Hey KZfaqrs, thanks for watching! Please note: there is an ERROR at 8:15 in our video. The equation KE = PE (kinetic energy equals potential energy) for the parabolic shape of the surface of the water is NOT a consequence of the conservation of energy as we wrongly state in the video (obviously energy is not conserved as the bucket must be spun by putting work into the system.) The equation KE = PE instead comes from setting the Lagrangian (KE - PE) equal to zero. Our many apologies for that mix-up! Next up -- if your initial response to this video is to ask, "why not just do such-and-such to the experiment (spin the masses, add more springs, throw a free-body, etc.)" to improve it -- STOP -- read this first. It may address your confusion. Due to the introductory nature of this video, we didn't go deeper in length into the essential argument Mach was making (we will follow up with it in future videos, not to worry!) about Newton's experiment. But we can lay it out a little more in-depth for the interested viewer here: Mach's argument was NOT about the lack of cleverness of Newton's experiment. He was not arguing that Newton's experiments were mechanistically insufficient for determining true motion, and could be fixed with some new addition that would detect motion in some way the old experiment might overlook. Rather, Mach's argument was about the essential limits of empirical knowledge. Many a philosopher have written books on this subject. There's Hume's "An Enquiry Concerning Human Understanding" -- or Kant's response to that book, "The Critique of Pure Reason". The conclusions of these works turn on essentially the same fact: that empirical knowledge is impossible without some type of aprioristic reasoning or prior knowledge of the system. Our goal with this video was to bring an example of that philosophical principle into the concrete realm of physics. Empirical knowledge hinges on measurement and observation; measurement and observation themselves hinge on a prior knowledge or a system of reasoning, from which more general conclusions may be extracted. In the stretched-spring example, the length of the spring is the "observation" or "measurement" which constitutes the raw empirical data. The understanding of what length the spring should take in an inertial system is the "apriori knowledge" or reasoning which allows the raw empirical data to be interpreted (i.e., via the logical statement: if spring length = inertial length, then frame = inertial; else frame = non-inertial) and a conclusion to be drawn. But if you don't already know the inertial length of the spring, the empirical knowledge of the length of the spring is in-itself meaningless -- an empty statement with no interpretation yet assigned to it. Thus, the knowledge of the length of the stretched spring can't be used to determined inertial-ness in a closed system, because assigning an interpretation to that length requires having access to a known inertial frame elsewhere. The key to understanding Mach's argument lies in then realizing that this problem extends to any measurement whatsoever. Without some prior (and as Kant would argue, "god-given" or "transcendent") knowledge, no raw data could have any meaning whatsoever. Thus, for every clever addition you can think up "just throw a free body off of yourself!" or "try spinning the globes!" or "add more springs!" you are in fact just importing additional a-priori systems of knowledge into the experiment, and then exploiting your prior knowledge of those additions to make a measurement of "absolute" motion -- and then claiming this measurement could still be made if no prior knowledge was ever had! But none of these additions would have any meaning without some knowledge of how those additions already work in inertial frames elsewhere. Another way to look at it: the argument for always being able to perform a test for absolute motion is based on the following inductive statement: "it works always elsewhere, so it must work here!" Since empiricism is essentially induction, this works fine as an empirical and scientific statement. But take away the "it works always elsewhere" (the rest of the universe) part of the logic, and what are you left with? A simple statement: "it works here" with no other justification. A very non-scientific statement, and why Mach would argue against it!

As Stanley lifted his bucket, he felt a connection to all buckets everywhere. This adventure, he decided, was for all of them.

In round one, the concept of "bucket", itself, references and depends upon the external gravity field. Astronauts on the ISS do not drink from cups (little buckets, containers with open tops) because rhe water only stays contained in the "bucket at rest" due to gravity. The equivalent experiment for space would require a closed container half filled with water, with the remainder as air. Preferably transparent. Shaking the container would distribute globules of each within the volume of the other. Whenever like globules touched, surface tension would merge them, until there were two distinct volumes, one of water, one of air. The interface surface would assume a roughly spherical shape by surface tension. At "absolute rest", the interface spheroid could occupy any position. In linear accelleration, the water would accumulate opposite the direction of acceleration. Spinning the container would cause the water to form a cylindrical interface outside of the air volume.

Try spinning the "stationary objects" connected by a spring. If they move closer together, then they were moving faster than now. Eventually you should be able to experiment until you minimize the length and find the absolute inertial rest state. If you spin them in one direction and they move apart, simply reverse the direction and repeat as above.

I think switching the third experiment's rope to a spring is what creates the need for remembering the state at rest. With the rope, you can always just pull on the rope at any place and the force of the two objects pull can be measured.

Perhaps I'm missing something, but I don't think you'd need to ascertain the size of the spring at absolute rest. In fact, you wouldn't need a spring at all. Why not just cut the cord. If the end goes flying away, it wasn't at absolute rest. If it stays in place, it is. Edit: I just realized that you might object to this idea on the same grounds that you objected to the bucket test in space - that the bucket of water would need to appear at relative rest in both scenarios. But that feels a little pedantic to me. In both cases, the bucket itself looks to be at rest, it's just the water that's moving or eventually completely gone. But if you necessarily need to still be observing the water, what about encasing it in a glass sphere that may or may not be rotating? Once it gets to an equilibrium, the water would be in two different states depending on absolute rest or not, but would also display relative rest for both. Or heck, get rid of the container altogether - m.kzfaq.info/get/bejne/eN6pmcxzrKnbmIU.html

One must distinguish between velocity and acceleration. Clearly, Newton had acceleration in mind. In the case of the bucket of water - when rotating the bucket, there are forces at work, hence the curve surface of the water, and the observer is in an inertial frame. But when the observer is rotating, the water surface is flat, but what is neglected in that case is that the rotating observer will experience a force, and is no longer in an inertial frame. And therefore, the rotating observer cannot claim that the bucket is at rest.

To determine whether or not you're rotating or not, couldn't you just let go of an object, and see if it stays motionless or not ?

14:38 _"The question then becomes: _*_How does the observer know whether the measurement they make corresponds to the shortest possible length of the spring or not?_*_ For in rotational frames, only the shortest possible length of the spring or its natural resting length indicates absolute rest. Every other length indicates varying amounts of rotation."_ Use a spring who's coil has no space at rest (ie. each loop of the spiral is in contact with the previous loop and subsequent loop). Thus, any visible space indicates rotation.

The spring works for Newton if you can vary the speed of rotation from wone observation to the other. The shortest would have the least spin. To find zero spin in that direction you would need to get the spring as short as it gets before getting larger again. At its shortest point would be the zero spin for that plane.

Crazy that Newton was so long ago and we still struggle to understand his genius. To have a set of physics and an understanding that lasts for so long

"Fire the sound engineer!" "The music is not loud enough."..I can still hear the very interesting lecture. Can think about the subject; But at least I can hear the music.

"Tension" could be an independent measurement. The absence of tension is rest, any positive tension is motion.

Regarding round 3 If the spinning object is a closed tube full of a compressible fluid then the observer would be able to observe the relative lack of pressure in the fluid at the center compared to the higher pressure at the ends of the tube and use that data to make some kind of deduction. This version would also work if there was air and water in the tube and the observer had to try and figure out why there was water at both ends of the tube and air in the middle. Also the limits of the tools used to observe the effects on the spinning object are relevant to the discussion. If the object was just a spring with no weights for instance the profile of tension in the spring would exist but it would look different.

Just put a lid on the bucket. If it's spinning the water will take the shape of hollow cylinder in the absence of other acceleration vectors (such as gravity). Make the lid transparent and you'll be able to see inside. Point to Newton. That said, one _could_ have a gravitational source spinning around the bucket, which would produce the same effect. So point to Mach, but not because of the water spilling out to space.

1. You have 2 globes attached to a spring like this: ⬤|/\/\/|⬤ 2. Attach identical spring and globe to the globe on right: ⬤|/\/\/|⬤|/\/\/|⬤ 3. Repeat step 2: ⬤|/\/\/|⬤|/\/\/|⬤|/\/\/|⬤ Compare the length of each spring. Now apply force to the rightmost globe (perpendicular to springs). With no prior knowledge the observer could discover there is some 'force' affecting the springs. Apply force from one side: the springs stretch more, From the opposite side: the springs shrink, Continue pushing. The springs reach the same size eventually. (They could achieve that trough trial and error with no instructions or without knowing what is it they want to find out) The observer could distinguish between the system rotating more, less and not rotating at all. They would just have no idea of knowing that not rotating is the inertial frame. And that when the springs have the same length, that is the inertial length of the spring. But still, the centrifugal force has to be absolute. If there are these 2 systems (one rotating one not) and 2 observers (one rotating one not). Then they would observe the same thing! One system would have spring more stretched than the other. The only think that would be relative is if they decide to label the state of 1st system to be rotating or label that the other state that. What is important is they could differentiate between each state and all observers would be in agreement!

Well the simple answer has to be that all measurements are relative. In order to conduct a measurement, there needs to be a standard against which whatever is being measured can be gauged. While a self contained system is rotating or doing whatever in empty space, an observer will be taking measurements against their own imposed standard, or indeed relative to empty space, otherwise no information is obtained and the experiment fails. The main difference in the approaches taken by Newton and Mach is whether or not the observer is external to the experiment or is part of the experiment. Therein lies the discrepancy in their results and conclusions. Thus motion can only be conclusively demonstrated by comparison to and against some other object or standard and is therefore relative to that object or standard.

Hi Dialect, great video. I have to say that i don't agree that the case of the spring requires knowledge about a different distant system, you just need that de observer can actually make an experiment (interact with the system). You can locally define the restness of the system as follows: "If, when you change the state of rotation of the system in any direction, the spring increases its tension, then the system is at rest. If there is a direction such that, when you make the system rotate in that direction, the spring decreses its tension, then the system is rotating in the opposite direction."

Well, you can use two systems of coils and masses, the masses made of the same material but with different volumes (so they don't have the same mass). If the systems have the same length they are at rest, if not they are rotating.

I would say there is a difference between being able to discern between a rotating and a resting frame, and being able to tell which is which. I always thought Mach's argument was about the first, not the second. As you say, for the second you need knowledge of the physics that you must have acquired in a system that you believed to be, say, resting in the first place. You don't need this for the first question. And I consider the first question much more meaningful. After all, you can just CALL a system resting if the spring is minimally stretched, and no one can prove you wrong because thats just your definition of rest.

Simplify the experiment a little, have just a ball of water in space. If the shape is oblate spheroid, then it's spinning. If it's perfectly round, it's at rest. After all, a bucket of water in space would never be flat, ignoring the fact it would freeze instantly. I think the hardest part of this experiment is getting anything to absolute rest, even empty space is expanding.

As I appreciate this channel a lot, let me play the Advocatus Diaboli: The tension in the rope or spring has an absolute observable: the point of rupture. And, if it is true that gravity generates observational differences in the bucket experiment, doesn't this mean that acceleration too would generate them, ultimately making it possible to tell an accelerating object apart from a stationary one? In addition to that, isn't the difference posited by a gravitational field only quantitative, that is, there's a difference in shape and behavior of the water, but not a difference in the ultimate fact that the water moves when the motion is on the bucket, but remains still when the motion is on you? I believe there's a long and fruitful discussion possible on this subject.

15:59 I don't think so- the observer could cut the connection between the two masses and measure whether they moved apart using the measuring stick. If the masses moved apart after cutting the string, the frame is not inertial. If they did not move after the severing of the spring, the frame is inertial. No calibration is needed to determine this.

This is my new favorite channel -- the production value eclipses that of anything I've seen on KZfaq! Your videos are extremely well thought out, and equally well presented. With this particular video, I do think that something is being overlooked here. With centripetal acceleration being given as a=v^2/r, and force given as F=ma, we see that the centripetal force scales proportionately with the masses of the objects at the ends of the springs. Thinking about this in a purely intuitive way, two space shuttles orbiting each other on opposite ends of a tether are going to exert much greater centripetal force on that tether than two Apple watches on a similar tether with a similar rotational velocity. So, your difficulty in calibrating this hypothetical rotational measurement tool can be resolved by attaching different weights of known masses, then measuring the tension at the same observed rate of rotation. Assuming you are in the linear region of spring tension where Hook's law holds, it should be possible to deduce the zero mass tension by linear regression of known nonzero mass data points. Alternatively, you can detach the masses and measure the relaxed spring length, although this neglects the nonzero but probably negligible mass of the spring itself, and the possibility that it (and you) are spinning when measuring it. Hence the suggestion to use large, known masses that should dwarf any negligible mass the spring might have. When you find a frame of rotation in which the spring tension is constant regardless of the masses selected, and when this tension is equal to the spring's natural resting tension (as measured or as calculated), then you have achieved rotational stationarity. 🙂

The final argument is bogus. And yes, I'll address the "a priori knowledge" argument thoroughly below. The rotating observer could orient the spring/weight system in different directions (the weights could be constrained by letting them slide on some rods). In zero gravity one could even just observe a sphere of water held together by surface tension (or a water filled balloon). If it rotates it becomes an oblate ellipsoid, unlike a sphere when not rotating. The axis of rotation would emerge to be special I.e. he doesn't need a refernece frame outside his rotating system to know he is in a rotating system. Also in a rotating frame of reference there's not only a centrifugal force, but also a coriolis force, which could also be measured. In fact it is possible to determine earths rotation even in some laboratory without any view of or access to the outside world, or any a priori knowledge beyond F=m*a, given sufficient experimental equipment. Foucaults pendulum is a well known experiment. Even without *any* prior knowledge at all eventually (after taking a few centuries deriving the laws of motion) phsicists in a rotating reference frame would find out that there is a special direction (the axis of rotation), and be able to determine that they are in a rotating reference frame and the angular speed with which they rotate. At some point they'd be able to counter that rotation and generate nonrotating environments for experiments (analogous to microgravity environments). In fact that's exactly what happened when physicists experimentally demonstrated, that it's not the fix stars and the sun that somehow rotate around a still earth but instead the earth is rotating about its axis. Up to that point no physicist or in fact any human had ever left their rotating reference frame: earth, yet they were able to distinguish between these situations; a rotating earth vs. a still earth with everything else moving around it, based on experiments they did in that same reference frame. Your "clever" argument about a priori knowledge just demonstrates your lack of understanding the physics or even the history of physics. It is unhelpful to pick up a thought experiment from 300 years ago, stretch it beyond some limit irrelevant to the underlying question, and based on those limitations crown a "winner" especially when the creator of said thought experiment is long dead and can't respond. This is not how physics works, neither as a science, nor in nature. It's like arguing that eventually the buckets would rust and the water evaporate, so Newton must've been wrong. The true problem with "absolute motion", i.e. (linear) acceleration, is that it is indistinguishable from the forces experienced in a gravity field, something that Einstein based his theory of general relativity on. Newtons bucket experiment is about absolute rotation (i.e. a separate case from linear acceleration), and for that Einstein coined the term "Mach's Principle". To my understanding Einsteins conclusion was, that if the whole universe (all masses in it) were rotating at a fixed rate it would be indiscernible from a situation without rotation. The Lense-Thirring effect seems to support this. There are really better discussions and arguments to be found on the subject of Mach's Principle with minimal search. The sad thing is, that this is really an interesting subject and scientific discussion, but the arguments presented in the video are just silly and lead to nowhere, or worse, a misguided illusion of understanding. If this video is supposed to demonstrate dialectical reasoning I'm not impressed.

15:53 Just move the spring around into various orientations to see if its length changes. Its length should be the minimal length whenever the spring is aligned with the axis of rotation

Such a great video. It addresses the concerns I have had with understanding inertial frames.

One of the things I seem to not really understand: You said that in the experiment with the two globes and the spring the observer in the rotating frame could not know that the length of the spring he observes ist not the shortest one. But why doesn't he just try to rotate the two globes in his frame? If he would by accident cause a rotation that at least partially counteracts the rotation of his own frame the spring should shorten, or am I missing something? Of course the observer would not a priori know which axis of rotation he had to chose. Additionally he could accidentally let the globes spin "too fast", i.e. such that in the inertial frame both globes spin in the opposite direction than the observer, but faster, in which case the spring would extend. But the observer is not limited to one experiment. He can vary the axis of rotation and the angular velocity with which he spins the globes in his frame arbitrarily often (systematically or randomly like in a Monte-Carlo-type experiment). And by varying in smaller and smaller steps he would eventually reach the point where he observes that the spring shortens, i.e. he is in a rotating frame himself, or he would give up when he is sure that the angular velocity of his frame had to be so small that the error introduced by assuming that he is in an inertial frame is negligible compared to his error of measurement. So the observer could either determine in potentially infinite time whether he is in a rotating frame or not, or he could determine in finite time whether he is in a rotating frame or approximately in an inertial frame. And the "approximately" would also be the case with any other realistic experiment because of measurement error, so it should not be a problem, especially because the error could be reduced arbitrarily by just varying in smaller steps (i.e. more repetitions of the experiment).

For anyone researching this, it's Principia Book I, Definitions, Scholia, Part IV. The 'pillars' are actually four: time; space; position; motion. Important to note that Newton makes a distinction between 'true' time, space, position, and motion "temporis, spatis, loci, et motus veri" and 'absolute' time, space, position, and motion, "temporis, spatis, loci, et motus absoluti", making the issue a little more subtle than how it is usually regurgitated.

Both thought experiments are limited in that they are attempting to observe only one type of movement while other types of movement are possible and the experiments cannot test for them. Are you moving or is it only me? Great vid!

Very good and well-explained, but I think you've changed the "2 connected bodies" example by swapping the cord for a spring, and then reasoning about the measuring the length of the spring and what meaning can be attributed to that measurement. In the original version, where a cord was used, there was no suggestion of measuring the tension in the cord by measuring its length (with its consequential need for a rest-state length-reference). If a reference-free method of determining the presence (in motion) or absence (at rest) of tension in the cord is possible, then the arguments used about length are not applicable in that original version. It's a pity that some discussion about the direct determination of whether or not tension is present wasn't at least covered. Is reference-free detection of cord tension possible in therory - and in practice?

There's a flaw in your argument. You could make the spring change in length by spinning it. Even if it seems stationary to you, it would apparently compress when rotated in a reference frame that is rotating in the opposite direction.

Time is fluid and variable. The time in the center of the bucket is moving less because there is less motion, therefore it is faster (high pressure), while the mass at the edge of the bucket is moving faster, therefore causing time to move slower (low pressure) and the difference in time pressure produces "lift" and in this case.

Take the spring experiment, and set up 2 of them axially aligned and counter rotate them at the same rate relative to yourself [the observer], then if they stretch the same amount then you must not be rotating, but if one stretches more than the other, this could be used to determine which way you are rotating, and by how much.

Thanks for this. Is it possible to fashion a spring that has uniform spacing when at "absolute rest" and nonuniform spacing when at "absolute motion"? That would solve the problem with Newton's hypothetical experiment(or would it?). I don't know how springs are made or their limitations.

@Dialect Hey in round 3: The observer could try to rotate the spring and then measure the differences in length without relying on external universe for information and proves whether the spring is in absolute motion or not. For example if the spring is rotating (absolute motion) in clockwise direction and if the observer rotates it in anti clock wise direction, then the lenght of the spring will decrease, instead of increasing. In case, when the spring is not actually rotating (absolute rest) then the spring length will always increase in either direction (clock wise or anti-clockwise)

Just rotate the object a little with your hands and let go. If the spring becomes shorter, you know it was spinning opposite the direction you rotated it in. If instead it becomes longer, rotate it back until it's back to its original length and keep rotating it. If the spring becomes longer again, you know was _not_ spinning. If it becomes shorter, you know it was spinning opposite the direction you're now rotating it in. Correct? Gyroscopic effects like precession would give you ways to test whether a rigid object is spinning. The video seems to assume that you can only look at these objects and can't interact with them in any way (maybe that was an oversight?). When you're able to interact with them, there seem to be all kinds of ways to tell whether they're spinning.

I find round 1 and 2 are no different really. If there were no friction between the bucket and the water. Wouldn't the water stay unmoving in the rotating bucket ? So one assumes a friction force between bucket and water. What if there were other forces, like capilary ones that suck water up at the edge ? So in order to evaluate all the forces that exist between bucket material and water, one would also need to be able to compare with the "unmoving" waterbucket setup. Just like the spring setup. I think...

15:26 observer can additionally rotate all that in random directions and if he finds one where spring is shorter than now or shortest at all then he found the natural state of the spring and also he found out that spring and masses were rotating before. Pretty simple !

If space and time are relative, motion cannot be absolute because change of places (in time) refers to 2 relative concepts.

I did the bucket experiment at age 4 at the beach on Galveston Island back in 1961. I'd just been given my new plastic pail and shovel. While our mother was waist-deep in the water catching "Blue Claw" crabs with sticks, strings and soup bones, I was filling my pail with beach sand and swinging it around in fast circles high over my head, spewing it out like a tornado until it was empty or I got too dizzy to finish. It wasn't my fault my little sister kept getting in the way. I blame science! Mom didn't buy it though. She took away my gravity bucket but there were so many other scientific things to use for "little kid scientist" study.

Isn't missing from this video a crucial argument of Mach: that we cannot tell whether we are measuring absolute rotation or just rotation relative to all the other masses in the universe. What if all matter of the universe would rotate with the bucket/spring. Would the water still curve? Would the spring still stretch?

Could you use 3 identical copies of the mass-spring-mass device and orient them in 3 orthogonal directions? I'd figure that would allow you to determine which axis you're rotating about.

I am absolutely eager to see your next video!

Seems like there are multiple mechanisms to determine whether you are in a rotating frame of reference. You could have a track parallel to the cord connecting weights with a weight that slides back and forth. If in a rotating frame of reference the Coriolis effect would impart a sideways force to the weight. Or you could spin up a gyroscope and notice if it mysteriously tries to rotate (actually resist rotating).

Place a thruster on one object perpendicular to the line through both objects. If nothing changes but the distance between the objects they're spinning, and the math should tell you how fast. (Would need a couple tests to determine the orientation)

Round four: spin two spinning buckets of whiskey. The eyeball drinks a drop each time relativity is proved due to coriolis effects spilling the whiskey and gets so drunk, doesn't care about absolute space proof anymore and starts talking about the aliens it sees instead!

Acceleration is absolute because the observer will see the spring extending. Therefore, acceleration is always observable.

Correction (?) - in a spinning spring experiment, an observer can apply equal forces to change the angular velocity of the spring in both directions and observe how much the spring expands or contracts for each application of force. The difference will reveal what angular velocity (with respect to the original observation) represents absolute rest.

Hollup, in the first round, what if you made the bottom of your bucket either hundreds of kilometers thick, or extremely dense, so that it had its own gravitational field that it could keep the water in the bucket even when the whole thing is spinning? I guess it depends on how local "local" is, perhaps a bucket is already too macroscopic. I'd be interested to know if there are any quantum effects that could be used to probe this question Edit: Well now after watching your other video on the twin paradox, I guess you could just define a new set of laws of physics by the principle of general covariance and then you'd be able to say that both are stationary solutions to your new laws, and who can say you're wrong if it all checks out. I can't tell if that feels like cheating or not...

Round 3: Just cut the connection between the two masses and the spring and look, whether it retracts. If it does, you're in rotation. If not, you're in rest. No outside information needed, you only have to bring scissors along ;)

In the two ball connected by a spring experiment. An alternative would be if you have two identical springs, both with no masses attached. Then one spring has masses attached to it. If the assembly is not rotating, the two springs will still be the same length. If the assembly is rotating, the two springs will be of different lengths. In this case we only need a ‘local reference’.

One thing I want to quickly note is I very much disagree on the presentation of the history and sides (labeling absolutists dogmatists), muddling some history of science (some things with Newton that are more slight). More particularly, Ernst Mach didn't have an irreversible impact on physics in the sense of a paradigm shift. Essentially, Mach's principle while an initial motivating principle Einstein himself had later rejected once he had cleaned out some of the remnants of his theory. So what exact impact did it have? Now, I am somewhat confused about your depiction of the bucket argument and have some criticisms. In round 1, mention that Mach wins because Newton needs a gravitational field. But all this gravitational field does is show what it needs to be concave. Rotating along with the bucket in free space, the bucket will still appear to be at relative rest and the water goes everywhere, so this would ultimately be a win for Newton since it has demonstrated two clearly distinguishable cases of a bucket at relative rest. In round 2, I agree. In round 3, fair point but you can tweak the argument. Suppose you attach a spring around the string. Now, you cut the string at the ends. You will the observe a stretching of the spring that wasn't there, caused by tension in the string that held the spring there before. So, in this form, Newton wins. So, I agree with Newton on all counts. But I do not believe in an absolute rest frame and am a full on relativist. How is this possible? I once again believe that the framework general relativity holds all the keys and allows the essential observations of both points of view to be right and I will draw out a depiction. See, a core assumption in all of these arguments is made, and that is the inherent description from a 'frame'. But what if, we considered instead there to be no intrinsic notion of a 'frame' and that all 'motion relative to a frame' is itself based on motion of observers to comprise that frame? Considering motion to be the 'evolution of a physical object throughout space and time', the idea of motion then is an absolute one, and it is the relative nature between two kinds of motion (of an object and of that frame) that then allows one to characterize motion in this relative way that leads to this sense of observationally distinct characterizations of motion. Physics is the study of absolute physical laws (to a given degree). If laws of physics do not hold in other frames, those aren't a law of physics but a law of physics in that frame. So, all laws of physics (albeit in a very different, tensorial form) are expected to hold irrespective of the choice of frame and be absolute, although the form of characterization once put against a certain frame may be different. Historically, this meant given the a priori picture of euclidean space, for the need of an absolute rest frame. But, with invariance of laws under inertial frames, physics with respect to relatively chosen inertial frames was sensible, where the nature of such a frame was seen as implicit. But, the advent of Einstein's theories of relativity gradually took time to undermine this idea, with the idea of coordinates not having intrinsic metrical meaning to be pretty much Einstein's summary on the difficulty of general relativity. With the global inertial frame dismissed, the intrinsic meaning of a 'frame' was lost. Here is then the description: consider the manifold of space-time which is physically defined as the coincidence of space-time events. An object's motion is simply a world-line on this manifold. Now then, when I say in my frame an event occurs at (5m, 12s), what that really mans is that I take a form of a meter stick and place a clock at the marking on the stick for 5 meters, then that event will be coincident on that marking on the meter sick when the clock reads '12 seconds' on its face. (this is the point coincidence argument) There is no intrinsic measure of time beyond this. I can more absolutely and mathematically describe this as a world-line for a clock and a world-line for the observer (and a world-line of a light beam defining their synchronization) that intersect and this intersection is the measurement of 'time' for that observer [there is a better definition overall in terms of cauchy surfaces but this is the more clear physical depiction]. Moreover, given the lack of meaning behind an 'intrinsic measure of time', means it comes down to a certain test of clock synchronization that this works which needs observers on either end. Thus, a frame is ultimately not a single observer but a prearranged collection of observers undergoing some understood motion connected in some way. It is up to experiment to find how these relate together. (details of this type of reasoning is in the idea of world-line congruencies and frame fields) In your spring example, you would need two observers on either end of the ruler to read out such a measurement. But notice-for this to make sense, they need to have clocks synchronized to which they can then read out both parts. It is up to experiment to then synchronize and see how our different measurements of time compare. If you were to try to do synchronization in rotation, you'd find that it would in fact fail (reading up on Born coordinates and Rindler coordinates would be helpful) and this would tell you that your frame is not inertial. The stars can be entirely forgotten about if you allow yourself a global enough arrangement of observers to consider your relation to so that in an empty universe. More realistically, you would observe the nature of forces of these objects (the geodesic equation as the 'law of inertia' is what connects these two although thats a whole separate point) Thus, the 'relational interpretation' is NOT between you and the stars, but you and the rest of the world-lines around you. Notice then that inertial and rotational motion are clearly distinguished by their relation to the metric of space-time (one is geodesic, one isn't) but that this doesn't mean that there is an absolute 'state of motion' (that is, a characterization with respect to a frame, so the typical description of 'rotation' or 'linear' motion in the coordinate way). Rotational motion can be seen with respect to a rotating observer to be 'at rest' and still account for all the observations around them and yet for inertial observers to be no more fundamentally special. Now, Mach's principle is often demonstrated as 'matter elsewhere influences inertia here'. That is, you start rotating and notice your arms come out and the stars rotate (or, the bucket spews out water). You identify the force on your arms based on the large-scale observation of the stars rotating around you. So, do the stars influence the inertia here? No. The core aspect of Mach's principle in relativity is hidden in the form of Einstein-field equations. In this form, matter elsewhere influences the space-time there which dictates the inertial world-lines there that gives information on the space-time and world-lines here. In the case of far away stars, to an approximation, inertial world-lines correspond with motion with the stars themselves that act in a certain way with respect to yours. You undergo your own entirely distinct world-line. But, would you be spinning, now have a background against which to compare to known inertial world-lines and then conclude you are not inertial but rotating. Do you find this to be a satisfying resolution, I find this to be very satisfying and tying up pretty much all loose ends.

Brilliant exposition, thank you. I've been scratching my head about this since I first heard about it. In particular I wondered how an isolated star 'knows' that it's spinning and therefore 'needs' to be an oblate spheroid. I just thought I was dumb... I still think I'm dumb but it appears I have good company.

Imagine finding yourself in a black void, lacking of everything except two masses connected by a string right in front of you and your first thought is "lmao am I spinning or what"

In my experience, whenever an argument descends into the depths of philosophy, everything falls apart and nobody can explain anything. It's like asking "but why" continually to any response to a question. It always ends up in "because that's the way it is". That last bit of throwing memory in there just puts us in this spiral of confusion. You can destroy any argument like this! What is 1+1 ends up with questions about what is "1", what is "+", how do you know, blah blah. Philosophy can often be a trap.

Great video! I'm going to add to the "why not just do such-and-such" chorus that you mention in your pinned comment. I hope you don't mind. But suppose you gradually apply torque to the spring-mass system to get it to rotate at different speeds. You don't need to reference an inertial frame to do this, and, pausing at each speed, the system will be in equilibrium, with no parts moving relative to each other. Your goal as an observer will be to find the rotation speed at which the spring length is at a local minimum. A system which minimizes the spring length will be in an inertial frame. So you will have identified an inertial frame without prior reference to one, or so it seems to me.

This channel deserves way more attention than it currently has.

I'm not sure if I got everything being said in this video. The question of Kantian philosophy as against empiricism and, on the other hand, rationalism has dutifully been raised. Now, of course motion has to be measured and acceleration can be detected by its effect. I think we are getting very good questions and explanation here, what I seem to have noticed, though, is that the dichotomy between mechanism and teleology has not extensively been considered: there is, to say it in a simplified manner, a matter of the point where a force is being applied and what the effects may be depending on the initial direction of, say, an object already in motion. That object in motion has a direction regardless of the fact that "there is" absolute direction or not.

I think it's easier to understand the limitations of the thought experiment if one imagines the observer as someone looking at a video feed from a camera attached to one of the balls. The observer cannot change anything in the system and would not feel any effects of gravity or rotational forces. Just a live image. Without knowing the properties of the spring it would be impossible to calibrate against a ruler even if a reference frame change occurs and the spring shortens. You will have no way say "this is the shortest it will ever go and therefore at rest, let me record the length now". This reminds me of the hosts in Westworld asking "is this now?" when they come back online...

Aren't these discussions about the relativity of ACCELERATION instead of MOTION?

Really great explanation, thank you!

Great job on most of these videos! 15:40 "Only by measuring the resting length of the spring at a time and place when they were certain there were no external forces at work could they ascertain what corresponds to absolute rest" Incorrect. Certain rotations would result in shortening and others in lengthening if a co-rotating observer believed they are at rest. However your point is still good on the issue of dependence on an external reference. The aspect of rotation to focus upon, however, is merely inertia. Straight lines are attempting to be preserved. However, there's something called frame dragging or "lense-thirring" effect that actually defies absolute motion as well. A round-the-world sagnac experiment (via satellite) verifies that space itself swirls around the earth out of sync with the earth's rotation. It comes down to the aether, of course. All of these attempts to define things without reference to something are an exercise in tarski's undefinability.

This is why many physicists dismiss "thought experiments" as nothing but hypotheses waiting to be tested. Assumptions in these scenarios are insidious and difficult to identify until it's necessary to explain why their conclusions are wrong.

One thing I find interesting about absolute motion arguments is that they always rely on rotational motion, not translational. Could it be possible that spacetime/motion is only absolute in orientation but is relative for any linear translation?

If the spring was stretched KZfaq rotation rather than gravity oven external body there would be some axis and Direction around which we could rotate the spring dual-mass system so that the spring would be shorter. In a rotating to mass system with the spring providing centripetal force the spring will always be stretched so you could always find the non rotational acceleration frame of reference by giving a spring 2 Mass system a torque until you found the minimum length of spring. That way you would know there was no rotation. Now does this finding actually agree with Newton or Mach? Well maybe neither. You don't need an external universe to determine rotation but you do need a system with at least two masses and a tether. So rotation is dependent on relative motion but it could be the relative motion of the parts of an isolated system in another wise empty universe.

the 3rd round is Newtowns. he suggested a string, where tension goes to zero in a measurable way... not crossing to negative tension. What gave the round away is you changing to spring, where the zero point is more subjective because you can cross over zero without noticing

In practice, it's easy to resolve the issue of the resting state of a spring connecting a pair of masses. Simply select a spring whose resting state is fully compressed, with each coil contacting the two coils on either side of it, but not exerting any pressure on those adjacent coils. Such a spring can be stretched, but cannot be compressed, making it an appropriate device for measuring the centrifugal force produced by rotation. When the experiment with attached masses is conducted, any measurable deflection of the spring will indicate rotation.

The “music” is competing with the dialogue. Too bad. I can’t listen to this. It’s so loud it’s not even background. Please Get rid of it.

The real problem I think lies in the nature of “thought” experiments as opposed to real world experiments: it is for instance impossible to do the bucket 🪣 experiment in gravity free space, as there the sentence “in the bucket” i.e. confined to the bucket has no meaning, the water would clump together and not exert pressure on the walls and thus friction would not drive the water ….. apart from the fact that water needs pressure to exist at all….. On the other hand, if no masses are attached to the spring, it has no reason to stretch even in a rotating system, so take the masses away or increase them and you’ll see a change in length … or not, and that decides and answers the question.

I think we can devise an experiment in 18:58 of video. Suppose we, on earth, knows which one of Red or Purple is at rest, but this information is not available to Red or Purple (To keep the argument simple). Let's say that in our view, Red is at rest, and purple is rotating clockwise. What will Red see? Red will see that the length of spring for Purple is long than his own, while Red is at rest and Purple is rotating. What will Purple see? Purple will see that the length of spring for Red is shorter than his own, while Purple is at rest and Red is rotating. They can use this information to see which one is at actually at rest and which one is rotating. Here comes a question, what if both of them were rotating at different speeds? The information of which one is at rest and which one is rotating is outside information obviously, and we want to devise an experiment for both of them to be sure if they are rotating or are at rest. Let's see what they can do. Both of them decided to come to rest w.r.t. to each other. In their perspective, both have same spring length while in our perspective, they could be at rest or rotating in same speed and phase. The problem reduces to can they both know what is the case? Let's see the Purple's perspective. Purple will see that he is at rest. He instructs Red to rotate clockwise, and then anti-clockwise. If the length of Red's spring increases both time, then they will conclude that they are at rest. If in one case, the length of Red's spring decrease, they can infer that they are both rotating. Is this consistent or I am making some mistake here? This is something like a test which we can do qualitatively, and no prior measurements or calibration is required. Only required information is that spring stretches when it rotates, and the stretch is more as the speed increases w.r.t. inertial frame

Circular motion, is not simple motion, because the objects are constantly changing their direction. This makes circular motion vastly different from straight line motion.

The internal tension of water in a spinning bucket is not distributed evenly. The outside edge (the water in contact with the bucket) experiences more friction (due to adhesion), so it will move faster than the center, which is only touching other water. It’s this gradient of adhesion that causes the outer parts to rotate faster than inner parts. This would be visible to an observer who moves with the spinning rim. Also, the outer water is under higher pressure than the center due to centrifugal forces. So, it’s pushed in the only available direction, where the pressure is lower: upward, into the atmospheric air. Since the total quantity of water is fixed, this pressure-based extrusion of the outer edge of water in an upward direction draws inner water away from center, causing the level there to drop. What you end up with is a parabola rotating around a central axis. Centrifugal forces are the result of phenomena that are external to the water and bucket. Gravity experienced by massive objects is just an effect arising from the inverse of these same phenomena, which is why gravity can be simulated on the inner surface of a spinning wheel. Mach was correct. Space is not fundamental, but is only an effect that exists relative to matter - the bifurcation of an underlying medium into both space and matter. The truth is that nothing is ever at rest, and no region of space is ever a true vacuum. By zeroing out both space and motion (by treating them as though they can go to zero), Newton was oblivious to the phenomena that give rise to both inertia and gravity, and thus the origin of centrifugal and centripetal forces.

In the bucket experiment if you give the bucket wall infinite height and if they are parallel, the idea would work outside of a gravitational field. If r of the water equals R of the bucket wall you have motion if any of the water is less than r the water would be at rest. r=R motion, r

Very important topic! Kind of surprised that no Einstein is mentioned; after all General Relativity is all about relative accelerations, which is equivalent of gravity. GR means relativity of any motion.

Newton's bucket experiment would support Newton where the bucket of water, absent of gravitational field (nearby mass), were accelerated towards the open end, then spun. This would hold true regardless of the direction of acceleration (and corresponding orientation of bucket and spin direction). However, in support of Mach, assume the above bucket of water, accelerating in the void, and rotating was large, and floating upon the surface, midpoint between the axis of rotation of the large bucket and its wall, was a platform with a smaller bucket of water, oriented normal to the surface of the water at that point of flotation (and traveling with the water of the larger bucket), and which the smaller bucket is spun, the water in this bucket would also climb up the walls of the smaller bucket.

This is by far the best (in fact the only) video of the in-depth philosophical arguments about the nature of reality which is essential before going into the maths, I've always wanted this. Newton's pillars of absolute space and time only came crashing down dramatically because of a simple change in the definition of reality. Seems to me reality is defined as the way light reveals it. That's because it is the fastest and that in turn is the only way to explain why it's constant for all observers regardless of their own speed which is totally counterintuitive. However, have this sneaky feeling (heresy) that Einstein's space - time models would crash and Newton's pillars rebuilt if another explanation was found and instantaneous communication was discovered. I know relativity is well borne out in experiments but they could be right for the wrong (or not completely right) reasons.

They just say "motion is relative" without distinguishing between linear velocity, acceleration, a single point spinning, or circular movement around a center point... For two setups, one with a rotating water bucket, and one with the water bucket at rest but the universe rotating around it: The centerpoint of the bucket would be the only place where these two could be considered to be the same system under different frame of reference. But for at other point, the two systems are different, because something different is going on in them: The walls of the bucket moving, vs. the surrounding stars and galaxies moving at much higher speed around it. For the spring's rest length: for a real spring, it could probably still be calculated by taking the material and shape into account, and the forces between the metal atoms. The rest length would be the result when no additional (centrifugal) forces are added to this.

2:34 : did you read it ? if not what to you like to read / what have you read to get your knowledge ?

I would say that the experiment with two spinning masses connected with a spring can still be done without calibration relative to some external system *if* the observer can vary the rate of spinning. If the spinning is varyingly slowed and sped up (slowly enough) the observer can see the spring stretch and contract and measure it. The observer can then measure the shortest length of the spring and use that as a reference.

I am with Mach on this, even the bucket in space, in stationary form the water would drift off, it is only kept in the bucket by gravity, also the bucket's own gravity, and the surface tension of the water are fundamental, but without going that deep, I just agree with the assertion that absolute motion is impossible, it has to be relative once you accept time and space to be

Also the experiment you show at the end can be determined who is in motion with time dilation. Quantum clocks at each end can determine motion. Also if you measure the length of the spring than synchronize the motion and have the come to rest relative to each other and measure again the change between measurements will who is moving relative to each other.

Personally, I'll never understand why the co moving reference frame isn't a universal standard for absolute rest. When you measure the same temperature of the CMB in all directions, the only objects that move relative to you are also moving relative to the CMB.

The water does not get ‘flung’ outwards towards the walls. This ‘centrifugal’ force is simply the inertia of the water trying to continue in a straight line.

Really impressive, including the comments! Subscribed instantly.

Wow! Super impressive production quality and presentation!

This is a beautiful thought experiment. Both Newton and Mach are correct in asserting that external information is necessary to make sense of this experiment which attempts to locate reality. The surprise is the fact that neither of them had any idea of the source or pathology of this external information. Even today, nobody understands what is absolute about rotational motion. We know, on rotating systems, that the speed and the angular acceleration are in lockstep. When the acc. is zero, the speed is zero and the system is stationary. This relation does not exist in linear motion. Anything slower than one percent of the speed of light is as good as stationary. If I ask you how fast you are moving right now, a question about linear motion, I would expect a common answer: Relative to what? the Earth, the Sun, Sag A*, or the local group? I suggest three of those answers must be wrong and nobody knows which it is. Here is another question nobody can answer: On the spinning spring experiment, what is it that is right here, right now, that is pulling on the spring? It is not gravity. It is not the Earth. It is not the Sun. It is the same thing that is influencing Foucault's Pendulum. What is it? I suggest that galaxies create their own inertial frame of reference. I use the term "Galactic Plasma" as a placeholder to label the massless plasma of the galaxy that is moving at c., functioning as a medium that is not stationary. Science has not found such a thing. I can explain many details of physics that are consistent with its existence, but I cannot prove it exists. Einstein believed there would have to be some kind of Aether. The Michelson-Morley experiment proved there is no stationary aether, but left us with no further explanation. Looking forward to the next video!

Dialect, you have produced an outstanding series of videos. The quality of analysis and presentation are exceptional, and the choice of subject is spot on. I believe understanding the Twin Paradox and Mach's Principle lie on the path to the next breakthrough in physics. The Twin Paradox illustrates that while time in Newtonian physics is one thing, time in relativistic physics are two quite distinct things. Two objects start at a common set of 4 coordinates, diverge in space, then meet up at a new common set of 4 coordinates. The start and finish points have common coordinate times, but the objects arrive at the finish with different (elapsed) proper time. Coordinate time and proper time are profoundly different. Coordinate time is a dimensional property, like space, that can exist without the presence of objects. Proper time is a scalar property of objects, like energy. Because we grow up seeing the world as Newtonian, I think most physicists don't appreciate how different they are. I postulate that coordinate time is actually a fourth spatial dimension, with baryonic matter arranged in the universe as a bubble, inflated by radiation pressure. Baryonic matter is held in place by minimal surface bubble physics, with gravity acting like surface tension in a soap bubble. Our 3D classical world is the bubble surface and the quantum world is 4D space. Baryonic matter therefore scales as R^3 and radiation scales as R^4. When baryonic objects move, they tug at the bubble surface, which is the origin of inertia, and explains why inertial and gravitational mass are equivalent. Minimal surface bubble physics is the mechanism of action for Mach's Principle, and provides the missing link between the distant stars and the motion of objects. Our place in the expanding bubble is the universal reference frame against which motion (including twins and buckets) can be assessed. These concepts lead to solutions for more than a dozen long-standing physics problems, including dark energy, dark matter, missing antimatter, the arrow of time etc. Details are given in three papers by Simon Brissenden on www.Researchers.one ; - "It's time to stop talking about time" - "Matching supernova redshifts with special relativity and no dark energy" - "Big Bubble Theory"

To decide whether the two space capsules connected by a spring are in motion, the spaceman only has to look out of the window. If the background stars are static, he is not in motion, but if they are apparently orbiting his spacecraft he will know he is in motion. So to make it a little bit harder, we will have a blind astronaut who cannot see the background stars. He decides to visit the other capsule at the opposite end of the spring. As he hauls himself along the spring he will notice the artificial gravity pulling him toward the capsule he has just left will get weaker, until at the middle of his journey he weighs nothing, but as he proceeds on his way he gets heavier until he reaches the space capsule at the far end, when he will be at his full starting weight.

Wait a minute... Instead of a bucket, we could have a rubber balloon with with water. The shape would be different, but the principal the same and it would work outside of a gravitational field as well. In no gravity (or free fall), it would be a sphere. A the rotation increases, it would bulge out into an elipsoid. And for the second part... YOU changed the measure of tension into a spring thereby changing the problem since you didn't have a 'zero' length. Newton said measure the tension, not make a spring. One very easy way to see if there is tension is to cut the string...

This was very thought-provoking, thank you!

We must admit that both phenomena exist. There is absolute time, space, motion, and there is relative time, space, motion.

I had the correct philosophical inference from the experiment without understanding why the experiment proved what I inferred. Thanks for the best explanation of the "bucket experiment". Bravo.

How does conservation of energy make the potential and rotational kinetic energy equal (8:51)? If initial energy state of the stationary bucket is zero, hasn't energy been added to raise both the amount of potential and kinetic energy from outside the system? Why would they increase equally? Sorry if this is a stupid misunderstanding, but I am genuinely confused about this step.

@Dialect You messed up in the 3rd round. The determination of the "rest state" can be determined without invoking an outside environment. Suppose for a moment that the observer decides to run an experiment on the weighted spring. First, the spring is spun clockwise at an ever increasing speed. Then the spring is spun counterclockwise in the same fashion. If the observer's frame of reference is in rotation, then one of the two spinning directions will cause the spring to compress before re-expanding. If the observer's frame of reference is at rest, the spring will only expand regardless of the direction of rotation. Even without outside knowledge, the inconsistency in behavior in the rotating frame of reference would be enough to signal that the observer's frame includes motion. No outside knowledge or reference frame required.

You don't need to know the at rest length previously. If at rest, every rotation you apply will lengthen the spring. BUT if you and the spring aren't at "absolute rest", but are actually spinning, then you can apply a particular spin which *shortens* the spring.

Rather than the philosophical dilemma, I'm more interested in whether spinning the rest of the universe would make the water spill out of everyone's buckets.

Okay, this doesn't beat Mach's general argument about empiricism, but a simple way to extract some information: if the system has two pairs of weights attached by a spring and they rotate at different speeds, you can at least be confident that the faster one (the one that's more stretched out) is not at rest. Newton probably wouldn't think that's good enough though, since it doesn't let you confirm whether something is at rest, only exclude it.

You dont need an external gravitational field in the first round, the water-filled bucket produces one by itself, it has mass afterall

Thank you for videos. You are always thoughtful and reasoning.