Does Space Time Have a Memory (Script) (Patreon)

There are cosmic events so powerful that they leave permanent marks on the fabric of the universe itself. Imagine two colossal black holes spiraling into each other, yes they send ripples in the fabric of spacetime—gravitational waves that we’ve only recently learned to sense. But ripples pass, leaving the pond or the universe  unchanged when they’re gone. But ripples aren’t the only type of wave. There’s another type of wave that leaves a permanent mark—a memory etched in that fabric of the universe. They’re akin to gravitational tsunamis, and we’re on the verge of being able to detect them.

What does it mean for the fabric of spacetime to remember? In physics, when we say that something has a “memory” of an event, we mean that it was changed by that event, and retains information about the event. The crease in a piece of paper retains the memory of the event of it having been folded. The pocked surface of the Moon remembers the comets and asteroids that have slammed into it in the past. On the other hand, your perfectly elastic strip of rubber has no memory of having been stretched in the past because it returned to its exact initial state.

We tend to think of spacetime as being elastic. That elasticity is why it supports waves—gravitational waves. But there are aspects to gravitational waves that do not leave the fabric of spacetime in the same state that it started in. Spacetime can be permanently changed by the passage of a wave—it can remember the wave. It’s not just gravity—the other forces of nature have memory effects also—but today we’ll explore gravitational memory effects and how to detect them.

First up, a quick recap on gravitational waves. In Einstein’s general theory of relativity, spacetime is an elastic fabric-like thing that is stretched and curved by the presence of mass and energy. And like any fabric, it can support waves. In the case of gravitational waves, these are produced by any accelerating mass. Distances along and perpendicular to the path of a gravitational wave oscillate by tiny amounts. Even the most intense sources of gravitational waves in the universe, like merging black holes, produce gravitational waves that are only barely detectable at Earth by the miracles of engineering that are the LIGO and VIRGO gravitational wave observatories.

The types of gravitational waves we’ve detected so far are ripples. They change distances in a completely elastic way, and after the wave passes spacetime returns to its previous state. Think about a boat floating on the surface of a calm ocean. If the surface gets a little choppy with regular surface water ripples, the boat just moves up and down—it bobs—as those waves pass. The same is true of the water molecules themselves—the waves just move these up and down—it doesn’t displace them in the direction of the waves.

Now imagine a tsunami comes. This type of wave is different because it drags the water with it rather than just moving the water up and down. It also drags the boat, which is obliged to move where the water moves.

Well, gravitational waves have this elastic component—the oscillatory waves that we’ve detected from black hole and neutron star mergers. But they should also have this non-oscillatory component. Spacetime isn’t just being stretched and squished—it’s being dragged along by the wave—potentially leaving gravitational memory effects that can leave a permanent imprint on the fabric of the universe.

Gravitational memory effects come in different flavors. To get a sense of them, let’s look at the effect of a basic gravitational wave on a ring of stars that surround the axis of the wave. As the wave passes by, those stars oscillate together and apart in a way that causes the ring to squish and stretch. Without the memory effect, this ring should return to its circular shape after the wave. But the memory effect can lead to a permanent, if tiny, displacement of the stars, so that the ring is warped after the passage. This is the “displacement memory” effect.

There’s also a velocity-kick memory effect, where the stars keep moving after the passage of the wave. That’s like the case of the rowboat in the tsunami. And there are more subtle effects, like the gravitational spin memory, which imparts angular momentum along the path of the waves.

If we believe the math of general relativity then gravitational memory effects kind of have to be a thing. Both pen-and-paper exploration and computer simulations of gravitational waves reveal them. That said, we’ve never seen these effects in the real universe. Regular gravitational waves are hard to detect due to them being so weak, and their memory effects are even weaker and so even harder.

Gravitational memory effects can’t be detected by the current observatories like LIGO. These effects occur when spacetime doesn’t fully return to its original state after a wave—there’s some non-elastic stretching, squishing, or whatever else. But the arms of LIGO are made of metal and concrete and are fixed to the solid ground—and all of this matter has its own source of elasticity that pulls the arms back towards their original lengths against this miniscule stretching of the fabric of spacetime. Also, LIGO is sensitive to much higher frequency signals than we expect for these gravitational memory effects, so probably wouldn’t see them anyway. At least not for individual events. It may be that after many, many more observations of black hole and neutron star mergers a faint memory signal will emerge in the combined data—but that’s a long way off.

In order to see these effects clearly, we need an observatory that is sensitive to low frequency signals and is free-floating in space so there’s nothing to resist a lasting change in distances. Fortunately, we’re currently building exactly such a device: it’s LISA—the Laser Interferometer Space Antenna led by the European Space Agency, which is scheduled to launch in 2035. LISA consists of three spacecraft arranged in a triangular formation, separated by 2.5 million kilometers, but otherwise works similarly to LIGO, using laser interferometry to detect tiny changes in that enormous distance.

LISA is expected to detect the low frequency gravitational waves from things like merging supermassive black holes—-millions to billions of times more massive than the merges detected by LIGO. It should detect displacement memory effects in these signals rather easily. Let’s see what these will look like.

The gravitational wave signature from merging black holes looks like this—an oscillating change in the relative lengths of the arms. Remember the alternating stretching and squishing of our ring. Absent of memory effects, the difference in arm lengths should return to zero after the passage. But with displacement memory, there should be a growing offset between the arm lengths that persists after the wave passes for a little while.

Due to the limited frequency range accessible to any gravitational wave detector, it’s not possible to make an absolute measurement of the permanent displacement from these memory effects. However, the change in the strain on the detector which occurs due to the displacement memory effect during a gravitational wave measurement should indeed be detectable.

We’ll have to wait until LISA flies to know for sure, but from our simulations it seems very promising. Just a few months ago a group of physicists simulated the binary merger of supermassive black holes, and found that a detectable displacement memory effect is at its strongest and becomes detectable right before the merger happens and persists for a while afterwards.

So what can we learn from gravitational memory if we observe it? Well, these effects are a robust and inevitable prediction of general relativity, so their detection would once again prove Einstein right. That’s been a favorite hobby of physicists for the past 110 years and is always a good time. But it’s even more exciting if we can find some subtle way in which GR gives an imperfect prediction and so needs to be modified or extended.

A popular reason to try to modify general relativity is to try to explain dark matter without the matter. Some physicists think that all of this extra, invisible mass that seems to fill the universe is just a result of our theory of gravity being a bit wrong. Modified gravity theories often try to add non-linear curvature terms to the Einstein tensor—weak adjustments to theory that may add up in their influence over vast distances to give the impression of their being an additional source of gravity. Well, gravitational memory effects have pretty distinct non-linear components to them. If we have the non-linear components of general relativity wrong, then we get a wrong prediction for the nature of non-linear gravitational memory effects. When we’re finally able to observe these memory effects, we may have a direct test that could determine whether the Einstein equation is perfect as-is, or if it needs the sorts of additions that might also explain dark matter.

These memory effects can also provide additional information about the sources of the gravitational waves on top of what we get from the oscillations that we currently observe. The familiar oscillatory signal from merging black holes gives us a measure of their masses, spins, orbital parameters, and the distance to the event. But these properties can be challenging to tease apart from each other. Any further informattion to help us decode the source of the waves can be helpful in doing that. In fact, we probably need to include these memory effects to even get the right answers when we start analyzing LISA data.

We may also be able to see the memory of ancient gravitational waves imprinted on the universe at its largest scales. We expect that the cosmic inflation which supposedly blew up the universe right at the Big Bang would have generated colossal gravitational waves. The accumulation of memory effects from these primordial gravitational waves could have left its mark on the clustering of galaxies and even on the expansion rate of the universe. Measuring these effects and understanding gravity’s memory may ultimately give us a window into the events that occurred at the very beginning of time.

The universe is old, but it remembers. It remembers its birth and it remembers its past cataclysms—they are etched into the subtle shifts and warps in its own fabric. This gravitational memory is very likely all around us, waiting for us to learn to read this cosmic archive.

We just need on our reading glasses—AKA our giant space laser triangle—and start to peruse the history of the universe written in the memory of spacetime.