Mechanism for inertial rotation sensing device for measuring spectral lines of rotating atoms seen by rotating observe

Heims, S. P.

English

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1 -3 S. P. Heims* Brandei s University 
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An i n e r t i a l  ro t a t ion  sensor is a device t o  measure absolute 
ro ta t ions ,  not merely t h e  ro ta t ion  r e l a t i v e  to  an observer. If a man is i n  
a vehicle i n  space, t h e  ro t a t ion  sensor f ixed  t o  the  vehicle should t e l l  
him h i s  r a t e  and direct ion of rotat ion r e l a t i v e  t o  an i n e r t i a l  frame of 
reference. In  t h e  course of t h o r e t i c a l  s tud ies  of ro ta t ion  phenomena it 
became apparent t ha t  various physical phenomena exist which, i n  pr inciple ,  
could pmvide mechanisms fo r  i n e r t i a l  r o  t a t  ion-sens ing devices , mechanisms 
which are qu i t e  different  f r o m  those t h a t  have been employed i n  t h e  past. 
The purpose of t h i s  note is  to  point out one such mechanism. 
Suppose a c r y s t a l  i s  ro ta t ing  r e l a t i v e  t o  an i n e r t i a l  frame, and 
spectroscopic equipment is  ro ta t ing  along w i t h  it . The equipment measures 
the spec t ra l  l i n e s  of t he  rotat ing atoms as seen by an observer who i s  a l s o  
rotat ing,  According t o  a theory given elsewhere'), some of the characteris-  
t i c  atomic frequencies seen i n  such an  experiment would dFffer from the  cor- 
responding frequencies in  a s ta t ionary experiment by an amount proportional t o  
and o f  t h e  order of the  ro ta t ion  frequency i tself ,  
s h i f t s  could, i n  pr inciple ,  be used t o  de tec t  rotation. 
quantum wchanics*) t he  magnitude of the l i n e  s h i f t  fo r  angular ve loc i ty  8 is 
Consequently the  frequency 
In the  language of 
* 
Research supported by the N a t i o n a l  Aeronautics and Space Administration 
G m d -  b"t3 - PgG- 6 1 2  
4w 
Assis tan t  Professor, Department of Physics. 
https://ntrs.nasa.gov/search.jsp?R=19650019898 2020-03-17T01:59:37+00:00Z
where 
l i n e  i n  question, and ? is the in te rna l  o r b i t a l  angular momntum operator f o r  
(11 and (21 re fer  t o  the  two s t a t e s  of the atom connected by the 
the  atom. Since usual ly  t h e  unperturbed energy leve ls  are degenerate, a 
degeneracy l i f t e d  by t h e  ro ta t ion ,  what w i l l  ac tua l ly  be seen i s  a s p l i t t i n g  
of t he  l i ne  in to  several  components with separation of  t h e  order of AV 
According t o  (1) the frequency s h i f t  occurs if the expectation value of LOW 
is d i f f e ren t  i n  states 
these expectation values  vanish or are very small, a phenomenon known a s  
12' 
$ +  
(11 and (21 b For some atoms or ions in crys ta l s  
o r b i t a l  quenching. However, i n  other cases,  e.g. t he  r a re  ear th  ions i n  r a r e  
ea r th  salts, these expectation values a r e  of t he  order of 131 f o r  the usual 
states of t he  ion. 
The experimental problem ant ic ipated is t h a t  t he  l i n e  s p l i t t i n g  OP 
s h u t  (1) must be observed for a line which has a width much l a r g e r  than AV12. 
Recent development of MASEE3 (microwave range of frequencies) and LASERS 
(op t i ca l  range) nakes it possible t o  see changes i n  t h e  s t ruc ture  or s h i f t s  
b 
i n  the center  of mass of spectral  l i n e s  of  less than a cycle/sec. However, 
t he  resolut ion depends on t h e  shape and width of the l ine.  So favorable 
conditions f o r  observing the e f f ec t  are:  
have very d i f f e ren t  expectation values f o r  Loa,  and (b) t h e  l i n e  i s  as narrow 
(a)  the two s t a t e s  i n  question 
.) 
as possible. One can choose e i the r  a l i n e  i n  the paramagnetic resonance 
spectrum or  i n  the opt ica l  spectrum, whichever gives the highest  resolution. 
F ina l ly  it is  noted that the frequency s h i f t  (1) can be distinguished from 
t h e  well-known Zeemnn e f f e c t  due to magnetic f i e lds ,  because t h e  la t ter  a c t s  
on t h e  spin as w e l l  a s  on t h e  o rb i t a l  angular momentum. Otherwise the d e t a i l s  
of the  ro ta t ion  e f f ec t  (Le . ,  de ta i l s  of the s p l i t t i n g ,  dependence on polariza- 
t i o n ,  e tc , )  c lose ly  resemble tha t  of ths Zeemann effect .  
3 .  c r* . - 
Refer enc e 8 : 
1. S. P. H e i m s ,  Physica 29, a30 (1963). -
2. P. A. M. Dirac, Quantum Mechanics, Third Ed. (Oxford, 1947). 


Inertial rotation sensor

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