How Do Glue and the Higgs Mechanism Contribute to Particle Mass?

[humanino]

Is there any difference? I am by no means expert on GR, but as far as I understand the curvature of spacetime IS the mechanism by which an object is pulled downward.

Yes, that is the principle of equivalence : an observer in a freely falling box can not perform an experiment⁽¹⁾ to decide whether there is a gravitational field around. The observer follows a geodesic in spacetime (not in space). So, that is all stated locally in an infinitesimal box, but remember that globally, we are NOT saying that observers do not fall !

Light carries energy and momentum, and energy and momentum are the source of gravitational field, not mass. Photons do couple directly to gravitons in perturbative general relativity.

This is a fundamental fact which cannot be explained satisfactorily⁽²⁾ by any mechanism
wMFPe-DwULM[/youtube] (1) Obviousl...g" in the sense Feynman conveys in the video.

 

[humanino]

This is a fundamental fact which cannot be explained satisfactorily⁽²⁾ by any mechanism

To follow up on that, as Feynman says above, although there is not satisfactory explanation to "why", we do have equations to describe what happens. In the case at hand, the equation is just E^2=\vec{p}^2c^2+m^2c^4 where in a given referential, energies and momenta do add up linearly (conservation of energy momentum) so we can infer that mass does not ! (because the equation is not linear)

In particle physics, mass is part of what defines a particle as a representation of the Poincare (restricted Lorentz) group (the other Lorentz scalar (or Casimir operator in terms of group theory) defining the particle being angular momentum). Mass is also the energy in the frame where the momentum is zero. A particle may be defined with a zero mass, but the system of several such particles with zero masses in general will not have a vanishing mass. For the total system in its rest frame, by definition of the rest frame you will get the sum of momenta being zero \sum_i\vec{p_i}=\vec{0}, and the sum of energies will give you the mass of the system, which will not equal the sum of the masses :
m=\frac{1}{c^4}\sqrt{ \left(\sum_i E_i\right)^2-\left(\sum_i\vec{p_i}\right)^2c^2} =\frac{1}{c^4}\sqrt{ \left(\sum_i E_i\right)^2-\vec{0}^2c^2} =\sqrt{\left(\sum_i\sqrt{ \frac{\vec{p}_i^2}{c^2}+m_i^2} } \right)^2}=\cdots \neq \sum_i m_i

 

[Orion1]

Since energy is dependent on reference frame (upon the observer) it is convenient to formulate the equations of physics in a way such that mass values are invariant (do not change) between observers, and so the equations are independent of the observer. For a single particle, this quantity is the rest mass; for a system of bound or unbound particles, this quantity is the invariant mass. The invariant mass m of a body is related to its energy E and the magnitude of its momentum p by:

mc^2 = \sqrt{E^2 - (pc)^2}

Invariant mass (rest mass):
m = \frac{\sqrt{E^2 - (pc)^2}}{c^2}

Invariant mass of the system:
m=\frac{1}{c^2}\sqrt{ \left(\sum_i E_i\right)^2-\left(\sum_i\vec{p_i}\right)^2c^2} =\frac{1}{c^2}\sqrt{ \left(\sum_i E_i\right)^2-\vec{0}^2c^2} =\sqrt{\left(\sum_i\sqrt{ \frac{\vec{p}_i^2}{c^2}+m_i^2} } \right)^2}=\cdots \neq \sum_i m_i

Quantum mass manifests itself as a difference between an object’s quantum frequency and its wave number:
m = \frac{\hbar}{\overline{\lambda} c} = \frac{\sqrt{E^2 - (pc)^2}}{c^2}

The result is that all energy in any system is quantized by its wave number:
\hbar c = \overline{\lambda} \sqrt{E^2 - (pc)^2}

\hbar c = \sum_i \overline{\lambda}_i \sqrt{ \left(\sum_i E_i\right)^2 - \left(\sum_i\vec{p_i} \right)^2 c^2} = \sum_i \overline{\lambda}_i \sqrt{ \left(\sum_i E_i \right)^2 - \vec{0}^2 c^2} = \sum_i \overline{\lambda}_i \sqrt{\left(\sum_i \sqrt{ \vec{p}_i^2 c^2 + m_i^2 c^4} \right)^2}

\boxed{\hbar c = \sum_i \overline{\lambda}_i \sqrt{\left(\sum_i \sqrt{ \vec{p}_i^2 c^2 + m_i^2 c^4} \right)^2}}
[/Color]
Reference:
http://en.wikipedia.org/wiki/Mass#Summary_of_mass_concepts_and_formalisms"
http://en.wikipedia.org/wiki/Wave_number"

 

[The_Duck]

I am just having great difficulty and confusion trying to figure how it is (by what mechanism) it is that gravity causes the photons added to the box to make force downward on the box.

I can see how if they were absorbed it would add weight to what absorbed them, but just their being in the box doesn't make sense to me how they would cause net force downward when in a gravitational field.

How about this:

Suppose instead of a photon you have a ball bouncing back and forth very fast between the floor and ceiling of the box. If this box is sitting on a scale, the mass of the ball inside the box should register. How does this happen? Well, because of gravity the ball is moving faster when it hits the ground than when it hits the ceiling, so if you average over time it exerts more "pressure" on the floor than the ceiling, and this shows up on the scale.

Now imagine a photon "bouncing back and forth between the floor and the ceiling" (I'm sure this is a horrible mangling of classical and quantum ideas but whatever). A similar thing happens: the photon gets http://en.wikipedia.org/wiki/Gravitational_redshift" as it descends and redshifted as it ascends, so it has more energy when it hits the floor, so it exerts more pressure on the floor than on the ceiling. Thus the scale registers extra weight because of the photon in the box. The Earth's gravity pulls more strongly on a box with a photon than one without a photon.

As Antiphon mentioned, from this and conservation of momentum you can deduce that light not only feels gravity, but produces it too.