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Author Topic: If I give an object some potential energy, does its mass increase?  (Read 95294 times)

Offline Farsight

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To you, perhaps. So now what happens if we don't use a solar powered rocket, but use a conventional rocket that obtained its energy from the system? Does the mass of the Moon still increase (and, because they are part of the same system, presumably by the same logic the Earth's mass would also increase)?
Again, it's cut and dried. If you use energy from the system to make one part of the system move faster, it somehow comes at the cost of making some other part of the system move slower. The moon is large compared to the earth, so it's more complicated than the cannonball. See http://en.wikipedia.org/wiki/Tidal_power and note where it says "This loss of energy has caused the rotation of the Earth to slow in the 4.5 billion years since formation. During the last 620 million years the period of rotation has increased from 21.9 hours to the 24 hours we see now; in this period the Earth has lost 17% of its rotational energy". The earth's rotation has slowed down, so you could say the earth has lost some mass. But you can't quite say "the moon" has gained some mass. Instead the subsystem that is the moon in its circular orbit has gained potential/kinetic energy, and hence mass.   
 

Offline Geezer

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I agree Geezer, but it's perfectly correct to count on it as 'potential energy' as that fits in all kinds of mathematical models describing the universe.

But when testing 'matter' and see if that plate isolated, after being lifted one meter, have gotten an increased energy I would expect the oposite. And if the 'jiggling' is less one meter up, then the mass should decrease as that is kinetic energy.

So it depend on what you choose to define as a 'system' I guess?
Maybe I'm thinking wrong though?

I agree. There is an increase in potential energy, and the math seems to be sufficiently correct. The question was "does the mass increase?". If someone wants to conduct the experiment I suggested, or they already have done something similar, we could find out quite easily.

Regarding the system, once you define what is in your system, you can't arbitrarily remove components of it and say they are no longer part of the system, even although the effects they produce are minimal. If you take the plate from one meter above Earth to 10 billion meters above Earth then bring it back to one meter again, it will have exactly the same PE that it had before.

By "jiggling", are you referring to the kinetic energy of the molecules that make up the plate?
 

Offline Geezer

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To you, perhaps. So now what happens if we don't use a solar powered rocket, but use a conventional rocket that obtained its energy from the system? Does the mass of the Moon still increase (and, because they are part of the same system, presumably by the same logic the Earth's mass would also increase)?
Again, it's cut and dried. If you use energy from the system to make one part of the system move faster, it somehow comes at the cost of making some other part of the system move slower. 

Who said anything about any part of the system getting faster? Are you saying there was, or was not, an increase in the mass of the Moon, the Earth, or the system in either or any of the cases?

If it's as "cut and dried" as you say, I'm sure you will be able to predict the outcome of the experiments.
 

Online yor_on

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yeah, by 'jiggling' I meant the 'motion' atoms create in matter, same as a gas 'jiggles' more as it gets hotter. and my thought was that the closer you move matter to a gravitational well the more 'jiggling' you will find.

And in this case, by removing matter from the well. I think the 'jiggling' should decrease. And as the 'jiggling' should transform into kinetic energy I would expect that piece of matter to become lighter, as the well recedes even though I'm not entirely sure on it.

It's a little like the photon transferring what we call mass due to being constricted inside that perfectly mirrored box. But a little more possible to test, maybe :)

It's like a drum skin. If you beat on it very fast will that increase its mass. I think it will.

===

Or make a really big hole :)
« Last Edit: 17/01/2010 20:44:10 by yor_on »
 

Offline Geezer

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yeah, by 'jiggling' I meant the 'motion' atoms create in matter, same as a gas 'jiggles' more as it gets hotter. and my thought was that the closer you move matter to a gravitational well the more 'jiggling' you will find.

And in this case, by removing matter from the well. I think the 'jiggling' should decrease. And as the 'jiggling' should transform into kinetic energy I would expect that piece of matter to become lighter, as the well recedes even though I'm not entirely sure on it.

It's a little like the photon transferring what we call mass due to being constricted inside that perfectly mirrored box. But a little more possible to test, maybe :)

It's like a drum skin. If you beat on it very fast will that increase its mass. I think it will.

===

Or make a really big hole :)

I think if there was any increase in the kinetic energy of the molecules in the plate, it would simply get warmer, just as it does when you heat it in an oven. As I understand it, sticking plates in ovens does not increase their mass  ;D

If it does, it would be quite easy to measure, or are we talking about a very minute increase in mass?
 

Online yor_on

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Yeah, it's very small if it is so. I mean, it is the atoms higher 'bouncing' frequency that will create what mass there will be more.

Lightarrow could probably count on it and RD and Maddidus and JP and . . .
Thinking of it, probably most all of you here, except me of course :::)))
Awh

*Takes out his pocket calculator*

"One , two, three, four, and? Where was I?"

Hang on a minute Geezer, I think I'm getting close here :)
 

Offline Geezer

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Ah! Then you would be referring to non-rest mass associated with relativistic effects. But I don't think that applies in this situation. The plate is static relative to Earth before and after it was moved, so I think we'll find it has exactly the same mass in both states.

And even if there was a very small change in mass, I don't think we'd want people to get the idea that its potential energy was caused by a change in mass. I think that would be very misleading.
 

Offline Farsight

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Who said anything about any part of the system getting faster?
I thought you did. Check out the wiki “orbital mechanics” article for how you accelerate an object in the orbital direction to gain altitude.   

Are you saying there was, or was not, an increase in the mass of the Moon, the Earth, or the system in either or any of the cases?
If you add energy to the system the system gains mass. If you don't, it doesn't. Mass is a measure of the energy content of a system, and overall the system isn’t moving with respect to you. However the earth and the moon are, so when you change their motion you wouldn’t say they've gained or lost mass. It’s akin to a gyroscope: if you spin it, you add energy, and when you consider it to be an overall system because you put it in a black box, you'd say it isn’t moving with respect to you, so you’d say it had more mass. But if you focussed on some moving portion of the gyroscope, you’d say it has more angular momentum rather than more mass.

If it's as "cut and dried" as you say, I'm sure you will be able to predict the outcome of the experiments.
Experiments are difficult to do. There's a lot of energy tied up in matter, for example only about 1 gram of matter was converted into energy by the Hiroshima bomb. So you can't realistically heat a container of gas and see that it weighs more. This is what Einstein said in his 1905 paper "Does the Inertia of a body depend upon its Energy content?". See http://www.fourmilab.ch/etexts/einstein/E_mc2/www/.
 

Offline Farsight

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But it does not contain more atoms due to the lift, neither does the atoms electrons, molecules, etc jiggle more due to that lift. In fact it should have the other effect as I see it, they should jiggle slightly less as the gravitation is less 1 meter above, and therefore also contain a slightly lesser vibrational energy than the plate had closer to the ground.
Imagine you used some aspect of this "jiggle" to operate a clock. Clock run slower nearer the ground, due to gravitational time dilation. That means the jiggle must be slower near the ground. 
 

Offline litespeed

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GPS Satellite clocks run FASTER then their counterparts on the earth's surface, when the observer is on the earth next to the ground clock. This is because the orbiting satellites are under the influence of two contradictory relativistic effects that are not equal.

Specifically, these satellites are subject relativity in TWO ways. The larger of the two  increases the speed of the satellite clocks by about 45 microseconds per day, as observed from the ground. This is because the satellites are significantly further from the earth's gravitational center.

However, the satellite clocks are also effected by speed. They are traveling quite fast relative to a ground observer, and time is accordingly slowed down by about 7 microseconds per day. Subtract 7 microsecond from 45 microseconds and the clocks need to be synchronized such that the overall effect is to decrease 37 microseconds per day.

http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps.html

PS: I know of one case in which potential energy can be hugely decreased in a given mass. Gunpowder. Remove all the charcoal from the mix and replace it with exactly the same mass of sand. And of course vice versa.

I do not know whether the mass of GPS satellites is increased or decreased when sent into orbit. This is because I do not have the math training to know whether the mass is decreased in proportion to the increased distance from the earth. I do know it is increased by the velocity transferred to them by accelerative forces.

However, the potential KINETIC energy of the speedy satellites is vastly greater then the one on the ground.
« Last Edit: 18/01/2010 17:22:36 by litespeed »
 

Offline VernonNemitz

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Vernon, I hold to that virtual particles 'exist' as you seem to do. Their interactions definitely prove it. That Feynman meant that we couldn't really say what they were, I take to mean that we can't really say what they are :). And we can't, but we can count on them and observe their interactions, whatever they might be.

Then I saw you support the Higgs field, sounds okay to me too. When it comes to the Higgs boson? Don't know, maybe the LHC will clear that up?

But now I see that you expect gravitons too? Isn't that contradictorily?
Or do you see string theory as encompassing all those descriptions?

First, thank you for letting me know this Message Thread was active again.

I don't know a lot about the proposed Higgs particle, but I think I can say this relatively safely, "Any proposed particle, if it actually can exist, already exists among the random/temporary virtual particles in the vacuum.  The "Higgs field" would thus be, in crude terms, the percentage of all the vacuum-self-energy virtual particles that are Higgs particles.  Whatever percentage that is, it is apparently enough (for theory to match observation) that ordinary particles are always able to interact with Higgs particles, and as a result most of them appear to possess mass."
 

Offline Geezer

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Farsight:

We reposition the Moon relative to the Earth using a conventional rocket (using energy from within the system).

I don't think anyone would argue that we have not altered the potential energy of the system (although I would not be totally surprised if someone did  :D)

There had to be a redistribution of mass within the system to accomplish this but;

Did the mass of the system change, and if it did, why did it change?

(BTW, no matter was converted into energy or vice versa during this process.)
 

Online yor_on

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Not bad Vernon :)
Gotta think on that one.

As always it seems to fall down to how defining that Higg's field.
You can define it as 'particles' but if you do you seem to need to have a 'soup' of them as inertia is expected to be existent everywhere (deep space too). Then again, if distance and time is 'elastics' then that seems to question the very grounds we stand on when discussing 'virtual particles'. Down there 'distance' as we see it might become something different which then would leave space :) for this 'soup' too.

I like to see it as a 'field', which doesn't define anything really? The reason why I do so is because I find 'forces' questionable, well not macroscopically then, but I differ between that and QM, and what might exist beyond that. And if we have 'isolated' Higgs bosons 'traveling' I suppose I will be wrong, or possibly that the 'transformations' between what's 'under QM', as I see 'virtual particles' to be, and our macroscopic world is more magical than I ever thought.

==

What I was thinking of Geezer when discussing that 'jiggling'?
Awh, did you have to ask me that one?

We have what we call 'invariant mass'. The definition for that is the mass that will be intrinsic to a object no matter  what frame of reference you place it in, space or a black hole.

So it can't be that one. As it is a result of the objects interaction in a gravitational field you might call it relativistic mass as you did, or maybe even momentum.

But if I would be right there, then you might have another problem :)
As gravity is everywhere, as far as I know, how do we get to the right 'invariant mass'?
« Last Edit: 18/01/2010 19:31:12 by yor_on »
 

Online yor_on

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Farsight "Imagine you used some aspect of this "jiggle" to operate a clock. Clock run slower nearer the ground, due to gravitational time dilation. That means the jiggle must be slower near the ground."

You make a very good point there. Time slows down relative an 'outside' observer when closer to a gravitational object. The way I was thinking of it was in the terms of potential energy, and that energy becomes more the further away you move your object from that 'impact zone' where gravity is at its highest.

==
Within limits of course as at some point it will no longer feel that gravitation (like deep space, Lagrangian points) enough to have the 'urge to move'.
==

Then i took that definition and compared it to the object (matter) it 'operated' on, and suggested that as we moved matter away from gravity its 'jiggling' would become less. As that 'jiggling' is transformed into kinetic energy the objects mass also would become less.
==

So if I choose your interpretation. Am I right in understanding it as that you associate 'slowing time' relative the observer as having less energy?

Which I then understand to lead to that a black holes energy level is less the closer you come to it as 'time' slows down relative our observer?
===
Or am I misunderstanding your suggestion?

Never the less, any which way the plate will differ in mass which then would lead to the question. Where exactly do we define the 'proper mass' for an object?
:)

---
So, now at last it almost makes sense :)
   
« Last Edit: 18/01/2010 20:01:05 by yor_on »
 

Offline VernonNemitz

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So now what happens if we don't use a solar powered rocket, but use a conventional rocket that obtained its energy from the system? Does the mass of the Moon still increase (and, because they are part of the same system, presumably by the same logic the Earth's mass would also increase)?

Details matter.  What sort of rocket is that?  If for purposes of thought-experiment you have magically introduced it from outside the Earth-Moon System, then you have introduced/added a great deal of potential energy (in the form of the rocket's potential ability to accelerate something like the Moon) to that System.  It should then be obvious that after the rocket has done its work, some potential energy has become real energy that has been added to the System, and thus the mass (that is, total mass-energy) of the Earth-Moon System would be greater than before.

On another hand, if the entirety of the rocket is constructed from Moon-matter, then its process of operation will cause a large amount of Moon-matter in the form of rocket exhaust to leave the Earth-Moon System at high velocity, and very likely the total mass-energy of that System, after the rocket does its work, will have become less than it was originally.

So, what would you prefer?  A proper answer DOES depend on the details!
 

Offline Geezer

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A proper answer DOES depend on the details!

Indeed it does. Which part of "conventional rocket" did you fail to comprehend?

If you are concerned about matter leaving the system, let's ensure that the system is large enough to include the exhaust from the rocket.

Now, did the mass (rest mass, naturally) of the system increase, or did it not? (I think this was the point of the original question.)
« Last Edit: 19/01/2010 03:28:21 by Geezer »
 

Offline Farsight

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So if I choose your interpretation. Am I right in understanding it as that you associate 'slowing time' relative the observer as having less energy?
Yes. If you think of a single electron, it's got spin and angular momentum. This occurs at a higher rate up in space than it does down near the surface of a planet. There's an energy difference between the two, and conservation of energy tells you this energy difference has to go somewhere. 

Which I then understand to lead to that a black holes energy level is less the closer you come to it as 'time' slows down relative our observer?
I'm thinking it's the other way around. It's hard to say much about the black hole itself, but if you consider a photon near to a black hole event horizon, it will look more energetic as you fall towards it. Its energy doesn't change at all, instead you're changing. All the electrons etc that make up your body and your clocks spin at reducing rate, so your measurement of time slows down. Hence the photon frequency appears to increase.   

Never the less, any which way the plate will differ in mass which then would lead to the question.
Agreed.

Where exactly do we define the 'proper mass' for an object?
It's a tricky one. When you lift the plate you give it some energy, so its mass increases slightly. But then when you lift yourself, you give yourself more energy. Ditto for all your measuring devices. So when you measure the mass of the plate again, it looks like it hasn't changed. If we try to say we should define proper mass in a place that is totally free from the effects of gravity, we've got another problem because there is no such place.
 

Offline Farsight

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Farsight: We reposition the Moon relative to the Earth using a conventional rocket (using energy from within the system). I don't think anyone would argue that we have not altered the potential energy of the system (although I would not be totally surprised if someone did). There had to be a redistribution of mass within the system to accomplish this but;

Did the mass of the system change, and if it did, why did it change?

(BTW, no matter was converted into energy or vice versa during this process.)
No, the mass of the system didn't change. All we've done is redistributed the energy within the system. We haven't changed the energy of the system, and mass is a measure of the energy of the system.

I notice that later on you said "rest mass, naturally". It's important to note that:

"The rest mass of a composite system is not the sum of the rest masses of the parts, unless all the parts are at rest. The total mass of a composite system includes the kinetic energy and field energy in the system".

See http://en.wikipedia.org/wiki/Mass_in_special_relativity#The_mass_of_composite_systems for details.
 

Offline litespeed

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Farsight - You wrote: "Did the mass of the system change, and if it did, why did it change?"

Potential chemical energy was thrust vectored towards the moon. Both the moon and the exhaust gases were accelerated and gained mass by E=mc2, as calculated by a stationary observer.

« Last Edit: 22/01/2010 20:54:41 by litespeed »
 

Offline Geezer

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Farsight: We reposition the Moon relative to the Earth using a conventional rocket (using energy from within the system). I don't think anyone would argue that we have not altered the potential energy of the system (although I would not be totally surprised if someone did). There had to be a redistribution of mass within the system to accomplish this but;

Did the mass of the system change, and if it did, why did it change?

(BTW, no matter was converted into energy or vice versa during this process.)
No, the mass of the system didn't change. All we've done is redistributed the energy within the system. We haven't changed the energy of the system, and mass is a measure of the energy of the system.

I notice that later on you said "rest mass, naturally". It's important to note that:

"The rest mass of a composite system is not the sum of the rest masses of the parts, unless all the parts are at rest. The total mass of a composite system includes the kinetic energy and field energy in the system".

See http://en.wikipedia.org/wiki/Mass_in_special_relativity#The_mass_of_composite_systems for details.

I would agree with that.  Does "all the parts are at rest" mean "at rest" in relative terms? Is the Moon "at rest" relative to the Earth? I think it almost is, but I'm not sure.
 

Offline Farsight

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I don't think that was me, litespeed, but yep, no problem. Give some part of the system some kinetic energy, and it makes a greater contribution to the system mass.

Geezer, I'd say it almost is, but not quite. The trouble with all the scenarios involving kinetic energy or just heat is that the mass increase is so very slight. I was looking for some experiment where it's been detected, but couldn't find anything.
 

Online yor_on

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Farsight.

"When you lift the plate you give it some energy, so its mass increases slightly. "

No, i don't agree to that one :)

What you create is a different balance between the plate and the 'highest gravitational point' in that same frame. The plate hasn't gained any measurable energy, as far as I know?

My idea is that if gravity can influence the 'jiggling' it should be less the further you move it from gravitational influences. And if that energy is converted to kinetic then it should read as if the plate is 'lighter' in that frame.

The potential energy we are discussing is the result of a known relation between the plate and gravity, not defined to the plate solely, but only as a relation.
 

Offline Farsight

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Tie your plate to a long string, yor-on, and give it almighty push. You did work on the plate, you gave it kinetic energy. So now it swings up to the top of its arc and pauses momentarily. Now freeze the frame and examine the situation. What happened to that kinetic energy? Where did it go? I'm sure we all agree it was converted into potential energy, but where is it? Did it escape up the string? No. Did it somehow leave the plate and move into the surrounding space, the region we call the gravitational field? We can't detect any experimental evidence for any energy leaving the plate. Besides, we know that if we push a plate away from the earth at 11.2 km/s, it has escape velocity, and takes the potential energy away with it. It has now escaped the earth's gravitational field, so there is no relation any more. There's only one conclusion you can draw from this: the potential energy is in the plate. Yes, "gravity influences the jiggling", but it makes it go slower, not faster. This is the only way the conservation of energy works, and gravitational time dilation is your proof.
 

Online yor_on

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Nice idea Farsight :)

First Vernon.
Rereading you and the lightbulb (induction)

A very cool example is from India where a lot of power disappeared from the Swedish built power plants as it was transmitted.

After using helicopters with IR in the night (searching for sources of warmth) they found cables (coils) buried under the ground leading to several villages ::))

quite clever..

Now, if we go back to your example. First of all you're introducing a momentum here, and you are limiting the 'force' of the rotation by the string attached. But even so, if you're not accelerating the plate it will be in what's called a 'uniform motion'.

Thingies in a uniform motion have a momentum, but it's unmeasurable as long as you don't have an interaction with some other frame of reference. That differs it from acceleration in where you directly can notice if you have gotten a larger momentum.

So what you see as energy transfered to a specific part of your new system I still see as a relation, where the potential energy can vary from null to ? depending on what other part you compare it too.

You might see it this way. If you do this on Earth and then let the plate hit the ground that relation will express itself as a certain kinetic energy getting released in the interaction as 'energy' in general.

Let a neutron star be you rotating, let the 'string' be gravity (frame dragging) and your plate be a object drawn by that.

Now, let another object travel beside it, getting slowly closer. As they meet there will be very little kinetic energy released.

It's all an relation, depending on your choice of reference frame. And that's why I don't see it as the plate having gotten any specific energy from rotating/ being lifted.

And when resting on that table it will be relative Earth an 'unmoving part of it' lifted out of the gravity, therefore having slightly less 'jiggling' What one could argue is that the rotational frame it is in is slightly increased, therefore counter balancing that loss of 'jingling'. But as it is a uniform motion it won't matter as I see it.
« Last Edit: 01/02/2010 02:52:20 by yor_on »
 

Offline Geezer

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A very cool example is from India where a lot of power disappeared from the Swedish built power plants as it was transmitted.

After using helicopters with IR in the night (searching for sources of warmth) they found cables (coils) buried under the ground leading to several villages ::))


I suspect that story was invented by some Norwegians. They've been making up stories for many centuries, so they are pretty good at it.

I have heard it's quite common for unauthorized persons to tap into the power system in India, but I'm fairly sure the inductive coupling story is a nordic saga or an urban legend.
 

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