Still trying to marry quantum mechanics with Einstein

Can energy act like mass, specifically in regards to gravity? According to Einstein’s general theory of relativity, yes.

E=mc2, Einstein’s famous equation from his theory of special relativity, tells us that matter and energy are somehow the same. This is the basis of nuclear power; mass can be transformed into light and heat.

But can energy act like mass, specifically in regards to gravity? According to Einstein’s general theory of relativity, yes.

Even the gravitational energy that binds the Earth together is affected by gravity. This follows from the strong equivalence principle, which says that all forms of matter are affected by gravity in the same way, regardless of what they are made of or where you do the experiment.

But it is a very hard principle to test, because the “mass” due to the gravitational binding energy of most things is tiny compared to an object’s ordinary mass. For the Earth, the contribution is less than one part in a billion.

I am part of an international team of scientists led by Scott Ransom of the US National Radio Astronomy Observatory which is surveying the sky with the Green Bank Telescope in West Virginia for exotic stars called pulsars.

Recently, we discovered a stellar system that provides an excellent way of testing the strong equivalence principle.

This system is made up of a pulsar orbited by a white dwarf every one and a half days, with a second white dwarf orbiting them both every 327 days.

A white dwarf is the leftover core of a Sun-like star which has gone through all the phases of its life. It is about the size of Earth, but 100,000 times as massive – so the gravitational force at the surface is 100,000 times that of Earth.

But that is still considered weak. The pulsar has the strong gravitational field. A pulsar is the collapsed core of a very massive star which is left behind after a supernova explosion.

The densest object that can exist without collapsing into a black hole, it packs more than the mass of the Sun into a sphere about 25 kilometers across.

Gravity on a pulsar’s surface is 100 billion times stronger than on Earth, and a pulsar’s gravitational binding energy is more than 10 per cent of its mass.

We still need a way of measuring the motions of the three bodies, and this is where pulsars really shine.

They have incredibly strong magnetic fields and rotate extremely quickly. This rotation accelerates charged particles that beam radio waves in particular directions in space, like a lighthouse casting light over the ocean.

When the beam is pointed towards Earth, we detect a radio pulse. These pulses work like the tick of a celestial clock, which we measure to an accuracy of a millionth of a second.

Motions of the pulsar towards and away from us due to its complex dance with the two white dwarfs cause variations in the times these pulses reach Earth, allowing us to determine the orbits of the three objects with extraordinary precision.

In this way, we can look for differences in how the pulsar and the inner white dwarf “fall” towards the outer white dwarf. Any difference would indicate that the strong equivalence principle does not hold.

But why try so hard to test an obscure principle? Because Einstein’s general theory of relativity is incompatible with the other great physics theory of the 20th century, quantum mechanics.

Einstein himself was aware of this incompatibility. He spent much of his later life trying to reconcile the two theories, and failed – and physicists are still struggling with the problem.

There is no accepted “theory of everything” that can accommodate both. Most approaches to the problem require some sort of modification to general relativity, and many possibilities have already been ruled out.

While the theories vary, almost every proposed alternative to general relativity that might allow quantum mechanics to work violates of the strong equivalence principle.

So we will keep observing this system, looking for small deviations to what is expected from ordinary gravity.

If we do not see any, it will be even harder to reconcile quantum mechanics and gravity.

But if we do, then we will finally have evidence that there really is something wrong with Einstein’s theory of gravity, and be one step closer to solving the greatest problem in theoretical physics.

Mallory Roberts is visiting professor of practice of physics at NYU Abu Dhabi.