the inconsistency of e=mc^2...?

Question

we know that e=mc^2. Here 'e' is equal to K.E + P.E. Now in case of a photon, P.E is ~ 0, then there is only K.E left which again is equals to 1/2mv^2 . Also here v = c as photon travels with the velocity of light, then it becomes as 1/2mc^2.
Now after equating this in e=mc^2 we get...

1/2mc^2 + 0 = mc^2 mc^2 gets cancelled
then
1/2 = 1
or
1=2

How is this possible?
Is this possible or I've done some mistake?
Please tell.....

Answer 1

The first mistake is using the simple approximation of K.E + P.E far beyond its applicability to purely mechanical systems.

The second is calculating the Newtonian kinetic energy with anything other than the rest mass, which is zero.

The photon is the quantum of the energy in an electromagnetic wave (light). You could calculate its energy directly using the quantum product of Planck's constant and the wavelength. You could calculate it indirectly by calculating or measuring the energy of a specific electromagnetic wave and dividing by the number of photons, both per second.

Answer 2

First, KE at very high speeds is not (mv^2)/2. The energy of the photon is mc^2.Here, m is the relativistic mass, which is NOT ZERO.you have to use the de Broglie relation to find the effective mass of the photon, which is determined by its wavelenght.At high speeds, KE=(m'c^2)(y-1), where m' is the rest mass and y=root of {1-(v/c)^2}.For photon, the relations between energy and momentum is, E=pc, where p is the momentum of the particle, which again shows that photon also behave as a particle. Anyway, its a very long discussion and i may not be able to explain you very clearly. If you are really interested in this, then you can refer to a book on B.Sc. Physics

Answer 3

You have obviously done some mistake. Who says that the energy of a photon is mc^2. The energy of a photon is hc/wavelength.
Photons of different wavelength have different energies.
E=mc^2 is the energy equivalent of mass m. You are confusing with formulas for two different things and equating them. Hence, incomprehensible results.

Answer 4

E=MC^2 refers to a some kind of P.E. of the mater. If the mass would be annihilated, the radiation would have that E.
Notice that a M will be infinity and use infinity E to move at C.

The photon has no mass.

Answer 5

NO.

E = mc^2 does NOT equal KE plus PE. Absolutely not.

Measurement of KE and PE are relative and frame dependent. This is perfectly obvious if you think about it (the PE of a 10 kg weight held by someone 10 m above you is 1000 J relative to you and 0 relative to them).

Go back to the text books.