Robotic motion in curved space defies standard laws of physics
phys.org
phys.org
Unless I'm missing something, it's fairly easy to understand why it works. The horizontal weights use Newton's 3rd law to rotate the bar in the opposite direction from their own motion. The vertical weights are used to alter the robot's moment of inertia relative to the constrained axis of rotation. (You could replace these weights with a single weight that slides along the radial bar toward and away from the center axis.) The moment of inertia determines how much the robot as a whole moves then the horizontal weights move, so if you move the weights one way, then change the moment of inertia and move the weights back the other way, you get a net change in position. This is why it doesn't work with a cylinder: because when the vertical weights are constrained to a cylindrical space, moving them doesn't change the robot's moment of inertia.
I guess the point is that in a true spherical (or otherwise non-flat) space, any robot with the appropriate moving parts can do this "swimming" just by moving its parts in the right way in space without pushing on anything, essentially "pushing" against the curvature of the space itself.
Now that I think about it, there's a conceptually simpler way to demonstrate the same thing. Imagine a "robot" made of two parts: a "gun" and a "bullet". The gun starts on the "equator" of a spherical space and fires the bullet due west. By Newton's 3rd law, the gun begins moving east. After some time, the bullet flies all the way around the equator and impacts the gun from the east. The gun catches it and its velocity once again becomes zero, but in the time between firing the bullet and catching it, the gun has progressed some distance to the east, and now the combined gun and bullet system that we started with has changed its position. The gun can reload and fire the bullet west again, repeating the process as many times as necessary to continue progressing around the equator.
IIRC einstein had to dip into math for imaginary numbers and non-euclidean spaces for his theory on general relativity, but imaginary numbers aren't the most intuitive in the physical world and one at first conception one wouldn't think it should be in there. Yet imaginary numbers do help in many computations - for example, 3d rotations use quaternions that use imaginary numbers.
Any kind of physics involving >1 dimensional Euclidean space inherently involves complex numbers.
I don't think this is the same as what's in the paper, as the axial position of the vertical motors appears to be symmetric relative to the angular position of the horizontal motors.
EDIT: Scratch that, just watched the video -- I misunderstood how the vertical motors were moving. They are indeed changing the moment of inertia. You're right -- I don't understand why the authors need to resort to Coulomb forces to explain this behavior.
(Aside -- you can use the above phenomenon to rotate in a swivel chair without relying on external forces. Start with legs and arms outstretched. Then: arms left, legs in, arms right, legs out, repeat.)
Yes. A 2D curved space. I think that's the point this is trying to demonstrate. Not that you can do some motions to rotate the position of the arm. You can obviously do that - that's how momentum/reaction wheels work to turn satellites without "pushing off anything".
But their demonstration does it with all the motion restricted to happen in the curved 2D space.
To imagine how one would work in a space ship, imagine a very long ship that acts like a particle accelerator. Take an atom from the front end, accelerate backward to near the speed of light so that it's mass increases say 1000 times. While that atom is flying backward, your ship that pushed on it moves in the opposite direction. Catch it again in the rear, and the ship must return to zero speed because of conservation of momentum, however the ship is now in a slightly different spot.
Move that atom back to the front of the ship, but slowly so it's mass stays low. Your ship moves backward, but not quite as far as it moved before. Do this again and again to translate the ship. The net velocity of the ship will always be zero though.
This also starts to resemble how a laser works internally (at least HeNe). Granted, that’s light and massless.
"Being sneaky" by moving things slowly, or catching things, just doesn't work. It will all add up. All movement will be undone.
I dunno if that works, but that's the part that matters in the explanation above, and that's the part you'll have to address.
All you're doing is converting a slow relativistic acceleration into an equal and opposite fast relativistic deceleration.
It’s a small effect that adds up over time. Even without this “speed it up to increase its mass” situation the OP is referring to, it seems to me that you could exploit something similar on a spacecraft for linear momentum, by allowing drag on, say, a tennis ball to be asymmetric by shooting it fast in one direction and slowly moving it back in the other. It’s not violating any laws of physics, just exploiting a second-order effect when the first-order effect isn’t going to get you anywhere. You’d eventually need to get rid of the heat, probably just by radiating it out into the void (and, naturally, it wouldn’t be an energy neutral situation, you’d need some kind of power source to make up for the losses)
I'm not sure others have read deeply into the article. While there's always some subtle ways friction can sneak its way, the authors account for the obvious.
The article has a lot of definitions, which makes the crux difficult to pinpoint. They use the word "shape" many times to describe the configuration of the four motors. I think this adds confusion. Let me try to summarize as I understand it without using the word "shape."
The authors are measuring the net position of the arm holding the two motor tracks. The arm can only rotate clockwise or counter-clockwise in the horizontal plane, so it suffices to measure the arm position using an angle - phi, with initial position being phi = 0.
The two motor tracks are oriented perpendicular to one another. A key point is that the motors do not travel up, down, left, or right. That's Cartesian thinking. Rather, they travel clockwise or counter-clockwise along their respective tracks. One track is vertical, the other is horizontal.
With this picture, the authors claim that the net horizontal position angle (phi) of the arm changes depending on how the motors move along their tracks.
None of this is particularly impressive (e.g. the motion of the motors may cause the arm to "wobble" one way due to issues with synchronization, weight differences, and numerous other causes).
The interesting part is this: If the vertically-oriented motors are made to move up-down on linear straight paths instead of curved paths, the net movement of the arm is not observed. Think about that for a moment...why should the path that the vertically-oriented motors take affect the horizontal rotation of the arm?
In Newtonian physics, acceleration/force in one direction cannot affect acceleration/force in a perpendicular direction. At any given moment, the vertically-oriented motors are perpendicular to the arm's rotation direction, so their motion should not affect its horizontal rotation in space. In particular, both the curved-vertical and linear-vertical paths are perpendicular to the horizontal at all times. Newton would predict that changing the path of the vertical motors from linear to curved would not affect the horizontal rotation...but it does.
> The interesting part is this: If the vertically-oriented motors are made to move up-down on linear straight paths instead of curved paths, the net movement of the arm is not observed
In the video, it looks like the same kind of net movement is observed with the cylindrical configuration as with the spherical configuration. With the cylindrical configuration the average position migrates by about 0.2rad and stays there, compared with 0.3rad for the spherical configuration. So the spherical configuration seems "better"(?) but it's hardly a convincing difference given how much slop there seems to be - there's even significant net rotation in the "plateau regime" where it's apparently supposed to stop migrating.
And why is there a "plateau regime" anyway? If they can pull off a delta-V with no momentum transfer, I'd expect the robot to keep migrating around in a circle. But it stops. The abstract says:
> While this simple geometric effect predominates over short time, eventually the dissipative (frictional) and conservative forces, ubiquitous in real systems, couple to it to generate an emergent dynamics in which the swimming motion produces a force that is counter-balanced against residual gravitational forces.
I think this translates to "it just stops working after a bit". What's your take?
I think their figures answer your questions...both theoretically and empirically. Figure 3 shows the difference between curved/linear vertical motion.
They effectively weigh less when they're far apart.
If you look from above (like their video), the curved track means that projected down to the plane it's rotating in they're closer to the axis.
> Notably, the robot’s ability to move does not violate the usual rule against movement without forces in three-dimensional space because the full three- dimensional dynamics in fact include normal forces on the robot supplied by the boom arm that confines it to the sphere.
(And I'm sure they would agree that you can even eliminate forces from the table itself from the equation, if you attach an identical robot on an opposite arm to supply that normal force from within the system.)
What I don't understand is -- given that the Euclidean physics are known, why was an experimental setup involved in this paper, as opposed to simply mathematical proof? Or is the experimental demonstration the purpose in and of itself?
However, the mathematics of it seems to have already been confirmed by a previous paper and the actual idea of changing orientation without exchanging momentum with anything is not novel.
You can turn a satellite by spinning up a flywheel and then reabsorbing the angular momentum when you reach the desired orientation.
Wouldn't 2 of those allow for 2 different centers of rotation. If so, we can just walk though space.
:-)
The same applies to the system they actually built, except that the nonconserved "momentum" is not the same as the usual notion. It's the conjugate momentum(https://en.wikipedia.org/wiki/Canonical_coordinates) for the coordinates on the surface.
In the system you describe, is it possible for the center of gravity of an isolated system to move without ejecting mass or light?
Besides, whenever we see statements about defying the laws of physics our immediate reaction should be to look deeper. Say, if some action seems to defy Newton then look to SR thence GR for the reason.
It's not just the title. The body itself seems to claim researchers have "proven" momentum isn't conserved:
"Until recently, physicists believed this to be a constant, following the law of conservation momentum. Now, researchers from the Georgia Institute of Technology have proven the opposite—when bodies exist in curved spaces, it turns out that they can in fact move without pushing against something."
By way of example, this linked press release contains the paragraph:
> While the effects are small, [ ... ], just as the slight frequency shift induced by gravity became crucial to allow GPS systems to accurately convey their positions to orbital satellites.
which is a /headdesk given the reality that ground based GPS receivers compute their positions using signals from several 'visible' transmitting GPS satellites; they do not "convey their positions to orbital satellites".
This doesn't detract from the source paper but it does highlight the quality of the lay press release.
(Note:
It's essential to correct for gravity induced shifts in timing given these exist because of relativity .. but the shifts themselves are not "crucial" to the triangulation; in a hypothetical universe where relativity didn't exist | had a minor effect in this usage case, the triangulation of GPS against moving stations would still work with either no correction for relativity or a different correction)
I actually think they may have been referring to the ground stations here, not the GPS devices you carry as a user, since they said "GPS systems" and not "GPS receivers". Presumably the satellites need to determine their positions based on the positions of the ground stations.
The satellites broadcast a rough guide to their collective positions (an almanac) to recievers and a precise guide to their specific exact location (the ephemeris) to ground clients (phones, GPS receivers, etc).
Master Ground control stations update the satellites with that information every four hours or so .. strictly speaking the satellites don't do any computation of their own position - they broadcast their weekly lapsed epoch signal and echo data frames from their last Master Ground Station update.
Orbital changes can result from solar wind pressure, magnetic forces, passing objects with mass, etc.
It's the GPS receivers that do the 'heavy' positional computations for individual fixes .. and the Master Stations that do the somewhat harder work of constellation updates.
( There's a wealth of accuracy processing that can be run in parallel or post - differential base station GPS, forward error correction, post aquisition corrections, et al )
[1] https://gssc.esa.int/navipedia/index.php/GPS_Ground_Segment
These people should be fired at once. They have no business writing propaganda about things they do not understand. We need better ethical guard rails in research institutions, this is ridiculous.
As an example, I once had a discussion with someone arguing that energy use was not a problem because we’ll soon have free energy because he read a badly written vulgarisation piece discussing arguments for local non-conservation of energy in some quantum interactions.
This gives people in general a very distorted view of what is and is not feasible. Which would not be too much of a problem if people did not then vote and behave based on this inaccurate perception.
1. Hold both weights out in front of you 2. Swing one to the side. 3. Swing the other one straight up over your head (or just pull it in next to your body) 4. Swing the first one (off to the side) back in front of you. 5. Swing the second one back down (or push it away from yourself) 6. You are now back at (1), but the chair you're in has turned slightly.
The phenomenon you're describing is a gyroscopic effect. The entire system (you, the chair and the weights) rotates. That is not what the authors have setup.
The author's system includes the weights and their tracks, but not the arm connecting them. The arm is the "space" (or surface) in which the weights and tracts reside. In your example, planet Earth would be the "space" (or surface).
In order for you to demonstrate their phenomenon, your chair would have to change position (translate) from where it started, not just rotate in-place.
The source of the confusion is that they are measuring translation with an angle. They can do this because their universe is very small. You could also measure your translation relative to Earth with an angle, but it would be a tiny angle as the Earth has a very large radius.
But the arm is a part of the system. Are they not accounting for the centripetal force through the arm?
(EDIT: Answering my own question, the preprint does include the text:
> Notably, the robot’s ability to move does not violate the usual rule against movement without forces in three-dimensional space because the full three- dimensional dynamics in fact include normal forces on the robot supplied by the boom arm that confines it to the sphere.
So the authors are (of course!) aware of this in 3D space. Their experimental setup is functionally no different from the swivel chair example.)
> In order for you to demonstrate their phenomenon, your chair would have to change position (translate) from where it started, not just rotate in-place.
No, by the same logic above, why can I not simply keep my upper arms stiff and declare them not part of the system? My lower arms and the weights are then "translating" through "space".
http://groups.csail.mit.edu/mac/users/wisdom/swimming.pdf
The paper is quite accessible but here is a short summary:
https://www.science.org/content/article/swimming-through-spa...