[HankRearden (OP)]

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?

[Soul Surfer]

no you've just increased it's potential energy

[HankRearden (OP)]

but isn't matter just potential energy?

[Ethos]

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'.

[lightarrow]

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 (OP)]

Good enough for me

[Stefanb]

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.
Even if you already got your answer  []

[wanhafizi]

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]

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

[Pmb]

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]

Welcome on this forum Pmb!

[lyner]

Yes, I'd endorse that.

[Pmb]

Thank you. It's nice to be here.

[Farsight]

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.     

[exton]

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]

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]

I wrote a speculative essay about this topic a number of years ago, that some of the readers here might find interesting.

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

Comments on it are welcome!

[lightarrow]

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]

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.

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.

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]

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.

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.