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Please answer this question of mine, thanks.

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  • $\begingroup$ Hi Swapnil. There is no special reason to expect that the lowest energy state of a system has zero mass. Rather the reverse in fact since it is the lowest energy state of the Higgs field that produces a mass for the fundamental particles. Can you extend you question to make it clearer what you are asking because at the moment the question isn't sufficiently clear to have any answer. $\endgroup$ – John Rennie Sep 26 '16 at 11:02
  • $\begingroup$ Ok, so lemme clarify this. We know that every system in the universe tries to achieve the lowest state of energy. We also know, mass is a form of energy. So why doesn't mass of every system get down to zero? $\endgroup$ – Swapnil Das Sep 26 '16 at 11:56
  • $\begingroup$ I have tried to answer exactly that question below. Electron, quarks and other stable particles do not spontaneously convert into energy, so that mass is always present in the universe. $\endgroup$ – user108787 Sep 26 '16 at 12:06
  • $\begingroup$ @SwapnilDas: energy is conserved so it can't just disappear. Mass is indeed a form of energy, and mass and energy can be interconverted, but whether it's in the form of mass or not energy is conserved. Why would converting mass to the equivalent amount of energy lower the total energy of a system? Rather the reverse I would have thought. $\endgroup$ – John Rennie Sep 26 '16 at 13:06
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There are two important (and common) misconceptions here:

  1. "Every system reaches it's lowest energy state" - this is not true. Indeed, up to some very large-scale cosmological effects, energy is perfectly conserved in a closed system, rather than minimized. What is indeed minimized, at equilibrium, is a particular subset of energy called free energy*.

  2. Minimization of free energy is subject to constraints given by conservation laws. For example, this means that while an electron and positron may spontaneously decay into massless photons, if they are close enough to each other, an isolated electron will not because it would violate both conservation of electrical charge and conservation of momentum. In our universe, there is a large imbalance between the amount of matter and anti-matter, so as a result it would not be possible for all of both to annihilate and leave only massless particles.

*The form of free energy in this link is valid for a system with a fixed volume. Other forms of free energy apply to closed systems with different constraints.

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Mass is not energy, this is a common misconception. Mass contains energy, but that doesn't mean what you might think. Energy is not a "thing", is a quality of a thing. Like colour. You can hold a blue ball, but you cannot hold "a blue". You cannot hold energy either, there is no such thing as "pure energy" any more than there is a "pure blue". (unless you are a hooloovoo)

There is a real world analogy, money. If you have money, you can buy a chair. You can also buy a phone. If you have a chair you can sell it and then buy a phone. You can represent that money in the middle of the exchange with dollar bills. But chairs are not made of phones, phones are not made of chairs, and neither are made of dollar bills.

Energy, like "worth", is just a number. Unlike worth, it has two special features, it is conserved, and the total amount is fixed. So while your chair's worth will change on it's own, and the total amount of money changes while I write this, the "energy worth" of a log is whatever it is and always will be.

This is extremely useful mathematically. I have a conversion that tells me if I burn a log I will get a certain amount "of energy". What I really get is light, exhaust gases and ash. The exhaust gasses are hot, and I have another conversion factor that tells me that if I have a certain amount of hot gas, I can turn that into a certain amount of rotary motion using, say, a turbine. And I have another that says if I have a certain amount of rotary motion I can turn that into a certain amount of electricity.

So in a manner of speaking, I turned a log into electricity. But I didn't, really. And that electricity has a certain amount of energy, so I could even say I turned a log into energy. But I didn't really do that either. No more than I turned a chair into a phone.

So back to the original question. Mass is not energy. It "has energy", in the same way an unburned log "has energy". If you freeze a log, it doesn't stop being a log. And that's what "lowest energy state" really means, freezing it.

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  • $\begingroup$ I don't think this is a particular useful way to think about things. If you have a bunch of particles zipping around in a box, their speed directly affects how much the box weighs by #E=mc^2$. So the energy can be described equally as being in the mass or in the kinetic energy of the particles. $\endgroup$ – Rococo Sep 26 '16 at 14:35
  • $\begingroup$ You're not measuring mass, you're measuring energy. Or the local stress tensor anyway. We confuse the two at low energy scales, in the same way we think the world is Newtonian at low energy scales. $\endgroup$ – Maury Markowitz Sep 26 '16 at 15:48
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Take a small system as a model of the universe, (which follows the same rules as the universe), such as the soap bubble shape shown below:

enter image description here

This simple model shows you how the soap bubble surface will assume a shape that minimises the potential energy of the bubble. Theoretically, when this bubble was made, it could have had an infinite number of shapes, but it's following the rule that potential energy is minimised, which gives it its distinctive hyperbolic shape.

But the electrons, protons and neutrons in the atoms that make up the soap/water material are stable. An elementary particle will not spontaneously convert itself to energy, so it retains its rest mass indefinitely.

So systems act to minimise their potential energy, but the elementary particles that make up the system are, if you like to think of it in potential energy terms, already at their minimum potential energy level. This is not the way they are normally viewed, but I include it in case it helps my explanation.

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    $\begingroup$ $E=mc^2$ does apply to rest mass. That is not the reason that lone particles cannot decay. $\endgroup$ – Rococo Sep 26 '16 at 14:20
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    $\begingroup$ Indeed, if $E=mc^2$ didn't apply to rest mass, what would it apply to? $\endgroup$ – WillO Sep 26 '16 at 14:36

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