Photons, bosons and mass?

[Highlord Laan]

Okay. While running though some online science videos, I stumbled across one on the Higgs Boson, the mass of particles, ect. One thing stuck out for me, because it's one of the few my unexercised mind remembered from high school physics.

Mass and energy are related, right? For something to have or carry energy, it must have mass, if something has mass, it inherently has energy. Electrons, protons, quarks, they all have mass, they all carry energy. But what about photons? They have energy, but do not have mass?

Doesn't that rather blatantly violate the law of conservation of energy? Obviously I'm missing something, misunderstanding something, or almost certainly both.

[SCRawl]

You should start by examining your premise. Why is it that you think something must have mass to have energy?

[MrDakka]

IIRC photons have zero rest/invariant mass, but they have momentum, which can be related to energy. The following links should help.

http://en.wikipedia.org/wiki/Energy%E2% ... m_relation
http://www.reddit.com/r/askscience/comm ... _momentum/
http://www.askamathematician.com/2010/0 ... t-no-mass/

[Borgholio]

Mass is only related to energy directly when you are trying to convert one to the other (E=MC squared). Otherwise, energy is not necessarily based strictly on mass. A lightweight particle traveling at high speed can possess far more kinetic energy than a massive particle at a slow speed. In that case, the amount of kinetic energy is related to the speed of the object, not *just* it's mass.

Likewise the energy state of an electron in an atom is based on the energy it absorbs from an exterior source, not the mass of the electron.

[Magis]

Anything that has energy has mass. Anything that has mass has energy. Mass and energy have an equivalency. That doesn't mean that mass and energy are the same thing - they have different units, after all. But the concept of mass and energy are inseparable. A particular quantity of energy is associated with a particular quantity of mass. The relationship is expressed mathematically through the famous E = mc2.

Here are some examples: when a particle is accelerated, its mass increases because its kinetic energy has increased. When you carry a rock up a hill, it's mass increases because its gravitational potential energy has increased. Those changes in mass are not easily measured because the change in energy is small, and the corresponding change in mass (measured in kilograms, for example) is extremely tiny -> m[kg] = E [Joules] / (9x10^16 [m^2/s^2]).

When a bunch of neutrons and protons come together to form a nucleus, their combined mass decreases because their potential energy has decreased - the reduction in mass is called the mass deficit, and the corresponding energy difference is the same as the binding energy of the nucleus. This change in mass is very measurable because the binding energy is enormous.

Photons have mass. One way to know for sure that they have mass is that they have energy. The amount of mass a photon has is expressed by E=mc^2, just like everything else. The mass-energy equivalency applies to photons just like it applies to everything else. It is often said that photons are massless, but you can essentially think of that is just a figure of speech. In proper terminology, photons have no invariant mass, meaning that there is no component of a photon's mass that is independent of the frame of reference.

In many introductory science classes and texts, it's common to encounter a phrase like, "the difference between chemical energy and nuclear energy is E=mc2" or "nuclear reactions produce so much energy because there is a change in mass". These types of phrases are completely misleading and they do a great disservice to students. E=mc2 always applies. It applies to water going over a waterfall, and the burning of fossil fuels, and to everything. Mass can never be separated from energy. Ever.

[Darth Holbytlan]

The problem here is that both mass and energy are not invariants. In different frames of reference—that is, for different observers moving at different velocities—mass and energy also differ. These are called relativistic mass and energy. But it is useful to also have measures for mass and energy that are the same in all frames of reference. These measures are called the rest mass and energy of an object, and are the same as the relativistic mass and energy as measured from a frame of reference where the object isn't moving.

Where things get confusing is that "mass" often means rest mass while "energy" often means relativistic energy. E=mc2 is the correct formula when both E and m are relativistic measures (or rest measures), but it is not correct when E is relativistic while m is a rest mass (often written m0). The correct formula in that case is E2=m02c4+|p|2c2, where p is the momentum of the object. This also means that when we talk about objects gaining mass as they accelerate (and therefore gain momentum), we're talking about their relativistic mass increasing.

So what about photons and other "massless" particles? They are always measured as traveling at c in every frame of reference, so there's no frame of reference in which to measure the rest mass or energy. But as you might guess from the name, the correct rest mass for them is 0. Plugging m0=0 into the formula above produces E=|p|c, which is the correct formula for the energy of a photon.

In summary: All things that have relativistic mass have relativistic energy (and vice versa), and all things that have rest mass have rest energy (and vice versa). Photons (and any particle that travels at the speed of light) have no rest mass and no rest energy, but they do have momentum and relativistic energy, and therefore relativistic mass.

[Kuroneko]

I would advise you to simply forget about 'relativistic mass'. It's a silly, useless concept. It was designed to preserve the Newtonian kinematic relations, such as p = mv, in special relativity: p = Mv, where M = m/sqrt(1-v²) = γm is the 'relativistic mass'. Except it really fails to do the very thing it was designed for: 'relativistic mass' is not actually any kind of mass at all, because it does not characterize inertia. In a hopeless attempt to keep the Newtonian formulas, people then invented 'longitudinal mass' γ³m and 'transverse mass' γm: when one forces special relativity into Newtonian mold, "mass" depends on direction.

In conceptually saner physics, there is only one kind of mass, and it is invariant across frames and directions. It simply the norm of the four-momentum vector (E,p): momentum in spatial directions is the regular momentum, and momentum in a time direction is energy, and the norm of the vector is m, where (mc²)² = E²-|pc|².

Anything that has energy has mass. Anything that has mass has energy. Mass and energy have an equivalency. That doesn't mean that mass and energy are the same thing - they have different units, after all. But the concept of mass and energy are inseparable. A particular quantity of energy is associated with a particular quantity of mass. The relationship is expressed mathematically through the famous E = mc2.

This is only underlines just how useless 'relativistic mass' is: since c is a constant, any and all mention of 'relativistic mass' is strictly equivalent to energy up to a factor of c². Thus, it is completely redundant at best: we already have 'energy', so there's no need for some special term of what to call it if we divide it by a constant.

But it gets worse. Taking 'relativistic mass' seriously invites wrong-headed thinking. Suppose you have a beam of light going in some direction, with total energy E. Its 'relativistic mass' is the E/c². Does that mean that the beam has can be turned into a particle of mass E/c²? Absolutely not: the actual mass of the light beam is zero, it is both invariant and conserved, and no physical process will turn the beam into a massive particle.

However, if you have light going in multiple directions, it will have some mass. That's because mass isn't additive; the mass of a system of is given by (mc²)² = E²-|pc|² using total energy and total momentum, rather than being the sum of the masses of its individual parts.

It is often said that photons are massless, but you can essentially think of that is just a figure of speech. In proper terminology, photons have no invariant mass, meaning that there is no component of a photon's mass that is independent of the frame of reference.

That is the exact opposite of reality. The norm of four-momentum is independent of the frame of reference, and the four-momentum of a photon has zero norm.

These types of phrases are completely misleading and they do a great disservice to students. E=mc2 always applies. It applies to water going over a waterfall, and the burning of fossil fuels, and to everything. Mass can never be separated from energy. Ever.

I think your phrasing does a much greater disservice to students. You're using 'mass' for something that's completely redundant with 'energy' and in the process conceptually muddying of one of the most important quantities of physics, one that is both invariant and conserved. Your approach is not just useless; it's actively harmful to understanding physics.

If one wants to get much of anywhere with understanding relativity, understanding four-momentum is essential. And in modern particle physics, understanding the mass as the Casimir invariant of the Poincaré group is likewise essential. Wigner's classification that enshrined this approach into quantum field is already 75 years old. It's way past time to move away from 'relativistic mass', or at the very least recognize that the unqualified 'mass' should refer to the much more useful invariant concept, rather than a rescaling of energy by a constant factor. (Well, that's already so in modern physics, and has been for many decades.)

[Zeropoint]

Absolutely not: the actual mass of the light beam is zero, it is both invariant and conserved, and no physical process will turn the beam into a massive particle.

Ahem: http://en.wikipedia.org/wiki/Pair_production

[Kuroneko]

Ahem: http://en.wikipedia.org/wiki/Pair_production

Yes? In the process γ + γ → e⁺ + e⁻ or similar, the mass before and after is the same. I've covered why above:

However, if you have light going in multiple directions, it will have some mass. That's because mass isn't additive; the mass of a system of is given by (mc²)² = E²-|pc|² using total energy and total momentum, rather than being the sum of the masses of its individual parts.

The same reason explains why the masses of protons and neutrons comes almost entirely from their gluon cloud, even though gluons themselves are individually massless.

[Magis]

I would advise you to simply forget about 'relativistic mass'. It's a silly, useless concept.

General relativity, like all scientific theories, is used to make meaningful predictions related to experimental observations, which is why it's useful. It's true that relativistic mass is conceptually a bit different from classical mass - and in fact the classical concept of inertia doesn't really apply in general relativity at all - but who cares? Why be caught up on semantics? Clearly relativity is useful because its predictions are reliable, and relativistic mass is a part of relativity.

In conceptually saner physics, there is only one kind of mass, and it is invariant across frames and directions.

I wonder how in your "saner physics" you account for things like increased gravitation from relativistic mass vs. invariant mass.

You're using 'mass' for something that's completely redundant with 'energy'

So what? In the field of electric circuits, current, voltage drop, and resistive heating contains a redundancy. That doesn't mean that each property isn't useful and that we should just throw one out and never talk about it.

and in the process conceptually muddying of one of the most important quantities of physics,

Apparently, according to you, virtually every physicist on Earth is on the wrong side of your "let's think about mass the same way as they did hundreds of years ago despite our increased understanding of physics" argument.

one that is both invariant and conserved. Your approach is not just useless; it's actively harmful to understanding physics.

You clearly misunderstood my point. My point is that it's wrong to suggest that changes in relativistic mass only occur on nuclear scales. Suggestion that relativistic mass changes occur only during nuclear interactions is in fact what actively harms a student's understanding of physics.

[Kuroneko]

General relativity, like all scientific theories, is used to make meaningful predictions related to experimental observations, which is why it's useful. It's true that relativistic mass is conceptually a bit different from classical mass - and in fact the classical concept of inertia doesn't really apply in general relativity at all - but who cares? Why be caught up on semantics? Clearly relativity is useful because its predictions are reliable, and relativistic mass is a part of relativity.

Physicists generally care about the conceptual clarity of their theories. Examples of relativists that are explicitly against the concept of 'relativistic mass' include Edwin F. Taylor and John A. Wheeler. Many are simply content to ignore it. If we widen those parameters to include people with a great stake in special relativity, which includes particle physicists, that includes a lot more.

I wonder how in your "saner physics" you account for things like increased gravitation from relativistic mass vs. invariant mass.

It deals with them very well, considering my "saner physics" is in fact the standard approach in modern relativity, in as much as one can be said to exist: in any case, though there are treatments of GTR that endorse 'relativistic mass' and others that explicitly repudiate it, most don't even bother mentioning it at all.

Moreover, in general relativity it's a mistake to think of mass (whether relativistic, invariant, transverse, or longitudinal) as the source of the gravitational field. The source of the gravitational field is the entire ten-component stress-energy tensor, and the gravitational charge is energy, not mass.

So what? In the field of electric circuits, current, voltage drop, and resistive heating contains a redundancy. That doesn't mean that each property isn't useful and that we should just throw one out and never talk about it.

But it is useless, the commonly used units of c = 1 make it doubly so. But even if one acknowledges it be a useful heuristic, it's still wrong to call it simply "mass" as you did, because that's definitely against the parlance of the overwhelming majority of physicists.

Apparently, according to you, virtually every physicist on Earth is on the wrong side of your "let's think about mass the same way as they did hundreds of years ago despite our increased understanding of physics" argument.

"Virtually every physicist on Earth"? Not even close. Just with the more famous GTR texts:
-- Weinberg, Gravitation and Cosmology (1972) acknowledges that 'relativistic mass' exists but promptly dismisses it in the same paragraph, saying that throughout 'mass' refers always to the invariant quantity.
-- Misner, Thorne, and Wheeler, Gravitation (1973), commonly though facetiously called "the Bible of general relativity", don't mention 'relativistic mass' anywhere, at all.
-- Wald, General Relativity (1984) does not acknowledge 'relativistic mass' anywhere at all. Wald introduces 'rest mass' at first, but then simply drops the qualifier in the same paragraph, calling it 'mass'. Elsewhere, he's not too careful: sometimes "rest mass", sometimes de-emphasized parenthetical "(rest) mass", and sometimes simply "mass".
-- d'Inverno, Introducing Einstein's Relativity (1992) does actually explicitly endorse 'relativistic mass'. He's kind of an odd duck, it seems to me.
-- Taylor and Wheeler, Spacetime Physics (1992) are explicitly against the concept: "[γm] is total energy, not mass."
Among relativists, endorsement of 'relativistic mass' appears to me to be spotty at best, and probably an outright minority in modern times, though most GTR books appear to simply ignore the concept altogether (as more examples, Hartle does that, and so does Carroll), with only a few being explicitly against it. Additionally, modern journal articles in GTR don't ever seem to use the concept.

Outside general relativity, things are more lop-sided. For example, Griffith's electrodynamics textbook calls relativistic mass archaic and old-fashioned, advising one to avoid it. And of course, for the particle physicists, 'mass' only ever means the invariant quantity, again because Wigner's classification makes that conceptually essential in quantum field theory.

[Zeropoint]

Yes? In the process γ + γ → e⁺ + e⁻ or similar, the mass before and after is the same. I've covered why above:

Well, it's a physical process that turns a beam of light into a massive particle.

[Kuroneko]

Yes? In the process γ + γ → e⁺ + e⁻ or similar, the mass before and after is the same. I've covered why above:

Well, it's a physical process that turns a beam of light into a massive particle.

If the photons are unidirectional, then pair production cannot happen, no matter how many photons there are in the light beam, how intense the light beam is, etc. Such a light beam is massless, so no physical process will turn any of it into anything massive (without taking away mass from something else, anyway). That's why I contrasted that case with photons going in multiple directions in the very next paragraph. Sorry if it was unclearly phrased.

[Zeropoint]

Pair production happens with individual photons, and I think we can agree that a single photon is unidirectional.

[Kuroneko]

Pair production happens with individual photons, and I think we can agree that a single photon is unidirectional.

Such a process would violate both conservation of four-momentum and conservation of mass. If what you're thinking of is pair production that can happen when one photon interacts with a nucleus, or whatever else, that's not a case of pair production with an "individual" photon.

That light of energy E traveling along one direction has E = |p|c has been known since the 1870s or thereabouts, and that this implies that its (invariant) mass is zero is introductory special relativity 101. The point of the original paragraph you're disputing is that you can't make create massive particles without mass already being there. The fact that you could use a single photon to take away mass from a nucleus and get a massive electron/positron pair out of the process does nothing to dispute that point.

Are we clear now? If I've made it insufficiently clear in my first post that I intended to take the light by itself, I've already apologized for that above and clarified my intended point: you can't get massive particles out of this light beam "without taking away mass from something else". Getting massive particles out of just light requires photons in multiple directions.

[Zeropoint]

As I understand it, pair production via nucleus doesn't take mass away from the nucleus, it simply uses the nucleus for momentum exchange. The mass of the electron/positron pair comes entirely from the energy of the photon.

Anyway, we all agree that energy CAN be turned into mass.

[Simon_Jester]

What definitions are you using for mass and energy? The classical ones?

[Kuroneko]

Anyway, we all agree that energy CAN be turned into mass.

Only as a crude analogy. If the photon has energy E in the rest frame of the nucleus (mass M), then the combined photon+nucleus system has mass m = √((M+E)²-E²) = M√(1+2E/M). So you're not turning energy into mass, because all the mass is already there. But you're right in that that does mean that the mass is taken (redistributed) from the combined system, not the nucleus alone.

What definitions are you using for mass and energy? The classical ones?

I'm using 'mass' to mean 'magnitude of four-momentum', which is used in both classical and quantum relativistic physics, and energy is its time component. A more general definition of 'energy' that can be applied equally well in both classical and quantum physics, ads well as both relativistic and non, would be 'Noether charge of time translation symmetry'.