Superposing Newton and Einstein

I’d like to tell you about a recently finished collaboration on a topic that sounds pretty simple but hides many complex issues. These issues are not only related to quantum physics and general relativity (though that’s the interesting part for me) but they are also of the sociological kind (I’ll get to that too).

Photo by Ace Visuals Co: https://www.pexels.com/photo/win-11-wallpaper-19931186/

The story goes back to the physicist Charles Darwin (I wrote about him a while back, the one who wrote one of the best popular books on quantum physics of all times) who explored the Schrödinger equation a year or two after its discovery in some very simple situations. In a paper published in 1927, he calculates how a freely propagating particle ought to move in quantum physics. “Freely” means that no forces act on it and classically this would mean it travels in a straight line. All such objects which travel at constant velocity are called inertial, but in quantum physics, their motion is more complicated than a straight line. As Darwin showed, the position of the particle broadens as it travels and, even though its centre of mass goes in a straight line, the particle can be found in a wider and wider range of places as time progresses. This is known as “spreading of a wave-packet”. The word wave-packet indicates that in quantum physics all particles are waves and the spreading means that the waves get wider and wider.

This spreading is a consequence of the Heisenberg Uncertainty Principle. If we know the position of the particle well to start with, its momentum is less known, which means that it can move in a greater number of different ways, and this is the reason for the spreading. So, with time, the particle is superposed across a larger and larger area.

The second calculation that Darwin does, and this is related to my recent paper, is that he asks what happens if a quantum particle falls in gravity. The first surprise is that it spreads at the same rate as a free particle, so gravity makes no difference in this domain. But, and here is the crux of the matter, a falling particle develops a phase that’s different to the freely moving one. And this phase goes as a cube of the time. Darwin predicted it, but it has never been measured before (until now!).

What’s more, the existence of such a phase has been called into question. Here’s where Einstein comes in. Contrary to Newton, Einstein said that freely falling objects are actually inertial frames. This is his famous falling lift example. If we were inside such a lift, and dropped an apple, this apple would be stationary with respect to us, just like in an inertial frame. The reason is that both we and the apple would be falling at the same rate with the lift. In fact, no experiment inside the lift could convince you that you are falling (short of looking outside of the lift or ultimately hitting the ground).

This explains why the spread of the wave-packet is the same with or without gravity (for otherwise, we could detect that we are in a falling lift using quantum wave-packet spreading!). But, the phase that Darwin calculated can be detected though it requires us to use bits outside of the lift (so that Einstein’s logic of internal frames is not violated).

How the phase would be measured was proposed by Chiara Marletto and myself in 2020. The idea is to superpose a particle in a stationary state (i.e., Newton inertial) with a state in which it is falling in gravity (i.e., Einstein inertial). This is exactly what the Israeli physicist Ron Folman and his research team did. They used a Bose condensate (about a million atoms cooled to such low temperature that they behave like one big atom) and created a superposition by using an external magnetic field (basically a Stern-Gerlach experiment, but with a Bose condensate). In one branch of the superposition, the condensate remained stationary and in the other it was thrown up and underwent a ballistic motion in gravity. The two branches were ultimately reunited and the resulting interference was measured. It is the final interference fringes that allowed him to confirm the time-cubed phase. It was a piece of great news for Chiara and me that our 5-year-old idea was finally realized.

And now for the sociological bit. The issue of the phase of accelerated objects caught my attention because Roger Penrose told me about it during a discussion we had in 2018 in Nottingham. Both Roger and Chiara and I were visiting Ivette Fuentes and he explained why he thought that the time-cubed phase might be a problem and that it might lead to a collapse of quantum superpositions. His argument is based on the fact that the quantum vacuum looks different from the perspective of stationary and accelerated objects. And this ambiguity of the vacuum in which the particle exists would have to be resolved, according to him by collapsing to one of the two options.

This was highly exciting to me. Give that someone like Roger doubted Darwin’s calculations, looked like a fantastic opportunity to make a further contribution. Chiara and I jumped on the opportunity and wrote our paper proposing the experiment. In fact, Chiara organised a meeting in Oxford in 2019 at which both Roger and Ron were present and this is how Ron learnt about the controversy. It was lucky that Ron took it seriously and so we now know the answer. It is perfectly fine to superpose the Newton and Einstein inertial motion – Darwin’s phase is real and nothing collapses.

Isn’t it beautiful how science works? Also, we now all ended up collaborating on this latest paper even though we came to it from different angles and different expectations. It’s possible to collaborate with people who have diametrically opposing views because experimentation is king. And in this instance, the experiment was on Chiara’s and my side.

But, like all good science, the story is not closed. Roger may still turn out to be right, but the object to test needs to be more massive than Ron’s condensate and it needs to be kept in a superposition for longer. His estimate is that the time of the experiment needs to be about 1000 times longer than what Ron did! Now I don’t believe that quantum physics will fail us even here, but we need to work harder to get to that limit.

Even more importantly, we have no consistent theory why quantum physics should fail. We have some intuitions along the lines outlined above, but this is not good enough. Suppose the experiment fails for some long enough times and large enough masses. Did it fail because of our inability to eliminate noise or because of a fundamental problem with quantum physics? Unless we have some firmer guiding principle, the answer will always be blowing in the wind…