The Forgotten Mystery of Inertia
americanscientist.org
americanscientist.org
By some strange mechanism he is able to make himself start spinning. At first it is worse: in one direction the reverse gravity increases in effect! So he reverses and is relieved to find that in the other it slowly abates. Though the sweet relief is strange. Because if he goes too far in that direction, he finds that the expulsatory force begins to increase again.
But eventually he finds the sweet spot and stays there, relieved, to find himself not being pulled apart. "This", he says to himself, "I shall call an inertial reference frame. It is so much more relaxing than the others."
Although, for us, it was always a spherical chicken.
Think of the universe as a rubber sheet over a table, being stretched in all directions. My understanding is that cosmic background radiation is on the rubber, stretching and moving with it just like all the matter is. If background radiation were on the table instead, there would be exactly one spot on the rubber that saw no motion relative to it, while spots very far away from that spot would see a huge amount of motion. If you went out far enough, you'd be seeing hard radiation from half the sky.
Or, as another view, though I find this one harder to think about, since here the expansion of the universe seems to confuse rather than clarify things: The background radiation you see at any given point is simply the photons radiated inward from a sphere of a very large radius centered on that point. Every point has its own such sphere, and if an observer sees a dipole component in its background radiation, it means that that observer is in motion relative to the average motion of the matter that those photons originally came out of.
That said, he’s drunk, so the answer is to piss into the luminiferous aether.
Here's a hint: It's relevant that the person is drunk. Another hint: Newton's third law.
I was also unclear on this: "The first triumph of general relativity was its exact prediction of the orbital precession of Mercury’s perihelion" —does a perihelion precess? I thought it was the planet which was precessing and the perihelion shifted (changing the shape of the planet's orbit?)
Also, I came across this (seemingly) related gem the other day: ("Why is Linear Motion Relative but Rotation Absolute?") https://www.quora.com/Why-is-linear-motion-relative-but-rota...
The faster the gyro spins, the less important the imparted velocity will be relative to the particle's speed, which is why a gyro is more stable the faster it spins.
That quote from the article really crystallized Mach's Principle for me. So continuing mikeash's great explanation... basically the rest of the universe is pushing the gyroscope into its stable position?
General Relativity would say somewhat the same thing, but in a very different form, with different results. GR would say that it depends on the geometry of the local spacetime, which, yes, does depend on all the mass in the universe, but not in the way that Mach's Principle would lead you to expect.
Note that GR, in contrast with Mach's Principle, does have experimental evidence.
Key point
Gyroscopic stability also explains why a spinning axisymmetric projectile, such as a football, can have its symmetric (long) axis stay aligned with its flight trajectory, without tumbling end over end when in flight. The spin imparts a gyroscopic response to the aerodynamic forces acting on the projectile, which results in the projectile long axis aligning itself with the flight trajectory. The physics involved here is a combination of gyroscopic analysis and aerodynamic force analysis due to drag and (potentially) the Magnus effect. This is quite complicated and will not be discussed here. However, there is a lot of literature available online on gyroscope physics, as related to projectile spin and gyroscopic stability, if one wishes to study this topic further.
I think that once you establish that angular momentum is a vector quantity that is entirely consistent with Newton's laws, then the particular case of the gyroscope becomes straightforward.
You’re totally right that gyroscopes are straightforward if you understand angular velocity as a vector quantity, but it’s not quite so intuitive.
Edit: I'm trying to think of a way to bring in angular momentum without having to derive it in full generality...
The same effect can occur during the acceleration of a gyroscope in a missile in space. Even tho there is no gravity. The effect of acceleration on the gyroscope is the same, causing it to maintain its orientation in space.
The faster a gyroscope spins, the more quickly it rights itself. and thus appears more stable. as it slows down, the righting effect fails.
Classically, you would expect the shape and position/rotation of the orbit to be constant. In reality, its rotation in the orbital plane changes due to GR.
My understanding of precession is that there are two levels of rotation: an object rotating on some axis A, with axis A rotating around another axis B. So in the case of the perihelion precessing, what would be the corresponding parts? I was assuming the only precession taking place was of Mercury itself because the axis it rotates on (axis A) rotates about some other B axis.
Edit: to clarify, if the above is a correct description of precession, then in order for the perihelion itself to precess it would need to be rotating, and the axis it's rotating about would need to be rotating about another axis. My understanding is that neither the perihelion nor the orbit are rotating, so they can't be precessing.
In the context use here, the precession in question is the rotation of the perihelion (or, if you want to think of it more akin to the above case, the semimajor axis of the ellipse) that rotates in the orbital plane (around the normal vector to the orbital plane).
From what I can tell using precession as a direct substitute for rotation is less common, even in astronomy—but maybe I've just had poor samples so far. I was thinking of it as: "Precession is a change in the orientation of the rotational axis of a rotating body." (https://en.wikipedia.org/wiki/Precession)
Actually, it would change even without GR. The orbital ellipse is only constant in the ideal two-body problem. The fact that planets aren't perfectly spherically symmetric, and the presence of the other planets, also cause the orbits to precess.
From the Wikipedia article I linked in my other post: "For Mercury, the perihelion precession rate due to general relativistic effects is 43″ per century. By comparison, the precession due to perturbations from the other planets in the Solar System is 532″ per century, whereas the oblateness of the Sun (quadrupole moment) causes a negligible contribution of 0.025″ per century."
Isn't that... intuitively wrong though? If you were spinning fast enough in space, your body would be ripped apart. If you were spinning and let go of an object near you, instead of floating in place, it would appear to retreat away from you rapidly.
I understand the example of how a person in a falling elevator can't tell if gravity is acting on them or not ... it's intuitive and there aren't any obvious contradictions. I don't get why these two examples are brought up together as similar obviously-true things that inspired relativity. It feels to me like it (the article / Mach / Einstein / physicists) is reaching for a parallel where there isn't one between cases that are only superficially similar.
Maybe the idea is that no other bodies around means that your own body would be uncontested in "frame-dragging" such to define that you aren't rotating? But what happens if you hold your arm out and throw a ball perpendicular to your arm? I can't imagine a type of rules of motion that would result in anything but your body being sent spinning slightly, with you seeing the ball retreat while appearing to orbit you and you being able to feel the blood rush a little more to the ends of your body away from the axis you're spinning on. The blood in your veins has inertia, and by changing the inertia of parts of your body, then of course you're going to get pushback from your blood. Maybe the ball being a separate body is now dragging the frame a bit such that you're now rotating relative to the frame, but if the ball has much less mass than you, it seems odd that the ball would have a great effect on the frame compared to you, and possibly continue to, no matter how far away it is from you. Every other effect at a distance rapidly diminishes with distance! This effect wouldn't be necessarily nonlocal (ie. faster than light), but it would seem to have a disrespect for distance not commonly found in physics. (Maybe the effect just diminishes outrageously slowly over distance, but I'm not sure this assails all of my concerns with the concept.)
But the spinning-in-an-empty-universe example is a situation that I don't even agree with Mach/Einstein about what would happen, much less about what it says about the world. Maybe they're right, but this difference makes the thought experiment a much different kind and arguably a less compelling one than the other.
Thanks for the link, I found it an interesting read!
Imagine a spinning glass ball with a 1cm radius doing one full rotation per second. If we draw a dot on its outer edge, at the end of 1 second that dot will have done a full turn. Given that its movement was a circle with radius 1, the distance the dot traveled was 2pi cm, for a speed of 2pi cm/s.
Now imagine that instead of drawing the dot on the outer edge, we drew it halfway between the center and the outer edge (somehow). This would place it 0.5cm from the center. It would still complete a full turn in 1 second, but now its distance traveled would be pi cm, for a speed of pi cm/s.
All this is to show that when the ball is spinning, the different particles it's composed of are moving at different speeds. On opposite sides of the ball, the particles are even moving in different directions. The faster the ball spins, the greater the difference in velocity of the different parts of the ball.
Rotation is inherently about different particles moving at different velocities. This is why there is an absolute reference frame for it: it is defined by these differences, so by reducing them to zero and making every particle in the ball have the same velocity, we can reach the "absolute".
At least, that's what it seems like to me.
Check out the second answer from 'Vesselin Petkov' which talks about a geometric case for the difference between the two. His answer overall seemed to me more interesting than the most upvoted one there.
It ends by saying that in general relativity, "rotation can be considered as existing only relative to a certain choice of coordinates after all", though, so there seems to be more to it.
Are the particles point mass?
From a physical standpoint, though, if you wanted to talk about the absolute center point, you'd have to talk about the lowest level of particles, which gets into the weirdness of quantum mechanics (or maybe a lower level exists?). At that point, I really couldn't say what happens.
And I don't think it matters if the particles are point mass or not, except possibly for the absolute center. The point is that the rotating object is not just one thing, but made up of smaller things that have different velocities and acceleration. These differences in velocities and acceleration are what rotation is.
If there exists something that is not made up of smaller things which also rotates, then that would prove me wrong.
Of course, all the above is just speculation by someone who's hasn't had a physics class since high school, so take it with a grain of salt.
I think every attempt to visualize this which imagines a single object rotating is doomed. Rotation inherently implies a difference in velocities, and some attractive force keeping those velocities changing to maintain a distance. So, the existence of any attractive force, together with inertia, implies rotation and the stickiness of direction of a gyroscope. But inertia itself already implied stickiness of direction, given that a change in direction would require acceleration...
Imagine the ball is floating in space, and you are watching things through a camera fixed to the ball. To you, the two dots will always appear stationary with zero relative velocity. So there is no way to determine your absolute reference frame.
Now suppose you are watching through an external camera, and suppose you observe the dots having a relative velocity. Is the ball spinning, or is the camera orbiting around the ball? Again, there is no way to tell.
In other words, you can determine that you're in a gravitational field by measuring the difference in force at different locations in the elevator.
There's also a lecture on inertial guidance in Feynman's tips on physics; it's more about the clever details of practical gyros.
Note that these explanations already presume rotation is absolute wrt an inertial frame.
This is clearly false... right?
If you translate the gyroscope, it won't be pointing at Kiev anymore, it will be pointing to the side of Kiev. The gyroscope doesn't magically point at a target, it provides a stable reference direction that the rest of the IGS can compute its deviation from, to adjust its course.
Consider a gyroscope spinning fast. so if all of a sudden you try a push its top northward then that instantaneous force pushes down on the north edge of the disk and up on the south edge.Those specific parts of the disk acquire momentum. However because the disk is spinning, the part of the disk that was north soon becomes south. and the southern piece that was moving up is now north. now the momenta of the influenced disk segments act to right the gyroscope. The same effect can occur during the acceleration of a gyroscope in a missile in space. Even tho there is no gravity. The effect of acceleration on the gyroscope is the same, causing it to maintain its orientation in space. The faster a gyroscope spins, the more quickly it rights itself. and thus appears more stable. as it slows down, the righting effect fails.
Angular momentum is a man made calculation and the upward pointing arrow is really just a make believe thing. If it were a real force, the whole gyroscope should float upwards. LOL. It is a shorthand to represent the average momenta of the influenced parts of the gyroscope.
So is linear momentum, really.
I agree that you can analyze an actual physical gyroscope just in terms of linear momentum without reference to angular momentum, though the calculations end up harder. But there are things that have angular momentum that doesn't obviously correspond to linear momentum (circularly polarized light and nonzero-spin elementary particles come to mind).
Can Mach's principle and equivalence principle be derived from some more fundamental laws or are they accepted as axioms?
The idea is that mass curves space. In this curved space, a 'straight line' is no longer straight. The upshot of this is that if you are standing still, a 'straight line' would actually mean falling down. By inertia, things want to move in straight lines, so we feel gravity. It is an apparent force like the centrifugal force.
If this talk of straight lines in curved space is confusing, consider what passes for a straight line on the surface of a sphere. It still 'curves'.
https://www.youtube.com/watch?v=e7LcmWiclOs
It just reinforces the (incorrect?) intuition that spacetime is "something" rather than nothingness between things. Why can't motion be relative to spacetime rather than other objects?
Slightly longer answer: To be relative to spacetime would (most likely) mean having a means of transmitting information faster than the speed of light, but information cannot travel faster than the speed of light. * "The world line (or worldline) of an object is the path of that object in 4-dimensional spacetime, tracing the history of its location in space at each instant in time." [0] Something that would exist relative to spacetime (as in, would not be confined by the laws that dictate spacetime) would have to be outside of a light cone [1]; "In flat spacetime, the future light cone of an event is the boundary of its causal future and its past light cone is the boundary of its causal past."
https://en.wikipedia.org/wiki/World_line
https://en.wikipedia.org/wiki/Light_cone
* I don't know very much about quantum entanglement, so if anyone would like to comment as to whether entanglement might appear to violate transmission of information faster than c, that'd be neat, but i have a suspicion that it doesn't because either because of (A) a reason depending on the fact that qubits aren't like bits or (B) that the separation of two entangled subsystems would constitute the actual transmission of information but would still necessarily be no faster than c.
You can describe the manifold using a coordinate system corotating with the gyroscope, the worldlines will still have a non-zero acceleration. There is absolutely no need for any matter field satisfying hyperbolic PDE's with faster than light characteristics.
For what it's worth, the reason we know spacetime exists and is not 'nothing' is because it carries energy around the universe. That's pretty much the main common property shared by things that exist.
"Taking the risk of sounding like a crackpot I will share some of my own thoughts on the subject - put together from bits and pieces I have stumbled upon.
It can hardly be argued that some knowledge is attempted hidden - mostly for the sake of power. And in my humble opinion, the mysteries of bodies in rotation is exactly one of those subjects.
This article is based on academic science and appropriately so, but when it comes to rotating bodies I don't think you will find the answer there - at least not in the post-Einstein era. You should at least go back to James Clerk Maxwell and his original 20 equations to get a hint of what's really going on. If Einstein himself was aware of the shortcoming of his theory or even put them there on purpose, is up for debate - leaving it to the reader to discover what's missing from the theory of relativity.
If one bothers to seek alternative sources of knowledge about rotating bodies, you will not be alone. And if you stick to it, you will find very interesting things indeed. Not only about rotating bodies themselves, but as to why some has determined it so important to keep the facts hidden.
Some events suggest that, at least in western science, the connection between rotating bodies and gravity was stumbled upon in the early post-war missile program when Wernher von Braun tried to put a rotating body on top of a rocket - believing that it would stabilize it.
There are of course scientists doing research into these things outside the constraint of normal academica and from time to time their findings find their way into the public domain. One example is experiments done by Dr. Bruce DePalma, which some are as simple as they are easy to duplicate.
For those of you curious enough to adventure into this field of alternative science, I wish you luck."
If "you" can exist in a massless universe (that which encompass all that exist) - then, by definition, "you" have no mass. So insofar as mass is connected to inertia is connected to angular momentum (the need for acceleration/force to alter the direction of movement) - then: no, you would not be able to detect "centrifugal forces" without any mass.
But, if "you" have mass and exist in a universe, that universe consist of at least the mass making up "you". Let's assume a sphere/clump of small magnets. Would it be possible to spin this sphere fast enough for it to disperse - tear itself apart? I would think so.
You need your angular rotation and the specific forces applied to your body (given by the accelerometers) to be then able to compute your position, speed... in the earth frame called NED (North East Down).
That's the very short version. You also need to know your Lla position to correct your gravity model, the error model of your sensor to correct them... Kalman filtering is always used (in my experience).
Here is a draw that seems accurate https://en.wikipedia.org/wiki/Inertial_navigation_system#Met...
Then if you want to go dirty hands, you will need these keywords : "inertial navigation mechanization". This PDF seems clear at first look (5s check) : http://www.ecsutton.ece.ufl.edu/ens/handouts/inertialnav_v2....
Kalman filtering can be overhelming but the course from D.Alazard is really great (still using it after 3 years in navigation field).
If you want a quick exemple, a north finder algo is very easy to understand (basic earth projection). It is also the first step of initialisation of a navigation system.
Maybe the author meant that a gyro's motion is not intuitive to most humans. That I can agree with. For me, even the fact that my smartphone is performing billions of calculations every second is non-intuitive. Doesn't mean I don't know how it works.
In this case it sounds like we've derived an algorithm that relates to the inputs and outputs, but the inputs that cause the formula itself are unknown.
My understanding is that if you go far enough back a lot of physics is like this, but it sounds like we can't even go very far back here.
We can predict the behavior of a gyro but there is still a fundamental question of what a gyro is relative to since GR tells us there is no universal reference frame. Are gyroscopes entirely local or does the gravity of distant galaxies present a sort of universal reference frame? Or is it something else entirely?
Something else entirely. You don't need other galaxies or a universal reference frame. Even if the gyroscope were the only thing in the universe, it would be easy to tell if it were spinning: a very tiny person standing on the inside rim would be held down if it were spinning, or free floating if it were not.
General Relativity may seem counterintuitive, but experimentally it really does seem to be the way our universe works. Starting out from the position that absolute motion is meaningless has proven remarkably fruitful. It's also something a lot of very smart people have been thinking about for a hundred years. Whether or not you find Mach's arguments plausible, they're fundamental philosphical claims and can't simply be dismissed through a half-baked thought experiment.
In that case, it wouldn't be drawing you outward no matter where you were located. So, spinning would be "you feel a gravitational force", and a ring of mass would be "you don't feel a gravitational force".
Is what the entire article is about! That our idea of an intertial frame of reference is incomplete.
If one can see that the gyro is still pointing in the same direction, then one has already defined a reference frame. I can see confusion if we had a gyro spinning inside a free-falling elevator (or even a closed box spinning in space). You can still tell the gyro is spinning because there are internal stresses that indicate the axis of rotation, if not the direction. The earth bulges at the equator because of its rotation, it would require much force to keep it spherical.
If it doesn't answer "why?", then it's incomplete. Perhaps at some point in our explorations of physics there will be axioms we must simply accept, but the gyro isn't it. We should have a reason for its behaviour.
I get what you're saying. We know what inertia does. We have the math to estimate is effect. We can measure it's affect. To be clear, we don't know how it works. In the vacuum of space, if your body begins to spin, a force will pull your arms away from your from your body. No one on this planet can unequivocally explain why this happens. No one can explain the mechanism for how gravity works. No one can explain why when something starts spinning, there is a force that makes it continue to spin, or why there is a need for force to stop it.
These are basic forces and our lack of understanding shows just how little we understand about the universe. This, after the smartest people, over 2,000 years have had a crack at it.
Steve Jobs said that people who have made everything are no smarter than you or I. Einstein said something similar. I find it a bit reassuring that some of the worlds most basic forces are yet unexplained. We are still in our infancy of figuring things out. Everyone should get to work. There's a lot to do.
I think this is the easiest to explain, because it's built on the others (specifically inertia). For some point in your spinning, your arm moves in some direction. Your center of mass changes its direction of movement, because you're spinning. Your arm still goes in the direction it was initially moving, pulling itself outward as the less floppy part of the body follows the spin inward a bit better. Your arm (and all your other parts) is just "trying" to go "straight", due to inertia, and can achieve it better than your other parts, because it has an easier range of motion to do so.
Inertia and gravity themselves are more fundamental, and certainly fit your descriptions (to my limited knowledge). We don't know at what level things in the universe are fundamental, instead of explainable by some additional turtle underneath. Hence we start smashing subatomic particles to see what's there.
I have no clue how science even could determine if some mechanisms are the "root" ones and not just derivative of something else. There's no guarantee that the physical workings of the universe make any sort of sense.
The universe is still full of many mysteries. If we knew the why, we'd stop doing science. Our understanding is incomplete and that's okay. It gives our species something to strive for.
Do you really understand particle physics well enough to truly understand how your cell phone works? We can predict, model, and observe. We can get results. We don't necessarily know or why the results are the way they are.
Edited to add: I find it interesting enough to sometimes point out that we used electricity before we even knew about electrons. Being able to do something doesn't mean understanding.
We used simple machines, long before we understood them.
There are infinitely many examples of this, from metallurgy to rolling bearings to gears (gear reduction has nothing to do with teeths), medicine, astronomy (humans have predicted the motion of the stars for thousands of years), ...
That's not true. You can have accurate and precise predictions without understanding why it behaves in that fashion. If, additionally, you can understand why it does then you have a better understanding of it.
No, the greatest level of knowing is having an explanation for why a gyro behaves the way it does.
> For me, even the fact that my smartphone is performing billions of calculations every second is non-intuitive. Doesn't mean I don't know how it works.
But imagine if your smartphone was of alien manufacture, and you lived in a world of exclusively analog technologies. Scientists and engineers could come to accurately predict your smartphone's behavior, and certainly a mathematical formalism could be given for it, but they wouldn't understand the physical basis for the billions of calculations it performed.
It would be a big mystery until physics advanced enough to understand how the circuitry worked.
This is the most superficial level of knowledge you can have. If you truly think about it, you know nothing about it.
The greatest level of knowing would be able to derive everything you just said from first principles about the gyro without knowing any of what you just mentioned. That is something that cannot be done. We do not know the root cause. Without that, we know nearly nothing.
"[...] the gravitational force the Earth exerts on you is canceled out in a freely falling elevator" and "[...] it is impossible to distinguish acceleration from gravity"? Seriously?
Isn't acceleration the result of force? Isn't gravity a force? When you are in free fall you accelerate, gravity doesn't "cancel out"!
Similarly in the falling lift there is no force making you float, just an apparent relative acceleration that you experience as a force.
https://arxiv.org/abs/1504.00333 https://www.google.com/search?tbo=p&tbm=pts&hl=en&q=ininvent... http://www.ru.nl/hfml/research/levitation/diamagnetic/ https://www.youtube.com/watch?v=9EPlyiW-xGI&t=684s (guy from CERN) etc. etc.
if u want to look at universe, look at magnetism, dielectricity and inertia. many research is being done on this and practical applications have already been made in several areas of science / technoloy.
Think people should get rid of relativity, as it's completly made to assume something is not moving just for the sake of being able to compute things... everything is moving ,everything is in constant flux.