PHY1020 BASIC CONCEPTS IN PHYSICS I The Problem of Motion 1 How can we predict the motion of everyday objects?
ZENO (CA. 490 430 BC) AND ONENESS Motion is impossible! If all is one as Parmeinides said then motion is just an illusion Zeno put together a number of paradoxes to show that motion does not really occur 2 Zeno and his paradoxes
ACHILLES AND THE TORTOISE Set-up: Achilles lets the tortoise start a little ahead of him to give him a head start During the race: Achilles must first get to the position where the tortoise started, during which time the tortoise has moved forward by some distance. Achilles then moves through this distance during which again the tortoise moves forward by some distance Conclusion: Achilles will never reach the tortoise no matter how fast he runs! 3 Achilles Arrogance
THE DICHOTOMY PARADOX Imagine a horse tried to run some distance, she must first run half that distance, but before that a quarter of the distance and so This motion is impossible! (it seems) 4 The horse that couldn t
THE SOLUTION TO THE PARADOX Physics Reason: Observers measure distances between objects, the real world does not. Thus its not that we have half of the final destination distance covered but that half of some distance has been past. Nature has no pre-destined aim! Mathematical Reason: Not us! 5 The nature of measurements
ARISTOTLE (CA. 384 322 BC) AND MOTION Axiom s of Aristotle s Theory of Motion: 1. No motion without a mover in contact with moving body 2. Distinction in mover: i. Natural motion - mover is internal to moving body ii. Forced motion - mover is external to moving body Held that objects tend to their natural place unless forced motion is imposed upon them 6 Objects tend to their natural place
ARISTOTLE S LAW OF MOTION Factors in his law of motion: F Force (weight) of mover R Viscosity or resistance of medium (Antiquity Nature abhors vacuums [Horror vacui]) V Speed (Not velocity) If F = R (or less than) then no motion occurs, but if F > R then 7 Speed depends on applied force and medium resistance
PROBLEMS Question: What hits the ground first a 1Kg ball or a 10Kg ball? Aristotelian Prediction: the 1Kg ball will take 10 times the time to fall the same length Reasoning: For some distance let T be the time taken to traverse that distance V1, V10 Velocity of objects; T1, T10 Falling time of objects because because Thus or 8 How do objects fall?
STRATO (CA. 335-269 BC) AND ACCELERATION - Emphasized the need for demonstrations (experiments) - Strato defined acceleration as the traversing of equal distances at shorter times - Claimed that Aristotle is correct but that during motion bodies accelerate 9 Enter Strato and the idea of demonstrations
PROOF OF ACCELERATION Strato used the water moving out of a Spout to show that force produces some acceleration since the drops must slow down to form separate entities from the main stream 10 Experimental demonstration
JOHN PHILOPONUS (CA. 490 570) - Refutation of Aristotle s inverse relation - Strengthening of experimental side - Proposal that objects fall at approximately the same rates irrespective of weight But this [view of Aristotle] is completely erroneous, and our view may be completely corroborated by actual observation more effectively than by any sort of verbal argument. For if you let fall from the same height two weights, one many times heavier than the other you will see that the ratio of the times required for the motion does not depend [solely] on the weights, but that the difference in time is very small.... John Philoponus' refutation of the Aristotelian claim that the elapsed time for a falling body is inversely proportional to its weight [1] [1] Cohen, W. R. and Drabkin, I.E., A Source Book in Greek Science (Cambridge, MA: Harvard University Press, 1992) 11 How do objects fall?
RESISTANCE TO MOTION Aristotle thought that motion was maintained by means of a force transferring power to a surrounding medium which then maintains the propagation Philoponus on the other hand reasoned that the power that propels an object forward must be internal and so selfmaintained meaning that objects could move through vacua 12 Battle of the Force Internal or Medium Driven
Jean Buridan (CA. 1300 1358) Following Philoponus Buridan held that motion after being caused is maintained by the object in question This was done by defining an inertia for moving bodies, that is an initial impetus that sets the object in motion causes a sustained mechanism that maintains motion This effective driving power would depend in some way on the initial speed and amount of matter This idea has the added effect that it can explain how objects stop moving as well, the resistance by a medium produces this stopping effect This is very close to our modern explanation of motion! 13 How do objects start to moving and what stops them?
GALILEO GALILEI (CA. 1564 1642) Constructed a model of motion using geometrical concepts such as distance and more importantly changes in this quantity The core of Galileo is that he thought of motion in concrete terms of change and so observation instead of philosophical reasoning "Nature is written in the grammar of mathematics and its characters are triangles, circles and other geometrical figures." 14 Motion should be thought of in terms of observables
UNIFORM MOTION "By steady or uniform motion, I mean one in which the distances traversed by the moving particle during any equal intervals of time, are themselves equal." Definition: Uniform motion is when the distance traversed is proportional to time of travel Claim: Uniform motion is undetectable under certain conditions. What knock on effects could this have for the Earth, could it be in motion? 15 The beginnings of Galilean relativity
UNIFORM ACCELERATION Galileo s definition: "A motion is said to be uniformly accelerated when starting from rest, if it acquires, during equal time-intervals, equal increments of speed." Speed is proportional to time of travel or This means where k is some constant 16 Is the same true of acceleration or is this special?
speed MEAN SPEED speed Introduced the idea of mean speed, which would be the speed needed to traverse the same distance in some particular time time Hence, 17 The same distance is covered in equal times
FREE FALL Galileo proposed that bodies fall with uniform acceleration (with the proviso that there is no wind currents or extra medium resistance as for example through water) This means that bodies fall with the same acceleration as long as the medium (air/water) does not pose too much resistance Thus, No mass factor! This means feathers and rocks fall at the same speed! 18 Back to falling bodies
THE EXPERIMENTAL TEST Galileo dropped two spheres of different masses from the top of the Tower of Pisa and found that they hit the ground at the same time Results: 1. Aristotle s theory of gravity is wrong, different weights fall at the same rate, or at least not as an inverse proportionality 2. Galileo s theory of motion with uniform acceleration correctly predicted the measured results 19 Galileo's Leaning Tower of Pisa experiment
CONCEPT OF TERMINAL VELOCITY Remembering Aristotles idea of when Force = Medium Resistance no motion can occur, Galileo said this for acceleration When Force = Medium Resistance no further acceleration occurs no matter the weight and a Terminal uniform Velocity is achieved 20 How fast can we fall?
PROBLEM WITH GALILEO Set-up: Imagine a sphere falling down an infinitely long inclined plane, the sphere will accelerate ad infinitum. This contradicts what happens in experiments when scientists try to speed particles past the speed of light thus disproving the high velocity extreme of Galileo s theory of motion 21 The Speed limit
NEWTON (CA. 1642 1727) - There is only one kind of force and it is linked to acceleration in a different way - Force produced acceleration! - and similarly acceleration produces a force - Did not differentiate between internal and external forces - Using a new notion of calculus he managed to intertwine concepts of position, speed and acceleration 22 Bringing everything together
NEWTON S LAWS OF MOTION Newton proposed three laws under which all motion could be described First law: An object remains at constant velocity unless acted upon by a force Second law: The acceleration of an object is directly proportional to the force applied on it and inversely proportional to the mass of the object. Furthermore the direction of acceleration is parallel to the force Third law: For every (force) action there is an equal and opposite reaction 23 Newton s Model of how Motion occurs
FALLING BODIES Keeping Galileo s idea of uniform acceleration of falling bodies, Newton managed to articulate this into a general principle (called the Equivalence Principle) 24 Newton s Apple
GALILEAN RELATIVITY AND NEWTON S AXIOMS Galilean relativity lies on the principle that the laws of motion are the same in all inertial (non-accelerating) frames On this Newton formed his axioms: 1. An absolute space exists in which motion can occur 2. All inertial observers share a universal measurement of time Light must travel instantaneously to satisfy the second condition 25 The Age of Absolutes
EINSTEIN IN THE HIGH ENERGY REGION In the high velocity regime Galilean relativity breaks down and Einstein s relativity theory must be used The principles here are changed to: 1. The Principle of Relativity The underlying laws of motion are not affected by the inertial frame in which measurements are made 2. The Principle of the Invariance of the Speed of Light The speed of light is measured to be the same in every inertial frame Einstein weakened Newton s absolute space and time axioms and said that it may be that different observers measure the length and period of events differently! 26 The Universal Speed Limit
A SHORT NOTE ON QUANTUM THEORY Over short distances particles jump from place to place, however on the large scale it appears as continuous motion An electron collides with a Hydrogen atom and scatters two further electrons 27 Quantum Nature
THE CURRENT STATE OF AFFAIRS The current problems in motion theory stem from trying to reproduce Einstein s relativity predictions (which are known to work) using the quantum theory 28 CERN