Talk:E=mc²

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1 Archives
2 Romanticizing about Albert Einstein and perpetuating myth
3 Merge with Mass-energy equivalence
4 Deleted statement suggesting that 100 C change in temp is equivalent to some quantity of energy or mass
5 A first order proof of E=mc^2
6 Matter losing mass as it falls down a gravity well
7 Local conservation of energy in general relativity vs. other theories

[edit] Archives

Talk:E=mc²/Archive1 ('06), 147kb

[edit] Romanticizing about Albert Einstein and perpetuating myth

The current introduction to the article states: "In these, he [Albert Einstein] showed that a unified four-dimensional model of space and time ("spacetime") could accurately describe observable phenomena in a way that was consistent with Galileo's Principle of Relativity, but also accounted for the constant speed of light."

That is pure myth. Historically, the fusion of space and time originated with Minkowski in 1908, who in fact stole the unification of space and time from the geometrization of relativity by Henri Poincaré. See http://www.univ-nancy2.fr/DepPhilo/walter/papers/einstd7.pdf

For that article, titled, Minkowski, Mathematicians, and the Mathematical Theory of Relativity, one directory states, "Minkowski claimed scientific priority for a great, new, geometric theory of relativity at the Cologne lecture of 1908, based largely on the work of Poincaré. Poincaré was purposely excluded from the meeting. 42 pages." http://www.everythingimportant.org/relativity/directory.htm --e.Shubee 19:27, 16 January 2007 (UTC)

Please remember in all this that people had been thinking of "unifying" space and time for a long time before 1907. Reimann worked on his geometry with this explicity purpose, 50 years before. It's one thing to think about unifying space and time, and something else to have the quantitative equations which give you the proper relationship between the two! Which in this case is a sort of hyberbolic geometry which which, even in flat space, isn't obvious. It was Einstein who came up with the quantitative relationships needed. It was Minkowski who realized they could be made into a new geometry. If it was Poincaire who supplied the program for this, or even Reimann, that's fine. Put them down as cheerleaders.

Remember, mathematicians are very good at this sort of thing, once they are given the physical clues as to which of the (very many) mathematical worlds describes the real one. It's the physicists who do that for them. David Hilbert, once told by Einstein what the requirements would be in a differential Reimann-style differential geometry to decribe gravity, worked out the math for of general relativity many times faster than Einstein had, and very nearly beat him into publication. That's fine. The point is that it took Einstein to set the physical constraints on the mathematical theory. For the early geometrization of SR, Minkowski gets credit for the geometric interpretation. For GR, Einstein managed to do it all himself, but Hilbert also got there independently, once Einstein told him what was needed. All these men were following in the footsteps of Reimann, Poincaire, and many others. But the crucial physical insight was Einstein's, and he gets the major credit. And should. S B H arris 20:02, 16 January 2007 (UTC)

You are in error on several points.

1) Riemannian geometry was not Riemann's attempt to unify space and time.

2) Poincaré was to first to geometrize special relativity in a mathematical sense.

3) Minkowski got the credit for the geometric interpretation but only because physicists are good at creating fictional realities that have nothing to do with the real universe.

4) Einstein is on record in opposing Minkowski's unified geometrization of space and time in 1908 with a silly whine saying it was too complicated. Read http://www.univ-nancy2.fr/DepPhilo/walter/papers/einstd7.pdf, which I have already cited.

5) Einstein could not have discovered general relativity in 100 years without the mathematicians of his day. If Einstein only had library access and a team of translators for all the published books and articles of the world, it wouldn't have helped him. Solving the objective of GR required talented mathematicians much smarter than Einstein to work on the problem.

6) Einstein didn't create GR all by himself. You are forgetting the contributions made by Marcel Grossmann, Tullio Levi-Civita, Hermann Weyl, Felix Klein, Emmy Noether, and a number of other mathematicians. See http://www.phys.uu.nl/~wwwgrnsl/abstracts/rowe990217.html

7) Modeling gravity as spacetime curvature isn't as brilliant as you think. There are at least four distinct physical forces in the universe yet only gravity is modeled as the curvature of spacetime. Who is to say that Einstein didn't take us in the wrong direction? Alternative points of view haven't been ruled out. There is no computing of geodesics in a geometric model of electromagnetism, for instance, when trying to figure out the trajectories of charged particles.

8) You're bringing up general relativity because the veneration of Einstein, a purely religious idea, is the essence of your denial.

9) You're defending the myth that in 1905 Albert Einstein unified space and time into a four-dimensional geometric model, now called spacetime, ignoring cited evidence to the contrary. --e.Shubee 21:47, 16 January 2007 (UTC)

Yes, this article incorrectly credits Einstein. Einstein was not the one to unify space and time into a 4-dimensional spacetime, and he was not the first to publish E=mc². The article should just explain the mass-energy equivalence, and leave the history for elsewhere. Roger 00:46, 26 February 2007 (UTC)

Albert Einstein indicated that gravity distorts space-time as modeled in rolling a ball on a rubber-sheet with heavier balls as masses in the solar system. The layman understands this to mean that light rays are also bent when passing close to large masses.

Tom Bearden asserts, et. al., that because of this distortion in space from gravitational fields (the rubber sheet metaphor) we must use Riemannian geometry not Euclidean geometry to describe space (near large masses).

Additionally, Mr. Bearden asserts that Einstein’s famous equation, E = mc², was over simplified, ignoring an electromagnetic wave effect on gravity. E² = p²c² + m²c⁴. I don't know what "p" is. Larry R. Holmgren 16:14, 10 March 2007 (UTC)

I think the problem is that when Einstein "developed" this concept of E=MC squared, he failed to recognize the true forfathers of the equation. Think of it this way: He was not working by himself when he came up with the "theory of relativity". He was merely attempting to translate something that he had read and tried to make it his own, ergo, Einstein's theory of relativity. User:69.229.109.185 30 March 2007

[edit] Merge with Mass-energy equivalence

I was surprised to find that there is another article on this same topic called Mass-energy equivalence. I would like to propose that information from that article be merged to this one. Additionally, I think Mass-energy equivalence is a more appropriate name for the article. Having an equation, however famous, as an article title is something of an anomaly on Wikipedia, and I think it would be far more appropriate for the article title to be the concept represented by the equation rather than the equation itself. (Naturally, E=mc² can and should redirect to Mass-energy equivalence following the merge.) Comments? Robert K S 14:59, 1 February 2007 (UTC)

I agree with the merger but think that E=mc² is a better topic title. --e.Shubee 22:26, 1 February 2007 (UTC)

I agree that the information should be condensed into one, since it refers to the same information. The title E=mc² is what most people would look for first (voice of experience here), but redirecting to the more appropriate title is a fine compromise. -- Haxwell 17:36, 11 February 2007 (UTC)

Can you think of any other articles on Wikipedia whose titles are equations? Even an article title of The Einstein equation (a la Ohm's Law) is more appropriate than E=mc² in this regard. Additionally, I have my doubts that many users arrive at this article by searching on the string E=mc². E=mc2, perhaps, but finding the superscript 2 special character and pasting it in, or using the Alt+numbered keypad code to generate it manually, is most unnatural. I would be willing to wager that most of this article's traffic comes from redirects or links from other articles. Robert K S 05:14, 15 February 2007 (UTC)

I got here by searching E=mc2 (no special superscripts); and I like the title this way. Also, note to Robert K S, you are completely wrong on your opinion, the E=mc² expression is the most famous equation in the history of human kind. Also, do you know how many equations Einstein has? Moreover, did you happen to note the 147kb worth of talk on this page compared to the one comment worth of talk on the other page? As to the merge, I'm ambivalent; the term "mass-energy equivalence" is common jargon, unrelated, necessarily, to Einstein. As a matter of fact, I'm going to add a nice image to this page from the walk of ideas. Later: --Sadi Carnot 06:17, 15 February 2007 (UTC)

It is a nice image. You say I'm "completely wrong", but I think you may misunderstand my point. From my first comment to this thread: "Having an equation, however famous, as an article title is something of an anomaly on Wikipedia..." In other words, it doesn't matter how famous the equation is. The English-language concept behind the equation, and not the mathematical notation of the equation itself, is the more appropriate article title on the English Wikipedia, because the words "mass-energy equivalence" have intrinsic meaning in English, whereas "E=mc²" does not have intrinsic meaning in English. (On a math wikipedia, sure, let's have equations as article titles, go to town. But here, English, not mathematics, is the language of choice, and should be used for article titles.) The article title should convey the concept the article expresses right off the bat, but mathematical notation cannot ever do so. Robert K S 17:34, 15 February 2007 (UTC)

Support merge The two articles are totally redundant. I never would have thought of typing "mass-energy equivalence" into Wikipedia's search field to find information on E=mc². I made a guess that "E=mc2" would get me to where I wanted to go and voilà, it took me to the right article. It was a good demonstraton of the power of Wikipedia. I was impressed. Even though Wikipedia can easily redirect, I think Mass-energy equivalence should be deleted, links to it redirected, and any of its unique and valuable text should be incorporated into this article. Greg L 19:39, 5 March 2007 (UTC)

Support merge The proposed merge would benefit individuals seeking information on the subject with no prior knowledge of it. The title "Mass-energy equivalence" is akin to the captions and various pictures in a newspaper, which serve the purpose of providing a general idea of the respective subject to busy readers. --69.156.210.102 18:17, 8 March 2007 (UTC).

Support merge The proposed merge is a great idea, there is no reason there should be two articles on the same topic.

[edit] Deleted statement suggesting that 100 C change in temp is equivalent to some quantity of energy or mass

I have deleted the following statement (now twice):

Raising the temperature of an object by 100 °C increases its mass by 2.3043 × 10^–36 g.^[1]

I hope the many reasons why it's false will be apparent. First, raising the temperature of a cup of water 100 C will require more heat than raising the temperature of a bathtub of water by the same amount. So there is OBVIOUSLY something wrong with the statement. Obviously, the statement is intended to be somehow particle or mass-specific, or intensive. That means we're talking about things like specific heat capacity to even have a chance to make statements like this one. However, even when we go to intensive quantities like numbers of moles or particles, we can't come up with an amount of energy or heat which is equalivalent to a given temperature change like 100 C, because different types of objects have different heat capacities, due to different compositions and different ways of storing heat. Thus, there is no direct comparison of temperature and energy in any system which holds, with a given constant converstion number. The reference given involves some confused use of Boltzmann's constant, and is applicable to heat capacities of ideal gases where heat capacity is 3/2 k per particle, but a specific energy (or mass) like this would still require a certain amount of gas, like perhaps one molecule. In fact, 2.3e-36 grams is 2.1e-22 J = 15 K_b per 100 C per particle. Somebody probably meant it to be 1.5 K_b, so it's off by a factor of 10, even talking about the amount of heat/mass which is stored as kinetic energy. But in any case, as noted, the mass of an object when heated increases as all the energy modes stored, not just the kinetic ones. A bad sentence all the way around. Wrong conceptually (in several ways), and quantitatively, too. S B H arris 05:01, 6 March 2007 (UTC)

[edit] A first order proof of E=mc^2

The following I will try to present in formulas as well (I have never used the formula translation tool before) but just to make sure, here goes the descriptive proof:

power = energy / time => (1) energy = power * time

(2) power = force * velocity

(1)+(2)-> (3) energy = force * velocity * time

(4) momentum = mass * velocity

(5) force = momentum / time

(4)+(5)-> (6) force = mass * velocity / time

(3)+(6)-> energy = mass * velocity / time * velocity * time =>

(7) energy = mass * velocity ^2

It has always bothered me, what people say, nothing travels faster than light. All of the equations used are elementary physics/mechanics and please notice that I havent used the sqare root adjustment for mass that uses the speed of light.

My proposal is simple. The above proof, if it holds, apart from being simple, makes no assumption about velocity, i.e. it holds for velocities greater than the speed of light, so maybe, much as people thought before breaking the sound barrier, the assumption that we can't go faster than light, is a myth. Naturaly if you believe in your heart its possible, this just removes any worries about you shrinking to nothing as you approach c. Your only other problem is a suitable "lane" to try this, most likely perpendicular to the plane of the solar system.

If you are intent to "shoot me down" my last defence will be to borrow a line from "Contact" [Carl Sagan,Zemeckis 1997, Jodie Foster, John Hurt] and say this: "Wanna go for a ride?"

Using formulas and using 'u' instead of 'p' for momentum to avoid confusing it with power:

$P = E / t$

$E = P t$

$P = F v$

$E = F v t$

$u = m v$

$F = u / t$

$F = m v / t$

$E = (m v / t) v t$

$E = m v 2$

wbP —The preceding unsigned comment was added by Pelorios (talk • contribs) 18:23, 6 March 2007 (UTC).

Pelorios, if you attach numeric quantities at each stage in your above logic (keeping careful track of all your "ones" and "twos", and "1.414s"), you will find that indeed, mass times the square of velocity relates to energy. But, more specifically, you will also find that it's not E = m • v², it's actually E = ½m • v². The latter is the classic formula for determining kinetic energy. Einstein's formula can not be arrived at via your method unless one leaves off such niceties as numeric values. An explanation for why nothing can go faster than the speed of light is more complex than this. Greg L 08:28, 7 March 2007 (UTC)

And Einstein's work did not and does not derive the constancy of the speed of light; this was known well before Einstein and served as one of his axioms. And I don't think you substantially appreciate the rather simple physical basis for special relativity and things like the Lorentz contraction (which in terms of time dilation is easily verified in the case of things like muons). --24.147.86.187 00:39, 8 March 2007 (UTC)

[edit] Matter losing mass as it falls down a gravity well

The below has been transplanted from Greg L’s talk page (Greg L 18:45, 14 March 2007 (UTC)):
–––––––––––––––––––––––––––––––––––––––––––

Anytime energy is added to a system, the system gains mass. For instance, lifting a one-kilogram mass upwards one meter against the force of one standard gravity increases its mass by 109.114 femtograms (1 fg = 1 × 10^–15 g).^[2]

There's a problem with this, and that is that it's not true! The energy is stored as potential in the system of Earth and mass as a whole, and not in the mass itself. So where exactly does this mass reside? Hard to say. Mass can be very tricky to locate, especially in g-fields. See mass in general relativity for some of the problems. In any case, if you actually do lift a 1 kg mass in Earth's gravity, nothing happens to the mass of the system at all. Since of course you just move mass from here to there, from the chemicals in your arm to the system of weight-raised-to-height. The gravitational field of the Earth as seen from a long way away, obviously does not change in processes like these (lifting things or avalanches, etc). Energy has to escape or enter the system for that. So, again a bad and wrong example for many reasons. S B H arris 21:50, 7 March 2007 (UTC)

“In any case, if you actually do lift a 1 kg mass in Earth's gravity, nothing happens to the mass of the system at all” No, that statement is not true. If it were, then why did you leave the one about hydro water? Matter going up or down: there's no difference. Matter falling into a gravity well looses mass. That's Einstein's way of looking at it. To the engineer, matter traveling closer to the center of the earth (or a floor) loses potential energy. The extent to which matter loses mass as it travels down a gravity well is equal to the potential energy lost as it does so. The reverse of this is matter gaining potential energy by being raised upwards (traveling upwards out of a gravity well). It's as valid for the kilogram weight going upwards as it is for water falling downwards. Greg L 05:40, 9 March 2007 (UTC)

No, mass falling down a gravity well does NOT lose mass. If two masses come together, are you going to tell me which one of them looses the mass? Is it split according to their ratios? All this is bad thinking. The system loses the mass of the potential energy, IF it's radiated as heat (otherwise it's retained as heat, or retained before contact as kinetic energy). Otherwise, not. Where the mass assocated with the g potential is, before that, is up for grabs. Generally, it's usually regarded to be in the g-field, but it doesn't have a location. As for hydro power, no mass is lost or gained when water falls or rises, except as sunlight enters or leaves the system. That complicates things there, but not in the simple arm-raising the weight example, where the system is closed, and therefore mass-energy obviously is conserved and constant. S B H arris 17:02, 9 March 2007 (UTC)

“No, mass falling down a gravity well does NOT lose mass” You are dead wrong. This is a fundamental and elementary truth and you are embarrassingly incorrect. “If two masses come together, are you going to tell me which one of them looses the mass?” In the case of the Earth vs. a kilogram, where the latter one overwhelmingly does the moving, yes. It’s ultra-simple: Two pieces of matter that are close to each other have less energy than the same two pieces a long way apart because you have to expend energy to separate them against the gravitational force that is pulling them together. Energy is proportional to mass. Ergo, closer together = less energy = less mass. This concept doesn't just apply for a kilogram, it applies to the entire universe. The total energy of the universe is exactly zero. The matter in the universe is made out of positive energy. A gravitational field in this sense is negative energy. If all the mass of the universe is brought together in a "big crunch", the resulting energy is zero. The bottom line is: If you take a kilogram of matter and measure its mass, and then lower it in an elevator to the basement where you measure it, you will find it lost mass. Don’t believe that statement? See Paragraph 1.3, here as well as that article’s main page, Einstein's Theory of Relativity versus Classical Mechanics. Oh, and were you tempted to disagree with some of what I wrote above? Well, Stephen Hawking wrote much of it in his A Brief History of Time. Please also see Talk:E=mc2, where I have an expanded explanation on all of this. Greg L 18:21, 9 March 2007 (UTC)

Sigh. Consider a couple of masses stably held apart. Draw a sphere around it. It's now a closed system, no energy or mass in or out. Now let the masses go. As they fall inward they lose potential and gain kinetic E, but the Lagrangian doesn't change. When they hit, they heat up. During all of this, it remains a closed system, and the mass and energy inside does not change. There's a discussion of this in Feynman in the relativistic kinematics portion of book #1. Although he omits the gravity part, it's just as obvious with springs or when kinetic energy is converted to heat. Through it all, if it's a closed system, mass is conserved. No matter what you do to it, or it does to itself. A nuclear bomb could go off inside that sphere, and so long as you didn't let light or heat out, the mass of the thing would not change. That's the whole point of these exercises. S B H arris 18:30, 9 March 2007 (UTC)

You're trying to change the subject. What you deleted was a statement that said that raising a kilogram upwards against Earth’s gravity increases its mass. I wrote nothing about how doing so increases the mass of the Earth/Kilogram system. Save me your "Sigh" business (I'm not going to bite on petty provacations), read the provided links, and then make your edits to the article. Greg L 18:35, 9 March 2007 (UTC)

I do not understand where your problem is. If raising the mass does not raise the mass of the system, it doesn't raise the mass of the mass, either. If you're suggesting that mass moves around inside the system during gravitational work, that's certainly correct (so long as none enters or leaves), but the location of gravitational mass is problematic, as I noted. None of your references are relevent to WHERE gravitational mass resides in a system where it's stored in a G-field. The article on mass in general relativity does bear on the issue, but if you read it, you'll soon take leave of the idea that when you lift a rock, the work you do against the field somehow "goes into" the rock (and not the Earth or field), and is nowhere else. Heck, you wouldn't even believe that in the case of work done against an electric field. Would you? If I had an electron and a positron close together, and I measured the electron mass by jiggling it back and forth, and then I put some work into the system by moving them apart against their mutual electic field, the whole system would mass more by the amount of work I put into it. But that work goes into the *field*. Actually the whole system. I couldn't detect it from trying to take the invididual mass of the electron again. It doesn't reside there. And no, I'm not changing the subject. The physical location of "mass" gained in work done against fields (ie, where in space IS the energy of the field) is exactly the subject. For gravity, it's an especially tricky one. S B H arris 19:31, 10 March 2007 (UTC)

You didn’t read the articles I provided, did you? Then read Note 6, which I just added. Greg L 19:34, 10 March 2007 (UTC)

…And you know, it’s time-consuming writing responses to you. I really wish you would read 1.3: Mass-Energy Conservation at a Microscopic Scale. This is but one section from a single page from a comprehensive treatise on Einstein’s equations titled Einstein's Theory of Relativity versus Classical Mechanics by Paul Marmet. This treatise is one of many topics available on the Intute: Science, Engineering and Technology Web pages, which is a shared resource of the Consortium of Academic Libraries in Manchester, U.K. However, since you seem to be reluctant to actually read any of this, and instead apparently prefer to continue to believe what you want to believe, I’ve quoted some of 1.3 for you below:

“

According to the principle of mass-energy conservation, the mass of the hydrogen atom in the basement is now different from its initial mass m_o on the first floor. It is slightly smaller than m_o and is now equal to m_b. Any variation of g with height is negligible and can be taken (with g) into account in equations 1.4 and 1.5.

”

And finally, just how the hell old are you? What is your education and background? Your profound self-confidence and the absolute certainty in your statements (“There's a problem with this, and that is that it's not true!”, “Sigh”, “I do not understand where your problem is”, and “No, mass falling down a gravity well does NOT lose mass”) over a fundamental and elementary point like how matter loses mass as it falls down a gravity well, is a hallmark of extreme youth. Why did you persist in twice writing again instead of first setting aside five minutes to read even the very first link I provided you? Lastly, your writing style seems intended to convey that you have some sort of uncanny insight into the deep inner workings of relativity and its equations (“So where exactly does this mass reside? Hard to say. Mass can be very tricky to locate, especially in g-fields.”). False claims of knowledge are another hallmark of extreme youth and can be rather embarrassing to watch when someone so predisposed fails to correctly fathom the relativity-equivalent of 1+1=2. Greg L 00:00, 11 March 2007 (UTC)

Um, I'm 49 years old, a fact you could have discovered from my user page, on which I wrote last year that I was 48.

I'm sorry to have to report that you're the victim of a bad textbook. I don't know if it's written by a crank, or what his problem is, but he's giving you bad physics. The frequency shift of atoms or nuclei at the bottom of a gravitational well is simply due to the fact that time runs slower there, by a factor of 1-phi/c^2, as seen from flat space (if you view the whole process of emission from there, photons start with a low frequency, and simply keep it). Which is the same as saying that photons climbing out of such wells suffer a gravitational doppler shift of the same amount (this is from the perspective of the ground, where photons start at a normal frequency, and gain in frequency, as they rise, since from the ground's perspective, clocks in space run faster). Both perspectives are correct, as they result in the same prediction: Low frequency at the bottom of the potential well, higher frequency when out of it. This stuff about lower mass of atoms in the bottoms of g-wells is nonsense. If it were literally true, you'd have a double effect, and would get a frequency shift from both the gravitational time/doppler effect, AND this wierd and wacky mass effect that your poor author is trying to push. But only one effect actually happens. The standard interpretation of it is not the one you're reading, sorry. Your author says: "Since the red shift measured corresponds exactly to the change of the Bohr radius existing between the source and the detector, we see that it cannot be attributed to an absolute increase of energy of the photon during its trip in the gravitational field." Alas, that actually is the standard interpretation of modern physics. I'm sorry, but it is. The photon loses energy as it goes up, as seen from the ground. From above, it already had low energy due to general relativistic slowing of ground clocks.

Again, BTW, I'm not trying to argue that mass is not lost when you lower something down a g-well and extract energy doing it. But that mass is lost from the system-as-a-whole, not particularly from the object that you lower. And oh, yes, atoms (and space itself) expand in a g-field (along ONE dimension!), so the Bohr radii are larger, indeed (but no longer "circular"). But that's a direct effect of gravity on the fabric of space itself-- the beginning of that black hole funnel. It's got nothing to do with atoms losing mass. Did I leave anything out? Oh, yes. Hawking is not God. He may be right about the universe having zero mass/energy total, or he may be wrong. There's intense debate on the subject right now in astronomy, and no general agreement. Also, since it's a system thing, it (again) has no direct bearing on our argument. A system gains mass as you add energy in any way (including pushing masses in the system apart). But in general with gravity it's impossible to say where the extra mass is LOCATED in space. It's the same situation with gravitational waves: energy is there, mass is there. But it has no particular location. S B H arris 04:31, 11 March 2007 (UTC)

17:02, 9 March 2007 (UTC): “No, mass falling down a gravity well does NOT lose mass.”
04:31, 11 March 2007 (UTC): “I'm not trying to argue that mass is not lost when you lower something down a g-well and extract energy doing it.”

Your arguments are clearly not consistent. Further, you are again trying to broaden the issue by arguing about frequency shifts and other topics that have nothing to do with what I wrote about (and you deleted). I don’t give a crap about Bohr radii and won't allow myself to be enticed off into the brush to chase a red herring. Further, your are now trying to say that 1) a comprehensive, thorough, and detailed Web site on relativity (Einstein's Theory of Relativity versus Classical Mechanics by Paul Marmet) should not be believed, 2) Stephen Hawking can’t necessarily be believed, and 3) you should be believed. This line of reasoning is pretty hard to swallow; particularly considering that your two statements above (a day and a half apart) are diametrically opposing positions.

E=mc² and the principal of mass-energy conservation are straightforward concepts with clear and unambiguous ramifications. Paul Marmet and Stephen Hawking are consistent and logical in their descriptions of how matter loses energy and mass as objects come closer together. Here’s the the consequence of what they say: Two spherical diamonds, each made of 83⅓ moles of ¹²C and each with a diameter of about 8.16 cm, are in space with their centers of mass separated by 8.16 cm. They are touching each other. Let’s say that 83⅓ moles of ¹²C precisely defines a kilogram in space (far from Earth and its gravity). The two-sphere system thus has a mass very slightly greater than 2 kg because of the potential energy latent in the fact that their 166⅔ moles of carbon isn’t concentrated into a single sphere; their two centers of gravity are separated by a minimal amount. Then you separate them by an additional meter. You had to put in 3.0 × 10^–9 J of work to accomplish this task. Their mutual gravitational attraction is 176 times weaker than when they were touching. According to E=mc², the now-separated system has 179,751,035,747,363,528.000 000 0030 J of energy, which is a mass of 2 × 10⁰ + 3.4 × 10^–26 kg.

But where is this added mass located? Earlier (before you flip flopped), you were arguing that the added energy and mass isn’t bound in the matter but that it’s “hard to say” exactly where it is (Wow… that’s helpful), but you seemed to imply that it’s somewhere in “g-fields.” However, two objects poses a combined gravity field that doesn’t change in total magnitude as their relative positions change. If one accepts Stephen Hawking’s explanation that matter is “positive energy” and gravity fields are a “negative energy,” and that these two energies equal zero as the Universe disappears in a Big Crunch, then it must follow that matter loses mass as it falls down a gravity well and it must follow that matter gains mass as it rises out of a gravity well. If your earlier argument were true (that the added potential energy and mass due to separating objects is bound in the gravitational field somewhere), then the Big Crunch would leave a big ball of matter and no gravity! Stephen Hawking’s concept is borne out by Paul Marmet’s 1.3: Mass-Energy Conservation at a Microscopic Scale. I really doubt these guys invented any of this; they’re just explaining it for us simple folk. Further, Stephen Hawking’s explanation handily explains how something (the Universe) could come from nothing (empty space seething with zero-point energy): what looks like something (the observable local Universe surrounding us), is really nothing more than “zero” that has been stretched until it formed a ±precipitate of gravity and matter.

And please don’t beg off a story about how your second statement above is consistent with the first because it includes the caveat that “you must extract energy while the object is falling down the gravity well and if you don’t capture this during the drop, then it doesn’t lose any mass.” That would clearly be a big, steaming, metric butt-load of weapons-grade bullonium and you know it. You’re flip flopping. You incessantly complain that what I’ve written it isn’t true but offer no explanation of your own (“I know the extra mass is not in the matter but it’s hard to say just where it is” amounts to “Pay no attention to that man behind the curtain!”). Trying to debate a subject like this with you is like trying to swat a house fly: logic doesn’t work and you change positions all the time. Greg L 23:54, 11 March 2007 (UTC)

ANSWER: You can shout "BS!" till the cows come home, but the reason I carefully qualified the two statements above, so that they are different, is because they represent two different situations, and I understand that. If you lower a mass, you extract energy in the process, and mass-energy of the system decreases, because you're removing it. Whereas, if the mass simple falls down the well (you let it fall), you're NOT extracting anything, and the mass-energy of the system remains constant as the mass falls. Simple as that. Apparently, you'd like very much to prove I'm contradicting myself on this point, but what I've written is clear enough and I can let it stand as proof that I'm not talking about the same situation.
Yes, I'm saying Marmet shouldn't be believed on this point about atoms getting less massive and enlarging in a g-field, and I gave a very clear reason why he's wrong. His prediction of enlargement and mass-decrease of atoms gives the well-known doppler gravitational frequency shift, and yet we know that's due to something else (gravity slowing of clocks), and NOT the effect Marmet describes. QED, he's wrong. There's no red herring here-- he's the one pointing out that his supposedly lowered mass gives what other physicists call the gravitational Doppler shift, not me. So he's the one who put his foot in it, not me.

On your example: "However, two objects poses a combined gravity field that doesn’t change in total magnitude as their relative positions change." Who told you THAT? It's certainly not true in general. If you add mass-energy (in the form of simple mechanical work) to the 2-sphere system from the outside, in order to separate them, they end up as a system having more mass, after you're done. That shows up in an (over all) larger (stronger) G-field, as seen from a long way away. (Where the field is viewed down the axis joining the spheres: having one sphere approach MORE than makes up for the other moving away by the same distance. The field is weakened in the plane orthogonal to the radius between spheres, but not to the same extent.) And that would be just as true if they were held together by a spring, which you stretched using a couple of outside ropes. The extra mass-energy and G-field due to it, is not due to formation of any new carbon atoms (certainly), and (indeed) its location is hard to place. No, all the carbon atoms don't get a little more massive. For an electrical situation (one sphere pos and the other equally neg), the energy to separate them goes into the E-field, and (guess what?) there actually is a difference in what you see in the field from far away, to correspond to the work you put into the system. Because the field at a distance is not exactly zero, but is a 1/R^3 dipole field, and you increase the dipole moment when you put in the work (as I "back of envelope" it for the far-field, all derivatives of these field strengths (dF/da) with respect to sphere separation ("a") vary as the inverse cube of distance R to the spheres, but in the case of the direction plane orthogonal to sphere-sphere axis, there's an extra factor of a/R which diminishes the effect, as compared with the direction of the sphere-sphere line). The total energy of the field ends up increasing as "a" increases. A similar thing happens with the total G-field, when you separate two masses--- you change the gravitational quadrupole moment. (Incidentally, both of these processes result in EM and gravitational radiation, especially if done quickly, but I assume we're going to do it in the limit of very slow processes, in order to minimize that). Anyway, that's the way it works.

Oh, as for Hawking. The total energy of the universe is really off topic, as it involves so many other kinds of matter and energy. Quite often cosmologists just ASSUME a flat universe and calculate things like dark matter and dark energy so total energy comes out to zero, using the estimates of positive energy (mass-energy) and negative potential (gravity) we have from observation. We certainly don't have enough data from observation to be able to tell directly any such value. Yes, G-potential-fields represent a sort of negative mass-energy, in the opposite sense of ordinary positive (non gravitational) mass-energy that shows up in the matter part of the matter+gravity stress-energy pseudotensor. Never said they didn't. Just said they were always hard to locate. A highly bound object is lighter (less massive) than a loosely bound one, but that doesn't mean that all the objects in it are somehow less massive. Do you think if the gravity of a neutron star or black hole gets large enough, it might just disappear in a zero-energy quantum fluctuation? Nope (although this very question did stop Einstein in the middle of the street once, when Szilard asked him about it). A neutron star masses less than the sum of its free neutrons, is all. Just as an atomic nucleus has a mass less than the total of the mass of its free nucleons. That doesn't mean each neutron in there somehow is individually less massive. The loss of mass associated with binding energy is a system property, and cannot be located to a place within the system. S B H arris 02:26, 13 March 2007 (UTC)

Gad, you’re still complaining that Dr. Paul Marmet is flat wrong about how atoms lose mass as they go down a gravity well. And Dr. Stephen Hawking’s theories are debatable. Tell you what hot shot: You go write a huge pile of Web pages on the subject of relativity that colleges in the U.K link to, and you go write a best-selling book on cosmology, and maybe people will one day cite you as an authority on the subject. Pardon me all over the place if I chose not to cite Sbharris at the moment. Greg L 20:00, 13 March 2007 (UTC)

Hey, you're free to talk to your physicist pals. Mine tell me I'm perfectly correct. When you pull apart two masses, using energy from the outside, that energy adds to the mass of the system. But there's no way of telling which of the two masses it "jumps" to--in fact the entire question is improper, because it presumes that it does. Or that it proportions itself somehow between the masses, and that you know the formula for how the proportionation happens. Yeah, what is it, Einstein? Anyway, Hawking doesn't speak to this point. Marmet seems to be saying the mass added all gloms onto the smaller (less massive) particle--- I presume he has a reason for that? And what if the two particles are closer to the same mass? Basically, you haven't convinced me that he knows, or that you know. Your arguments are a mess and not self-consistant. Nor are Marmet's, for reasons discussed. I think I've said about all I have to say about it. I'll wait for inputs from people with degrees in physics. S B H arris 21:05, 13 March 2007 (UTC)

Who do you think you’re kidding? Well, please cite these experts of yours. Greg L 21:26, 13 March 2007 (UTC)

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The following is the original, parallel debate originally posted here. Greg L 18:45, 14 March 2007 (UTC)

Anytime energy is added to a system, the system gains mass. For instance, lifting a one-kilogram mass upwards one meter against the force of one standard gravity increases its mass by 109.114 femtograms (1 fg = 1 × 10^–15 g).^[3]

“In any case, if you actually do lift a 1 kg mass in Earth's gravity, nothing happens to the mass of the system at all.” No, that statement is not true. If it were, then why did you leave the one about hydro water alone? Matter going up or down: there's no difference. Matter falling into a gravity well looses mass. That's Einstein's way of looking at it. You know that's true don't you? If you don't then you shouldn't be editing this article. To the engineer, matter traveling closer to the center of the earth (or a floor) loses potential energy. The extent to which matter loses mass as it travels down a gravity well is equal to the potential energy lost as it does so. Does that surprise you? It shouldn’t. See 1.3 - Mass-Energy Conservation at a Microscopic Scale. The reverse of this process is matter gaining potential energy by being raised upwards (traveling upwards out of a gravity well). It's as valid for the kilogram weight going upwards as it is for water falling downwards.

I left the hydro section alone because it's confused by the issue of mass-energy (sunlight) entering the system from the outside. In that case, mass of the system is increased if water is lifted (but not if it's lifted by energies internal to the system, such as the arm of somebody). But when sunlight does the job, it's the mass of the entire system that increases, not particularly the mass of the lifted water. The energy gained when sunlight is added to the system can be viewed as being stored in the gravitational field as much as anything else. In any case, it'd hard to say where it is, and it's certainly improper to view it as being stored as extra mass in the raised water. S B H arris 03:51, 13 March 2007 (UTC)

“The gravitational field of the Earth as seen from a long way away, obviously does not change in processes like these (lifting things or avalanches, etc).” Sheesh. Yes, that's true. But it doesn't support your position one twit! Yes, the Earth system doesn't gain mass when one raises the kilogram upwards one meter. Do you know why? What if a bunch of Indiana Jones-style sand falling onto a seesaw platform lifted the kilogram weight upwards? See? Obviously, the sand lost potential energy — and mass — as the kilogram gained. Regardless of the type of machine (even if its a human machine) that is employed to to lift the kilogram’s weight upwards one meter, it ultimately accomplishes 9.80665 J of work while accomplishing the task. All that's happening is work and a transfer of energy (and small amounts of mass) from one object or system to another.

Yes, indeed, but you seem to believe that the mass and potential energy have "jumped" onto the raised kg like a flea onto a cat. That's a bad way to view it, and it's really without foundation.S B H arris 03:51, 13 March 2007 (UTC)

“Since of course you just move mass from here to there, from the chemicals in your arm to the system of weight-raised-to-height.” There, although that sentence is mangled almost beyond recognition, I can tell what you meant: you had the proper concept right in front of you but you didn't grasp its significance in order to realize it’s a non sequitur that undermined your point! Chemical energy of the human metabolism was expended in the process of lifting the weight. Ultimately, the human body is a combustion machine that oxidizes carbohydrates. The reaction byproducts (mostly carbon dioxide and water) have a teeny bit less mass — about 0.1 µg per day — than the fuels going into the reaction. Except in this case, the inefficiency of the human body is such that it lost much more energy and mass into the ambient environment than ever went into the kilogram while lifting it. Again… All that's happening is work and a transfer of energy (and small amounts of mass) from one object or system to another.

The "system" which holds the gravitational potential energy of a lifted rock, is rock-plus-Earth. It's not the rock (or water, or sand) per se. It's improper to view it as such. S B H arris 03:51, 13 March 2007 (UTC)

If you still doubt what I’ve written here, more good reading can be found at Einstein's Theory of Relativity versus Classical Mechanics as well as Stephen Hawking’s A Brief History of Time.

Since you didn't grasp this, then others will doubtlessly fail to do so too. Accordingly, I added two explanatory sentences right after the sentence in question to illustrate the concept. I also added three more sentences to the end of the paragraph regarding how this is all about the exchange of energy and mass. Greg L 06:37, 9 March 2007 (UTC)

By using the earth as your reference frame, you're implicitly sneaking in additional information about the combined system. You're only able to specify a location for that extra mass by taking the special case where you pick your frame of reference to be one of the bodies in a two body system. To define a location for that mass you still need information about the entire system, and then to arbitrarily pick a reference point within that system, which is exactly what SBHarris has been saying. What if I decide my reference point is the object being lifted? Then it's the earth that's getting heavier. KonradG 03:49, 13 March 2007 (UTC)

I don't know this stuff very well, but in "references" note #6 is not appropriate. It's a footnote, not a reference, and the webpage it links to is apparently a set of very short excerpts from A Brief History of Time. The webpage does not include anything that helps me understand what you all are arguing about. Could you all agree on what to say and how, and leave out the long footnote? Enuja 23:33, 12 March 2007 (UTC)

One editor seems to think that Hawking's view that the universe has zero energy is relevant here. I happen to agree that it isn't. Not only that, but it's not even an agreed-on view in astronomy, however much Hawking might be enamoured of it. In any case, potential energy is stored in gravitational fields as well as electric and magnetic and other fields, and I feel this statement that mass and energy used in lifting a mass of water (if they come from sunlight, say) are stored completely on the lifted water (as in the example) and not (say) at all in the Earth or the gravitational field of the Earth, is improper. And wrong. Citing Hawking's views of the energy of the universe aren't going to help this bad view. S B H arris 04:00, 13 March 2007 (UTC)

Gad, you’re still complaining that Dr. Paul Marmet is flat wrong about how atoms lose mass as they go down a gravity well (“Yes, I'm saying Marmet shouldn't be believed…”). And you say Dr. Stephen Hawking’s theories are debatable. Tell you what hot shot: You go write a huge pile of Web pages on the subject of relativity that colleges in the U.K link to, and you go write a best-selling book on cosmology, and maybe people will one day cite you as an authority on the subject. Pardon me all over the place if I chose not to cite Sbharris at the moment. For the complete history of Sbharris’s writings on this topic, see my user talk page. Greg L 20:12, 13 March 2007 (UTC)

P.S.: I just got off the phone with one of the authors of The Apache Point Observatory Lunar Laser-Ranging Operation (APOLLO) paper (132 kB PDF, here) written by five people, some of whom work for the University of Washington, Dept. of Physics. This is the experiment where researchers are looking for extremely small violations in Einstein’s Strong Equivalence Principle (SEP) by measuring the Earth/Moon distance with lasers. Yes, raising a kilogram upwards against gravity increases its mass. That’s what he/she confirmed. I’ve e-mailed him/her the link to this Wikipedia article and asked him/her to review what I’ve added. In the mean time, please leave the disputed text alone so people with Ph.D.s and lots of expertise in this subject can review it. I’ll ask his/her permission to post his/her response here — and to cite his/her name — after he/she responds. Greg L 20:48, 13 March 2007 (UTC)

Hillarious. So the extra mass "knows" to go into the raised kilogram and not the raised Earth. Remember, you're just separating two objects with a force, and yet all the energy of your doing so just jumps to one of them, and sits there. That's some smart energy. I can't wait for the equation which tells how your physicist friend knows this. Standing by (but I think you're in for a red-faced admission that the addded mass doesn't have a location in space you can point to). S B H arris 21:12, 13 March 2007 (UTC)

The only thing that is hillarious, is your saying people should believe Sbharris, but to not believe Dr. Hawking and Dr. Marmet. Greg L 21:43, 13 March 2007 (UTC)

Greg, I think you're missing the point. It's not a question of whether you can measure a mass increase, but whether that measurement is *observer-independent*. Your example only works because you've arbitrarily defined your reference frame to be the two-body system minus the object being lifted. Of course the relativistic mass is going to appear in that object, since that's the only thing left. KonradG 22:59, 13 March 2007 (UTC)

KonradG: I don't understand why you feel I chose an "arbitrary" frame of reference. As I wrote, the frame of reference is an absolute one, i.e., relative to the center of mass of the two objects being separated. A mass measurement must be observer-independent; one can not have a situation where different observers (above or below the object) arrive at different mass measurements. Lifting a weight upwards one meter against Earth's gravity is simply an issue of adding potential energy into an object by increasing its separation from the center of the Earth. What I wrote is explicitly and unambiguously supported by Dr. Paul Marmet in his 1.3: Mass-Energy Conservation at a Microscopic Scale. This is but one section from a single Web page from a comprehensive treatise on Einstein’s equations titled Einstein's Theory of Relativity versus Classical Mechanics. The concept that matter loses mass as it falls down a gravity well is vividly illustrated by Stephen Hawking’s in his A Brief History of Time when he said that precisely zero energy remains if all the matter in the Universe fell down the entire gravity well of the Universe in a Big Crunch.

The only way that Sbharris has been able to deal with this fact is to simply declare that Dr. Marmet and Dr. Hawking are incorrect. Hey, life’s damn simple when you deal with problems that way, isn’t it? I don't know why I bothered to contact the researcher who participated in the APOLLO laser ranging experiment looking for any violation of Einstein’s Strong Equivalence Principle (SEP). Today, that individual said: “Yes, raising the height of an object above Earth increases its mass” and elaborated as to why this is the case. Kinda black & white don't you think? Sbharris’s solution to this bit of news: declare that the relativity researcher is incorrect too! Wow… As I said before, pardon me all over the place if I chose not to cite the likes of Sbharris and instead chose to cite experts like Dr. Marmet. Greg L 00:35, 14 March 2007 (UTC)

This is a reference frame issue. From Chapter 20, Section 4, page 467 of Gravitation by Misner, Thorne, Wheeler (the bible of General Relativity):

"Anybody who looks for a magic formula for "local gravitational energy-momentum" is looking for the right answer to the wrong question. Unhappily, enormous time and effort were devoted in the past to trying to "answer this question" before investigators realized the futility of the enterprise. Toward the end, above all mathematical arguments, one came to appreciate the quient but rock-like strength of Einsten's equivalence principle. One can find in any given locality a frame of reference in which all local 'gravitational fields' (all Christoffel symbols, all gamma(alpha,mu,nu)) disappear. No gammas means no 'gravitational field' and no local gravitational field means no 'local gravitational energy-momentum.'

"Nobody can deny or wants to deny that gravitational forces make a contribution to the mass-energy of a gravitationally interacting system. The mass-energy of the Earth-moon system is less than the mass-energy that the system would have if the two objects were at infinite separation. The mass-energy of a neutron star is less than the mass-energy of the same number of baryons at infinite separation. Surrounding a region of empty-space where there is a concentration of gravitational waves, there is a net attraction, betokening a positive net mass-energy in that region of space (see Chapter 35). At issue is not the existence of gravitational energy, but the localizability of gravitational energy. It is not localizable. The equivalence principle forbids."

An increase in gravitational potential energy therefore cannot be localized in any single mass or field in a way that is invariant for all observers. Whether the mass of an object raised in a gravitational field rises depends on where you look at it from. In particular, an observer remaining near the object raised, say in close orbit around the raised object, will not see the raised object's mass increase. On the other hand, an observer in a fixed position relative to the Earth would plausibly see the object's mass increase as it moves through the Earth's gravitational potential. Someone above wrote, "one can not have a situation where different observers (above or below the object) arrive at different mass measurements...." In fact, you can, just as in Special Relativity different observers arrive at different mass measurements of the same object depending on relative motion. It is meaningless to speak of mass changes without clearly specifying the observer dependence. Brian Wowk 06:35, 14 March 2007 (UTC)

Brian and Steve are correct: the kilogram mass remains mass-invariant as it is raised or lowered in a gravitational field. The energy change is accommodated by (i.e. stored in) the gravitational field itself. I refer you to Alan Guth who says

"Since the negative energy of a gravitational field is crucial to the notion of a zero-energy universe, it is a subject worth examining carefully. In this appendix I will explain how the properties of gravity can be used to show that the energy of a gravitational field is unambiguously negative. The argument will be described [in the appendix] in the context of Newton's theory of gravity, although the same conclusion can be reached using Einstein's theory of general relativity."" (See Guth's "The Inflationary Universe" (ISBN 0224044486) Appendix A).

Guth considers the work that can be extracted from a collapsing spherically symmetric shell of matter; the argument has obvious application here also. --Michael C. Price ^talk 09:49, 14 March 2007 (UTC)

I looked at the Marmet web page that is used as a cite support the apparent absolute mass increase argument. Marmet discusses the famous Pound Rebka experiment in which a red shift of gamma rays is seen when gamma rays climb through a distance in Earth's gravity. He shows how this can be explained as mass change in the atoms lowered in the field. This is not surprising since it is common in physics for different interpretations to give equivalent and results. However the mass change interpretation of this experiment proves nothing about any absolute change of mass. For if the emitter and absorber are lowered together, rather than separated by a distance in the gravitional field, no red shift or apparent mass change will be recorded. It's all relative.

There is another problem that needs to be addressed. Marmet was a well-known iconoclast with unconventional interpretations of a great many topics in physics. Encyclopedia articles on important mainstream physics topics should cite mainstream sources when necessary. Listing of Marmet's writings on General Relativity on crank dot net (http://www.crank.net/einstein.html) is prima facie cause for not using Marmet cites in a mainstream encyclopedia article involving GR.

The current article text claiming that mass-energy increase is uniquely confined to single bodies rather than the composite system when gravitating bodies move apart is misleading, and should be changed. It isn't even true classically. Brian Wowk 16:25, 14 March 2007 (UTC)

Good quotes Brian. Thanks. I wish I had the book. But I carefully read what you quoted and believe you are misinterpreting its meaning. It’s clear to me what the first section (two paragraphs) you quoted are addressing: gravitational energy is not localizable. It does not address the issue of whether a matter-based body can be localized; that’s pretty much a “Well… Duhhh issue isn’t it? Further, the second paragraph in the first section you quoted from is merely supporting what I wrote: that according to the Einstein’s Strong Equivalence Principal, gravity’s self-energy has inertial and gravitational mass. The second paragraph you quoted says nothing more.

The third paragraph (the very last section you quoted) Brian, simply supports what Dr. Stephen Hawking wrote in his A Brief History of Time (and which I cited): that matter loses mass as it falls down a gravity well. More specifically, that when all the matter that exists falls down the biggest gravity well in existence, it looses all its mass and gravity disappears; there is zero net energy (mass) in the Universe. This is just an extreme example of scaling the effect to the largest possible dimensions. What Hawking — and now Guth — wrote both support what Dr. Paul Marmet wrote in his 1.3: Mass-Energy Conservation at a Microscopic Scale (and which I also cited), which simply states that when matter is lowered down a gravity well, it loses mass. Except that Dr. Marmet accomplishes this via an example at the other extreme: with a single hydrogen atom.

I simply wrote — and cited — what one author (a Ph.D. in the subject) explicitly wrote, and what two others support via analogy at a grand scale. I don’t have the supreme confidence that Sbharris and others do, where I would simply announce that I am so damn expert in the subject, that I will declare that a published Ph.D. author is flat wrong. Dr. Paul Marmet wrote his 1.3: Mass-Energy Conservation at a Microscopic Scale and I cited it. Please note that this citation is but one section, from a single page, from a comprehensive treatise on Einstein’s equations titled Einstein's Theory of Relativity versus Classical Mechanics. In turn, this treatise is one of many topics available on the Intute: Science, Engineering and Technology Web pages, which is a shared resource of the Consortium of Academic Libraries in Manchester. What did he exactly write? This:

“

”

Note further, that yesterday I contacted one of the researchers who helped test, to extreme precision, Einstein’s Strong Equivalency Principal (SEP), and who helped write The Apache Point Observatory Lunar Laser-Ranging Operation (APOLLO), T. W. Murphy, Jr. et al. University of Washington, Dept. of Physics (132 kB PDF, here). That individual also said "Yes, raising the height of an object on Earth increases its mass.” Sbharris declared this person to be wrong too (in addition to Dr. Hawking, Dr. Marmet, and apparently any other famous Ph.D. who disagrees with him).

It seems clear to me that the issue here is that Sbharris et al. feels that the added energy and mass caused by separating objects is bound in the gravity field, not in the object that was moved. I apparently don’t have anywhere near the brass to simply declare that because I am a Wikipedia contributor (*insert drum roll and heavenly voices here*), that I am expert enough to declare all these guys are full of crap. I do however, poses enough capacity to think logically to recognize the fallacy of thinking that separating two bodies against the force of gravity adds the energy (and equivalent mass) into the gravitational field and not the body that one accelerated and moved. Think: matter creates gravity. According to the Strong Equivalence Principal, gravity has a self-energy (and an equivalent mass). The only thing that creates a gravitational field in the first place is mass. The only thing. So why would someone think that added potential energy would add directly to the gravitational field and handily bypass the mass? This, in spite of the fact that all four authors mentioned above are consistently saying that matter loses mass as it goes down a gravity well?

Note too that while I was talking to the researcher who participated in the SEP experiment (using Lunar laser-ranging) the individual explained to me that an object falling down a gravity well doesn’t loose mass — at least at first. It loses only if it is lowered down a gravity well. Why? Because as it falls, stationary matter (and its equivalent energy), plus its potential energy (and its equivalent mass) become moving matter (and its equivalent energy), and kinetic energy of motion (and its equivalent mass). Please think about this. If you do, you will realize that this too fully supports the notion that the added energy and mass resides in the body. This also makes it logically impossible for the added energy and mass to go into the gravitational field. Here’s why I think this is the case:

A gravitational field can have no knowledge of the velocity of the falling object, only its position. The magnitude of the combined Earth/object gravity doesn’t change appreciably as an object is either lowered or falls towards the center of the Earth. Before an object falls, it has maximum potential energy and maximum mass. Shortly after it begins falling, it rapidly exchanges potential energy for the kinetic energy of motion. Let’s assume it’s falling in a vacuum so frictional losses aren’t an issue. Accordingly, (since some potential energy converted into kinetic energy) the object’s mass hasn’t hardly change at all. OK, stop. Let’s examine two scenarios at this point: 1) one object is falling and still retains the energy (and mass) associated with its kinetic energy; and 2) let’s consider another object that was lowered by a machine (human or mechanical) so there was no conversion of potential energy into kinetic energy. From the point of view of Earth’s gravity field, both objects are in the same position. So where is the missing energy and mass in the one that was slowly lowered? Answer: it’s in the object, not the gravity field. OK, let’s continue the drop. As the object continues to fall closer to the center of the Earth, Earth’s gravitational force on the falling object decreases so its potential and kinetic energies (and mass) diminishes. By the time the object creeps to the center of the Earth, its total energy is at a minimum. So too is it’s mass. However, if someone lowers the object one meter and accomplishes work against the force of gravity (but no conversion to kinetic energy), its total energy and mass diminishes. Note that the above logic is in accordance with the writings of all the above-mentioned published Ph.D. authors and doesn’t depend on the rather brassy argument of saying they’re all wrong. ~~I will shortly revise what I wrote so some instances of “falling” are changed to “are lowered” (or equivalent words).~~ Come to think of it, I'll leave the classic word “falling” alone with regard to Einstein’s teachings. What the SEP researcher said is a transitory condition. The concept of matter falling into a gravity well applies for a single atom being lowered to the basement just as well as for all the matter in the Universe falling into a Big Crunch. Greg L 18:33, 14 March 2007 (UTC)

I also carefully explained to you that there was a difference between letting the body fall, and lowering it. At that time, you ignored me and chose to believe I was contradicting myself. I'm glad now you chose to believe somebody else, explaining the same distinction.
But now, if you'll continue with this same situation, you'll see that it actually does not support your point of view. A falling body does not contain the extra mass attributable to its kinetic energy, except in certain reference frames. In the frame of the body, it never appears, for example. Thus, kinetic energy is yet another example of mass in a system which isn't localizable, and may appear as a righteous and real quantity in a system (like this example one!), but yet doesn't have a location where you can point and say "Everybody agrees it's right THERE". A rock falling down a g-well trades gravitational potential for kinetic energy, and the mass of one sort of energy becomes the mass of the other sort. But YOUR problem in using this example is that (notice) the mass associated with the object's kinetic energy is not IN the falling object. It's in the system. From the object's point of view, it resides in the approaching Earth. From the Earth's view, it resides in the object. From frames intermediate, it is partitioned between them. Why would you imagine that mass from gravitaional potential in this system acts in any other way, than the mass associated with the kinetic energy being created as the system collapses? Come on-- you're being really recalcitrant here. Marmet's on the crank pages. Hawking is not a crank but is talking about the entire system of the universe, in which we reference total system mass (which is not localized to planets or suns or something). And your third lunar laser ranging guy hasn't got a name. Give it to me, and his statement, and I'll write him an email, explaining to him how and why he's wrong. I'll be glad to. S B H arris 18:59, 14 March 2007 (UTC)

You know, when I was talking to that researcher and said I’d e-mail him/her a link to this article, we spent about 45 seconds agreeing on how I would write subject line for the e-mail; he/she wanted to be able to quickly find it. You know why? Because the researcher — who specializes in relativity — gets so much spam and e-mail from “cranks” (the researcher’s words). It’s funny since that is exactly what you are saying the researcher is. Sbharris, who adds to Wikipedia articles, will e-mail the researcher “explaining to him how and why he's wrong.” Authoring Wikipedia articles can be rewarding at times. This is a textbook example of why Wikipedia suffers in extremely technical articles. No reputable author will touch it because they don’t get attribution and any moron in a hurry can go and revise it all willy nilly. What are you, unemployed? I’ve got to get to work. I’ll be back on later tonight so see your latest. Greg L 19:22, 14 March 2007 (UTC)

…and then I checked my e-mail. Here’s the entire contents of what the researcher specializing in relativity e-mailed me (I asked him/her to review the Practical examples section):

Hello

here are a few comments on the first part of the article

"...rarely 100% efficient..." The conversion is always 100% efficient in the sense that the change in energy is always c^2 times the change in mass.

But it is rare to convert all the mass into energy.

the notion of "realtivistic mass" is outmoded and confusing. I would not discuss it al all.

the section on other works at the end doesn't serve much useful purpose because many of the references are only of vague historical (but not scientific) interest.

{closing salutation deleted}

{name deleted}

He/she didn’t seem to have a problem with what I wrote. Note too that the "...rarely 100% efficient..." is from the last paragraph of the “Practical examples” section. I had deleted most of that particular paragraph but one Mr. Sbharris put it all back in. My edits also make no mention of "relativistic mass" so this, in addition to the last comment, makes it clear that the researcher read much more than I asked the him/her to. I’ll e-mail back to make doubly sure the researcher reviewed my contributions. Well, I guess Sbharris has a mighty low opinion of this researcher now!! Tell me Sb, what are your qualifications that embolden you to challenge a published researcher who investigated Einstein’s Strong Equivalency Principal and makes you want to e-mail this individual “explaining to him how and why he's wrong.”? Do tell, what are your qualifications that make you so willing to challenge published experts. As I said earlier, I really need to get to work now. Back later. Greg L 19:58, 14 March 2007 (UTC)

I'm sorry that I haven't had the patience to read the entire flamefight before posting, so I hope this is not redundant. It should be obvious from reductio ad absurdum that the entire mass gain from raising a kilogram above the Earth cannot in principle reside completely in the kilogram in question. Imagine that the Earth weighed one kilogram, or rather, that you are somehow sitting between two identical kilogram objects somewhere in space. If you "raise" one of them by separating it from the other, where does the change in mass go? There's no way of choosing. Now, if you make one of them heavier, maybe you could argue that the majority of the mass change goes only to one of them. In the limit of infinite mass, you could say that all the mass change belongs to one object. However, the Earth does not have an infinite mass, although it may be a good approximation in practice when compared with one kilogram. I have the impression that Greg's point of view has a implicit geocentric assumption that should be made explicit to clarify why he assigns the change in mass to the kilogram. Leaving mass aside for a moment and going back to classical physics, it is basic knowledge that the potential energy change does not "belong" to the kilogram but to the Earth-kilogram interaction. Therefore the statement made in the footnote that "the potential energy — and mass — the kilogram gains by rising out of Earth’s gravity well is independent of its position relative to an observer" is simply not correct in principle. The kilogram does not gain potential energy--the system does. --Itub 10:44, 16 March 2007 (UTC)

`[edit] Local conservation of energy in general relativity vs. other theories`

Since the previous article is getting rather long, I'll start a new one to simply note that it was noted quite early by everybody that general relativity, unlike other field theories, doesn't have any local conservation of energy (and consequently no local conservation of mass or exact physical location [i.e., to any arbitrarily small volume] of gravitating mass-energy, in space). This bothered quite a few people, including Hilbert and Einstein. The basis for the underlying problem in terms of how the theory was constructed, was finally located by Noether, who merely noted that it wasn't fixable, and was indeed a feature of the math used in the theory itself. The following article has been pointed out to me, and contains a good discussion of the problem which bears on all we're discussing here. [1] In a gravity field, you simply cannot finally locate and "conserve" mass-energy, except globally (by drawing your integral surfaces far away, in flat space). In gravitatinoal fields, mass-energy is impossible to pin down locally (to an arbitrarily small volume, so you can talk about an absolute mass-energy-density which everybody agrees on). This includes the absolute physical location of the total energy associated with the kg being raised in the g-field in our sample problem, and which is transfering potential energy TO that field (not just to the physical region where the kg is located). Here's a quote from the article, from a paper by a physicist at UCLA.

To illucidate these matters further, we discuss in some detail field theories of matter, gravity, electromagnetism, etc. in both special and general relativity. In special relativity these theories have a `proper energy theorem' in the sense of Hilbert and we will show how `proper energy theorems' give a principle of local energy conservation. In general relativity, on the other hand, the proper energy theorem becomes improper in that the energy-momentum tensor for which the theorem holds is gauge dependent. As will be shown below, there is transfer of energy to and from the gravitational field and it has not meaning to speak of a definite localization of the energy of the gravitational field in space(5). Consequently we do not have a principle of local energy conservation in spacetime regions in which there exist gravitational fields.

SBHarris 20:22, 14 March 2007 (UTC)

You know, when I was talking to that researcher and said I’d e-mail him/her a link to this article, we spent about 45 seconds agreeing on how I would write subject line for the e-mail; he/she wanted to be able to quickly find it. You know why? Because the researcher — who specializes in relativity — gets so much spam and e-mail from “cranks” (the researcher’s words). It’s funny since that is exactly what you are saying the researcher is. Sbharris, who adds to Wikipedia articles, will e-mail the researcher “explaining to him how and why he's wrong.” Authoring Wikipedia articles can be rewarding at times. This is a textbook example of why Wikipedia suffers in extremely technical articles. No reputable author will touch it because they don’t get attribution and any moron in a hurry can go and revise it all willy nilly. What are you, unemployed? I’ve got to get to work. I’ll be back on later tonight so see your latest. Greg L 19:22, 14 March 2007 (UTC)

…and then I checked my e-mail. Here’s the entire contents of what the researcher specializing in relativity e-mailed me (I asked him/her to review the Practical examples section):

Hello

here are a few comments on the first part of the article

"...rarely 100% efficient..." The conversion is always 100% efficient in the sense that the change in energy is always c^2 times the change in mass.

But it is rare to convert all the mass into energy.

the notion of "realtivistic mass" is outmoded and confusing. I would not discuss it al all.

the section on other works at the end doesn't serve much useful purpose because many of the references are only of vague historical (but not scientific) interest.

{closing salutation deleted}

{name deleted}

Let me check something. Greg, do you understand that as a box containing a heavy object is lowered by a rope into a uniform gravitational field at uniform speed that nobody inside that box will measure the mass of the object to decrease? Do you accept that the appearance of mass change depends on observer position? If so, maybe this can be resolved quickly.

By the way, toward the end of the last section the discussion was getting inappropriately personal. SBHarris is justifiably concerned about his position being misrepresented to the consulting physicist, whose position might in turn be misrepresented here. This can happen without malice simply because the issues are complicated. Brian Wowk 21:36, 14 March 2007 (UTC)

Last thing first. "Getting personal" with Sbharris is an unavoidable part of addressing a legitimate editorial problem: I'm citing reputable sources and his arguments basically boil down to "your Ph.D.s are all wrong but I’m right.” Further, he’s even prepared to e-mail a researcher who makes a living doing experiments on subjects like relativity (and who participated in a landmark paper on an experiment that confirmed Einstein’s Strong Equivalence Principal with remarkable precision) to tell them how and why they are wrong! Endlessly badgering contributors with that sort of crap doesn’t fly. And implicit behind all of this crap is that he'll sneak in and delete stuff that he disagrees with after the winds of disagreement with him die down. Again, pardon me all over if I cite world-recognized authors and choose not to cite Sbharris. Note further that the relativity researcher (working at a university) who I talked to and e-mailed took pains to instruct me on how to address the subject line of my e-mail because he gets so many e-mails from "cranks."

Now the first thing. Mass is the measure of a body’s resistance to accelerating (distance integrated across time squared). When you explicitly write that people inside the box (at the same level as the kilogram weight) observe no change in its mass, you seem to be implying that people outside the box will observe different masses for the kilogram inside the box depending upon their location relative to the box. Is that what you think? I might parenthetically add that I agree actually with your premiss at a certain level: if the people in the box drag out their "international prototype" (reference kilogram), and compare their test mass to their international prototype using a balance beam scale, there will be no observable change because both hunks of matter lost equivalent amounts of mass. But if one applies a force of one newton and watches the kilogram’s acceleration with a laser (which provides both meter-stick and clock effects), what do you think different people will see from different vantage points?

I've got to tell you that arguing endlessly about this stuff isn't my cup of tea. I don't like it. I've cited two sources that say that all matter in the universe loses all its mass as it falls down the largest gravity well in the Universe. Some of you don't think that means that matter going down a gravity well loses mass. I can't help that. I further cited a published Ph.D. who said lowering a single hydrogen atom to the basement makes it lose mass. Some of you say this Ph.D. is wrong too. I can't help that either. In response to endless challenges from you-know-who, I contacted a published expert in relativity who said "Yes, raising a kilogram upwards against the force of Earth's gravity increases its mass. The response from you-know-who is that the researcher is wrong and he wants to e-mail the researcher to tell him how and why he’s wrong. I asked that expert to review what I wrote and he/she responded with no problems (with what I wrote anyway). Well, we all know what you-know-who’s response will be to that: the expert is really really wrong now! Contributing to this particular article is about as rewarding as wiping my rear end with poison ivy because of the intellectual arrogance of a few (people who think they've got advanced concepts on relativity figure out better than the experts). I didn't know what I was getting myself into when I landed here.

Now, I'm done arguing with you people. Period. If you delete what I wrote. Fine. Cite your sources and do it well. If I think it's garbage, and feel like it, I'll be back. I might add ^{[citation needed]} to it. I might revert it. Whatever I do, I'll politely and logically explain what I've done to the betterment of the article. As you can see from the entire sordid history written above (I'm talking the entire topic above this one too), I've patiently tried to patiently explain and justify what I've written. There has to be a logical conclusion to this process. Unfortunately, there simply can't be when arguing with certain types of people (the one's who think they've got it all figured out and the experts are all wrong). As much as Sbharris wants me to think that the researcher who helped conduct the APOLLO experiment and write the report is all wrong and Sbharris is right, any right-thinking person would think that notion is nutty on the face of it. This discussion page experience has been too weird for me to handle. This all simply demonstrates why the Wikipedia way of arriving at correctly written, highly technical articles is going to be a tough row to hoe. Goodbye. Greg L 23:19, 14 March 2007 (UTC)

Generally speaking, web-published papers by authors who have a listing on crank.net are not a good source for wikipedia articles.

See for instance http://www.newtonphysics.on.ca/BIGBANG/Bigbang.html as to why Paul Marmet deserves his crank.net entry as "Cranky".

Meanwhile, E. Noether's discovery of the deep connection between symmetries and conservation laws. (English)

also cited, has been published (at a conference proceeding), unlike the Marmet article.

[A] Teicher, Mina (ed.), The heritage of Emmy Noether. Proceedings of the conference, Bar-Ilan University, Ramat-Gan, Israel, December 2--3, 1996. Ramat-Gan: Bar-Ilan Univ., The Emmy Noether Research Institute of Mathematics, Isr. Math. Conf. Proc. 12, 67-81 (1999).

It's a much higher quality reference.

The statement that an object in and of itself gains mass when it raised is not, IMO, correct as written. It would need to be qualified significantly to be correct, and would need a much better citation than the one from Paul Marmet, or some "anonymous researcher".

Anonymous researchers are just not acceptable under WP:Verifiability

I think the statement that an object in and of itself gains mass when raised in a gravitational field could be justified if one considers only stationary systems and the Komar mass. (I do not have a suitable reference which directly says this at hand, however direct computation of the Komar mass supports this. Since the computation is rather technical, it probably needs a full reference to meet WP:Verifiability).

However, with more general notions of mass such as the ADM mass, while one can compute the mass of a system, one cannot in general assign that mass a location. This statement has been documented in the article by Mina Teicher previously quoted by SBHariss.

Thus I substantially agree with SBHaris on this issue, and disagree with Greg L.

I think that possibly some compromise could be worked out if Greg L. could qualify his statements more precisely, and find some better references (i.e NOT web-published papers by Paul Marmet).

Pervect 02:31, 15 March 2007 (UTC)

Thank you. I have considered this a good-faith discussion, but when it gets to the point that simple questions of logic are just referred off to the statement of some anonymous Ph.D. who I cannot contact to verify he thinks what he supposedly thinks about these specific issues, and the only cites in evidence are from a living crank (who is on Greg L's. side) and a dead recognized genius (who I think's on mine), we're in trouble. We could push the discussion along with we had somebody with credentials we could talk with. For example, we don't even know if Greg L's pet APOLLO researcher has been specifically asked to vet the specific sentence in question, and Greg L.'s been cagey about that very issue (see above). So what reason do I have to trust all this, at fourth-hand? Marmet seems to think all gravitational added energy shows up in the smaller of the masses, AS measurable mass, IF there's a big disparity in magnitude of the masses (as in the atom, or the kg, vs. the Earth). But what if the two masses pushed apart, have the same mass? Do they equally divide the energy and equally increase in mass? Is there a (purportedly linear) equation to describe this? I'm skeptical. I have a right to be. I don't believe it. Neither do the other posters so far, of whom I have good reason to believe one is a relativist, and the other of which I know is a Ph.D. physicist. Greg L, if your response is "Sionara, but my secret Ph.D. says you're full of it, and my published Ph.D.'s a crank, but at least is published" I don't think you'll fly. We'll eventually get Thorne or somebody on this page to discuss the issue, and that will be the end of it. SBHarris 20:01, 16 March 2007 (UTC)

Actually Marmet died in 2005. There is great irony that Marmet would be cited in a discussion that decries Wikipedian ignorance about subtleties of General Relativity when Marmet's main claim to fame was repudiating the entire field of relativity in favor of his own cranky theories. Would the anonymous relativity worker cited in this thread, who has such trouble with crank emails, have accepted an email from Marmet?? Brian Wowk 23:20, 16 March 2007 (UTC)

In any case, it's been two days since Greg L declared that he refuses to continue the discussion, apparently abondoning any attempts at reaching a consensus. As all the other participating editors (SBHarris, MichaelCPrice, Brian Wowk, Pervect, Itub and myself) seem to be in agreement, I believe we now have a consensus by default. KonradG 04:55, 17 March 2007 (UTC)

I fixed the contentious sentence that started this enormous thread. Someone else needs to fix the hydroelectric power generation example, which suffers from the same problem. Hydroelectric power has so many complex E=mc2 issues that I don't think it's pedagogically useful in this article, and should be deleted. Brian Wowk 06:45, 17 March 2007 (UTC)

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Talk:E=mc²

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Contents

[edit] Archives

[edit] Romanticizing about Albert Einstein and perpetuating myth

[edit] Merge with Mass-energy equivalence

[edit] Deleted statement suggesting that 100 C change in temp is equivalent to some quantity of energy or mass

[edit] A first order proof of E=mc^2

[edit] Matter losing mass as it falls down a gravity well

`[edit] Local conservation of energy in general relativity vs. other theories`

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