# Introduction to Special Relativity for a twelve year old

1. Oct 9, 2012

### sarsonlarson5

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. Oct 9, 2012

### ImaLooser

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. Oct 9, 2012

### ghwellsjr

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.
That is a lofty goal. If you think you can do that, you will find SR to be a piece of cake.
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.

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4. Oct 9, 2012

5. Oct 9, 2012

### robphy

Albert Einstein's Theory of Relativity - In Words of Four Letters or Less

More seriously,
learn spacetime diagrams as soon as possible:
Spacetime Physics by Taylor and Wheeler
(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/General-Relativity-B-Robert-Geroch/dp/0226288641
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/Ideas-That-Shaped-Physics-Frame-Independent/dp/0072397144
or the earlier Traveler's Guide to Spacetime
https://www.amazon.com/A-Travelers-Guide-To-Spacetime/dp/0070430276
(Unit Q introduces Quantum Mechanics.)

Flat and Curved Spacetimes by Ellis and Williams
https://www.amazon.com/Flat-Curved-Space-Times-George-Ellis/dp/0198511698

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6. Oct 9, 2012

### ghwellsjr

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. Oct 9, 2012

### harrylin

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.

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8. Oct 9, 2012

### Intrastellar

I hope you realise that our 12 year old has already done calculus I,II. Special Relativity shouldn't be much harder than it

9. Oct 9, 2012

### harrylin

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. Oct 9, 2012

### Staff: Mentor

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. Oct 9, 2012

### robphy

I would personally not recommend Greene's book.
In my opinion, it's best to learn relativity from a relativist.

12. Oct 9, 2012

### Cbray

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. Oct 10, 2012

### Demystifier

Cbray, I think he's a normal 12 year old, not a genius like you.

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14. Oct 10, 2012

### bcrowell

Staff Emeritus
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. Oct 10, 2012

### sarsonlarson5

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 highschool, 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. Im 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. Oct 10, 2012

### FreeMitya

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.

Last edited: Oct 10, 2012
17. Oct 10, 2012

### FreeMitya

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. Oct 11, 2012

### sarsonlarson5

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. Oct 11, 2012

### FreeMitya

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. Oct 11, 2012

### sarsonlarson5

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. Oct 11, 2012

### FreeMitya

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. Nov 20, 2012

### Cbray

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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23. Nov 21, 2012

### mathwonk

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24. Nov 21, 2012

### Jorriss

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. Nov 21, 2012

### Cbray

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 text books, and I'm studying 3-4 years ahead of my age and go to a public school. I fail at noticing your point.