What exactly is the Rest mass energy? I know the usual goes Like it is total energy stored in mass $m$ that is in Rest. so for someone moving relative to the frame that the mass $m$ is in (a rest frame) the value of mass $m$ increases by factor of $\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$. but I cannot find intuitive. is it the total amount of energy that can be converted from the Rest mass $m$? and how the mass increases when observing from or on the moving from? and where does the increased mass come from? please explain it me intuitively.
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5$\begingroup$ the value of mass m increases by factor… You’re talking about relativistic mass, which is an obsolete concept. It’s not just unintuitive, it is pointless and confusing. Today “mass” means the Lorentz-invariant mass, which does not increase. (This is the mass that Dale’s answer is talking about.) What is increasing is the energy, and it is intuitively obvious that an object has more energy when it’s moving than when it isn’t. $\endgroup$– GhosterCommented May 24 at 3:42
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2$\begingroup$ Rest mass energy is the rest energy. Is rest mass energy taken from a reference? Which page? $\endgroup$– Qmechanic ♦Commented May 24 at 5:33
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$\begingroup$ Some books still use relativistic mass, but it's been deprecated for decades. Please see physics.stackexchange.com/a/133395/123208 $\endgroup$– PM 2RingCommented May 24 at 5:38
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2 Answers
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The problem with asking for an intuitive explanation is that intuition is not an objective feature of an explanation. Intuition is something that is personal and it is developed individually from experience. What is intuitive for me may not be intuitive for you.
That said, what makes this intuitive for me is the understanding that energy and momentum are not separate things but are both part of a unified four-dimensional vector called the four-momentum: $(E/c,p_x,p_y,p_z)$. Then mass is just the magnitude of that vector. $m^2 c^2=E^2/c^2-p_x^2-p_y^2-p_z^2$
This is intuitive to me because understanding it in terms of this representation allows me to use all of my previous experience with vectors and geometry.
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In physics today, mass always refers to rest mass. When referring to other types of mass, such as "relativistic mass" or "invariant mass," one always adds an extra qualifier to be clear.
With this in mind, mass does not increase with speed and does not depend on the observer measuring it. For example, the mass of the electron is always $9.1093837 \times 10^{-31} Kg$ no matter who measures it.
Rest mass energy is defined to be $E_0 = m c^2$. It is the total energy in a static object of mass $m$. This energy can be extracted from this mass through fusion, fission, etc.
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$\begingroup$ But when study fusion or fission the Mass is moving So it has to be a relativistic Mass. Otherwise errors in the calculations can go significantly high right? $\endgroup$– HelloCommented May 24 at 5:42
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1$\begingroup$ No, we still use mass. We just use a different formula for energy and momentum which takes relativistic effects into account. Energy is NOT defined by $E=\frac{1}{2} mv^2$ and momentum is NOT defined by $p=mv$. $\endgroup$– PraharCommented May 24 at 6:06