Is there a size or duration limit on fields having mass?

[slatts]

I've read that matter and energy fields occupy all of space, and that space is integral with time, so I'm wondering whether it might be consistent with contemporary physics for undetectably small proportions of the mass of matter and / or energy to occupy arbitrarily large proportions of an infinite spacetime. (I'm assuming that levels registered as "zero" would be indistinguishable from "undetectably small" levels, since the resources that could be devoted to their registration would always remain less than infinite.)

Let me make clear that, by infinite spacetime, I'm meaning just that: infinite space and infinite (both "past-eternal" and "future-eternal") time. Also, I'm including gravity with energy, since I've heard that it functions as "negative energy" in the context of General Relativity.

However, if consistency with our physics over arbitrarily large proportions of spacetime might exist for any "positive" and / or "negative" versions of energy and / or matter, while it would be prohibited for any of the others, I'd like to know that as well. By the same token, I'm hoping someone really familiar with this stuff could let the rest of us know whether it might just be the case for spacelike separations without being the case for timelike separations. My very sketchy knowledge of the subject has me guessing that it would be the case for lightlike separations, but, if that more specific conclusion is wrong, I'd like to know.

Thanks very much, in advance, for whatever help you can give me in making sense out of the mishmash of terminology involved. (Yes, I'm sorry I don't know much math, but, if it can be pronounced, it can be put into verbal language, and that's where its application might help with a few social issues.)

 

[Drakkith]

I've read that matter and energy fields occupy all of space, and that space is integral with time, so I'm wondering whether it might be consistent with contemporary physics for undetectably small proportions of the mass of matter and / or energy to occupy arbitrarily large proportions of an infinite spacetime.

What do you mean? Mass is a property of an object. It cannot extend out beyond that object, be it a particle or a galaxy.

 

[slatts]

I had understood any field to be a sort of object having some mass, as well as an infinite extent, and had read that a field's particles were concentrations of its energy. That "fields" have energy is mentioned in the unchallenged Wikipedia article about them, and it's my understanding that both matter and energy always have some mass. Googling "field has mass" brings up several hits, including a few on Physics Forums: Someone mentioned difficulty seeing how that would be compatible with the superposition principle, which had occurred to me also; in fact, I'd been guessing that the impossibility of superposition might be the characteristic distinguishing a particle from its field.

I've done some teaching, years ago, and I think that explanations of how the big bang happens everywhere almost simultaneously might be a lot easier to get across if it could be seen as beginning in some environment more plausible than absolute nothingness, which, if you give it its standard description of something so dark that it won't even carry photons, which has been shrunk down to an absolute zero volume, won't get much out of a classroom full of kids except a rolling of eyeballs. The bubble of false vacuum that has taken over some functions of the big-bang singularity in a lot of the inflationary cosmologies has been described (by Guth, for instance) as being about the size of a marble but weighing as much as the universe, which is better, but still maybe a little stranger than it needs to be. I mean, the thing seems to have had some texture (the wrinkles that evolve into galaxies, right?), so would it just spoil everything if it would connect with stuff just a little more familiar, like the field that we've all seen making toy magnets work since kindergarten? I mean, does it really have to be a perfect ball whose isolation only St. Augustine could fully imagine?

That, basically, is what I'm asking--can the deepest physics be cut just a little looser from the Whichness of What, or does it all hang together in such delicately enormous complexity that looping a strand or two into the magnetic field that's still here is verboten? (If the answer is "yes", I'm prepared to accept it--I haven't taught in decades--but I just don't think it's anything that the billions of the world's villagers who are still trying to get a crop in could relate to, or, frankly, give a hang about!)

 

[Chalnoth]

I had understood any field to be a sort of object having some mass, as well as an infinite extent, and had read that a field's particles were concentrations of its energy.

Nope. Mass is a peculiar property that not all fields have. The photon field, for example, has no mass.

Mass is the energy that remains if a particle has no kinetic energy. Photons only have kinetic energy.

 

[Orodruin]

You cannot just take terms and assume a meaning for them. When we talk about massive fields, it does not mean that there is a mass everywhere in the Universe. As Chalnoth already noted, it is a field property which tells us things about how the excitations of the field behave, i.e., it gives us the dispertuon relation for the excitations.

 

[Drakkith]

I've done some teaching, years ago, and I think that explanations of how the big bang happens everywhere almost simultaneously might be a lot easier to get across if it could be seen as beginning in some environment more plausible than absolute nothingness,

If you look at the history of the universe, as you go back further in time the universe becomes more dense. At no point does the standard model say, "Here lies nothingness, from which emerged somethingness". Instead what happens is the standard model says, "Oh! My math just stopped working! I must not know physics well enough to make predictions prior to this point in time." The idea that the universe emerged from nothingness is not a rigorous prediction. It might be better if all these shows and books just said that we don't know where the universe came from.

which, if you give it its standard description of something so dark that it won't even carry photons, which has been shrunk down to an absolute zero volume, won't get much out of a classroom full of kids except a rolling of eyeballs.

I'd roll my eyes too. That's not a correct description of the very early universe. We don't know what the conditions were like prior to about 10^-43 seconds. After this point we know that the universe should have been very hot and very dense, cooling off as it expanded from there. See more here: http://pages.uoregon.edu/jimbrau/astr123/Notes/Chapter27.html
Note that any mention of "the big bang" should be taken as an arbitrary point in time which we label t = 0, not as a single event like an explosion.

 

[slatts]

Nope. Mass is a peculiar property that not all fields have. The photon field, for example, has no mass.

Mass is the energy that remains if a particle has no kinetic energy. Photons only have kinetic energy.

Thank you for the clarification. Just so I can get a better grip on this, could you tell me whether the photons are considered to have existed as part of a more general "matter" field, prior to their "decoupling" from it? (In other words, in what way was the matter field different, immediately after their decoupling? I'm guessing that it would have lost kinetic energy, but, then, I'd forgotten that something which never stops moving would not even have "rest mass", so my guesses aren't working out too well.)

 

[Chalnoth]

Thank you for the clarification. Just so I can get a better grip on this, could you tell me whether the photons are considered to have existed as part of a more general "matter" field, prior to their "decoupling" from it? (In other words, in what way was the matter field different, immediately after their decoupling? I'm guessing that it would have lost kinetic energy, but, then, I'd forgotten that something which never stops moving would not even have "rest mass", so my guesses aren't working out too well.)

Sorta kinda.

In the standard model, you get two kinds of particles: fermions and gauge bosons. These stem from certain symmetries. One way to visualize this that sort of grasps the idea is to imagine a large polyhedron (say, a 20-sided figure). Each vertex of the figure is a fermion, while each face is a boson. At high energies, all of the bosons are the same, and all of the fermions are the same. But at low energies, the symmetry is broken and some of the fermions start acting differently from other fermions, while some of the bosons start acting differently from other bosons.

These fermions make up the matter particles because no two fermions can take up the same space at the same time (the Pauli exclusion principle). The bosons interact with the fermions, and create the forces (strong, weak, and electromagnetic). An unlimited number of bosons can exist in the same state.

So the photons do come from the same higher-order structure, but because they are spin-1 (which makes them bosons), they are fundamentally different from the spin-1/2 fermions (electrons, protons, neutrons, neutrinos, etc.).

One last thing: mass is not fundamental. It turns out that if you try to add mass as a fundamental property to particles in the standard model, you get a contradiction in the math. All particles must be fundamentally massless, and obtain masses as a result of their interactions. One way to think of this is that there is a background field that some particles interact with while others don't. A photon doesn't interact with the field at all, but the interaction between an electron and this field makes it so that the electron has energy even without having any movement.

 

[slatts]

One...thing: mass is not fundamental. It turns out that if you try to add mass as a fundamental property to particles in the standard model, you get a contradiction in the math. All particles must be fundamentally massless, and obtain masses as a result of their interactions. One way to think of this is that there is a background field that some particles interact with while others don't. A photon doesn't interact with the field at all, but the interaction between an electron and this field makes it so that the electron has energy even without having any movement.

Please correct me if I'm wrong, but it's sounding like the mass of any particular field, if it's the type of field that has any, might just be the sum of the masses of the particles proper to it, either upon, after, or in between their interactions with each other.

I wish I could look at this thread more continuously, but, even so, I'd like to put the very helpful info the three respondents have given me so far into the context of the aims I sketched in its Post #3. Trying to "get a visual" on events that occurred well before primates invented language (let alone math) may be tricky, but I think it just may turn out to be, say, politically (or philosophically, or spiritually) important, on a planet whose inhabitants appear intent on (just for instance!) remaking it into the next Venus. To that end, please let me take the liberty of making an assumption that the inflationary cosmology might be correct, since it is reportedly (per the Planck Satellite group in its 2015 data release) compatible with current data from observations, at least in some of its models of the universe. (I'm asking that favor not because I consider the scientists among the opponents to that theory to be wrong, but because, on account of the heavy press it's received since 1981, it's the cosmology with which I'm most familiar, aside from those more directly traceable to purely oral traditions.)

At least when you have to dance around the math as much as I do (and you also flunked Dancing 101), you get an impression that there may not have been any multi-particle structure even as large as a molecule, within the "inflating" (exponentially expanding) region. (This may not be clear to some of my patient readers, because the ending of inflation, whether "locally universal" or "unequivocally universal", has been surprisingly omitted from some threads dealing with the characteristics of the Big Bang, with which I've seen it identified in other threads that were comparably recent: An expansion that may never end, and is currently accelerating, has been identified, but seems, so far, to be largely due to inertia.) Now, except for a few unfortunates near some of the more extreme volcanic eruptions and / or meteor hits, it seems unlikely to me that any people anywhere would, before about 1905, have ever seen a plasma that was, for them, distinguishable from gases, liquids, or solids.

I'm sure that the majority of the people of this Earth have heard of an expansion of space bouncing planets around, but, for them to take it seriously, I think it needs to be made clearer that the bouncing mostly occurred before the planetary material had even become planets, and, in fact, largely or entirely before any of it had even become material. What my own question about this potentially serious mishmash of terminology comes down to is, "Back when the expansion was exponential, how do we know whether it was the space that was expanding, or the superpositioned fields filling the space which were expanding"? (Sorry, but it wouldn't fit into the title space.)

 

[Drakkith]

At least when you have to dance around the math as much as I do (and you also flunked Dancing 101), you get an impression that there may not have been any multi-particle structure even as large as a molecule, within the "inflating" (exponentially expanding) region.

I doubt there were. If my very limited understanding of inflation is correct, there is a 're-heating' process in which the potential energy of the inflation field is converted to matter and radiation, which is what then forms the hot, dense plasma that occupied the very early universe. What existed prior to these particles and radiation is not well known.

(This may not be clear to some of my patient readers, because the ending of inflation, whether "locally universal" or "unequivocally universal", has been surprisingly omitted from some threads dealing with the characteristics of the Big Bang, with which I've seen it identified in other threads that were comparably recent: An expansion that may never end, and is currently accelerating, has been identified, but seems, so far, to be largely due to inertia.)

Most threads dealing with the big bang here at PF have little need to talk about inflation, as it usually either isn't relevant to the discussion or including talk about inflation would just complicate an already confusing topic.

What my own question about this potentially serious mishmash of terminology comes down to is, "Back when the expansion was exponential, how do we know whether it was the space that was expanding, or the superpositioned fields filling the space which were expanding"?

I believe both of those statements are equivalent.

I'm sure that the majority of the people of this Earth have heard of an expansion of space bouncing planets around, but, for them to take it seriously, I think it needs to be made clearer that the bouncing mostly occurred before the planetary material had even become planets, and, in fact, largely or entirely before any of it had even become material.

I have no idea what you're talking about here. Expansion is never described as causing objects to 'bounce around'.

 

[slatts]

Well, I was basically making--maybe a little too sarcastically--a plea to keep science less fictional (and, consequently, more realistically effective socially) by leaving "space" as nearly synonymous with "nothing" as it had been until the mass media got a hold of the subject about 1929. This unfortunate (and potentially disastrous) usage does not prevail on the staffers' side of this forum, as Chalnoth (for instance) generally seems to refer to "vacuum energy", which is much less likely to result in that eyeball rolling which turns off research money. But its victims seem to wander in pretty regularly among the "starter" members.

 

[PeterDonis]

could you tell me whether the photons are considered to have existed as part of a more general "matter" field, prior to their "decoupling" from it?

Chalnoth answered "Sorta kinda," but I think a clearer answer would be simply "no". What Chalnoth was describing was how the different fields we know of (the photon field and all the other fields in the Standard Model) fit into a larger structure. But that larger structure is not a "more general matter field". It's an abstract structure describing the symmetries of the equations describing the fields.

Please correct me if I'm wrong, but it's sounding like the mass of any particular field, if it's the type of field that has any, might just be the sum of the masses of the particles proper to it, either upon, after, or in between their interactions with each other.

No. The "mass" of a field, in quantum field theory, is just a constant in the Lagrangian. (For a "massless" field, this constant is zero, i.e., the "mass term" does not appear in the Lagrangian.) Each field has its own constant (mass) associated with it.

Part of the problem may be that you are confusing different meanings of the term "mass". The meaning I just gave is the relevant one if you're talking about quantum fields; but earlier in this thread you were talking about "mass" more as a synonym for "energy", which is a different concept. Mixing them together is only going to cause confusion.

 

[Chalnoth]

Please correct me if I'm wrong, but it's sounding like the mass of any particular field, if it's the type of field that has any, might just be the sum of the masses of the particles proper to it, either upon, after, or in between their interactions with each other.

No, definitely not. The mass is the internal energy of the particles (which are excitations of the field, not the field itself).

A proton, for example, is made up of three quarks* and a bunch of gluons. The quarks are a few MeV in mass each, and the gluons are massless. But the proton's mass is about 938 MeV. Only a small fraction of the mass is in the quarks. The rest is in the binding energy between the quarks.

* The proton has three quarks in the ground state, but because the binding energy between them is so large, quark/anti-quark pairs occur as well. But again, their mass doesn't add up to the mass of the proton. The mass is the energy of the total collection of quarks and gluons that make up the proton.

 

[slatts]

No, definitely not. The mass is the internal energy of the particles (which are excitations of the field, not the field itself).

A proton, for example, is made up of three quarks* and a bunch of gluons. The quarks are a few MeV in mass each, and the gluons are massless. But the proton's mass is about 938 MeV. Only a small fraction of the mass is in the quarks. The rest is in the binding energy between the quarks.

* The proton has three quarks in the ground state, but because the binding energy between them is so large, quark/anti-quark pairs occur as well. But again, their mass doesn't add up to the mass of the proton. The mass is the energy of the total collection of quarks and gluons that make up the proton.

Thanks very much for the reply, which is entirely consistent with Drakkith's of post #10, and leaves me thinking that a "field" in physics is very much like a "field" in the most basic English lexicon, except that it lacks the dirt under it. So, if interviewees could just please start getting at least a bit cranky with pop-sci. reporters who are itching to Astound their readers, or at least a little more insistent on use of the word "space" where "vacuum energy" would be more sensible, maybe the taxpaying voters who look at their articles would be just a bit less apt to confuse their content with the most antiquated elaborations of theology, and, consequently, less apt to put the content of those articles on the back burner of their real lives.

 

[PeterDonis]

The mass is the internal energy of the particles (which are excitations of the field, not the field itself).

Note that, as I pointed out in my previous post, this "mass" is not the same as the "mass" of the field, which, as I noted, is a constant in the Lagrangian.

leaves me thinking that a "field" in physics is very much like a "field" in the most basic English lexicon, except that it lacks the dirt under it

I'm not sure why. As I pointed out, the "mass" Chalnoth was talking about is the energy stored in excitations of the field, which is not the same as the "mass" of the field itself. Knowing things about the energy of field excitations doesn't necessarily tell you anything about the field itself; after all, we knew that "particles" had mass (energy) before we knew that they were excitations of quantum fields.