Invariance of Physical Law Relativity Invariance of Physical Law MARLON FLORES SACEDON

Five Greatest Theory in Physics PHYSICS Relativity Quantum Mechanics CLASSICAL MECHANICS (sometimes called Newtonian mechanics or classical mechanics): the theory of the motion of material objects. CLASSICAL THERMODYNAMICS the theory of heat, temperature, and the behavior of large arrays of particles. ELECTROMAGNETISM: the theory of electricity, magnetism, and electromagnetic radiation. RELATIVITY: the theory of in variance in nature and the theory of high-speed motion. QUANTUM MECHANICS: the theory of the mechanical behavior of the submicroscopic world Mechanics Classical Mechanics Electromagnetism Thermodynamics

In 1905, Albert Einstein published four papers of extraordinary importance. Analysis of Brownian motion The photoelectric effect (for which he was awarded the Nobel Prize) Two papers for Special theory of relativity (opposing drastic revisions in the Newtonian concepts of space and time).

The laws of physics are the same in every inertial frame of reference. Einstein’s first Postulate The laws of physics are the same in every inertial frame of reference.

The story of Mavis and Stanley man Stanley

The story of Mavis and Stanley

𝑣 𝑚 𝑆 ′ =10𝑘𝑝ℎ (velocity of man according to Mavis) 10 kph 150 kph Y X Z S 𝑣 𝑚 𝑆 ′ =10𝑘𝑝ℎ (velocity of man according to Mavis) 𝑣 𝑚 𝑆 = 𝑣 𝐵 𝑆 ′ + 𝑣 𝑆 ′ 𝑆 (velocity of man according to Stanley) 𝑣 𝑚 𝑆 =10𝑘𝑝ℎ+150𝑘𝑝ℎ=160𝑘𝑝ℎ

the motion of the source.. Einstein’s Second Postulate The speed of light in vacuum is the same in all inertial frames of reference and is independent of the motion of the source..

Einstein’s Second Postulate The speed of light in vacuum is the same in all inertial frames of reference and is independent of the motion of the source.. c 150 kph x 𝑣=𝑐+150𝑘𝑝ℎ 𝑣=𝑐 (velocity of light does depend on medium) Einstein’s second postulate immediately implies the following result: “It is impossible for an inertial observer to travel at c, the speed of light in vacuum.”

This is Galilean transformation equations Y’ X’ Z’ 0’ S’ Y X Z S Velocity of moving frame 𝑢 X=? X’ 𝑢𝑡 𝑥= 𝑥 ′ +𝑢𝑡 Differentiating with respect to time t 𝑑𝑥 𝑑𝑡 = 𝑑𝑥′ 𝑑𝑡 + 𝑑(𝑢𝑡) 𝑑𝑡 𝑣= 𝑣 ′ +𝑢 This is Galilean transformation equations 𝑑𝑥 𝑑𝑡 = 𝑑𝑥′ 𝑑𝑡 +𝑢

Summary Einstein’s first Postulate The laws of physics are the same in every inertial frame of reference. 𝑣 𝑣𝑒ℎ𝑖𝑐𝑙𝑒/𝑒𝑎𝑟𝑡ℎ =150𝑘𝑝ℎ 𝑣 𝑚𝑎𝑛/𝑣𝑒ℎ𝑖𝑐𝑙𝑒 =10𝑘𝑝ℎ 𝑣 𝑚𝑎𝑛/𝑒𝑎𝑟𝑡ℎ = 𝑣 𝑚𝑎𝑛/𝑣𝑒ℎ𝑖𝑐𝑙𝑒 + 𝑣 𝑣𝑒ℎ𝑖𝑐𝑙𝑒/𝑒𝑎𝑟𝑡ℎ =10𝑘𝑝ℎ+150𝑘𝑝ℎ=160𝑘𝑝ℎ Einstein’s Second Postulate The speed of light in vacuum is the same in all inertial frames of reference and is independent of the motion of the source.. Speed of light ( c ) 𝑣 𝑣𝑒ℎ𝑖𝑐𝑙𝑒/𝑒𝑎𝑟𝑡ℎ =150𝑘𝑝ℎ x 𝑣=𝑐+150𝑘𝑝ℎ 𝑣=𝑐=3𝑥108 𝑚/𝑠

TIME DILATION

What is TIME DILATION?

What is TIME DILATION?

What is TIME DILATION?

TIME DILATION

TIME DILATION FORMULA This equation is called TWIN PARADOX

Problem 1: High-energy subatomic particles coming from space interact with atoms in the earth’s upper atmosphere, in some cases producing unstable particles called muons. A muon decays into other particles with a mean lifetime of 2.20µs as measured in a reference frame in which it is at rest. If a muon is moving at 0.990c relative to the earth, what will an observer on earth measure its mean lifetime to be? ∆𝑡= ∆𝑡 𝑜 1− 𝑢 2 𝑐 2 ∆𝑡= 2.20𝜇𝑠 1− (0.99𝑐) 2 𝑐 2 ∆𝑡=15.6𝜇𝑠

Problem 2: An airplane flies from San Francisco to New York (about 4800 km, or 4.80x106 m) at a steady speed of 300 m/s (about 670 mi/h). How much time does the trip take, as measured by an observer on the ground? By an observer in the plane? New York San Francisco 4.80x106m 𝑣= 𝑠 𝑡 ∆𝑡= ∆𝑡 𝑜 1− 𝑢 2 𝑐 2 Time dilation formula: 𝑡= 𝑠 𝑣 1.60 𝑥104 𝑠= ∆𝑡 𝑜 1− (300 m/s) 2 𝑐 2 ∆𝑡= 4.80x106m 300 m/s 1.60 𝑥104 𝑠= ∆𝑡 𝑜 1− (300 m/s) 2 (300,000,000 m/s) 2 ∆𝑡=1.60 𝑥104 𝑠 (about 4.5 hrs) ∆𝑡 𝑜 ≈1.60 𝑥104 𝑠

Which one’s the grandmother? Situation: A 20-year-old woman had given birth to a child and then immediately left on a 100-light-year trip (50 light-years out and 50 light-years back) at 99.5% the speed of light. Which one’s the grandmother? Grand mother ∆𝑡= ∆𝑡 𝑜 1− 𝑢 2 𝑐 2 100 𝑦𝑟𝑠= ∆𝑡 𝑜 1− (0.995𝑐) 2 𝑐 2 Grand daughter 30 yrs. old 100 𝑦𝑟𝑠= ∆𝑡 𝑜 0.0998749 80 yrs. old ∆𝑡 𝑜 =10 𝑦𝑟𝑠 The child she left behind at home could have had a baby 20 years after her departure.

ASSIGNMENT

ASSIGNMENT

ASSIGNMENT

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