Spacetime rotations, understanding Lorentz transformations

[Music] welcome back to science click today space-time rotations we live in a geometric space in which we can move turn measure lengths or angles each person has their own frame of reference a unique point of view of the universe of which we are the center and through which we locate objects around us taking this person's frame of reference for example the car is moving but in the driver's frame of reference it is the person on looking which moves frames of reference describe the universe from a given point of view three axes are enough left right up down forward backward at the beginning of the 20th century this Paradigm was turned on its head when we understood that time is actually a fourth dimension of the universe there is a fourth axis which must be taken into account in this video we will try to explain this revolution which has since allowed scientists to unify space and time but also the electric and magnetic fields or momentum and energy [Music] let's imagine a street in which a person a is standing on the sidewalk and a person B is driving a car the car moves forwards relative to the street and to describe its motion we will construct a space-time diagram to do this we freeze each instant and stack the images on top of one another they thus form a block which represents the flow of time in this block the two persons move towards the future each drawing their own world line person a follows a straight line towards the future while person B who is moving traces a tilted path each slice of the diagram pinpoints their location at a given time at this stage the situation is described from the point of view of the road in the reference frame of person a what would the diagram look like if we ask the driver to draw it from his point of view in his reference frame B is at the center of the universe to form his diagram we must therefore shift all slices one after the other to replace him at the center of the scene the car is now Motionless and it is person a who seems to be moving backwards we have just performed a Galilean transformation Shifting the slices of space allows us to change our frame of reference in this way physicists understood as early as the 17th century that motion depends on the Observer for a B is in motion but for B it is a who moves neither of these two statements is more valid than the other motion is relative if B decides to throw a ball the speed of the ball will seem faster for a since it is moving with the car according to Galileo we can add up velocities to change reference frames while this idea may seem natural and intuitive a discovery made at the dawn of the 20th century came to question it all imagine that A and B both turn on a flashlight neglecting the presence of the air which slows it down light escapes from the two lamps at 299 million 792 458 meters per second viewed from the road we would expect that the ray launched by B moves slightly faster since it should add to the motion of the car however against all expectations the two beams have exactly the same speed with astonishment physicists discovered that this precise speed is absolute any object moving at 299 million 792 458 meters per second will have this exact speed in all reference frames it is called the speed of light this finding came as a drastic shock how is it possible that this speed does not add up to that of the car why unlike the ball thrown by B earlier does light not change speed from one frame to another to grasp the extent of the problem imagine that a emits one light Ray on each side in her reference frame both Rays have the same speed but in B's reference frame the diagram becomes slanted for him light should move faster in One Direction than the other and yet it Remains the Same the solution to this Paradox will be found at the beginning of the 20th century for the speed of light to remain constant in accordance with observations the diagram must be distorted by shifting not only slices of space but also slices of time this manipulation is the only one allowing us to change reference frame while preserving the speed of light in both directions and without distorting either straight lines or the volumes of the diagram we call this a Lorenz transformation the idea behind it is shocking time and space warp and change direction depending on the Observer the duration between events the order in which they occur and even the length of objects become relative measurements which change from one point of view to another these two events for instance occur one second apart in this first frame but 1.1 Seconds Apart in this other frame and the car is four meters long in its own frame but slightly shorter in the frame of the road when a body moves relative to us its clock seems to tick in slow motion and its length seems contracted this is special relativity let's slightly digress for one moment viewed from above a city can be depicted on a map that identifies the layout of its Road Network if we rotate this map the position and direction of the roads seem to change this is just an illusion the orientation of the map is arbitrary it is an abstract description of the world which does not impact reality physicists quickly made the analogy between the space-time diagram and the map like a map our diagram is only an abstract representation of the universe and like with a map we can change our point of view to look at it in other words the Lawrence Transformations which allow us to switch reference frames are somewhat equivalent to the rotations of our map this idea makes sense because like rotations Lawrence Transformations preserve straight lines and volumes but unlike classic rotations Lawrence Transformations seem to distort the diagram they do not preserve distances between points some move away While others get closer and while rotations draw circles they draw hyperbolas [Music] how could such Transformations be equivalent to rotations the genius idea to explain this will be brought by ponkari and minkowski they invented a new way of measuring distances within the diagram the minkowsky metric according to them our diagram is abstract and does not Faithfully represent real distances through space-time somewhat like a world map which deforms the surface of the Earth to make it flat even though it may not look like it all the points which make up a hyperbola would actually be the same distance from the center the hyperbola would be the analog of a circle the curve whose points are all the same distance from the center by changing frame of reference All Points slide along these hyperbolas while remaining at the same distance from the center thanks to the minkowsky metric the analogy becomes perfect and the Lawrence Transformations are indeed analogous to rotations they are hyperbolic rotations unlike a classic rotation which can turn in all directions a hyperbolic rotation distinguishes two types of directions on the one hand durations which can be brought onto the time axis and on the other hand lengths which can be brought onto the space axis durations and lengths are intervals of a different nature intervals of time or of space and light rays form a cone which separates them fundamentally whatever the frame of reference a duration remains a duration and a length remains a length hence since each Observer advances towards their own future it is impossible to go back in time we are confined Within These light cones and in all frames of reference the future Remains the future a classic rotation always ends up looping on itself after 360 degrees but a hyperbolic rotation can rotate indefinitely because the angle of the rotation is no longer measured along a circle but along a hyperbola which extends to Infinity we can thus rotate space-time as much as we want the angle of a space-time rotation is called rapidity it measures how fast one frame of reference moves relative to another the rapidity of the car for instance is the angle between its own frame and that of the road if the car accelerates its rapidity increases if it accelerates for an infinitely long time it would end up reaching the speed of light thus the speed of light actually amounts to an infinite rapidity it is the maximum speed that an object could only reach in theory when accelerating for an infinitely long time light is infinitely fast when B throws a ball it is not its velocity or its speed which are added to that of the vehicle but its rapidity thus when B emits light the speed of the car does not add on since the rapidity of light is already infinite by revealing all these Concepts physicists have gradually discovered the geometry of space-time far from being an abstract diagram space-time is now a physical entity endowed with distances and rotations this new vision has allowed scientists to understand that time and space are only dimensions of a single object space-time space-time allows us to better understand the notion of acceleration for instance an object is said to accelerate when its motion is altered by changing either speed or Direction in space-time we understand that these two cases are both rotations a classical rotation or a hyperbolic rotation accelerating actually amounts to Turning within space time space-time also unifies electric and magnetic fields an electric field generates a force which accelerates charged particles while a magnetic field generates a force that makes them turn these two situations are in fact analogous just like the magnetic field the electric field makes particles turn only with hyperbolic rotations within space time the electric field is the time version of the magnetic field finally this Vision allows us to unify the Notions of momentum and energy energy is actually the time version of momentum while one measures movement through space the other measures movement Through Time a stationary object for example has no momentum it does not move through space but it has energy because it moves through time towards the future if the object accelerates its speed changes it turns within space time and gains both momentum and energy by approaching the speed of light these two quantities tend to Infinity Lawrence Transformations are only abstract rotations of our map of the universe changes of reference frame which don't affect the true geometry of space-time in the Years following these breakthroughs Einstein and his contemporaries will discover that space-time can in fact get distorted explaining the phenomenon of gravity theory of general relativity is born however special relativity was not abandoned for all that just like the Earth which is curved but seems flat on a small scale space-time is still adequately described on a small scale by the minkowsky metric the basis of our understanding of the universe today new theories are trying to understand this geometry at the fundamental scale is space-time perfectly smooth or rather cut up into small grains Does it include more Dimensions which could be curled up and therefore invisible at our scale or maybe it fluctuates with quantum agitations ideas and theories abound in the hope of one day achieving a fundamental understanding of the universe [Music] [Music]

Channel: ScienceClic English

Views: 402,547

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Id: qdycfWfAtsM

Length: 15min 36sec (936 seconds)

Published: Wed Jul 26 2023