I Real life example of the energy contained at E=γmc^2

[Orodruin]

I think the equation e=mc^2 should be interpreted as telling us that energy has mass, not that mass is energy. Mass is the unambiguous term, defined by Newton's laws. Energy is ambiguous, since it implies something usable, but its usability depends on the state of our technology and our intentions, and anyhow the usability is limited by the laws of thermodynamics.

As has already been pointed out in this thread, mass in relativity is not defined through Newton’s laws (which are not Lorentz invariant!), but through the square of the 4-momenta of which energy is a component. As such, mass is nothing but the rest energy of a system. The fact that this corresponds to the inertia in the rest frame is the mass-energy equivalence.

Energy in no way implies ”usefulness” - this I have also already pointed out.

 

[DrGreg]

$(\gamma-1) mv\simeq mv^2/2$

I think you meant to say
$$(\gamma-1) mc^2\simeq mv^2/2$$

 

[Ibix]

I think you meant to say
$$(\gamma-1) mc^2\simeq mv^2/2$$

Indeed - now corrected above. Thanks.

 

[Herman Trivilino]

I think the equation e=mc^2 should be interpreted as telling us that energy has mass, not that mass is energy.

Mass is equivalent to rest energy. Two names for the same thing.

 

[Dadface]

We've just begun studying about relativity, and I find it amazing that bodies have the energy of E=γmc^2. Even at rest they have E=mc^2.
But where exactly is this energy present in real life? For example the keyboard I am currently typing this post with has a huge amount of energy, according to this equation, but how is it usable?

I think some of the best places to find the presence of "this energy in real life" is to observe nuclear reactions including electron positron annihilation and pair production. There are numerous other reactions which result in mass/energy changes but there are problems in making the necessary observations. For example if we burn methane with oxygen we can easily measure the resulting heat energy and we can equate this to the mass difference between the reactants and the products. But we can't (yet) measure this mass difference accurately by mass measurement techniques. With annihilation/pair production we can measure the energy of gamma rays, for example by using gamma ray spectroscopy techniques and we can measure the mass of electrons and positrons using mass spectoscopy/penning trap techniques.