The central idea of Einstein’s theory of gravity is the principle of equivalence. That is, objects will fall at the same rate under gravity regardless of their mass or composition. As long as there isn’t air resistance, a feather and a bowling ball dropped at the same time will strike the ground simultaneously. But what if one object is rotating and another is not? Will they fall at the same rate? 

We know that the rotation of a body can affect how things fall. When a body such as Earth rotates, it creates an effect known as frame dragging, which twists space and time slightly. Computer simulations of merging black holes show that two rotating black holes would merge at a different rate than if they weren’t rotating. So on a large scale gravity is affected by rotation.

This has led some theorists to wonder whether such a rotational effect might be a way to connect Einstein’s gravity with the quantum theory of atoms and molecules. It turns out that atoms and other quantum particles have a property known as spin. If we imagined an atom as a small sphere, we can imagine its spin as the rotation of that spin. The catch is that atoms are not little spheres, and spin is not physical rotation. Spin is an inherent property of a quantum object that behaves similar to the type of rotation we see every day.

So, would an atom with spin fall at a different rate than one without spin? More specifically, does the principle of equivalence hold for quantum objects with spin? A recent experiment tested this question by comparing the free fall of rubidium atoms with different orientations of spin.

The team compared the gravitational acceleration of atoms with spin +1 and -1. To use our rotating sphere analogy, this would be like comparing a sphere rotating clockwise about its north pole vs one rotating counterclockwise. They found that the two orientations of spin fall at the same rate to within 1 part in 10 million, which was the limit of observation for their experiment. In other words, spin has no affect on the rate at which an atom falls.

This result isn’t entirely unexpected. It’s been generally thought that the equivalence principle holds for both classical and quantum objects. The experiment does, however, rule out some of the more radical models trying to unify gravity and quantum theory.

Now we know the equivalence principle holds even for a quantum top.

Paper: Xiao-Chun Duan, et al. Test of the Universality of Free Fall with Atoms in Different Spin Orientations. Phys. Rev. Lett. 117, 023001 (2016).  arXiv:1602.06377 [physics.atom-ph]

The post Einstein’s Top appeared first on One Universe at a Time.

The popular press has been abuzz about a new proposal to use the solar system to test string theory.  Turns out that is a bit over-hyped.  The actual paper, published in Classical and Quantum Gravity outlines an idea to use the motion of planets and moons to test what is known as the equivalence principle.  The reason string theory gets mentioned is that most string theory models violate the equivalence principle slightly.  Saying this paper proposes a test of string theory is a big stretch.

The basic idea of the equivalence principle was made famous by the (likely mythical) experiment where Galileo dropped things off the leaning tower of Pisa.  The purpose of the experiment was to show that different objects fall at the same rate.  In other words, the rate at which an object falls doesn’t depend upon its mass.

In Newtonian physics, inertial mass is what determines how easy or difficult an object is to move, and gravitational mass determines how strongly a body is attracted to the Earth (or any other gravitational mass).  Since everything near the Earth falls at the same rate, the gravitational mass must be proportional to the inertial mass. That is, the two masses are equivalent, which is the heart of the equivalence principle.

When developing general relativity, Einstein used the equivalence principle as the foundation. His basic argument was that, without some external point of reference, a free-floating observer far from gravitational sources and a free-falling observer in the gravitational field of a massive body each have the same experience. Likewise an observer standing on the surface of a massive body and an observer which uniformly accelerates at a rate equal to the body’s surface gravity have identical experiences. Thus, the free-float and free-fall frames can be considered equivalent. In order to formulate general relativity mathematically, Einstein strengthened this argument to yield what is known as the strong equivalence principle:

The ratio between the inertial mass of a particle and its gravitational mass is a universal constant.

This is the version of the equivalence principle that everyone tries to test, because if it doesn’t hold up, then you’ve shown that general relativity is not the final theory of gravity.  Measuring a violation of the equivalence principle would also open the door to certain quantum gravity models, of which string theory is one approach.

In the paper, the authors start by assuming that the equivalence principle is violated by a small amount, and then calculate how that violation would show up in the motion of planets and moons in the solar system.  Specifically they look for what is known as the Nordtvedt effect, where the relative motion of different masses would shift due to a violation of the equivalence principle.

What they find is that based on current observational data, the inertial and gravitational masses can differ by no more than one part in ten billion.  This is a pretty strong result, but other experiments have validated the equivalence principle to five parts in a hundred trillion, so there is nothing new here.  The paper is interesting because they use planetary motion, but it’s really more of a proof of concept rather than a new scientific result.

Of course none of this really has anything to do with string theory, but it makes for a cool headline.

Paper:  Overduin J, Mitcham J, Warecki Z. Expanded solar-system limits on violations of the equivalence principle. Class. Quantum Grav. 2014;31(1):015001-.

The post To the Test appeared first on One Universe at a Time.

I’ve been preparing for an intro physics class Monday, and that means covering Newton’s laws of motion. Since it is an introductory class I don’t discuss the nature of mass too deeply. Essentially I tell my students that there is inertial mass, given by the second law of motion, and a gravitational mass given by Newton’s law of gravity. I then go on to say that since everything near the Earth falls at the same rate, the gravitational mass in the law of gravity must be proportional to the inertial mass in Newton’s second law. That is, the two masses are equivalent, which is the heart of the equivalence principle.

But things are never quite as simple as they seem, and the concept of mass is no exception. In Newtonian physics there are not two types of mass, but three. There is the inertial mass, which determines the acceleration due to an applied force; there is the passive gravitational mass, which interacts with the local external gravitational field; then there is the active gravitational mass, which creates the external gravitational field in which other particles interact. Newton assumed that all three types of mass were one and the same, and it is generally assumed that Newton’s was correct, but nothing in general relativity requires it, and there is (as yet) no experimental evidence to validate it.

Acceleration “looks” like gravity.

When Einstein first proposed the principle of equivalence as a foundation to general relativity, his basic argument was that, without some external point of reference, a free-floating observer far from gravitational sources and a free-falling observer in the gravitational field of a massive body each have the same experience. Likewise an observer standing on the surface of a massive body and an observer which uniformly accelerates at a rate equal to the body’s surface gravity have identical experiences. Thus, the free-float and free-fall frames can be considered equivalent. In the same manner, the uniform acceleration frame and the surface frame are equivalent. This is known as the weak equivalence principle:

All effects of a uniform gravitational field are identical to the effects of a uniform acceleration of the coordinate system.

In order to formulate general relativity in terms of general covariance, Einstein later strengthened this argument to yield what is known as the strong equivalence principle:

The ratio between the inertial mass of a particle and its gravitational mass is a universal constant.

It is this latter principle which was experimentally validated by the classic Eötvös experiment, which determined that objects fall at the same rate regardless of their material consistency.

The strong equivalence principle does not require that all masses are equal. It only requires that an object’s inertial and passive masses are proportional. Although the equivalence principle says nothing about active mass, conservation of momentum does. If you apply conservation of momentum to two gravitationally interacting objects, you find that momentum is only conserved is if the active mass of an object is proportional to its inertial and passive masses. Thus in order to relate all three masses, we need not only the equivalence principle, but also the conservation of energy-momentum.

Matter vs. antimatter. Source LBNL.

The constants of proportionality can be wrapped into the gravitational constant, so it would seem we can simply follow Newton, set all three types of mass equal to each other and be done with it. There is, however, a catch. Although we can arbitrarily set the magnitudes of active and passive mass equal to each other, it is possible for them to be opposite in sign. In other words, if there was some weird type of matter that gravitationally repelled other masses, the equivalence principle and conservation of momentum would still hold true. The equivalence principle has been tested between regular matter, which requires all three masses to be the same. Since ordinary matter is mutually attractive we can say that Newton’s assertion is correct for matter.

But what about anti-matter? No one has been able to test this assumption, so we can’t say for certain. It is possible that active mass is negative for antimatter, which would mean it falls upward in a gravitational field. If that is the case, then although general relativity would still apply to regular matter, it wouldn’t apply to matter + antimatter. Since general relativity is a powerful and experimentally validated theory, it is generally assumed that Newton’s assertion would hold for anti-matter as well. But the only way to know for sure is to test it.

Recently we’ve been able to create usable quantities of anti-hydrogen, which will finally give us the chance to put antimatter to the test. It’s generally thought that antimatter will fall downward just like regular matter, but if it doesn’t, it will be time for some new ideas for gravity.

The post Equivalent Principles appeared first on One Universe at a Time.