1. Aug 3, 2011

### kirkulator

I was reading in a book on relativity that Einstein's theory of special relativity only applied to uniform motion [straight line, nothing getting slower or faster].

Is this book simply outdated, is this true? Or has his theory been extended to accelerating objects as well?

Relating this to the acceleration of the universe expansion, by the way.

Thanks a lot,
Amanda

2. Aug 3, 2011

### tiny-tim

Hi Amanda!

Einstein's theory of special relativity only applies to observers with uniform motion …

the object observed can have any motion.

3. Aug 3, 2011

### xts

Yes, and no.

Special Relativity is a theory describing kinematics regardless acceleration.

General Relativity is a theory incorporating acceleration and gravity. SR is its special case (approximation) valid for low gravitation and low acceleration.
We know from observation, that GR is true (in the sense that in those cases when GR predictions differ measureably from SR, like Mercury orbit precession, GR is consistent with observation)

Statement that 'special relativity only applies to uniform motion' is similar to 'newtonian mechanics only applies to bodies at rest' - as for moving bodies it is only an approximation of SR. We know that whenever Newtonian mechanics makes prediction different than SR, SR is closer to experimental results. But does it invalidate Newtonian mechanics?

4. Aug 3, 2011

### HallsofIvy

Einstein wrote his "Special Theory of Relativity" in 1905. Yes, that theory dealt only motion at a constant speed. In 1915, he published his "General Theory of Relativity" which dealt with gravitation as well as accelerated motion.

5. Aug 3, 2011

### ghwellsjr

At the end of section 4 of Einstein's 1905 paper, he describes what is the origin of the Twin Paradox in which a clock traveling in a closed circle arrives back at its starting point with less time on it than one that remained at the starting point. This is not a straight line as the OP asked about.

The Theory of Relativity as presented in Einstein's 1905 paper allowed only inertial frames of reference but the objects defined in them could accelerate, correct?

6. Aug 3, 2011

### PAllen

Correct, else how do talk about force?

Since Einstein, it has become established that you can treat accelerated observers in special relativity.

7. Aug 3, 2011

### Finbar

Yes thats correct. Tiny Tim is correct. But there is some confusion on this since one can consider accelerating observers in flat spacetime and this would be strictly general relativity even though there is no gravitational field. Some people define special relativity to be the relativistic theory of flat spacetime and therefore claim it can describe accelerating observers.
Sean Carroll seems to use this definition in his book which leads to much confusion.

The reason for this confusion is that once a theory in flat spacetime is formulated in a nice geometrical way(i.e. the minkowski metric) going to a non-inertial frame is just a mathematical step(a change of coordinates) and doesn't effect the physics. So it seems a bit silly that one can go from special relativity to general relativity just by changing coordinates. Hence why some people think of "special relativity" as just the flat spacetime limit of general relativity.

Hope that makes sence

8. Aug 3, 2011

### PAllen

MTW and quite a few other books (most I've seen since 1960) take the view that SR can treat accelerated observers.

9. Aug 4, 2011

### bcrowell

Staff Emeritus
FAQ: Does special relativity apply when things are accelerating?

Yes. There are three things you might want to do using relativity: (1) describe an object that's accelerating in flat spacetime; (2) adopt a frame of reference, in flat spacetime, that's accelerating; (3) describe curved spacetime. General relativity is only needed for #3.

A prohibition on #1 is particularly silly. It would make SR into a trivial theory incapable of describing interactions. If you believed this, you would have to stop believing, for example, in the special-relativistic description of the Compton effect and fine structure in hydrogen; these phenomena would have to be described by some as yet undiscovered theory of quantum gravity.

#1 often comes up in discussions of the twin paradox. A good way to see that general relativity is totally unnecessary for understanding the twin paradox is to pose a version in which the four-vector equation a=b+c represents the unaccelerated twin's world-line a and the accelerated twin's world-line consisting of displacements b and c. The accelerated twin is subjected to (theoretically) infinite accelerations at the vertices of the triangle. The triangle inequality for flat spacetime is reversed compared to the one in flat Euclidean space, so proper time |a| is greater than proper time |b|+|c|.

#2, accelerated *frames*, is less trivial. It's for historical reasons that you'll see statements that SR can't handle accelerated frames. Einstein published special relativity in 1905, general relativity in 1915. During that ten-year period in between, nobody really knew what the boundaries of applicability of special relativity were. This uncertainty made its way into textbooks and lectures, and because of the conservative nature of education, some students are still hearing, a century later, incorrect assertions about it. There is an overwhelming consensus among modern relativists that the boundary between SR and GR should be defined as the distinction between flat and curved spacetime, not unaccelerated and accelerated observers.[MTW 1973,Penrose 2004,Taylor 1992,Schutz 2009,Hobson 2005]

In an accelerating frame, the equivalence principle tells us that measurements will come out the same as if there were a gravitational field. But if the spacetime is flat, describing it in an accelerating frame doesn't make it curved. (Curvature is invariant under any smooth coordinate transformation.) Thus relativity allows us to have gravitational fields in flat space --- but only for certain special configurations like uniform fields. SR is capable of operating just fine in this context. For example, Chung et al. did a high-precision test of SR in 2009 using a matter interferometer in a vertical plane, specifically in order to test whether there was any violation of Lorentz invariance in a uniform gravitational field. Their experiment is interpreted purely as a test of SR, not GR.

MTW 1973 -- Misner, Thorne, and Wheeler, Gravitation, 1973, p. 163: "Accelerated motion and accelerated observers can be analyzed using special relativity." p. 164: "An accelerated observer can carry clocks and measuring rods with him, and he can use them to set up a reference frame (coordinate system) in his neighborhood."

Penrose, The Road to Reality, 2004, p. 422, "It used to be frequently argued that it would be necessary to pass to Einstein's general relativity in order to handle acceleration, but this is completely wrong. [...] We are working in special relativity provided that [the] metric is the flat metric of Minkowski Geometry M."

Taylor and Wheeler, Spacetime Physics, 1992, p. 132: "DO WE NEED GENERAL RELATIVITY? NO! [...] 'Don't you need general relativity to analyze events in accelerated reference frames?' 'Oh yes, general relativity can describe events in the accelerated frame,' we reply, 'but so can special relativity if we take it in easy steps!'"

Schutz, A First Course in General Relativity, 2009. Schutz equivocates on pp. 3 and 141 about the status of accelerated observers in SR, but says, "[...] the real physical distinction between these two theories is that special relativity (SR) is capable of describing physics only in the absence of gravitational fields, while general relativity (GR) extends SR to describe gravitation itself."

Hobson, General Relativity: An Introduction for Physicists, 2005, sec. 1.14, discusses "Event horizons in special relativity" from the point of view of accelerated observers, using coordinates defined in their accelerated reference frames.

Chung -- http://arxiv.org/abs/0905.1929

10. Aug 5, 2011

### tiny-tim

hi ben!
(using somewhat theological language …)

who then is my neighbour?

can the prodigal twin (in the standard twin paradox) use SR in his accelerated frame(s) to calculate precisely the age of the stay-at-home twin, or is the latter not sufficiently "in his neighbourhood" to do that?

11. Aug 5, 2011

### PAllen

They can. The patch they can't extend consistent Fermi-Normal coordinates to is on the 'other side' - the direction they are accelerating away from.

Also, all of spacetime can be coordinitized by the accelerating twin if they use a different simultaneity definition - giving up on normal coordinates. (For example, a coordinate system based on radar time can cover all of space for the accelerated twin; this doesn't change the fact that an accelerating observer will have a horizon; it is analogous to the fact that the coordinate misbehavior of Schwarzschild horizon can be eliminated by different coordinates).

12. Aug 8, 2011

### kirkulator

thanks so much for all the great input! it helped a lot. I've been reading some material from scientists who are very dim on the validity of relativity, though ive seen that experimental data has been recorded [atomic clocks and such] but some sure seem to think its not sound, and possibly may not even be applicable. Possibly they are nutcases. hahaha. : )

13. Aug 9, 2011

### TrickyDicky

That is like saying that since the special relativistic formula E=mc^2 has mass in it, SR can handle non-uniform gravitational fields.
The fact is to do (1) and (2) you implicitly have to use more assumptions and postulates than those of SR , so you end up with something that resembles SR but in fact has plenty of extra assumptions since the original postulates only admit uniform motion and linear transformations. If people wanna call this new beast SR is their problem but it will keep causing a lot of confusion with the bonus problem that conclusions derived from the SR+unspecified assumptions might or not be valid depending on the extra postulates.
On the other hand there are results from SR from wich we can derive consequences to the general case (like the above mentioned relation between mass and energy).

Yes, but note that you are adding the Equivalence principle to SR here, this combination was the starting point for Einstein to build GR.
The bottom line is the original 1905 SR is different than SR+EP.

14. Aug 9, 2011

### bcrowell

Staff Emeritus
They are nutcases. Here is some info on the experimental evidence for relativity: http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html