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Natsirt
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Since E=mc2, that means that mass is energy and energy is mass right?
In units where c=1 they do have the same units. But the full equation is m^2=E^2-p^2, so they are not generally the same. The simplified equation only applies for p=0.Natsirt said:Since E=mc2, that means that mass is energy and energy is mass right?
ModusPwnd said:This is a complicated question and I look forward to reading others responses. In short, I think the answer is no. That equality states an equivalence/equality in a context. Four quarters equals a dollar bill. That does not mean that four quarters is a dollar bill. It means that they are equal/equivalent in a context.
ttreker said:Nicely put doesn't make it true. Wherever you find four quarters, you don't find a dollar.
If x is conserved then any f(x) is also conserved. Mass is a function of E and p and since E and p are conserved then m is conserved also.ModusPwnd said:From what I remember, noether's theorem states that a symmetry implies one and only one conserved quantity.
That equation is wrong, in general, as it's been wrote to you.Natsirt said:Since E=mc2
No. But a system's mass could be defined as "the energy of that system in a frame of reference where its momentum p is zero".that means that mass is energy and energy is mass right?
Natsirt said:So this is what I think all this means. When calculating the energy of rest mass you times the mass by C, but you also have to times mass by P and the P would be the same as C so squaring C in e=mc2 doesn't make the final calc higher than it should be. Or mc^2 times mp^2
DaleSpam said:Yes, it is the invariant mass: ##m^2 c^2 = E^2/c^2 - p^2##
E and p are components of the four-momentum, and m is its norm (neglecting factors of c). Conservation of the four-momentum implies conservation of E, p, and m, but only m is invariant. The other terms are conserved but not invariant. Conservation of the four-momentum is due to space-time translational symmetry (translation in space and time) per Noether's theorem.
DaleSpam said:Yes, it is the invariant mass: ##m^2 c^2 = E^2/c^2 - p^2##
E and p are components of the four-momentum, and m is its norm (neglecting factors of c). Conservation of the four-momentum implies conservation of E, p, and m, but only m is invariant. The other terms are conserved but not invariant. Conservation of the four-momentum is due to space-time translational symmetry (translation in space and time) per Noether's theorem.
Natsirt said:What do you mean: four-momentum?
lightarrow said:That equation is wrong, in general, as it's been wrote to you.
No. But a system's mass could be defined as "the energy of that system in a frame of reference where its momentum p is zero".
As you see, they are not exactly the same thing, even if there is a relationship between them.
Note that the difference is not only "formal": a photon has zero mass but has non-zero energy, for example.
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lightarrow
Natsirt said:What do you mean by non-zero energy? And how are thinking of momentum in your description, I know p=MV but are you thinking of it differently to make the explanation clearer in you head? Thanks for your help I think I'm close to understanding.
SciKim said:Yes they are the same. Mass and energy are equivalent, and you can look up plenty of articles online about mass-energy equivalency.
Yes, according to Einstein's famous equation, E=mc², mass and energy are two forms of the same thing and can be converted into each other.
Mass and energy are related through the principles of special relativity, where mass can be converted into energy and vice versa. Mass is a measure of an object's resistance to acceleration, while energy is a measure of an object's ability to do work.
Yes, mass can be converted into energy through nuclear reactions, such as fusion and fission, where a small amount of mass is converted into a large amount of energy.
Mass is a property of matter that determines its resistance to acceleration, while energy is a measure of an object's ability to do work. Mass is a constant value, while energy can take on many different forms.
The concept of mass-energy equivalence has revolutionized our understanding of the universe by providing a deeper understanding of the relationship between matter and energy. It has also played a crucial role in the development of technologies such as nuclear power and the atomic bomb.