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- Thread starter roboticmehdi
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Potential energy doesnt fit inside, because its just that--potential. By the same argument, everything has stupid amounts of potential energy, since everything moves relative to a black hole. However, just because the earth, for example, could enter a black hole and gain infinite energy in the singularity, doesn't mean that it has infinite energy now. Potential refers to the future and things that have not yet happened, so it wouldn't make sense if future events could affect the current energy/mass of particles. Thats paradox city.

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jtbell

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JUST WHERE DOES THE POTENTIAL ENERGY FIT IN THE E=MC^2 EQUATION ?

The gravitational potential energy of the two spheres must be included in E. As the kinetic energy of the spheres increases, their potential energy decreases correspondingly. The total energy remains constant, and therefore so does the mass of the system.

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zonde

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Amount of potential energy depends from position of objects.nothing depends on relative positions of objects

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- I want to find the energy of this system. Does energy depend on mass ? Yes it does, energy is equal mass times c squared.

- What does mass depend on? on lorentz factor, m=mo*y.

-What does lorentz factor depend on? speed only.

So energy depends on mass, mass on lorentz factor and lorentz factor on speed. So energy depend on speed only( as a variable I mean, of course mo and c are constant at all times). So see energy does not depend on relative position.

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Just blowing SA's answers off because you think you know better isn't a good way to learn, however.

Anyway -the mass of a bound system is not, in general, equal to the sum of the masses of its component parts as you have assumed. However, the difference will be negligible.

I should add that this is the basic answer, which glosses over some subtle points peculair to gravitation as a binding energy source.

If we change the problem to nuclear binding nergy, not only do we not have to worry about some of these subtle issues, we have well-known measured resutls

See for instance the wiki article on binding energy http://en.wikipedia.org/w/index.php?title=Binding_energy&oldid=506322211

Mass change

Mass change (decrease) in bound systems, particularly atomic nuclei, has also been termed mass defect, mass deficit, or mass packing fraction.

The difference between the unbound system calculated mass and experimentally measured mass of nucleus (mass change) is denoted by Δm. It can be calculated as follows:

Mass change = (unbound system calculated mass) - (measured mass of nucleus)

i.e., (sum of masses of protons and neutrons) - (measured mass of nucleus)

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For a composite system, E=mc^2 is more useful in computing the mass of the composite system, given the energy, than it is computing the energy, given the mass. If you have two particles that are bound by some attractive force, the total mass of the two-particle system is not going to be equal to the sums of the masses of the particles. For two particles moving nonrelativistically, the total mass will roughly be given by:

m

where m

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Thank you stevendaryl ! Thats the answer I was looking for.

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Dont go start with energy to find mass. start with mass to find the energy. Think like this:

- I want to find the energy of this system. Does energy depend on mass ? Yes it does, energy is equal mass times c squared.

- What does mass depend on? on lorentz factor, m=mo*y.

-What does lorentz factor depend on? speed only.

What you wrote is just not true. There is nothing in SR that says that mass only depends on the lorentz factor. What SR says is that

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Yes, particles have potential energy, and just like in high school, potential energy and kinetic energy are conserved. The issue here is then: why potential energy didn't add some mass too? Kinetic energy did add mass, through factor [itex]1/ \sqrt{1-u^2}[/itex].

We have gravity in the mix? We are not within the realm of special theory of relativity anymore, then! Space is no longer Minkowski space. We need general theory of relativity here. And what does it say? It says: clocks run slower in strong gravitational field. So how do we calculate speed [itex]u[/itex]? Well, we must know what time it is... So things become more complicated in gravitational field. Furthermore, the reference frame is no longer inertial. You can't just swap observers. They see world differently one from another.

Furthermore, You know about analogy between accelerated elevator and gravitational field? Object standing still in gravitational field and object accelerated in elevator feel the same force acting. It's the same thing. It's called equivalence principle. And accelerated object is moving. So it has some velocity. So it has some extra mass. This picture is equivalent to object not moving, but being in gravitational field. Two pictures are equivalent. So: gravity adds to mass.

Keyword: equivalence principle.

This is how Einstein himself described it for general audience: http://www.marxists.org/reference/archive/einstein/works/1910s/relative/relativity.pdf

I hope this helps a bit.

Cheers.

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Hi.

Finally, changing a referent potential energy level in general theory of relativity impacts the measurable forces, unlike the change of referent energy level in classical physics. So the original question is quite a complex one.

Cheers.

Finally, changing a referent potential energy level in general theory of relativity impacts the measurable forces, unlike the change of referent energy level in classical physics. So the original question is quite a complex one.

Cheers.

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Some experimental evidence:

For electrical and nuclear potential energy, see http://www.livingreviews.org/lrr-2006-3 , section 2.1.1. For gravitational potential energy, see 3.6.1.

And of course we need the usual warning that the source of gravity is not scalar mass-energy but the stress-energy tensor. For experimental evidence that pressure is a source of gravity, see the discussion of the Kreuzer experiment here: http://www.lightandmatter.com/html_books/genrel/ch08/ch08.html#Section8.1 [Broken]

For electrical and nuclear potential energy, see http://www.livingreviews.org/lrr-2006-3 , section 2.1.1. For gravitational potential energy, see 3.6.1.

And of course we need the usual warning that the source of gravity is not scalar mass-energy but the stress-energy tensor. For experimental evidence that pressure is a source of gravity, see the discussion of the Kreuzer experiment here: http://www.lightandmatter.com/html_books/genrel/ch08/ch08.html#Section8.1 [Broken]

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