Lawrence Miles' perpetual motion machine

[Farsight]

That's wrong. A gravitational field has a positive energy density. That's why "the energy of the gravitational field shall act gravitatively in the same way as any other kind of energy". That's on page 185 of the Doc 30 translation of The Foundation of the General Theory of Relativity. It's why General relativity is non-linear. What EternalSceptic said is right.

[Hellbound]

Originally Posted by Farsight

That's wrong. A gravitational field has a positive energy density. That's why "the energy of the gravitational field shall act gravitatively in the same way as any other kind of energy". That's on page 185 of the Doc 30 translation of The Foundation of the General Theory of Relativity. It's why General relativity is non-linear. What EternalSceptic said is right.

Just out of curiosity, what's the value of G, the constant for gravitational energy?

How does that compare to, say, Couloumb's constant?

Or, really, the constants associated with the forces produced by any other field besides gravity?

[Ziggurat]

Originally Posted by Farsight

That's wrong. A gravitational field has a positive energy density. That's why "the energy of the gravitational field shall act gravitatively in the same way as any other kind of energy". That's on page 185 of the Doc 30 translation of The Foundation of the General Theory of Relativity. It's why General relativity is non-linear. What EternalSceptic said is right.

No. You seem to think that this quote contradicts what I said, but it doesn't. What I said pertains to the sign of the energy. But your quote says nothing about the sign, only that you must include that energy (whatever it is) in the calculations just as you do any other form of energy. The quote is right, your interpretation of it is wrong.

[edd]

Originally Posted by Farsight

That's wrong. A gravitational field has a positive energy density.

Lets look at it from a classical perspective. Take two positive electrical charges. Their lowest energy state is when they're infinitely far apart and can't feel each other. Bring them together. To do this you have to do work, which goes into the electric field between them. Obviously there's a positive energy density there, because if you let go of the charges they'll start moving apart and gain kinetic energy.

So if you've got two masses and let them attract you'll have to put energy into the field to get them apart again, so it's natural to describe the field's energy density as negative, isn't it?

[Farsight]

Originally Posted by Hellbound

Just out of curiosity, what's the value of G, the constant for gravitational energy?

It's

.

But note it doesn't have the units of energy. It's got odd-looking units because it's a conversion factor, a constant of proportionality for .

Originally Posted by Hellbound

How does that compare to, say, Couloumb's constant?

It's somewhat similar. But not totally. Gravity is different to electromagnetism. The biggest difference is that there's no repulsion. If you're going to use electromagnetism as an example it's important to stick with electrostatic attraction.

Originally Posted by Hellbound

Or, really, the constants associated with the forces produced by any other field besides gravity?

You start to see some bigger differences, such asymptotic freedom. It's important to bear these differences in mind.

[Farsight]

Originally Posted by Ziggurat

No. You seem to think that this quote contradicts what I said, but it doesn't. What I said pertains to the sign of the energy. But your quote says nothing about the sign, only that you must include that energy (whatever it is) in the calculations just as you do any other form of energy. The quote is right, your interpretation of it is wrong.

No it isn't. A massive body like a star is comprised of positive energy, and so is its gravitational field. A smaller body with no detectable gravitational field such as a cannonball is comprosed of positive energy too. Whilst binding energy is said to be negative, it isn't actually negative energy, it's just a way of talking about less positive energy.

[ben m]

Originally Posted by Farsight

That's wrong. A gravitational field has a positive energy density.

Nope. Work it out. Compute the volume integral of a^2 around two masses close together. Now pull the masses far apart---obviously the gravitational energy has gone down---and compute the volume integral again. You'll find that the net field has gone UP. Higher field integral = lower stored energy.

Do the same thing for E&M and you'll find the opposite; higher field integral (E^2) = higher energy density.

[Ziggurat]

Originally Posted by Farsight

No it isn't. A massive body like a star is comprised of positive energy, and so is its gravitational field. A smaller body with no detectable gravitational field such as a cannonball is comprosed of positive energy too. Whilst binding energy is said to be negative, it isn't actually negative energy, it's just a way of talking about less positive energy.

And yet, the only thing that changed about the two configurations (the masses near each other versus the masses far apart) is the gravitational field, namely the integral of the square of the field increases when they are at a lower potential. So how does having more field squared lead to less positive energy?

Easy: the field squared is negative energy. That is the only mathematically consistent answer you can get.

[MattusMaximus]

Originally Posted by Farsight

No it isn't. A massive body like a star is comprised of positive energy, and so is its gravitational field. A smaller body with no detectable gravitational field such as a cannonball is comprosed of positive energy too. Whilst binding energy is said to be negative, it isn't actually negative energy, it's just a way of talking about less positive energy.

Farsight, as has already been pointed out to you, this assertion is incorrect. The fact that the potential energy associated with gravitational fields is negative is a standard calculation in undergraduate physics courses on mechanics. In fact, here's the math: http://hyperphysics.phy-astr.gsu.edu/hbase/gpot.html#ui

Would you care to show the math proving your assertion that gravitational potential energy is positive?

[Farsight]

Originally Posted by edd

Lets look at it from a classical perspective. Take two positive electrical charges.

It's better to take a positive particle and a negative particle. If you take two positive particles you're drawing a parallel between gravity and electromagnetism that would involve gravitational repulsion.

Originally Posted by edd

Their lowest energy state is when they're infinitely far apart and can't feel each other. Bring them together. To do this you have to do work, which goes into the electric field between them. Obviously there's a positive energy density there, because if you let go of the charges they'll start moving apart and gain kinetic energy.

I would caution against the energy goes into the field between them but otherwise I'm happy with what you've said. Ignoring gravity and assuming they're at rest a long way apart, a positron has a mass-energy of 0.511MeV, and proton has a mass-energy of 938MeV in round numbers. Both are positive values. When you push them together you do work on them, and together the total mass-energy is more than 938.511MeV. Let's say it's now 938.512MeV. When you let them go they move apart with a total kinetic energy of 0.001MeV. The positron gets the lion's share of this because it's much less massive than the proton, and for simplicity we disregard the proton motion.

Now repeat the scenario with an electron and a proton. Ignoring gravity and assuming they're at rest a long way apart, the electron has a mass-energy of 0.511MeV, and proton has a mass-energy of 938MeV in round numbers. Both are positive values. You sit there and wait, and after a while you notice that they start moving towards one another. Again for simplicity we disregard the proton motion. When they meet we say the electron emits a 13.7eV photon and goes into an orbital. We now have a hydrogen atom, and the mass-energy is 938.511MeV less 13.7eV. We now have a mass deficit, and we say the binding energy is -13.7eV. But there's no actual negative energy present, just less positive energy. The mass deficit is actually a system energy deficit, but because it's something of a one-sided system, we lump it onto the electron for simplicity. To get the electron away from the proton we have to give it kinetic energy of 13.7ev. We give it a bit more for luck, and watch as the electron moves away from the proton. It slows down as it does, but it's off and away, the proton isn't ever going to get it back. The kinetic energy we gave to the electron is converted into mass-energy within the electron, correcting the mass deficit. The total energy of what was a hydrogen atom and is now a proton, is diminished.

Originally Posted by edd

So if you've got two masses and let them attract you'll have to put energy into the field to get them apart again, so it's natural to describe the field's energy density as negative, isn't it?

No. Whether it's an electromagnetic field or a gravitational field, the field energy density is positive. And you don't put energy into the field to get them apart, you put energy into one of the masses. We substitute the proton with the Earth and substitute the electron with a cannonball. Ignoring the motion of the Earth for simplicity, we strap rockets to the cannonball and fire it straight up at 11km/s, giving it considerable kinetic energy. We can give it a bit more for luck, and watch as the cannonball moves away from the Earth. It slows as it does, but it's off and away, the Earth isn't ever going to get it back. The kinetic energy we gave to the cannonball is converted into mass-energy within the cannonball, correcting the mass deficit. The total energy of the Earth including its gravitational field, is now diminished.

[Ziggurat]

Originally Posted by Farsight

We now have a mass deficit, and we say the binding energy is -13.7eV. But there's no actual negative energy present, just less positive energy.

Yes: there's less positive energy because the integral of the field squared is less when a proton and an electron are close together.

But the opposite happens to gravity when two objects approach. The potential decreases, but the integral of the field squared is larger.

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No. Whether it's an electromagnetic field or a gravitational field, the field energy density is positive.

Obviously it cannot be for gravity, or else gravity would be repulsive. Your higher-energy configuration has a lower integrated field squared. The sign is backwards if gravity had a positive energy density.

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And you don't put energy into the field to get them apart, you put energy into one of the masses.

No, you don't.

[edd]

Originally Posted by Farsight

It's better to take a positive particle and a negative particle. If you take two positive particles you're drawing a parallel between gravity and electromagnetism that would involve gravitational repulsion.

There's an important reason I didn't. Take two equal point masses and let them end up at the same location and you have the field from one point with twice the mass. Take equal positive and negative electric charges and let them end up at the same location and you haven't got twice the field of either the positive or the negative charge - you have no field left at all.

[MattusMaximus]

My God, this discussion with Farsight is like the nightmare discussion I have with my high school AP students on occasion who cannot (or will not) do the freakin' math and who instead keep insisting that "energy can't be negative!"

[Hellbound]

Originally Posted by MattusMaximus

My God, this discussion with Farsight is like the nightmare discussion I have with my high school AP students on occasion who cannot (or will not) do the freakin' math and who instead keep insisting that "energy can't be negative!"

I dunno.

I still shake my head at "I prefer to use logic, not math".

Analogy:

"I prefer to speak English, not language!" After which one hears strings of Pidgin.

[quarky]

Awful glad you geeks are here. Really.

[Farsight]

Originally Posted by quarky

Awful glad you geeks are here. Really.

Sadly there's people peddling bad science here on JREF. When you try to put the record straight via the evidence and the explanation and the Einstein, they just won't have it.

Originally Posted by edd

There's an important reason I didn't. Take two equal point masses and let them end up at the same location and you have the field from one point with twice the mass. Take equal positive and negative electric charges and let them end up at the same location and you haven't got twice the field of either the positive or the negative charge - you have no field left at all.

If you had no field left at all you wouldn't have to do work to separate the particles. And in the real world the particles don't end up at the same location anyway. The hydrogen atom has a magnetic moment. It's a magnet. A magnetic field is a trace of where two electromagnetic fields don't quite mask another. And as you know, even a fridge magnet can can overcome the force of gravity.

Originally Posted by Ziggurat

Yes: there's less positive energy because the integral of the field squared is less when a proton and an electron are close together. But the opposite happens to gravity when two objects approach. The potential decreases, but the integral of the field squared is larger.

You're confusing positive and negative charge with positive and negative energy. An electron's electromagnetic field has a positive energy density. That's a +1. A proton's electromagnetic field has a positive energy density. That's another +1. You have to do work to push two electrons together, and you have to do work to push two protons together. In both cases your work is converted into potential energy which increases the mass of the system. Now let's look at what you said:

"If you move two like electric charges apart, their potential energy does decrease, and that's mathematically equivalent to saying that 1² + 1² < (1+1)².

So the +1 applies to either an electron or a proton. So your "What I said pertains to the sign of the energy" and your "1² + (-1)² > (1-1)²" is wrong. And by the way, you don't move two like charges apart, they move apart when you let go.

When you let an electron and a hydrogen form a hydrogen atom, there's a trace of the two electromagnetic fields left called a magnetic field. This isn't some region of space where there's a negative energy density. If you throw a whole heap of hydrogen atoms together so those magnetic fields mask one another, there's another trace left called a gravitational field. That isn't some region of space where there's a negative energy density either.

Originally Posted by Ziggurat

Obviously it cannot be for gravity, or else gravity would be repulsive. Your higher-energy configuration has a lower integrated field squared. The sign is backwards if gravity had a positive energy density.

A gravitational field has a positive energy density. That's why "the energy of the gravitational field shall act gravitatively in the same way as any other kind of energy". Your signs represent chirality and the result of field interaction, not energy density.

Originally Posted by Ziggurat

No, you don't.

Yes you do. You give the cannonball kinetic energy. You don't wave your arms around trying to give it to the gravitational field.

[MattusMaximus]

Farsight, can you show us the math which proves your assertion that the potential energy associated with a gravitational field is positive?

*crickets chirp*

[edd]

Originally Posted by Farsight

If you had no field left at all you wouldn't have to do work to separate the particles. And in the real world the particles don't end up at the same location anyway.

Sure, they won't end up at the same point, but once they're reasonably close what I said isn't very far from wrong - you can trivially calculate the field from a dipole and see how it changes as the dipole shrinks to zero, and in that limit what I said was fine.

Quote:

The hydrogen atom has a magnetic moment. It's a magnet. A magnetic field is a trace of where two electromagnetic fields don't quite mask another. And as you know, even a fridge magnet can can overcome the force of gravity.

I think a magnetic field is something maybe just a little different from two electromagnetic fields not masking each other. I mean for a start when you say 'electromagnetic field' there, presumably you mean electrostatic, as if a magnetic field is already there you've got a circular argument (a magnetic field is a trace of two electric and two magnetic fields not quite masking?). And two electrostatic fields combined do not produce a magnetic field.

[MattusMaximus]

Originally Posted by edd

I think a magnetic field is something maybe just a little different from two electromagnetic fields not masking each other. I mean for a start when you say 'electromagnetic field' there, presumably you mean electrostatic, as if a magnetic field is already there you've got a circular argument (a magnetic field is a trace of two electric and two magnetic fields not quite masking?). And two electrostatic fields combined do not produce a magnetic field.

I noticed that Farsight made this mistake earlier when he referred to Coulomb's Law as an expression of electromagnetism. Some "physics expert"

[Ziggurat]

Originally Posted by Farsight

You're confusing positive and negative charge with positive and negative energy. An electron's electromagnetic field has a positive energy density. That's a +1. A proton's electromagnetic field has a positive energy density. That's another +1. You have to do work to push two electrons together, and you have to do work to push two protons together. In both cases your work is converted into potential energy which increases the mass of the system.

I have made no mistake at all. I have, in fact, explicitly said that the electromagnetic field carries positive energy, always.

Quote:

Now let's look at what you said:

"If you move two like electric charges apart, their potential energy does decrease, and that's mathematically equivalent to saying that 1² + 1² < (1+1)².

So the +1 applies to either an electron or a proton. So your "What I said pertains to the sign of the energy" and your "1² + (-1)² > (1-1)²" is wrong. And by the way, you don't move two like charges apart, they move apart when you let go.

The +1 and -1 refers to the sign of the field. Square it to get the energy and you always end up with a positive number, regardless of the sign of the field. But if the fields cancel (as they do with two opposite charges placed together), then that cancellation happens before you do the squaring. They don't cancel if the charges are far apart. So my math is correct, and your objection is nonsensical.

Quote:

When you let an electron and a hydrogen form a hydrogen atom, there's a trace of the two electromagnetic fields left called a magnetic field. This isn't some region of space where there's a negative energy density. If you throw a whole heap of hydrogen atoms together so those magnetic fields mask one another, there's another trace left called a gravitational field.

No, actually, it really isn't. Gravity is not a remnant of the magnetic field, and the magnetic field is not a remnant of the electric field. This is rather obvious since the fields do not act the same way on a charge. The electric field and the gravitational field do not exert a velocity-dependent force, and the gravitational field does not exert a charge-dependent force.

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A gravitational field has a positive energy density. That's why "the energy of the gravitational field shall act gravitatively in the same way as any other kind of energy".

You continue to misinterpret this sentence.

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Your signs represent chirality and the result of field interaction, not energy density.

They represent nothing of the sort.

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Yes you do. You give the cannonball kinetic energy.

One can move objects together or apart at arbitrarily low velocities, so that kinetic energy at any stage in the process is as low as you want to make it. In addition, one can consider the situation of the two masses at rest with respect to each other but at different separations, so that the kinetic energy is identically zero for the comparison of interest. The missing energy isn't kinetic.

I can understand how someone might have trouble wrapping their head around the idea of fields containing energy, since fields are somewhat abstract things. But once you've accepted that (and you claim to have done so), then the sign of the energy contained within a field becomes obvious through some rather simple calculations of the sort I did above. But you failed to do this. You literally can't figure out that 1+1=2 and 2*2=4.

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You don't wave your arms around trying to give it to the gravitational field.

You have given absolutely no reason for why one should not. Every attempt you have made has been an epic failure. But then, why should you break your streak just for me?

[Tubbythin]

Originally Posted by Farsight

Sadly there's people peddling bad science here on JREF.

Yep. Some of them don't even understand units.

Quote:

When you try to put the record straight via the evidence and the explanation and the Einstein, they just won't have it.

Indeed.

[ben m]

Originally Posted by Farsight

A magnetic field is a trace of where two electromagnetic fields don't quite mask another.

I think this is a garbled attempt to reference the old "what does a current-carrying wire look like to a moving observer" calculation. Except it's entirely garbled.