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Einstein's E=MC2 May Breakdown in Outer Space





University of Arizona physicist Andrei Lebed has stirred the physics community with an intriguing idea yet to be tested experimentally: The world's most iconic equation, Albert Einstein's E=mc2, 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=mc2, 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=mc2 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=mc2. 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."  

"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=mc2 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.

Lebed's calculations indicate that the electron can jump to a higher energy level only where space is curved. Photons emitted during those energy-switching events (wavy arrow) could be detected to test the idea. 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.

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=mc2, 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."

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

The Daily Galaxy via University of Arizona


Is an apparent mass-gravity effect equivalent to saying the speed of light is affected by/within a gravity gradient?

Could it be tested in a zero g airplane.

Cesar - my guess would be no, because space is still curved for the "vomit comet". Basically, those zero-g simulating plane rides are taking advantage of the principle of equivalence (only in reverse - your velocity towards the gravity well equals the acceleration due to gravity, thus you feel no force of gravity despite still being in curved space).

Still - at least it's testable and won't require yet-to-be-invented technology, yet-to-be-discovered math, or another billion years of observations to test, unlike most of the other alterations to relativity that have been suggested recently. It's also the first one I've read about that doesn't sound like it was thought up under a tinfoil hat!

I'm still taking bets that gravity doesn't exist at all, it's merely an effect of inertia (momentum) and expansion. See "The Situation of Gravity".

Of course this means no photon torpedoes either. Trekies won't like that!

I'm not sure I understand in what sense space would be "flat" if you send an experiment probe 2 or 3 Earth radii into space. The gravitation effect of the Sun far exceeds that of the Earth; wouldn't it still be "curving" space?

Is there any location, anywhere in the universe that is not effected (however faintly) by some gravitational forces? What would be considered perfectly flat space (free of curvature)?

Peter, I agree but out beyond the Oort cloud you might find flat space. How about the Solar wind? If it has hydrogen atoms in it, then it should stop radiating as it gets out into intersteller space.

This theory sounds too obvious - although, that's not a reason to discount it of course - but why would someone NOT have thought of this before?


Good but the space aroung the spacecraft will always be curved due to its own gravity.Would that affect the experiment anyway ?

ok firstly i been doing some calculations on a similar subject, point one i want to make is that i can calculate a planets gravity to the milligram and by the second using a formula that does not, i repeat does not use any kind of assumed out the window went Newtonian's constant and i get a more accurate measure of gravity by knowing what it is and not assuming a number i am told. there is Einstein's first mistake. the second is simple, if energy is mass then nothing can travel faster than light, erm neutrino's for one and of course there is the little fact that everything we see circles something that is rotating faster than light (black holes), Einstein was correct to admit that he thinks he got it wrong, because for one the u.s nearly vaporised the earth's atmosphere using his energy mass calculations, every single satellite and space rocket we have sent up has to make periodic course corrections when using this math, space is not curved either, rotation is the only curvature in affect round a body. i have the math, The only reason E=MC2 works is because its not that far of what the true calculation of energy and mass are here on earth, take it anywhere else as your all finding is pointless, just like the assumption of fixed gravity, nice try but a very close miss, if somebody wants to contact me from the team doing this theory im happy for the owners of the publication to forward my email to them and i can explain whats wrong no problem.

space is curved where objects are concerned

How the small size asteroid get independent directional travel against sun or other massive planets gravity force. When it enters the sun family it must attract by any one of the planet or sun. If it is true earth will get n number of asteroid everyday and it will be filled by foreign particles.

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