E = mc^2, so how can anything have zero mass?

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In summary: This is a consequence of the full relativistic energy formula.In summary, E = mc^2 is a special case of the more general energy formula E^2 = (m_0c^2)^2 + (pc)^2. The massless particles have m_0 equal to zero but still have momentum. This formula only applies in the rest frame of the particle and does not account for momentum. For more information, please refer to the Relativity FAQ subforum.
  • #1
goldust
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E = mc^2 results in c^2 = E / m, and division by 0 is undefined.
 
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  • #2
Oops, my bad. Should be in the Special & General Relativity section.
 
  • #3
goldust said:
Oops, my bad. Should be in the Special & General Relativity section.
Done.
 
  • #4
goldust said:
E = mc^2 results in c^2 = E / m, and division by 0 is undefined.

##E=mc^2## is a special case of the more general ##E^2=(m_0{c}^2)^2+(pc)^2##. The massless particles have ##m_0## equal to zero but ##p## non-zero.
 
  • #5
E also equals FD: so how can force or distance ever be zero?
 
  • #6
E = mc^2 only applies in the special case where the particle in question is in its rest frame. Photons do not have a rest frame.
 
  • #7
Nugatory said:
##E=mc^2## is a special case of the more general ##E^2=(m_0{c}^2)^2+(pc)^2##. The massless particles have ##m_0## equal to zero but ##p## non-zero.

The 'p' in that is momentum, correct?
Yet momentum is m * v, mass times velocity. I understand that photons have a velocity of c, but their mass...? If you use the argument that it isn't talking about rest mass, but total mass, then isn't it sort of circular logic?
 
  • #8
goldust said:
E = mc^2 results in c^2 = E / m, and division by 0 is undefined.

Please read the Relativity FAQ subforum.

https://www.physicsforums.com/forumdisplay.php?f=210

Zz.
 
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  • #9
ModestyKing said:
Yet momentum is m * v, mass times velocity.
Not in general. Photons have momentum but 0 mass, and for massive objects momentum is unbounded as v approaches c.
 

1. How can energy and mass be equivalent?

According to Einstein's famous equation, E = mc^2, energy and mass are equivalent because they are different forms of the same thing. In other words, mass can be converted into energy, and vice versa. This concept is known as mass-energy equivalence.

2. If energy and mass are equivalent, does that mean anything with mass can be converted into pure energy?

No, not all objects with mass can be converted into pure energy. The conversion of mass into energy requires a very specific process, such as nuclear fission or fusion, which only occurs in extreme conditions.

3. How can anything have zero mass if E = mc^2?

While it may seem counterintuitive, it is possible for some particles to have zero mass. These particles, such as photons, have energy but no rest mass. Therefore, their mass in the E = mc^2 equation is equal to zero, resulting in the equation E = 0.

4. Can E = mc^2 be applied to everyday objects?

Yes, E = mc^2 can be applied to everyday objects, but the amount of energy produced would be minuscule. This equation is more commonly used in the study of subatomic particles and nuclear reactions.

5. How did Einstein come up with the equation E = mc^2?

Einstein's famous equation was a result of his theory of special relativity, which he developed through thought experiments and mathematical equations. He realized that energy and mass were equivalent and could be converted into each other, leading to the famous equation E = mc^2.

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