Thread: Help with relativity!?!

I have built myself a great basic understanding on the theory of relativity, but I want to get more in depth with it. Basically I want to start understanding the math of it! I have seen many videos on Einsteins relativity, but none go in depth with the math. So what I want to know is what math do I need to know (I love math so new topics are interesting to me), what other science related stuff I need to understand, and anything else. Thank you in advance! Oh and is there a good website to understand tensors?!?

Try these sticky threads by members Markus Hanke and Janus (although member Janus focused less on mathematics and more the concepts):
http://www.thescienceforum.com/physi...ty-primer.html
Solving the Einstein Field Equations
Special Relativity Primer


Other members (including the ones already mentioned) such as xyzt, tk421, KJW, SpeedFreek and Guitarist should be able to give you more information.

Originally Posted by MindlessMath

I have built myself a great basic understanding on the theory of relativity, but I want to get more in depth with it. Basically I want to start understanding the math of it! I have seen many videos on Einsteins relativity, but none go in depth with the math. So what I want to know is what math do I need to know (I love math so new topics are interesting to me), what other science related stuff I need to understand, and anything else. Thank you in advance! Oh and is there a good website to understand tensors?!?

You may want to start here, it is an excellent "book" and it is free.
This one is also excellent (and free). You want volume II.

Originally Posted by MindlessMath

I have built myself a great basic understanding on the theory of relativity, but I want to get more in depth with it. Basically I want to start understanding the math of it! I have seen many videos on Einsteins relativity, but none go in depth with the math. So what I want to know is what math do I need to know (I love math so new topics are interesting to me), what other science related stuff I need to understand, and anything else. Thank you in advance! Oh and is there a good website to understand tensors?!?

You start with relativity, if i were you i would start with mechanics, thermodynamics, and optics, maybe electronics. You know, the practical, and visible/logical physics.

Unless you already understand those, then follow the other guys advices..

Originally Posted by Zwolver

Originally Posted by MindlessMath

I have built myself a great basic understanding on the theory of relativity, but I want to get more in depth with it. Basically I want to start understanding the math of it! I have seen many videos on Einsteins relativity, but none go in depth with the math. So what I want to know is what math do I need to know (I love math so new topics are interesting to me), what other science related stuff I need to understand, and anything else. Thank you in advance! Oh and is there a good website to understand tensors?!?

You start with relativity, if i were you i would start with mechanics, thermodynamics, and optics, maybe electronics. You know, the practical, and visible/logical physics.

Are you intimating that relativity is not logical? Less logical?

Originally Posted by MindlessMath

I have built myself a great basic understanding on the theory of relativity, but I want to get more in depth with it. Basically I want to start understanding the math of it! I have seen many videos on Einsteins relativity, but none go in depth with the math. So what I want to know is what math do I need to know (I love math so new topics are interesting to me), what other science related stuff I need to understand, and anything else. Thank you in advance! Oh and is there a good website to understand tensors?!?

The theory of relativity is built on an area of mathematics called differential geometry, which naturally incorporates tensor calculus on manifolds. In order to understand this, you need a very solid grounding in single & multivariable calculus, as well as linear algebra. I would hence recommend you ensure that you are reasonably familiar with those before going any further.

As for tensors - to be perfectly honest, if you want to really understand these ( in the context of relativity ), then there isn't a substitute for a good textbook on the matter. Which one to get depends largely on what level of understanding you are hoping to achieve, so perhaps you can write a few words on that, and I might be able to give you a recommendation.

Alright guys thank you a lot! I should be able get further with relativity in my sophomore year when I finish my college physics class, and my calculus... other than that I'm good so thank you guys again!

Originally Posted by xyzt

Originally Posted by Zwolver

Originally Posted by MindlessMath

I have built myself a great basic understanding on the theory of relativity, but I want to get more in depth with it. Basically I want to start understanding the math of it! I have seen many videos on Einsteins relativity, but none go in depth with the math. So what I want to know is what math do I need to know (I love math so new topics are interesting to me), what other science related stuff I need to understand, and anything else. Thank you in advance! Oh and is there a good website to understand tensors?!?

You start with relativity, if i were you i would start with mechanics, thermodynamics, and optics, maybe electronics. You know, the practical, and visible/logical physics.

Are you intimating that relativity is not logical? Less logical?

I mean by logical, laws you can measure at home, with a multimeter, a thermometer, a newtonmeter and a lux cell.

Most of the laws from relativity can't be measured with simple items, and thus should be used purely theoretically. I prefer the practical side (non theoretical) of physics myself. I can't really grasp laws those laws i can't measure myself.. I can learn the laws, but they never stick, untill i can measure them myself..

Originally Posted by Zwolver

Originally Posted by xyzt

Originally Posted by Zwolver

Originally Posted by MindlessMath

I have built myself a great basic understanding on the theory of relativity, but I want to get more in depth with it. Basically I want to start understanding the math of it! I have seen many videos on Einsteins relativity, but none go in depth with the math. So what I want to know is what math do I need to know (I love math so new topics are interesting to me), what other science related stuff I need to understand, and anything else. Thank you in advance! Oh and is there a good website to understand tensors?!?

You start with relativity, if i were you i would start with mechanics, thermodynamics, and optics, maybe electronics. You know, the practical, and visible/logical physics.

Are you intimating that relativity is not logical? Less logical?

I mean by logical, laws you can measure at home, with a multimeter, a thermometer, a newtonmeter and a lux cell.

Most of the laws from relativity can't be measured with simple items, and thus should be used purely theoretically. I prefer the practical side (non theoretical) of physics myself. I can't really grasp laws those laws i can't measure myself.. I can learn the laws, but they never stick, untill i can measure them myself..

The simple reason you sit in front of a functioning computer is the DIRECT consequence of QED. What more DIRECT proof do you need?

Originally Posted by Zwolver

Most of the laws from relativity can't be measured with simple items, and thus should be used purely theoretically. I prefer the practical side (non theoretical) of physics myself. I can't really grasp laws those laws i can't measure myself.. I can learn the laws, but they never stick, untill i can measure them myself..

I prefer theoretical as of it involves more math, and math brings me joy

Originally Posted by Zwolver

Originally Posted by xyzt

Are you intimating that relativity is not logical? Less logical?

I mean by logical, laws you can measure at home, with a multimeter, a thermometer, a newtonmeter and a lux cell.

Most of the laws from relativity can't be measured with simple items, and thus should be used purely theoretically. I prefer the practical side (non theoretical) of physics myself. I can't really grasp laws those laws i can't measure myself.. I can learn the laws, but they never stick, untill i can measure them myself..

That is not what logical means.

As far as practical goes, your GPS would not work if it did not account for relativistic effects. I'm not sure how much more practical you can get.

Originally Posted by Zwolver

laws you can measure at home, with a multimeter, a thermometer, a newtonmeter and a lux cell.

I'm afraid there is more to physics than just classical mechanics from 400 years ago.

Most of the laws from relativity can't be measured with simple items

Relativity is about clocks, rulers, and accelerometers; it just so happens that the laws of relativity coincide with Newtonian mechanics in the comfort of your home. To actually measure relativistic effects that deviate from classical mechanics, you have to either move very fast, and/or place yourself in a very strong gravitational field. That's just the nature of things.

Now don't hate me for the next line I'm about to say, I'm 11 but I absolutely LOVE science. I understand fusion, fission, watch Steven hawking's shows with what my Dad says is outstanding comprehension, but there is one thing that confuses me, where can I find a list of all Einstein's equations, because I would love to decipher them. (that is if I can lol)

Originally Posted by frumpydolphin

Now don't hate me for the next line I'm about to say, I'm 11 but I absolutely LOVE science. I understand fusion, fission, watch Steven hawking's shows with what my Dad says is outstanding comprehension, but there is one thing that confuses me, where can I find a list of all Einstein's equations, because I would love to decipher them. (that is if I can lol)

Ok, don't take what I have to say the wrong way - I really admire your love of science, and would like to encourage you to pursue it. However, having said that, at the age of 11 you are quite simply missing the mathematical basics which are needed to understand the Einstein equations, and for the same reason you shouldn't expect to be able to "decipher" them. But just to satisfy your curiosity, I will write them down for you anyway :



The quantity is called the Einstein tensor, and roughly represents the "geometry of space-time". is called the energy-momentum tensor, and measures everything that can be a source of gravity, such as mass, energy, stress, momentum etc etc. The is a proportionality constant. The "tensors" in this equation have subscripts because they are in fact a collection of different components; each subscript runs from 0...3, so what looks like one equation above is really just shorthand for a system of many equations.

What this equation tells us is thus that the geometry of space-time is determined by the presence of energy-momentum; in other words - gravity is just a manifestation of geometry ( and not a force, as in good old Newtonian mechanics ), which is in turn determined by things like mass, energy, momentum etc etc. Given your young age I wouldn't bother trying to understand the underlying mathematics, but if you get the basic idea, then you already know more than most kids your age

Originally Posted by Markus Hanke

Originally Posted by frumpydolphin

Now don't hate me for the next line I'm about to say, I'm 11 but I absolutely LOVE science. I understand fusion, fission, watch Steven hawking's shows with what my Dad says is outstanding comprehension, but there is one thing that confuses me, where can I find a list of all Einstein's equations, because I would love to decipher them. (that is if I can lol)

Ok, don't take what I have to say the wrong way - I really admire your love of science, and would like to encourage you to pursue it. However, having said that, at the age of 11 you are quite simply missing the mathematical basics which are needed to understand the Einstein equations, and for the same reason you shouldn't expect to be able to "decipher" them. But just to satisfy your curiosity, I will write them down for you anyway :



The quantity is called the Einstein tensor, and roughly represents the "geometry of space-time". is called the energy-momentum tensor, and measures everything that can be a source of gravity, such as mass, energy, stress, momentum etc etc. The is a proportionality constant. The "tensors" in this equation have subscripts because they are in fact a collection of different components; each subscript runs from 0...3, so what looks like one equation above is really just shorthand for a system of many equations.

What this equation tells us is thus that the geometry of space-time is determined by the presence of energy-momentum; in other words - gravity is just a manifestation of geometry ( and not a force, as in good old Newtonian mechanics ), which is in turn determined by things like mass, energy, momentum etc etc. Given your young age I wouldn't bother trying to understand the underlying mathematics, but if you get the basic idea, then you already know more than most kids your age

Hmm... Now I know what the subscript is

Markus or anyone else, If you could provide a links with some lessons on multi-variable calculus, linear algebra, and anything else you suspect I might not know that would be wonderful!!!

Originally Posted by frumpydolphin

Now don't hate me for the next line I'm about to say, I'm 11 but I absolutely LOVE science. I understand fusion, fission, watch Steven hawking's shows with what my Dad says is outstanding comprehension, but there is one thing that confuses me, where can I find a list of all Einstein's equations, because I would love to decipher them. (that is if I can lol)

Well you're lucky you realized you like science at such a young age, If I would have realized I liked it so much when I was younger I would have finished calculus by now! I'm not saying you can't decipher Einstein's equations, but it involves a lot of math you don't learn at your age yet... I myself am 15 now, I am close to knowing enough math, but I am not there yet... I started teaching myself math at the age of 13. At your age if you start studying ahead you'll get there before basically anyone else at your age.

I admire your affection for the sciences at such a young age!

Originally Posted by MindlessMath

Markus or anyone else, If you could provide a links with some lessons on multi-variable calculus, linear algebra, and anything else you suspect I might not know that would be wonderful!!!

Try here:

Mathematics | MIT OpenCourseWare | Free Online Course Materials

Originally Posted by MindlessMath

Markus or anyone else, If you could provide a links with some lessons on multi-variable calculus, linear algebra, and anything else you suspect I might not know that would be wonderful!!!

There is also this; Approved Textbooks | American Inst. of Mathematics

Originally Posted by Markus Hanke

Originally Posted by Zwolver

laws you can measure at home, with a multimeter, a thermometer, a newtonmeter and a lux cell.

I'm afraid there is more to physics than just classical mechanics from 400 years ago.

Most of the laws from relativity can't be measured with simple items

Relativity is about clocks, rulers, and accelerometers; it just so happens that the laws of relativity coincide with Newtonian mechanics in the comfort of your home. To actually measure relativistic effects that deviate from classical mechanics, you have to either move very fast, and/or place yourself in a very strong gravitational field. That's just the nature of things.

Yeah, i know that... I was just giving an opinion, like starting with the basics first, not to jump in to deep. I like the classical mechanics because everything about this is know, no weird unexplainable effects, just geometry, vectors and some differentiating/integrating.

And yes, newtonian mechanics coincides with general and special relativity. In the end it is based upon one another, that is why you should first understand the foundation, before plunging yourself into the jungle that is relativity..

Originally Posted by Zwolver

before plunging yourself into the jungle that is relativity..

Jungle? Seriously?

Originally Posted by Zwolver

In the end it is based upon one another, that is why you should first understand the foundation, before plunging yourself into the jungle that is relativity..

Yes, I agree. A thorough grounding in classical mechanics is of course essential before one can understand modern physics.

Originally Posted by Markus Hanke

Originally Posted by frumpydolphin

Now don't hate me for the next line I'm about to say, I'm 11 but I absolutely LOVE science. I understand fusion, fission, watch Steven hawking's shows with what my Dad says is outstanding comprehension, but there is one thing that confuses me, where can I find a list of all Einstein's equations, because I would love to decipher them. (that is if I can lol)

Ok, don't take what I have to say the wrong way - I really admire your love of science, and would like to encourage you to pursue it. However, having said that, at the age of 11 you are quite simply missing the mathematical basics which are needed to understand the Einstein equations, and for the same reason you shouldn't expect to be able to "decipher" them. But just to satisfy your curiosity, I will write them down for you anyway :



The quantity is called the Einstein tensor, and roughly represents the "geometry of space-time". is called the energy-momentum tensor, and measures everything that can be a source of gravity, such as mass, energy, stress, momentum etc etc. The is a proportionality constant. The "tensors" in this equation have subscripts because they are in fact a collection of different components; each subscript runs from 0...3, so what looks like one equation above is really just shorthand for a system of many equations.

What this equation tells us is thus that the geometry of space-time is determined by the presence of energy-momentum; in other words - gravity is just a manifestation of geometry ( and not a force, as in good old Newtonian mechanics ), which is in turn determined by things like mass, energy, momentum etc etc. Given your young age I wouldn't bother trying to understand the underlying mathematics, but if you get the basic idea, then you already know more than most kids your age

Thanks for acknowledging my age, and if the variables were replaced I could maybe figure something out.

Originally Posted by Markus Hanke

Originally Posted by Zwolver

In the end it is based upon one another, that is why you should first understand the foundation, before plunging yourself into the jungle that is relativity..

Yes, I agree. A thorough grounding in classical mechanics is of course essential before one can understand modern physics.

While that's very likely to be true in practice, I like to think that it is in principle possible to derive advanced physics from first principles and forgo Newtonian physics altogether.

Originally Posted by KJW

While that's very likely to be true in practice, I like to think that it is in principle possible to derive advanced physics from first principles and forgo Newtonian physics altogether.

Yes, I agree.

Originally Posted by MindlessMath

Originally Posted by frumpydolphin

Now don't hate me for the next line I'm about to say, I'm 11 but I absolutely LOVE science. I understand fusion, fission, watch Steven hawking's shows with what my Dad says is outstanding comprehension, but there is one thing that confuses me, where can I find a list of all Einstein's equations, because I would love to decipher them. (that is if I can lol)

Well you're lucky you realized you like science at such a young age, If I would have realized I liked it so much when I was younger I would have finished calculus by now! I'm not saying you can't decipher Einstein's equations, but it involves a lot of math you don't learn at your age yet... I myself am 15 now, I am close to knowing enough math, but I am not there yet... I started teaching myself math at the age of 13. At your age if you start studying ahead you'll get there before basically anyone else at your age.

I admire your affection for the sciences at such a young age!

Then do you know any websites where math is explained.(go for around 7th grade level)