Exploring Einstein's special relativity

exploring einstein's special relativity

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Introduction: Maxwell's equations

Special relativity

introduction: maxwell's equations

index

IThe importance of Maxwell's equations

1.0

James Clerk Maxwell

1.1

Maxwell's equations

1.2

electromagnetic waves

1.3

the importance of maxwell's equations

Maxwell's equations are fundamental equations in classical electromagnetism that describe how electric and magnetic fields interact and propagate. They are crucial in modern physics for several reasons, particularly in the context of relativity.

Maxwell's equations unified the previously separate phenomena of electricity and magnetism into a single framework.

1.1

james clerk maxwell

James Clerk Maxwell was a Scottish physicist born on June 13, 1831, in Edinburgh, Scotland. He showed exceptional mathematical talent from a young age. Maxwell attended the University of Edinburgh and later Cambridge University, where he excelled in mathematics and physics.

Throughout his career, Maxwell made significant contributions to various fields of science, including electromagnetism, statistical mechanics, and optics. His most famous achievement came in 1864 when he formulated the set of equations known as Maxwell's equations.

Throughout his career, Maxwell made significant contributions to various fields of science, including electromagnetism, statistical mechanics, and optics. His most famous achievement came in 1864 when he formulated the set of equations known as Maxwell's equations.

Maxwell's work also contributed to the development of the kinetic theory of gases, color theory, and the understanding of the nature of Saturn's rings. He was a pioneer in the application of mathematical methods to physical problems and played a crucial role in the transition from classical to modern physics..

Maxwell's life was tragically cut short when he died of abdominal cancer at the age of 48, on November 5, 1879, in Cambridge, England. Despite his relatively short life, his contributions to science had a profound and lasting impact, and he is widely regarded as one of the greatest physicists of all time.

1.2

maxwell's equations

PAY ATTENTION!

We will study the simplified form of Maxwell's equations!

Equation 1: Gauss's Law for the Electric Field

This equation states that The flux of the electric field through a closed surface is equal to the sum of the charges enclosed by the surface divided by the permittivity of free space

Equation 2: Gauss's Law for the Magnetic Field

This equation states that The flux of the magnetic field through a closed surface is zero, indicating the absence of magnetic monopoles.

Equation 3: Faraday's Law of Electromagnetic Induction

This equation describes how a changing magnetic field (B) induces an electric field (E) in a closed loop.

Equation 4: Ampére - maxwell's law

This equation relates the curl of the magnetic field (B) to the current (i) and the rate of change of the electric field (E). It incorporates Maxwell's addition to Ampère's Law, known as the displacement current term.

1.3

electromagnetic waves

discovering electromagnetic waves

Electromagnetic waves are a fundamental aspect of nature, characterized by the propagation of electric and magnetic fields through space. These waves carry energy and information and have a wide range of applications in modern technology.

Maxwell's equations predicted the existence of electromagnetic waves, including light.

Key characteristics of electromagnetic waves include their wavelength, frequency, and amplitude. The wavelength is the distance between successive peaks or troughs of the wave, while the frequency represents the number of wave cycles per unit of time. The amplitude determines the intensity or strength of the wave.

The speed of light, denoted by the symbol "c," is the speed at which electromagnetic waves propagate through a vacuum. In a vacuum, such as outer space, light travels at approximately 299,792,458 meters per second, or about 186,282 miles per second. This speed is considered to be the ultimate speed limit of the universe according to the theory of relativity proposed by Albert Einstein.

One of the most significant implications of electromagnetic waves is their role in the transmission of energy and information over long distances without the need for a physical medium. This property enables wireless communication, such as radio, television, and cellular networks, as well as various forms of remote sensing and imaging.

Overall, electromagnetic waves are essential in numerous fields, including telecommunications, medicine, astronomy, and scientific research. Their diverse properties and applications continue to drive technological innovation and deepen our understanding of the universe.

Special relativity

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What does special relativity study?

2.0

Reference frames

2.1

Special relativity postulates

2.2

Two consequences of postulates

2.3

what does special relativity study?

Special relativity studies how different observers, who can be in motion with respect to each other, perceive the same event

2.1

Reference frames

Each observer has her own coordinate system (and clock) and each measures the event with respect to this coordinate system, this is what we call REFERENCE FRAME

In SPECIAL RELATIVITY we talk about INERTIAL REFERENCE FRAMES

In an inertial reference frame the PRINCIPLE OF INERTIA is valid:

An object at rest will remain at rest, and an object in motion will continue in motion with the same velocity and in the same direction, unless acted upon by an external force.

2.2

Special relativity postulates

The laws of physics are the same in all inertial frames

The speed of light in a vacuum, c, always has the same value in any inertial reference frame, no matter how fast the observer and the light source are moving with respect to each other

2.3

two Consequences of postulates

Thanks to Lorentz!

The transformations that allow the transition from the coordinates of one reference frame to another are the Lorentz transformations.

Time dilation

When you measure the time that the ray of light needs to complete the path, you will obtain different results if you measure it on the rocket or on the ground

Time measurement standing on the ground

Time measurement standing on the rocket

But...

The measures of time reffered to the different reference frames are connected:

v is the relative speed of the two observers

If v is very much less than c...

Length contraction

You can measure the speed of the rocket when your are on the Earth or when you are on the rocket.

On the rocket

On the Earth

Thank you!