How does the theory of relativity explain changes in mass and energy?

In summary, the theory of relativity shows that the total energy of a particle is equal to its rest energy (mc^2) plus its relativistic kinetic energy, which takes into account the change in momentum with a change in velocity. This is represented by the equation E^2 = (mc^2)^2 + (pc)^2, where p is the momentum and ɣ is the Lorentz factor. The relativistic Doppler shift also affects emitted radiation, but it is not related to the mass of the emitting object.
  • #1
Crazy Tosser
182
0
So, by the theory of relativity: [tex]m=\frac{m_{0}}{\sqrt{1-\frac{v^2}{c^2}}}[/tex]

But then, we have [tex]E=mc^2[/tex].

So if you have (relative to YOU) a very fast moving body, when it radiates, the radiation is actually of higher energy than it would be if the body was static?
 
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  • #2
The E in E=mc^2 is only the rest energy of the particle. It does not include any Kinetic Energy.
 
  • #3
bassplayer142 said:
The E in E=mc^2 is only the rest energy of the particle. It does not include any Kinetic Energy.

KE, as in [tex]mv^2/2[/tex]? No, it doesn't. But my question was just that, do relativistic effects on the mass modify the energies of the emitted waves?
 
  • #4
Crazy Tosser said:
KE, as in [tex]mv^2/2[/tex]? No, it doesn't. But my question was just that, do relativistic effects on the mass modify the energies of the emitted waves?

No. There is a relativistic effect on emitted radiation which is known as the relativistic Doppler shift, but it doesn't have anything to do with the mass of the object doing the emitting (ignoring gravitation).
 
  • #5
Crazy Tosser said:
So, by the theory of relativity: [tex]m=\frac{m_{0}}{\sqrt{1-\frac{v^2}{c^2}}}[/tex]

But then, we have [tex]E=mc^2[/tex].

No, we don't. We have [tex]E=m_{0}c^2[/tex]
 
  • #6
WarPhalange said:
No, we don't. We have [tex]E=m_{0}c^2[/tex]
[tex]E=m_{0}c^2[/tex] is the energy of a particle at rest.
[tex]E=mc^2[/tex] is the total energy of a particle.
So,
[tex]mc^2[/tex] = [tex]m_{0}c^2[/tex] + relativistic kinetic energy.
 
  • #7
That's why you should go with the full equation...

E^2 = (mc^2)^2 + (pc)^2

Since m is the rest mass, you have to add the energy from the momentum, p, which (when regarding mass bearing objects) is...

p = ɣmv
ɣ = (1-v^2/c^2)^(-1/2)

So there you get a change in momentum with a change in velocity, changing the total energy of the object and giving you the energy of the same object at rest (E = mc^2) when not at rest (E^2 = (mc^2)^2 + (((1-v^2/c^2)^(-1/2) * m * v) * c)^2).
 

Related to How does the theory of relativity explain changes in mass and energy?

1. What does "E=mc^2" mean?

The equation "E=mc^2" is known as the mass-energy equivalence equation, which describes the relationship between mass (m) and energy (E). It means that the amount of energy (E) contained in a mass (m) is equal to the mass (m) multiplied by the speed of light (c) squared.

2. How does changing the value of m affect the equation?

Changing the value of m, which represents mass, will directly affect the amount of energy (E) in the equation. As mass increases, so does the amount of energy. Similarly, decreasing mass will result in a decrease in energy. However, the speed of light (c) remains constant, so the relationship between mass and energy will always follow the same formula.

3. Can mass be converted into energy?

Yes, according to "E=mc^2", mass and energy are interchangeable. This means that given a certain amount of mass, it is possible to calculate the equivalent amount of energy. This concept is important in understanding nuclear reactions and the release of energy from atoms.

4. How did Einstein come up with this equation?

Albert Einstein developed the equation "E=mc^2" in 1905 as part of his theory of special relativity. He was trying to reconcile the laws of electromagnetism with the laws of motion, and the equation was a result of his attempts to unify these concepts. It has since become one of the most famous and influential equations in physics.

5. What real-world applications does "E=mc^2" have?

"E=mc^2" has many implications in various fields, including nuclear energy and weapons, space travel, and particle accelerators. It also plays a crucial role in understanding the behavior of objects moving at high speeds and has been confirmed countless times through experiments and observations in the field of physics.

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