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frankuitaalst
2008-Sep-09, 07:50 AM
I'm a little confused about the Energy - Mass relationship : E=mc².
E is said to be the total (internal) energy of a mass , in which are included heat , chemical energy , nuclear energy aso...
The expression is further extended to take into account the kinetic energy into the expression E²=m²c²c²+p²c² . This still is quite comphrehensible .

But how about potential energy of such a particle in a gravity potential field ?
Is potential energy in this case considered as an external source of energy , and thus covered by the field energy ?

Second question :
some mass can also have a charge such as protons , electrons , ions...etc...
I can imagine that having or not having a charge changes the "internal energy" of a particle . Is this correct ? Or is the property of having a charge is considered of only having an influence in an external field ?
Is there an analogue formula E= Q.c² ?

I think my confusion comes for a great deal from the mass-charge analogy when we consider the following equations : Ep=GMm/r and Ep=kQq/r² , giving an analogy between Mass energy and Charge energy .
As I'm typing this I realise that both energies are potential energies and therefor may be considered as "external" energies and therefor not appearing in the E=mc² formula.
But I don't know if this is correct .

Digix
2008-Sep-09, 12:17 PM
1 question is not so easy to answer, because gravity has some more relativistic effects.
but generally if you measure mass of system of 2 stationary bodies that are far away and close to each other first one will have more mass.
however it is hard to tell to which body all that mass belongs.

and it is really interesting question in general that if we have 2 charges or 2 mases where energy is stored in the field between them and in what form
since if energy is stored in the field between these points then you can bend field lines by using gravity.

also if you remove charges of mases very fact that energy will be released and become photon or graviton wave

WaxRubiks
2008-Sep-09, 02:47 PM
I thought all those energies, etc, contributed to the mass of the object. That result you obtain by weighing something.

frankuitaalst
2008-Sep-09, 04:14 PM
I thought all those energies, etc, contributed to the mass of the object. That result you obtain by weighing something.
Thinking about heat : means that if you heat up something it increases its mass. Makes sense , although th DeltaM will be very small.
I'm not sure about potential energy , therefor my post .
Or is potential energy just the energy which is possible gainable in a potential field ( a characterisc of the field itself , not of the matter ) which can be converted to velocity and in this way adds up to the mass ?

The charge energy ( if any ) in contrary is a mystery to me . Antiparticles do seem to have the same mass .

Digix
2008-Sep-09, 04:26 PM
I'm not sure about potential energy , therefor my post .
Or is potential energy just the energy which is possible gainable in a potential field ( a characterisc of the field itself , not of the matter ) which can be converted to velocity and in this way adds up to the mass ?
.

If we have brick above ground then for distant observer earth should look more heavy than same earth with same brick on the ground.

but which part of that system keeps all that energy? does brick became more heavy because you lifted it, or the earth gains mass , or maybe the void in between them is responsible for keeping all that additional mass.

Hornblower
2008-Sep-09, 08:25 PM
If we have brick above ground then for distant observer earth should look more heavy than same earth with same brick on the ground.

but which part of that system keeps all that energy? does brick became more heavy because you lifted it, or the earth gains mass , or maybe the void in between them is responsible for keeping all that additional mass.

Here is my take on it. If I carry the brick to the top of a tower, the total mass of the brick and Earth will be ever so slightly more than before, because of the energy added to the combination in the form of gravitational potential. The source of that energy is my muscles, and I will be slightly lighter as a result of having expended that energy.

Digix
2008-Sep-09, 08:39 PM
Here is my take on it. If I carry the brick to the top of a tower, the total mass of the brick and Earth will be ever so slightly more than before, because of the energy added to the combination in the form of gravitational potential. The source of that energy is my muscles, and I will be slightly lighter as a result of having expended that energy.

if you just brought brick on the roof then of course you lost energy, brick gained it, whole system is unchanged

assume small planed and brick that is falling down with start velocity of 0 so at that moment if just hangs in some height just as when you throw it up and it stops in the max height for short time
and another exactly same planet where that same size brick is lying on the ground.

since first setup have more energy it will have more mass, and second less, but where that mass is contained? there are no muscles and nothing that holds that brick

alainprice
2008-Sep-09, 08:41 PM
I'm gonna go out on a limb and say, no, the gravitational potential does not affect the energy of an object(locally). For the distant observer, there are corrections to be made, but if you're right next to the brick, it's still a brick at rest.

Hard for me to explain other than saying, there is no absolute frame of reference, be careful.

WaxRubiks
2008-Sep-09, 10:14 PM
but isn't time dilated in a gravitational field?

therefore, maybe, from a long way away, a brick on the Earth surface, might weigh less than a brick that is raised out of that space-time warp field created by the Earth, say to 2 million miles away from Earth.

I don't know, if that's true though.

Digix
2008-Sep-09, 10:19 PM
I'm gonna go out on a limb and say, no, the gravitational potential does not affect the energy of an object(locally). For the distant observer, there are corrections to be made, but if you're right next to the brick, it's still a brick at rest.

Hard for me to explain other than saying, there is no absolute frame of reference, be careful.

that is to be expected, but if there is no local difference in mass of brick that is in the ground level and the one which is in 10m level, then from where does it take energy to become hotter when it hits the ground?

aslo same can be asked that if there is vacuum capacitor where is his energy stored? in the empty space? how vacuum can store energy?

frankuitaalst
2008-Sep-09, 10:22 PM
If we have brick above ground then for distant observer earth should look more heavy than same earth with same brick on the ground.

but which part of that system keeps all that energy? does brick became more heavy because you lifted it, or the earth gains mass , or maybe the void in between them is responsible for keeping all that additional mass.
Well in this case the system must gain mass if an external force does action to lift the brick , so the whole system gains energy , thus mass .
Is this correct .
The increase of the energy is : GmM/r1-GmM/r2 for both bodies .
Does this mean that both earth and brick gain the same amount of mass ?

Digix
2008-Sep-09, 10:35 PM
Well in this case the system must gain mass if an external force does action to lift the brick , so the whole system gains energy , thus mass .
Is this correct .
The increase of the energy is : GmM/r1-GmM/r2 for both bodies .
Does this mean that both earth and brick gain the same amount of mass ?

it is obvious that whole system gets energy and gains mass but we don't understand what place keeps that additional "relativistic" mass.
do the brick weigh more if it is lifted up? or the earth gains mass is someone from outside raises brick?

frankuitaalst
2008-Sep-09, 11:25 PM
it is obvious that whole system gets energy and gains mass but we don't understand what place keeps that additional "relativistic" mass.
do the brick weigh more if it is lifted up? or the earth gains mass is someone from outside raises brick?
According to above both gain mass by (GmM/r1-GmM/r2 )/c² so their mass becomes:

* Mass Earth = M+GmM (1/r1-1/r2 )/c²
* Mass Stone = m+GmM (1/r1-1/r2 )/c²

I think it really gets interesting if we move now the lever and let the stone fall again ...

undidly
2008-Sep-09, 11:26 PM
but isn't time dilated in a gravitational field?

therefore, maybe, from a long way away, a brick on the Earth surface, might weigh less than a brick that is raised out of that space-time warp field created by the Earth, say to 2 million miles away from Earth.

I don't know, if that's true though.

Wrong way around.
The brick on Earth weighs more than the brick in space by 1 part in 10^9.

Time dilation is the result or the cause of this.
How can we measure the mass (not the weight) of the brick?.
Easy answer is use two bricks with a spring between and see how fast they oscillate together and apart.
Put them on Earth and they oscillate more slowly by 1 part in 10^9.
Back in space ,add a very little mass to each so that each weighs more by
1 part in 10^9 greater than it did.The oscillation slows to be the same as the pair on Earth.
Have the pair on Earth increased in mass or has time dilation done it?.

This works for all things.Electrons orbit more slowly and so emit a redder
light (when they shift to a lower energy level) than the same atom in space.

Radio transmits at a lower frequency too (on Earth) and all by the same amount.
Communications between Earth and space must take this into account.
In a G well mass is higher ,time is slower.They cause each other.

Your wrist watch mechanism is more massive ,so runs slowly.
This is NOT ATM.This is GR.

Digix
2008-Sep-10, 12:14 AM
all that is right if we take into account GR, but it is nor vital. in that case we have mass defect because instead of energy increase sum of mass of earth+brick becomes less even if the brick was laying on the ground.
I am talking about full relativistic mass not only about rest mass. obviously something must compensate that difference. since if we let the brick fall down it will gain energy which will convert into rest mass(in form of heat) when it hits ground

Digix
2008-Sep-10, 12:21 AM
According to above both gain mass by (GmM/r1-GmM/r2 )/c² so their mass becomes:

* Mass Earth = M+GmM (1/r1-1/r2 )/c²
* Mass Stone = m+GmM (1/r1-1/r2 )/c²

I think it really gets interesting if we move now the lever and let the stone fall again ...

so do you say that stone becomes more heavy as it is lifted? seems that it contradicts with gps clock slow down as undidly said.

undidly
2008-Sep-10, 12:57 AM
so do you say that stone becomes more heavy as it is lifted? seems that it contradicts with gps clock slow down as undidly said.

The stone (brick) becomes lighter as it is lifted.It has LESS total energy as it is lifted.Potential energy is more but that is all it is,not real.
There is another energy in the mass which gets less as the mass is lifted but I dare not say here as the mods may see it as ATM.
It is a physical reason for a little known part of GR.

undidly
2008-Sep-10, 01:11 AM
According to above both gain mass by (GmM/r1-GmM/r2 )/c² so their mass becomes:

* Mass Earth = M+GmM (1/r1-1/r2 )/c²
* Mass Stone = m+GmM (1/r1-1/r2 )/c²

...

frankuitaalst

This is just what I have been looking for.
What is the name for this mass increase effect?.
What is the mass increase for a supergalaxy,enough to make dark matter unnecessary?.

Digix
2008-Sep-10, 02:02 AM
frankuitaalst

This is just what I have been looking for.
What is the name for this mass increase effect?.

these formulas are just sum of rest mass at ground level and potential energy. they have no specific name. only formula used here is e=mc

however i warn you that always when I attempted to use mass as non constant all threads end in the complete mess. because GR supporters like to have rest mass as constant and manipulate space time around.

What is the mass increase for a supergalaxy,enough to make dark matter unnecessary?.
that probably wont work, because gravity will eat some mass and potential energy will add some other amount of mass so effect will cancel in some degree, also that relationship is nonlinear and you need to so some complex calculations.

frankuitaalst
2008-Sep-10, 07:26 AM
these formulas are just sum of rest mass at ground level and potential energy. they have no specific name. only formula used here is e=mc

however i warn you that always when I attempted to use mass as non constant all threads end in the complete mess. because GR supporters like to have rest mass as constant and manipulate space time around.

that probably wont work, because gravity will eat some mass and potential energy will add some other amount of mass so effect will cancel in some degree, also that relationship is nonlinear and you need to so some complex calculations.
Well , I'm not sure if the formula is fully correct ( see my original post ) . I came to it after the hint of Digix concerning the stone .
In this case GR is not applied , only SR .
Point is I think that if we apply an external force and action to a system we have a gain in energy , which results in a gain of mass , as the total systems energy get higher . This "energy" difference wasn't there before the stone was lifted .
This increase is an effect of the gravitational field of both bodies .
But this seems to be in contradiction with your statement saying the mass should diminish according to GR ?

frankuitaalst
2008-Sep-10, 10:25 AM
I've tried to put some elementary maths behind the idea of lifting a stone due to an external force in Earths gravitational field in order to find out if there is really an increase in mass and how big it is .
Picture in annex .
Interesting is the last phase were the stone again hits the ground .
While the stone has yet velocity compared to the initial condition ( and also Earth has a little velocity ) its energy is increased by the amount 1/2mv².
This is fully in accordance with the E=mc²+1/2mv² equation .

However : to calculate the 1/2mv² we need to know where the velocity comes from . This velocity is acquired while the stone was lifted before to a hight of r2-r1 relative to the initial position in the gravitational field.
So I guess E=mc²+1/2mv² remains valid in a gravitational field and potential energy should not be added to this equation ( condition v<<c ) ?

Looking at the formulas at the end I see now there's a certain recurrancy in the formulas . m = f(m,M,v,c) and M=g(m,M,v,c) . Perhaps some iteration should be done to find m and M ?

Hornblower
2008-Sep-10, 10:56 AM
Suppose a brick is hanging by a string. Total mass of system includes the gravitational potential of the separation of the brick and the ground.

If the string breaks, the brick starts falling. During the fall, the gravitational potential is transformed into kinetic energy. Total mass is unchanged.

When the brick hits the ground, the kinetic energy changes to heat. No immediate change in total mass of system.

The heat radiates into space as infrared radiation. When it is gone, total mass of what is left of the system is slightly reduced.

If we expand the boundaries of the system to include the propagating infrared at any given future time, the total mass is unchanged.

frankuitaalst
2008-Sep-10, 11:12 AM
Suppose a brick is hanging by a string. Total mass of system includes the gravitational potential of the separation of the brick and the ground.

If the string breaks, the brick starts falling. During the fall, the gravitational potential is transformed into kinetic energy. Total mass is unchanged.

When the brick hits the ground, the kinetic energy changes to heat. No immediate change in total mass of system.

The heat radiates into space as infrared radiation. When it is gone, total mass of what is left of the system is slightly reduced.

If we expand the boundaries of the system to include the propagating infrared at any given future time, the total mass is unchanged.
I can agree fully with this . Gravitational energy of this system is fully part of the total energy . So the mass of the system takes into account the geometrical configuration of the system .
If we consider the same system but the brick hanging at 1/2 of its hight this time , the total energy and therfor the mass of the system would be less ?

Hornblower
2008-Sep-10, 11:19 AM
I can agree fully with this . Gravitational energy of this system is fully part of the total energy . So the mass of the system takes into account the geometrical configuration of the system .
If we consider the same system but the brick hanging at 1/2 of its hight this time , the total energy and therfor the mass of the system would be less ?

If we have exactly the same collection of atoms and the separation is less, then the answer is yes.

frankuitaalst
2008-Sep-10, 11:41 AM
If we have exactly the same collection of atoms and the separation is less, then the answer is yes.

Understood . "Same mass" , but due to another configuration nevertheless different mass . Not easy to visualise at first , but makes perfect sense .
Reasoning in terms of energy helps a lot in this case .

Rests the second question of my OP : what about energy ( and thus the mass effect ) of charges ?

Do an electron and a positron have the same "mass" ?
I guess in this case again the filed theory dominates ?

Hornblower
2008-Sep-10, 12:41 PM
Understood . "Same mass" , but due to another configuration nevertheless different mass . Not easy to visualise at first , but makes perfect sense .
Reasoning in terms of energy helps a lot in this case .

Rests the second question of my OP : what about energy ( and thus the mass effect ) of charges ?

Do an electron and a positron have the same "mass" ?
I guess in this case again the filed theory dominates ?

I don't know enough about particle physics to comment on the relationship between the charge and the total energy of an isolated charged particle.

Let's look at a pair of oppositely charged bodies held together by the resulting static cling. For now let's take the OP equation as correct.

If we forcibly separate the bodies, the resulting total mass will be slightly greater than when they were in contact. The change is related to the amount of work done on the bodies by Einstein's famous equation. I see this as a direct analogy to forcibly separating gravitationally bound bodies. The added energy is now electrostatic potential.

In the particular case of an electron and a positron, they have equal mass, equal but opposite charge, and about 511,000 electron volts of energy apiece. They are antiparticles to each other, so if they come together they are transformed into a pair of gamma photons, which fly off in opposite directions with zero rest mass and 511,000 electron volts of electromagnetic energy apiece. In any system that contains them, they make the same contribution to the total system mass as did the original particles.

Clear as mud? Welcome to a small piece of modern physics.

Digix
2008-Sep-10, 01:54 PM
This increase is an effect of the gravitational field of both bodies .
But this seems to be in contradiction with your statement saying the mass should diminish according to GR ?

if we observe system of 2 bodies then potential energy will add to total mass,
but if we look at the brick in space it will seem a bit lighter to us, ans if we look at the earth from the brick point it will seem that when we got up earth became more heavy too. that is why theory is about relativity because everything is relative nothing is absolute.

just if you do some calculations you cant change reference frames as you wish, you must do everything from one reference frame
most GR users like to adjust time-space units to keeps mass and light speed constant. so they don't care about all that relativistic energy at all.

if we do not use spacetime manipulations, lots recalculations are required, and we need to be careful what cancels and what does not.

since blackhole mass = sum of masses of what falls into it without taking into account nearly infinite potential energy of everything. then I guess now that earth + brick will have same amount of energy and mass no matter how far or close apart they are, most likely GR effects cancel potentional energy completely

a1call
2008-Sep-10, 03:02 PM
*- Potential energy of a brick suspended at some height is analogous to the potential energy stored in a spring.

*- A compressed spring weighs more than an uncompressed spring

*- dissolve a compressed spring in a jar of acid and compare it to dissolving an uncompressed spring in an equal jar of acid. The compressed solution will be warmer.

*-The stored energy in a spring or suspended brick that can be measured as mass/weight experimentally, can probably be traced at molecular level as compressed molecules in reaction to the tension exerted by spring/gravity which when dissolved in acid are released making the solution warmer

*- The same compressed molecules obviously manifest their state as weight/slower-oscillation-between-spring-connected-bricks but the mechanics of this manifestation is beyond me