one would postulate a window-breaking-particle that by fundamental law of nature corresponds to this very frequency...

Bending of spacetime is mathematically described by the metric tensor, which is a mathematical object with two vector indices. The lowest mode of vibration of closed string contains such an object with two indices. Higher modes of vibration create objects with a higher number of indices, so they don't create metric tensor. Unfortunately, I don't know any simpler way to explain it.