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Difference between the special and general relativity 
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#1
Jan413, 05:27 AM

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can you explain me please the difference between the special and general relativity
i did some research and only what i found and what i understand and i ' m not sure is that te SR is applied only in inertial frame and the GR is applied in the noninertial frame correct me please if i ' m wrong and i m sure i ' m 


#2
Jan413, 07:14 AM

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#3
Jan413, 07:51 AM

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General relativity is just describing gravity in a relativistic setting. The equivalence principle hints to the idea that gravity is spacetime curvature.
In special relativity much attention is given to inertial frames, because they are equivalent. However, SR can perfectly handle other frames like accelerating ones, just as in Galilean relativity (classical mechanics) you can describe accelerating observers. The key difference between classical mechanics and relativity is that, while in classical mechanics only linearly accelerating observers can locally pretend they are in a gravitational field, in GR every observer can locally pretend he/she is in a gravitational field. The class of "equivalent observers" is thereby enhanced :) 


#4
Jan413, 09:20 AM

P: 270

Difference between the special and general relativity
Simplistic answer: SR is a world without gravity while GR includes gravity. Gravity forces us to recognize the difference between proper acceleration and coordinate acceleration, which are equivalent in SR.



#5
Jan413, 09:31 AM

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Although SR can handle noninertial frames there is never any advantage to using them. Remember, there are no privileged frames in SR, any frame is just as good as any other frame. If you stick with Inertial Reference Frames (IRF's) in SR, then you have the distinct advantage of being able to use the Lorentz Transformation to trivially convert a scenario defined in one IRF to any other IRF. If you want to use a noninertial frame in SR, there is no standard way to convert the coordinates of one frame into another frame and there is also not even a standard definition of what a noninertial frame is. My advice to anyone wanting to learn SR is to stick with a single IRF at a time. Don't pay any attention to those people who want you to have a different reference frame for every observer. That just leads to unnecessary confusion. Any IRF can handle all the observers and all the objects no matter how they accelerate. There is nothing privileged about any particular frame in SR, not even one in which an observer is at rest. 


#6
Jan413, 10:57 AM

P: 14

thanks everyone that really helped me



#7
Jan713, 01:34 PM

P: 5,632

Carlo Rovelli offers this insight:
Whadda ya mean by that?? Example: In SR, if you move along at a constant velocity, your time ticks off at a steady pace. Not so in GR...Proper time along a path [called a worldline] IS an observable but it is not 'ticks at a steady pace'.....because as the worldine is traversed, as you move through spacetime, the spacetime background is, in general changing....the spacetime background is dynamic, so time proceeds 'erratically'...at an uneven pace. So the concept of time is weakened some what in GR. Some confusion may arise due to historical changes in 'special relativity: According to Wikipedia, Clock Hypothesis, "The clock hypothesis wasn't included in Einstein's original 1905 formulation of special relativity and therefore special relativity was unable to make predictions for accelerated systems. Since then, it has become a standard assumption and is usually included in the axioms of special relativity...." " 


#8
Jan713, 02:38 PM

P: 5,632

Nugatory
Example: In SR an inertial, that is, non accelerating observer, moves at at steady velocity along a straight line. No acceleration is felt. In GR, where spacetime is curved, an inertial observer moves along a curved trajectory...where no acceleration is felt....called a geodesic. If there is no gravity, such a curved spacetime defaults to SR...flat spacetime. And, as I noted in my prior post, that observer moving along such a curved trajectory does not have a steady tick of time....it varies according to 'gravitational potential'....related in GR via the metric tensor. 


#9
Jan713, 04:55 PM

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#10
Jan713, 05:27 PM

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But to return to O.P.'s question about the difference between SR and GR, the comments in the previous paragraph apply to SR as well as GR. What makes SR special is that in the special case of flat spacetime: 1) It is always possible to find a coordinate system in which coordinate time corresponds to proper time along a timelike geodesic; just use the frame in which a clock following that geodesic is at rest. 2) There is always a simple linear relationship between proper time and proper and coordinate time in other frames. 3) The geodesics are straight lines, which simplifies that math no end. Indeed, it simplifies the math so much that we don't generally have to throw the machinery of the metric at it. But if we do, it works just fine, and learning to do this is a pretty good first step for someone who understands SR and wants to move on to GR. 


#11
Jan713, 05:42 PM

P: 5,632

Nugatory
But in your next post, I am unsure about : in other words, there is not external time parameter in GR....and that fact is a bit different than SR...along the lines of what you posted: "The thing that can change 'erratically' is the mapping between coordinate time for a particular observer using a particular coordinate system and proper time..." I am attempting to reflect this idea from Carlo Rovelli...what do you think?? [Just was reading it and I did not think my post would be controversial..] First part of TIME section: 


#12
Jan713, 06:45 PM

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I think that when Rovelli said that spacetime is "dynamical", I think he just meant that while the definition of SR includes a specification of the metric, the definition of GR specifies an equation that describes the relationship between the metric and the properties of matter in spacetime. So the metric is "dynamical" only in the sense that we need to solve an equation to find it.



#13
Jan813, 01:20 AM

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#14
Jan813, 06:35 AM

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dido:
Since this is your discussion, post if you are interested in this latest discussion.....if not, I'll start a separate discussion as I am trying to figure out exactly how time is weakened in GR versus SR as described by Rovelli. 


#15
Jan813, 08:15 AM

P: 5,632

too late [LOL] : from Marcus introducing Tomita Time:



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