# Difference between the special and general relativity

• dido28
In summary: As they move, they experience accelerating forces, because the space-time background is constantly changing. So the concept of 'proper' time is weakened in GR."
dido28
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

dido28 said:
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

It's often explained that way, but that's not quite right; SR works in non-inertial accelerating frames. The key difference is that SR applies in flat space-time, while GR is more general and works in both flat and curved space-time.

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 :)

dido28 said:
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
Special Relativity cannot handle gravity, you need General Relativity for that.

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.

thanks everyone that really helped me

Carlo Rovelli offers this insight:

...Einstein’s discovery that spacetime is not a fixed background, as it was assumed in special relativistic physics, but rather a dynamical field.

Such a dynamical field is how gravity, that is, spacetime curvature, is formulated.

Whadda you 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..." "

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Nugatory

The key difference is that SR applies in flat space-time, while GR is more general and works in both flat and curved space-time.

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 space-time 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 space-time defaults to SR...flat space-time.

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.

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Naty1 said:
The key difference is that SR applies in flat space-time, while GR is more general and works in both flat and curved space-time.
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 space-time 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 space-time defaults to SR...flat space-time.
Either I am totally misunderstanding you, or we are saying the same thing. I use general relativity to deal with the general case of non-zero curvature. In the special case of of zero curvature the more general methods of general relativity still work just fine, but in this special case these methods reduce to special relativity.

Naty1 said:
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.

If you speak in terms of proper time, a clock traveling on any timelike worldline, whether geodesic or not, ticks at a steady pace, tautologically measuring one second of proper time per second. 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'd as soon start another thread if we're going to discuss the physical significance of this mapping - it's far afield from the original topic).

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 space-time:
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.

Nugatory

Either I am totally misunderstanding you, or we are saying the same thing.

We ARE saying the same thing...I was attempting to provide an example.

If you speak in terms of proper time, a clock traveling on any timelike worldline, whether geodesic or not, ticks at a steady pace,

steady tick only for that observer...not for another inertial observer as in SR...

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:

Time is affected even more radically by the quantization of gravity. In conventional QM, time is treated as an external parameter and transition probabilities change in time. In GR there is no external time parameter. Coordinate time is a gauge variable which is not observable, and the physical variable measured by a clock is a nontrivial function of the gravitational field...

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.

Fredrik said:
So the metric is "dynamical" only in the sense that we need to solve an equation to find it.
That's missleading; the metric is dynamical in the sense that it represents two physical degrees of freedom. You wouldn't say that the el.-mag. field is dynamical b/c you have the inhomogeneous Maxwell equation to solve for it; it's dynamical b/c it represents two physical photon polarizations.

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.

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

...In GR, "coordinate time" is not really a time---it's neither observable nor physically meaningful. On the other hand, observer time is not defined until one has already fixed on a particular curved space-time geometry. So observer time cannot be used if the geometry itself is included as part of the dynamics.

## 1. What is the main difference between special and general relativity?

The main difference between special and general relativity is that special relativity describes the laws of physics in a stationary or uniformly moving inertial frame of reference, while general relativity includes the effects of gravity and describes the laws of physics in a non-uniformly moving or accelerated frame of reference.

## 2. How does special relativity explain the concept of time dilation?

In special relativity, time dilation is explained by the fact that the speed of light is constant and the laws of physics are the same for all observers in an inertial frame of reference. This means that time appears to pass slower for objects moving at high speeds relative to an observer, as measured by that observer.

## 3. How does general relativity explain the bending of light by gravity?

In general relativity, gravity is described as the curvature of spacetime caused by the presence of mass and energy. This curvature affects the path of light, causing it to bend when it passes close to massive objects such as stars or galaxies.

## 4. Can you give an example that illustrates the difference between special and general relativity?

An example that illustrates the difference between special and general relativity is the phenomenon of gravitational time dilation. In special relativity, time dilation is caused by relative motion between two observers, while in general relativity, it is caused by the curvature of spacetime due to the presence of massive objects.

## 5. How has the understanding of relativity changed over time?

The understanding of relativity has evolved over time as new discoveries and experiments have been made. Initially, Einstein's theory of special relativity revolutionized our understanding of space and time, followed by his theory of general relativity which explained gravity in a new way. Since then, further advancements have been made in our understanding of relativity, including the discovery of gravitational waves and the confirmation of many predictions made by the theories.

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