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What is mass?

  1. Apr 10, 2014 #1
    I understand that mass isn't weight. When I look up "what is mass?", I come across all kinds of videos explaining the difference between mass and weight, but that is not what I am looking for. I'm trying to understand the concept of mass, fundamentally, because it doesn't really mean anything to me right now and makes it difficult for me to concretely grasp the many physical formulas and concepts that involve mass because of this.

    Wiki defines it as "a property of a physical body which determines the body's resistance to being accelerated by a force and the strength of its mutual gravitational attraction with other bodies", but all this says is what mass does, not what mass is.

    To me this is like: If I ask "what is an atom?" and people respond "it's something that forms covalent bonds", I still don't know what this "something" is. If it's defined as "the smallest unit an object consists of", then I can mentally represent what the concept is about (because cutting things into smaller pieces is something I come across in my daily life); it becomes something more concrete. I'd like "mass" to be as clear in my mind, but it isn't.

    Can you please explain it to me?
    Do we even know what mass fundamentally is or do we only know it's there because we empirically observe its effects, but do not know what it fundamentally is?

    Mass is sometimes defined as "the amount of matter" that something has, but even "matter" I don't really understand as a fundamental concept. Intuitively, I saw it as "the tangible elements that objects are made of", and objects are made of atoms, so that led me to try to understand it as the amount of atoms objects have, but that makes no sense because things are made out of billions and billions of atoms, so something that has a mass of 3 kg wouldn't exist. What does this "3" refer to if it isn't the amount of atoms? How can you quantify something that isn't fundamentally defined?

    Maybe I sound a little dense, and I'm sorry for that, but I'm just not wrapping my head around this one. Thank you if you're willing to spell things out for me. =/
  2. jcsd
  3. Apr 10, 2014 #2


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    We don't know what mass fundamentally is!
    Some people may say its just another form of energy and they're right but then we should know what is energy which again we don't know.
    I guess we need some undefined concepts and axioms to start any system including physics. Energy is one of those undefined concepts.
  4. Apr 10, 2014 #3


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    Talking about mass. But only it's effect.
    This is a difficult concept but maybe someone can figure this one out someday!
    We don't know what the mind is. We don't know what the ego is. But we can see it's effect in this world.
    A lot of things we only know exist because of the effects they have.
    They only knew a blackstar existed because of the stars drawn to them.
    Last edited by a moderator: Sep 25, 2014
  5. Apr 10, 2014 #4
    Thank you for your answers!

    I now understand that mass is only defined by its effects, so I realize that my biggest problem is related to quantification. I don't understand how people came up with a system to quantify mass.

    I tried to figure it out using the formula for mass, which is F= m . a and my issue was the following:

    a: Acceleration as a concept is very straightforward. It's a measure of the distance in relation to the time in which it is traveled. In order to measure distance, we've taken an arbitrary amount of space and called it a meter and an arbitrary amount of time and called it seconds. Nothing to look for there, it's all arbitrary.

    F: Same with force. In order to quantify it, we arbitrarily decided to equal 1 unit of force (newton) with what is needed to make an object of 1 kilogram have an acceleration of 1 meter per second.

    m: But when it comes to mass, I don't see what they used to quantify it (given that it's definitely not the amount of atoms contained in an object). You could say that it's that which causes the needed force to accelerate the object to be greater the bigger it is, but then there's a loophole in the definition (force is defined in terms of mass and mass is defined in terms of force). So what basis was used to standardize the measurement of the concept of mass?
    Last edited by a moderator: Sep 25, 2014
  6. Apr 10, 2014 #5
    As with defining a meter or a second, mass was also arbitrarily chosen. The kilogram is a block of metal that sits somewhere in France (I think). That block of metal was defined to the 'the kilogram'.
  7. Apr 10, 2014 #6


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    According to Isaac Newton and other classical physicists - mass is the quantity of matter.

    Matter in turn was stuff you can touch: dirt, water, air, rocks - but not light, heat, shadows.
    Matter is stuff you can transform and manipulate. All forms of matter have mass, and you can show equivalent mass with a balance scale, or via weight on a calibrated spring scale.

    Mass is a fundamental property of sub-atomic particles such as electrons, neutrons, protons. Each quantity of mass also contains energy (which you can obtain via nuclear reactions, for example) such that E=mc^2.

    You may find this NIST article of interest:

    And proposed future standards, such as counting atoms:
  8. Apr 10, 2014 #7


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  9. Apr 10, 2014 #8


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    Personally, I think this is a meaningless distinction. What does this even mean?

    Let's suppose that there is a person and you ask "who is this person". I can say, "he is John". That is one way of identifying a person, his name. Now, you ask "but all this says is his name, not who he is"? So I start to describe John in terms of his properties "He is 5'10" tall, 36 years old, red hair, brown eyes, he is socially awkward, he likes football ...". Now you say "but all this says is what he is like, not who he is". So I can describe John in terms of his relationships "he is Mary's husband and Autumn's father and he runs the laundromat on 35th and State and he is part of ...".

    If you still aren't satisfied then what else are you looking for? Beyond a name, a set of properties, and a set of relationships, what does it mean to you to know what something "fundamentally is"?
  10. Apr 10, 2014 #9


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    Of course...I think we were missing this. And this is exactly the reason that there should always exist axioms and undefined concepts because somewhere you run out of things to relate your concepts to and run out of properties to associate to concepts!
  11. Apr 10, 2014 #10
    I have a similar problem. I don't know what's an apple. I've seen many web pages explaining that apples and bananas are not the same thing. Many pages also described an apple in terms of its properties. They mentioned that it is a sweet juicy fruit but all failed to tell me what it is. I understand that apples are a fruits but when I tried to understand what is a fruit I found that a fruit is defined in terms of its properties, origin, and biological function but all the pages I read failed to describe what a fruit really is. I still don't know what is an apple.
  12. Apr 10, 2014 #11


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    Acceleration is the time rate of change of the velocity, which in turn, is the time rate of change of position.

    You will find that all measurement systems are arbitrary to some extent. The yard was based on the distance from someone's nose to the tip of his finger. The meter has been defined several times. Originally, it was supposed to be 1/10,000,000 of the distance along a quadrant of the earth from the equator to the north pole. When it was found to be impractical to physically survey that quadrant, other equally arbitrary definitions were substituted.

    The fact that something is arbitrary is not necessarily a disqualification to being useful. If enough people agree to observe the same set of arbitrary measurements, then we have a convention which can be applied consistently.

    As a result of Newton's Second Law of Motion, force and mass were related by F = m a

    Originally, the gram was defined as the weight of 1 cc of pure water at the temperature of melting ice.


    Later, other standards were developed, since water has a tendency to evaporate and it also changes density with temperature. A physical standard kilogram mass was fabricated and kept at Paris.

    We can't measure mass directly, but we can measure the effect which gravity has on a standard mass. We can measure this effect on other bodies, and a comparison of the two measurements will determine the ratio of the mass of the given body to the standard.
  13. Apr 10, 2014 #12
    ...dauto, I don't know if I'm supposed to take this as a mockery or a benevolent explanation of what you think is wrong with my way of thinking. If it's the former, know that it's very disturbing and I'd like you to not do that again in the future. It's counterproductive to try to embarrass people for doing what this forum is about - seeking help.

    I'm not rejecting definitions in terms of any property, I gave the example of the atom to clarify what terms would help me understand. Then I further clarified that it was actually more a matter of how it's measured that was problematic to me.

    If it's the latter then it's okay. Thank you all of you who made the effort to help me, I understand it a lot better already! :)
  14. Apr 10, 2014 #13


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    Actually, it's not all circular, because we have other equations which specify some properties of force and mass. One equation by itself tells you nothing, but when you have a whole set of equations which all fit together, you achieve a powerful consistent meaning.

    but we also know from Newton's third law:
    ##F_{12} = -F_{21}##
    We can now combine the laws to say: If two objects are pushing off each other and accelerate at equal rates (in opposite directions), they have the same mass.

    We also have the conservation of mass. By extension, if you add two masses together, you get a larger mass through addition. Now you can apply the same force to a different mass and calculate the acceleration.

    Mass is just this quantity that appears in a lot of equations, and the fact that many equations use the same quantity makes it a powerful concept. I would not worry about any underlying meaning of mass beyond what is in the equations. Physics is just about making models that match our experiments. If you ask why too many times, you end up with philosophical nonsense.
  15. Apr 10, 2014 #14


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    Ah, then I would recommend jtbell's post #7 link to the BIPM website.
  16. Apr 10, 2014 #15
    It also works with the original second law (F=dp/dt). But than you additionally need the definition of momentum (p=m·v) and the transformation (Galilei or Lorentz) to get a full definition of mass (as used by Newton).
  17. Apr 11, 2014 #16
    My comments were not intended as mockery. They are just my slightly dorky way of pointing out that there really isn't any difference between understanding what something is and understanding its properties.
  18. Apr 11, 2014 #17
    Okay, thanks to you too then (the Internet makes it difficult to know how to take things, sorry!)
  19. Apr 11, 2014 #18
    I look at it differently. In my judgement, you were on the right track when you focused on F = ma. Suppose we could specify force independently of mass, by, say, measuring the tension in a spring. So force would not be just mass times acceleration, but something that stands on its own. Once we agree that this is possible, then we have a precise definition of mass. It is simply the proportionality constant between the net force that you apply to a body and the acceleration that the body experiences in response to the force.

  20. Apr 12, 2014 #19


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    There are at least three different definitions of mass.
    (1) Quantity of matter
    (2) Amount of inertia
    (3) Gravitational charge.
  21. Apr 12, 2014 #20

    Andrew Mason

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    If one starts with the premise that:

    1. the laws of motion are the same in all inertial reference frames, and
    2. time and space are absolute,

    the concept of mass as a quantity of matter naturally emerges.

    We can define a unit of force as the physical phenomenon that causes a one unit change of velocity of a unit body in one unit of time. One unit of force applied to each of two identical unit bodies at the same time for the same duration would result in the same change of velocity. If that was not the case, then after the force ended (at the same time for both unit bodies), the bodies would define two different inertial frames of reference in which either: 1. the laws of motion were not the same, or 2. time and space were measured differently. In that case, one of the premises would be negated.

    One unit of force on each body is a total of two units of force. Therefore, the force required to change the motion of two unit bodies in a given time period is double that required to make the same change of motion of a one unit body. So we conclude that the force is proportional to the number of unit bodies of matter for a given change in motion per unit time.

    Newton conceived that matter must consist of fundamental units and that the mass of a macroscopic body depends on how many of these units it contains. He was basically right - very close. The units are nucleons - protons and neutrons. The mass of a macroscopic body is very close to being exactly proportional to the number of nucleons it contains. [There is a slight difference between the mass of a neutron and the mass of a proton+electron. Also the masses of different nuclei are not exactly proportional to the number of nucleons because of different binding energies, but the differences are very small.]

    The definition of mass as "quantity of matter" begs the question: how does one define the mass of a particles smaller than a nucleon? For fundamental particles, such as electrons, neutrinos, positrons, quarks, anti-quarks etc., the definition of mass has to change, because they are not made up of nucleons. When defining something that is fundamental the best you can do is describe its qualities. For fundamental particles, we define their masses by the way they respond to forces as if they were macroscopic bodies, using m = F/a .

    Last edited: Apr 12, 2014
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