Physics Has Demoted Mass
nautil.us
nautil.us
A particular advantage to intuition comes with the famous e=mc^2. Since c is 1, and 1^2 is 1, e=m. Energy and mass are completely equivalent. Strong force binding energy in a proton is mass. The only bit that's not straight from binding energy is from the Higgs mechanism, which is where the mass of the electron (and the quarks themselves) comes from. Matt Strassler has an excellent explanation of that: https://profmattstrassler.com/articles-and-posts/particle-ph...
Henry Poincaré wrote exactly this in 1902 in "the science and hypothesis" Nous sommes acculés à la définition suivante, qui n'est qu'un aveu d'impuissance : les masses sont des coefficients qu'il est commode d'introduire dans les calculs.[0]
I am also happy for the reference to the excellent blog of Matt Strassler
It's because of people's fondness for legacy and backwards compatibility that we don't use natural units all the time, and still write "e=mc^2". I find this insane, personally, but that's just the way it goes.
I guess I should add that apparently this is still controversial? But in my mind, the only reason for this is that people find meaning in units. In this case, ME being the same property implies duration being exactly the same as length, which implies spacetime is a unified, regular 4D manifold. ME not being the same property implies time is special. I've been fully persuaded that duration is fundamentally exactly the same thing as length, so I've chosen my side, in case there's any serious controversy.
Definitely not. Everything couples to the stress-energy tensor, but not every type of particle has rest/invariant mass. No one really speaks in terms of relativistic mass anymore. (So a photon has energy but no rest mass.)
I'm well aware of the practical value and conceptual clarity of natural units. They are just not being explained well in this thread. "What the teacher really meant was..." is not a good defense when the student doesn't understand.
There is a "real" distinction between [light]seconds of distance and seconds of time, but it's a difference in what is being measured, not in how it is quantifiable. Measuring them with the same units doesn't imply that they are perfect substitutes, any more than one could arbitrarily replace an ounce of gold with the same weight of feathers; in practice, they are non-interchangeable enough that gold is even measured with a different type of "ounce". Likewise with spacetime: for most purposes human non-physicists think about, they are completely non-substitutable. So practically, it works well to use a "Troy" sort of system for one. But it's a purely human distinction.
I agree! Please read my comments carefully. I am not arguing against the usefulness or deep conceptual importance of natural units! I am critiquing the terrible explanations being given in this thread.
> Likewise with spacetime: for most purposes human non-physicists think about, they are completely non-substitutable. So practically, it works well to use a "Troy" sort of system for one. But it's a purely human distinction.
No! Space and time are not interchangeable in any universal sense even if they are universally linked by a symmetry. A space-like interval and a time-like interval cannot be interchanged with each other by a Lorentz transformation. The distinction between space-like and time-like intervals is observer independent.
There's only so much clarity you can fit into a HN comment.
Not more than changing unities from meters to feet, or kg to pounds.
When two unities are related by a constant, they are measuring the same thing.
Yes but that is still true (E=m) if c<>1, since c is a constant. It's just a question of scale, isn't it?
James Joule discovered that heat and work can be related by:
h = kw
But really, this isn't a relationship between heat and work. This is a statement of equivalence. The constant of 4.184cal/J just tells you how the two units differ. They both describe the same property. Really, h = w. The version with k is only needed if you insist on using the traditional, different units on the left and right sides.
The same is true of e = mc^2. This does not tell you how two different fundamental properties are related, it merely tells you how two units, traditionally considered separate, actually measure the same underlying property. Really, e = m. The c^2 is only needed if you insist on using J on one side and kg on the other.
That is to say, you absolutely can have a kilogram of energy. If you have an object with a mass of one kilogram, you do have a kilogram of energy. Physicists and engineers don't typically use that unit for energy, but there's no reason they couldn't, and likewise no reason they couldn't use joules for mass.
So any time two physical quantities are related by a constant factor -- even if said constant factor has what we currently think of as "units" (and even particularly weird units like squared speed) -- they are fundamentally equivalent. I'm still mulling this over, but it's a pretty fascinating mental revelation for me.
Edit: I also want to say that I didn't find the comment I replied to rude in any way. It's direct and straightforward, but that's pretty common around here.
In natural units, c is "unitless" (AKA dimensionless), by definition.
Maybe someone has a link that goes into more depth on why all of this is okay?
When using a pseudo-Riemannian manifold one uses a metric signature where (keeping it simple, cf. "metric signature" on wikipedia) coordinates on orthogonal dimensions of can take one sign, or the opposite sign and a constant multiplier. In the Lorentzian case there will be one dimension taking one sign, and one or more taking the other; the choice of whether the solitary dimension takes a + or - sign is a matter of convention or preference. Conventionally the solitary dimension also takes the constant multiplier and is called the timelike dimension. A Lorentzian signature (minuses, 1) or (1, plusses) guarantees that one can describe paths through the manifold as null, timelike, or spacelike, and this gives one a causal structure.
Our universe can be well represented by a Lorentzian manifold (3, 1) or (1, 3), and this has been tested to exquisite precision. It does not tell us the value of the constant c, but we can determine that from tests of causal relations, the boundaries of which will be null. Alternatively, a massless pointlike object will always travel on null geodesics.
One runs into c being set to unity in systems geometrized units in relativity often; it's very handy to have mark off coordinates as e.g. "-seconds" vs "c seconds" (-,+,+,+ aka (1,3)) as long as one doesn't mess up one's dimensional analyses (which is unfortunately easy).
As a concrete example, the line element for (1,3) flat spacetime using Cartesian coordinates is dS^2 = -c^2dt^2 + dx^2 + dy^2 + dz^2. Compare the formula for Euclidean distance in the (Euclidean flat) plane between points p = (p1,p2) and q = (q1,q2) for (x,y) coordinates: d(p,q) = sqrt((q1-p1)^2 + (q2-p2)^2), which we could rewrite as dx = q1-p1, dy = q2-p2, ds = sqrt(dx^2 + dy^2) or ds^2 = dx^2 + dy^2. In Euclidean 3-space, we add another axis: ds^2 = dx^2 + dy^2 + dz^2. In Lorentzian 4-spacetime, we have to change the sign, so ds^2 = dx^2 + dy^2 + dz^2 - c^2dt^2. Note that we are not restricted to use any particular unit of distance or system of units; dx could be in metres, miles, astronomical units, light-years, gigaparsecs or practically anything else, while dt could be in seconds or fortnights or any other handy unit of time. When setting c to unity, we do need to choose appropriate units for dx (and dy and dz ...) vs dt. In SI units, that's seconds and light-seconds, but we could use another system if we wanted.
Notably we aren't restricted to Cartesian coordinates, however if we were to change to some other system of coordinates (e.g. polar ones) the line element would need to reflect that. For example, in the Lorentzian 4-spacetime case, we would write ds^2 = dr^2 + r^2 * dtheta^2 + r^2sin^2(theta)dphi^2 -c^2dt^2.
Finally, when using SI units (for example), one can see very clearly that a path taken by an object moving much slower than the speed of light is totally dominated by the amount of time between starting point and finishing point, because the value of c is large. Using the (+,-,-,-) metric signature [ds^2 = c^2dt^2 - dx^2 - dy^2 - dz^2], a large c helps make it clear that lightlike paths through spacetime are shorter, and purely timelike paths (where dx=0, dy=0, dz=0, dt != 0) have extremized length, since we don't subtract anything from cdt. This is the root of the explanation of the twin paradox in flat spacetime: the twin moving quickly compared to the speed of light takes a shorter path between together1 = (x1,y1,z1,t1) and together2 = (x2,y2,z2,t1) than the twin moving slowly compared to the speed of light. In the extreme, twin A holds x=const,y=const,z=const, whereas twin B's x coordinate is only equal to twin A's at the start and end of the journey. This holds up under any system of coordinates; we could consider r=const vs changing r in spherical coordinates, for instance.
That is clever, but you've already adjusted the mass to take into account the fact that you are now setting c=1. This reminds me of computer programming where, for the sake of an easy-to-read clarity, I decide to take one line of code and make it two. Basically, instead of doing this:
e=mc^2
You have decided to make it two lines of code:
m=mc^2
e=m
I often do that, especially if I'm working with junior devs and I want the code to be as easy as possible for them to read (90% of the time).
It's clever, but everyone should remember the assumption that allows this: the mass has already been adjusted to reflect the reality that of c=1.
Inertia is not merely something that depends on mass. It is mass.
(though from a brief web search, it is not typically presented as such)
For example, I said E=M. But that's for objects at rest. For an object in motion it's E^2=m^2c^4+p^2c^2. In natural units that turns into E=m+p. The energy of a photon is hf, where h is Planck's constant and f is the frequency. That energy is entirely the photon's momentum. And that's without getting into the issues of invariant mass or relativistic mass increases...
E² = m²c⁴ + p²c²
https://en.wikipedia.org/wiki/Unicode_subscripts_and_supersc...
A number of early computer systems used teletypes for I/O, and had programming languages in which exponentiation was expressed by moving a half line up, and array subscripts by moving a half line down.
But yeah, having a "next-is-superscript"-token would probably be cleaner than individual code points for every little glyph that might be a superscript...
Since mass also determines the speed of time to the observer, isn't a time machine basically just a thing that converts energy into mass?
I've never seen an author use metaphors or similies so poorly before. To draw parallels between something hard to grasp and something made up and vaguely defined in an effort to explain the former is.. ill advised at best. Then there's the fact that the author spends forever to explain basic chemistry then jumps into color charge in such a way that anyone not already intimately familiar with at least the terminology of quantum physics would never be able to understand, then the author jumps from topic to topic seemingly in a race to drop references to as many different concepts as possible without actually explaining any of them, almost like a student writing an essay then going back and swapping words with a thesaurus to seem better informed.
Even the science aside, the writing itself is rather atrocious. The author "answers" mysteries he never even asked or previously posed, and expects readers to already know what he's trying to say so he can refer to that in his explanations of why he said it.
Then the author has a tendency to jump from field to field, converting apples into oranges with the help of a long-dead scientist only so he can add them together in the most basic way and then convert them back to apples again. But he got to prove that he knows of Avagdro, so obviously there's that.
Usually Nautilus articles are written much better than this. If you value your sanity or actually care to understand the topic discussed, do yourself a favor and look elsewhere.
And jet, he knows his reader very well, and he delivers important bits of knowlege in very digestable form. Sure, this is not a substitution for reading a book.
But his target audience will never read that book, nor perform any research on their own.
Now i firmly remeber what QCD exist and firmly believe I don't know what it is about. Isn't it good, by itself?
There is no difference. They are two words that mean the same thing.
There are different kinds of mass-energy, some types are easy to convert into others, some types move at the speed of light, some don't. But there is nothing distinguishing mass from energy.
It was a revelation to see photons attracted by gravity - but once you realize it's energy that has a gravitational field [not just the particles we call mass], it would be surprising if photons were not attracted by gravity. (Although photons moving only at the speed of light have different equations governing their motion under acceleration.)
Now, all that said,
There is a distinction between things that only move at the speed of light, and things that never do. But the words energy and mass [as commonly used] do not properly fit those two categories.
That's not completely accurate. Chemical energy and binding energy are also Lorentz-invariant.
The only type of energy is not Lorentz-invariant is velocity energy, so you are putting your distinction in the wrong place.
On top of that, there are other violated invariants.
The weight of a lump of iron near a magnetar is greater than the weight of the same lump of iron near an identically massing neutron start.
This is because the potential energy of the iron is greater near the magnetic field, so its mass (as seem by the magnetar) is greater, and so is the gravitational attraction between them.
This means you can't just say "No velocity, the mass is identical", it's not - the extra potential energy means extra mass.
Or in other words there is no such thing as mass as distinguishable from energy.
The question is once it's there: Do the magnetar and the neutron star see different masses for the lump of iron?
Imagine the magnetar and the neutron star at the tips of an L, and the iron at the vertex.
In Newtonian mechanics, kinetic energy is rotationally but not Galilean invariant, sure. But in GR in a local inertial frame the pressure T^{ij}, i=j, i!=0 sure looks like kinetic energy \gamma m(v^i)^2. [1]
Should we really strongly distinguish between the pressure and T^00 just because in a local inertial frame the latter looks like \gamma mc^2 ? Sharpen the question by considering vastly different frames of reference.
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[1] https://en.wikipedia.org/wiki/Kinetic_theory_of_gases#Pressu...
The real mindbender is when you stop thinking about "things" and only consider the field values at each point in spacetime, where there is a strong relationship between the field values at here-and-now p1 and then-and-elsewhere p2. The "distinction" between field-values-at-p1 and field-values-at-p2 is largely a matter of identifying whether the spacetime interval between p1 and p2 is "lightlike", "null", or "timelike", which can be done in a Lorentzian spacetime like ours.
In a toy case where there is one massless particle in a spacetime, if its identifying non-vacuum field value is at p1, we can show that if p1 and p2 are not lightlike-separated, then the field value at p2 must be the vacuum value. Alternatively, if the particle is non-massles then if p1 and p3 are lightlike separated, then the value at p3 must be the vacuum value. In this way we can constrain where in the spacetime the particle may be found, and this is the core of the Initial Value Formulation of General Relativity[1]). That is the door to modern general relativity, and it's a pity it wasn't invented while Einstein was still alive.
In this view, if "things" move, it is only because we treat a pattern of field values as a "thing" and we decompose the spacetime into a space+time by deliberately making a (very weakly constrained) choice of time-separated spacelike volumes. But the fundamental picture is that the only objects are interacting fields which permeate the whole of spacetime taking on some value at each point, these fields including matter fields (and the energy-momentum tensor) as well as the metric (another tensor field).
> photons attracted by gravity ... energy has a gravitational field ... photons moving only at the speed of light
Here you have, without realizing it, split the various interacting matter fields up so that you can assign a worldline to one particular field value, then split up spacetime and applied coordinates so that you can cut up the worldline into "photon at t1", "photon at t2", "photon at t3". Then you have made a choice of gauge so that you can talk about a "gravitational field" which the photon appears (to an observer making those choices) to feel (and change! although you didn't point that out). These are perfectly reasonable things to do, but it is perhaps worth doing so deliberately and with the understanding that for each such choice there are other options.
> the words energy and mass [as commonly used] do not properly fit "things that only move at the speed of light and things that never do"
Well, if there is an identical field value in a massless field at lightlike-separated p1 and p2 then there will be an identical contribution into the values of energy-momentum tensor at p1 and p2. If we consider the components of the energy-momentum tensor, we can (in a suitable set of local coordinates) treat the 00 component of the tensor as "rest mass" with other components as other forms of energy (e.g. the 11, 22 and 33 components together can be treated as kinetic energy) or momentum (e.g. the non-diagonal components are momentum fluxes). The whole tensor is the source of spacetime curvature, not just the time-time component, which is the closest to what one would in common usage think of as mass.
Again, the crucial thing is that behind the common usage there are a substantial number of important choices that are not made by "nature", but rather by a person describing the relationship of some set of field values at some points in spacetime.
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[1] https://en.wikipedia.org/wiki/Initial_value_formulation_(gen...
tl;dr If you decompose matter all the way down, mass doesn't just "add up the parts to the whole". Not by several orders of magnitude!
https://www.youtube.com/watch?v=Ztc6QPNUqls&feature=youtu.be...
A force of a very special kind, because all other forces are strong, short-ranging (they need to interact, the only not-mechanical force) and repelling.
We have gravitational, weak, e/m and strong interaction.
Electromagnetic has the same range, only most objects seem to be neutral.
"Mechanical" force is normally electromagnetic.
The weak force is weak, but not as weak as gravitation (assuming normal charges)
The strong force has indeed short range but is attractive.
Gasping. For. Air.
I love that an article on units gets a unit conversion massively wrong.
Lost due to use of imperial units: 1998 Solar Heliospheric Observatory 1999 Mars Climate Orbiter
But he doesn't need to go into quarks for that. Simply comparing the masses of protons and neutrons (+ electrons) to the mass of an atom shows they're different. There's a little bit less mass due to the lower energy of the bound nucleons. Quarks certainly make the effect more dramatic though.
A more practical objection to using mass is that nobody can agree on what the word means. Does a photon have mass? Yes or no, depending on if you're thinking of relativistic or rest mass. If you call it energy, there's no ambiguity.
If I could recommend he change anything though, it would be the horrible mixture of units - MeV/c^2, atomic mass units, and grams. The author surely has the time to convert them all to the same unit so the reader can easily compare them. That would eliminate the need to explain Avogadro's law. It's a completely redundant complication of chemistry and has nothing to do with the fundamental concepts he's focusing on.