Mass of the Earth

[Perikles]

In BBC news today, there is an article about the changing mass of the Earth. In it, Dr Chris Smith is quoted as saying

"Nasa has calculated that the Earth is gaining about 160 tonnes a year because the temperature of the Earth is going up. If we are adding energy to the system, the mass must go up,"

What I have set in bold baffles me, and I suspect he is being quoted out of context. But is the statement necessarily true?

[Strange]

Sounds right. Remember that energy causes gravity, as well as matter. So, if you add energy you effectively increase the mass.

(I hope that is right because I have had a similar argument discussion on another forum...)

[Jeff Root]

I would expect that thermal energy from deep inside the
Earth (leftover from the planet's formation, from decay of
unstable isotopes, or whatever) would reach the surface
and radiate away at a much higher rate than the increase
from increasing temperatures at the surface. And a few
tons of meteoritic material are added each day. I don't
remember how much air is lost each day, but probably
less than meteorites add.

Edit to add:

Okay, that's what the BBC article is all about.
Never mind.

-- Jeff, in Minneapolis

[Strange]

The article does go on to say that more energy is being lost in these and other ways than is being gained.

[Perikles]

Yes, but disregarding the main thrust of the article and whether energy is being gained or lost, why would an increase in energy necessarily mean an increase in mass? Why would the rest mass of the Earth change if, say, an increase in energy is due to an increased angular rotation?

[grapes]

In the scheme of things, according to the article, where does 160 tonnes fit in? I mean, in comparison to meoterites gain and atmosphere loss.

[Strange]

Yes, but disregarding the main thrust of the article and whether energy is being gained or lost, why would an increase in energy necessarily mean an increase in mass? Why would the rest mass of the Earth change if, say, an increase in energy is due to an increased angular rotation?

How are you defining or thinking of the mass of the earth? Are you thinking of it as the amount of "stuff" in there (the number of atoms, or something similar)? In which, case, it may not make sense. Mass is not just a measure of how much matter there is; it is also a measure of the gravity caused by (or experienced by) something.

Both matter and energy are causes of gravity. Add energy and you increase the "amount of gravity produced". That is the same as adding mass; no, it is adding mass.

[Strange]

In the scheme of things, according to the article, where does 160 tonnes fit in? I mean, in comparison to meoterites gain and atmosphere loss.

It is a really, really tiny contribution.

I have only skimmed through the article but it looks quite good.

But overall, Dr Smith has calculated that the Earth - including the sea and the atmosphere - is losing mass. He points to a handful of reasons.

Now read on ...

[Perikles]

Both matter and energy are causes of gravity. Add energy and you increase the "amount of gravity produced". That is the same as adding mass; no, it is adding mass.

I'm not disputing anything, I'm saying I don't understand it (hence the Q and A section). Is your statement a direct consequence of GR, and if so, could you point me to where I might read more about this?

[Strange]

There is an overview here: http://en.wikipedia.org/wiki/Introdu...ces_of_gravity (I'm sure there is a better description somewhere)

I'm not disputing anything

I didn't mean to suggest you were, I just wasn't sure where your doubts came from.

[Jeff Root]

There are two fundamentally distinct ways of defining mass:

Inertial mass is the measure of how strongly matter resists
being accelerated by a force. Newton defined it as m=F/a.

Gravitational mass is the measure of how strongly matter
attracts and is attracted by other matter gravitationally.
Newton defined it as m1 = F * r² / G * m2, where
m1 and m2 are two masses, r is the distance between
their centers, F is the force between them, and G is the
universal gravitational constant.

No difference has ever been detected between inertial
mass and gravitational mass. Einstein asserted, as a
postulate of general relativity, that they are one and the
same thing.

General relativity says that gravity is curved spacetime,
and that energy is what curves otherwise flat spacetime.

Mass is the most compact form of energy: A little bit of
mass contains a lot of energy. So mass is very effective
at producing gravity.

-- Jeff, in Minneapolis

[the giant peach]

In BBC news today, there is an article about the changing mass of the Earth. In it, Dr Chris Smith is quoted as saying
What I have set in bold baffles me, and I suspect he is being quoted out of context. But is the statement necessarily true?

Dr Chris Smith is a Pathologists. He clearly know less than you about the topic here, so who knows why he is prognosticating on it. A few questions to illustrate the foolishness of his assertion:

• what kind nuclear process is converting the heat into mass?
• what drives the process counter to entropy? What stops it running the other way about?
• if Global Warming heat is turning into mass, how come it is nevertheless still there as heat also?
• ..and how come only 'special' GW heat is converted into mass - what stops all the rest of the heat in the world disappearing down that rabbit hole?
• So have we finally found the answer to Global Warming - just package it all up as mass?

The man is talking rubbish. Without a nuclear reaction we have that mass and energy are each conserved. With a nuclear reaction mass and energy are related through Einstein's E=mc^2. But there is no nuclear reaction going on here!

[Perikles]

I obviously need to do a considerable amount of homework and catch up on GR. Half a century ago, my physics degree course included SR, but the equivalence of energy and mass seemed restricted to variation of mass with speed. The equation was E = mc2/sqrt(1-v2/c2). A binomial expansion of that gives E = mc2 + 1/2 mv2 + ... I always took the mc2 to be a fixed rest energy, to which kinetic energy was added. So either that was the thinking at the time, or I just misunderstood. Or that is the difference between GR and SR.

[profloater]

This is very interesting but does not the original quote kind of suggest that energy is being converted into mass as a corollory of (or evidenced by) the surface temperature going up? Surely that interpretation is incorrect isn't it? (I don't mean to start a new question).

[the giant peach]

Nobody needs to do any homework!

The OP is correct to be baffled. You don't even have to ask how the heat gain is supposed to be converted into a mass gain. Just the fact that the quote in the BBC assumes that the energy gained through global warming presents both as heat (global warming) and as mass - both at the same time - should be enough to convice you that the BBC has got this embarrassingly wrong.

Then a little school physics will tell you that there is no nuclear process going on here to drive the E=mc^2 equation anyway. And if it did, and it ran in the direction suggested (energy to mass) then that also would be a first for science. I'm sure entropy would come into that somewhere, and it points the other way.

And any number of other questions, like how come all the rest of the earth's heat is not also subject to the same mysterious process and turning spontaneously into mass.

[Strange]

This is very interesting but does not the original quote kind of suggest that energy is being converted into mass as a corollory of (or evidenced by) the surface temperature going up? Surely that interpretation is incorrect isn't it? (I don't mean to start a new question).

I think it is basically the same question. The important point is that the energy is not being converted to matter but it does contribute to the total mass of the Earth. The energy in that paragraph is the extra thermal energy due to global warming. (Or have I missed your point completely?)

[the giant peach]

mass is a property of matter. You can't have mass on its own with no matter.

[cjameshuff]

Dr Chris Smith is a Pathologists. He clearly know less than you about the topic here, so who knows why he is prognosticating on it. A few questions to illustrate the foolishness of his assertion:

• what kind nuclear process is converting the heat into mass?
• what drives the process counter to entropy? What stops it running the other way about?
• if Global Warming heat is turning into mass, how come it is nevertheless still there as heat also?
• ..and how come only 'special' GW heat is converted into mass - what stops all the rest of the heat in the world disappearing down that rabbit hole?
• So have we finally found the answer to Global Warming - just package it all up as mass?

• No nuclear reaction is necessary.
• There is no process. Nothing is counter to entropy.
• The heat is contributing to mass, not turning into mass.
• All heat contributes. What is being discussed is specifically the additional contribution due to global warming.
• That you ask this shows a fundamental misunderstanding of what is being discussed. There is no "rabbit hole" that heat is disappearing into.

The man is talking rubbish. Without a nuclear reaction we have that mass and energy are each conserved. With a nuclear reaction mass and energy are related through Einstein's E=mc^2. But there is no nuclear reaction going on here!

The lack of nuclear reactions is completely irrelevant. E = m*c^2 does not imply or require any such thing. The misunderstanding is yours.

[the giant peach]

so please explain the magic - how does "heat contribute to mass"

[Perikles]

I think it is basically the same question. The important point is that the energy is not being converted to matter but it does contribute to the total mass of the Earth. The energy in that paragraph is the extra thermal energy due to global warming. (Or have I missed your point completely?)

I thought it was the same question as well. Now I am still confused. How would you define the difference between matter and mass?

[Strange]

Dr Chris Smith is a Pathologists. He clearly know less than you about the topic here, so who knows why he is prognosticating on it.

I assume he is talking about it because he is also a broadcaster; this is a summary of a story from the BBC's "More or Less" radio program, which is always worth listening to.

[Strange]

I thought it was the same question as well. Now I am still confused. How would you define the difference between matter and mass?

I suppose matter would be defined as stuff made from leptons (http://en.wikipedia.org/wiki/Elementary_particle). Mass is a property of matter. Some of it comes from the mass of the leptons, a large part of it comes from the binding energy holding those together.

[Strange]

And any number of other questions, like how come all the rest of the earth's heat is not also subject to the same mysterious process and turning spontaneously into mass.

It is. I did a rough calculation for a similar discussion on another forum and came up with the total thermal energy of the earth being about 2x10¹⁴kg which is about 0.000000003% of the total mass of the earth.

[the giant peach]

It is. I did a rough calculation for a similar discussion on another forum and came up with the total thermal energy of the earth being about 2x10¹⁴kg which is about 0.000000003% of the total mass of the earth.

so if all the earth's heat is turning into mass then we should all be frozen solid by now. You can't have it both ways - it can't manifest itself as heat and as mass simultaneously.

As to other's suggestions that heat "contributes" to mass, please explain the mechanism. Just to be clear about the original quote from the BBC:

"Nasa has calculated that the Earth is gaining about 160 tonnes a year because the temperature of the Earth is going up. If we are adding energy to the system, the mass must go up," says Dr Smith.

So Dr Smith is unambiguous - adding energy to a system increases its mass. Apparently.

[the giant peach]

I assume he is talking about it because he is also a broadcaster; this is a summary of a story from the BBC's "More or Less" radio program, which is always worth listening to.

I know he is a broadcaster, he goes by the name of The Naked Scientist. The thing is, he puts himself forward as a specialist. Which he is, just not in that field. In that field he is just a layman.

[NEOWatcher]

And any number of other questions, like how come all the rest of the earth's heat is not also subject to the same mysterious process and turning spontaneously into mass.

I think it's a matter of the way it's worded.
Before the phrase "global warming" was common, the accepted term was "greenhouse gas". I've heard of the greenhouse effect all my life (or it seems so).

So; if I project my understanding of this onto the story, then the heat of global warming is not from the warming itself, but from the extra heat that is trapped by the greenhouse effect that causes the global warming.

[trinitree88]

I think it's a matter of the way it's worded.
Before the phrase "global warming" was common, the accepted term was "greenhouse gas". I've heard of the greenhouse effect all my life (or it seems so).

So; if I project my understanding of this onto the story, then the heat of global warming is not from the warming itself, but from the extra heat that is trapped by the greenhouse effect that causes the global warming.

Neo. Yep....and to help minimize the carbon dioxide levels, forty years ago they pretty much banned the outside burning of trash and leaves in peoples' back yards in the USA....a fall ritual for millions. That leaves them to decompose in landfills where some still produce carbon dioxide, but a lot more of the carbon escapes as methane, which is ~ 25 times more efficient as a greenhouse gas. Since businesses operate landfills at a profit....you don't see them going out of business even though they are a big source of the problem.

[phunk]

Nobody needs to do any homework!

The OP is correct to be baffled. You don't even have to ask how the heat gain is supposed to be converted into a mass gain. Just the fact that the quote in the BBC assumes that the energy gained through global warming presents both as heat (global warming) and as mass - both at the same time - should be enough to convice you that the BBC has got this embarrassingly wrong.

Then a little school physics will tell you that there is no nuclear process going on here to drive the E=mc^2 equation anyway. And if it did, and it ran in the direction suggested (energy to mass) then that also would be a first for science. I'm sure entropy would come into that somewhere, and it points the other way.

And any number of other questions, like how come all the rest of the earth's heat is not also subject to the same mysterious process and turning spontaneously into mass.

Energy doesn't "turn into" mass, it's equivalent to mass. When you add energy to a system, its gravity and inertia increase the same as if you added an equivalent (E=mc²) amount of mass.

[profloater]

In that case I thank Perikles for raising this point which I had never appreciated before.

[the giant peach]

Energy doesn't "turn into" mass, it's equivalent to mass. When you add energy to a system, its gravity and inertia increase the same as if you added an equivalent (E=mc²) amount of mass.

Energy does turn into mass, and mass into energy. That is exactly what E=mc^2 means.
Mass into energy - that is what atomic bombs do, mass converted into energy. Explode an atomic bomb in a closed system and the outcome is less mass that your started with (and a lot more energy).
Energy into mass - happens in high energy particle beam collisions. But, crucially, it isn't hapening when the earth warms up through global warming. The heat energy remains very much as plain old heat, the earth gets warmer (so they say).

You seem to be implying that enegy is (figuratively) like the shadow of mass, the two accompany each other about inseparably, their relative quantitly governed by E=mc^2
But an amount of energy is not at the same time an amount of mass - the two are interconvertible, the equivalence given by E=mc^2
Just like kinetic and potential energy can be converted one to the other, as a mass bouncing on a suspended spring. So you if you start the system with the spring fully stretched all the energy is PE. It is not simultaneously present as KE. But when you release the spring and the mass boings up to its maximum velocity, then all the energy is converted to KE. There is a one-to-one conversion (excepting friction losses etc). So mass and energy are interconvertible.

EDIT
or have I been guilty of confusing mass with matter and regarding the two as identical concepts?