Special Relativity
David W.Hogg
School of Natural Sciences
Institute for Advanced Study
Olden Lane
Princeton NJ08540
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hogg@ias.edu
1December1997
Contents
1Principles of relativity1
1.1What is a principle of relativity? (1)
1.2Einstein’s principle of relativity (2)
1.3The Michelson-Morley experiment (3)
1.4The“specialness”of special relativity (5)
2Time dilation and length contraction7
2.1Time dilation (7)
2.2Obrving time dilation (8)
2.3Length contraction (9)
2.4Magnitude of the effects (10)
2.5Experimental confirmation (10)
3The geometry of spacetime13
3.1Spacetime diagrams (13)
3.2Boosting:changing reference frames (13)
3.3The“ladder and barn”paradox (15)
3.4Relativity of simultaneity (16)
3.5The boost transformation (16)
科学名言3.6Transforming space and time axes (17)
4The Lorentz transformation19
4.1Proper time and the invariant interval (19)
4.2Derivation of the Lorentz transformation (20)
4.3The Lorentz transformation (20)
4.4Velocity addition (21)
4.5The twin paradox (22)
5Causality and the interval25
5.1The ladder and barn revisited (25)
5.2Causality (26)
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5.3Nothing can travel faster than the speed of light (26)
6Relativistic mechanics29
6.1Scalars (29)
6.24-vectors (29)
6.34-velocity (30)
6.44-momentum,rest mass and conrvation laws (30)
6.5Collisions (31)
6.6Photons and Compton scattering (32)
6.7Mass transport by photons (33)
6.8Particle production and decay (34)
防拐骗教案6.9Velocity addition(revisited)and the Doppler shift (34)
6.104-force (34)
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7Optics and apparent effects:special relativity applied to astronomy37
7.1Doppler shift(revisited) (37)
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7.2Stellar Aberration (38)
7.3Superluminal motion (38)
7.4Relativistic beaming (39)
7.5The appearance of passing objects (40)
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7.6A simpleminded cosmology (40)
心理换位References43 Index45
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Preface
For me,the wonder of special relativity lies in its success-ful prediction of interesting and very nonintuitive phe-nomena from simple arguments with simple premis.
The notes have three(perhaps ambitious)aims: (a)to introduce undergraduates to special relativity from its founding principle to its varied conquences,(b)to rve as a reference for tho of us who need to u spe-cial relativity regularly but have no long-term memory, and(c)to provide an illustration of the methods of the-oretical physics for which the elegance and simplicity of special relativity are ideally suited.History is a part of all science—I will mention some of the relevant events in the development of special relativity—but there is no attempt to prent the material in a historical way.
A common confusion for students of special relativity is between that which is real and that which is
appar-ent.For instance,length contraction is often mistakenly thought to be some optical illusion.But moving things do not“appear”shortened,they actually are shortened. How they appear depends on the particulars of the obr-vation,including distance to the obrver,viewing angles, times,etc.The obrverfinds that they are shortened only after correcting for the non-fundamental details of the obrvational procedure.I attempt to emphasize this distinction:All apparent effects,including the Doppler Shift,stellar aberration,and superluminal motion,are relegated to Chapter7.I think the are very impor-tant aspects of special relativity,but from a pedagogical standpoint it is preferable to parate them from the ba-sics,which are not dependent on the properties of the obrver.开机密码忘记
I love the description of special relativity in terms of frame-independent,geometric objects,such as scalars and 4-vectors.The are introduced in Chapter6and ud thereafter.But even before this,the geometric proper-ties of spacetime are emphasized.Most problems can be solved with a minimum of algebra;this is one of the many beautiful aspects of the subject.
The notes,first written while teaching ctions of first-year physics at Caltech,truly reprent a work in progress.I strongly encourage all readers to give me com-ments on any aspect of the text∗;all input is greatly ap-preciated.Thank you very much.
