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### Author Topic: If I give an object some potential energy, does its mass increase?  (Read 95270 times)

#### HankRearden

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##### If I give an object some potential energy, does its mass increase?
« on: 19/07/2009 23:09:39 »
So matter can basically be thought of as just potential energy because matter can be turned into energy and theoretically vice-versa, does that mean when I lift up a plate and increase it's potential energy, i've technically increased its mass?
« Last Edit: 23/07/2009 21:04:07 by chris »

#### Soul Surfer

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• keep banging the rocks together
##### Re: If I give an object some potential energy, does its mass increase?
« Reply #1 on: 19/07/2009 23:34:26 »
no you've just increased it's potential energy

#### HankRearden

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##### Re: If I give an object some potential energy, does its mass increase?
« Reply #2 on: 19/07/2009 23:39:18 »
but isn't matter just potential energy?

#### Ethos

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##### Re: If I give an object some potential energy, does its mass increase?
« Reply #3 on: 20/07/2009 01:11:18 »
but isn't matter just potential energy?

Mass is not potential energy, it is condensed energy E=mc^2. And BTW, I have a problem with the term 'potential energy' anyway. I understand what physicists mean when they use this expression, I just think it is not an appropriate use of the word 'potential'.
« Last Edit: 20/07/2009 01:18:00 by Ethos »

#### lightarrow

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##### Re: If I give an object some potential energy, does its mass increase?
« Reply #4 on: 20/07/2009 11:20:41 »
So matter can basically be thought of as just potential energy because matter can be turned into energy and theoretically vice-versa, does that mean when I lift up a plate and increase it's potential energy, i've technically increased its mass?
The mass is increased, but not the mass of the plate: the mass of the system Earth-plate.

#### HankRearden

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##### Re: If I give an object some potential energy, does its mass increase?
« Reply #5 on: 21/07/2009 02:40:50 »
Good enough for me

#### Stefanb

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##### Re: If I give an object some potential energy, does its mass increase?
« Reply #6 on: 22/07/2009 07:15:26 »
E(p)= m x g x h Right?
So yes, mass is involved with the equation. However, because other variables are involved, mass and potential energy are not the same and cannot be manipulated as such.

#### wanhafizi

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##### Re: If I give an object some potential energy, does its mass increase?
« Reply #7 on: 23/07/2009 05:37:50 »
So matter can basically be thought of as just potential energy because matter can be turned into energy and theoretically vice-versa, does that mean when I lift up a plate and increase it's potential energy, i've technically increased its mass?

I saw a documentary of LHC experiment, they were saying, mass of the protons will increase as the energy increase. Yes, mass....

#### lightarrow

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##### Re: If I give an object some potential energy, does its mass increase?
« Reply #8 on: 23/07/2009 09:45:15 »
I saw a documentary of LHC experiment, they were saying, mass of the protons will increase as the energy increase. Yes, mass....
That's false, even if you can find this concept even in some books.
http://www.thenakedscientists.com/forum/index.php?topic=16789.0
http://www.thenakedscientists.com/forum/index.php?topic=21363.0
« Last Edit: 23/07/2009 09:47:08 by lightarrow »

#### Pmb

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##### If I give an object some potential energy, does its mass increase?
« Reply #9 on: 26/07/2009 00:38:25 »
So matter can basically be thought of as just potential energy because matter can be turned into energy and theoretically vice-versa, does that mean when I lift up a plate and increase it's potential energy, i've technically increased its mass?
You're thinking of mass-energy. The term "potential energy" refers to a different kind of energy. There are two ways the potential energy of a body can change. One can change the internal potential energy of a body. That kind of change will cause the rest mass of the body to change. The same thing will happen if you were to change the internal kinetic energy of the body increases (e.g. if the particles which make up the body vibrate faster).

Another way to change the potential energy of a body is to change its position in a field. Depending on what one means by "mass" its also possible that the mass by changing body’s potential energy. If the field is a gravitational field and one changes the position of the body in the gravitational field then there will be change in the mass of the body. This mass is related to the body’s rest mass m_0 by (let T = proper time)

m = (dt/dT) m_0

For they typical kind of gravitational field (i.e. corresponding to a time-orthogonal spacetime)

dt/dT = 1/sqrt[ 1 + 2*Phi – v^2/c^2]

where Phi = gravitational potential

The mass is then

m = m_0/sqrt[ 1 + 2*Phi – v^2/c^2]

Don’t confuse this with proper mass (aka “rest mass”)

Wanhafizi wrote – “I saw a documentary of LHC experiment, they were saying, mass of the protons will increase as the energy increase.”

They were speaking of the inertial mass of the proton, not its proper mass. When particle physicists speak of mass they are often referring to proper mass. However when relativists use the term “mass” they can mean one of several things. For example, in the lecture notes from Alan Guth’s “The Early Universe” course at MIT he explains that light has mass according to its energy. In this context he’s referring to what other relativists refer to as “relativistic mass.” This kind of mass is often spoken of in general relativity. It also goes under various other names such as simply “mass”  but also inertial mass, relativistic mass, active gravitational mass and passive gravitational mass.

#### lightarrow

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##### If I give an object some potential energy, does its mass increase?
« Reply #10 on: 26/07/2009 15:05:45 »
Welcome on this forum Pmb!

#### lyner

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##### If I give an object some potential energy, does its mass increase?
« Reply #11 on: 26/07/2009 15:59:08 »
Yes, I'd endorse that.

#### Pmb

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##### If I give an object some potential energy, does its mass increase?
« Reply #12 on: 27/07/2009 12:52:52 »
Thank you. It's nice to be here. :)

#### Farsight

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##### If I give an object some potential energy, does its mass increase?
« Reply #13 on: 29/07/2009 23:04:43 »
So matter can basically be thought of as just potential energy because matter can be turned into energy and theoretically vice-versa, does that mean when I lift up a plate and increase it's potential energy, i've technically increased its mass?
The answer is yes, but there's a catch.

Mass is a measure of the amount of energy that is not moving in aggregate with respect to you. A photon has no mass because it is moving with respect to you, and you cannot normally vary the speed of that photon. But there is a way to make it not move in aggregate: you employ pair production to convert a +1022keV photon into an electron and a positron. Forget the positron and consider the electron, ignoring its relatively slow motion after pair production. The energy is no longer moving laterally at c, instead it's moving in a circular fashion which we label as electron spin. You can then accelerate the electron as a whole, and the resistance to motion is a measure of its mass. See what pmb was saying above about proper mass and relativistic mass. The proper mass of the electron is the amount of energy tied up as that electron. The kinetic energy is the extra energy you give it by making it move, and the relativistic mass is the total.

Back to the plate: imagine it's out in space, and is falling to earth. Ignore air resistance. Just before it hits the ground the plate is moving at a considerable velocity. It now has kinetic energy. So the total energy of the plate appears to be greater than that of the plate up in space. However, it isn't, because gravity is a pseudoforce. This is not generally understood, but the key to understanding it is to consider two masses that fall together and coalesce. Energy causes gravity, and the  gravity caused by these two masses does not increase as they coalesce. No net energy is being added to this system. In similar vein no net energy is added to the falling plate. The total energy in that plate travelling at 11 km/s near the surface of the earth is the same as the total energy of the plate when it was motionless up in space. So if you catch that plate and cool it down, the total energy of the plate is now less than that of the plate at altitude. The reason is quite obvious when you look at gravitational time dilation. Everything in that plate, be it atoms or electrons is now moving at a slightly reduced rate when compared with the plate up in space. You can't measure this locally because it affects your clocks too. But you can measure it non-locally by comparison, as demonstrated by the GPS clock adjustment. This reduced rate means the energy locked up in the cold motionless plate at ground level is less than that of a cold motionless plate up in space.

So if you lift that plate up, then if the temperature of the plate is the same, the total energy tied up as mass in that plate is increased. Thus the mass increases. But here's the catch: if I had some device that could lift a plate up into space without giving back that 11 km/s of kinetic energy, that plate is going to get awfully cold. And there's a wrinkle too: light is deflected by gravity twice as much as matter, and when you compare a blue-shifted 511keV photon with a falling electron, there's an imbalance. But I'll save that one for another day.

Hi Pete.
« Last Edit: 29/07/2009 23:07:18 by Farsight »

#### exton

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##### If I give an object some potential energy, does its mass increase?
« Reply #14 on: 29/07/2009 23:45:26 »
The total energy in that plate travelling at 11 km/s near the surface of the earth is the same as the total energy of the plate when it was motionless up in space. So if you catch that plate and cool it down, the total energy of the plate is now less than that of the plate at altitude. The reason is quite obvious when you look at gravitational time dilation. Everything in that plate, be it atoms or electrons is now moving at a slightly reduced rate when compared with the plate up in space.

I don't follow. What's this talk of cooling things down - why did the plate heat up? Do you mean that we hypothetically catch the plate by turning its kinetic energy into thermal energy?

#### Pmb

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##### If I give an object some potential energy, does its mass increase?
« Reply #15 on: 30/07/2009 02:24:04 »
Hi Farsight!! How are you?

Conversations about mass can get confusing because its almost guaranteed that different people will be using different definitions of mass. What I spoke about above is often referred to as relativistic mass. What Farsight is talking about is what is often referred to as rest mass. Farsight’s comments can only be applied to special circumstances. Namely for bodies not subjected to stress.

#### VernonNemitz

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##### If I give an object some potential energy, does its mass increase?
« Reply #16 on: 31/07/2009 17:25:38 »

http://www.nemitz.net/vernon/STUBBED2.pdf

#### lightarrow

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##### If I give an object some potential energy, does its mass increase?
« Reply #17 on: 31/07/2009 18:14:17 »
Back to the plate: imagine it's out in space, and is falling to earth. Ignore air resistance. Just before it hits the ground the plate is moving at a considerable velocity. It now has kinetic energy. So the total energy of the plate appears to be greater than that of the plate up in space. However, it isn't, because gravity is a pseudoforce.
Do you mean that, according to GR, gravitational field doesn't exist (since it's actually spacetime warping) and so that region of space cannot have energy (= cannot have mass)? And so when the plate falls, since its kinetic energy increases, its proper mass have to decrease, to keep its total energy constant?

#### Farsight

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##### If I give an object some potential energy, does its mass increase?
« Reply #18 on: 01/08/2009 12:50:19 »
Quote from: exton
I don't follow. What's this talk of cooling things down - why did the plate heat up?
The plate doesn't have to heat up. If it was a steel plate and you're accelerating it and decelerating it with a railgun you're turning electrical energy into kinetic energy and vice versa. But kinetic energy is usually dispersed as heat. Plus damage and noise etc, but usually there's a lot of heat.

Quote from: exton
Do you mean that we hypothetically catch the plate by turning its kinetic energy into thermal energy?
Yes. Imagine you've got a metal container full of cold gas travelling at 11km/s through space. You catch the container and stop it with a rail gun. But those gas molecules are still doing 11km/s rattling around inside the container. So your gas is now hot. It's actually a little more than 11km/s because the average velocity of a gas molecule in air at room temperature and pressure is about 0.5km/s.

Quote from: Pmb
Hi Farsight!! How are you?
Pretty great thanks Pete. Of course, things could be moving faster and I could do with some more free time. For example the wife is off to Cheltenham all day with her sister leaving me holding the baby. But I'm as happy as Larry. And you?

Do you mean that, according to GR, gravitational field doesn't exist (since it's actually spacetime warping)...
Heck, not at all. If you're in a place where you fall down, you're in a gravitational field. It exists all right.

..and so that region of space cannot have energy (= cannot have mass)?
No. Space has an energy to it, but we don't think of this as mass. Mass is a property of something that resists being moved, and you can't exactly move a region of space from A to B.

And so when the plate falls, since its kinetic energy increases, its proper mass have to decrease, to keep its total energy constant?
Yes, that's what I'm saying. Think about two bodies m1 and m2. Imagine you're some way off in space, feeling the effect of their combined gravity. You're measuring the energy content of that two-body system. Now imagine they've fallen together and coalesced into one body M without losing any energy (think of them as being made of water or something). You don't feel any extra gravity, because no net energy has been added to that system by the two objects falling together. People say the kinetic energy has come from the potential energy of the gravitational field, but that's missing the trick. The gravity of the two-body system doesn't increase, and nor does it reduce. You can take this further by thinking of a spherical shell, where the gravity you experience is the same as what you'd get with a central point mass, see http://hyperphysics.phy-astr.gsu.edu/HBASE/Mechanics/sphshell.html. The important point is that gravity is a pseudoforce like Einstein said, because no energy is added to the system. A falling body doesn't feel any force, and no force is acting upon it. If you're in freefall you can't feel any force, because there isn't any. A falling plate is not accelerating. Instead it's "accelerating" in line with the principle of equivalence when it isn't falling any more. The kinetic energy of that falling plate didn't come from the earth via some magical mysterious action-at-a-distance force. It didn't come from the gravitational field either because that would also involves action-at-a-distance, and gravity is a local effect. It isn't a force it's a pseudoforce, so no energy is being delivered. Instead the kinetic energy comes from the plate itself. But it's very slight, compare 11 km/s to 299,792 km/s for an initial indication, or better still look at the GPS clock adjustment: http://en.wikipedia.org/wiki/Global_Positioning_System#Relativity. And do note that it's a scale-change which affects your measuring devices and everything else. Some might say if you can't measure any difference there is no difference, but if you take mass as a measure of the amount of energy tied up in an object, then conservation of energy is telling you something important here. All good stuff to think about.

#### lightarrow

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##### If I give an object some potential energy, does its mass increase?
« Reply #19 on: 01/08/2009 13:10:55 »
Do you mean that, according to GR, gravitational field doesn't exist (since it's actually spacetime warping)...
Heck, not at all. If you're in a place where you fall down, you're in a gravitational field. It exists all right.

..and so that region of space cannot have energy (= cannot have mass)?
No. Space has an energy to it, but we don't think of this as mass. Mass is a property of something that resists being moved, and you can't exactly move a region of space from A to B.
Then I don't understand what mass you are talking about: in a region of space which is not moving (with respect to some frame S) and in which you have energy, you also have mass: m = E/c2. Example: an electrostatic field has mass (I mean, proper mass = invariant mass). When you give energy (let's say electromagnetic energy) to an hydrogen atom, for example, you also give mass to the system, which goes in the electromagnetic field; the proton's and electron masses don't vary at all.

If you tell me that a system of two still masses, let's say two still planets, do interact through a gravitational field, then you *have* to ascribe a mass to that field and any variation of the system's energy = system's mass, comes out to belong to the field.

In the second part of your post, however, you keep the focus on the fact that gravity is a 'pseudo' force, that is, that there's no force at all; then there is no field, so why do you say instead: "Heck, not at all. If you're in a place where you fall down, you're in a gravitational field. It exists all right."? Don't understand.

Quote
People say the kinetic energy has come from the potential energy of the gravitational field, but that's missing the trick. The gravity of the two-body system doesn't increase, and nor does it reduce.
That's not correct. A field's energy density goes as the square of the field, so you cannot simply sum the effects of the two masses. If the masses' configuration varies, the field's energy varies as well. When the two masses are closer, the field's energy increases *in absolute value* and since the gravitational field's energy is negative, it means that the field's total energy is decreased. This is the reason of the fact that total system's energy is conserved.
« Last Edit: 01/08/2009 14:17:52 by lightarrow »

#### Pmb

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##### If I give an object some potential energy, does its mass increase?
« Reply #20 on: 01/08/2009 22:04:44 »
The important point is that gravity is a pseudoforce like Einstein said, because no energy is added to the system.
Einstein never said that gravity was a pseudoforce. Einstein argued that the gravitational force is of the same nature as inertial forces. Some Newtonians argue that since there is no source of such a force that it’s not “real” and hence terms like pseudoforce, apparent force, and fictitious force were coined. But others disagreed with that notion and Einstein was one of them. Einstein argued that inertial forces should be thought of as being real. It’s also wrong to assume that there is no potential energy in the gravitational field or that there is no mass equivalence to that potential energy. Einstein’s field equations are non-linear because gravity itself is a source of gravity.

For more on inertial forces see my web page http://www.geocities.com/physics_world/gr/inertial_force.htm

Pete

#### lightarrow

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##### If I give an object some potential energy, does its mass increase?
« Reply #21 on: 02/08/2009 12:20:43 »
For more on inertial forces see my web page http://www.geocities.com/physics_world/gr/inertial_force.htm
Nice site. Thank you Pmb.

#### Farsight

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##### If I give an object some potential energy, does its mass increase?
« Reply #22 on: 02/08/2009 18:00:35 »
Then I don't understand what mass you are talking about: in a region of space which is not moving (with respect to some frame S) and in which you have energy, you also have mass: m = E/c2.
I know what you mean. For example if you have a mirrored box and introduce a photon, the mass of the box is increased in line with the photon's energy. This is because mass is a measure of the amount of energy that is not moving in aggregate with respect to you.

Example: an electrostatic field has mass (I mean, proper mass = invariant mass). When you give energy (let's say electromagnetic energy) to an hydrogen atom, for example, you also give mass to the system, which goes in the electromagnetic field; the proton's and electron masses don't vary at all.
Yes, an electrostatic field has mass. But the electron's electric field is part of what it is. It isn't some central point particle with some set mass surrounded by an electric field with some variable mass. If you examine an electron at rest, you will deem its mass/energy to be 511keV. If you put that electron into your mirrored box, the mass of the box will increase accordingly. If you replace the stationary electron with a fast-moving electron bouncing back and forth inside the box, the increase in mass is greater. If you then replace your box with a proton that keeps the electron local to itself, the faster-moving electron means your hydrogen atom has more mass. But the electric field hasn't increased. The electron and the proton still exhibit unit charge.

If you tell me that a system of two still masses, let's say two still planets, do interact through a gravitational field, then you *have* to ascribe a mass to that field and any variation of the system's energy = system's mass, comes out to belong to the field.
A region of empty space is not empty of energy, and OK, in this respect one can ascribe mass to it (he said grudgingly). A planet is surrounded by a region of space which exhibits a gravitational field, and there is energy "density" in that region of space. But the gravitational field itself is only there because there's a gradient in the energy density. No gradient means no gravitational field. You can see this very easily if you consider uniform space. There's no gravity at all.

In the second part of your post, however, you keep the focus on the fact that gravity is a 'pseudo' force, that is, that there's no force at all; then there is no field, so why do you say instead: "Heck, not at all. If you're in a place where you fall down, you're in a gravitational field. It exists all right."? Don't understand.
Try this: if you're in a windowless box in free-fall you can't feel any force and you can't feel any acceleration. As far as you're concerned there is no gravitational field, you're just floating in space in an inertial reference frame, and nothing is falling down at all. But if I snap my fingers and give you a window, you change your mind pronto. You switch your reference frame from the box to the ground, and you are utterly convinced of the existence of that gravitational field. But you still can't feel any force acting upon you.  I snap my fingers again to give you a soft landing, whereupon you do feel a force which intensifies then levels off, but persists. You feel the force when you're standing on the ground, not when you're falling down.

Quote from: Farsight
People say the kinetic energy has come from the potential energy of the gravitational field, but that's missing the trick. The gravity of the two-body system doesn't increase, and nor does it reduce.
That's not correct. A field's energy density goes as the square of the field, so you cannot simply sum the effects of the two masses. If the masses' configuration varies, the field's energy varies as well.
What you've said here is a restatement of your earlier position. Let me try to work things through to explain things better. You start with a universe full of nothing but space. This space has an inherent energy. This isn't always obvious, but it's there, and there's a fixed amount of this "vacuum energy". But because space is uniform, there is no gravity.

You'll be aware that if you combine two out-of-phase photons you're left with no photons, but conservation of energy tells you the energy has not vanished. Instead it's now in the local space. OK, now do this in reverse across the board, such that a portion of your vacuum energy is converted into photons. Your uniform space is now full of photons. It isn't quite as uniform as before, but it's still fairly uniform, and there is still no discernable gravity.

Now use pair production to convert a portion of your photons into electrons and protons, and antiprotons and positrons. Let's forget the antiprotons and positrons, and say the electrons and protons take the form of hydrogen, also forgetting about helium. OK, if this was absolutely uniform, there's still no discernable gravity. The universe would be a ball of energy including vacuum energy and photons and hydrogen (and neutrinos etc too but forget them as well). The point is that it's still fairly uniform, and there is no gravity. There's no space beyond this universe to hold it all in, and no gravity within to pull anything towards the centre, so it would keep on expanding just like it always has done.

But this hydrogen isn't uniform. There's irregularities and variations, and hence there's just a little bit of gravity to make it start clumping together. Then the hydrogen forms clouds and galaxies and suns and planets, and there's gravity galore. There's gravity every where you look. There is no place in this universe where there is no gravity. But the sum total energy in the universe hasn't changed a bit. All that's happened is that the variations in energy density have been intensified.

When the two masses are closer, the field's energy increases *in absolute value* and since the gravitational field's energy is negative, it means that the field's total energy is decreased. This is the reason of the fact that total system's energy is conserved
This sounds like a restatement too. The gravitational field is only there because the masses are there. And those masses are made of energy. They're made of positive energy, there's no such thing as negative mass, and no such thing as negative energy. Go back to your hydrogen, and then consider the electrons and protons. The electrostatic field of each is a region where we see an energy density diminishing in line with the inverse square rule. When you clump them together to make a planet, then whilst there's no net charge, the electrostatic energy densities don't cancel. There's still an electrostatic energy density diminishing in line with the inverse square rule. Hence the mass/energy of the planet "conditions the surrounding space" and because it isn't uniform, we've got a gravitational field.

There is a relative negative to gravity, in that time dilation means everything is going slower down here than it is up there. Imagine a spinning plate up in space. Let's say it's doing 1000rpm. Because it's spinning, its got more energy, so its got more mass. Now compare it with a similar spinning plate down on the planetary surface. It too is doing 1000rpm, but because of the time dilation, it's actually spinning slower than the plate up in space. Hence its got less mass. Now think of pair production and treat an electron as a "spinning photon", and compare two identical motionless plates one up in space and one down on the planetary surface. You can liken every electron in each as a kind of spinning plate. Those on the surface are spinning slower, so the plate on the surface has less energy and so less mass.

Einstein never said that gravity was a pseudoforce. Einstein argued that the gravitational force is of the same nature as inertial forces. Some Newtonians argue that since there is no source of such a force that it's not 'real' and hence terms like pseudoforce, apparent force, and fictitious force were coined. But others disagreed with that notion and Einstein was one of them. Einstein argued that inertial forces should be thought of as being real. It's also wrong to assume that there is no potential energy in the gravitational field or that there is no mass equivalence to that potential energy. Einstein's field equations are non-linear because gravity itself is a source of gravity. For more on inertial forces see my web page http://www.geocities.com/physics_world/gr/inertial_force.htm
Yes, I know about the non-linearity. Hmmn, maybe pseudoforce is the wrong word, shame I've used it elsewhere. You'll be aware that what I've been generally finding is that people say "Einstein said x" when actually he didn't. Hence I wince at the thought of being guilty of the same. I was just looking at what you said back in January:

"This assumes that what is referred to as a pseudoforce doesn't fall under the category of a force. The name pseudoforce is used by those scientist who choose to think/define of a force in way such that an inertial force is not a force. But that is a subjective way to do things. Einstein proposed that the gravitational force is identical in nature to inertial forces (like the Coriolis force or the centrifugal force). Since scientists had come to think of inertial forces as not "real" forces this led some scientists to conclude that gravity is not a "real" force. Hence leading scientists use the term pseudoforce to refer to the gravitational force. However this is not what Einstein's theory implies and is not how Einstein himself viewed it. Einstein considered gravity to be a "real" force and concluded that inertial forces like the Coriolis force is also a "real" force. In his book on relativity, Wolfgang Pauli points out that its perfectly fine to think of the gravitational force as either a real force or a "fake" force, so long as you think of the gravitational force as the same kind of force as an inertial force.

I hope we can all agree that gravity is not fake. If we think of a compressed spring, as in an airgun, we can consider the compression to represent potential energy. When we release the spring this potential energy is converted into kinetic energy and no longer persists. When we stand on the surface of the earth and look at the plate up in free space, we say it has gravitational potential energy. But (let's ignore the sun) it's just a plate in space. It isn't in a gravitational field. When the earth rolls up to the plate, the plate's potential energy is converted into kinetic energy, and no longer persists. But it isn't the gravitational field that had the potential energy, it was the plate. The gravitational field is not reduced when the plate falls, because energy causes gravity, and all we've done is converted some of the energy of the plate into kinetic energy, leaving the plate itself in a reduced-energy state with a slightly reduced mass. As a result of encountering that plate, the gravitational field of the earth is now slightly increased. At no point did the force of gravity add any energy to the earth-plate system, just as the centripetal force doesn't continually add energy to a ball whirled on a string.

#### lyner

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##### If I give an object some potential energy, does its mass increase?
« Reply #23 on: 02/08/2009 19:21:17 »
Quote
You'll be aware that if you combine two out-of-phase photons you're left with no photons
I don't want to interrupt the flow but that statement begs the question.
"If you combine" implies that they are produced at the same place and at the same time - else there wouldn't be cancellation everywhere.  I have a feeling that violates Pauli, for a start*. If they are  heading for each other then yo will get a standing wave when they are actually crossing. No energy problems either way.
If you want to talk in terms of phase, then you are talking waves and if you produce cancellation of two waves in one direction, the energy pops up elsewhere, in another direction.

Edit * Because they would have to be produced by superposed fermions.
« Last Edit: 02/08/2009 19:43:33 by sophiecentaur »

#### lightarrow

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##### If I give an object some potential energy, does its mass increase?
« Reply #24 on: 02/08/2009 20:45:04 »
Example: an electrostatic field has mass (I mean, proper mass = invariant mass). When you give energy (let's say electromagnetic energy) to an hydrogen atom, for example, you also give mass to the system, which goes in the electromagnetic field; the proton's and electron masses don't vary at all.
Yes, an electrostatic field has mass. But the electron's electric field is part of what it is. It isn't some central point particle with some set mass surrounded by an electric field with some variable mass. If you examine an electron at rest, you will deem its mass/energy to be 511keV. If you put that electron into your mirrored box, the mass of the box will increase accordingly. If you replace the stationary electron with a fast-moving electron bouncing back and forth inside the box, the increase in mass is greater. If you then replace your box with a proton that keeps the electron local to itself, the faster-moving electron means your hydrogen atom has more mass.
Ok up to here.

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But the electric field hasn't increased. The electron and the proton still exhibit unit charge.
1. The electromagnetic field  have to be evaluated after the atom has given away the surplus of energy due to the initially fast moving electron, for example by emission of photons.
2. After that, you will see that the electric field has decreased, with respect to when the electron and the proton were far apart; it means that the total energy of the field (in all 3D space) has decreased. If you make the computations, you see that it has decreased exactly of the electric potential energy variation. Where has this energy gone? With the photons carrying the surplus of energy.

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A region of empty space is not empty of energy, and OK, in this respect one can ascribe mass to it (he said grudgingly). A planet is surrounded by a region of space which exhibits a gravitational field, and there is energy "density" in that region of space. But the gravitational field itself is only there because there's a gradient in the energy density. No gradient means no gravitational field. You can see this very easily if you consider uniform space. There's no gravity at all.
I sincerely don't understand this. Consider a region of space in the void with a uniform electric field E. The energy density is (1/2)ε0E2, so it's uniform as well, so its gradient is zero. Would you deduce that the field is zero?

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That's not correct. A field's energy density goes as the square of the field, so you cannot simply sum the effects of the two masses. If the masses' configuration varies, the field's energy varies as well.
What you've said here is a restatement of your earlier position. Let me try to work things through to explain things better. You start with a universe full of nothing but space. This space has an inherent energy. This isn't always obvious, but it's there, and there's a fixed amount of this "vacuum energy". But because space is uniform, there is no gravity.
Why not? I see what you intend after in your post, but it doesn't seem correct to me. Consider a rubber band which is initially stretched in a large circumference and then released; in every point of the rubber band, in the band's frame of reference, elastic forces pull in two opposite directions, so the point doesn't move along the circumference, ok, but that's different from saying that elastic forces don't act on the band: it quickly contracts in the other dimension. Monodimensional 'people' living in the rubber band would see that distances from any two points in its universe are decreasing.

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When the two masses are closer, the field's energy increases *in absolute value* and since the gravitational field's energy is negative, it means that the field's total energy is decreased. This is the reason of the fact that total system's energy is conserved
This sounds like a restatement too. The gravitational field is only there because the masses are there. And those masses are made of energy. They're made of positive energy, there's no such thing as negative mass, and no such thing as negative energy.
Can you prove it?
« Last Edit: 02/08/2009 20:56:28 by lightarrow »

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##### If I give an object some potential energy, does its mass increase?
« Reply #24 on: 02/08/2009 20:45:04 »