Beginner Resources for Special & General Relativity

• B
• DeltaForce
In summary, Don't be confused by the physical quantities and the units we use to express them. The Lorentz transformation and Minkowski diagram work well with geometric units, which avoids the use of units like meters and minutes.
DeltaForce
TL;DR Summary
I'm completely new to Special and General Relativity. I have some background in newtonian/classical physics. But in class, special and general relativity is mind-boggling to me. I have a hard time learning/wrapping my head around it. So I'm looking for good online resources to strengthen my understanding of it.
Like I said, I'm new to Special and General Relativity. It really sucks when I space out for 2 minutes in class and for the next 30 minutes I'm completely lost until the teacher brings up a new topic. I'm looking for supplementary materials (online preferably as I'm away from home) that can strengthen my understanding of the topic. I've looked at khan academy and youtube videos but it still doesn't quite click for me

I don't want to sit in class and pretend to understand the material; I actually want to understand it. So if you have any advice or tip you can give me for learning this sort of physics, I will also take with gratitude. Also, currently, I'm a bit hazy in the Lorentz transformation and the Minkowski diagram department, so if anyone have some resource that focus on explaining that would be great as well.

To get a basic grasp and intuition for SR, a great resource is simply playing around with the Lorentz transformation and Minkowski diagrams. Just start by evaluating time plus a single spatial dimension (that’s the most that hand-drawn Minkowski diagrams will allow you to easily depict anyway). Also start by making yourself comfortable with geometric units where ##c = 1##. This will be helpful in the long run.

In many beginner texts you will often see the Lorentz transformation like this: $$x’ = \frac{x-vt}{\sqrt{1-v^2}}\\ t’ = \frac{t-vx}{\sqrt{1-v^2}}$$ All this does is take an input—the coordinates of an event (something that happens at a particular time in a particular place) in one inertial frame of reference—and outputs the coordinates of that same event for a different inertial frame of reference.* As an example, you could start with a situation where one inertial observer witnesses a bunch of simultaneous flashes of light spaced all along his ##x##-axis and evaluating what a different observer traveling with velocity ##v## relative to him would see.

*There are some caveats that go along with that, such as the two frames must share an origin (the event labeled as ##(0,0)##), and all observers must compensate for travel time of light when they assign times to events. The interesting results of SR most clearly manifest themselves when travel time of light is compensated for.

kent davidge
For the Minkowski diagram, my teacher used "ct" as the unit y-axis and "x" as the unit of x-axis
where x is distance.
I presume that c is light speed and t is time for the y-axis. I think they are multiplied together? I thought that speed times time is distance/displacement
I'm a bit confused as to why both the x-axis and y-axis are "distances" or is it something else.

Before I can grasp the set-up of the graph, my teacher went on to talk about worldlines, time intervals, and space-time. So I'm confused about the Minkowski diagram, like very confused...

It's convenient to have a light ray on a space-time diagram be a line at a 45 degree angle.

Scaling the time t by the universal constant "c" is just a a way of doing this. There are a number of equivalent ways of thinking about this, I don't want to confuse you too much by introducing one that's incompatible with your class, if you're struggling a little bit with it.

DeltaForce said:
I'm a bit confused as to why both the x-axis and y-axis are "distances" or is it something else.
There are members here more knowledgeable than I who can really explain the significant profundity of geometric units, but the superficial gist of it is that it’s typographically convenient for the math formulas to work in units where the speed of light, ##c##, equals 1, and as @pervect mentioned, convenient for the Minkowski diagrams as well.

Note that in post #2 the units in the Lorentz transformation don’t work out if you’re using e.g. the metric system of units. You can strategically insert ##c##’s (which in the metric system has units of meters per second) to make the units work out, but then you have a bunch of ##c##’s all over the place. Geometric units avoids this.

DeltaForce said:
For the Minkowski diagram, my teacher used "ct" as the unit y-axis and "x" as the unit of x-axis
where x is distance.
I presume that c is light speed and t is time for the y-axis. I think they are multiplied together? I thought that speed times time is distance/displacement
I'm a bit confused as to why both the x-axis and y-axis are "distances" or is it something else.

Don't confuse the physical quantities with the units we use to express them.

If you walk at a speed of 4 miles per hour, then you can say that the grocery store 1 mile down the road is "a 15-minute walk away." You're still talking about a distance, but you're expressing that distance in units of time. Your speed serves as a unit-conversion factor here: divide the distance (in miles) by the speed to express the distance in time-units.

Of course, your speed isn't a universal constant. Even if you managed to maintain a perfectly steady pace, different observers would disagree on your velocity. We can't all use @DeltaForce's walking speed as an agreed-upon standard for converting between distance- and time-units.

But ##c## is both constant (unchanging) and invariant (everyone agrees on it). It's nature's ready-made distance/time unit-conversion factor, and using it to express times and distances in the same unit turns out to be extraordinarily convenient. To do this, either divide all distances by ##c## or multiply all times by ##c##. (Or set ##c = 1##.)

So ##c \Delta t## isn't "a distance"; it's a time-interval expressed in units of distance.

Pencilvester and kent davidge
SiennaTheGr8 said:
to express times and distances in the same unit turns out to be extraordinarily convenient
and I think, is mandatory if you are summing up terms

DeltaForce said:
Before I can grasp the set-up of the graph, my teacher went on to talk about worldlines, time intervals, and space-time. So I'm confused about the Minkowski diagram, like very confused...

What textbook are you using for the course? You can also ask your instructor for a list of sources such as textbooks and websites.

1. What is the difference between special and general relativity?

Special relativity deals with the relationship between space and time in the absence of gravity, while general relativity includes the effects of gravity on the fabric of space-time.

2. What are some good beginner resources for learning about special and general relativity?

Some good beginner resources include books such as "A Brief History of Time" by Stephen Hawking, online courses like "The Einstein Revolution" on Coursera, and videos from educational channels like PBS Space Time.

3. Is it necessary to have a strong background in mathematics to understand relativity?

While a basic understanding of mathematics is helpful, it is not necessary to have a strong background in order to understand the basic concepts of relativity. Many beginner resources explain the concepts in a way that is accessible to those without an advanced math background.

4. What are some real-world applications of relativity?

Relativity has many real-world applications, including GPS technology, nuclear power plants, and the study of black holes. It also plays a crucial role in our understanding of the universe and the laws of physics.

5. Are there any common misconceptions about relativity?

One common misconception is that relativity only applies to objects traveling at near the speed of light. In reality, the principles of relativity apply to all objects, regardless of their speed. Another misconception is that relativity is only relevant in outer space, when in fact it has implications for our daily lives on Earth as well.

• Special and General Relativity
Replies
8
Views
1K
• Science and Math Textbooks
Replies
5
Views
2K
• Special and General Relativity
Replies
1
Views
771
• Special and General Relativity
Replies
7
Views
1K
• Special and General Relativity
Replies
1
Views
861
• Special and General Relativity
Replies
7
Views
2K
• Special and General Relativity
Replies
22
Views
2K
• Special and General Relativity
Replies
21
Views
915
• Special and General Relativity
Replies
9
Views
2K
• Special and General Relativity
Replies
53
Views
4K