Newton vs. Mach: The Bucket Experiment

it's a debate that's raged for millennia which aspects of our reality are absolute and which are merely relative when it comes to the concept of motion two physicists held opposing views and to resolve the differences in their philosophies they invoked a simple thought experiment that involved well a bucket and some water but does this experiment really prove that motion has absolute meaning or does it actually demonstrate the opposite that motion is just a relative construct [Music] today we'll pit these two thinkers against one another to find out this is dialect with newton versus mock the bucket experiment when newton introduced his groundbreaking theories in the late 1600s he framed them against a mathematical background that contained three absolutes time space and motion time space and motion the vulgar conceive these quantities only in their relation to sensible objects he wrote but absolute time flows uniformly without regard to anything external absolute space always remains similar and immovable absolute motion is the translation from one absolute place to another absolute place although some were skeptical of these definitions the success of newton's theories in describing motion and gravity gave no real reason for physicists to question them over the following centuries but in the late 1800s the skepticism of one physicist ernst mock would have an irreversible impact on the course of physics newton has grown unfaithful to his resolve to investigate only actual facts mock declared in his signature text the science of mechanics the question whether emotion is in itself uniform is senseless we reach our ideas through the interdependence of things upon one another in his ensuing critique of newton mach declared that no one is competent to predicate things about absolute space or motion that they are purely mental constructs his ideas helped propel a young albert einstein towards the theory of relativity and soon in the wake of relativity's massive success two of the three pillars of newton's absolutes time and space came crashing down but today newton's final absolute motion still stands that is all our modern theories of reality are framed against a mathematical background which posits one particular type of motion acceleration as absolute and although mock was ahead of his time in realizing that both the ideas of absolute time and absolute space were soon to fall his critique of newton's concept of absolute motion never experienced similar validation and so modern physicists have split into two camps those who believe newton's assertion about absolute motion to be correct and those who believe mock's critiques will eventually come to fruition [Music] particularly what mock found lacking about absolute motion was the experiment cited by newton to justify it the bucket experiment newton had observed that if you took a bucket filled with water and started to spin it the water inside would go from being flat to having a concave shape according to newton this difference proved motion was absolute how exactly well let's break it down newton notes that there are exactly two points over the course of the experiment that the bucket and the water will be relatively at rest [Music] the first point is before the bucket has been spun when both the bucket and the water aren't moving the second point is after the bucket has been spun and its motion having been communicated to the water via friction the water takes a concave shape at this point both the bucket and the water are spinning at the same rate together and from the perspective of an observer who is rotating along with them the entire apparatus will appear to be at rest now according to newton if the observer in the spinning frame didn't already know the bucket was rotating they could deduce it from the fact that the shape of the water is concave conversely if we had an observer who was rotating with respect to the still frame so that relative to them the bucket and the flat water appeared to be spinning they could deduce that the bucket was actually at rest by the flat shape of the water thus the first picture with the water in the bucket being flat represents absolute rest while the second picture with the water being curved represents absolute motion distinctions such as these newton argued always make it possible to distinguish between motion that is true or real and motion that is only apparent but mock fired back that this argument was too abstract the centrifugal forces which seemingly caused the water in the bucket to take its concave shape aren't produced by an absolute rotation he argued but by a rotation relative to the mass of the earth and the other celestial bodies [Music] every statement about motion mock believed implicitly carries an abbreviated reference to the rest of the universe and thus removing the rest of the universe from the picture leaves us unable to define what we mean by motion in the first place [Music] both newton and mock seem to make compelling points but who is ultimately right to resolve this metaphysical face-off we're gonna have to step into the rink and get our hands a little wetter with the bucket experiment [Music] first let's ask what actually gives the water its concave shape well as our bucket begins to spin the water inside gets flung outwards towards the walls with nowhere else to go this water is forced to rise [Music] gravity however keeps it from rising too much and as a result the surface of the spinning water achieves a rotational equilibrium next conservation of energy tells us that in this state of equilibrium the kinetic energy of a spinning ring of water at a distance r from the center of the bucket will be equal to its potential energy mgh since the velocity of the spinning ring is simply the angular velocity of the bucket times the rotation radius we can see after a little algebra that the height of the ring of water is thus proportional to the square of its distance from the center of the bucket meaning the overall shape of the water will be a parabola but the height of the water is also dependent on another parameter the strength of the nearby gravitational field g and if we dial down the strength of that field to zero we see that the height of the water goes to infinity what this implies is that spinning our bucket in zero gravity would actually result in all the water being ejected from the bucket [Music] a fact which tells us something that newton neglects to mention that is that the concave shape of the water is not just a consequence of the bucket spinning but rather a consequence of its spinning in the presence of a gravitational field the implication of course is that in the absence of such a field the shape of the water's surface no longer acts as an indicator of rotational motion [Music] of course one could contend that this doesn't affect newton's argument since if we spun our bucket in zero gravity we'd have one picture of total rest and one picture where our water is flying all over the place but newton's objective with the bucket experiment was not to demonstrate a case where motion and rest were easily differentiated but rather to find a case where motion and rest appear essentially indistinguishable and then show that even in these instances such telltale differences can always still be found the problem then is that for the bucket experiment to fulfill this criteria that is for there to be a state of rest for the system which is only apparent the bucket is required to inhabit a gravitational field thus to make his case that true motion can always be locally distinguished within a system newton is actually forced to invoke a nearby mass external to that system meaning his experiment could not be reproduced in the absence of external matter since this falls more in line with mock's argument than it does with newton's we're crowning mock the winner of this first round likely realizing the bucket experiment was a little too contextual newton in his writings offers up a second experiment take two globes attached to a cord and spin them around in a circle about their center of mass [Music] then by investigating the tension produced in these chords one could determine the quantity and direction of the circular motion considered even in an immense vacuum where there was nothing external or sensible with which the globes could be compared now this experiment unlike the bucket one has the benefit of being able to be reproduced in the absence of external matter but in keeping with the bucket experiment it offers two states of apparent rest along with a theoretical way to measure the difference between them to see how this measurement could occur it might be easier for us to envision our two masses as attached by a spring rather than a cord as the masses rotate centrifugal forces push them outwards stretching the spring a stretched spring therefore indicates absolute rotation and by measuring how much the spring has stretched one can determine the exact magnitude of force causing the rotation with this simple definitive seeming argument newton claims the title as our second round winner establishing a concept of absolute motion that could be empirically verified even in the absence of all other matter in the universe who wins the final round well to find out we need to think about what the bucket experiment is really saying let's recall again that newton's original argument relied on there being two distinct points of view of relative rest one in which the bucket and water are at rest with respect to one another and the water is flat and one in which the bucket and water are at rest with respect to one another but the water is curved similarly for the masses attached to the spring in a vacuum in both pictures the masses and the spring are at rest with respect to one another but in one picture the spring is stretched and in the other it isn't now the picture of the stretched spring is supposed to correspond to absolute motion but we also have to recall the fact that the observers in these frames don't know whether they're spinning or not and therefore don't have access to information from the outside that would indicate to them prior to their measurements made inside their frame whether or not their frame is inertial let's say that besides the spring is a rod of much stiffer material with markings along it to indicate the length between coils of the spring the observer can then read the markings to measure the length between coils and thereby determine how much the spring has stretched 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 in the bucket experiment only flat water could indicate absolute rest but here the problem is trickier here the observer has to know prior to making any measurements in their frame what length corresponds to the natural undeformed state of the spring and to know that the observer would have had to previously have calibrated their spring rod measuring device in a frame that was already known to be inertial such as in a laboratory back on earth [Music] 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 stretching or compressing the spring could an observer ascertain what picture of the spring corresponds to absolute rest thus even in the empty universe version of newton's experiment observers would still have to import information from inertial frames that existed elsewhere in order to draw any conclusions about the state of their motion that means in one way or another an observer has to reference an external environment no matter how distant or removed this environment is knowledge of the local system cannot ultimately be untangled from the greater environment [Music] so what does this mean for newton's argument well it means the globes and chord experiment does not actually meet the criteria for which newton devised it the criteria of reproducibility in an empty universe and because of that it falls short of proving absolute motion in the same way the bucket experiment fell short it relies on the presence of an external system in order to demonstrate absolute motion and well at least to us this seems most in keeping with mock's assertion that all our principles of mechanics are experimental knowledge concerning the relative positions and motions of bodies now were we to expand newton's argument to allow observers in our rotating systems to retain a memory of how substances and materials behaved in inertial systems elsewhere then clearly his case still stands and to some degree this must have been newton's reasoning because obviously an observer who doesn't know anything about how buckets or water work wouldn't be able to draw any conclusions about the state of their motion from the bucket experiment either [Music] but newton clearly also wanted to prove knowledge of absolute motion was a localized phenomenon which would always reveal itself under careful enough isolated scrutiny [Music] yet if you allow your observers enough memory memory of how say springs buckets cords and water behave elsewhere in other systems at other times this is equivalent to expanding the system of reference beyond a spatio-temporally localized point of view thus newton can't have it both ways knowledge of absolute motion can't both be always discernable and always localized one of the two has to go but if we try to preserve localization at the cost of memory this means observers could potentially disagree on their states of motion with no empirical experiment able to differentiate between them on the other hand if we try to preserve discernibility and require that motion must always be empirically verifiable we have to invoke memory sufficient enough to reference a greater collective of systems [Music] essentially this leaves us with two primary resolutions to the bucket experiment one absolute motion is real and localized but knowledge of it is not always possible [Music] this is equivalent to saying that although observers may potentially disagree on who is or isn't moving motion is still real and governs how our universe works this would however make absolute motion an unobservable phenomenon something which physics and science in general tends to disfavor two what we perceive as absolute motion is actually an emergent property of a network of systems that cannot fundamentally be isolated from one another meaning motion at some level must ultimately be relative so which of these answers is it does absolute motion have real meaning outside our mathematical descriptions or is it simply a poorly defined concept a relic of dogmatic belief that like absolute space or absolute time needs to be fundamentally re-examined well for the time being it's up to you to decide so let us know what you think in the comments because until next time this has been dialect thanks for watching you

Channel: Dialect

Views: 251,536

Keywords: physics, education, newton, mach, motion, philosophy, wrong, debate

Id: Jz3mOlUOGoY

Length: 21min 11sec (1271 seconds)

Published: Fri Feb 18 2022