How does the kinetic energy of quarks contribute to the mass of macroscopic objects?

Question

As we know, most of the mass of ordinary matter comes from the kinetic energy of quarks. This means kinetic energy of quarks contributes to the mass of any object.

However take a look at this question.

Does a moving object curve space-time as its velocity increases?

A moving star does not bend space-time any more than if it were not moving. (One example given was that a moving star won’t collapse into a black hole just because its moving). This seems to be a contradiction. In the first case motion of quarks do contribute to bending (by contributing mass). In the second case, the motion of the star does not. Both make sense. But how do we resolve the contradiction?

Let's take a more macroscopic example. If we had a many asteroids moving in random directions in a region of space, would the motion increase the bending of space-time (say the observer far away from the asteroid field). Imagine that you shrink down the asteroids and increase their number so you have a gas of small particles. This “motion in random directions” translates to internal energy and that contributes to the bending of space time, just as the kinetic energy of quarks contributes to the bending of space-time. And in fact, enough of this can cause a black hole.

The interesting thing is you can’t transform to a frame where none of the asteroids or small particles are in motion. In the case of a single star in motion, you can transform to frame where the star is not moving.

This question seems related: Does relativistic mass exhibit gravitiational effects?

Article by Wilzcek on "mass without mass". I think this article is a good answer to the question. http://www.aip.org/pt/nov99/wilczek.html

Other notes:

In the case of a star, the stress-tensor determines how space-time curves. The stress-tensor is a coordinate independent object. So it doesn’t matter what particular coordinates you use to do your calculations. In other words, whether you are in some frame co-moving with the star or in spaceship moving by the star, calculated metric tensor should be the same.

In the case of a gas, there is no frame in which the particles are all standing still with respect to that frame. You stand still with respect to some particles, but other particles are then moving and so on. The component of the stress-energy tensor change, but the result is the same.

So motion does add to the curvature of space time, but only if you can’t transform it away.

Answer 1

I think two concepts are being confused here. The concept of invariant mass, and the concept of relativistic mass. In particle physics the relativistic mass is no longer widely in use as it tends to confuse newcomers.

As we know, most of the mass of ordinary matter comes from the kinetic energy of quarks. This means kinetic energy of quarks contributes to the mass of any object.

This is misrepresented. The mass of the proton comes from the invariant mass of all its constituents, which include gluons and quark antiquark pairs. It is the length of the four vector and it is a Lorenz invariant.

A moving star does not bend space-time any more than if it were not moving

That is because its invariant mass stays invariant.

In the first case motion of quarks do contribute to bending (by contributing mass)

It is not the motion of the quarks that contributes to observable mass, it is the addition of internal four vectors. The conglomerate of four vectors within a proton appear because of the strong interaction between the quarks . No such strong interaction exists in the asteroid examples. Gravity is extremeley weak.

As long as one remains in the Lorenz frame there can be no contribution from motion to gravitational bending. If one goes to beginning of the universe energies where gravity, once it is correctly quantized , is a strong interaction , then one can revisit this. At those energies no asteroids are hypothesized.

Answer 2

Actually I am a student of fs.c so I can be wrong. I have been searching the almost same problem for 3 days on internet but what come in my understanding is that bending of space-time depend upon REST MASS not RELATIVISTIC MASS because bending of space-time depend upon energy-momentum as this quantity( energy-momentum) remain same for relative observer (as you have already read ~Does a moving object curve space-time as its velocity increases?) This means energy-momentum is not affected by RELATIVISTIC MASS but depend upon REST MASS which in turn depend UPON ENERGY IN REST FRAME OF REFERENCE As rest frame of reference is that frame of reference in which matter's particle (just like box with particles) have net momentum zero and rest mass depend upon energy. So if u have large box and if u put asteroids in it and then increase their random energy then energy-momentum increase and space-time curve.

Answer 3

the elephant in the room. one does not "have" kinetic energy, it has to have an energy source, otherwise all matter would have decayed billions of years ago. And we would never have got here to talk about it! So the kinetic energy of quarks have to be supplied with some type of universal field, perhaps among many fields. And this field(s) consequently gives mass.