Can particles interact without a mass?

[nonamebrand]

TL;DR Summary

Is it possible for particles, any of them to have had some role in the beginning of the universe, despite not having mass?

I recall reading someone questioning if it were possible for the higgs boson to be the primordial atom which led to the start of the universe. I was just wondering if that could even be possible, since the higgs field was zero and couldn't have given these particles any mass. (please be kind, I'm not a physicist, I'm not in school for physics, I was just reading about it and was curious.)

 

[Orodruin]

Mass is not a requirement for interactions.

 

[mathman]

All particles have "mass", although for photons it is called energy.

 

[Orodruin]

All particles have "mass", although for photons it is called energy.

This is not correct. Mass by definition in relativity is rest energy and a photon has none.

 

[mathman]

This is not correct. Mass by definition in relativity is rest energy and a photon has none.

Rest mass is not the same as (total) mass. It's simply a matter of definition. Think of the Lorentz transformation which defines "mass" in terms of rest mass and velocity.

 

[Orodruin]

Rest mass is not the same as (total) mass. It's simply a matter of definition.

In modern nomenclature, there is only one mass - what was previously referred to as rest mass or invariant mass. A photon has zero mass. Concepts such as relativistic mass have fallen completely out of fashion as they are not needed and lead to confusion.

 

[PeterDonis]

It's simply a matter of definition.

Even to the extent this is the case, the OP of this thread makes clear that he is using "mass" to mean "rest mass", since he talks about the Higgs boson giving particles mass, and the only meaning of "mass" that makes sense in that context is "rest mass".

 

[PeterDonis]

I recall reading

Can you give a reference?

 

[kimbyd]

Summary:: Is it possible for particles, any of them to have had some role in the beginning of the universe, despite not having mass?

So, you've already gotten your direct answer, but I thought I might extend it a little bit because I think it's fascinating.

As others noted, mass is simply not a requirement for any interactions. For an interaction, you essentially need to just have two particles which connect in their equations of motion. In practice what happens is that the interaction has a charge associated with it, and a force-carrying particle which connects to that charge. Any particle that has that type of charge connects to the relevant force-carrier. Like with the electromagnetic force, the charge is the electric charge, and the force carrier is the photon.

There are also cases where the force carrier itself has charge, such as with the strong nuclear force.

But the real reason why I find your question so interesting is that the equations which describe all of this stuff do not allow mass. Period. It's easy enough to modify the equations of motion to add mass to them, but it leads to a contradiction (I forget the details).

This is where the Higgs mechanism comes in: it's an interaction in the standard model which gives particles effective mass depending upon how they interact with the Higgs field. And it's why the Higgs boson was predicted decades before it was discovered.

So, far from lack of mass preventing interactions, interactions between massless particles are what creates mass in the first place!

 

[Vanadium 50]

But the real reason why I find your question so interesting is that the equations which describe all of this stuff do not allow mass. Period. It's easy enough to modify the equations of motion to add mass to them, but it leads to a contradiction (I forget the details).

Probably because this isn't quite right.

The force carrier cannot have mass.

The matter particles can, in general, have mass. There are cases where they don't, but it is not a general prohibition.

If interested in discussing this further, it probably belongs in its own thread.

 

[PeterDonis]

The matter particles can, in general, have mass. There are cases where they don't, but it is not a general prohibition.

Not a general prohibition, but a Dirac mass term for the fermions is prohibited in the Standard Model, since it would require left- and right-handed fermions to belong to the same representations of the gauge groups, and they don't.

 

[Vanadium 50]

So, we're going to hijack this thread, as well as take it beyond B level. OK, you're the Mentor.

In QED, a mass term is allowed.
In electroweak theory, it is not allowed because the couplings are chiral.
QCD is complicated. I don't know the answer there. The couplings certainly are not chiral, but flavor has many subgroups that I'd have to think about harder.

 

[PeterDonis]

In QED, a mass term is allowed.
In electroweak theory, it is not allowed because the couplings are chiral.
QCD is complicated. I don't know the answer there. The couplings certainly are not chiral, but flavor has many subgroups that I'd have to think about harder.

In the Standard Model, though, all fermions are in some representation of all of the gauge groups, so if a mass term is not allowed for any of them, it's not allowed, period.

 

[Vanadium 50]

Well sure. Nature has all the forces in it.

 

[kimbyd]

To sum up a bit of the above discussion, because it is a B thread:

The Higgs mechanism was originally proposed to solve some weirdness with the weak nuclear force. As Vanadium 50 mentioned, the force carriers very clearly cannot have mass. But the force carriers for the weak force do. The Higgs mechanism was proposed to solve that problem.

It was later discovered that matter particles can pick up mass from the Higgs field as well through a different mechanism. And the fact that the weak force is not left/right symmetric turns out to also exclude fundamental mass for the matter particles.

So it really does look like mass isn't a fundamental property of anything, at least in our universe.

 

[PeterDonis]

Moderator's note: Discussion of the initial state of the universe has been moved to a new thread in the Beyond the Standard Model forum:

https://www.physicsforums.com/threads/initial-state-of-the-universe.1005071/

 

[ohwilleke]

Photons undeniable have a "role in the beginning of the universe" and lack rest mass. So do the gravitons that are generically parts of any quantum gravity theory. So do gluons which give rise to baryon mass dynamically but do not themselves fundamentally have rest mass.

 

[Prishon]

Summary:: Is it possible for particles, any of them to have had some role in the beginning of the universe, despite not having mass?

I recall reading someone questioning if it were possible for the higgs boson to be the primordial atom which led to the start of the universe. I was just wondering if that could even be possible, since the higgs field was zero and couldn't have given these particles any mass. (please be kind, I'm not a physicist, I'm not in school for physics, I was just reading about it and was curious.)

*If* you believe in the Higgs field in its present form (I dont) then its energy was high when the field was zero.

 

[Prishon]

*If* you believe in the Higgs field in its present form (I dont) then its energy was high when the field was zero.

What about gluons?

 

[PeterDonis]

What about gluons?

What about them? You realize you're responding to yourself, right?

 

[PeterDonis]

*If* you believe in the Higgs field in its present form (I dont)

This comment is out of place in a "B" level thread, and even in a more advanced thread, it would need to be supported by some kind of reference to an alternative model. Otherwise it is personal speculation and off limits here at PF.

 

[Prishon]

What about them? You realize you're responding to yourself, right?

Was I responding to myself? I can't see that. I have to get used a bit here. It's my day...☺ Dont gluons have zero mass while interacting with one another?

 

[PeterDonis]

Dont gluons have zero mass while interacting with one another?

Yes. As was already indirectly implied in post #9 and stated explicitly in post #17.

 

[PeterDonis]

Was I responding to myself?

Yes: the quote in that post is from a previous post by you.

 

[Prishon]

Yes: the quote in that post is from a previous post by you.

So I should have posted the comment on its own? I will figure out the bedt ways to do it. Would you know if I made this comment for you on its own?

 

[PeterDonis]

So I should have posted the comment on its own?

If you were just making the comment about gluons that you made in post #22, you could have made that on its own, without quoting anything, sure.

I will figure out the bedt ways to do it.

The best way to make sure you are posting what you intend to post is to proofread your post before you post it.

 

[ohwilleke]

*If* you believe in the Higgs field in its present form (I dont) then its energy was high when the field was zero.

The "running" of the Higgs field at high energies to which you allude is really an "advanced" or "intermediate" level issue rather than one that makes much sense at a basic level, but since you mention it, I'll briefly sketch out these considerations.

Moreover, all statements about what happen at extremely high energies need to be taken with a grain of salt because we can't probe those energy scales experimentally, or with observational evidence.

Nonetheless, it is possible, consistent with the Standard Model of Particle Physics, for the Higgs field to go to zero for a very brief moment, but almost immediately, it goes from zero to non-zero but extremely small, which is qualitatively different (i.e., different in kind, and not just different in degree).

The Universe has an upper energy bound, i.e. the energy scale of the Big Bang itself, rather than admitting infinitely high energies. This is in the general vicinity of the GUT scale or the Planck scale:

The most powerful collider to date, the Large Hadron Collider (LHC), is designed to reach a center of mass energy of 1.4x10⁴ GeV in proton-proton collisions. The scale 10¹⁶ GeV is only a few orders of magnitude below the Planck energy of 10¹⁹ GeV[.]

So, above that threshold, describing the laws of physics in the Universe is basically a category error, because there is no such Universe to have laws of physics. We don't know precisely what that threshold is, but it is undoubtedly finite, so any theory that is asymptotically safe as a result of an ultraviolet (i.e. high energy) upper bound at that scale, can be consistent and complete, even if it can't be generalized to arbitrarily high energy scales.

The mass of the Higgs boson and its beta function (i.e., the formula which governs how the strength of the Higgs field weakens at higher energy scales and can be determined exactly from first principles in the Standard Model) implies that the Higgs field weakens to zero in the general vicinity of the maximal Big Bang energy, although uncertainties in the Higgs boson mass and top quark mass which go into this calculation introduce considerable uncertainty into determining this threshold.

The beta function of the Higgs field used to determine when it reaches zero also omits the impact of gravity, which can safely be ignored at LHC energy scales, but which is material in determining at what energy scale the Higgs field weakens to zero at energies close to that of the Big Bang like the GUT scale, because if quantum gravity really exists, the existence of quantum gravity alters the exact terms of the Higgs field beta function, tweaking it in a way that is material in the extremely high energies of the first few moments of the Universe.

Note also, that even if the Higgs field went to zero (making the masses of all of the fundamental particles in the Standard Model zero), none of the three Standard Model forces (electromagnetism, the strong force, and the weak force) go to zero at these energies as shown in Figure 7a below. And, since hadrons (i.e. protons and neutrons and pions and kaons) all have masses that come from the strong force, rather than from the Higgs field, even in the theoretical limit of quarks with zero mass, the Universe would not cease to have massive particles interacting via the three Standard Model forces and gravity, even at this high energy threshold.

ADVANCED DETAILS

As the charts below illustrate, the Standard Model running of the Higgs field may be well defined and non-zero to a scale in excess of the GUT scale, but not quite to the Planck scale, although this could break down at a scale with a best fit value of 10¹⁰ GeV (which is a million times higher in energy that the peak LHC energies and a million times lower than the GUT scale). But considerable uncertainty that could increase that threshold by many orders of magnitude.

This observation is closely related to the determination that the Higgs vacuum is "metastable", although within reasonable experimental and theoretical uncertainty (even before considering beyond the Standard Model physics at high energies that can't be ruled out from other observations) for the reasons set below which explain why the zero value of the Higgs field and metastability are so entwined:

Higgs vacuum sits very close to the border between stable and metastable within 1.3 standard deviations of being stable. . . .

Vacuum stability depends on the ultraviolet behaviour of the Higgs boson self-coupling λ, that is, its behaviour at the maximum possible energy scales. The SM couplings evolve with changing resolution (energy scale) according to the renormalization group, as shown in Fig. 7a. The weak SU(2) and QCD SU(3) couplings, g and gs, are asymptotically free, with 𝛼𝑖=𝑔2𝑖/4𝜋 decaying logarithmically with increasing resolution, whereas the U(1) coupling 𝑔′ is non asymptotically free, rising in the ultraviolet. The top quark Yukawa coupling y_t decays with increasing resolution. The running of the Higgs boson self-coupling λ determines the stability of the electroweak vacuum. Instability sets in if λ crosses zero deep in the ultraviolet part of the spectrum and involves a delicate balance of SM parameters. With the SM parameters measured at the LHC, λ decreases with increasing resolution. This behaviour is dominated by the large Higgs boson coupling to the top quark (and also QCD interactions of the top). Without this coupling, λ would rise in the ultraviolet. In Fig. 7a, λ crosses zero around 10¹⁰ GeV with the top quark pole mass of m_t = 173 GeV and m_H = 125 GeV. This situation signals a metastable vacuum with lifetime greater than about 10⁶⁰⁰ years (ref.137), much longer than the present age of the Universe, about 13.8 billion years (see also Fig. 1b). Figure 7b shows the sensitivity of vacuum stability to small changes in m_t. If the top mass is taken as 171 GeV in these calculations, the vacuum stays stable up to the Planck scale. The measured 125 GeV Higgs boson mass is close to the minimum needed for vacuum stability with the measured top quark mass.

So, the Higgs vacuum could be just barely stable at this upper bound. Similarly, one published paper notes that:

Once radiative corrections are taken into account, the stability of the Higgs vacuum is very sensitive to the value of the top quark mass.

The the top quark pole mass has an experimental uncertainty about about 0.17% (about 300 MeV/c² according to direct measurements but realistically somewhat larger than that given the spread of determinations by different means) which is still material for many purposes including this one.

 

[PeterDonis]

The Universe has an upper energy bound, i.e. the energy scale of the Big Bang itself, rather than admitting infinitely high energies

Where are you getting this from? Do you have a reference?

 

[ohwilleke]

Where are you getting this from? Do you have a reference?

It follows from the fact that there is a finite amount of mass-energy in the Universe, and conservation of mass-energy (with the possible exception of dark energy/cosmological constant which is negligible at the time of the Big Bang by construction), which is very basic and uncontroversial premises of the Big Bang theory of cosmology. See, for example, https://en.wikipedia.org/wiki/Chronology_of_the_universe (setting for temperatures in the very early instants of the Universe in Standard Cosmology).

Even if you consider gravitational negative energy as a concept (which I am referencing not as authority but just to clarify my terminology) which is more advanced and controversial, it still gets you only to zero, which is also obviously finite.

A good background discussion of asymptotic safety which I oversimplify in my comment can be found in this published open source paper (Eichhorn 2019) (particularly Part 5). See also here and here. Also here (discussing distinction between classical GR singularity Big Bang at infinite temperature and limitations on that in a quantum gravity scenario).

 

[Prishon]

It follows from the fact that there is a finite amount of mass-energy in the Universe, and conservation of mass-energy

But that is exactly the question. Where did you get that from?

 

[PeterDonis]

It follows from the fact that there is a finite amount of mass-energy in the Universe

Only in the observable universe. The universe as a whole is spatially infinite.

conservation of mass-energy

Which is a local concept in GR, not a global one. In a non-stationary spacetime, such as the spacetime that describes our universe as a whole, there is no conserved global energy.

which is very basic and uncontroversial premises of the Big Bang theory of cosmology

I think you are either misunderstanding or misstating the theory.

 

[PeterDonis]

Even if you consider gravitational negative energy as a concept (which I am referencing not as authority but just to clarify my terminology) which is more advanced and controversial, it still gets you only to zero

This concept of "total energy" is meaningless since it is zero for any spacetime whatever in GR.

 

[PeterDonis]

A good background discussion of asymptotic safety which I oversimplify in my comment can be found in this published open source paper (Eichhorn 2019) (particularly Part 5). See also here and here. Also here (discussing distinction between classical GR singularity Big Bang at infinite temperature and limitations on that in a quantum gravity scenario).

All of these are speculative quantum gravity models, not mainstream cosmology. Discussion of them belongs in the Beyond the Standard Model forum, not here.

Also, it is rather inconsistent of you to first emphasize that all physics above energy scales we can currently probe is speculative and should be taken with a grain of salt, and then to inundate us with such speculations.

 

[Prishon]

Why should energy not be conserved globally?

 

[PeterDonis]

Why should energy not be conserved globally?

In GR, it's more that there isn't even a well-defined global concept of "energy" except in a special class of spacetimes (the stationary spacetimes).