# Talk:Mass

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Wikipedia Version 1.0 Editorial Team / Vital

## Article is too technical

I added a "too technical" tag to the article. This is supported by the following discussion sections (and probably others):

"Mass" is such a common and fundamental quantity that an article on it in a general encyclopedia should be accessible by everyone (or at least there should be a clear distinction between the common meanings and the advanced physics ones). Brian Jason Drake 08:19, 22 September 2009 (UTC)

Brian Jason Drake 08:19, 22 September 2009 (UTC)

## Concept?

Not having had much success before, I will ask again, in its own section:

1. Why do we refer to "mass" as a "concept" and not a quantity?
2. How can a "concept" have units?

Brian Jason Drake 08:28, 22 September 2009 (UTC)

I've gone ahead and rewritten the introduction with some operational definitions of mass. It's far from perfect but it's a start. Strad (talk) 23:25, 22 September 2009 (UTC)

## active, passive, and inertial masses

by definition of active and passive gravitational mass, the force on mass1 due to the gravitational field of mass0 is:

$F_1 = \frac{Mass_0^{act} * Mass_1^{pass}}{r^2}$

likewise the force on a second object of arbitrary mass2 due to the gravitational field of mass0 is:

$F_2 = \frac{Mass_0^{act} * Mass_2^{pass}}{r^2}$

By definition of inertial mass:

$F = mass^{inertial} * acc$

if mass1 and mass2 are the same distance r from mass0 then by the experimentally proven Weak equivalence principle they fall at the same rate (their accelerations are the same)

$acc_1 = \frac{F_1}{mass_1^{inertial}} = acc_2 = \frac{F_2}{mass_2^{inertial}}$

hence:

$\frac{Mass_0^{act} * Mass_1^{pass}}{r^2 * mass_1^{inertial}} = \frac{Mass_0^{act} * Mass_2^{pass}}{r^2 * mass_2^{inertial}}$

therefore:

$\frac{Mass_1^{pass}}{mass_1^{inertial}} = \frac{Mass_2^{pass}}{mass_2^{inertial}}$

in other words, passive gravitational mass must be proportional to inertial mass for all objects.

Further by Newtons third law of motion:

$F_1 = \frac{Mass_0^{act} * Mass_1^{pass}}{r^2}$ must be equal and opposite to
$F_0 = \frac{Mass_1^{act} * Mass_0^{pass}}{r^2}$

it follows that:

$\frac{Mass_0^{act}}{Mass_0^{pass}} = \frac{Mass_1^{act}}{Mass_1^{pass}}$

in other words, passive gravitational masses must be proportional to active gravitational mass for all objects. Lemmiwinks2 (talk) 00:35, 25 September 2009 (UTC)

The above Newtonian formulas are utterly irrelevant: there is no distinction between "active" and "passive" gravitational force in Newtonian gravity. The distinction is made solely by advanced theoreticians working with General Relativity. Only a post-graduate physics student would be qualified to understand the distinction. I don't know why it is even mentioned in Wikipedia, let alone in the intoductory paragraph.77Mike77 (talk) 15:46, 16 February 2013 (UTC)

To summarise, inertial, active gravitational and passive gravitational masses must all be proportional, assuming the following are all true:
• the equivalence principle
• Newton's second law of motion
• Newton's third law of motion
Brian Jason Drake 06:46, 25 September 2009 (UTC)
I have created a list of known places where the above comment appears. Brian Jason Drake 11:41, 29 September 2009 (UTC)
Lemmiwinks2 deleted the section on their talk page containing that list. Revision 318510298 was the list revision containing that list. A cleaned-up version of the above comment now appears in the article "Equivalence principle". Brian Jason Drake 07:44, 28 October 2009 (UTC)

## Weight and amount section partly irrelevant

The discussion in the Mass#Weight_and_amount section is partly irrelevant to this section. The fact that the two sides of a balance scale are subject to the same gravity force because they are so near is such a tiny detail that needs certainly not be mentioned in this section. So, all the part about gravity being almost equal on the Earth is scarcely relevant and would be better separated in a section immediately preceding Mass#Weight_and_amount, called Mass#Weight_and_mass.--Pot (talk) 09:02, 26 September 2009 (UTC)

I think it would be better to completely rewrite that section as something concerning "Measurement of mass". Much of the current speculation about atomic weights and the atomic mass unit is quite simply wrong, for example! On the other hand, I think it is fair to mention that masses in the everyday range of around one kilogram are usually measured by comparing weights in a constant gravitational field. Physchim62 (talk) 12:08, 26 September 2009 (UTC)
If we are speaking about the second paragraph of the Mass#Weight_and_amount section I agree completely. But, for a start, it would be better to split it and put it into a new section that precedes the current one. Once this is done, it will be easy to rewrite it. As it stays now, the second paragraph has tone and content which are quite extraneous to the rest of the section. --Pot (talk) 12:14, 27 September 2009 (UTC)

## Confusing and clumsy reference to mass/energy equivalence

"Special relativity provides a relationship between the mass of a body and its energy (E = mc2). As a consequence of this relationship, the total mass of a collection of particles may be greater or less than the sum of the masses of the individual particles."

The statement only makes sense with reference to sub-atomic particles, yet this important distinction has not been made; rendering the statement misleading to anyone not already in posession of a detailed understanding of the subject matter. A better way to introduce the subject, would be to simply say that: According to The Theory of Special Relativity mass and energy are equivalent, and related by the formula... This equivalence is apparent in fission and fusion reactions, whereby mass is converted to energy, by th process of splitting or fusing atoms. Airophile (talk) 06:52, 29 October 2009 (UTC) --99.156.167.179 (talk) 01:22, 4 November 2009 (UTC)drerennc99.156.167.179 (talk) 01:22, 4 November 2009 (UTC)

The problem is that mass is NOT "converted" to energy. This is popular misconception (one of the most pervasive in science) and it's just wrong. Those of us who know better have to deal endlessly with people who think they know what E = mc^2 means. It MEANS that mass and energy are the same thing, and neither one appears without the other. Both are separately conserved (for a given observer) over time. The only way either one increases or decreases is if you're looking at a sealed system and you let some escape. Then both mass and energy go out together, however, the total (including what escaped) remains the same. This article would be much simpler if it said "Mass is a conserved quantity (it can neither be created or destroyed), and special relativity did not change this understanding. However, relativity did add the fact that all types of energy have a mass, and this mass is added to systems when the energy is added, and the mass is subtracted when the energy leaves." SBHarris 03:46, 27 January 2010 (UTC)

## Lead sentence is inconsistent within itself

"In physics, mass (from Ancient Greek: μᾶζα) commonly refers to any of four properties of matter, which have been shown experimentally to be equivalent: inertial mass, active gravitational mass and passive gravitational mass."

It says "four properties", then lists only three. Facts707 (talk) 07:31, 17 January 2010 (UTC)

Fixed. Strad (talk) 15:53, 17 January 2010 (UTC)

## Quantum mechanics / Higgs boson

I've been confused for a long time by the fact that this article doesn't mention at all quantum mechanics. For instance, we have lots of QM articles that discuss the (hypothetical) role of the Higgs in giving mass to particles (which would imply it's responsible for everything that we perceive to have mass). However, the word Higgs doesn't appear anywhere in this article, nor as far as I can tell does anything related to quantum mechanics. How so? bogdanb (talk) 14:04, 19 January 2010 (UTC) MASS —Preceding unsigned comment added by 66.91.105.146 (talk) 01:56, 25 March 2010 (UTC)

I have tried to address it. I believe I got the gist of it right, but the presentation may still be improved. I think the presentation of the classical Euler–Lagrange equation, the Schrödinger equation and the Dirac equation side-by-side is useful towards understanding where this m is coming from (its pedigree is the term for kinetic energy in classical mechanics), but because the wave function in the Schrödiger equation really corresponds to p (the impulse) in the classical case, the m now appears in the denominator. So, I believe the presentation can still be improved in the interest of making this accessible to the moderately educated reader. Perhaps somebody can help me, or else I'll try to fiddle with it some more myself. --dab (𒁳) 20:07, 13 December 2011 (UTC)

## Blatant plagarism

In the section about equivalence of inertial and gravitational masses, the paragraph detailing galileo's experiments has at least two full sentences written by Stephen hawking in his book "a briefer history of time" . More plagiarism may be present but I have not investigated beyond that point —Preceding unsigned comment added by Ahuramazda8 (talkcontribs) 20:58, 8 November 2010 (UTC)

## Recent edit - WP:OR?

A recent edit by Ggonzalm states "The difficulties in obtaining a single definition of mass are probably caused by the lack of a unified theory of physics. For this reason Einstein, Schrödinger and others pursued a geometric unified theory. It was clear to them that... " IMO, this either requires references or might be considered original research. WikiDMc (talk) 15:50, 8 March 2011 (UTC)

## Question - Mass and curvature of spacetime

Ok comments coming from an novice.

We know mass curves space time right. We have learnt that from lensing of light around stars / galaxies etc.

Shouldn't mass be represented as a fundamental forumla for the curvature of space time then? Is this formula already out there?

I'm just thinking the curvature exists well outside the volume that is matter, i.e. by light curving around the galaxy, so the mass formula should decrease at some function of the distance.

E=MC^2 has always bothered me as a fundamental law, its seems to much of an oversimplication using a scalar value taken from matter. It seems like mass should be expanded to properly account for space time. In other words, energy / mass is what the universe is and trying to describe it in a fundamental formula that does not acknowledge the dimesion it is framed in seems odd.

Also a single curvature for say the sun is a massive simification isnt it? In reality wouldn't space time be more of a cumulative craterfield from each mass from a fundamental particle.

Are people getting me here?

Cheers

Clayton Fairs

I guess I think I know what you mean: you figure that the "E=MC^2" sprinkled with some hand-waving about "curvature" you were fed by the media is a "massive simplification". You are spot on, it is a massive simplification. The problem is, the full description is right there, only, it is fiendishly difficult to solve, so even sharper minds than either of ours are reduced to assuming massive simplifications, simply because if you don't simplify, you are not going to get any result. --dab (𒁳) 20:44, 13 December 2011 (UTC)

Thank you for the response and the link provided. Hopefully one day I'll have some time to go back to uni and study Physics in depth. Regards, Clayton

## mass as length

Last lines in "Unit of mass" section include "...identified with its inverse Compton wavelength (1 cm−1 ≈ 3.52×10−41 kg)". I guess it should be just "1 cm" instead of 1 cm−1. Am I missing something? manya (talk) 11:25, 30 September 2011 (UTC)

you may have missed the word "inverse", as in, λ= 2π/m, in natural units. --dab (𒁳) 11:28, 13 December 2011 (UTC)

## The gram (g) is electronvolt is common in particle physics.

This is what Wikipedia tells in the first chapter. I can't understand neither am able to improve. Please discuss. --193.56.241.75 (talk) 12:21, 12 October 2011 (UTC)

Thanks for spotting that error. I've restored the missing information. I hope it makes sense now. I'm surprised that this (accidental?) deletion was not spotted and corrected earlier. Dbfirs 08:12, 19 November 2011 (UTC)

## An idea if not inane

I'm not maven but to me, the current definition is not felicitous therefore I devise the following with the help of theories of gravity.

Since gravity or changing curvature of spacetime is the innate property of matter therefore

1- A mass of an object may be defined as "a quantitative might of its prime acceleration [gravitational]" - A prima facie might of its prime acceleration"

2- A mass of an object may be defined as "a qualitative appraise of its distortion of spacetime"68.147.52.247 (talk) 05:01, 11 January 2012 (UTC)Eclectic Eccentric Khattak No.1

Go look at mass in general relativity. The devil is in the details of how you "quantitate." SBHarris 05:53, 11 January 2012 (UTC)

## Mass in quantum physics?

I have a somewhat oddball question that doesn't appear to be covered by this section. Is the mass of a particle distributed according to its wave function? What happens to the mechanics of a particle when the wave function becomes distributed over a classical-sized region of space? (E.g. for a very weakly-interacting particle.) Does a gravitational field just further disperse the wave function?

Is this something that we have an answer for? If so, can it be covered in this section? Thank you. Regards, RJH (talk) 20:20, 14 May 2012 (UTC)

The answer is no, not exactly. Mass is concentrated around a fundamental particle in some small region, and the size of that region is not related to the wave function. You can think of the wave function as a probability (and phase) of the particle being at a particular place. The mass is concentrated at that place.
It might seem like a confusing and arbitrary distinction until you add a second particle. In a two-particle system, there is only one wave function, and it is a function of the two positions, i.e. 6 real number parameters $\Psi(x_1, y_1, z_1, x_2, y_2, z_2)$. So you would find the gravitational potential energy with a 6-dimensional integral averaging the probabilities of the two positions, and the integrand would have the particle masses concentrated at points (or small regions). -- Tim Starling (talk) 23:40, 14 May 2012 (UTC)
Thanks Tim. It's weird to think about, but then so is quantum mechanics. Regards, RJH (talk) 16:26, 15 May 2012 (UTC)

## History of inertial mass

There is some (modern) history of gravitational mass with Kepler etc. Very much less so with inertial mass. If history is no part of this article, shouldn’t there be at least a reference to the pages about inertia, about impetus? — Preceding unsigned comment added by DominiqueM (talkcontribs) 14:57, 29 July 2012 (UTC)

## Active versus passive gravitational mass

Does this distinction need to be made in the initial definition? The average person isn't interested in arcane distinctions that are meaningless outside of General Relativity and advanced field theory. The average person deals with the common-sense world of Newtonian gravity, in which the distinction is meaningless. If two objects have the same mass, they interact gravitationally according to the formula, and it is impossible to say which is "active" and which us "passive". This seems to have been introduced into physics teaching several decades ago, for some reason. It is of no value to people who are not taking a PhD in physics.

Newton would have done it this way: take a known mass M, an unkown mass m, at distance r (between centres of mass), and measure the force pulling them together. Use the formula to calculate the unknown, m, which is THE gravitational mass. (You could make the larger mass, M, the unknown instead, and measure THE gravitational mass the same way). There is no meaning to the words "active" and "passive" in this Newtonian picture.

Later in the article, if, say, the behaviour of a lepton near the event horizon of a black hole is being discussed, the words "active" and "passive" could be introduced. It is of no value to someone buying a pound of butter.

This link gives an idea of where this distinction arose http://www.edition-open-access.de/sources/5/chapter_21.html

It is quite out of place in the basic layman's definition of mass that should begin a wikipedia article.

77Mike77 (talk) 21:53, 11 February 2013 (UTC)

I don't know why it is being said that this is an advanced topic. Consider the test proposed by Galileo to drop two masses from the tower of Pisa. Since the mass of the Earth dominates and the gravitational effect is therefore effectively the same for both test objects, what is tested is their passive gravitational mass. The Earth is the mass generating the 1g field at the surface hence that field is G times its active gravitational mass. That is quite simple even in the Newtonian view. George Dishman (talk) 19:33, 7 July 2014 (UTC)

## Article is a disaster!

This article is such a mish-mash of re-writes, irrelevant technical details, and distantly related trivia, that it is worth preserving as a spectacular example of how badly things can go wrong. Nevertheless, I will (fairly soon) attempt to re-write the introductory paragraphs so that wikipedia readers can gain some useful and relevant information from the article. It should be trashed, except that it is an interesting freak show. This is no insult to the contributers, it's just that there is so much patchwork that the quilt has been lost. 77Mike77 (talk) 16:20, 16 February 2013 (UTC)

And it's still a mess. There's even two sections named "Newtonian gravitational mass". I just moved what I can only describe as an inline footnote into the mess of footnotes already here. This article needs work, pretty badly. I'm going to downgrade the quality from "B"to "C". Hopefully I can help fix this.Forbes72 (talk) 22:27, 3 December 2013 (UTC)
Everything seems ok when you consider it alone, but the overall structure is ridiculously scattershot. The history of the kilogram is laid out 4 times?!
• "Since 1889, the kilogram has been defined by the international prototype kilogram.[note 2]The other two ad hoc units are the second and the kelvin. Historically, both the kilogram and the kelvin are derived from physical properties of water, while the second is derived from the length of the solar day on Earth."
• "The gram was first introduced in 1795, with a definition based on the density of water (so that at the temperature of melting ice, one cubic centimeter of water would have a mass of one gram; while the meter at the time was defined as the 10,000,000th part of the distance from the Earth's equator to the North Pole). Since 1889, the kilogram has been defined as the mass of the international prototype kilogram, and as such is independent of the meter, or the properties of water."
• "When the French invented the metric system in the late 18th century, they used an amount to define their mass unit. The kilogram was originally defined to be equal in mass to the amount of pure water contained in a one-liter container. This definition, however, was inadequate for the precision requirements of modern technology, and the metric kilogram was redefined in terms of a man-made platinum-iridium bar known as the international prototype kilogram."
• Also, the original kilogram was defined to be equal in mass to a liter of pure water (the modern kilogram is defined by the man-made international prototype kilogram). Thus, the mass of the Earth in kilograms could theoretically be determined by ascertaining how many liters of pure water (or international prototype kilograms) would be required to produce gravitational fields similar to those of the Earth.
This is just silly. Forbes72 (talk) 03:04, 4 December 2013 (UTC)

Yes, it is a total disaster. Some improvements were made a while back to bring the general tone of it down from the clouds, to a level that an undergraduate science major might understand, but those were all reverted. The article, as it is, would be incomprehensible to a layperson, a high school student, a first year physics student, or just about anyone else. There is no point in wasting time trying to improve it, because it just gets reverted and further mangled. This article is an epic fail.77Mike77 (talk) 23:46, 4 December 2013 (UTC)

## Re "faster" and "slower" as vocabulary re Time.

I basically reverted a recent edit about the rate of time passing on the Earth, compared to outer space. There is a common confusion of words about "fast" and "slow", re time. In a heavy gravitational field, time travels more slowly (e.g. at the event horizon of a black hole, time doesn't pass at all, and events are frozen). A clock at the earth's surface will tick more slowly than a similar clock in outer space. The confusion arises from thinking that this slowness "expands" the time, but when you think about it, the fact that the clock ticks more slowly means that less time is registered on the clock, compared to a similar clock in outer space.77Mike77 (talk) 00:50, 22 March 2013 (UTC)

Everyone please weigh in so we can reach a consensus and have a good (and stable) lead section.

This is (supposed to be) a current encyclopedic article about the concept of mass in physics. Steve Quinn has apparently written his own lead section to make it, at best, an article about how mass was understood in the nineteenth century. Of course it's useful to say how the contemporary concept of mass has special cases that correspond to the classical definition, but those special cases are no longer primary to the way mass is understood and the way the term mass is used by physicists today. You can't completely redefine mass away from its mainstream definition in physics, even if you found a couple of articles or essays related to classical aspects of mass or the calibration of the standard kilogram, or by quoting Newton, whose views are obviously not the most current in the scientific community. Perhaps some of this material could go somewhere in a section of the article, but certainly not as the entire lead.

Here are a few specific comments as well:

In physics, mass ... refers to the quantity of matter in an object.

To whom in modern physics are you attributing this statement? The term "matter" by itself isn't even defined unambiguously in physics today -- it has several meanings in different context. Precisely what definition of matter are you referring to? According to mass-energy equivalance, every type of energy has mass, not just "matter".

Even if you mean rest mass (which you didn't say) a system can have rest mass without having any matter in it -- for example if you had massless box containing nothing but light bouncing around inside it, this system has mass while it's at rest (which can in principle be measured inertially/gravitationally). (If that system as a whole is a body having a nonzero velocity in some frame of reference, then it will also have momentum and thus its total (relativistic) mass will be greater than its rest mass.)

Or what about the example of the positron, which the anti-particle of the electron, called "anti-matter" by some definitions, but it has exactly the same rest mass as an electron (both masses are positive, btw).

Also, the basic unit for mass is the kilogram (kg). [1][2]

The kg is the unit we use by convention to measure and quantify mass; it is not basic or fundamental to the meaning or definition of mass itself. In fact, physicists often use a different system of units in which the units of mass are the same as those of energy, since they're equivalent anyway.

Using the kilogram helps simplify because it correlates with other basic units.

In other words, the basic unit of force, the newton, is the push or pull that changes the velocity of a 1 kilogram (mass) object by 1 meter per second, when the force acts upon the object (mass) for one second. Therefore, how much force needed describes the quantity of mass, or quantity of matter. This can be called an operational definition, which helps describe mass. Similarly, with an operational definition, Isaac Newton stated that mass is a measured quantity arising from a substance's conjoined "density and bulk". [1][3][4]
On the other hand, inertial mass is a quantitative measure of an object's resistance to changes in uniform velocity, (acceleration).

"On the other hand" suggests that inertial mass is 2nd physical quantity or concept, separate from mass itself which was being discussed before this sentence.

In addition to this, gravitational mass is a quantitative measure that is proportional to the magnitude of the gravitational force which is
1. exerted by an object (active gravitational mass), or
2. experienced by an object (passive gravitational force) when interacting with a second object.

Now you've introduced gravitational mass as seemingly a third distinct kind of mass. As explained in the article itself, inertial and gravitational mass are equivalent, not separate. When one says that a system has a certain mass, it isn't necessary to specify whether you mean its inertial or gravitational mass, because these will not be different. There is only one modern concept of mass in physics, regardless of the fact that it is involved in multiple phenomena and can be measured in multiple ways (inertia, gravity, etc.).

Even if some of what I said above is mistaken, we should consider what level of technicality we want to get into immediately as the lead of the article.

DavRosen (talk) 08:04, 7 July 2013 (UTC)

I didn't notice any discussion here. Now I have. This is the modern definition of mass, I didn't invent it. I added refs, and the lead is built on the former lead. It got rid of the confusion, where the description of interial mass was being confused for the description of mass, just before I changed the lead. The basic unit for mass is the kilogram, check the literature. I'll come back and review the rest of your comments later. ---- Steve Quinn (talk) 22:30, 9 July 2013 (UTC)
Hi Steve. "Quantity of matter" is just one traditional "definition" of mass, and it's fine to state it as such. Unfortunately, it isn't actually used to perform physical science or engineering (with the possible exception of people who study mass unit standards themselves) today because nothing follows from it: stating that definition doesn't help you measure mass, nor predict mass, nor create or destroy or convert [rest] mass, nor determine what effects or phenomena result from mass, nor how physical systems will be affected by mass, nor determine the relationship between mass and energy, force, etc. It also isn't useful because it defines mass in terms of something even more ambiguous: matter. Just look at how many ways matter can be defined in the modern context (i.e. beyond just saying "atoms"), and you'll see that defining mass in terms of matter leaves you almost nowhere. Many of the definitions of matter involve mass (or rest mass), so then the definitions become circlular: you can't define both matter and mass in terms of one another.
Fortunately, the other traditional definitions of mass are operational and much more useful: mass is a quantity that manifests in its well-known inertial and gravitational effects; using terms like "quantity of matter" have no effect on these phenomena. Inertial and gravitational mass aren't distinct physical quantities; they're just two (or 3) types of phenomena manifested by one physical quantity called mass. This isn't controversial; it has been known since Galileo's experiments and culminating with Einstein's equivalence principle.
You are confusing a physical quantity with its units -- these are not the same thing. Mass is a valid physical concept under any (consistent) system of units. You don't learn anything about the physics of mass by studying the properties of the standard kilogram bar. If you can't explain the concept of mass in a way that's independent of the kilogram itself, then you don't understand mass. Of course the fact that we do, by convention, use the kilogram, is an important fact in itself that should be stated, but it doesn't define or lead to an understanding of the physical quantity called mass. There is no reason to mention other units like the Newton in the lead section of this article. The lead should just state what mass is (possibly mentioning multiple conceptions of this), in the simplest possible terms. Further elucidations can go in particular sections of the article, where appropriate.
DavRosen (talk) 23:27, 9 July 2013 (UTC)
At the moment, essentially, I don't have a problem with the current lead. And "quantity of matter" can be inferred from the introduction of the NIST reference I provided, and the Scientific American article again, agrees, with this description. When discussing "rest mass" then kinetic and potential energy contribute to a particle's mass. If you want to put something about that in the lead, to show a distinction, that would be fine with me.
At the same time, I see describing matter in terms of the Newton demonstrates another characteristic of mass, because it is simple (rudimentary) and shows its relationship to a simple process. In other words, it shows that scientific endeavors that account for mass are not static. There is a dynamic involved. The "Newton" equation shows how mass can come in to play, and it seems to me that this would be both helpful and interesting to the reader. Maybe we could elaborate on this in a new first section.
Additionally, I don't appreciate having motivations misattributed to me. For example stating "Steve Quinn has apparently written his own lead section...", "You can't completely redefine mass away from its mainstream definition in physics..." and so on. I did neither of these things, and really such statements are irrelevant to creating a quality article. I find it is best to discuss the editing, as much as possible. In any case, I don't start attributing motivations to other editors - believe me - it doesn't go over well. Have you heard of "edit wars"? Well, that is one way they start; especially if two or three start hurling such things at each other. Then things get really out of hand, as you can imagine. Perhaps review WP:CIVIL.
Also, articles do have flexibility, within reason. It would be OK to include the Force (Newton) equation in the lead with all the basic units, because it is related to mass.
My intent for the lead was to distinguish terms, which I see you have done. I was not, and am not meshing anything together. Again, this was a misattribution of motivations, and perhaps also a misreading - since you have kept the same intact. In any case, it serves its purpose, does it not? ---- Steve Quinn (talk) 02:20, 10 July 2013 (UTC)
I have a source here that directly supports what I am saying [1]. I was trying to remember where it is when working on the introduction, but could not recall. This is the HyperPhysics site, which is hosted by Georgia State University's Department of Physics and Astronomy [2]. I think it is well known to the Physics community on Wikipedia. ---- Steve Quinn (talk) 02:55, 10 July 2013 (UTC)
Steve, you're right -- sorry I didn't do a better job of assuming good faith. DavRosen (talk) 05:18, 10 July 2013 (UTC)
To illustrate a problem with mass as a quantity of matter, mass is already a physical quantity before mentioning matter. Say the mass of a given body is 1 kg, i.e. the quantity of mass in or of the body is 1kg. If mass is the quantity or amount of matter, then the quantity or amount of matter in or of the body must also be 1 kg. So we have 1 kg of mass and also 1kg of matter. How does this help define what mass is or means? As far as quantities go, it seems to make mass and matter simply act like synonyms, and we still don't know what either of them is or means.
Okay, that hyperphysics ref says "The mass of an object is a fundamental property of the object; a numerical measure of its inertia; a fundamental measure of the amount of matter in the object." So right there it gives two definitions, inertia and amount of matter. (It brings in gravitation later.) The site uses the inertia and gravitational aspects of mass quantitatively all over the place, but can you find anywhere that it actually uses the definition of mass as a measure of the amount of matter in any substantial way? Also, I thought you objected to calling mass a property of something when you said "Mass is a physical quantity not necessarily a [physical property]]".
I'm not entirely satisfied with the current lead, but it's getting there. I only made what I felt were the least-controversial changes so as to avoid an edit war. It still gives the impression that there are actually three or four physical properties needing to be separately defined, although they end up being numerically equal. I'd like it to be clearer that mass is a single property that can be *defined* by the two or three observable/measurable phenomena. Just focusing on the first paragraph, the 1st para should stand on its own and explicitly answer "what is mass" at a simplified level, e.g.:
In physics, mass (from Greek μᾶζα "barley cake, lump [of dough]") is a property of a physical system or body, observable and measurable as a resistance to acceleration or in the strength of its mutual gravitational attraction with other bodies. In many common situations, mass can be thought of as representing the quantity of matter in an object. It is often measured using a mass balance or scale. The SI unit of mass is the kilogram (kg).
The reason for "in many common situations" is that systems with no matter at all can still have mass -- even light itself has mass (not rest mass, but it's never at rest anyway) which causes it to curve when it passes by large bodies like stars, and light can even orbit a black hole due to gravitational attraction, just like any body having mass can orbit another body.
DavRosen (talk) 05:18, 10 July 2013 (UTC)

In any common situation it is just WRONG to consider an object's mass to be the amount of "matter" in it. First of all, there is no good definition of "matter" (as pointed out above) so using it here is doubly confusing. Second of all, even for the energy entities that nobody considers "matter", they all add mass to closed systems in special relativity. A hot bar of iron has more mass than when it was cool. Here we observe the mass of the heat we added, but heat is not matter. The same would happen if we added light, mechanical work, or any type of energy at all. Lastly, there are not trivial proportions if we define "matter" as those elementary fermions (quarks and leptons) that have rest mass. In that case most of the mass associated with matter (98% of it) is NOT MATTER. Rather, it is kinetic energy and other massless particles associated with massless fields, like gluons. So in most ordinary circumstances with that defintiion of matter, an ordinary object's mass is 50 times the amount of matter in it, and the rest consists of the mass of trapped massless gluons, adding mass to closed systems of baryons, even though the gluons themselves are massless. Thus, I suggest that rather than have to explain this in the lede, let us avoid the word "matter" like the plague right here. SBHarris 22:53, 10 July 2013 (UTC)

Dave, in any case, I think your proposed lead is good and I think we should use that. If Sbharris's content can be incorporated as well, I think that would be great. --Steve Quinn (talk) 07:01, 11 July 2013 (UTC)
A photon is an elementary particle, the quantum of light and all other forms of electromagnetic radiation [3]. A photon is massless, has no electric charge, and is stable [4]. The photon is currently understood to be strictly massless. If the photon is not a strictly massless particle, it would not move at the exact speed of light in vacuum, c. Its speed would be lower and depend on its frequency. [5]. The speed of light is the speed at which all massless particles and associated fields (including electromagnetic radiation such as light) travel in vacuum. [6].
It seems to me that light does not have mass. I think that saying it does have mass, is a misunderstanding of some sort.---Steve Quinn (talk) 07:01, 11 July 2013 (UTC)
One photon had no mass, but two photons (so long as not traveling in the same direction) do have a mass. An invariant mass. If trapped in a system, a system rest mass. This allows mass conservation during particle decay (like neutral pions decaying to photons). Matter converts to non matter! But the requirement of two photons to carry mass is the reason you never see a single massive particle decay to a single photon! SBHarris 16:00, 11 July 2013 (UTC)
I think this is beyond the scope of this article and I am not going to get into nit picking. We have whole articles and the science of relativity that are based on the massless photon, and the fact that light travels at the speed of light, therefore light has no mass, otherwise it would travel at a speed less than "c". ---- Steve Quinn (talk) 18:04, 11 July 2013 (UTC)

Steve, I agree that amount of "matter" is not fundamental to the modern understanding of mass, and the lead should reflect that.
On the other hand, we shouldn't bury a notable viewpoint, just because we (as editors) don't agree with it or even can disprove it by some argument. Especially if that viewpoint may (whether intentionally or not) represent a [flawed] attempt to capture some valid aspects of the article's subject.
For example, "amount of matter" (or "quantity of matter") may suggest intuitively that we can choose to talk about mass as "stuff" (whether material or not), beyond being "merely" a property of a system. When you transfer "stuff" from one system to another, you expect one system to now have less of it and the other system to have more of it, by the same amount unless some transformation or conversion of the "stuff" also occurs. E.g. "I transferred 1 kg of mass". You wouldn't say "I transferred 3 kg/m^3 of density" from one system to another -- there's no reason the second system's density would increase in general by the same amount by which the first system's density decreased. This may correspond to mass being an extensive quantity (or additive) while density is an intensive property. If a system comprised two identical (but isolated/non-interacting) subsystems, then, for any extensive property like mass (or volume, moles of hydrogen, electric charge, or of course any form of energy for example), the system would have twice the amount of it as either subsystem has.
Amount or quantity may also allude to it being a ratio scale, meaning it has a non-arbitrary "zero" and that it is possible to say one system has "twice as much" or twice the magnitude compared to that of another system, as is the case with all the extensive and intensive examples above as well as absolute temperature(an intensive ratio scale), but unlike an interval or location scale such as degrees Celsius, or today's date (say Julian day), or electric potential, or my latitude or longitude, all of which have a zero value as merely a reference point which could just as well have been chosen differently.

As for the first sentence of lead starting with "mass can be described as an associated measure of the total quantity of energy in an object", this is true but it doesn't directly tell us very much about the nature of mass, until we find out something about the nature of that measure being alluded to, and put it all together.
If this were an article about mass as merely a physical quantity, then we could simply define it as E/c^2 and refer the reader to Energy article for E, and to Mass-energy equivalence for the formula itself. Otherwise, this article should be about the concept of mass (especially the modern one but also eventually the historical ones), which can't be separated from inertia/gravitation, because these are the particular characteristic measures/manifestations/phenomena/consequences/effects/behaviors of energy that characterize the concept of mass.
When we say light bends as it passes by massive bodies "because it has mass", we mean that it exhibits those inertial/gravitational phenomena that collectively characterize mass (relativistic mass in this case). When we say a body gets "heavier" as it accelerates towards the speed of light, we don't simply mean "it has more energy, of which, as usual mass is simply one measure", but that it has more inertia.
That's why I (and now Steve) favor a first sentence involving something like:

Mass is a property of a physical system or body, observable and measurable as a resistance to acceleration or in the strength of its mutual gravitational attraction with other bodies.

This captures this nature of mass in the simplest possible terms, and it captures the aspect of it that held in the 19th century as well as today. It doesn't mention energy, but that could be in the second sentence, or maybe worked into that 1st sentence.
DavRosen (talk) 19:07, 11 July 2013 (UTC)

Your idea to start with inertia and gravitation-source/sink as the definition, is a good one, and I approve. Feel free to move it around. Then (if you like) you can add that we also know that the "stuff" we're talking about as mass is ALSO always a property of all kinds of energy (the ability to do work = force X distance), as though it was the universe's bookkeeping agent to "remember" how much energy has been stored or deposited, as a never-changing-quanity in the universal "bank." Or perhaps the total does change as the universe expands, like some currency inflation (pun). Energy is a very squirelly thing, and it's not at all obvious how the different types of energy are like each other-- the frequency of a wave, the velocity of a particle, the storing of potential in a field. But they all leave behind this calling card of increased inertia and gravitation/space-time bending that we call "mass."

To me the oddest thing is that this "mass" sometimes has no location, anymore than the energy associated with it does. Where (for example) is the mass of the kinetic energy of two particles A and B relative to each other? From the viewpoint of A, the extra kinetic mass-energy is all located at B, and from the view of B, it is all located at A. From an observer in the COM frame, it is divided between the two. So where IS it? Hard to say. It's stored in the structure of space-time somehow, as a RELATIONSHIP between the two particles, that has no specific THERE or SPOT. They could be light years away from each other and the universe still keeps track of the balance, which is somewhere associated with the two, but no place in particular, anywhere in the universe inside their light cone. The reminds me of nothing so much as quantum entanglement. Kinetic energy must be stored as entanglements, otherwise it makes no sense at all. The same with the energy of photons, which individually do not HAVE an energy, since it can be anything you like (pick your observer). Only when we get to photon pairs are we forced to stop that game, and now (again) behold, it's all in relationships. Long distance relationships if you must, but relationships it is. Grav waves and EM waves have points where the fields are zero, and energy/volume is zero. So where is the energy carried by the wave? Spread out over a volume; one part of space doing something different relative to ANOTHER. It's always like that. Nothing is pinned down.

Finally, I'm sorry to be longwinded, but your idea that we use the horrid word "matter" as a stand-in for the "stuff" that we transfer from here to there as "mass" and that has "energy", I think it's a bad idea. The "stuff" we're talking about is mass-energy. It is mass (which always has energy), or energy (which always has mass). Only when pinned down as nice stopped particles with a rest mass is all this pretty and looks like "stuff." Otherwise, it's not stuff!! It looks like kinetic energy, which doesn't look like stuff, and has no location. It looks like EM radiation, which isn't any stuff you can hold in your hand ("How do you hold a moonbeam in your hand...?"). It is E or B fields, which aren't stuff, but force fields. Other force fields as well-- virtual pions, or weakons or gluons or whatever. This is not what anyone ever meant by matter, which originally was a word that differentiated things from the realm of pure energy. But pure energy has mass! Most of the mass of ordinary things is not particles with rest mass. Calling that stuff "matter" is cheating. If that's "matter" then the only thing that isn't "matter," is field-free vacuum. And perhaps vacuum with static gravitation fields in it. SBHarris 00:39, 12 July 2013 (UTC)

Dave, I already altered the lead with your opening statements, and follow up sentences. Then I added Mr. Sbharris' contributions after that. So, I would think that the opening of this discussion is a step or two behind the editing of the article; except I see that Dave and Sbharris have already done some deft copy editing. Maybe I am in a time warp or time loop after discussions of photons, light, relativity, and energy. Anyway, the lead is really good, especially after the copy editing. I am really glad we have been discussing this. ---- Steve Quinn (talk) 01:04, 12 July 2013 (UTC)
Sbharris, I appreciate the statement you made in the edit history: "Your mass is mostly gluons and glueballs, and who is to say if these are 'matter'??". I think this is a really good point, and one that I didn't think about before this. I think this would be a good point to add in the lead paragraph. We know it is gluons, "glueballs???", and quarks, but are we really referring to matter? Also, I see some really good points being made in the three paragraphs of your previous entry. Such concepts and possible conclusions are certainly mind blowing. Yes, where is the kinetic energy located? Also, why not use the following from your first above paragraph: "But they all leave behind this calling card of increased inertia and gravitation/space-time bending that we call "mass."" We can give a background explanation, as you did in the first paragraph. That is really clear to me what you are saying. Based on energy is conserved (in a closed system?) and mass is conserved, where the heck does it really go? Anyway, I say, let's use everything we can from these three paragraphs ----Steve Quinn (talk) 01:45, 12 July 2013 (UTC)

Wow it was a chore getting up to date on all the discussion about the lead here. Anyway, I think the move away from defining mass as a collection of "matter" or "stuff" was a good idea. I've made a couple modifications to the lead, but it seems to me that the main gist of the thing is intact. First, scales do *not* measure mass, they measure *weight*. Mass is never measured directly. Second, I've removed the link to physical system. The reference to physical body seems more than sufficient, and it helps cut jargon. Thirdly, I've made the bullet points on inertial and gravitational mass into a more comprehensive list of the ways in which mass is determined. I feel like the lead is significantly more straightforward this way, but of course this is not definitive.Forbes72 (talk) 22:46, 3 December 2013 (UTC)

## Distinction between mass and weight

The distinction between mass and weight is a recent aspect as scientific concept.--86.120.44.145 (talk) 18:56, 15 July 2013 (UTC)

## Weight vs. mass

This is explained well enough in mass versus weight, weightlessness and even weight. But it's hard to summarize in three paragraphs. Weight is the force of mechanical contact forces, and results in mechanical stresses, like the ground pushing up on your shoes (or an elevator floor, or rocket deck, or giant centrifuge pushing on you). Weight is NOT simply a "force of gravity" or caused by a force of gravity, since if only the force of gravity acts on you (as in orbit or any type of free fall), you are weightless and don't feel weight.

To put it another way, you certainly feel the force of weight, but nobody has ever felt any naked unopposed force of gravity (the best you can feel is gravity gradients, and then only if large). So this has to be said correctly. What we feel are the forces that RESIST gravity, and that's all.

I probably haven't done a great job, but what was in the article before, was just flatly wrong, and something had to be done. SBHarris 01:48, 17 July 2013 (UTC)

## Kepler doesn't belong here

The article goes into some detail about Kepler's modeling of the planets' motions. But Kepler used geometric and proportional reasoning, and this was not tied to mass at all. From the article: "Johannes Kepler was the first to give an accurate description of the orbits of the planets, and by doing so; he was the first to describe gravitational mass." This doesn't follow at all. The motion of the planets is governed by their masses,(in the modern understanding) but Kepler believed that they were governed by the proportions of platonic solids and the music of the spheres. Galileo's experiments and Newton's laws are obviously relevant, but I think Kepler doesn't deserve a whole section here. Forbes72 (talk) 02:57, 6 December 2013 (UTC)

## Inertial mass

The article says

$\frac{m_X}{m_Y}=-\frac{\boldsymbol{a_Y}}{\boldsymbol{a_X}}\!.$

which is probably wrong (or at least an abuse of mathematical notation), as aY and aX are supposed to be elements in a vector space and vector division is not defined there. Suggest taking norms before performing division. Thanks. JacobRodrigues (talk) 13:34, 27 December 2013 (UTC)

The notation was certainly incorrect. Anyone familiar with the subject would know what was meant, but the mistake was lazy. Additionally, using X and Y to denote the objects instead of Cartesian coördinates seems confusing. I have changed it to objects 1 and 2 instead. Forbes72 (talk) 02:43, 21 January 2014 (UTC)

## Lede discussion - continued.

My general impression of this article is that it is a mess. Its a mash-up of distinct meanings for the term "mass" and badly fails to spearate meanings from their repsective contexts of use. Worse, the most used meme is wrong...or rather obsolete. Velocity does not impart mass to an object or system. I am watching Leonard Susskind's video lectures The Theoretical Minimum, specifically Special Relativity and Electrodynamics (2012), Lecture 3. (http://theoreticalminimum.com/courses/special-relativity-and-classical-field-theory/2012/spring/lecture-1). At 1 hour 00 minutes 30 seconds he states that the concept used in most of THIS article, that mass is variable, is NOT used by any physicists he knows of, and is an anachronism, only being used in physics (undergraduate) textbooks. Since there seems to be general agreement here, in this case, that Wikipedia should go with the textbooks rather than with modern Scientific usage (ie with the teachers, rather than with the professionals), I'm probably sneezing into a strong wind, but I felt I should at least point out that the consensus here is not shared by at least one eminent Physicist, and moreover he states it is shared by virtually none. He specifically states that mass is what was previously called rest mass, that it IS invariant (since it is defined as the mass at rest) and that photons DO NOT HAVE any. He also states that the mass of a system of bound particles is less than the mass of the individual particles (due to the energy used in bonding, by implication by (some of) the potential energy of the system) and has NO contributions from velocity. At the least this viewpoint (the modern view) should be given prominent position. The different meanings (including the obsolete one) should be separated and then the theory should be developed for each separately. I suspect that Classical Physics, Special Relativity, General Relativity, the Standard Model (particles), and possibly even the Λ-CDM model have distinctly different definitions for the term. Keep in mind that the same term can be used for an "atomic" particle as well as for systems of particles in some (or all?) of these domains.

Here are two other things I think are wrong:

First: The lede states that mass is difficult to "directly" measure. I don't know what that means. I think mass is EASY to measure. I can do it gravitationally or inertially quite easily (depending on precision). The symmetry breaking (LOL) between weight and mass only occurs when the gravitational curvature is substantially different from "standard". (A recent paper in Science magazine described a technique to differentiate the difference in gravity equivalent to a couple of inches of altitude at sea level. Not easy.) It is just factually not true that mass is difficult to measure. This point of view seems to be confused about what measurement is, or perhaps the author thinks he has some clear idea of what constitutes a direct (compared to an indirect) measurement. Comparisions are direct (1-to-1 correspondance is the most fundamental mathematical operation). I can compare two masses EASILY.

Second: Quote:"From a fundamental physics perspective, mass is the number describing under which the representation of the little group of the Poincaré group a particle transforms." Unquote. This monstrosity from section "Weight vs. Mass". Need I say more?

Needs a rewrite. Needs clarity. And definitely needs more on Higgs Boson and the conceptual difference between say claiming that the mass of a proton (as a particle) is X and that the mass of a proton (as a system of particles and fields) is mostly "energy".173.189.72.14 (talk) 22:30, 12 February 2014 (UTC)

## Re recent correction

"The kilogram is 1000 grams (g), which were first defined in 1795 as one cubic decimeter of water at the melting point of ice."


This is still awkward, because it wasn't 1000 little grams that WERE defined as a cubic decimeter of water; rather, a kilogram WAS defined as that. Hard to correct...maybe this: "The kilogram is 1000 grams (g), and was first defined in 1795 as one cubic decimeter of water at the melting point of ice."77Mike77 (talk) 23:52, 11 March 2014 (UTC)

1. ^ a b Jabbour, Z. J., and S. L. Yaniv. "[http://www.nist.gov/calibrations/upload/j61jab.pdf The kilogram and Measurements of Mass and Force." Journal of Research-National Institute Of Standards And Technology 106.1 (2001): 25-46.
2. ^ Cite error: The named reference Cromwell was invoked but never defined (see the help page).
3. ^ Crowell, Benjamin; Conceptual Physics (April 5, 2013). Chapter 1. Conservation of Mass and Energy. pp. 9–11.
4. ^ Kane, Gordon (September 4, 2008). "The Mysteries of Mass". Scientific American (Nature America, Inc.). pp. 32–39. Retrieved 2013-07-05.