# What truly is mass, and is there a direct way to measure it?

We know a mass of an object of one kilogram as an object that weighs W = mg = 9.8 N and we reference it to that, (when it should as a fundamental parameter describe weight not the opposite). But if we were to describe mass to an alien civilization on an alien planet we are exchanging knowledge with, by sending them a one kilogram object, according to their gravity they will measure it differently.

Also their star could be curving space time in such a way, or their velocity according to SR will cause them to perceive mass on our planet -if they observe from away- differently.

If we asked a crew on a space ship moving at a speed close to the speed of light wrt us, or moving in a gravitational field they don't know about, to measure the mass of our planet, they will get different results. On the same principle, we could be measuring the mass of far celestial objects like planets, differently.

I perceive space time as full of curves and irregularities. We know the about some of these and we don't about others. I mean we know about the earth's gravity, the sun's but we ignore the effect of the galaxy and the cluster, dark matter, and who knows what else. Besides we change our position all the time with relation to these external factors that bend spacetime. So our measurements to an outside neutral observer, say these aliens could change.

I've found definitions of mass like "the quantity of matter in an object" but that seems like the good old: mass = volume x density, but mass is the more fundamental quantity than either of them, with which theses parameters should be described by mass not the opposite, not to mention how relative these other quantities are, considering SR and GR. Or "The resistance of an object to acceleration" but again you have to describe how fast that object is moving and what spacetime it's in according to SR and GR.

So what makes us so confident that mass is such a universal value, when we built everything on a concept referenced by our own gravity, and maybe our own reference frame?

How do we describe mass to the aliens, who don't know about our (g)?

How do we measure the mass of celestial objects say planets, by units like kilograms, and pounds, while they are not subject to the earth's gravity, (I'm well aware of the difference between weight and mass). I mean that's what they will weigh -ignoring their own gravity- if they were in our atmosphere on a huge scale? So what's the method?

Bottom line Is there a direct way to measure mass like we do with other fundamental values like length and temperature, other than using a scale or equations, i.e not depending on other physical parameters to describe it?

--Forgive the length..

• I know some might think this is a duplicate and I read most related questions. But if you read on you'll understand I have another point here.. – Force Apr 15 '13 at 0:33
• If there's a particular question (or questions) you think people might consider this a duplicate of, the thing to do is link to it and explain in the body of the question why this is not a duplicate. – David Z Apr 15 '13 at 0:35
• @David I did so by describing the definitions of mass, and why I'm confused about them. Besides the questions at the end, I didn't find any direct answered to them. Still do you have any suggestions? – Force Apr 15 '13 at 0:39
• It's the title that might cause this impression, that's why I added the word truly for distinction.. – Force Apr 15 '13 at 0:41
• I don't see any links. What I mean is to include something like "This question is related but it doesn't address how [blah blah blah]. I also looked at this question but I'm still confused about [blah blah blah]." Here's an example that I asked a while ago (look at the last paragraph). – David Z Apr 15 '13 at 0:45

You ask, "How do we describe mass to the aliens, who don't know about our (g)?" This is an example of a class of questions referred to by Martin Gardner as "Ozma problems." The classic Ozma problem is how we describe to aliens the distinction between right and left; the answer is that we do it by describing the weak nuclear force.

Your statement of your Ozma problem seems a little ambiguous to me. Essentially you're asking how we describe to the aliens a unit of gravitational mass. (You don't say so explicitly, but it seems clear from context that you don't mean inertial mass.) Futhermore, there is a distinction bewteen active gravitational mass (the ability to create spacetime curvature) and passive gravitational mass (what we measure with a balance). Not only that, but your question could be interpreted as asking whether we can compare with the aliens and see whether the value of the gravitational constant $G$ is the same in their region of spacetime as it is in ours.

We can easily establish 1 g as a unit of inertial mass. For example, we can say that it's the inertia of a certain number of carbon-12 atoms.

The equivalence principle holds for us, so presumably it holds in experiments done by the aliens as well. This establishes that our 1 g unit of inertial mass can also be used as a unit for the passive gravitational mass of test particles.

You didn't ask about active gravitational mass, but the equivalence of active and passive gravitational mass is required by conservation of momentum, and has also been verified empirically in Kreuzer 1968. Cf. Will 1976 and Bartlett 1986.

The other issue is whether $G$ is the same for the aliens as for us. Duff 2002 has an explanation of the fact that it is impossible to test whether unitful constants vary between one region of spacetime and another. However, there are various unitless constants that involve $G$, such as the ratio of the mass of the electron to the Planck mass.

A more fundamental difficulty in the fundamental definition of mass is that general relativity doesn't seem to offer any way of defining a conserved, global, scalar measure of mass-energy. See, e.g., MTW, p. 457

Bartlett, Phys. Rev. Lett. 57 (1986) 21.

Duff, 2002, "Comment on time-variation of fundamental constants," http://arxiv.org/abs/hep-th/0208093

Kreuzer, Phys. Rev. 169 (1968) 1007

MTW: Misner, Thorne, and Wheeler, Gravitation, 1973.

Will, “Active mass in relativistic gravity: Theoretical interpretation of the Kreuzer experiment,” Ap. J. 204 (1976) 234, available online at adsabs. harvard.edu.

• I believe it was Larry Niven who wrote the classic Ozma SF story; in which as the protagonist space walks to greet the aliens they extend their left hand to shake! – Pieter Geerkens Apr 15 '13 at 2:18
• @PieterGeerkens: Cool! What was the story? – Ben Crowell Apr 15 '13 at 2:21
• That was a very long time ago. If I had remembered the title of the story I would have added it to the previous comment, but unfortunately it escapes me. However your mention of the WNF above immediately recalled it's plot to memory. Of course the two spaceships would have lit up like furballs as soon as they got that close to each other, but why spoil a great story with trivia. – Pieter Geerkens Apr 15 '13 at 2:26
• Important nitpick: The equivalence of magnitudes of active and passive gravitational mass is required by conservation of momentum; the sign could theoretically differ, though of course it's never been observed to. briankoberlein.com/2013/09/07/equivalent-principles – Dax Fohl Nov 15 '16 at 16:17

I'll reduce your question to its simplest expression: "What is mass?"

And give you my best, simplest answer:"It is a measurement of how much an entity opposes acceleration or deceleration". I believe that in the end it all comes to that...

• I am on earth. I am accelerating at g in free fall. My mass is 63 kg. My weight tends to be 0 N in free fall and my acceleration is g. Would you please comment on my mass at instance? – Anubhav Goel May 3 '16 at 0:20

re "If we asked a crew on a space ship moving at a speed close to the speed of light wrt us, or moving in a gravitational field they don't know about, to measure the mass of our planet, they will get different results.":

This is only true of aliens too naïve to have built or operated the apparatus they are flying; other aliens will well understand the Lorentz transformation, and be able to calculate the rest mass as the relevant (constant) attribute of any object of interest.

• It's more about finding another definition for mass, and a direct way to measure it than what the aliens are about.. I invented the aliens for this purpose – Force Apr 15 '13 at 1:26
• And my point is that you are apparently inventing windmills solely for the purpose of tilting at them. Your question is much more interesting if you work from the existing acknowledgement that NO-ONE KNOWS WHAT INERTIAL MASS IS. Feynman famously admitted as much in his memoirs. It is believed to be identical to gravitational mass solely on a preponderance of empirical evidence, with no theoretical basis whatsoever. – Pieter Geerkens Apr 15 '13 at 1:30
• Then you should have simply answered with "No one knows what inertial mass is" instead of mocking the question. Which if troubled you as such, you should of simply avoided answering it. – Force Apr 15 '13 at 1:47
• @Force: I am rarely accused of having tact. I believe your question has merit at its core, but that this is being obscured by the creation of phantom windmills to tilt at. Feynman died over 25 years ago, so maybe his is not the last word on the subject. If you improve your question, You might attract answers from community members more knowledgeable, and current, than myself. – Pieter Geerkens Apr 15 '13 at 1:53
• There is a little bit more here: physics.stackexchange.com/a/142845/43402 – bright magus Feb 2 '16 at 10:38

Is there a direct way to measure mass like we do with other fundamental values like length and temperature, other than using a scale or equations, i.e not depending on other physical parameters to describe it?

The answer by @BenCrowell is adequate. Here I want to emphasize the more general aspect of what physics terms mean, and in a sense what physics is about.

Physics starts with observations, data, i.e.measurements. Measurements need units and these preexisted the effort of finding a theory of everything that will describe all of matter as we know it. When mathematical theories of physics are proposed, the matter of units inevitably is raised. By the end of the nineteenth century it was realized that many units used to describe data could be transformed into other units. Thus the concept of fundamental units appeared : the minimum number of units which one can use to describe physical phenomena. Example: the CGS system.

The simplest system comes from particle physics where one uses the Planck units five in number :

the gravitational constant, G,

the reduced Planck constant, ħ,

the speed of light in a vacuum, c,

the Coulomb constant, (4πε0)^−1 (sometimes k_e or k), and

the Boltzmann constant, k_B (sometimes k).


Notice that mass is not there, which means one needs equations to define it. Temperature and length are not there either.

So if we meet aliens these are the most basic units on which to agree in order to have a common definition of anything measured in physics.

Of course the method of identifying mass with a specific sample, as Ben says will define mass for the aliens, but equations cannot be ignored if one wants to exchange knowledge in physics.

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