A drunk awakens in a void and finds his arms, legs, in fact all extremities are bing pulled outward by some reverse gravity. It is quite unpleasant.
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."
Only locally, though. The next galaxy cluster over has a uniquely privileged inertial reference frame, too, but it's in motion (and accelerating!) relative to ours.
I think you are wrong, observers in different galaxies will agree on the inertial reference frame in which the background radiation is isotropic. The relative velocity between different galaxies will show up as different dipole components in the measured background radiation, but if you compensate for that, you should get the same inertial reference frame no matter from which galaxy you measured.
I'll admit to not being a physicist and to being easily confused by the subject, so I'll just use a silly little metaphor to check whether I'm thinking straight, and try to avoid terminology I don't fully understand (which, since I don't have a particularly strong understanding of even special relativity, means not using relativity terms at all):
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.
Since you're the only thing in this hypothetical universe, you better make sure your urea makes it to escape velocity (which shouldn't be hard), otherwise you'll make it rain.
Anyone know of (or want to give) a clear explanation of how gyros behave? I found the article to be unclear on a number of points.
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?)
Gyros are really simple! Think of the gyro's ring as a series of independent particles flying around really fast in a horizontal circle. Now you push up at one point on that circle. Does the circle move up at that point? No. You're applying a force to each particle only very briefly before it moves past and you're pushing on the next one. But you do impart some upward velocity on the particle during its brief time under your influence. This causes it to follow an upward path away from the point where you're pushing, which will continue until the circular path brings it back down. This will tilt the entire circle along the axis connecting the center of the circle to the point where you're pushing.
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.
I think the phrase "...which will continue until the circular path brings it back down" requires a bit more explanation. At this point, you seem to be switching from treating the rotating ring as a stream of independent particles to being a rigid body, but if you treat it as a rigid body from the start, the first part is no longer obvious.
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.
If each particle is only tethered to the center, how does the circle bring it down again? If the tethers are all fixed to one another, we're back to rigidity.
Edit: I'm trying to think of a way to bring in angular momentum without having to derive it in full generality...
a spinning disk 'averages' its mass distribution. 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.
Yes, though I think you can avoid the question of why just "those specific parts of the disk" by considering a dumbbell (two joined, point masses spinning around an axis perpendicular to the center of the rod joining them) rather than a disk or ring, and a continuous torque. If you are pushing northwards on the axis, the maximum rate of change of the instantaneous velocities of the point masses is when they are aligned north-south, and when they are aligned east-west, there is no change in their instantaneous velocity from the applied torque. Integrate this over one revolution, and you get the axis tipping in the east-west plane. A picture would really help, maybe I can find one on the web...
indeed it tips perpendicular to the direction of applied force. and this is what happens in reality. try spinning a bicycle wheel holding its axle on both ends. now try to twist the axle and it curiously wants to move the wheel in a perpendicular direction.
You could imagine that they’re connected to the center of rotation with a string or something. You just need centripetal force, not a rigid connection to anything. Although that may still be more than what you’re after....
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.
Inertia is not a property intrinsic to an object but depends upon all the mass in the universe.
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?
Don't rely much on Mach's Principle. It's a philosophical statement with exactly zero experimental evidence.
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.
I once built a simple mass-spring physics engine, and this exact effect what was causing the wheels of my car-like mass-spring blob to bend "funny". It was only after I slowly debugged it (by removing friction, then gravity, softer springs, slower timescale etc) that I felt I really got how these forces come about.
Um, I must be missing something here, because feel like I have a pretty simple solution to why there's only a single rotational reference frame, and this is a problem that apparently eluded Einstein, if I'm to believe your link.
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".
>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".
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.
But if you were the camera you'd feel a force, or not, right? It's not like being in an elevator in free-fall, where you can't tell whether you're accelerating downwards or sitting still in flat space.
True, but the GP suggested that you can find the absolute reference frame by looking at the relative velocities of the dots (independent of any force measurements).
The elevator analogy breaks down if you're larger than a point-particle in a point-elevator. Gravity's force varies with distance, causing tidal forces on your body, allowing something large/sensitive enough to feel the difference. Gravity stretches you whereas uniform acceleration does not, and non-uniform acceleration compresses you.
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.
If it were gravitational there would have to be a mass in the right place to cause it. Maybe you could look at how the force changed as you moved around?
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.
Whoa. I kept reading past that, and the third answer by Logan R. Kearsley is almost exactly what I said, but better. I should have kept scrolling the first time I opened the link!
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.
I don't think a point can rotate. What would it mean if it did? There would be no observable change. So no, I don't think the absolute center point moves.
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.
The most fundamental particle can't rotate, because that would imply that parts of it had different velocities from other parts... but it doesn't have parts at all, by initial definition. So, Democritus' atoms imply that rotation is not a fundamental motion.
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...
I'm no physicist, of course. I had thought that 'spin' was metaphorical or analogous, like quarks' color and flavor, but Wikipedia asserts that it was originally considered to be rotation about an axis. So, I've no real clue. :)
>Certainly if you were alone in the universe, he thought, there would be no way to tell if you were rotating, so there could be no centrifugal force if you started to spin with respect to, say, another person.
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.)
I'd agree with your intuition in both cases, but it's worth pointing out the equivalence principle (falling in an elevator) isn't necessarily immediately obvious (which I know is not something you claimed). Feynman complained about philosophers who would claim it's obvious that motion was always relative but then wouldn't understand that the same thing didn't apply to rotational motion.
Let me refine that part: I think that what would physically happen in the elevator example is apparent to most (someone with knowledge of Newtonian physics may agree with the idea that the interior of a falling elevator acts identically with the interior of an unmoving gravity-less elevator), but people without knowledge of relativity and the experiments that lead to it may disagree about what the elevator example means about physics and the world.
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!
My (undergraduate) understanding of the precession of the orbit of Mercury is that the longitude of the periapsis in Sun coordinates changes over time. The shape of the orbit stays the same, unless maybe it's changed a bit by perturbations from the outer planets.
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.
Hmm, but if the perihelion changes position and the orbit doesn't change shape, the only other option is that the entire orbit shifts—is that it?
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.
"Precession" is just another word for rotation. It sounds like you're thinking of a spinning top, whose rotation axis will precess (rotate) around another axis (usually the local vertical).
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).
Thanks, that article does clear it up. So the orbit doesn't change shape nor does it shift, instead it rotates (from the article: "More precisely, it is the gradual rotation of the line joining the apsides of an orbit"—so I guess the ellipse major axis rotates).
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)
its rotation in the orbital plane changes due to GR.
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."
> If it is spinning extremely rapidly, the gyroscope remains rigidly locked in the direction it has been set, its sights fixed on...Kiev—hence the term inertial guidance systems.
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.
He elides the inner workings of an inertial guidance system because it's not really necessary. The point is that the gyroscope provides an absolute reference point, which seems weird in the face of relativity.
I agree, but the intro is all about how this magical gyroscope is pointing at Kiev, even making a point about how the gyro is doing it after being separated from the rest of the rocket.
Sure. It also has to be powered up and aligned to a known attitude and position within a not-too-distant past, because actual gyroscopes have friction and are not perfectly locked in space. Either the guy didn't actually know how they worked or he was pulling a prank.
that a spinning gyroscope does not topple has not much to do with Mach, Einstein, the universe or any such big idea. I can explain it much more simply.
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.
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).
The equivalence principle follows naturally from the geometry of general relativity.
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'.
So there was the animation that Caltech put out today or yesterday of the neutron star collision that was just detected, and it visualized gravitational waves moving outward from the stars:
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?
I think you’ve confused the notion of nothingness, which may or may not even be real in practice, and spacetime, which is definitely a thing. Gravity is a result distortions in that thing.
Short answer: because tachyons don't exist (i.e. haven't been found)
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."
* 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.
This isn't true. Given a manifold that satisfies the vacuum Einstein equations and given a world line in that manifold, it can be shown that the world line is undergoing acceleration using only local calculations/measurements. The worldline of a particle on the edge of a gyroscope will have a non-vanishing acceleration and this can be computed using local calculations/measurements.
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.
The only thing that is not an object (as such) that remains in spacetime are fields, whose state evolves according to the principle of relativity. Thus ensuring that you cannot measure your position relative to spacetime without getting "you are right here" as a pretty-much useless answer.
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.
Reading this bought immediately to mind watching Eric Laithwaite's Royal Society Christmas Lecture on the peculiar properties of gyroscopes. It's a shame he apparently pretty much deluded himself, because it was a great lecture
I can fit two thumbs in the header that won't go away. It's like reading trough a letterbox. Luckily I can use reader view but it would be better if it wouldn't be necessary at all.
This reminds me of inertial navigation system demo's that I saw a while ago [1]. I'd suspect that the targeting gyroscope in an ICBM would look very similar to that system.
One question I've never seen answered to my satisfaction: If you created a gyroscope with two counter-rotating disks somehow identical in moment and location, would it fight precession symmetrically, or act like a block of matter with nothing rotating inside it?
Aren't those the same alternative? If something is fighting precession symmetrically, then isn't it acting like a block of matter with nothing rotating inside it?
a standard gyro fights precession at 90 degrees to the attempted off-axis rotation, and shows way more rotational inertia than can be accounted for by the mass involved.
"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."
> Would you feel centrifugal forces in an empty universe? Does the law of inertia mean anything in an empty universe? Mach would give a resounding “no” to both questions: Inertia is not a property intrinsic to an object but depends upon all the mass in the universe.
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.
I don't get how the gyroscope is used in missile guidance.
How is the gyroscope mentionned in this article pointing at Kiev? How do you read it on the gyroscope and how is the position 'set' in the device?
Actually, the gyroscope will give your angular rotation. It can be achieved through different technics (MEMS gyro, mecanical gyro...) but the final goal will always be to give you your angular rotation.
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).
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 I'm wrong but it's wrong to say we don't know how a gyro works. We can accurately and precisely predict the behavior of a gyro, derive the mathematical equations necessary and the model we use is general for all moving objects. This is the greatest level of knowing you can have.
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 physics (and in many other areas) it is unsatisfying to wave your hands and say "it is so because our measurements prove it". A theoretical model that explains why the measurements come out the way they do is far more valuable because it leads to other insights.
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?
> 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.
Walk around to the opposite side of the gyro wheel. If the acceleration is due to the rotation of the gyroscope, it still points out radially. If it was due to a mass out beyond the rim, you're falling on your head.
What if the mass is distributed in a ring surrounding the gyro at a distance? How would you distinguish between spinning versus mass in that case?
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.
> What if the mass is distributed in a ring surrounding the gyro at a distance? How would you distinguish between spinning versus mass in that case?
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".
Seems to me the main difference is that all the particles in the gyro are trying to go in a straight line, but can't due to being a part of a rigid structure. You should be able to tell the difference by dropping a ball bearing. It will land "straight down" if it's gravity, but move "to the side" if it's rotating.
which is obvious because a gyro is not rigid and has parts the move relative to each other, but would the entire system feel a force if exerted on it and correct it's orientation? What would it be "pointed" at? If it did, wouldn't that imply an absolute point of reference?
>> 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.
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.
> This is the greatest level of knowing you can have.
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.
I'm not a physics major. So I may have made a major booboo in explaining this.
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.
> In the vacuum of space, if your body begins to spin, a force will pull your arms away from your from your body.
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.
You're speaking to the "how" that means how it responds to stimuli, but the article is speaking to the "how" as in why. The greatest level of knowing is not having rules for inputs and corresponding outputs, but the algorithm that controls it.
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.
> This is the greatest level of knowing you can have.
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.
Not enough. There's no reason why those can't be further reducible. We've already reduced most of those laws into more fundamental principles via Noether's theorem, for instance.
We can accurately predict lensing well enough to see the impact on particles of light - over billions of miles. We can't explain it.
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.
> 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), ...
>>We can accurately and precisely predict the behavior of a gyro, derive the mathematical equations necessary and the model we use is general for all moving objects. This is the greatest level of knowing you can have.
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.
In general relativity you can easily show with Noether's theorem, that in an space time with rotational symmetry there is a conserved quantity that in flat space is conservation of angular momentum.
> We can accurately and precisely predict the behavior of a gyro, derive the mathematical equations necessary and the model we use is general for all moving objects. This is the greatest level of knowing you can have.
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.
"[...] 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"!
General Relativity states that gravity and acceleration are equivalent, so yes, they cancel out. Unless you look outside you cannot tell whether you are in an elevator standing on ground on Earth (1g), or in space accelerating upwards at 1g.
It does because the frame is not inertial. There is a fictitious force “pushing you upward” because the elevator is accelerating downward. The fictitious force pushing you upward perfectly cancels the gravity pulling you downward and you feel no net force inside the frame.
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.
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."