rocket.png

Rocket

Theme A - Space, Time & Motion

thermometer.png

Thermometer

Theme B - The Particulate Nature Of Matter

water-wave.png

Water Wave

Theme C - Wave Behaviour 

magnifying-glass-tilted-right.png

Magnifying Glass Tilted Right

Theme D - Fields

microscope.png

Microscope

Theme E - Nuclear & Quantum Physics

<ul>
	<li>Proper length is the length of an object as measured by an observer at rest relative to that object.</li>
	<li>To measure proper length, both measurement events must be done simultaneously.</li>
	<li>Fun fact: Proper length is also the longest length you can determine for an object!</li>
</ul>

<ul>
	<li>Objects appear to contract in length when observed from a frame that is moving relative to the object. This is known as length contraction.</li>
	<li>Real-world example: Think of a train passing by you at super high speeds. If you could observe it under the laws of relativity, it would look shorter than if it was stationary!</li>
</ul>

<ul>
	<li>In a stationary frame S: L0​ = x2 &ndash; x1</li>
	<li>In a moving frame S&prime;: Length changes to L&prime; = \(\frac {L_o}{y}\)where &gamma; is the Lorentz factor (more on that soon!).</li>
	<li>Important formula: L0 ​= &gamma;L&prime;</li>
</ul>

<ul>
	<li>It&#39;s represented by &gamma; and can be calculated using: &gamma; = &radic;1&minus;c2v2​1​</li>
	<li>Basically, it helps us understand how much an object contracts or time dilates due to relativistic speeds.</li>
</ul>

Spaceships &amp; Lorentz Contractions

<ul>
	<li>Scenario: Priya and Orhan have 16m long spaceships. Priya zips at 0.5c relative to Orhan. a. Priya&#39;s spaceship seems 13.9m long to Orhan. b. Similarly, Orhan&#39;s spaceship appears 13.9m long to Priya.</li>
	<li>Real-world analogy: It&rsquo;s like seeing two race cars moving so fast on parallel tracks that they seem shorter than their actual parked length!</li>
</ul>

An Intergalactic Journey

<ul>
	<li>Destination: Alpha Centauri, 4.4 light-years away. a. To a spaceship moving at 0.40c, the distance appears shorter: 4.0 light-years! b. Journey takes 10 years for those on the spaceship, but 15.4 years for people on Earth.</li>
	<li>Think of it this way: If you were on that spaceship, by the time you return, your friends on Earth would have aged more than you!</li>
</ul>

Rod (1.5m) zooms at 0.8c past a lab. a. Lab observes the rod to be contracted in length (remember the formula!) b. There&rsquo;s also a difference in how long the rod seems to take to pass through a light gate in the lab&#39;s frame.

Goal: Reach in 5 years (ship time). a. Using data from previous examples, we derive an equation for velocity. b. The velocity is calculated in terms of the speed of light.

<ul>
	<li>Things moving at high speeds (close to light speed) don&rsquo;t behave like our everyday experiences.</li>
	<li>Length can appear to contract, and time can appear to dilate. The faster you move, the weirder things get!</li>
	<li>Lorentz factor &gamma; helps translate between these weird relativistic observations and our usual ones.</li>
</ul>

Study Tip 📖: Relativity can seem bizarre at first. Always relate it back to real-world examples and scenarios, and practice with multiple problems to solidify understanding. Happy studying! 🚀🌌

Theme A - Space, Time & Motion

Unlocking Proper Length & Relativity: Deep Dive Into Lorentz Transformations

Table of content

Intro to proper length

How is proper length affected by motion?

Mathematics of proper length

Deep dive - lorentz factor 🧠

Unlock the Full Content!

Theme A - Space, Time & Motion

Unlocking Proper Length & Relativity: Deep Dive Into Lorentz Transformations

Table of content

Intro to proper length

How is proper length affected by motion?

Mathematics of proper length

Deep dive - lorentz factor 🧠

Unlock the Full Content!