Why General Relativity (and Newton's Laws) tell us The Sky is Falling Up

the lore of physics has it that in 1589 Galileo dropped different masses from the Leaning Tower of Pisa to demonstrate that all objects regardless of their constitution accelerate at the same rate towards the Earth an experiment which would help Inspire Newton's laws of gravity but it would take over 300 years and a little prodding from Einstein for physics to realize that this interpretation was wrong indeed if Newton and the theorists of his era had looked a little more deeply into their own laws they might have realized that it was Galileo the Tower of Pisa and the ground that were accelerating up all along this is dialect with the sky is falling up ordinary intuition from our everyday experience tells us that Things fall down apples water sometimes people so naturally when we attempt to describe the laws of nature at a place like the surface of the Earth we try first and foremost to fit those laws to such intuitions and indeed this is exactly what Newton did in attributing the falling of everyday objects to the universal force of gravity but sometimes ordinary intuition is a pretty bad guide and it can take a little deeper reasoning to sort the truth out take the concept of time for instance classical physics defined time as a mathematical absolute doing so because this was in keeping with everyday intuition but some philosophers weren't happy with the assumption that all clocks everywhere must tick at the same rate and they asked that an empirical operative definition be instead given to the concept of time that is they demanded that clocks and time be defined via an experiment which could actually be physically carried out rather than assumed via a mathematical abstraction after Einstein provided exactly the specifications for such an operative definition of time in his 1905 Landmark paper the theory of special relativity was born and in consequence time was shown to be a rather extraordinary counter-intuitive phenomenon likewise applying an operative definition to the concept of length shows that space itself does not conform to our everyday intuitions but what happens if we apply an operative definition to the concept of motion specifically acceleration indeed not long after developing special relativity Einstein himself considered this question in the context of asking whether a man falling off a building could measure his own weight well it turns out there are a number of operative definitions you can give to accelerated motion and indeed you can apply them right here at the surface of the Earth but only if you're ready to accept their astounding implications [Music] as it is written in his principia naturalis Newton's first law states that every body perseveres in its state of rest or of uniform motion in a right line unless it is compelled to change that state by forces impressed thereupon [Music] now in conjunction with Newton's Second Law which relates Force to acceleration this implies an obvious way to detect true motion by measuring whether a body deviates from rectilinear uniform motion let's apply this to an observer on a rocket ship who say is unaware of their state of motion to try to determine it they toss an object off of themselves if this object floats away with uniform motion then from Newton's first law they can deduce that the frame of the rocket ship is inertial I.E that it's at rest or moving with constant velocity this is like what you see with astronauts in zero gravity environments when they're floating around looking all cool and whatnot now if our Observer tosses the object off themselves and it instead falls to the ground then Newton's Laws now imply that a force must be involved one that either accelerated the object to the ground or one that accelerated the ground to the object if this Observer is equipped with sufficient prior knowledge of their system foreign knows that their object contains no internally acting forces and isn't magnetically attracted to the floor or anything of that sort meaning that it is a free body they can rule out the possibility that the object was acted upon by a local Force that leaves a second possibility that the object never accelerated at all and rather it was the floor of the rocket ship that accelerated up to meet it note here that this would give rise to an apparent downward motion of the object even though its true motion remained a uniform line at least until it gets hit by the floor thus The Observer now has an operative definition for motion that is they have an experiment by which to define whether their frame is accelerating or not this is the free body test foreign The Observer might also have used an accelerometer in the form of something such as masses attached to a spring or they could have relied on haptic input from their nervous system both of which are essentially more sophisticated reformulations of the free body test okay now let's have our Observer put such definitions into practice at the surface of the Earth [Music] um first they take a loose object and toss it off themselves what happens well just like on the accelerating rocket ship it falls to the ground next they use an accelerometer masses attached to a spring they notice that the spring compresses again just like on the rocket ship next they use their nervous system to feel their own weight and they notice they feel just as heavy as being on a rocket ship accelerating at 9.8 meters per second squared through space in fact all and every experiment they perform at the surface of the Earth will give indistinguishable results from being on an accelerating rocket ship the next question then naturally is what is an observer allowed to conclude from this well an objection that could be raised from the get-go is that the free body test can't be performed at the surface of the Earth because the body isn't free at all rather it's being acted upon by the downward force of gravity so unlike when we were in the rocket ship here we can't rule out the possibility that a force acted locally to accelerate our object to the ground as to the other possibility that the ground accelerated up well this doesn't seem to fit with our everyday intuition nor with the larger picture of the Earth being round and all so we like Newton probably feel pretty comfortable declaring at this point that the reason the Apple falls to the Earth is in fact because of the force of gravity [Music] alas there's something that throws a huge wrench into this idea the same varies something that Galileo demonstrated with his Tower of Pisa experiments all those centuries ago it's the fact that gravity accelerates all objects equally meaning there is no such thing as a body free from the gravitational force mutually charged objects are free from the electromagnetic force but no object can ever serve as the standard of our definition of a free body in a gravitational field thus we have at once lost the very thing we set out to construct a definition for true motion because now our Observer on the rocket ship has no way to distinguish whether it was the floor that accelerated towards their object or whether they're simply in the presence of a gravitational field which has rendered their free body not so free after all even worse with no way to make such a distinction motion seems to lose its meaning an observer accelerating in a car for instance has equal right to say that they are motionless because they can just claim there is a sideways directed gravitational field in their proximity acting to accelerate every loose object towards the back of the vehicle this fact is encapsulated by what's known as the equivalence principle which as Einstein put it is the physical equivalence between a homogeneous gravitational field and an accelerated frame of reference now over the decades the equivalence principle has been interpreted by many as indicating that there is in fact no difference between true and apparent motion that they are interchangeable via the addition or subtraction of a gravitational field such a view is purported for instance by Eugene carteriansky in his twin paradox video but this interpretation neglects an extremely important caveat to the equivalence principle namely that it applies only locally that is over very small regions of space and short durations of time this means it is not true that no experiment can distinguish between a uniform gravitational field and acceleration indeed if we are willing to give our observer in the car a little more latitude in their measurement takings there is an additional experiment they can perform to determine if their motion is real or apparent that is after a few seconds they can take their foot off the accelerator when they do this they will notice that the gravitational field in their vicinity instantaneously vanishes the instantaneity is key here because according to the theory of special relativity nothing can travel faster than the speed of light The Vanishing of the gravitational field thus cannot be attributable to any real counteractive Force meaning the observer in the car must conclude the field was fictitious this means at last we can establish a test for true motion here's how if there exists some local switch we can find to make a gravitational field in our immediate vicinity instantaneously vanish then we know that in fact this gravitational field cannot have been real and that previously we had been undergoing true motion in the case of the car the switch is the accelerator pedal in the case of the rocket it's the firing of the rocket engines now in a similar manner let's ask is there something we can do at the surface of the Earth to instantaneously switch off the gravitational field there because if we can indeed find such a switch this will distinguish for us whether the force causing all objects to fall down is a real one or rather if it is merely an apparent one caused by an erroneous Judgment of motion from an accelerated frame of reference it turns out there is such a switch what is it exactly well go to the top of a tall building and step off of it the instant you step off the building the gravitational field in your immediate vicinity instantaneously vanishes or as Einstein wrote ceases to exist you can prove this to yourself by performing the free body test for inertial motion as you fall just like the unaccelerated observer in the rocket ship you will discover that neglecting air resistance if you toss objects off yourself while falling these objects will float away with uniform motion carry a spring with you it won't compress try to weigh yourself on a scale and you'll get a reading of zero according to Newton's Laws you therefore must conclude that your frame of reference is inertial and that you are not accelerating yet if you look down the Earth is definitely getting closer and closer but if you aren't accelerating this leaves one and only one logical possibility it is the earth that is accelerating towards you go to any spot in a gravitational field and you can always find a way to make the field vanish in your immediate vicinity jump a few feet up in the air off the ground and this action immediately causes a Vanishing of the force field around you and just like with The Disappearance of the force fields in the car or the rocket this Vanishing indicates you are no longer undergoing accelerated motion and when your feet hit the ground again The Field's instantaneous faster than the speed of light reappearance indicates your accelerated motion has resumed indeed anywhere you do observe a gravitational field then is simply a sign that your frame of reference is accelerating [Music] this means that nowhere do gravitational fields actually exist and that gravity in its Newtonian conception is entirely a fiction at the surface of the Earth then nothing truly ever Falls rather the ground the trees the buildings and the sky itself are continually accelerating upwards at 9.8 meters per second squared towards anything that might happen to be in their way you may be inclined to scoff at all this how can the Earth accelerate in every direction at once if the ground Falls up towards an apple in North America then this means everything at the opposite end of the Earth must be falling into the sky well there is one important fact left to mention and it's that only uniform gravitational fields can be made to wholly vanish using the switch method and though a gravitational field like what you see at the surface of the Earth is very nearly uniform there is a slight decrease in the strength of the field as we go higher up as well as a slight radially inwards rotation of the field direction as we move laterally outwards so for our Observer who steps off the building roof what actually vanishes for them is the uniform component of this field now for every point of The observed gravitational field there's a vector corresponding to the strength and direction of the field there the component which vanishes then is precisely the one corresponding to the vector at the center of the free-falling Observer to find what remains of the true gravitational force then we must subtract this Vector everywhere from the field doing this towards the top of the frame where the field is weaker will find a small upwards pointing Force left over doing it towards the bottom of the frame where the field is stronger leaves a small downwards pointing Force left over lastly towards either side we'll find small inwards directed forces left over these are the tidal forces or real gravity we can't make a traditional force field out of them but unlike the downward directed gravitational force these tidal forces can't be transformed away moreover they can be detected if the Observer free falling off the building has precise enough measuring equipment with them they will notice that objects towards the edge of their frame will slowly start to deviate from rectilinear motion and begin to move together contrarily objects towards the top and bottom of the frame will slowly move apart indeed it's these title forces that from a global standpoint are ultimately responsible for the attraction between bodies in general relativity however at a place like the surface of the Earth these tidal forces are so incredibly small that they are only responsible for an imperceptible fraction of the attraction of an object towards the ground the rest of that attraction is entirely due to the ground hurtling up towards the object at 9.8 meters per second squared [Music] that is why indeed it is entirely factual to say that the sky is falling up all this requires a great deal of suspension of ordinary intuition but we promise that once you start to see things this way the theory of general relativity begins to make a whole lot more sense moreover such an understanding opens the door to What's called the river model of general relativity wherein we can picture mass and energy to be continually sucking space inwards like a vacuum or a drain but that's all for future videos for now just trust us that all your lingering questions will be answered this has been dialect thanks for watching foreign [Music]

Channel: Dialect

Views: 165,476

Keywords: general relativity, physics, gravity, education, equivalence principle, free fall, acceleration

Id: GuLL_upE4zk

Length: 22min 39sec (1359 seconds)

Published: Sat Nov 05 2022