Criticisms on the theory of the constancy of the speed of light are answered. It is shown that the new theory is not logically inconsistent for the reasons expressed

Hsu, J. P.

Sherry, T. N.

English

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The new four . dimensional symmetry theory with universal
time introduced b y Hsu (1) was criticized in a recent article. (2)
The new theory has been expounded more recently by Chiu, Hsu
and Sherry. 
(3)
	
In Reference 2 , the authors claimed to have
shown logical inconsistencies in the original work of Hsu.
;Moreover, they assert that any attempt to work with such a
symmetr y framer•:ork is wrong, by appealing; to a derivation of
the Lorentz transformation based on hypotheses which are
different from these in Reference 1 . As a result, they
reject entirely the new symmetry theory.
We wish to comment on their article and to answer all
their criticisms in this note.	 First we acknowledge that
cerain of their criticisms of the new symmetry theory, as
originally presented, are valid. This was noted independently
by the present authors, and the corresponding changes have
been made in the theory. (2) ' (a), ilowever, other of their cri-
ticisms arise from misunderstanding; the text of our work.
Their further assertion that any such space-light transformation
17
between inertial frames is wrong and roust he disri 5nd, wt!
also answer.	 This is quite a hasic and subtle paint that has
to do with the or iginal hypot heses upon which one hu i 1 d q one's
theory. their argument essentially compares the space 5 W
transformation in our theory with the allowed transf"trations
in a di f ferent theory.	 A scient i f is theory should h- Ksm+issed
on the basis of ^ ont radiction with established experiment rithc ► tf,a.,
cuntra;lic:tiun with a tlieur}' I;u11t on di fferent hypothc•	 sha ll no-,
discuss in what sense thc 1 hcorie•s are di i ferent .
Ihe authors in their carl ic y piper ;1 , shoe: • that t hvc
believe that the concepts of space and time should havo special
symmetry propvri ies. 	 'this rrno"nts to a g s"ming that sl acu r
,M
and time t must cWrrT_!^' under the transformation between in-
ertial frames.	 They claim that "the relativit y principle
I for physical laws) together with the homogen y i t y and isotropy
of space and the homogeneity of time" leads to an nn^c )t , c i f icy(t
universal constant IT which is the coefficient of time in th,
'This is basically the sauce as Robertson's definition of interval
1	 1
as 4?
1 
_ 
'it
	 1.	 As pointed out in Ref. (1) , this very
definition excludes the possibility of the universal time.
ri
trarsf0 ► .:.atloll and is the upper limit of speeds for physical ohiects. This
has been correctly criticized in that the coefficient of time, T , is
impl ic: i t ly assumed (in their derivation) to be unwhanged unJor
transformations.	 Our work, however, relies In hi"dslhht on
the fact that the Lorentz transformations forma four-dimensinnal
symmetry group of r and Ot .
	
It is not space and time, as such,
which possess the homogeneity and isotropy properties, h a rt rMher
space and the plodut t of T and time. 	 The paint to note here is
that the coefficient of time is assumed to he unchanged in special
relnt ivity and one derives uniquely the Lorentz; tr%nsformat ion.
but we hold that the four-diriler ► sional symmetry scheme aIlo"s one
to make a different assumption, thereby obtaining a different
group structure.
In our approach, we beg in with a four - dimensional fromewprk
which we identify as the three space dimensions and a fourth di-
0
mcnsion x	 The symmetry properties are then expressed for x,v,r-
and x 0 .
	
We yet have to specify, by an additional postuiNte, hot•.,
X  is to be identified.	 It is clear that the identification
X  
= ct R (or At R) (5)
where c is a universal constant and t  is to he called the
11
t ime givcs it:`• tht'	 t>c .'i:tl	 Iheory of reI:It it it i'.	 Iin+,_t•c.r, we
mu"t re ol;ni r that I 	 iS :t Mart	 ► 1:tr C hoke • f (I r X, tti)c'
I7 ►
tIt;. t ot ht'r ch, ices inav : 11so he	 If 	 ttit' rave t i lt' altc:rn:t-
ti ne chuice:
c^
x	 _.	 lit
u
where t it , %-.h i, h	 ca 1 I t hc t i l- . , or the !,n i ver' ,^a l t ime,	 i
to Ile the saute i ► t a I I t I.wmv^. , and h i	 not t o he tilt i Mersa I I;.'
constant.	 In	 I	 tilt' cot' fl icIcttt f ! t l tc tu1iX • crsaI tire.
iS a fc,ttctioil I 1 tilt' fuur'- :i ►ncris orta1 t r:tnsforuiat in t t,	 We
note here,	 t i ► a t	 :t` :I resit I t oI , t I li	 proper? y tilt' t ► r;rta I a rl;tt-
filents to show that tilt' coot t i(_ icnt of the t ime t';tr ► 'thlt' Shotticl
he ident ic:;t1 to the om.-way ^pcod of I iK,ht do It() t ft',I 1m,;
t 1 rough.	 'I ht' ;ic t tt:t 1 wot'1, i nl, ottt o 1 t he speed o f I i ght	 :in(
the di ffe • rt'nt :.I)et'cl:: t•:hic'h can in	 it)Ic OCC1.11— iti git't'n
deta i l in our Srcond	 (_i)	 t. c, st ress tltrtt one stunt he
ca re I'll 	 in interpret in.; the cocFfic ► cttt oh time iti such a
theory which	 a di I Icrvnt cmlccpt o 	 t iris, 	A thcc,r
coils itits o f a scheme of, ctltt;tt ioil,;, t	 ► tcr t;_iti	 tIle titles
f"or aImIvinit and lit (CLPrct i lit-_ the egIlat i(,n1. (; l
'Ilia IdioIC irux in tuidcr'SI;Indin}; the ticw four- dinicnsior+al
svmmetr) I it's in the operat ion,t I mean 1 1t; of t intc.	 The till iveI-S a I
't,
time can be realized by the following clock system: (8)
Suppose there is only one set of clocks located everywhere
in in%- ono inert ial frame, sa y the f frame. one can synchronize
these clocks so that the speed of light is isotropic a::d has
the constant va 1 ue c in f'.	 All observers in d i f rerent frames
use this set of clocks (which -ire everywhere in space) to
record time, e.g., usi ►► 1; the clock nearby anoccurrcnce to
record its time.	 (Of course, we assume that there are observers
located everywhere in ever y t rame.)	 Ill 	 wa 3 , all observers
have a common un iversaI time.	 1t is really not necessary to
duplicate identical set of clocks for each frame. 	 1':ith such
a clock system, the one-way speed of light in a different
f-ran►c f' will not he isotropic.
The major reaso ►► we feel such a formulation of four - -d imen-
sional theory is justified and worthwhile is that it involves
a classical-like concept of t ime kind, nevertheless, does not
contradict previous experim^, nts.	 .also, our theory possesses
many features qualitatively the same as those of special rela-
tivity; for example, in each frame there is a limiting velocity
in any direction—the limiti.ni; velocity is the 'speed of light
in that direction'
21
2 . A1N'SWLRS TO CRITICISM
We must first make some points related to the authors'
introduction. (2)	 To begin with, our universal time must he
distinguished from the Newtonian concept of time. While it
is universal, it is not absolute in the Nestorian sense.
(See Section 1 and Reference 3.) Secondly, we take issue
with their describing x  as "a product of... a relative speed
of light c multiplied by a universal time t " .
	
In fact UK
is at the root of many of their misunderstandings and criticisms.
As explained in Section 1 and in our second paper, (3) the co-
cificient of the universal time is not to he confused with the
speed of light.	 It is a function which specifies
	
the framc-
of reference with respect to the particular universal time
being used. Certain of its values are related to the different
operational spee:ls of light (one-way or two-way, etc.) . 	 But
one cannot require that all its values he physically identified
in such a manner.
Let us now consider the difficulties with the new theory
which are pointed out. (1)	In their criticism (1), they Maim that
2"
the 'Principle of Relativity' is not im p lemented in the work.
From the discussion in Section 1 it should be evident that in
terms of' x,ti, ,z and x o , our theor\ • is indistinguishallle from
the special theory of relativity.	 We interpret the 'Principle
of Relativity' as the statement that the form of the Iati:s of
Physics should he the same in all inertial frames of reference.
Clearly, since an inertial frame is labelled by x,y,z and x 
(whatever the subsequent identification of x o ). we c learly
have impleinc tit ed it.	 Khat is not true is that physical con-
stants, or rather those constants usually described as imnor-
t ant 'physical constants', take the same nwnerical 	 value in
all inertial frames.
I'he main point of criticism (2) is valid.	 It was erroneous
to discuss relative velocity between inertial frames with tiro
distinct values.	 This point has been overcome in our seco"'d
Pape r. (3) We plight also note at this stage that the space light
transformations relate the events
(c.t,x,y,--)	 and (c't,x',y',z')
L3
It is not idle semantics to emphasize that all the 	 ((,ordinr ► tes
of an event (or a point) should have the same dimensions,
namely that of a lc:ngth y r+nd the same covariant trarisformal ion
property, namely that of n 4-vector.
Criticism (3) arises from the misun(lerstandillg alluded
to in the first paragraph of this section.	 Since tl ► c coeffi-
cient of t is not of itself a speed of light L in expression
(1) c' is not the speed of light at a point x',y',z', t
we do not have the contradiction alluded to. 	 We explain ir ►
detail in our second paper 
(3)
	 that sped ficat ion o r opc. r; ► t inn: ► 1
constraints on x and t can lead to an identification of certain
of the values of c' as speeds of light. The constraints are
that x rind t should he the space and time coordinates of a
ph y sical particle. The choices of x and t which five the pro-
blems from the authors' point of view (2) are thus seen not to
be a problem for the speed of light.
Their statement , " Thus he (11su) interprets x as a particle
velocity which is then required to satisfy x < c`/v " in criticism
(3) is wrong. There i s simply no such requirement k < c`/v
for a particle velocity stated in Reference 1 . The particle
24
velocity v is, of course, restricted by the mass formula m(v)
m/(1-v`/c 2 ) 112 given by equation (21) in Reference 1 .
In answer to their criticism (4), we do not allow a physi-
cal speed to be greate-, than the speed of light in any frame.
Our velocity transformation law is such that if' the speed in one
frame is less than the speed of' light in the same direction,
then it is a,so true in the primed frame. 	 In this it is no
different qualitatively from the special theory of relativity.
To reemphasize, if a velocity is less than that of light in
WIP frame, it is true in all frames. Hence a physical velocity
is limited b y the velocity of light.
The authors' final section is adequately answered in Section
1. With our understanding of reference frames it is clear that
the space-light transformations are valid. The onl y quibble
•	 is the identification of time. We refer on this point to Refer-
ence ( 3) .
2^
3.	 C0 ,CI,11SInN
Ill
	
we have answered each and every one of the
'criticisms raised by the authors. 	 'I ]Vi t is, Ire have ShOWTI
that the new theory is not logically inconsistent — at least
not for the reasons they express.	 It remains to he seen
whether or not any inconsistency	 can occur.	 It scen ' s to
us, because of the approach explained in Section 4, that no
internal inconsistency cai, occur.
It appears that the universal constancy of the speed of
light is not essential to the understanding of natural phen-
omena or for the foundations of physics. What remains to he
discussed, however, is whether or not the non-universality
I	 of the light speed and the universal time can he of henefit
in physics. Will it reduce the number of fundamental universal
constants of physics in the future ? 2,(I)	11ill it simplify the
setting; up of clock sv%tems?i,l lwi it help the Common people
to understand the fundamental concepts of space and time in
Dirac. believed that, in the ph y sics of the suture, the Planck
,
_onstant, the electromagnetic coup ling; strength and the light
speed cannot be all funL;amental constarrts and that only two
of them is fundamental,
? i,
I,hysics? After all, the universal times(11) in the ncr: thcoi-y
is essenti.-ily the common-sense- time. We feel that the time
is ripe to discuss these questions.
I
'Wheeler suggested that the concept of universal time could
he defended from the viewpoint of the evolution of our uni-
verse as a whole. (10)	 ' I'll is is in harmony with the C lock
s y stem discussed in Section I and References (3) and (8).
L7
ltcfer(.r ccs
lisu,	 I (,un,1 , Phys.	 (,,	 317 ( 197()) .
2.	 T. M. Falotas and A. R. Lee, slrhtr► it.ted to Fouli'l, I'f^v^
C. B. Ch III, J. 1 1 . I1" ►.i and 'I . ti. Sherr y , s ► rhn,it tcd to
Found. Phys. ((:PT 1,rchrint 011 7-qZ)
4.	 .l.	 I'. Ilstr, 1.rratIim and Addend ,un of	 ► (cif .	 1 ,	 I'„ ► rrnd-	 I'hvs.
(i r ► press) ; see a I So f'uuncl . Phys . ( t o b y t,ul, I i shcd I anal
"(Quantum 1.Iectrodynamics V;1thin th,• F rameworl ,,f a :vw
Dour- dImctnsionaI `;yuunctry" ! t r, ; ► 1, 1, c. ; ► r in Folln,l Phys. ) .
'I'.	 1%1.
	 f:; ► lutr; , ► nd A.	 It.	 L(.-v,	 Ain	 0^".1;
X14,
	 00o ( 107(,) .	 sue also li. Rreit oil hvrger,	 ► , )vo Ci1:1, -I It
11,,	 I	 ( 1'.)71) ;	 V.	 Inc rgi	 r ► n,I	 V.	 Gorin i ,	 J,	 ,1: ► 11 i	 P1Ivs.	 I0,
1518 ( 19o8); '. 11.1. I.Fvy-Lchlond, Am. J. Phys. .14, Z -'	 197(-).
t,.
	
S. Maika jan, Aw.	 J. i I lys. 4 .1, 908 ( 1970) .
7. 1'. A. M. Dirac,	 I.vct ► rrvs clrl QIla11turn I ivl 1 	 1 1 ► v„rv,	 1Aca,lcI'lic
1)ress,	 I tic .	 19(x(,)	 1,.	 1.
8. .J.	 1'. Ilsu, "'I'hv Ana Ivsis of 'I ime" , 1lrvllril ► t.
^.	 1'. A	 M. Dirac, SCiC11t i I is AMCFi^• an ^t ► ", ':^,.	 4`;- 1'.1
( 11103) .
A. Wheeler, 1lrivatc c()nvcrS; ► t ion.
Scl, loge I, l i me and the I'1 ► vs i ca I Wor I d	 (!love I - , Now York
1908), Ch. 7 and 8; Found. PLys. 7, ,_'45 111177 ► .
28
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Critical comments on the constancy of the speed of light

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