Introduction to Special Relativity for a twelve year old

In summary: These will help you understand the mathematics behind SR. After that, read through some of the more conceptual papers on the subject, like the one by Geroch.
  • #1
sarsonlarson5
35
0
Hello!

I am currently a twelve-year old, and I am interested in learning about Relativity. I have heard that there are two main fields relativity is divided into - special relativity, and general relativity. Although some people have said that general relativity is considerably harder than special relativity, I am not sure if I even have the knowledge required to understand either fields in the first place.

I have taken a Calculus I/II course and a rather limited AP level Physics course. I have an excellent Physics teacher to help me. Would this level of knowledge in mathematics and Physics be enough to get me started on Special relativity? My goal for Physics is to learn all the math and Physics necessary needed for learning Quantum Physics/accelerator Physics by the time I am fourteen.

If I am asking ignorant questions or making unplausible comments, please excuse me, as I have little of Modern Physics.

Thank You.
 
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  • #2
Hello!

I am currently a twelve-year old, and I am interested in learning about Relativity. I have heard that there are two main fields relativity is divided into - special relativity, and general relativity. Although some people have said that general relativity is considerably harder than special relativity, I am not sure if I even have the knowledge required to understand either fields in the first place.

I have taken a Calculus I/II course and a rather limited AP level Physics course. I have an excellent Physics teacher to help me. Would this level of knowledge in mathematics and Physics be enough to get me started on Special relativity? My goal for Physics is to learn all the math and Physics necessary needed for learning Quantum Physics/accelerator Physics by the time I am fourteen.

If I am asking ignorant questions or making unplausible comments, please excuse me, as I have little of Modern Physics.

Thank You.

The mathematics of special relativity is simple and basic trigonometry, so you have plenty of math. The difficulty is the conceptual weirdness. It contradicts preconceptions. If you are good at emptying your mind of preconceptions then you won't have much trouble with it.

General requires tensor calculus, which you don't want to deal with yet.
 
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  • #3
Hello!

I am currently a twelve-year old, and I am interested in learning about Relativity. I have heard that there are two main fields relativity is divided into - special relativity, and general relativity. Although some people have said that general relativity is considerably harder than special relativity, I am not sure if I even have the knowledge required to understand either fields in the first place.

I have taken a Calculus I/II course and a rather limited AP level Physics course. I have an excellent Physics teacher to help me. Would this level of knowledge in mathematics and Physics be enough to get me started on Special relativity?
You've got more than enough math and physics to understand Einstein's Special Relativity, especially if you just want to understand the basics. It just takes a little algebra.
My goal for Physics is to learn all the math and Physics necessary needed for learning Quantum Physics/accelerator Physics by the time I am fourteen.
That is a lofty goal. If you think you can do that, you will find SR to be a piece of cake.
If I am asking ignorant questions or making unplausible comments, please excuse me, as I have little of Modern Physics.

Thank You.
For starters, I would suggest that you read the first few sections of Einstein's 1905 paper in which he introduced SR to the world. See if you can grasp one section at a time and asks questions if you need help.

I really admire you and your drive. We want to help you achieve your goals.
 
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  • #5
Albert Einstein's Theory of Relativity - In Words of Four Letters or Less
http://www.muppetlabs.com/~breadbox/txt/al.html

More seriously,
learn spacetime diagrams as soon as possible:
Spacetime Physics by Taylor and Wheeler
http://www.eftaylor.com/download.html#special_relativity
(There are also links to new introductions on General Relativity and Quantum Mechanics.)

General Relativity from A to B by Geroch
https://www.amazon.com/dp/0226288641/?tag=pfamazon01-20
Though deceptively simple looking, this was eye-opening (on my third re-reading) because of its emphasis on measurements and the operational meaning of concepts. They helped clarify the physics encoded by the mathematical formalism I had seen in more mathematical relativity texts.

Six Ideas that Shaped Physics - unit R by Moore
https://www.amazon.com/dp/0072397144/?tag=pfamazon01-20
or the earlier Traveler's Guide to Spacetime
https://www.amazon.com/dp/0070430276/?tag=pfamazon01-20
(Unit Q introduces Quantum Mechanics.)

Flat and Curved Spacetimes by Ellis and Williams
https://www.amazon.com/dp/0198511698/?tag=pfamazon01-20
 
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  • #6
I urge you to only read the paper written by Einstein that I referenced in post #3. These other papers supposedly written for children are not what Einstein would endorse because they misrepresent what Einstein said. The first one in post #4 claims that experiments have been done to show that light propagates for everyone at c (Einstein's second postulate) which is not true. The first paper in post #5 claims that people can see that a ray of light travels at c, which is not true. You cannot watch a ray move at c.

Here's the truth and the point that many people, including these two authors get mixed up. We can measure the round-trip speed of light by using one clock and a mirror some measured distance away. All inertial observers will get the same result when they calculate the "average" speed of light. But no one can observe or measure if the light took the same amount of time to get to the mirror as what it takes for the reflection to get back to the starting point. Einstein makes this point over and over again in his 1905 paper. And it's a very important point because unless and until you understand this, you will always have a mixed up understanding of Special Relativity.

You can understand Einstein's explanation, you don't need something supposedly written for children that actually misrepresents Einstein's theory.
 
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  • #7
ImaLooser said:
[..] The difficulty is the conceptual weirdness. It contradicts preconceptions. If you are good at emptying your mind of preconceptions then you won't have much trouble with it. [..]
In fact, it's not needed to "empty your mind" in order to learn "weird" things, if you heed the following warning:
ghwellsjr said:
I urge you to only read the paper written by Einstein that I referenced in post #3. [..]
Here's the truth and the point that many people [..] get mixed up. We can measure the round-trip speed of light by using one clock and a mirror some measured distance away. All inertial observers will get the same result when they calculate the "average" speed of light. But no one can observe or measure if the light took the same amount of time to get to the mirror as what it takes for the reflection to get back to the starting point. Einstein makes this point over and over again in his 1905 paper. And it's a very important point because unless and until you understand this, you will always have a mixed up understanding of Special Relativity. [..]
Do I need to say that I fully agree with that? (you can of course "measure" what you first defined, but that only tells you that a number of things are still the same).
You can understand Einstein's explanation, you don't need something supposedly written for children that actually misrepresents Einstein's theory.
Well, in a parallel thread someone complained that Einstein's paper is long-winding. And clearly, the phrasings are not all that simple and the third section is certainly too complex and technical for a twelve year old. Also illustrations would be very helpful. But the introduction and first two sections are likely readable for a twelve year old, and they just contain the basic insight that many more popular presentations lack. For the continuation I don't know a good simple presentation. However, one can simply skip section 3 (the derivation), and just jump to some basic results which are discussed in section 4.

So, for an introduction to SR, the introduction + sections 1, 2 and 4 of http://www.fourmilab.ch/etexts/einstein/specrel/www/ are not bad at all. If someone knows an introduction text that presents roughly the same with with illustrations and simpler sentences (without making up weirdo stuff), that would be great.

PS. Still much easier may be to start with Maxwell's theory as maintained in the second postulate, then go through MMX and Lorentz contraction (all from a "stationary frame", and with one clock and one ruler), then add time dilation (light clock) and tell that as a consequence the PoR follows. Next introduce relativity of simultaneity. However, I don't know an introduction that does that.
 
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  • #8
harrylin said:
In fact, it's not needed to "empty your mind" in order to learn "weird" things, if you heed the following warning:

Do I need to say that I fully agree with that? (you can of course "measure" what you first defined, but that only tells you that a number of things are still the same).

Well, in a parallel thread someone complained that Einstein's paper is long-winding. And clearly, the phrasings are not all that simple and the third section is certainly too complex and technical for a twelve year old. Also illustrations would be very helpful. But the introduction and first two sections are likely readable for a twelve year old, and they just contain the basic insight that many more popular presentations lack. For the continuation I don't know a good simple presentation. However, one can simply skip section 3 (the derivation), and just jump to some basic results which are discussed in section 4.

So, for an introduction to SR, the introduction + sections 1, 2 and 4 of http://www.fourmilab.ch/etexts/einstein/specrel/www/ are not bad at all. If someone knows an introduction text that presents roughly the same with with illustrations and simpler sentences (without making up weirdo stuff), that would be great.

PS. Still much easier may be to start with Maxwell's theory as maintained in the second postulate, then go through MMX and Lorentz contraction (all from a "stationary frame", and with one clock and one ruler), then add time dilation (light clock) and tell that as a consequence the PoR follows. Next introduce relativity of simultaneity. However, I don't know an introduction that does that.
I hope you realize that our 12 year old has already done calculus I,II. Special Relativity shouldn't be much harder than it
 
  • #9
montadhar said:
I hope you realize that our 12 year old has already done calculus I,II. Special Relativity shouldn't be much harder than it
Many people have trouble with section 3, even those who had all kinds of calculus. However, there are many derivations available that can replace that section, including Einstein's own simple derivation here:
http://www.bartleby.com/173/a1.html
(it refers to fig.2 in SECTION XI which is linked at the top of the page)
 
  • #10
You might try the popular book The Elegant Universe by Brian Greene. It doesn't always present the physics precisely as it actually exists, but it does give you a feel for how some of the peculiar phenomena observed in special relativity come about, and how they are related to the geometry of 4D spacetime.

Chet
 
  • #11
I would personally not recommend Greene's book.
In my opinion, it's best to learn relativity from a relativist.
 
  • #12
Not to sound arrogant, but, a lot of people actually truly believe they understand Calculus (i.e. most people who take the courses online or at school), yet they barely understand the true meaning and understanding of it and just learn methods to solve problems - I use to be like this.

But on topic, special relativity is easy, I recommend doing basic mechanics, Newtonian mechanics to angular momentum before starting. General relativity is extremely difficult you'll probably encounter it 3rd-4th year university, and most people still struggle with it - Mainly because of the mathematics involved.

I'm 16, I've been studying since I was 12. I really emphasise this, I learn't calculus at 12 too, I thought I understood it since I could do most calculus problems and do everything most year 11 and 12's could do, but last year, I re-read calculus in a much more advanced and formal book, and trust me, I did not have a deep understand of it and I actually felt quite 'beginner', and it was weird because a lot of people were graduating from year 12 like this - I recommend you do look into formal books like this too later on. I started physics early last year, I don't think you'll be even able to do quantum physics by the time you're 14. One, I recommend doing first year physics 2-3 times, but each time go to a more formal book, for example, start off with Tipler (Physics for Scientists and Engineers - includes small amount of single variable calculus) then move onto another one but with more formal mathematics which includes Vector calculus for example. I really emphasise this because you can absorb quite a lot of information and be so powerful and have such a deep understanding.
 
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  • #13
Cbray, I think he's a normal 12 year old, not a genius like you.
 
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  • #14
OP, in the future, please don't post something like this to start a thread and simultaneously send it to people using personal messages. Just start the thread and see what responses you get.
 
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  • #15
Hello!

Thank You for all the helpful advice. I will look into Einstein's original paper, and see if I can piece together the concepts. I have previously looked at some special relativity basics (Einstein's elevator thought experiments). THey didn't seem to complex, but I assume this is because that is only the basics. I get confused when I start looking into warped space-time and its various effects.

Cbray- I do not consider myself as an expert at Calculus, not at all. However, the class I took for Calculus was at a high school, and I had an excellent teacher. He made sure that we all really understood the concepts in Calculus, and not just the simple mechanics. (I knew the basic mechanics when I was eleven, but I only really understood what I was doing when I took that class).

Of course, this may be what you thought when you were twelve. :) Thank You for the tips on expanding my understanding of Calculus. I want to make sure that I really know and understand what I am doing in math - not just performing the mechanics.

I also have one more small question. I previously stated that I wanted to complete the math/physics courses to be ready for quantum physics and accelerator physics by the time I was fourteen. I am sorry if that statement was completely unplausible - I have little knowledge on how difficult either of these courses are. However, I am curious to know what mathematics and physics courses I do need for the physics I wish to learn.

Once again, Thank You for all the helpful tips.

P.S. I attend a unique public school, which gives me complete access to high school and college courses. Since the high school/ middle school is located on the campus of a college, I have access to several higher level courses at no fee, and with no restrictions.
 
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  • #16
ghwellsjr said:
You can understand Einstein's explanation, you don't need something supposedly written for children that actually misrepresents Einstein's theory.

Indeed, special relativity shouldn't be a problem for most people to understand, even young people. It almost seems the older the physics is, the easier it is to understand it (at least in my experience). To the OP, I remember grasping relativity at around your age (I didn't understand the maths involved, but I got a pretty good grasp of the physical proposals). Of course, it wasn't from reading Einstein's paper, but it was an accurate explanation and was not "written for kids". Good to see that some young people still want to supplement their minds.
 
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  • #17
I also have one more small question. I previously stated that I wanted to complete the math/physics courses to be ready for quantum physics and accelerator physics by the time I was fourteen. I am sorry if that statement was completely unplausible - I have little knowledge on how difficult either of these courses are. However, I am curious to know what mathematics and physics courses I do need for the physics I wish to learn.

I'm not exactly an authority, but I'll just say I'd be very impressed if you were to start studying quantum physics at fourteen. Unless you have been identified as considerably talented, should you not pace yourself? Perhaps your best action would be to consult one of your teachers about your goals.
 
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  • #18
Hello!

What does make quantum physics particularly difficult? (I don't mean to sound like I think it is easy.) I believe that you need to know calc 1-3, differential equations, linear algebra, and multivariable calculus as a math prerequisite. I am not sure what the physics prerequisites are. Or is Quantum Physics simply difficult to understand?

I do go to a public school for gifted children were accelerated learning is heavily encouraged. I do not know if I am capable though - and I do not want to rush through things too fast. I also have to worry about my school grades, as I would be taking several of these courses at the college (which are paid by the public school), and the grades I get would count as high school credits. Are there any questions you may ask me to see if I might be capable of such an endeavor?

Thank You.
 
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  • #19
Hello!

What does make quantum physics particularly difficult? (I don't mean to sound like I think it is easy.) I believe that you need to know calc 1-3, differential equations, linear algebra, and multivariable calculus as a math prerequisite. I am not sure what the physics prerequisites are. Or is Quantum Physics simply difficult to understand?

I do go to a public school for gifted children were accelerated learning is heavily encouraged. I do not know if I am capable though - and I do not want to rush through things too fast. I also have to worry about my school grades, as I would be taking several of these courses at the college (which are paid by the public school), and the grades I get would count as high school credits. Are there any questions you may ask me to see if I might be capable of such an endeavor?

Thank You.

Have you been officially registered as gifted? This may seem like a silly question, but you say you don't know whether you are capable of going to that school. Is a certain score on an intelligence test a pre-requisite at that particular school? I personally don't take psychometrics very seriously, but I'm sure being identified as gifted wouldn't hurt.

Quantum physics or quantum mechanics, if you will, by my understanding (again, I'm not an authority), is one of the most intricate branches of physics. Richard Feynman once joked that no one is smart enough to understand quantum mechanics (paraphrased). A simplified example is the wave-particle duality that particles exhibit; that is, they behave both as particles and as waves. I'm not sure if being proficient in the mathematical prerequisites necessarily means quantum mechanics is going to be easy. I don't know you personally and a couple of posts on the internet is insufficient to gauge another's intellectual potential, but fourteen seems a bit early to begin studying it. Then again, you could be exceptionally talented. Talk to one of your teachers.

All that being said, you're interested, which is key. Like I said, it is very pleasing to see a youth take such intellectual initiative (then again, who am I to call you a youth, as I'm only eighteen).
 
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  • #20
I meant that I do not know if I am capable of trying to learn quantum physics at such an early age. I do not know if this helps, but the school that I go to is a fairly prestigious school.

I hope I don't seem like a snob. :)
 
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  • #21
I meant that I do not know if I am capable of trying to learn quantum physics at such an early age. I do not know if this helps, but the school that I go to is a fairly prestigious school.

I hope I don't seem like a snob. :)

In case you didn't read my post before I edited it, I included an example of what makes quantum physics so puzzling.

And no, you don't seem like a snob. I'm not so insecure that I'm intimidated by people who are registered as gifted (or "giftoids", as I call them). You do seem intelligent, and I only want to encourage you. Sure, try quantum physics when you're fourteen. If it's too hard, there is no shame in putting it on hold. You go to the same school that gave us Taylor Wilson, so you at least have quality of education taken care of.

As a side note, may I make a few recommendations for nurturing your mind? If you don't already read recreationally, do so. Read as much as you can. Read fiction, non-fiction. Don't just focus on maths an physics. Never stop educating yourself, and expose yourself to a variety of topics.
 
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  • #22
I meant that I do not know if I am capable of trying to learn quantum physics at such an early age. I do not know if this helps, but the school that I go to is a fairly prestigious school.

I hope I don't seem like a snob. :)

It's irrelevant which school you go to, prestigious schools are obviously where most doctors, or lawyers come out of, but you can rarely find someone truly passionate about something and they are usually distributed fairly evenly. Natural intelligence is pretty much quite irrelevant until you start doing your own research (unless you're lower then average) or GR (lol), I have even a hard time believe natural intelligence actually exists.

Just go and start studying, you have to do single and multi variable calc, linear algebra (including eigen values - VERY IMPORTANT!), differential equations mathematical wise, then do modern mechanics and EM. I don't know why you're so keen, QM isn't as exciting at first (it is later though for sure!) and if you rush things it will be a complete waste of time and you'll end up hating it. Physics is the hardest thing to study, and blasting through to QM is not going to make you any better then someone who just waited till their in 2nd year to start it.

I'm not trying to say your bad or anything, you just need to take your time with physics (i.e. make sure you're absorbing everything properly), physics is incredibly beautiful and rushing through to the end is not the point - I thoroughly recommend doing single-variable calc first, and then starting your physics. Make sure you've done all the essentials before hand (i.e. functions, trig, logs, etc).
 
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  • #24
Cbray said:
It's irrelevant which school you go to, prestigious schools are obviously where most doctors, or lawyers come out of,
Don't you imagine most doctors and lawyers just went to normal public high schools? And what school you go to can matter a lot. This school is giving him access to college courses as a 12 year old, and he's succeeding in them, as opposed to many high schools in america which do not have precalculus.
 
  • #25
Jorriss said:
Don't you imagine most doctors and lawyers just went to normal public high schools? And what school you go to can matter a lot. This school is giving him access to college courses as a 12 year old, and he's succeeding in them, as opposed to many high schools in america which do not have precalculus.

And that holds you back from going out and buying a book? You can find the equivalence in a book anywhere instead of dropping lots of money on a school. I've learn't most of my knowledge from textbooks, and I'm studying 3-4 years ahead of my age and go to a public school. I fail at noticing your point.
 
  • #26
Oh btw, hit up the international olympiad in a few years. I'm going to do it just for the sake of getting in a university in America (there's really no other point) since I find the physics departments in places like UC Berkeley and UCLA incredible - I hope to do my under and post grad work there, it's much harder as an international student from Australia to go to America, so it's something I can guarantee my acceptance. Though since your from America you probably don't need to bother, so lucky haha.
 
  • #27
I wonder if it wise of you to solicit advice on this topic from complete strangers, when you say you have a good physics teacher to help you. I suggest that such a teacher who knows not only physics but who also knows you, can give the most appropriate advice. In my opinion, some of us advisers here are at least partially using this opportunity to toot our own horns. Notice for example in my advice above I could not resist pointing out that I had also read about relativity as a child. And I suggest you remember to just try to relax a bit. it is of no importance at all whether you learn quantum theory when you are 14 or much older. Louis de Broglie said he spent over 25 years contemplating the subject. He said this in a book my father gave me as a young child, hoping to prod me into becoming a prodigy of some kind. I greatly enjoyed reading the book some 30 or 40 years later. Learning is for enjoyment and enriching your life, not obsessing about being the youngest person to read some book or other.

By the way you sound quite normal and well adjusted. You also seem to have a fortunate opportunity to expand your education. But I again caution you to proceed as seems interesting to you, and not in order to live up to the expectations of some other people. Gee whiz, if you don't take time to explore recreationally at 12, when will you ever? Good luck to you.
 
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  • #28
What does make quantum physics particularly difficult? (I don't mean to sound like I think it is easy.) I believe that you need to know calc 1-3, differential equations, linear algebra, and multivariable calculus as a math prerequisite. I am not sure what the physics prerequisites are. Or is Quantum Physics simply difficult to understand?

A full-bore QM course at upper undergraduate or graduate level does pretty much require the math background you describe. However, that is not where most students (in the US at least) get their first exposure to QM.

Most colleges and universities have an "introductory modern physics" course which follows the usual two-semester calculus-based introductory physics course. It covers basic relativity and QM (e.g. simple one-dimensional situations like the "particle in a box", applications in atomic physics, nuclear physics, etc., and some history of the subject. It often requires only calculus I-II as a prerequisite, and introduces basic concepts of complex numbers, differential equations etc. as necessary.

A typical textbook for such a course is https://www.amazon.com/dp/013805715X/?tag=pfamazon01-20.
 
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  • #29
Cbray said:
And that holds you back from going out and buying a book? You can find the equivalence in a book anywhere instead of dropping lots of money on a school. I've learn't most of my knowledge from textbooks, and I'm studying 3-4 years ahead of my age and go to a public school. I fail at noticing your point.

There is a big problem with self-studying. Namely, you never really know whether you know the material or not. And you can't get feedback on the things you do or the exercises you solve. It's very easy to grow bad habits while self-studying, and nobody is there to correct them.

There have been quite a few people on this forum who said they were self-studying calculus. But whenever they said something about it, I immediately noticed that they were doing it wrong and that they really needed a teacher to guide them. They thought they were doing quite well though and they thought they knew the material.

Taking actual and formal college courses (should) eliminate the problem a bit. You have to do homework, mid-terms and exams. So you get constant feedback on your performance.
 
  • #30
micromass said:
There is a big problem with self-studying. Namely, you never really know whether you know the material or not. And you can't get feedback on the things you do or the exercises you solve. It's very easy to grow bad habits while self-studying, and nobody is there to correct them.

There have been quite a few people on this forum who said they were self-studying calculus. But whenever they said something about it, I immediately noticed that they were doing it wrong and that they really needed a teacher to guide them. They thought they were doing quite well though and they thought they knew the material.

Taking actual and formal college courses (should) eliminate the problem a bit. You have to do homework, mid-terms and exams. So you get constant feedback on your performance.

Just as an addition to most post, it is good to have a tutor to make sure you're going along well who's doing physics in university (which is what I'm currently doing) and if you have any questions ask them every week or so.
 
  • #31
Hello!

I think that micromass may have a point. When I study from textbooks and research papers, I often make a few mistakes, and I don't even realize them until a while. (For example, I used to use one moment of inertia for all rotational mechanics problems until I figured out why I was getting many of the problems wrong). However, I think reading Einstein's original paper can work out, because I can ask my physics teacher if I don't understand something, or I am getting something wrong.

Thank You.
 
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  • #32
I don't know what you mean by reading 'Einstein's original paper'? Okay sure, you make a really stupid mistake by being careless of what you're reading. Does that imply that the information in the book isn't good enough for your standards?

Sure, you need to ask a few questions you're curious about, hire a tutor every 2 weeks. You think Richard Feynman asked a teacher at school about a careless mistake? NO! Because he didn't make careless mistakes, he spent years ripping his hair out throughout mathematics and physics to make sure he understood the true meaning of something, and found huge pleasure of doing so using textbooks and became one of the greatest physicists of all time. Maybe it isn't the quickest root to building a cyclotron or studying quantum mechanics, but he was brilliant at everything by the end. As I said earlier, since not everyone is Richard Feynman, hire a tutor every once and a while. I don't know the reasoning behind the doubt that textbooks 'don't work' and there is a 'BIG PROBLEM' with self studying, so I'd have to disagree with micromass.
 
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  • #33
Hello

Throughout the forums, people stated that the best way to learn special relativity is to read Einstein's original paper. So I was just saying that I will take their advice and start reading the paper. There's no harm in trying to figure out something on my own - it is fun to do anyway. Like Cbray said, if I make a mistake, I'll just take time to try and figure it out on my own. Only if I'm really stuck and I don't know what to do after lots of time spent on figuring it out, I'll ask for help. I guess I should probably stop posting on what I should do, and get around to doing it itself. :)

Thank You for your help.
 
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What is special relativity?

Special relativity is a branch of physics that explains how objects move at high speeds and how time and space are affected by this motion. It was developed by Albert Einstein and is a fundamental theory in modern physics.

Why is it important to learn about special relativity?

Special relativity helps us understand how the universe works, from the smallest particles to the largest galaxies. It is also the basis for many modern technologies, such as GPS systems and particle accelerators.

How does special relativity differ from Newton's laws of motion?

Newton's laws of motion only apply to objects moving at low speeds, while special relativity is needed to accurately describe objects moving at high speeds, close to the speed of light. Special relativity also takes into account the effects of gravity on space and time.

What is the theory of relativity in simple terms?

The theory of relativity states that the laws of physics are the same for all observers, regardless of their relative motion. It also explains how time and space are relative, meaning they can appear differently to different observers depending on their motion and position.

Can you give an example of how special relativity works in everyday life?

One example is the time dilation effect, where time appears to pass slower for objects moving at high speeds. This is why astronauts on the International Space Station age slightly slower than people on Earth, since they are moving at a very high speed relative to the Earth's surface.

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