# Defining SR and GR?

1. Mar 6, 2006

### Mattara

The other day, I was trying to explain what SR & GR were for some non-science friends of mine. I started speaking of motion with constant speed, the postulates of SR, the spaceship and the ball, time dilatition, twin paradox and so on. Needless to say, they didn't understand what I was talking about and that wasn't only because they wern't interested in science (I might not be able to explain this so good).

So I turn to you, the users of PF, who I'm convinced can help me. Can you clearly define SR(T) and GR(T) only using no more than, say 5 lines so that I better can explain it to my friends?

Cheers,

2. Mar 6, 2006

### Severian596

I think I would use four sentences to describe SR, then say that GR is basically SR as it exists "in real life" because it takes gravity and acceleration into account. SR usually relies on strict, specific circumstances for its equations to yield correct results (as the results would appear in real life). Due to its complexity and the fact that it takes gravity and acceleration into account (aka, curvature of spacetime), GR yields results that apply to our real world instead of to the "special world" of flat spacetime.

I spent my 5 sentences talking about how I think you should use 5 sentences...sorry!

3. Mar 6, 2006

### Mattara

Severian596, thanks for the moving over from SR to GR idea. Great!

With the definition, I was more thinking like:

Special & General Relativity is the...

4. Mar 6, 2006

### RandallB

Mattara
To avoid letting SR & GR seem to be the same thing I’d suggest:

1) Special Relativity & General Relativity are not the same thing, with SR being more compatible with QM while GR is in conflict with GM.

2) Special Relativity is considered classical with a speed limit, set as “c”; where the speed of “infinity” is defined as 1 or “c”.

3) Defining infinite speed as the limit “c”, requires non-linear formulas for adding or “combining” speeds and factors for “dilation” and “gamma”.

4) An analogy of classical 3-D Special Relativity can be created in an imaginary 4-D Minkowski “Space-time”; but any complete solution there can also be solved with a detailed classical 3-D Special Relativity solution.

5) General Relativity is not classical, using as many as 10 parameters to create what physicists call an “independent background”, indeterminate and can be curved, to hold what we understand to be our 3-D reality.

But you should be sure you understand all 5 completely yourself as I cannot imagine they would not each generate more questions like “Why?”.

5. Mar 6, 2006

### Mattara

Okay.

Special Relativity is the area within physics which is based on the assumption that the speed of light in a vacuum is a constant and the assumption that the laws of physics are invariant in all inertial systems. General Relativity is a generalization of Special Relativity to include gravity.

Is this correct? Do you think it will not generate many (if any) questions?

6. Mar 6, 2006

### Severian596

Holy Crap RandallB! Although your well thought out explanations are no doubt correct (I can't personally grade them though, you know way more than I do), if Mattara's friends are anything like mine their eyes would glaze over half way through #1. I personally think the language invovled in these definitions is too advanced for most audiences.

I recommend trying to achieve that Hawking-like ability to communicate in terms of things that non-physics oriented people understand. If you compare things in terms of QM, be prepared to explaine Quantum Mechanics, and that's just no help at all! :D

"Special & General Relativity is the theory that time and space are not absolute. Contrary to cartesean coordinate systems where the X, Y, and Z axes are always rigid, SR & GR assert that the "scale" we use to measure these aspects of reality change for two observers who are travelling at some velocity relative to each other. Don't forget to consider time as the "fourth" axis! The idea that there's a point in the universe that could be considered the origin of a huge XYZ grid to describe the universe is false."

Last edited: Mar 6, 2006
7. Mar 6, 2006

### Severian596

You know, that's not bad, but it may leave them saying, "So a ball always falls down? Duh! And what does the speed of light have to do with falling balls anyway?" But I'm just trying to prep you for their possible responses!

8. Mar 6, 2006

### Mattara

Every bit of help is greatly appreciated. Thank you Severian596 for your reply!

9. Mar 6, 2006

### Severian596

Sure man, I hope you find at least some of it helpful. I just know that if I brought RandallB's list to my wife she'd rather not hear it. It would be like explaining the rules of one game which she doesn't know how to play in terms of another game which she doesn't know how to play. I don't think it would work.

10. Mar 6, 2006

### RandallB

No it’s not ---- But if you don’t want any questions, and they don’t really care about it any more than you probable do about the details of say a household budget and time management. Then you might reach your objective of no questions.

11. Mar 6, 2006

### Severian596

I can't tell by your text tone what you mean here. Mattara's initial question was: "Can you clearly define SR(T) and GR(T) only using no more than, say 5 lines so that I better can explain it to my friends?"

So is your answer to this question no? Because your explanation was not oriented towards a non-science audience, and your second comment made it sound like Mattara either has to throw the college textbook at his friends or he'll have to shoot for the non-too-noble sounding objective of "no questions in response." I think there's a happy medium where he can stimulate their interest using everyday words. Do you?

12. Mar 6, 2006

### Ich

You could either clearly define it or explain it to your friends. You can´t have both.

13. Mar 6, 2006

### Mattara

Okay, that is true. What would the clear defintion be then?

14. Mar 6, 2006

### pmb_phy

Einstein was the one to define these terms. He defined SR as relativity in inertial frames and GR as relativity to general frames of reference, including that of the gravitational field. I can produce the source of these definition upon request.

Pete

15. Mar 6, 2006

### RandallB

I qouted the question so no text tone intended. He asked :
“GR is a generalization of SR -- Is this correct?”
And of course it is not correct, may also mean Mattara's understanding may not be complete enough yet to explain too much. Even less knowledgeable friends should not be left with that incorrect assumption. If it were that simple how would you explain to them that it took ten years for Einstein to get GR after SR. They are very different things.

Sure I thing his idea that generating next to no questions is not realistic.
The happy medium is to be sure you know what your talking about your self first, not just repeating someone else’s idea of “the clear definition”. If only it was that easy, books would be much shorter than they are. Then he needs to judge how much of what to give based on who he’s talking to.

Does anybody think a novice is going to get the basics of SR and GR both in a couple one liners or less than five minutes without questions?

16. Mar 6, 2006

### pervect

Staff Emeritus
Special relativity is basically a replacement for Newton's laws. Newton's laws (which hopefully even your non-science friends will be familiar with) work fine at low velocities, but when velocities approach the speed of light, one needs to take into account relativistic effects.

General relativity is operationally our relativistic replacement for Newton's law of gravity, and is the current "standard" theory of gravity.

17. Mar 6, 2006

### Thrice

You could try explaining it historically. People have known since galileo that motion is measured relatively. However maxwell's equations predicted a constant speed - c - and nobody knew what frame to measure it from (eg the speed of sound is measured relative to the medium). All attempts to find some ether to measure it had failed when einstein proposed special relativity.

In overturning galilean relativity, einstein also killed newtonian gravity. GR, you could say, is a theory of gravity.

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18. Mar 6, 2006

### pervect

Staff Emeritus
In SR, space-time is consided to be globally Lorentzian. The Lorentz interval is introudced as the fundamental geometric object which describes space and time. The Lorentz interval, i.e the quantity $\Delta t^2 - \Delta x^2 - \Delta y^2 - \Delta z^2$ is defined, any any inertial obsever will obtain the same value for this quantity.

In GR, we change the view, so that space-time is a 4 dimensional manifold, which has at any point a tangent space that is Lorentzian.

This is equivalent to the way that we view the Earth's spherical surface (a 2-dimensional manifold) as having everywhere a tangent space that is Euclidean (i.e a flat plane).

One might say that the Earth is globally round, but locally flat. Similarly, in GR, one says that the geometry of space-time is locally Lorentzian.

Unfortunatly, this sort of defintion is not going to be useful for talking about GR and SR to one's non-scientist friends. I would suggest that my earlier response would be more useful in that context.

ps - GR can be considered to be a generalization of SR (from inertial frames to non-inertial frames and curved space-times) in spite of RandallB's remarks. The process of making this generalization is not an easy one, however.

[add]The line between GR and SR can be a bit hazy at times, but usually the distinguishing feature of GR is that it introduces a metric tensor. Thus if one analyzes an accelerating space-ship in a coordinate system with a flat metric, one is doing SR, but when one analyzes an accelerating space-ship in a coordinate system in a non-flat coordinate system (i.e. one with a metric tensor that is not constant) one is considered to be doing GR. This point may be arguable.

Last edited: Mar 7, 2006
19. Mar 6, 2006

### Oxymoron

Since relativity deals with our inability to detect absolute motion, meaning physics is unchanged under coordinate transformations. Therefore I would simply say that:

SR = Deals with the symmetry in physics with respect to coordinate transformations in inertial frames.

GR = Deals with the symmetry in physics with respect to a general frame (this includes accelerating frames).

So SR is simply a special case of GR and they both deal with physical symmetries.

20. Mar 6, 2006

### Hurkyl

Staff Emeritus
That's a unfortunately (seemingly) common misconception.

I think, historically, that GR is what introduced differential geometry into physics, and therefore people seem to equate the two.

But differential geometry is just a mathematical technique, and it can be employed profitably in SR as well -- in particular, SR has absolutely no problem dealing with noninertial frames.

SR and GR differ, at least, in their description of the geometry of the universe.

SR claims "We can construct an inertial' coordinate chart that is defined everywhere!"

GR merely claims "We can construct coordinate charts that are approximately inertial', that are defined at least on small regions of space-time".

21. Mar 7, 2006

### Oxymoron

Ah well, sorry about that. It seems Im a victim of an urban legend. :(

Last edited: Mar 7, 2006
22. Mar 7, 2006

### robphy

To follow up on Hurkyl's comment...

The modern geometric viewpoint is that
Special Relativity is faithfully described by Minkowskian geometry
(which uses an affine space R4 with a [uniform] metric tensor field of Lorentz-signature [which encodes the "speed of light"-postulate in the light-cone structure]). Implicit in the above is the group of Lorentz transformations which act on the entire spacetime. This is where the "relativity"-postulate is encoded.

In this viewpoint, SR/Minkowski geometry can handle "[accelerating] non-inertial frames",
just like Euclidean geometry can handle non-Cartesian coordinate systems [e.g. spherical-polar coordinates]... the appropriate Pythagorean-theorem still holds in the entire space! It is likely that ordinary geometry and trigonometry are not sufficient tools in this case... calculus and possibly other differential geometric methods are required.

For which circumstances will Euclidean geometry fail?
For spaces that are not [um..] Euclidean, e.g., a cylinder or a torus [spaces of zero intrinsic curvature which has closed geodesics] and a sphere [a space with curvature, seen by the convergence of initially parallel lines]. To deal with these cases, we have to weaken the restriction and allow generally non-Euclidean spaces with generally nonzero curvature. [As long as one doesn't venture too far away from home and/or have not-so-sensitive measuring devices, Euclidean geometry may be sufficient.]

In the Lorentzian case, the analogue is that the geometry of General Relativity involves a generally non-flat [with nonuniform metric], non-R4 spacetime manifold. Instead of the Lorentz group, we have the group of diffeomorphisms which act on the entire spacetime. [The spacetime of Special Relativity is therefore a special case.]

Of course, there's more to General Relativity than the geometry of its spacetime [i.e. its kinematical structure]... there's a dynamical "[field-]equation of motion" that relates the matter-sources to the curvature, which in turn dictates the motion of test particles and fields. [In SR, there are no matter sources to curve spacetime... the Minkowski spacetime is said to be a vacuum solution of the field equations.]

Last edited: Mar 7, 2006
23. Mar 7, 2006

### pmb_phy

Sorry RandallB but you are incorrect. Just crack open A first course in general relativity, Bernard Schutz page 3 (which is the exact same way Einstein defined it.)
The rest contradicts Einstein's views so I will omit them. I take Einstein's views over all others.

Pete

24. Mar 7, 2006

### RandallB

As if a layman is going to understand how large the “generalization” is, based on what a “metric tensor” is; yah right.

This little generalization significantly changes the view of relativity. Making GR incompatible with Quantum understanding as expressed in Quantum Mechanics.
Even if the generalization is not an easy one, don’t you think we’d have a “generalized” agreement between QM and GR after 80 years of working on it if it were just a generalization?

Excusing it with a “metric tensor” just obscures the point that GR is very different from SR, designed by Einstein to resolve the inability of SR to solve gravity. QM assumes all forces can be defined by an exchange of force particles (gravitons – Higgs fields) and this idea IS compatible with SR.
Einstein completely abandoned that idea, and in GR specifically defines Gravity as the result of curves (geodesics) in an entirely new geometry of reality (Masses on trampoline membranes). That is no simple generalization (ten years of effort), but it can be simply expressed as a huge difference in concepts between SR & GR to a layman. Understanding that there is a difference in fundamental concepts is one thing, comprehendible even by layman. It’s the actual understanding of the detailed concepts, if they are really that interested, that you are not going to convey in a one liner. Then they are going to need to join you in those long books to deal with “metric tensor”; how space-time (t, x, y, z) is not the same as a GR 4-D manifold (a, b, c, d); what “tangent space” means; indeterminate background independence; etc.

Just because Pop Scientists on TV do a bad job of this doesn’t mean you have to follow their example. If you don’t want to share with them the fundamental idea that SR and GR are dramatically different, just tell them it’s to complex for you to explain and stick to SR alone.

25. Mar 7, 2006

### Hurkyl

Staff Emeritus
RandallB:

---- For this post, I'm only speaking geometrically.

GR is defined as "SR is `locally correct'".

SR clearly satisfies this condition. Therefore, SR is clearly a special case of GR. Conversely, GR is a generalization of SR. There is no ambiguity here. :tongue:

GR did not build upon SR by adding nifty mathematical gadgets to do more interesting things -- it's exactly the opposite. GR removed some of the structure of SR. GR is a less powerful theory than SR.

More powerful mathematics, such as tensor analysis, are required for GR because GR has less structure than SR, and is thus much more difficult to study. SR has this nice, flat, global structure, and if we respect it, the mathematics is very easy. GR doesn't have a similar structure that makes it similarly easy to study.

This is wrong. Quantum mechanics can and is done on curved space-times.

I would say otherwise, because people seem to get it exactly backwards. People seem to think that GR postulates all these new and weird things -- the reality is that GR postulates less than SR. This has two consequences:
(1) GR requires more powerful mathematics, because it has less structure that can be exploited.
(2) GR is less restrictive, and is thus applicable to more things.