INERTIAL FRAMES. time-independent manner. Physical laws take the same form in all inertial frames. Is the Earth an inertial frame of reference???

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1 INERTIAL FRAMES In physics, an inertial frame of reference (also inertial reference frame or inertial frame or Galilean reference frame or inertial space) is a frame of reference that describes time and space homogeneously, isotropically, and in a time-independent manner. Physical laws take the same form in all inertial frames. Is the Earth an inertial frame of reference???

2 THE EARTH AS INERTIAL FRAME If one tries to treat the Earth as an inertial frame, one gets violations of Newton's laws because of the Coriolus forces and precessions of Foucault pendula. BUT In many little experiments you can ignore these effects because the regions involved are too small to be important and the forces involved are large compared to the gravitational force from the Sun on the objects studied.

3 GALILEAN TRANSFORMATIONS In physics, a Galilean transformation is used to transform between the coordinates of two reference frames which differ only by constant relative motion within the constructs of Newtonian physics.

4 This set of equations is known as the Galilean Transformation. They enable us to relate a measurement in one inertial reference frame to another. In this example we see a motion along only the x axis. IMPORTANT The property of the sum of speed applies only in the speed direction!

5 EXERCISE - GALILEAN TRANSFORMATIONS PROBLEM: There is a frame reference R moving with a speed V=(10 m/s,0 m/s,0 m/s), respect to another frame reference R. When time t=6.5s the position of one dot P is (7m, 3.5m, 8m). What is the position of P in the frame reference R if the two origins were the same at t 0 =3.5s?

6 EXERCISE - GALILEAN TRANSFORMATIONS SOLUTION: we can apply Galilean transformation We can calculate t as difference between actual time and the zero time. x=x +v x t = x +v x (t-t 0 ) = [7+10( )] = 37m The frame reference R moves only along x axis, so the other values are the same: y=y =3.5m, z=z =8.0m, t=t =6.5s

7 Contradictions between mechanics and electromagnetic laws 1. Light speed of 3X10^8 m/s is measured with respect to a reference frame? If so, what is this reference frame? 2. A charge in motion generates a magnetic field, but this field disappears with respect to a reference frame that moves with the charge?

8 TWO CHOICES 1. The light speed isn t a constant and we can t have a relativity principle! We have to find a frame reference with respect to the light speed is 3X10^8 m/s 2. Relativity principle is valid, so we can t use Galilean transformations.

9 CHOICE 1 - THE ETHER A possible explanation of the invariance of the light speed is the ETHER. Light travels through the ether, a very tenuous substance, like sound travels through the air. If this explanation applies, we would be able to detect an observer s motion through ether.

10 CHOICE 1 - THE ETHER Ether should have an high density to carry the light so fast, but should be also very tenuous to allow the motion of planets without friction. High density = high speed. For example sound travels faster in liquids and non-porous solids than it does in air. It travels about 4.3 times as fast in water (1,484 m/s), and nearly 15 times as fast in iron (5,120 m/s), as in air at 20 degrees Celsius.

11 Michelson/Morley experiment (1887) A splitter cube: 1 incident light 2 50% transmitted light 3 50% reflected light

12 Wave interference Wave interference is the phenomenon that occurs when two waves meet while traveling along the same medium. >>> THE SUM IS VECTORIAL <<< Let's suppose that each displaced upward 1 unit at its crest and has the shape of a sine wave. As the sine pulses move towards each other, there will eventually be a moment in time when they are completely overlapped. At that moment, the resulting shape of the medium would be an upward displaced sine pulse with an amplitude of 2 units

13 Wave interference Constructive Interference: the two interfering waves have a displacement in the same direction. In this case, both waves have an upward displacement; consequently, the medium has an upward displacement that is greater than the displacement of the two interfering pulses. Destructive Interference: the two interfering waves have a displacement in the opposite direction. For instance, when a sine pulse with a maximum displacement of +1 unit meets a sine pulse with a maximum displacement of -1 unit, destructive interference occurs.

14 Michelson Morley experiment If the Earth is traveling through an ether medium, a beam reflecting back and forth parallel to the flow of ether would take longer than a beam reflecting perpendicular to the ether because the time gained from traveling downwind is less than that lost traveling upwind.

15 Language You demonstrate a physical law (by means of experimental evidence) but you prove a theorem by means of reasoning Experiments have demonstrated that the theory o relativity is true Lorentz prooved the validity of his transformations for velocity A physical law is valid/holds/applies Galilean transformations hold in mechanics You say at rest with respect to An observer at rest with respect to S You say to detect a physical effect Michelson didn t detect the effect of an ether wind

16 Language You say: to travel along a path or to travel a distance Light travels along the path AB You say: as a result (di/in conseguenza) As a result Michelson concluded that light was independent of the motion of the observer You say inertial frame A reference frame where a body at rest remanis at rest unless it interacts is called an inertial frame You say to make comparison between Let s see in which way we can make comparison between two framer of reference

17 Language You say: it is approaching to us/receding from us Light does not travel slower/faster when emitted by a star receding from us/approaching to us You say: to affirm/contend/claim an idea The experimenter in S contends that the signal does not arrive simultaneously ad A and B You say to entail (implicare) Does the theory of relativity entail that simultaneity is subjective? You say to carry out an experiment Michelson carried out his famous experiment in 1887