Can you please simplify Special and general relativity into basic principles please?

[Hashirama_Senju]

What are the main principles for both theories that everything else branches off?

[Endercreeper01]

The fundamental concept of general relativity is that gravity bends space-time. The curvature is described by

[latex]R_{ab} - 1/2 R g_{ab} + \Lambda g_{ab}=\frac{8\pi G}{c^4} T_{ab}[/latex]

And also by the metric tensor, [latex]g_{ab}[/latex].

[latex]ds^2=g_{ab}\sum dx^a dx^b[/latex].

The fundamental concept of special relativity is that nothing can travel faster then light.

Relative velocity is given by

[latex]v'=\frac{v+u}{1-\frac{uv}{c^2}}[/latex]

and this ensures that the relative velocity never exceeds the speed of light.

The energy required to accelerate an object to a velocity v is

[latex]E=\frac{mc^2}{\sqrt{1-\frac{v^2}{c^2}}}[/latex]

This value approaches infinity as v approaches c, so you would need infinite energy to get something to the speed of light. Because you can't have infinite energy, nothing can be accelerated to the speed of light.

Edited February 23, 2014 by Endercreeper01

[timo]

I'm not sure that "the fundamental concept is [a cryptic arrangement of greek and latin letters without any trace of explanation]" really helps much. The equations being syntactically wrong doesn't really help, either: The first equation shold probably have all-lower indices and the 2nd one has a misplaced sum-sign (assuming the unlabeled sum is supposed to sum over a and b). Minor typos, though. Not explaining what the symbols stand for is the big problem.

 

On topic: I am not sure that in physics there is that one statement from which everything else derives. Even though that's admittedly how physics is often sold to students. One might be tempted to say that some hocus-pocus statements like "spacetime is described as a manifold with intrinsic geometrical properties" or "the speed of light is the same for all observers" were such fundamentals. But that's just ignoring that those statements need of a lot of other assumptions, a framework to "live in", to even have any meaning.

[Strange]

What are the main principles for both theories that everything else branches off?

 

That the speed of light is constant for all observers.

[Endercreeper01]

the 2nd one has a misplaced sum-sign (assuming the unlabeled sum is supposed to sum over a and b)

The sum stands for a sum over the coordinates. The metric tensor is a matrix, and so it will be distributed for each coordinate.

[Endercreeper01]

I was just assuming that the OP already knew about the equations of Relativity. I just sorted the 2 theories into fundamental concepts and equations.

[ajb]

..."spacetime is described as a manifold with intrinsic geometrical properties" ...

This is one of the basic principles of Einsteinian relativity, but it means nothing to most people without some prior knowledge as noted by timo.

 

Hashirama_Senju will have to clarify his question and existing level of knowledge before anyone can give a more meaningful answer.

Edited February 24, 2014 by ajb

[md65536]

There are the 2 main postulates of SR:

1. The laws of physics are the same in any inertial frame (no privileged frame of reference).

2. The speed of light is c as measured in any inertial frame.

 

The result is that time, length, and simultaneity are relative, depending on frame of reference instead of being universal.

 

 

For GR there is the equivalence principle: Inertial mass is equal to gravitational mass. A particular gravitational field is equivalent to a particular accelerating frame. The consequence is that spacetime is curved.

 

(I don't know what else there is but I don't know much especially about GR.)

 

 

 

There are other principles too, like the "clock postulate" and some principles of geometry.

[ajb]

For GR there is the equivalence principle: Inertial mass is equal to gravitational mass. A particular gravitational field is equivalent to a particular accelerating frame. The consequence is that spacetime is curved.

I think what that really tells us is that we have a smooth manifold and a (symmetric) connection as the underlying structure of space-time. In particular one can always find coordinates in the neighborhood of a point such that at that point the Christoffel symbols of the connection vanish. Loosely, normal coordinates are inertial frames.

[Questionist]

I'm terrible at math equations but can you explain something to me about the above mentioned ones.

Are we talking about needing progressively more energy per unit of velocity to, even in a vacuum, up to the point where travelling close to the speed of light would become nearly impossible?

Is this really true? When we fly rockets outside of the gravitational pull of Earth and the with minimal matter interference, do we actually need progressively more energy to propel something faster and faster? How then would concepts like Sun Sails work? Would their acceleration be progressively slowed? From what I hear that is not the case...

 

 

 

*If you want change the word progressive to exponential!

Edited April 11, 2015 by Questionist

[swansont]

I'm terrible at math equations but can you explain something to me about the above mentioned ones.

 

Are we talking about needing progressively more energy per unit of velocity to, even in a vacuum, up to the point where travelling close to the speed of light would become nearly impossible?

 

Is this really true? When we fly rockets outside of the gravitational pull of Earth and the with minimal matter interference, do we actually need progressively more energy to propel something faster and faster? How then would concepts like Sun Sails work? Would their acceleration be progressively slowed? From what I hear that is not the case...

 

 

 

*If you want change the word progressive to exponential!

 

It's true even classically. KE = 1/2 mv²

 

Incremental increases in energy result in smaller and smaller increases in speed. When approaching the speed of light, this effect becomes more pronounced (and that equation is no longer good)

[Questionist]

But photons don't have mass?

[studiot]

Questionist

But photons don't have mass?

 

 

Rest mass = 0

The function y = {exp(x) - 1} starts and zero and becomes asymptototic to infinity without problem.

[md65536]

I'm terrible at math equations but can you explain something to me about the above mentioned ones.

 

Are we talking about needing progressively more energy per unit of velocity to, even in a vacuum, up to the point where travelling close to the speed of light would become nearly impossible?

 

Is this really true?

 

Yyyyup. I like to think things through using common sense so I'll try to explain it as I understand it:

 

Imagine that you have a ship with enough fuel to accelerate to half the speed of light. Suppose after that, you meet up with a refueling ship that is traveling at that same speed (you're now relatively at rest with it). You refuel, and can accelerate to half the speed of light relative to that ship. Suppose you can repeat this indefinitely, and there is always a refueling ship ready at whatever speed you get to. Can you reach the speed of light by repeating this a finite number of times?

 

Remember that the speed of light is equal to c in all reference frames. If you are traveling at the speed of light, you are traveling at that speed relative to all inertial observers. But after every acceleration, you end up in a new rest frame, and now have to accelerate all the way from v=0 to v=c relative to that new observer. In each rest frame light is still faster than you are by a speed of c. You can never catch up... It's as if you've not made any progress at all.

 

Does that make sense? Even if it does, you're still repetitively moving faster relative to an observer in that first rest frame, so why do you never reach a speed of c relative to it? It is because relative velocities aren't additive. Instead, using the "composition of velocities" formula, you can repeatedly compose 0.5c (or anything less than c) and the result will still be less than c after any finite number of repetitions. In other words after each acceleration phase, you've greatly changed your velocity relative to an observer you were recently at rest with, but only slightly changed your velocity relative to an observer that was already traveling at near-c relative to you.

 

That's what the maths will describe.

[Questionist]

No, it doesn't make sense to me that you will not be able to travel faster than what anyone can observe. But that's for the other topic.

 

 

Rest mass = 0

The function y = {exp(x) - 1} starts and zero and becomes asymptototic to infinity without problem.

Why the heck are you using words like asymptotic. Who except for a physicist would know what that means. I mean I've heard of it within some general discussions about computers to but geez.
You want a civil discussion while you sound as a besserweisser? I've clearly stated I'm not a student of physics and I don't like and so I don't understand non-linear math (unless I really try, and then just the basics).

Anyway say that it doesn't matter because infinity is so large and its mass is so small (0?)
I still don't understand how something with no mass can fit the classical physics model concerning kinetic energy.

Edited April 11, 2015 by Questionist

[swansont]

 

Why the heck are you using words like asymptotic. Who except for a physicist would know what that means.

 

People who've studied a little math. Which is a prerequisite for doing any kind of physics at all. Without it the best you'll be able to do is learn the pop-sci version of it.

[Questionist]

after googling a bit, never encountered exp but encountered lim. Anyway, since I barely touch functions nowdays try to explain it to me and other people like me when we ask questions in other ways.

[studiot]

 

questionist

post#10

*If you want change the word progressive to exponential!

post#17

after googling a bit, never encountered exp but encountered lim.

 

 

Are you extracting the Michael?

 

I'm sorry I thought you said your were studying or working in computers.

 

exp is computer language for exponential.

Edited April 11, 2015 by studiot

[Questionist]

i know it means exponential but I dont know what you mean by something equals exponentional of something else minus 1.
I then googled about it and it meant 2.7xx something something. Never used it in my life.

 

Anyway as I told you I hate non-linear math and I don't understand it very well. Programing is very logical and I haven't been programing anything that requires advanced math alone.
If you can't handle that fact, fuck off and don't reply to my posts.

Edited April 11, 2015 by Questionist

[Strange]

How then would concepts like Sun Sails work? Would their acceleration be progressively slowed? From what I hear that is not the case...

 

Solar sails are not able to accelerate things to speeds where relativistic effects become noticeable so their effectiveness won't be affected by this.

 

One of the places where we are able to accelerate things to a significant fraction of the speed of light is in particle accelerators (like the LHC). In this case, the increasing amount of energy needed to keep accelerating the particles is exactly what is predicted by relativity.

[studiot]

One of the things any successful apprentice has to learn is that machinery of any kind, including computers, is completely unforgiving as it follows the immutable laws of physics.

 

No amount of bluster or cat calling will make a poorly serviced motor or ill programmed computer run well.

Edited April 11, 2015 by studiot

[Questionist]

I'm not constructing hardware. So I don't need to know the constantly changing and evolving knowledge about the probably contentiously morphing common law of Physics ;-)

 

Solar sails are not able to accelerate things to speeds where relativistic effects become noticeable so their effectiveness won't be affected by this.

 

One of the places where we are able to accelerate things to a significant fraction of the speed of light is in particle accelerators (like the LHC). In this case, the increasing amount of energy needed to keep accelerating the particles is exactly what is predicted by relativity.

 

I'm not arguing relativity on the basis of it being a correct model or not. Only that every thought experiment produced from it results in absolute hilarity.

Holes through already invisible (non-measurable) dimensions, time travel in general, some form of difference in aging without any reference to particle decay or biology. I mean it's ridiculous.
Add to it string theory and you've got some 9 dimensions impossible to even phantom.

Edited April 11, 2015 by Questionist

[Klaynos]

Whether you or any other person thinks it's ridiculous doesn't really matter. Experiments show that that is how the universe behaves. The universe doesn't care about the thoughts of a group of air descendents on a small green planet orbiting an unremarkable star.

[Strange]

You are mixing up speculative, almost sci-fi, ideas like time travel and "holes through dimensions" (whatever that means) with an apparently very confiused idea of time dilation and then rejecting the theory because those things don't make sense.

 

So ultimately it comes down to the fact that you think the theory is wrong because you, personally, don't understand it. That isn't how science works.

[Questionist]

Partly scientists have been withdrawing in the last few decades from the most grandiose claims that still sit in the backbone of the theory of general relativity at least.

If my understanding is wrong then I would be glad.
So explain to me. If I were to be in a space rocket constantly traveling at high speeds, exactly what effect would t hat have on my biological age in relation to others on earth according to your understanding of said theorie(s)

Whether you or any other person thinks it's ridiculous doesn't really matter. Experiments show that that is how the universe behaves. The universe doesn't care about the thoughts of a group of air descendents on a small green planet orbiting an unremarkable star.

 

Our planet is exceptional, so I say the universe cares. Besides, once we get massive railguns and photon cannons we will take over that puny universe.

Edited April 11, 2015 by Questionist