Do Gravitational Fields Increase the Rest Mass of Protons and Photons?

[cbd1]

Does proton diameter increase with the addition of energy, such as thermal energy? I guess this is also to ask if a particle's rest mass can increase.

And, if a proton can gain rest mass, does the diameter correlate with it?

 

[Matterwave]

I think that it is possible if the quarks inside the proton go to a higher energy level...that may increase the rest mass of the proton (a composite particle)...but I'm not sure about this since I don't know much about quantum chromodynamics.

 

[Vanadium 50]

No, because all protons are identical.

 

[Deric Boyle]

Sorry Sir Vanadium, but I didn't get your above post.
What relation do "all protons being identical" have with "protons rest mass"?
I'd be glad to know.
Thanks in Advance!

 

[ZapperZ]

Sorry Sir Vanadium, but I didn't get your above post.
What relation do "all protons being identical" have with "protons rest mass"?
I'd be glad to know.
Thanks in Advance!

What he means is that a "proton" has a set of definition, and one of them is a specific mass value. If something that comes along and has all the same characteristics, then you can say "ah ha! That is a proton". Why? Because all protons should be identical to each other. If something comes along with all the same characteristics but, say, with a different mass, then it isn't a proton. It is something else.

So the question on whether a proton (or any other identified particles in the Standard Model/http://pdg.lbl.gov/2010/listings/contents_listings.html" ) can "gain rest mass" is rather meaningless.

Zz.

 

[Deric Boyle]

Oh.. Thank you very much.
Hm.. then according to the basic convention if the rest mass of some known particle is increased(how?) then it is called something else(as I infer from the particle data).What I think here is that even if increase the rest mass of that particle,for example a hardon, its family wouldn't change, that is if it was hadron it'll remain a hadron (under our hypothetical process of increasing the rest mass)?
(Am I correct?)
Edit:- Thanks Fredik for the correction
(is my above proposition/thought correct.Please teach me.)

 

[ZapperZ]

Oh.. Thank you very much Sir.
Hm.. then according to the basic convention if the rest mass of some known particle is increased(how?) then it is called something else(as I infer from the particle data).What I think here is that even if increase the rest mass of that particle,for example a hardon, its family wouldn't change, that is if it was hardon it'll remain a hardon (under our hypothetical process of increasing the rest mass)?
(Am I correct?)

I have no idea what you just said here.

BTW, as a friendly advice, you might want to consider not addressing any and all members of this forum with a "sir". There ARE women physicists in here, and you'd be inadvertently insulting them by assuming them to be males.

Zz.

 

[Fredrik]

I don't know if this was a deliberate typo, but the word is "hadron", not "hardon". Hadrons are particles made up of quarks. Hardons are rigid bodies that sometimes enter black holes.

 

[ZapperZ]

I don't know if this was a deliberate typo, but the word is "hadron", not "hardon". Hadrons are particles made up of quarks. Hardons are rigid bodies that sometimes enter black holes.

It's a common typo which even I have made. :)

Zz.

 

[czelaya]

I don't know if this was a deliberate typo, but the word is "hadron", not "hardon". Hadrons are particles made up of quarks. Hardons are rigid bodies that sometimes enter black holes.

 

[Dickfore]

Hardons are rigid bodies that sometimes enter black holes.

tempted siggin' it.

 

[Deric Boyle]

(Hey! I've corrected it now please spare me.It was just a typo.Now don't go on refraining it)
I've a new question:-
How are protons 'excited' (or the quarks within), is it a 3-body QM problem(I don't think so)?How is it related to proton's rest mass?
Thanks in advance!

 

[Drakkith]

From Wikipedia:

The invariant mass, rest mass, intrinsic mass, proper mass or just mass is a characteristic of the total energy and momentum of an object or a system of objects that is the same in all frames of reference related by Lorentz transformations

Since you can always think of yourself as being "at rest" in your frame, then any addition of energy would NOT increase the rest mass.

 

[daumphys]

We are going with the Universe expansion.
So, is the rest mass the measured mass when we go with the Galaxy moving?

 

[jtbell]

Since you can always think of yourself as being "at rest" in your frame, then any addition of energy would NOT increase the rest mass.

This holds only for a single non-composite particle. When you add energy to a system of particles, the rest mass (invariant mass) of the system does increase, even though the rest masses of the individual particles do not change.

The rest mass of a system does not equal the sum of the rest masses of its component particles, in general.

 

[Deric Boyle]

I know that the sum of the rest masses of the constituent particles,of ,say, hadron, doesn't equals that of the ensemble they make.But thanks for reminding.So is a proton modeled as a three body problem with the 'bodies' being quarks.Or... is it something more complex(like introduction of 'gluons' in the model)?Any refrence if one can provide,I'll be really grateful.

 

[cbd1]

This holds only for a single non-composite particle. When you add energy to a system of particles, the rest mass (invariant mass) of the system does increase, even though the rest masses of the individual particles do not change.

The rest mass of a system does not equal the sum of the rest masses of its component particles, in general.

I want to question about how the "invariant" mass can increase with energy. I suppose we could use the transistor idea for this. We say that the invariant mass of a charged transistor is higher than the invariant mass for that same transistor when it is not charged. So, we say that the photons in the charged transistor add to the rest mass of the system, though they do not add any fermion particles.

When you take the total energy of the charged transistor and divide it by c², you get a larger mass than you would have from only the fermions in the system (the uncharged transistor's invariant mass).

My question is how the photons add rest mass to the system, when photons have no rest mass themselves? Can we assume that the photons have been absorbed into the fermions in the transistor, giving them more rest mass?

When we say that gravity gives a force on bodies towards the earth, it is easy to see that the uncharged transistor has the force of gravity on its fermions, giving the transistors weight on the ground. The photons flying around above the ground do not have gravitational force applied to them, and they do not have weight on the ground. This makes clear and simple sense. But things get stupid when you put these photons into the transistor.

Somehow, the photons which did not have weight outside the transistor, all of a sudden have weight, and contribute it to the transistor upon the ground, making it heavier. It seems to me like this is not correct as the law doesn't apply universally. The photons have no weight outside the transistor, but they have weight within the transistor? The photons do not add anything into the transistor for gravity to give force on. Might it be that the added weight with the photons is simply the addition of their radiation pressure? (This could account also for the increase in inertial mass.) In this way, the photons would not actually require rest mass, though they seem to add mass to the body. (They add energy, which has a mass equivalent by e=mc2, but they don't at any point really technically give mass to the transistor, only radiation pressure within it.)

 

[fzero]

A more relevant analogy would be the hydrogen atom. Let the atom be in the $$n^\text{th}$$ energy eigenstate, with energy $$E_n$$ and be at rest in the center-of-mass system. Then the relativistic energy of the system is

$$m_p c^2+ m_e c^2+ E_n,$$

while the momentum is zero. Then the invariant mass of the system is obtained by dividing by $$c^2$$:

$$m_n = m_p + m_e + \frac{E_n}{c^2}.$$

Since

$$E_n = - \frac{ 13.6~\text{eV} }{n^2},$$

the excited states $$n>1$$ have a larger mass than the ground state mass $$m_1$$:

$$m_{n>1} > m_1.$$

We could also add energy to the proton to create an excited, but still bound, state. This particle has the same quantum numbers as a proton, but has a larger mass. These have been seen in nature and are the N baryons listed on this page: http://pdglive.lbl.gov/listing.brl?fsizein=1&exp=Y&group=BXXX005

 

[jtbell]

In general relativity, mass per se is not the "source" of gravity. Instead, the "source" of gravity is the stress-energy tensor, whose components are constructed from energy and the components of momentum. Mass enters into the picture only insofar as it contributes energy to the system.

 

[cbd1]

We could also add energy to the proton to create an excited, but still bound, state. This particle has the same quantum numbers as a proton, but has a larger mass. These have been seen in nature and are the N baryons listed on this page: http://pdglive.lbl.gov/listing.brl?fsizein=1&exp=Y&group=BXXX005

So it is possible then for a fermion to gain rest mass? In the example with the transistor, could it be that the photons are absorbed by particles (e.g. electrons) which then have the increased mass?

I know there is also a decrease (or increase?) in rest mass when a proton and electron join to make an hydrogen particle, which is different from the addition of the individual rest masses. Could this be considered as a change in rest mass from one or the other fermions?

Also, when nucleons join together into a large nucleus, the nucleons are known to contribute less mass than their individual masses, correct? Would this be interpretable by the nucleons actually decreasing in their individual rest masses?

I could also say that I am trying reconcile this problem for quantum gravity, as I find that only fermions can be accelerated by gravitational fields. (Photons are more so redirected than accelerated, they gain no speed towards the object, as a fermion does in gravity. But this is a different discussion.) Basically, otherwise, how could gravity give more force to an object with increased energy while there is no increase in the mass of the particles within the system? <--(Separate question.)

 

[fzero]

So it is possible then for a fermion to gain rest mass? In the example with the transistor, could it be that the photons are absorbed by particles (e.g. electrons) which then have the increased mass?

I know there is also a decrease (or increase?) in rest mass when a proton and electron join to make an hydrogen particle, which is different from the addition of the individual rest masses. Could this be considered as a change in rest mass from one or the other fermions?

Also, when nucleons join together into a large nucleus, the nucleons are known to contribute less mass than their individual masses, correct? Would this be interpretable by the nucleons actually decreasing in their individual rest masses?

I can generalize the example above to any bound state. Let C be the bound state particle made from N particles with masses $$m_i$$. There is a binding energy $$B$$ which is defined as the difference in potential energy of the unbound configuration with respect to the bound state. In this convention $$B$$ is positive for a stable bound state. If the binding energy is negative, the bound state will quickly break apart to the more favorable energetic configuration. Then the mass of the bound state C satisfies

$$m_C = \sum_i^N m_i - B/c^2.$$

None of the individual particles change in mass. The binding energy is responsible for the fact that the mass of the composite object is smaller than the sum of the constituent masses.

I could also say that I am trying reconcile this problem for quantum gravity, as I find that only fermions can be accelerated by gravitational fields. (Photons are more so redirected than accelerated, they gain no speed towards the object, as a fermion does in gravity. But this is a different discussion.) Basically, otherwise, how could gravity give more force to an object with increased energy while there is no increase in the mass of the particles within the system? <--(Separate question.)

You are ignoring the fact that light that passes into a gravitational field is blueshifted to a higher frequency. This is the effect of gravitational acceleration for massless particles. They do not change speed, but their energy increases due to the acceleration.

 

[cbd1]

None of the individual particles change in mass. The binding energy is responsible for the fact that the mass of the composite object is smaller than the sum of the constituent masses.

You are ignoring the fact that light that passes into a gravitational field is blueshifted to a higher frequency. This is the effect of gravitational acceleration for massless particles. They do not change speed, but their energy increases due to the acceleration.

Thank you. I'm wondering if you could give an explanation for why a gravitational field will apply less force to the H atom than it would to the proton and electron individually while they were separate?

Second, does gravitational blueshift actually increase the energy of the photon? My understanding of GR was that the photon is not actually increased in energy, but rather the frequency becomes shorter relatively due to the relatively slowed rate of time.

 

[fzero]

Thank you. I'm wondering if you could give an explanation for why a gravitational field will apply less force to the H atom than it would to the proton and electron individually while they were separate?

Gravity couples to the energy-momentum of a system. Because of the binding energy the bound state is a lower energy configuration than the separate constituents.

Second, does gravitational blueshift actually increase the energy of the photon? My understanding of GR was that the photon is not actually increased in energy, but rather the frequency becomes shorter relatively due to the relatively slowed rate of time.

As a photon approaches a massive body, its potential energy decreases. The frequency of the photon must increase by conservation of energy. The total energy, which is the sum of hf and the potential energy, does not change.