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Comment on “on the possibility of a three-temporal Lorentz transformation”
Volume 73A, number 1
PHYSICS LETI’ERS
20 August 1979
COMMENT ON “ON THE POSSIBILITY OF A THREE-TEMPORAL LORENTZ TRANSFORMATION” Dipankar RAY Department of Physics, Queen Mary College, London El 4NS, England Received 5 June 1979
In a recent paper it has been suggested that, strictly speaking, light speed invariance is not fully consistent with ordinary space geometry unless our concept of time is drastically modified. This note argues against that paper.
Ziino [1] felt that, given our present concept of time, the two following postulates of special relativity are inconsistent: (a) Ordinary space is three-dimensional and eucidean. (b) Light speed is invariant,
idea that a free particle moving in space has three degrees of freedom. According to Ziino [I] this can be remedied only by a drastic change in the notion of time. However, it is easy to see that the above argument is false. The fact thaty is determined by x, v and t0, is
His argument is as follows: in special relativity the motion of a free particle in a plane is given by
simply another way of saying that the usual two degrees of freedom, namely (x, y), can be replaced by another set of two degrees of freedom, namely (x, v). It does not in any way reduce the number of degrees of freedom to one. Moreover, it has nothing to do with light speed invariance but holds in the newtonian system as well. Therewehavexv~t,yvytandu2v~+v~. As before, x can be determined from y and vice versa if v and t are known.
x(t(tA))
=
vX t(t0)
,
y(t(tA))
=
vY t(t u )
where t is connected with the proper time t0 by t(t
0
0
)=t
2/c2)1/2
/(l
—
v
(1)
andv2v~+v~. Ziino [11has argued that, since from the above equations, x can be determined from y and vice versa if v and t 0 are known, the particle in question does not have two degrees of freedom but only one. Similady, a particle moving in space does not have three degrees of freedom. Since eqs. (1) are obtained from a Lorentz transformation which is a consequence of the invariance of the speed of light, it is argued that the invariance of the speed of light is inconsistent with the
4
Thus, according to the present author, Ziino’s [1] argument is not correct.
Reference [1J G. Ziino, Phys. Lett. 70A (1979) 87.
PHYSICS LETI’ERS
20 August 1979
COMMENT ON “ON THE POSSIBILITY OF A THREE-TEMPORAL LORENTZ TRANSFORMATION” Dipankar RAY Department of Physics, Queen Mary College, London El 4NS, England Received 5 June 1979
In a recent paper it has been suggested that, strictly speaking, light speed invariance is not fully consistent with ordinary space geometry unless our concept of time is drastically modified. This note argues against that paper.
Ziino [1] felt that, given our present concept of time, the two following postulates of special relativity are inconsistent: (a) Ordinary space is three-dimensional and eucidean. (b) Light speed is invariant,
idea that a free particle moving in space has three degrees of freedom. According to Ziino [I] this can be remedied only by a drastic change in the notion of time. However, it is easy to see that the above argument is false. The fact thaty is determined by x, v and t0, is
His argument is as follows: in special relativity the motion of a free particle in a plane is given by
simply another way of saying that the usual two degrees of freedom, namely (x, y), can be replaced by another set of two degrees of freedom, namely (x, v). It does not in any way reduce the number of degrees of freedom to one. Moreover, it has nothing to do with light speed invariance but holds in the newtonian system as well. Therewehavexv~t,yvytandu2v~+v~. As before, x can be determined from y and vice versa if v and t are known.
x(t(tA))
=
vX t(t0)
,
y(t(tA))
=
vY t(t u )
where t is connected with the proper time t0 by t(t
0
0
)=t
2/c2)1/2
/(l
—
v
(1)
andv2v~+v~. Ziino [11has argued that, since from the above equations, x can be determined from y and vice versa if v and t 0 are known, the particle in question does not have two degrees of freedom but only one. Similady, a particle moving in space does not have three degrees of freedom. Since eqs. (1) are obtained from a Lorentz transformation which is a consequence of the invariance of the speed of light, it is argued that the invariance of the speed of light is inconsistent with the
4
Thus, according to the present author, Ziino’s [1] argument is not correct.
Reference [1J G. Ziino, Phys. Lett. 70A (1979) 87.