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From $E=mc^2$ it seems mass and energy are interchangeable.

I can understand that mass is distinguishable, one type from another, such as protons and electrons.

But in the reverse process, how is it possible that the energy that became one particle is completely indistinguishable from the energy that became a different type of particle.

Shouldn't there be only one type of particle? does this imply that energy is some kind of composite thing with the potential to be this or that, like a stem cell in biology. or is it a simple thing?

Take an electromagnetic wave (photon) as an example (which is massless). it is completely indistinguishable from another photon of the same frequency. yet one can "condense" into one kind of particle and the other into a different kind. how is this possible if both photons were completely indistinguishable.

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Energy is a measure of a certain quantity well defined in the study of the behavior of nature.

how is it possible that the energy that became one particle is completely indistinguishable from the energy that became a different type of particle.

It is like asking about two sets of marbles "how come there are 19 marbles in one set and 19 marbles in the other". The number that describes one set is completely indistinguishable from the number that describes the other set, yet these are two different sets of marbles.One has to distinguish measurement ( context) from content( particles).

It is true that with special relativity the distinction between mass and energy does not exist because of the E=m*c^2 , but mass is also a measure. Particles are distinguished by their quantum numbers not just their rest mass. It is a multidimensional description of what a particle is, with many measures. Thus given enough energy particles can appear within the rules of quantum number development , but energy is always carried by particles from the table of elementary particles. It is an attribute, something that a particle has, like its quantum numbers, not an independent entity.

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isn't energy more than an attribute? photons for example are a form of energy since they are massless – good_ole_ray Jun 16 '13 at 6:51
Nope. Photons are not a form of energy, but they can have energy. The fact that a photon is massless means that it has no mass energy, but like any other particle, it can still have kinetic energy. – David Z Jun 16 '13 at 6:55
What David says. If you study the table of elementary particles in the link you will see that the photon is a particle. – anna v Jun 16 '13 at 6:57
ok, so even if it is a particle. it can be converted to energy and then to various different particles, right? – good_ole_ray Jun 16 '13 at 7:00
Not exactly. A particle carries energy, as the protons in the LHC. Interacting with other particles part of that energy is converted to new particles . There is no point in spacetime that is just energy. Have a look at Feynman diagrams, which are the mathematical description of what happens : in the figure an electron meets a positron and their combined energy via an off mass shell photon makes a quark antiquark pair and a gluon. There is not "pure energy" – anna v Jun 16 '13 at 7:05

Actually, mass is not distinguishable. Or more precisely, it doesn't even make sense to talk about whether mass is distinguishable. Different kinds of particles are distinguishable, but the particle is not the same thing as the mass. Mass is just a property of a particle, just as energy is, or velocity, or momentum, or position.

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i see. but nevertheless there is something distinguishable, like the kind of particle. – good_ole_ray Jun 16 '13 at 6:46
Yeah, but it's not the mass. – David Z Jun 16 '13 at 6:53
well I would add that the particles in the table in the link I gave are distinguished because each has many different quantum numbers plus a characteristic rest mass, which is also a similar attribute. – anna v Jun 16 '13 at 7:01

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