Getting Einstein in a twist

Gravitomagnetism is probably the coolest part of Einstein’s gravity that you’ve never heard of.

It is caused by a moving or rotating body and it has no equivalent in Newton’s theory. Even better, the effect due to the rotation of the Earth has been measured and is one of the pieces of evidence for Einstein’s gravity (General Relativity; often just called ‘GR’ by lazy physicists).

A recent paper (click on ‘pdf’ on the right side of the linked page to get the manuscript) uses this effect to constrain an alternative theory of gravity .

What is Gravitomagnetism

Einstein vs Newton

The key difference between the two theories (Einstein’s and Newton’s) is that Einstein interprets gravity as being “geometry”. What physicists mean by this is that there isn’t a “force”, i.e. the two bodies don’t directly pull each other. Instead, these bodies bend and warp space-time around them (don’t get too hung up on the jargon, space-time just means the thing that bodies travel through).

Think of a trampoline: if there is nothing on it, then it appears flat, and a ball rolled across it will go in a normal straight line. But, if someone stands in the middle of a trampoline, then a ball rolled across it will take a curved path, and possibly even end up at the feet of the person stood on the trampoline, as if it had been “attracted” to them. Of course, we cannot directly see the trampoline that we all travel on (i.e. spacetime), so we measure it by seeing how things travel along it.

This is a bit like looking at airplane paths: if one makes a flat map of the earth, and plots the trajectories that airplanes travel along, then they will seem oddly curved, leading one to wonder if they are wasting fuel! But, the airplanes are actually travelling through a curved geometry (because the surface of the Earth is a sphere, not a flat sheet), and looked at on the surface of a sphere the lines that airplanes travel along are indeed straight.

This standard picture of Einstein’s gravity is analogous to the Newtonian gravity that we all learn in school, just pictured differently. If one couldn’t see the trampoline, then one would see the ball “attracted” to the feet of the person stood on the trampoline, like a force was acting upon it. However, there are extra things predicted by Einstein’s GR that have no equivalent in Newtonian gravity.

Gravitomagnetism

One of these extra things is gravitomagnetism (so called because some of the maths is analogous to “normal” magnetism).

Gravitomagnetism is caused by the movement of massive bodies, such as their rotation. Now we have to stretch (pun intended) our trampoline analogy quite far: if we imagine our person in the centre of the trampoline to turn on the spot, we don’t expect anything to happen. But imagine if the person’s feet were glued to the trampoline. Now, if the person starts rotating, then the fabric of the trampoline itself will start to rotate, so let us imagine that the fabric is stretchy enough to be pulled around by the person without snapping. If the ball is rolled across the trampoline again, it will start to move in a circular motion, rotating in the same direction as the person as the person at the centre, because the ball will be pulled around by the fact that the fabric of the trampoline is being pulled around. Almost as if the trampoline itself is now acting like a turntable. Viewed from a Newtonian-type perspective, there is now an additional force pushing the ball around the trampoline, rather than only the force pulling the ball directly into the middle. This gravitomagnetism effect due to rotation is known as “frame dragging”. There are also other gravitomagnetic effects that can be caused by moving masses, but frame dragging is the coolest one.

This presumably all sounds a little bit like science fiction… but one of the amazing results of the 21st century is that the gravitomagnetism effect of the Earth has been measured. A satellite called Gravity Probe B was launched in 2004, and measured gravitomagnetism in several ways, including a measurement of the frame dragging of the Earth. It found a value that is consistent with the Einstein value, within a particular uncertainty value (i.e. error bar). Future observations will look to make this uncertainty smaller.

So what is this new paper then?

This recent paper is not about Einstein’s gravity, it is about a specific alternative theory of gravity called MoG (which stands for MOdified Gravity; yes I know, physicists sometimes aren’t very good at names). One of the real revolutions that came about from Einstein’s theory is that even the alternatives to it typically see gravity as geometry (like Einstein), rather than a force (like Newton). This means that these alternatives also contain the extra stuff like gravitomagnetism, they just might predict different values for it. Indeed, any theory which couldn’t explain the Gravity Probe B measurement of the Earth’s gravitomagnetism would be quickly discarded as a competing theory.

In this paper, the author Qasem Exirifard shows that for the Earth, the MoG gravitomagnetism effect is bigger than the General Relativity value:

The Greek letter ‘alpha’ that appears in this equation is just a parameter that is in the MoG theory, whose value isn’t known and must be measured by experiment. It causes a difference between the strength of gravity in MoG and in GR.

The paper then uses the measurements from Gravity Probe B (and others) to show what the allowed values are for the parameter ‘alpha’. The measurement of the frame dragging effect shows that ‘alpha’ must be less than 0.25. One of the other, more complicated, gravitomagnetic effects pushes this much further, saying that ‘alpha’ must be less than 0.0037. Note that the closer the observations push this parameter towards zero, the less this theory is different from GR. This sort of work, where observations are used to see how much room there is for things to deviate from the expected result, is a routine part of day-to-day science.

The really promising part comes in the conclusions, where the author points out that in other environments (such as the recent black hole shadow observation), ‘alpha’ is required to have a value close to 1.0 if MoG is to explain these observations. This is clearly different to the limits on ‘alpha’ derived in this paper. The author points out that the theory must be shown to have a solution that simultaneously allows these two different values of ‘alpha’ in these two different environments. No-one has done this yet, so we don’t know if it is possible. However, if someone can show that it isn’t possible, then the combination of these observations could rule out this competitor to Einstein’s theory.

Picture credits:
Einstein and Newton from wikiquote, click links for full provenance.
Frame dragging by Annie Rosen; I was unable to locate further information.

A brief dark sector primer

The universe doesn’t behave the way we think it should.

We have a wealth of evidence that the way galaxies form and move, the way gravity affects light, and the very expansion of the universe itself, do not behave the way we would expect from the matter that we can see.

Such observations are the reason for physicists’ claims that 95% of the universe is composed of things other than “normal” matter, i.e the stuff which makes up the world that humans see and inhabit.

Being logical creatures, physicists invented “dark matter”, to wit “extra stuff floating around in the universe that we can’t see”. This is perhaps not the most imaginative name that could have been chosen…

When some new observations (the history of this is often over-simplified and focussed on the work behind the 2011 Nobel Prize, which isn’t quite correct) suggested a second invisible thing was needed in the universe, one which behaves differently from the dark matter, a new name was needed. Hence, “dark energy” was born.

Note that I am intentionally not going into much detail here; this post is mostly just to set the scene that we don’t know what 95% of the universe is made of, and that we explain our current observations of the universe using two different invisible things: dark matter and dark energy. I will naturally go into more detail on most of the topics alluded to here in future blog posts, as I introduce things that are currently being worked on.

I will just mention that the current model of cosmology comprises the simplest possible possibilities for the dark sector: cold dark matter (which doesn’t move fast and only talks to itself and other things via gravity) and a cosmological constant (as the dark energy). This latter has been famously (and melodramatically) called Einstein’s “biggest mistake” or “greatest blunder”.

However, the science is not settled yet. No dark matter particle has yet been found in nature, and we only have gravitational evidence for the dark sector. This latter is the reason why one possible alternative to the dark sector is that we are not using the correct theory of gravity: perhaps Einstein was wrong? I must admit to having a soft spot for this possibility.

Maybe the current simplest model of a cosmological constant plus cold dark matter will ultimately win and a dark matter particle will be found. Maybe the answer will turn out to be something that no-one has thought of yet. Let us find out together!