negative energy/gravity

[granpa]

when 2 oppositely charged particles spontaneously merge their electric fields cancel. but when 2 masses spontaneously merge their gravitational fields add.

 

particles with spin can spontaneously align parallel in which case their fields add or they can spontaneously align antiparallel in which case their fields cancel. it depends, I gather, on whether they are spin 'up' or spin 'down'.

 

it is well known in electrostatics that the energy in the electric field at any given point is proportional to the square of the intensity of the field at that point.

 

all very simple and entirely mainstream yet the following post was declared 'nonsense' on a certain other forum. (it was in response to a question about why the energy in the gravitational field is considered to be negative energy)

 

the energy in a field is proportional to the square of its intensity. take 2 electrons that are far apart. the energy is each of their fields is 1 unit. move the 2 electrons till they overlap completely and now the field is twice as strong which means that it holds 4 times the energy that either electron had originally and twice the energy that both held. so obviously it takes energy to force 2 electrons together. like repel. unlike attract.

 

but gravity is different. like attract. take 2 masses that are far apart and bring them together. energy was released yet now the field is twice as strong.

 

the magnetic interactions of particles can go either way depending on whether its spin up or down.

 

I have no idea why. what did I do wrong?

Edited February 1, 2009 by granpa

[Mr Skeptic]

The gravitational potential energy is only always negative if you consider the gravitational potential at infinity to be zero. It doesn't really matter what you consider the gravitational potential energy to be because what we measure is differences in energy. It just so happens that the maths are simpler if you consider the gravitational potential energy at infinity to be zero, so that is what most people do.

[granpa]

for any isolated system of 2 interacting charged particles the sum of the kinetic energy and the potential energy is constant (energy is conserved). as the kinetic energy becomes larger the fields become smaller. therefore both energies are considered positive.

 

for any isolated system of 2 interacting masses the sum of the kinetic energy and the potential energy is also constant but as the kinetic energy becomes larger the fields also become larger. therefore the energy in the field is considered negative.

 

http://en.wikipedia.org/wiki/Gravitational_energy

Gravitational energy is the energy associated with the gravitational field.

 

According to classical mechanics, between two or more masses (or other forms of energy-momentum) a gravitational potential energy exists. Conservation of energy requires that this gravitational potential field energy is always negative.

Edited February 1, 2009 by granpa

[Mr Skeptic]

Does not follow.

 

11+(-6)=5

12+(-7)=5

20+(-15)=5

 

By your reasoning, both these numbers must be positive.

[swansont]

the energy in a field is proportional to the square of its intensity. take 2 electrons that are far apart. the energy is each of their fields is 1 unit. move the 2 electrons till they overlap completely and now the field is twice as strong which means that it holds 4 times the energy that either electron had originally and twice the energy that both held. so obviously it takes energy to force 2 electrons together. like repel. unlike attract.

 

Show mathematically that this is true. I have Q1 at one point and Q2 at another. What is the field mid-way between them?

[granpa]

Show mathematically that this is true. I have Q1 at one point and Q2 at another. What is the field mid-way between them?

 

nothing in that post would apply to that situation. I said nothing about the field at any one point. it was about the total energy in the field of one isolated electron vs the total energy in the field of 2 electrons that completely overlap.

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Does not follow.

 

11+(-6)=5

12+(-7)=5

20+(-15)=5

 

By your reasoning, both these numbers must be positive.

 

since 'both these numbers must be positive' then I assume you are referring to the example of the 2 charged particles. in that case the first positive number refers to the knietic energy and the second negative number refers to the total energy in the field. as the kinetic energy becomes higher the field becomes smaller. in fact if the 2 charges are equal then the field will eventually vansh completely. therefore the energy in the field must approach zero as the kinetic energy approaches its maximum. otherwise (by your reasoning) when the field vanishes completely you would still say that it holds energy.

Edited February 1, 2009 by granpa
Consecutive posts merged.

[Klaynos]

Can you mathematically define "total energy in the field" for me please? Because I'd assume that was an integral of the PE over all space due to the charge?

[granpa]

I already have.

 

the energy in the field at any one point is proportianal to the square of the intensity of the field at that point. integrate over all space of the field to get the total energy.

 

this is well known in elecrostatics.

 

http://sfbay.craigslist.org/forums/?act=Q&ID=50107820

Edited February 1, 2009 by granpa

[Mr Skeptic]

The energy gained by a particle moving in a field resulting from an inverse square law is [math]k\int^b_a\frac{1}{r^2} dr = -\frac{k}{b} - (-\frac{k}{a}) = \frac{k}{a} - \frac{k}{b}[/math], where r is the distance and k is a constant which depends on the specific of the situation, eg k=G*M*m for gravitation. This says nothing about the energy in the field, only a change in energy. Most physicists will say let a = infinity by default, then call -k/r the gravitational potential from infinity to r. IE, the particle would have gained -k/r potential energy (or lost k/r, if you prefer) if it moved from infinity to distance r. If r is infinity, then the potential is zero, otherwise it will be negative. This makes sense -- as the object falls closer, it has less potential energy.

[Klaynos]

The energy gained by a particle moving in a field resulting from an inverse square law is [math]k\int^b_a\frac{1}{r^2} dr = -\frac{k}{b} - (-\frac{k}{a}) = \frac{k}{a} - \frac{k}{b}[/math], where r is the distance and k is a constant which depends on the specific of the situation, eg k=G*M*m for gravitation. This says nothing about the energy in the field, only a change in energy. Most physicists will say let a = infinity by default, then call -k/r the gravitational potential from infinity to r. IE, the particle would have gained -k/r potential energy (or lost k/r, if you prefer) if it moved from infinity to distance r. If r is infinity, then the potential is zero, otherwise it will be negative. This makes sense -- as the object falls closer, it has less potential energy.

 

This was going to be my point.

[granpa]

The energy gained by a particle moving in a field resulting from an inverse square law is [math]k\int^b_a\frac{1}{r^2} dr = -\frac{k}{b} - (-\frac{k}{a}) = \frac{k}{a} - \frac{k}{b}[/math], where r is the distance and k is a constant which depends on the specific of the situation, eg k=G*M*m for gravitation. This says nothing about the energy in the field, only a change in energy. Most physicists will say let a = infinity by default, then call -k/r the gravitational potential from infinity to r. IE, the particle would have gained -k/r potential energy (or lost k/r, if you prefer) if it moved from infinity to distance r. If r is infinity, then the potential is zero, otherwise it will be negative. This makes sense -- as the object falls closer, it has less potential energy.

 

thats fine and true but irrelevant.

 

"This says nothing about the energy in the field".

 

thats why its irrelevant. we are specifically talking about the energy stored in the field. which at any one point is proportional to the square if the field intensity at that point. integrate over all space holding the field to get the total energy stored in the field. when 2 antiparticles collide their field vanish so the energy stored in their fields must be defined in such a way that it becoms zero at that point.

 

if you are unaware of this fact from electrostatics then you shouldnt be arguing against it. you should look it up.

[Klaynos]

I already have.

 

the energy in the field at any one point is proportianal to the square of the intensity of the field at that point. integrate over all space of the field to get the total energy.

 

this is well know in elecrostatics.

 

http://sfbay.craigslist.org/forums/?act=Q&ID=50107820

 

 

I was just checking that's what you were using.

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thats fine and true but irrelevant.

 

"This says nothing about the energy in the field". exactly.

 

we are talking about the energy stored in the field which at any one point is proportional to the square if the field intensity at that point. integrate over all space holding the field to get the total energy stored in the field. when 2 antiparticles collide their field vanish so the energy stored in their fields must be defined in such a way that it becoms zero at that point.

 

I don't like the term energy "stored" it's a potential not stored.

 

If that was the case, surely when you get an electron-positron annihilation you would not get out particles with the total energy of the combined rest masses of the electron - positron pair?

 

When you get two particles close together you don't just get the sum of their charages, you get dipolar fields...

[Mr Skeptic]

Keep in mind that the major point of defining potential as it is, is to completely dance around defining how much energy is in the field, because it usually does not matter, and there is not a good way to do so. When an electron and positron annihilate, their mass and the energy of their fields (which accounts for at least some of their mass) gets converted into photons, which we can measure.

 

 

"This says nothing about the energy in the field".

 

thats why its irrelevant. we are specifically talking about the energy stored in the field. which at any one point is proportional to the square if the field intensity at that point. integrate over all space holding the field to get the total energy stored in the field. when 2 antiparticles collide their field vanish so the energy stored in their fields must be defined in such a way that it becoms zero at that point.

 

Feel free to show mathematically what that is, and that it works. If you show what it is, we might tell you whether or not it works for you. All that is missing is your equation forf field intensity (which might be different from the standard definition since your definition of potential seems to be different).

 

if you are unaware of this fact from electrostatics then you shouldnt be arguing against it. you should look it up.

 

Hm, the definition of potential I gave is used everywhere and works nicely, why are you arguing against it?

[granpa]

I was just checking that's what you were using.

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I don't like the term energy "stored" it's a potential not stored.

 

If that was the case, surely when you get an electron-positron annihilation you would not get out particles with the total energy of the combined rest masses of the electron - positron pair?

 

When you get two particles close together you don't just get the sum of their charages, you get dipolar fields...

 

thank you for the response.

 

I dont think getting into rest mass is necessary. the formula relates the kinetic energy of the particles and the energy in the field up to the point that the field disappears. thats good enough for what I am saying. you can interpret it any way that is convenient for you.

 

I'm not sure what you mean by 'sum of charges' and 'dipolar field'. the dipole field is exactly what I've been talking about.

[swansont]

when 2 oppositely charged particles spontaneously merge their electric fields cancel. but when 2 masses spontaneously merge their gravitational fields add.

 

So what exactly is the problem?

[granpa]

the question that was asked (not by me but by the person I was responding to) is why is gravitational potential energy considered negative.

 

the question that I asked is why was my post declared to be 'nonsense'.

[Mr Skeptic]

The answer to the other is "because it is easier".

[swansont]

It's by definition and convention. Attractive forces result in negative potential energies when you consider the energy at arbitrarily large distances to be zero. F = -grad(U)

[granpa]

your definition of potential seems to be different

 

its standard mainstream textbook electrostatics. look it up.

 

 

why is everyone dancing around the question that I asked? why was my post declared to be 'nonsense'?

[swansont]

why is everyone dancing around the question that I asked? why was my post declared to be 'nonsense'?

 

Because it didn't answer the question? It's not the reason why the energy is considered negative. See my previous post.

 

Anything beyond that, I don't know. You'd have to ask the people who called it nonsense. Context matters, too. I can't find your response anywhere but here when I Googled; we only have your perspective of the exchange.