Observer (special relativity)

The term observer in special relativity refers most commonly to an inertial reference frame. Less often it may refer to an arbitrary non-inertial reference frame; in particular, a Rindler frame is sometimes called an "accelerating observer". In such cases an inertial reference frame may be called an "inertial observer" to avoid ambiguity. Note that these uses differ significantly from the ordinary English meaning of "observer". Reference frames are inherently nonlocal constructs, covering all of space and time or a nontrivial part of it; thus it does not make sense to speak of an observer (in the special relativistic sense) having a location. Also, an inertial observer cannot accelerate at a later time, nor can an accelerating observer stop accelerating.

Physicists use the term "observer" as shorthand for a specific reference frame from which a set of objects or events is being measured. Speaking of an observer in special relativity is not specifically hypothesizing an individual person who is experiencing events, but rather it is a particular mathematical context which objects and events are to be evaluated from. The effects of special relativity occur whether or not there is a sentient being within the inertial reference frame to witness them.

History

Einstein made frequent use of the word "observer" (Beobachter) in his original 1905 paper on special relativity and in his early popular exposition of the subject^[1]. However he used the term in its vernacular sense, referring for example to "the man at the railway-carriage window" or "observers who take the railway train as their reference-body" or "an observer inside who is equipped with apparatus". Here the reference body or coordinate system—a physical arrangement of metersticks and clocks which covers the region of spacetime where the events take place—is distinguished from the observer—an experimenter who assigns spacetime coordinates to events far from himself by observing (literally seeing) coincidences between those events and local features of the reference body.

This distinction between observer and the observer's "apparatus" like coordinate systems, measurement tools etc. was dropped by many later writers, and today it is common to find the term "observer" used to imply an observer's associated coordinate system (usually assumed to be a coordinate lattice constructed from an orthonormal right-handed set of spacelike vectors perpendicular to a timelike vector (a frame field). See Doran.^[2]). Where Einstein referred to "an observer who takes the train as his reference body" or "an observer located at the origin of the coordinate system", this group of modern writers says, for example, "an observer is represented by a coordinate system in the four variables of space and time"^[3] or "the observer in frame S finds that a certain event A occurs at the origin of his coordinate system".^[4] However, there is no unanimity on this point, with a number of authors continuing a preference for distinguishing between observer (as a concept related to state of motion) from the more abstract general mathematical notion of coordinate system (which can be, but need not be, related to motion). This approach places more emphasis on the many choices for description open to an observer. The observer is then identified with an observational reference frame, rather than with the combination of coordinate system, measurement apparatus and state of motion. See, for example, Kumar and Barve^[5] and others:^{[6][7][8][9] [10]}

Coordinate system is frequently alternatively referred to as reference frame, or frame. … we shall use the latter (frame) when emphasizing … state of motion, rather than the scales of the coordinates. In this sense, the study of one reference frame yields the characters of a family of coordinate systems of the same kind (e.g. of the same motional state).

— J X Zheng-Johansson and Per-Ivar Johansson: Unification of Classical, Quantum and Relativistic Mechanics and of the Four Forces p. 13

It also has been suggested that the term "observer" is antiquated, and should be replaced by an observer team (or family of observers) in which each observer makes observations in their immediate vicinity, where delays are negligible, cooperating with the rest of the team to set up synchronized clocks across the entire region of observation, and all team members sending their various results back to a data collector for synthesis.^[11]

"Observer" as a form of relative coordinates

Egocentric direction or relative direction is a concept found in many human languages. In English, a description of the spatial location of an object may use terms such as "left" and "right" which are relative to the speaker or relative to a particular object or perspective (e.g. "to your left, as you are facing the front door.")

The degree to which such a description is subjective is rather subtle. See the Ozma Problem for an illustration of this.

Some impersonal examples of relative direction in language are the nautical terms bow, aft, port, and starboard. These are relative, egocentric-type spatial terms but they do not involve an ego: there is a bow, an aft, a port, and a starboard to a ship even when no one is aboard.

Special relativity statements involving an "observer" are in some measure articulating a similar kind of impersonal relative direction. An "observer" is a perspective in that it is a context from which events in other inertial reference frames are evaluated but it is not the sort of perspective that a single particular person would have: it is not localized and it is not associated with a particular point in space, but rather with an entire inertial reference frame that may exist anywhere in the universe (given certain lengthy mathematical specifications and caveats.)

Usage in other scientific disciplines

The term observer also has special meaning in other areas of science, such as quantum mechanics, and information theory. See for example, Schrödinger's cat and Maxwell's demon.

In general relativity the term "observer" refers more commonly to a person (or a machine) making passive local measurements, a usage much closer to the ordinary English meaning of the word. In quantum mechanics, "observation" is synonymous with quantum measurement and "observer" with a measurement apparatus and observable with what can be measured. This conflict of usages within physics is sometimes a source of confusion.

References

1. ^ Albert Einstein, Relativity: The Special and the General Theory.
2. ^ Chris Doran & Anthony Lasenby (2003). Geometric Algebra for Physicists. Cambridge University Press. p. §5.2.2, p. 133. ISBN 978-0-521-71595-9. http://www.worldcat.org/search?q=9780521715959&qt=owc_search. .
3. ^ Richard A Mould (2001). Basic Relativity. Springer. p. p. 21. ISBN 0387952101. http://books.google.com/books?id=lfGE-wyJYIUC&pg=PA336&dq=coordinate+observer&lr=&as_brr=0&sig=ACfU3U0QVE6JX8f6dfSkeexNiw1JW3NCMw#PPA21,M1. 
4. ^ Richard L. Faber (1983). Differential Geometry and Relativity Theory: an introduction. CRC Press. p. p. 134. ISBN 082471749X. http://books.google.com/books?id=ctM3_afLuVEC&pg=PP1&dq=isbn:082471749X&sig=ACfU3U1JcOftoaq6_y2T1QVx5cd-tM-iMg#PPA134,M1. 
5. ^ A. Kumar, Shrish Barve (2003). How and why in Basic Mechanics. Orient Longman. p. p. 115. ISBN 8173714207. http://books.google.com/books?id=czlUPz38MOQC&pg=PA115&dq=%22characterized+only+by+its+state+of+motion%22+inauthor:Kumar&lr=&as_brr=0&sig=ACfU3U36HY3RerJYLWRlfJaGxRw7EqzIeA. 
6. ^ J X Zheng-Johansson and Per-Ivar Johansson (2006). Unification of Classical, Quantum and Relativistic Mechanics and of the Four Forces. Nova Publishers. p. p. 13. ISBN 1594542600. http://books.google.com/books?id=I1FU37uru6QC&pg=PA13&dq=frame+coordinate+johansson&lr=&as_brr=0&sig=ACfU3U1VAkGbfRjt_GTknoX6WRLWP-AVZw. 
7. ^ Jean Salençon, Stephen Lyle (2001). Handbook of Continuum Mechanics: General Concepts, Thermoelasticity. Springer. p. p. 9. ISBN 3540414436. http://books.google.com/books?id=H3xIED8ctfUC&pg=PA9&dq=physical+%22frame+of+reference%22&lr=&as_brr=0&sig=ACfU3U1tEWQICZdsXeuLyfmH2PoLgZnMGA. 
8. ^ P. Cornille (Akhlesh Lakhtakia, editor) (1993). Essays on the Formal Aspects of Electromagnetic Theory. World Scientific. p. p.149. ISBN 9810208545. http://books.google.com/books?id=qsOBhKVM1qYC&pg=PA149&dq=coordinate+system+%22reference+frame%22&lr=&as_brr=0&sig=ACfU3U0xhpZ2lI99UPiYQCOL6oJ0ALO5uA. 
9. ^ Graham Nerlich (1994). What Spacetime Explains: Metaphysical essays on space and time. Cambridge University Press. p. p.64. ISBN 0521452619. http://books.google.com/books?id=fKK7rKOpc7AC&pg=PA64&dq=%22idea+of+a+reference+frame%22&lr=&as_brr=0&sig=ACfU3U2wsO42pqLOJ453eeIzk7ztXTa6uQ. 
10. ^ Han-Chin Wu (2005). Continuum mechanics and plasticity. CRC Press. p. p. 165. ISBN 1584883634. http://books.google.com/books?id=OS4mICsHG3sC&pg=PA165&dq=frame+observer&lr=&as_brr=0&sig=ACfU3U0OyqyTqI35ZrORcrTOSRTC6JPf9g. 
11. ^ Oliver Davis Johns (2005). Analytical Mechanics for Relativity and Quantum Mechanics. Oxford University Press. p. p. 318. ISBN 019856726X. http://books.google.com/books?id=PNuM9YDN8CIC&pg=PA318&dq=coordinate+observer&lr=&as_brr=0&sig=ACfU3U3TRrg4EVCiIW8btVgFdR49PD9RUg. 

See also

• Frame of reference
• Observer