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Recently, I've been looking through some physic articles and found some equations of relativity. In those articles it was said that the relative mass varies depending on whether it's moving or not. So if a object is moving really fast it has more mass than a resting object.

The thing is, since we are moving through the universe at a really high velocity, could we say that the mass we can measure is actually higher than our real mass? Is the mass we can measure our real mass or should we use any equation to get it?

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    $\begingroup$ No, there is only one mass for any object , that does not change no matter how fast it travels, if you read this link, it might make sense profmattstrassler.com/articles-and-posts/… $\endgroup$
    – user108787
    Aug 13, 2016 at 15:32
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    $\begingroup$ Have a look at Why is there a controversy on whether mass increases with speed? $\endgroup$
    – ACuriousMind
    Aug 13, 2016 at 15:38
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    $\begingroup$ First, the (relativistic) mass of a moving object is higher than its rest mass in the direction of motion, but not in orthogonal directions, so you need to be careful about this distinction. Second, of course, you are never moving relative to yourself, so your own relativistic and rest masses (as measured by you) are equal. $\endgroup$
    – WillO
    Aug 13, 2016 at 16:49
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    $\begingroup$ @WillO Those that use "relativistic mass" to talk about the coordinate inertia, recognize that they need two of them. The one that is usually talked about $\gamma m$ is the "transverse mass" $m_T$. The one along the direction of motion ("longitudinal mass") changes by a larger factor $m_L = \gamma^3 m$. So the "mass" is different both longitudinally and transversely, but more so longitudinally. Yet another reason to abandon the terminology. $\endgroup$ Aug 13, 2016 at 17:59
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    $\begingroup$ I don't think the warnings you've gotten here are stern enough, so here's my own: Never, under any circumstances, should relativistic mass be used. Trash it, wipe it from you mind. If a book uses it, throw out the book. Seriously. There are hundreds of special relativity texts written, and the world will lose nothing if we burn any book that uses the notion. You can't expect to learn anything from an author who uses such a term, because that author fundamentally does not understand relativity. $\endgroup$
    – user10851
    Aug 14, 2016 at 4:20

3 Answers 3

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I think your confusion stems from the fact that many old textbooks use the term "relativistic mass" misleadingly. In the realm of special relativity there is in fact only one mass (rest mass), which is an inherent property of any particle/object, defined over the energy-momentum relation:

$ m = \frac{\sqrt{E^2 - (pc)^2}}{c^2} $

This mass is invariant under a Lorentz transformation, as the energy-momentum relation is invariant under a Lorentz transformation (if you're familiar with covariant notation: $p_{\mu} p^{\mu}$ is a scalar, otherwise just prove it explicitly for an arbitrary Lorentz boost and rotation (Lorentz boosts and rotations generate the proper Lorentz transformations)).

The misunderstanding comes from the fact that many authors mistakenly incorporate the $\gamma$ factor in the mass, thus obtaining a mass that depends on the reference frame. Find a great discussion in Relativistic mass (Wikipedia).

I hope this helps :)

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Rest mass is an attribute of an object which remains the same in all frames. As you suggest, the total mass of an object is different from its rest mass if it has kinetic energy (meaning it is moving). However, in most cases where we measure a mass, we keep the mass holding still while we take the reading. In this case the object is motionless in the frame we are measuring in, so in that frame, its total mass and rest mass are identical.

If you were measuring the mass of a fast moving object (perhaps by measuring a momentum transfer), you would see the total mass as being higher than the rest mass because it had kinetic energy. However, in most cases we don't do this because it's harder to measure masses that are moving. Also, in realistic situations (sub-relatavistic speeds in the frame we are measuring in), the difference wouldn't matter for almost all meaningful measurements.

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Supposing that you do want to use the convention where "relativistic mass" is a valid concept (because I don't think that "don't do that" suffices as a complete answer to your question):

You ask, does an object have a relativistic mass when it's sitting still on Earth? The answer is "yes, of course". An object always has a relativistic mass. For an observer at rest with respect to the object, though, its relativistic mass equals its rest mass. The speed with which the Earth zips around the Sun, or the galactic nucleus, or anything else doesn't matter; if you're conducting an experiment here on Earth, and the parts of your experiment aren't moving at ludicrous speed relative to one another, then you won't observe a relativistic mass that's noticeably different from the rest mass. That's what makes relativity relativity.

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