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IndustriaL
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What is the difference between Special Relativity and General Relativity?
dextercioby said:Nonetheless,special relativity deals very well with the problem of a pointlike particle moving through space-time with a constant acceleration "a".
Daniel.
mathman said:From a layman's point of view, special relativity is concerned only with inertial systems (no acceleration), while general relativity does not have that restriction. In particular G.R. is a theory of gravity.
Special relativity applies only to coordinate systems which correspond to inertial frames while general relativity applies to all coordinate systems.IndustriaL said:What is the difference between Special Relativity and General Relativity?
No. That is a misconception. Special relativity was created in part to explain things happing at low speeds. Even at low speeds Lorentz contractions play a role in the electric field of a slowly moving wire. To determine the separation of events in spacetime as measured in a moving frame you can't neglect relativity if the events have a large spatial seperation.εllipse said:To put it in even simpler, very generic terms. Special relativity is the theory of what happens at very fast speeds, ...
GR addresses all sorts of motion. In fact, according to Einstein, you can have a flat spacetime - change frames of reference and you "produce" a gravitational field. In this case the only mass working here is the mass of the "distance stars."...while general relativity is the theory of what happens with very dense masses.
Thanks for the link Rob. Please note that Stachel does not adhere to the "The modern view [used by working relativists] ..." comment you made. He adhere's to Einstein's views on GR and not to the view found in, say, Wald. Remind me in the future to e-mail his article on this point to you.robphy said:εllipse,
Your statement reminds me of something called the "Bronstein Cube"
which this first link attributes to Penrose
http://www.physik.fu-berlin.de/~lenzk/PICS/bronsteincube.gif
I heard about this from lectures by Stachel
http://physics.syr.edu/research/hetheory/minnowbrook/stachel.html
(click on the thumbnails with cubes)
Essentially, this diagram suggests relationships between the different theoretical regimes using certain limits of fundamental constants.
pmb_phy said:No. That is a misconception. Special relativity was created in part to explain things happing at low speeds. Even at low speeds Lorentz contractions play a role in the electric field of a slowly moving wire. To determine the separation of events in spacetime as measured in a moving frame you can't neglect relativity if the events have a large spatial seperation.
GR addresses all sorts of motion. In fact, according to Einstein, you can have a flat spacetime - change frames of reference and you "produce" a gravitational field. In this case the only mass working here is the mass of the "distance stars."
Pete
Do you think the same person would understand Rob's post?εllipse said:Do you think someone asking what the difference in SR and GR is will know what Lorentz contractions are? I posted an answer in words anyone could understand.
I think we can agree that this part of the εllipse's description is fine:εllipse said:To put it in even simpler, very generic terms. Special relativity is the theory of what happens at very fast speeds, while general relativity is the theory of what happens with very dense masses.
εllipse said:To go further, special relativity solves the problems Newtonian physics has with high speeds; general relativity solves the problems Newtonian physics has with very large gravitational fields.
pmb_phy said:Do you think the same person would understand Rob's post?εllipse said:Do you think someone asking what the difference in SR and GR is will know what Lorentz contractions are? I posted an answer in words anyone could understand.
The main fact I'm pointing out is that SR is not just for high speed motion. That was pretty clear in my post
Please don't get me wrong Rob. I see nothing with your post. I think its nice to have different people here posting different views at different levels. A discussion works best that way here. I was unable to determine the level of sophistication of the poster but he seems to read a lot about physics and relativity from his profile so it seems he'd at least have heard of the Lorentz transformation.robphy said:Without much context on what the original poster already knows, it is my preference to first give a precise though-possibly-advanced answer (which can be simplified with clarifications as needed) rather than give an imprecise and possibly-misleading answer that has to be cleaned-up or thrown out later.
[I must also admit that one reason for that first answer I gave was to try to defeat misconceptions, particularly those stemming from the historical development of the subject, and to advocate the modern terminology and interpretations used in practice.]
pmb_phy said:Btw - what do you find wrong with historical matter if it works better for some people? In his text "Concepts of space," Max Jammer has an foreword by Einstein in which he discusses the importance of history in science. It is well worth your read. I can scan and e-mail if you wish as always.
Pete
To understand a subject, one must tear it apart and reconstruct it in a form intellectually satisfying to oneself, and that (in the view of the differences between individual minds) is likely to be different from the original form. This new synthesis is of course not an individual effort; it is the result of much reading and of countless informal discussions, but for it one must in the end take individual responsibility. Therefore, I apologise, if apology is necessary, for departing from certain traditional approaches which seemed to me unclear, and for insisting that the time has come in relativity to abandon an historical order and to present the subject as a completed whole, completed, that is, in its essentials. In this age of specialisation, history is best left to the historians.
- J.L. Synge in Relativity: The Special Theory (1956), p. vii
A great example is to be found in the American Journal of Physics. With so many people saying "Gravity is a curvature in spacetime" some people take that to mean that a uniform gravitational field will have spacetime curvature. There is an article in AJP by someone who assumes the Riemann tensor must be zero for such a field and when he gets a non-zero value he is pleased with himself. The problem was that "uniform gravitational field" means "zero Riemann tensor." His lack of knowledge and relying on such ideas as "Gravity is a curvature in spacetime" and ignoring what a gravitational field really is (as Einstein knew all too well) led him to make this serious error in his article. The author, the editor and the referees all got it wrong since it was published.He will, however, be grateful to the historian if the later can convincingly correct such views of purely intuitive origin.
pmb_phy said:With so many people saying "Gravity is a curvature in spacetime" some people take that to mean that a uniform gravitational field will have spacetime curvature.
I hope you understand how happy you've made me by this comment.Zanket said:Agreed. Such quotes are an example of how many sources on GR make the subject way more complicated than it is.
pmb_phy said:I hope you understand how happy you've made me by this comment.
"inertial frame A local frame in free fall" - If you add that the frame need not be local if the spacetime is flat then I agree.
"local In a vicinity or having a volume throughout which the tidal force is negligible" - I agree. But its better if you add that the volume is a 4D volume of spacetime and not of simply space.
"nonuniform gravitational field (curved spacetime) The gravitational field of a nonlocal frame" - I disagree. Nonlocal can include flat spacetime. The correct definition is a gravitational field with non-zero tidal forces/gradients.
A wee bit-o-math for yee!
"uniform gravitational field (flat spacetime) The gravitational field of a local frame" - I disagree. A uniform gravitational field is a gravitational field where the tidal forces are zero.
"Once that is understood, it follows that flat spacetime is synonymous with a uniform gravitational field," - I disagree. Whether there is a uniform gravitational field is present will depend on the coordinates you choose. Thus you can "produce" a uniform gravitational field by changing coordinates to that associated with a uniformly accelerating frame of reference.
Thanks! I got the right drugsZanket said:Welcome back!
No. This is definitely wrong. In a small region of spacetime about a point P in spacetime is referred to as a local spacetime coordinate system if the gravitational force vanishes at P and the gravitational force at small distances from P may be ignored. Local pertains only to free-fall motion. So local can contain both flat and curved spacetime. In fact One can say that at a point P in spacetime one can choose coordinates which can be locally flat at P but also curved at P. I'm standing on the Earth which we will consider to be a perfect sphere for the sake of arguement. Think of yourself as standing on this sphere with rulers to measure distances and the ruler has a certain degree of precision. With your ruler you constuct a "small" equilateral triangle. But ignoring small variations you determine that the sum of the interior angles is 180 degrees. Then you say "However if you beef up the precision of your measurements you will determine that it really is a sphere. You can say that your coordinate is restricted to the "small" region and it is therefore is is locally flat coordinate system. But you know that the surface really isn't flat so you also say that the survace is curved where the triangle is located.In the definitions I gave, a local frame comprises only flat spacetime, ..
In spacetime if you're in a globally inertial frame then the entire spacetime is flat. If you're in a frame in which an enormous region is flat but outside that region there is curvature then ther is no term defined for this example.A geometrical property is called local, if it does not pertain to the geometric configuration as a whole but but depends only on the formof the configuration in an (arbitrarily) small neighborhood of the point under consideration.
No! Because I messed up. Thanks for catching that.Can you elaborate as to when flat spacetime is not synonymous with a uniform gravitational field?
pmb_phy said:Yes. I believe the difference in our notions are due to differences in the way we choose to define "local." I typical go by the book on most occations. I will specify when texts different with respect to a definition. But the term "local" has a well defined definition which is uniform throughout the literature.
In a small region of spacetime about a point P in spacetime is referred to as a local spacetime coordinate system if the gravitational force vanishes at P and the gravitational force at small distances from P may be ignored. Local pertains only to free-fall motion.
You can say that your coordinate is restricted to the "small" region and it is therefore is is locally flat coordinate system. But you know that the surface really isn't flat so you also say that the survace is curved where the triangle is located.
There is controversy regarding local coordinate systems in the GR literarture. The 100% correct definition of "local" means that at the origin of the coordinate system the gravitational force vanishes. If the spacetime is curved then points away from the origin have a non-gravitational force in general.
If you're in a frame in which an enormous region is flat but outside that region there is curvature then ther is no term defined for this example.
Can you provide the exact quote. E.g. some authors use the term "space" to refer to "spacetime".Zanket said:Agreed, except for the last sentence, because my books disagree with you that “local” pertains only to free-fall motion.
Keep in mind that they are not simply referred to as "local" amd that makes quite difference. No matter ho small the spatial portion of space is,given enough time the experiment will violate the Principle ofAnd note that if “local frame” implies free-falling, then “local gravitational acceleration” can confuse.
If referres to whether the region of spacetime you're interesting in is small enough so that not enough time has passed so that the curvature that you speak of can't be measured.I’m confused. Doesn’t a tidal force (what I assume you mean by “gravitational force”) vanish at any point?
The reference frame of interested is a frame of reference attached to the origin which the coordinate system is in free-fall along with the point P.And if a “local spacetime coordinate system” is anchored by a fixed point P, then how can “local” pertain only to free-fall motion? Is P free-falling (i.e., is the coordinate system in free fall)?
I agree that it may confuse people. In this case if the experiment runs for a long enough time then the tidal forces cannot be neglectedWhen “local” is defined as negligible tidal force throughout, there will not be confusing (to me) statements like “local can contain both flat and curved spacetime”.
Sure it does. Where did you great that idea??Zanket said:Black Holes and Time Warps, a local frame is a frame having a negligible tidal force throughout, but it need not be free-falling.
I do agree that different texts make any distinguishment ment.In the former book a free-falling local frame is called a “free-falling frame” and in the latter it is called a “local inertial frame” (distinct in the book from the “inertial frame” of special relativity, where free fall is not mentioned). The book Exploring Black Holes calls this a “free-float frame” or an “inertial frame”. Four terms for the same thing, one of which overrides the “inertial frame” of special relativity. Maddening! I think it’s best to do away with the superfluous “free-float frame” and keep only the “inertial frame” that mentions free fall, since the inertial frame of special relativity does not exist in reality. Then it is clearer that a free-falling local frame is the inertial frame for practical applications of special relativity.
Where my books disagree on terms, I feel free to define my own, ideally from a melding of them where the term can be simply defined.I can see that may be troublesome. I like that a local frame need not be free-falling, because then I have a term for a frame throughout which the tidal force is negligible, and which is being noninertially accelerated, such as the frame of the room I’m in now, about which I can say that, for practical purposes, the local gravitational acceleration is 1g throughout. What is your term for such a frame?I very much a confusion for you. Me too.And note that if “local frame” implies free-falling, then “local gravitational acceleration” can confuse.
Whether the gravitational force exists depends on the origen f the frame of reference. That is locally inertial.I’m confused. Doesn’t a tidal force (what I assume you mean by “gravitational force”) vanish at any point?
If so, why the conditional “if”? And if a “local spacetime coordinate system” is anchored by a fixed point P, then how can “local” pertain only to free-fall motion? Is P free-falling (i.e., is the coordinate system in free fall)?
This goes to a distinction between “negligible”, “infinitesimal” and “zero”. My books tend to be wishy-washy on these. To me, “negligible” is the only one useful for practical purposes, so I reject the others. Then I would say that the surface is flat locally, where the triangle is located, where “local” is defined as a region having negligible curvature throughout.
When “local” is defined as negligible tidal force throughout, there will not be confusing (to me) statements like “local can contain both flat and curved spacetime”. After reading your Earth example I interpret this to mean that “local contains both flat and curved spacetime, as one alternates between deeming the tidal force throughout to be negligible or not”. I think a definition serves better when it is unambiguous.
Once you work with this for a bit you'll become an expert and some teachers may lend you their copy.
Pete
pmb_phy said:Can you provide the exact quote. E.g. some authors use the term "space" to refer to "spacetime".
pmb_phy said:Sure it does. Where did you great that idea??
Regarless of the strength of the tidal forces the region of spacetime mus be kept small. That means that you can't run an experiment for too long or you will measure tidal gradients
Keep in mind that they are not simply referred to as "local" amd that makes quite difference. No matter ho small the spatial portion of space is,given enough time the experiment will violate the Principle of
Equivalence.
The reference frame of interested is a frame of reference attached to the origin which the coordinate system is in free-fall along with the point P.
The main difference between Special Relativity and General Relativity is that Special Relativity deals with the laws of physics in inertial reference frames, while General Relativity includes the effects of gravity and accelerated motion.
According to Special Relativity, time dilation occurs when an object moves at high speeds, causing time to pass slower for that object compared to a stationary observer. This is due to the fact that the speed of light is constant and time is relative to the observer's frame of reference.
In General Relativity, gravity is explained as the curvature of space-time caused by the presence of mass or energy. This means that objects with mass will cause a distortion in the fabric of space-time, causing other objects to move towards them.
In General Relativity, light is affected by the curvature of space-time caused by massive objects. This results in the bending of light, as it follows the curved path of space-time around the object instead of traveling in a straight line.
Yes, both Special and General Relativity have been extensively tested and confirmed through various experiments and observations. They are used in many modern technologies, such as GPS systems, and have practical applications in fields such as astronomy and astrophysics.