^{2}, may be correct or not depending on where you are in space.

With the first explosions of atomic bombs, the world became witness to one of the most important and consequential principles in physics: Energy and mass, fundamentally speaking, are the same thing and can, in fact, be converted into each other.

This was first demonstrated by Albert Einstein's Theory of Special Relativity and famously expressed in his iconic equation, E=mc^{2}, where E stands for energy, m for mass and c for the speed of light (squared).

Although physicists have since validated Einstein's equation in countless experiments and calculations, and many technologies including mobile phones and GPS navigation depend on it, University of Arizona physics professor Andrei Lebed has stirred the physics community by suggesting that E=mc^{2} may not hold up in certain circumstances.

The key to Lebed's argument lies in the very concept of mass itself. According to accepted paradigm, there is no difference between the mass of a moving object that can be defined in terms of its inertia, and the mass bestowed on that object by a gravitational field. In simple terms, the former, also called inertial mass, is what causes a car's fender to bend upon impact of another vehicle, while the latter, called gravitational mass, is commonly referred to as "weight."

This equivalence principle between the inertial and gravitational masses, introduced in classical physics by Galileo Galilei and in modern physics by Albert Einstein, has been confirmed with a very high level of accuracy. "But my calculations show that beyond a certain probability, there is a very small but real chance the equation breaks down for a gravitational mass," Lebed said.

If one measures the weight of quantum objects, such as a hydrogen atom, often enough, the result will be the same in the vast majority of cases, but a tiny portion of those measurements give a different reading, in apparent violation of E=mc^{2}. This has physicists puzzled, but it could be explained if gravitational mass was not the same as inertial mass, which is a paradigm in physics.

"Most physicists disagree with this because they believe that gravitational mass exactly equals inertial mass," Lebed said. "But my point is that gravitational mass may not be equal to inertial mass due to some quantum effects in General Relativity, which is Einstein's theory of gravitation. To the best of my knowledge, nobody has ever proposed this before."

Lebed presented his calculations and their ramifications at the Marcel Grossmann Meeting in Stockholm last summer, where the community greeted them with equal amounts of skepticism and curiosity. Held every three years and attended by about 1,000 scientists from around the world, the conference focuses on theoretical and experimental General Relativity, astrophysics and relativistic field theories. Lebed's results will be published in the conference proceedings in February.

In the meantime, Lebed has invited his peers to evaluate his calculations and suggested an experiment to test his conclusions, which he published in the world's largest collection of preprints at Cornell University Library (see More Info).

"The most important problem in physics is the Unifying Theory of Everything – a theory that can describe all forces observed in nature," said Lebed. "The main problem toward such a theory is how to unite relativistic quantum mechanics and gravity. I try to make a connection between quantum objects and General Relativity."

The key to understand Lebed's reasoning is gravitation. On paper at least, he showed that while E=mc^{2} always holds true for inertial mass, it doesn't always for gravitational mass.

"What this probably means is that gravitational mass is not the same as inertial," he said.

According to Einstein, gravitation is a result of a curvature in space itself. Think of a mattress on which several objects have been laid out, say, a ping pong ball, a baseball and a bowling ball. The ping pong ball will make no visible dent, the baseball will make a very small one and the bowling ball will sink into the foam. Stars and planets do the same thing to space. The larger an object's mass, the larger of a dent it will make into the fabric of space.

In other words, the more mass, the stronger the gravitational pull. In this conceptual model of gravitation, it is easy to see how a small object, like an asteroid wandering through space, eventually would get caught in the depression of a planet, trapped in its gravitational field.

"Space has a curvature," Lebed said, "and when you move a mass in space, this curvature disturbs this motion."

According to the UA physicist, the curvature of space is what makes gravitational mass different from inertial mass.

Lebed suggested to test his idea by measuring the weight of the simplest quantum object: a single hydrogen atom, which only consists of a nucleus, a single proton and a lone electron orbiting the nucleus.

Because he expects the effect to be extremely small, lots of hydrogen atoms would be needed.

Here is the idea:

On a rare occasion, the electron whizzing around the atom's nucleus jumps to a higher energy level, which can roughly be thought of as a wider orbit. Within a short time, the electron falls back onto its previous energy level. According to E=mc^{2}, the hydrogen atom's mass will change along with the change in energy level.

So far, so good. But what would happen if we moved that same atom away from Earth, where space is no longer curved, but flat?

You guessed it: The electron could not jump to higher energy levels because in flat space it would be confined to its primary energy level. There is no jumping around in flat space.

"In this case, the electron can occupy only the first level of the hydrogen atom," Lebed explained. "It doesn't feel the curvature of gravitation."

"Then we move it close to Earth's gravitational field, and because of the curvature of space, there is a probability of that electron jumping from the first level to the second. And now the mass will be different."

"People have done calculations of energy levels here on Earth, but that gives you nothing because the curvature stays the same, so there is no perturbation," Lebed said. "But what they didn't take into account before that opportunity of that electron to jump from the first to the second level because the curvature disturbs the atom."

"Instead of measuring weight directly, we would detect these energy switching events, which would make themselves known as emitted photons – essentially, light," he explained.

Lebed suggested the following experiment to test his hypothesis: Send a small spacecraft with a tank of hydrogen and a sensitive photo detector onto a journey into space.

In outer space, the relationship between mass and energy is the same for the atom, but only because the flat space doesn't permit the electron to change energy levels.

"When we're close to Earth, the curvature of space disturbs the atom, and there is a probability for the electron to jump, thereby emitting a photon that is registered by the detector," he said.

Depending on the energy level, the relationship between mass and energy is no longer fixed under the influence of a gravitational field.

Lebed said the spacecraft would not have to go very far.

"We'd have to send the probe out two or three times the radius of Earth, and it will work."

According to Lebed, his work is the first proposition to test the combination of quantum mechanics and Einstein's theory of gravity in the solar system.

"There are no direct tests on the marriage of those two theories," he said. " It is important not only from the point of view that gravitational mass is not equal to inertial mass, but also because many see this marriage as some kind of monster. I would like to test this marriage. I want to see whether it works or not."

**Explore further:**
Doubly special relativity

**More information:**
The details of Andrei Lebed's calculations are published in three preprint papers with Cornell University Library:

xxx.lanl.gov/abs/1111.5365

xxx.lanl.gov/abs/1205.3134

xxx.lanl.gov/abs/1208.5756

## antialias_physorg

However gravity not only deforms space but spacetime (gravity slows apparent time) - so the number of jumps from low to high orbital within a gravity field should be slightly lower than expected. I wonder if this might offset (or even cancel out) the higher number of expected jumps in his experiment.

## Whydening Gyre

Valeria's "flow" metaphor of water ripples seems increasingly appropriate...

## antialias_physorg

Also it might be worth looking at black holes for telltale signatures of inordinately increased rates of emission - though that one might be hard to differentiate given that there are a whole slew of very energetic/photon producing mechanisms going on in that vicinity.

In the end it's just on of those things that are relatively easy to test.

(possibly even just looking at the differences in an aparatus on a high flying plane vs. one submerged in the ocean might be enough - depending on what the average rate of such events is and how much hydrogen you use)

## cantdrive85

## antialias_physorg

If you look at the math (principle of least action) then massive bodies can't straighten paths. The path a massive body takes in a warped spacetime IS straight. Always. (notice: 'spacetime - not 'space'. So we're talking about worldlines here)

That's what general relativity is about (actually space bending is no the pinciple of the minimum action. Minimal time dilation is - which renders the straightest possible path through spacetime. The path an object will take is thus that the time it takes is shortest)

http://en.wikiped...operties

Quote: "there is no gravitational force deflecting objects from their natural, straight paths. Instead, gravity corresponds to changes in the properties of space and time, which in turn changes the straightest-possible paths that objects will naturally follow"

## ValeriaT

## Lurker2358

You could test that easy enough by just re-doing the experiment for every increase of 1 Earth radius out from the Earth to see if there is some relationship. However, to get a good sample you might need to do the experiment a few hundred times at each location. Suggests you'd need an ion engine craft so you can speed up and slow down before orbital distances change too much too quickly.

## ValeriaT

## antialias_physorg

Erm. No. Dense objects collapse because there are no forces that can sustain an equilibrium state (e.g. in stars where the temperature drops beyond the threshold for sustaining enough fusion to keep pumping out photons). Dense/collapsing ojects do not gain mass. They just become more dense.

Neither inertial nor gravitational mass changes during collapse (let the sun collapse to a black hole and the Earth's orbit would be totally unaffected. The inertial and gravitational mass would still be the same) so there is no violation of the equivalence principle, here.

## ValeriaT

## ValeriaT

## antialias_physorg

At their point: Yes. Further out? No. Replace the Earth with a singularity of Earth mass. The gravity characteristic outside what is now Earth radius wil be identical.

Spacetime doesn't 'gain mass'. That's just blurb.

That's just more baseless blurb.

No, because the volume integral over the exact center of a massive sphere is zero - so OF COURSE will there be no gravity force there.

## ValeriaT

At any case, at the moment when curvature of space-time (and gravitational force) depends on another parameters, than just bare mass of object, an equivalence principle gets violated there.

## ValeriaT

## Modernmystic

Might be important to consider the inherent negative energy density of "empty" spacetime too. Although I'm sure this has been accounted for. OR perhaps on such small scales this is so negligible as to be simply ignored?

It seems to be hard to take into consideration ALL the variables that are in nature. I do think that the first comment on the thread may indeed point to a variable that might not have been considered.

## ValeriaT

## ValeriaT

Yes, it is complicated - so we should use mental shortcuts and intuitive reasoning. The derivations based on pile of equations are nice, but they're nontransparent and it can bring its own errors into reasoning.

## cyberCMDR

## Maggnus

You may also want to consider how this researcher presented his case:

I think I found something odd when doing some calculations.

These are may calculations, can you all check them.

My calculations might be suggesting this odd thing I mentioned.

If I am right we might be able to see some sign of it if we do this.

See how that works?

No, we shouldn't! In fact, hell no we shouldn't! Because it's complicated you should be going exactly the opposite way of what you say here; that is STOP be so lazy using "mental shortcuts" and put away your useless "intuitive reasoning" and work out the actual answer. Your own answers found this way may surprise you.

## TheKnowItAll

## Q-Star

That doesn't seem to have served you very well.

## vacuum-mechanics

This is what we always hear, but what which we never herd is how empty space could be curved! Maybe this physical view could help us to understand it.

http://www.vacuum...18〈=en

## VendicarD

The answer is no, provided the speed of g = c.

Mg is defined not only by Mi but by the self energy of the gravitational field that it Mi generates.

Since this energy is distributed through space, so too is Mg. Yet Mi is measured as a much more local phenomenon which on small scales is dominated by quantum effects.

Mi as measured by impacts then will differ from Mg since the impacts only change the extended field of Mg slowly over time.

The only alternative is to conclude that Mi can not be measured unless the cumulative effects of the experiment used to do the measurement are done through the entire future of the universe.

Precise definitions of Mi and Mg are needed to make more precise statements.

## VendicarD

## Torbjorn_Larsson_OM

Also, the Standard Model of particles works on the strong equivalence principle, that all laws of physics locally look the same as in flat space. The SM "space" here is an appropriate fiber-bundle on an appropriate 4-manifold. I hear particle physicists would rather give up unitarity of gravity than the equivalence principle, now that BH "firewalls" is a gedanken problem. (See Sean Carroll's blog.)

@ Valeria: "dark matter violates the equivalence principle." What is ascertained without evidence can be rejected without evidence. (Actually DM lives under gravity, sams as visible matter, in the standard cosmology.)

@ Modernmystic: "the inherent negative energy density of "empty" spacetime". Standard cosmology spacetime is flat, zero energy density. It is the particle vacuum that has negative energy density.

@ vacuum-mechanics: Science is no reason to start spout anti-science.

## ValeriaT

## ValeriaT

## ValeriaT

## ValeriaT

## Maggnus

You link to a Feynman interview, or more precisely a soliloquy in a much larger interview, immediately after you make such a statement, yet by the very statement you make, you show you do not understand what he is saying!

## ValeriaT

## Maggnus

I agree, and I am not in any way suggesting it is! The scientific method has evolved into what it is over many many years. There is good reason that it is done the way it is.

## ValeriaT

What the contemporary people don't understand at all is, the violations of general relativity with quantum mechanics and vice-versa isn't some matter of some esoteric physics at the whole boundary of our observational limits. The transition between quantum mechanics and general relativity is continuous and it goes just through human observer scale, because the quantum mechanics manifests itself bellow millimeter scale (magnetic domain), the general relativity above the million kilometer scale (gravity lensing). The mutual violation of these two theories therefore cannot happen somewhere at the cosmological or Planck scale - but primarily right here - at the quite common scale of human observers.

## ValeriaT

## ValeriaT

## Maggnus

The rest of your comment is incomprehensible.

## Maggnus

-Sam Harris

## Whydening Gyre

Operative word - evolved. Which, by definition, means it will continue to do so ad infinitum. Which also means there are infinite variables involved that shape that evolution. To say "science" has at this point reached it's highest and most complete state and cannot evolve further, is to say we hve covered ALL those variables and know all there is about whatever it is.

Wrong.

## ValeriaT

## antialias_physorg

Huh? Of course you'd get an event horizon - at about a centimeter distance from the singularity as seen from the outside (from the inside distance are more tricky). But if you go to the distance where the original Earth's surface was you'd experience 1g (and further out you'd experience exactly the same g forces that you experience now when moving away from Earth. E.g. the Moon would stay in the same orbit.

You really don't understand what motivates a scientist, do you? You are so petty that you think money is the only motivation there is? If scientists could afford to subsist they would PAY institutions to allow them to go there and do science.

## ValeriaT

## Whydening Gyre

Not used improperly - just defined improperly. Let's use the more appropriate - change.

"Science" is about determining the level of change that is no longer perceptable in an object/thing/particle(if you will), and then pronouncing that definition to be the end of all change for the studied object.

## Whydening Gyre

It is about the DEFINITIION of change.

IMHO the absolute basic state of the Universe is nothing. Or - no change. Since the most basic LAW of the Universe is - change, the basic algorythm or mechanic of this is what we should pursue. Science approaches this thru the examination of the PARTICLES that are created and therefore affected by this state and law.

Want a TOE? Never gonna find it using current method.

However, like everything else - methods change...:-)

## Whydening Gyre

We look at an object or concept and examine to determine if there are constituent parts or processes that contributed to that "finished product". When we can't SEE any further reductions, we declare it to be absolute.

Anyway, these are just my own observations, therefore causing me to reach conclusions by definition. One thing I am absolutely certain of, though - Even those will change...

## baudrunner

The evidence that hydrogen atoms will exhibit different dimensions in different places in outer space can be used to determine the universal static reference point, given that Earth is just a frame of reference, not the actual artifact. Our very motion through space contributes to our mass, and depending on the seasons alone, H2 should exhibit subtle differences in mass because direction of orbit changes. Then, of course, there is the motion of the sun around the galactic center, and the galaxy's motion through the universe, and over all their respective relationships with other masses.

## Maggnus

@Valeria - and again, you show your lack of understanding. You continue to champion aether (for example) even after you have been shown not only that it does not work, but why it does not work. Where is the logic in that?

## ValeriaT

## Maggnus

## ValeriaT

## julianpenrod

## julianpenrod

## Whydening Gyre

But - what if (from a different scalar POV) it was?

Dont we constantly devise new methods and devices to refine our resolution of observations?

## Q-Star

Because gravity is not a scalar quantity, is a force quantity, it solved with the field equations. So E = mc^2, with no other terms only works for inertial reference frames, frames not experiencing significant acceleration or gravitational forces.

Once something is affected by gravity (or acceleration), it is no longer in an inertial frame.

## Ducklet

## EyeNStein

## vincepaul_13

Perhaps this was merely badly phrased. Photons are emitted as a surplus of energy when electrons revert from a higher energy to a lower energy state. Orbital electrons _absorb_ energy to move from a lower to a higher energy state. I can understand that this is a "paired" event, where the increase in energy state is transient, and inevitably reverts, so that the photon emission is preceded by the low-to-high event, but the energy for that event comes from _somewhere_, possibly including photons, which might throw off the calculations of mass accretion if not properly accounted for. Anyone else catch this?

## Maggnus

And Jesus wept......

## yash17

E = mc2 as mass energy equivalence equation; No!

E = mc2 is derived from F = ma (Newton's laws) and E = Fd Joule's laws (d = distance).

## Whydening Gyre

You are just not looking at it from a correct POV. Gravitational effects are scalar, so the source must be - just the way nature works. I posit we will discover this fairly soon given the rate of new tools being developed to determine this sort of thing

## AmritSorli

## Q-Star

"Gravitational effects are a force". One of the four fundamental forces. Forces by definition are vector quantities. NOT scalar. That's just the way physics are done and unless your TOE redefines physics as we now know them,,,, gravity won't stop being a force (vector rather than scalar).

Are you not an Australian? Or another Australian?

## Whydening Gyre

Anyway, since gravitational effects are observed to chenge along with density and volume of matter (both scalable), I define it as scalable. If it is additive, it means scalable.

Is gravity a function of mass or the other way around?

## Q-Star

Define it any way you want, but, no one will know what you are thinking. If you are postulating a new concept in physics, just say so and explain.

Nonsensical question. One is the result of the other. And the other is the result of the one.

Gravity is a force, it has magnitude AND direction, a vector quantity, not a scalar. If you are in some space, say between the Earth, the Moon and the Sun. The gravity that you experience is not the scalar sum of the three components, it is the vector sum of the three components (with each of the them being affected by the others). It's what makes three body mechanics so difficult.

2 plus 2 won't get you there, you'll be needing some derivatives and integrals to get close to the answer.

## Whydening Gyre

Ok, so scalar is just magnitude. Tell me the direction of gravity and.... pushing or pulling?

By giving gravity vectorable attributes, you mean it is in motion(with the attribute of direction), hence a part of a flow? Therefore, analogous in nature? To me, the only part of "direction" in gravity function is towards other gravity function which it then combines with and just increases in magnitude. That's not really a "direction", however.

Kinda nonsensically cryptic answer, isn't it...?

Hardly. And - No need to be snide - gives the appearance of arrogance...

I am just trying to balance sensory derived conclusions and the (what appear to be) counter intuitive definitions of others more informed than I am.

Sheesh

## antialias_physorg

See the direction of a vector. You can define it both ways (pushing or pulling) but that just depends on how you want to use the signs in the math behind it. (Though be aware: once you decide on one way you have to stick to it)

No. It just means that there is -at least- a gradient (first derivative of a scalar field with respect to space).

Gravity is part of natuire. There is no 'analogy' needed here.

No. You just can't have the one without the other. So asking for a speration into gravity and (effective) mass is nonsensical.

## antialias_physorg

To elucidate this a bit further: A flow is a derivativ with respect to space AND time (the transport of something accross a surface boundary in a given time interval). It can be represented by a vector with 4 components (x,y,z, and t).

Gravity is a vector with 3 components x,y,z (There is no time component. The gravity of a given/constant mass does not change with time.)

Gravity can INDUCE a flow (in a very literal sense a stream running downhill is a gravity induced flow, because if you put an imaginary surface through the stream then there will be a material transport through that surface during a time interval - which is what is called a 'flux' in physics)

## Ober

## Whydening Gyre

## ValeriaT

## Q-Star

I think that you are having trouble communicating because you seem to be using terminology incorrectly. Vectors are not scalars. Vectors have direction and magnitude. The word direction does not mean flow or movement.

Gravity is a vector because there is a line between the two bodies. It is a force between two masses. It is a field which has magnitude (strength) and direction (space between the bodies.)

You can not separate mass from gravity, and ask which causes which. Gravity doesn't flow, it just IS.

## Whydening Gyre

## Q-Star

No apologies necessary,,, I enjoy gobbledygook as much as anyone, but if you want to play the fool, don't get your feelings hurt when you get seen and treated as a fool.

It's a science site, if your musings, ponderings and ramblings aren't somewhat informed, then you'll probably need to start yet another sock puppet or two to find someone to take you seriously.

And yes, there are stupid questions. Whoever told there were not was practicing very weak sophistry.

Oh yeah, before I forget,,,, that "big picture" thingy,,, you got that wrong also. (More weak sophistry.)

## ValeriaT