Shulou(Shulou.com)11/24 Report--

How does the left foot step on the right foot to heaven? Maybe you can break one foot and send it flying downward at super-fast speeds (preferably at the speed of light), and it can fly upward a short distance (after all, the whole body is much heavier than one foot). The good news is that scientists have theorized that stretching and contracting might provide motivation without having to do it in such a horrible way.

In movies about space exploration, there is sometimes a nightmarish scene in which astronauts float in space, with nothing to throw, and no matter how much they wave their limbs, they can't make even the slightest progress toward the space station, a distance that seems close but far away. This is the reality determined by the laws of physics. Under the condition that there is no external force involved, in the initial state of rest, no matter how much you toss, you will only stay where you are. At most, the torso will rotate a little as the limbs wiggle, but once you return to the initial position, all struggle will be futile.

Source: Unsplash

Back on reassuring Earth, similar to the desperate struggle in space, we still need to change our physical form to move. After all, standing straight, there are no elevators, vehicles and other power sources under our feet, so of course we can only stay where we are. Obviously, no matter where you are, whether it is a bird soaring in the sky, a fish swimming in the water, or a snake crawling, including us humans, you have to transform the biological energy in your body into mechanical energy to move.

But if you remove the air from the wings of a bird, the water from the sides of a fish, or the rough ground beneath our feet, then no matter how deformed our bodies are, they can't use the reaction forces provided by the environment to move forward. That's what makes space special-the vacuum, where we can't exchange momentum with the environment and thus can't change position-seems like a foregone conclusion.

However, in 2003, MIT astronomer Jack Wisdom published an article in Science suggesting that there was a flaw in this inference: if spacetime in which astronauts live is curved, then changes in the shape and position of objects probably no longer follow the basic law of conservation of momentum. That is to say, in curved space, astronauts can "swim" in vacuum by waving their limbs in a certain way.

Curved Spacetime and Geometric Phase Spacetime can be curved, which is equivalent to an object falling not straight down, but out of thin air to fall to the ground in an arc, or even not falling at all, but turning and flying far away. For those of us accustomed to Earth's gravity, this is somewhat incredible.

So how does curved spacetime arise? According to Einstein's general theory of relativity, developed more than a century ago, we know that matter with mass causes distortions in spacetime, which in turn direct the motion of matter.

It is difficult to imagine how high-dimensional space combined with the time dimension can be described, but spacetime can be imagined as a huge elastic membrane. Massive objects, such as stars, placed on the thin film of spacetime like a shot put, cause dents in the thin film, i.e. distortions in spacetime. Planets with relatively small masses move centripetally in the hollows of the membrane like marbles.

Obviously, significantly curved spacetime usually occurs near massive objects, such as stars and black holes. But in fact, spacetime curvature is everywhere, and the gravity we feel is also caused by the Earth's mass pressing the concave spacetime membrane. Only on a cosmic scale, the curvature of the space we live in is close to zero and can be regarded as flat space.

According to general relativity, the curvature of space affects the motion of matter. As creatures in flat space, it is easy to imagine motion on a two-dimensional plane. As shown above, we raise our right hand horizontally, starting from a point, without changing the orientation of our body, completing a closed path on the plane and returning to the starting point. Also note down the direction our right hand is pointing all the way, and you will find that the direction recorded at the beginning and at the end does not change, which is common sense.

But if the plane becomes spherical, following the same closed path, the direction of the right hand changes. This change in angle (phase) is not caused by active rotation of the body, but is entirely determined by the geometric properties of the space in which the motion path is located, so it is also called geometric phase.

So even if we can't see the curvature of space, we can tell if the curvature of space is zero. The unique geometric characteristics of curved space make some physical phenomena that are not allowed to occur in flat space, such as "swimming" in curved space through periodic geometric deformation without external force driving.

Although the "curved" space in the laboratory can theoretically derive the "space swimming" guide, how to verify this strange phenomenon experimentally has become a huge challenge. Obviously, humans are not yet able to experiment near black holes.

In a recent study published in the Proceedings of the National Academy of Sciences (PNAS), a team of researchers at the Georgia Institute of Technology, in collaboration with other universities, constructed a model of curved spacetime in the laboratory. You might wonder how humans can bend spacetime in the lab.

In fact, strange motions in curved space can occur not only in space distorted by matter, but can also be equivalent to motion of objects on curved surfaces. From this, the research team cleverly built a robot that can change its shape,"Swimmer," which can move freely on curved surfaces.

▲ Spherical "swimmer" and cylindrical "swimmer": composed of adjustable base, air bearing, power arm, curved track and four servo motor counterweights. (Photo source: original paper)

As shown above, the skeleton of the swimmer robot is two curved tracks that intersect at right angles, and four motors that precisely control speed and position move freely on the tracks. The whole robot is connected to the fixed base by an air bearing. Because the friction coefficient of the air bearing is extremely low, theoretically, the "swimmer" can actively rotate around the air bearing in the horizontal plane during the process of changing the position of the motor. Adjusting the curvature of the intersecting orbit and the radius of rotation of the robot around the bearings is equivalent to adjusting the curvature of the space in which the swimmer is located. In the image above, the researchers created two warriors, the spherical "swimmer" and the cylindrical "swimmer"(dotted box at the top right of the image above), by adjusting the curvature of the orbit in the vertical direction.

▲ Swimmer needs to change shape periodically according to figure a above. Figure b shows the definition of the robot shape transformation: the angle combination transformation of the motor counterweight and the spherical center; and the definition of the robot motion displacement: the angle of the whole deviation from the initial position. (Photo source: original paper)

Counterintuitive Swimmer According to theory, the four motor weights of the spherical Swimmer need to cycle through positions in the order shown in Figure a above. Because rotation is limited to the horizontal plane, the effects of friction and gravity on the motion process can be minimized. Adjusting the position of the heavy object is actually equivalent to changing the shape of the entire robot. Looking at the changes in Figures a1 to a5, it is clear that the spherical swimmer successfully pushes itself a small step around its axis in the horizontal plane through a shape-changing cycle.

And the experiment also gives basically consistent results. "The phenomenon predicted by theory occurred, and it was so counterintuitive that as the robot changed its shape, it would actively move on the sphere in a way that was independent of environmental interactions. Zeb Rocklin, a physicist at Georgia Tech who led the study, said:

▲ In the absence of external forces, the Swimmer rotated an angle visible to the naked eye around its axis in 4 minutes by its own deformation alone. (Photo source: original paper)

At first glance, this is puzzling. But it's like adjusting the position of a car in a parking space. We repeat the cycle of out, turn, and back several times, and we can achieve a slight lateral translation. In parking, we drive a distance and eventually return; we change direction and eventually recover; and we change lateral positions without returning to the original change. The same is true of deformation motion in curved space. In periodic transformations, it seems that all parameters remain constant throughout the cycle, but there is a variable-geometric phase-that accumulates in periodic motion and appears as a spatial displacement.

Interestingly, the researchers found that although there is no external force driving in the horizontal direction, the rotational displacement caused by deformation causes a small friction force to accumulate on the bearings, accumulating reverse momentum for the robot. After stopping the periodic deformation, the robot will return to its initial position under the action of reverse momentum.

But astronauts in space don't have to worry about this problem (there is no friction). After discovering that they are in curved space, their first and most important need is to find a periodic "deformation" scheme that suits their bodies. Unfortunately, since human body mass is relatively evenly distributed, unlike the Swimmer model, which has weights at the ends of our limbs, this means that we are less efficient at adjusting moment of inertia by stretching and contracting our limbs.

Obviously, humans are not destined to be "swimmers" in space. But the good news is that curved spaces with greater curvature can help us improve our efficiency, provided that the humans in them can withstand more twisting and stretching. Yes, in curved space, it is no longer gravity that we have to overcome, but the forces that try to bend our bodies and move our heads and feet in different directions.

We were saved in the nightmare. We only hoped that we could "wriggle" to our destination before the oxygen ran out.

But if we can do that, it means that spacetime is distorted in an unprecedented way where we are--which is bad news, because it probably means we are near a deadly black hole.

Paper links:

https://www.pnas.org/doi/10.1073/pnas.2200924119

Reference link:

https://www.sciencealert.com/robot-shows-its-possible-to-swim-through-the-emptiness-of-a-curved-universe

''Swimming in Spacetime: Motion in Space by Cyclic Changes in Body Shape''

https://mp.weixin.qq.com/s/SrQ8d6pP6jik7ZzdF0yRPA

This article comes from Weixin Official Accounts: Global Science (ID: huanqiukexue), Author: Bu Zhou Revision: Erqi, Wang Yu

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