Q&A

# What's the meaning of "outdated" in physics?

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I was recently reading some questions here and there saying that "relativistic mass is outdated". I saw someone saying that "outdated" doesn't mean the concept is wrong. My question is what physicists mean by "outdated"? Not everyone was saying that relativistic mass is outdated. Some physicists still say that relativistic mass term.

a hotter body is more massive than a colder body (that's an example of relativistic mass, some says it's utter nonsense but they explain it some other way, the more information is available here (a book?) I can't remember anything from the book so not including anything).

When I heard the "outdated" term first then I thought they are actually saying that the concept isn't correct the way others are explaining but the equation is helpful and peoples are misunderstanding it. And their explanation goes this way ..........................................................................

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That sounds like something I'd say, so I'll explain this from my point of view, in particular regarding 'relativistic mass'.

An 'outdated' theory or piece of terminology isn't typically mathematically 'wrong'. Rather, a given law or piece of terminology being outdated would typically mean that there is a newer theory or term that is either more consistent with other theories or terminology, or makes those theories or terminology easier to learn/understand, or the outdated term needlessly messes with our intuition of what that terminology means. I would consider something outdated if learning it does not help (or potentially even hinders) our intuition/understanding of physics.

In terms of relativistic mass $m_{\text{rel}}$, this comes in to play in equations like $$E = m_{\text{rel}}c^2 = \gamma m_{\text{rest}}c^2.$$

There are a number of things to note here. Perhaps the simplest one is that in units where $c=1$ (which is a common thing to do), $E=m_{\text{rel}}$, so relativistic mass is just energy (albeit in different units to what we use in everyday life), so from that perspective, it's creating another term when a perfectly good one already exists.

The second thing to note about this is that at non-relativistic speeds, the energy is approximately given by $$E = m_{\text{rest}}c^2 + \frac{1}{2}m_{\text{rest}}v^2,$$ or 'rest energy' + 'kinetic energy'. Before taking a course in relativity, this is what we're used to using and seeing because this is what occurs in daily practical life. While, at these speeds, $m_{\text{rest}} \approx m_{\text{rel}}$, we're just not used to the concept of mass increasing with speed because our experience indicates that energy changes with changing speed while what we typically consider as 'mass' remains constant. Even writing out higher order terms, relativistic mass does not appear.

While you can define a relativistic mass and nothing breaks (if you're careful enough), it opposes our intuition of what mass is without offering anything new, making it a concept that is unessecary to learn to understand physics or relativity. Quite simply, what is the purpose behind adding extra terminology, when other terminology for the same thing already exists, then having to spend time learning that extra terminology when it brings no new understanding of physics?

As such, I would consider 'relativistic mass' to be outdated because it is a mathematically valid term that was used more often in the past and that it is unessecary to learn to obtain a complete understanding of present day relativity.

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