# Q & A: Why is a proton heavier than three quarks?

Q:
I heard that protons are made up of two up quarks and a down quark but sth doesn't makes sense,the total mass and electric charge of these quarks doesn't equals the mass and charge of a proton.how is that possible?i don't find anything on the internet so please help me
- ana (age 13)
Iran
A:

The electric charge of two up quarks and a down quark does add up to the charge of a proton:

up quark (+2/3) + up quark (+2/3) + down quark (-1/3) = proton (+3/3 = +1)

No problem there. But you're right that the masses of the three quarks don't add up to anywhere near the mass of a proton. A proton is almost 100 times heavier than the three quarks!

According to special relativity, the mass of an object increases when it has more energy (for example, when it's moving faster). When we talk about the mass of quarks and protons, we mean their mass when they aren't moving. This is called the "rest mass."

As you noticed, the rest masses of two up quarks and a down quark don't add up to the rest mass of a proton. They only account for about 1% of the proton's mass. The other 99% comes from the energy that holds the quarks together inside the proton. The quarks are bound together by the "strong nuclear force," a fundamental force (like gravity) that is transmitted by particles called gluons. There are lots of gluons moving around all the time inside the proton, and their energy (plus the energy of the quarks, which are also moving) increases its mass.

Physicists can calculate about how much the energy of the quarks and gluons should increase the mass of the proton, and it's pretty close to what we actually measure... but calculating it exactly is a very difficult problem that scientists are still working on.

Rebecca H.

p.s. As a possible follow-up, you may wonder why the proton holds together if its energy is bigger than the sum of the rest energies of the three quarks. Don't things usually fall into a lower energy state? The key is that a quark by itself has huge energy because it gives off a field that increases the energy of the space near it. Those quark rest masses really just give the starting energy costs to make a quark+antiquark pair. Seperating them takes much more energy. So the proton has much lower energy than it would if the three quarks were separated, even though it has more energy than you'd calculate from just their rest masses.

BTW, this is a reminder that the rest mass of a combination of particles is not the sum of their rest masses, even if they don't interact.

Mike W.

(published on 06/16/2015)

## Follow-Up #1: our mistake fixed

Q:
Not a question, but noticed a typo in the electric charge calculation. Should be 2/3 + 2/3 - 1/3 = 3/3 = 1 instead of 1/3 + 1/3 - 1/3
- Dan (age 39)
Los Angeles, CA, USA
A:

Thanks! I've made the edit above.

Mike W.

(published on 10/09/2016)

## Follow-Up #2: typo

Q:
I believe you may have a typo in your "p.s.". If I'm following you correctly, I believe the last sentence should read: "So the proton has much lower energy than it would if the three quarks were separated, even though it has *more* energy than you'd calculate from just their rest masses."
- Andrew M. (age 29)
Washington, DC
A:

Thanks for catching that!

(published on 10/04/2017)