We present a brief overview of the different kinds of electromagnetic
radiations expected to come from (or to be induced by) space-like sources
(tachyons). New domains of radiation are here considered; and the possibility
of experimental observation of tachyons via electromagnetic radiation is
discussed

Folman, Ron

Recami, Erasmo

English

arXiv

We present a brief overview of the different kinds of electromagnetic radiations expected to come from (or to be induced by) space-like sources (tachyons). New domains of radiation are here considered; and the possibility of experimental observation of tachyons via electromagnetic radiation is discussed

Folman, R

Recami, E

CERN Document Server

ON THE PHENOMENOLOGY OF TACHYON RADIATION. ()
Ron Folman
Physics Department, Weizmann Institute of Science, Rehovot, Israel.
and
Erasmo Recami
Facolta di Ingegneria, Universita Statale di Bergamo, Dalmine (BG), Italy;
I.N.F.N., Sezione di Milano, Milan, Italy; and
Dept. of Applied Mathematics, State University at Campinas, Campinas, S.P., Brazil.
Abstract { We present a brief overview of the dierent kinds of electromagnetic radi-
ations expected to come from (or to be induced by) space-like sources (tachyons). New
domains of radiation are here considered; and the possibility of experimental observation
of tachyons via electromagnetic radiation is discussed.
PACS nos.: 14.80.P ; 52.25 ; 41.10 ; 03.30 .
Keywords: Tachyon radiation; Cherenkov radiation; Refraction index; Drag eect; Plas-
mas.
0() Work partially supported by INFN{Sezione di Catania, MURST and CNR (Italy), and by CNPq
(Brazil).
1
1. Introduction { The theoretical possibility of existence of Superluminal (V 2 > c2)
particles has been discussed thoroughly and seems to need no introduction.1 Recently,
this topic received new impulse by a series of interesting experimental results, about the
seemingly Superluminal speeds associated both with evanescent waves (let us recall the
Cologne, Berkeley and Florence results),2 − 4 and with electron neutrinos5 and muon
neutrinos.6
In the past, all experiments performed with the aim of detecting tachyons had re-
ported |in practice| negative results;7 but those searches were mainly devoted to look
for the electro-magnetic (EM) emission signature of tachyons, on the basis of poor theo-
retical assumptions. In the following, we rst dene the dierent forms of expected EM
radiation due to tachyons, and then re-examine previous conclusions about tachyon radi-
ations. Finally, we discuss a possible framework for future experiments. We shall always
conne ourselves within the realm of (relativistic) classical physics. Below, we shall call
\bradyon" any sub-luminal (v2 < c2) particle.
2. Radiation denitions { Since it seems that clear denitions are still lacking with
regard to the possible forms of EM radiation, let us dene what follows:
Denition a): << Let us call IER any EM radiation induced from a medium by a particle
(bradyon or tachyon), i.e., coming from the medium after that the particle has excited
it.>> This radiation can a priori be conic (\coherent" ) or not. Dened as such, this
radiation cannot be induced by any particle (in particular, by any tachyon) in vacuum
[unless one assumes a suitable vacuum structure, passing to quantum eld theories].
Denition b): << Let us call CER (Cherenkov EM radiation) any IER provoked by a
particle which is outside its \allowed speed{region": i.e., by a bradyon endowed with a
speed w larger than the light speed v in the medium, or by a tachyon which happens to
possess a speed W smaller than the light speed V in a suitable medium.>> Notice that
also CER is not necessarily conic, a priori.
Denition c): << Let us call OER (ordinary EM radiation) any radiation emitted di-
rectly by the particle itself, due to its acceleration or deceleration.>> Dened as such,
this radiation can be emitted by a particle (e.g., by a tachyon) also in vacuum, of course.
In this note, we shall not deal with this kind of radiation [for details cf. refs.1]. Here, let
us only recall the following, particular cases:
case A1 ) CER(B): in a medium with proper refraction index n0, we may have CER from
a bradyon B when v < w < c, that is to say, only when n0 > 1; in this case the CER is
conic;
2
case A2 ) CER(T): in a medium with proper refraction index n0, we may have CER from
a tachyon T when c < W < V , that is to say, only when n0 < 1; in this case the CER will
be non-conic, since the tachyon position will always remain inside the (spherical) waves;
while:
case B1 ) OER(B): in vacuum (for instance), the OER from a bradyon B is non-conic;
case B2 ) OER(T): in vacuum (for instance), the OER from a tachyon T will be on the
contrary conic.
3. Tachyon radiation domains { Recami and Mignani1 observed that the experi-
mental searches for (tachyonic) CER(T) had probably failed due to the mere fact that no
such radiation is expected to be emitted by the vacuum, nor by normal sub-luminal me-
dia. They overlooked, however, that |as we saw for example under point A2 ) above|
a CER(T) can come also from suitable sub-luminal media. We want here to discuss such
a possibility. Let us specify that below we shall refer ourselves to sub-luminal observers
O only, while a medium cam be either sub-luminal [u2 < c2] or Super-luminal [U2 > c2]
with respect to the observer O.
Recami and Mignani had based themselves on their generalization of the \drag eect"
for Superluminal speeds, i.e., on their extension of the apparent ( = relative to the observer
O) velocity v  c=n of light, in a moving medium, for tachyonic media.1 The equation
for the \apparent" refraction index n(u) was [both for subluminal and for Superluminal
speeds u]:
n  n(u) =
n0c+ u
c+ n0u
: (1)
In ref.1, however, only the particular case was considered in which the proper refraction
index n0 of the considered medium is larger than 1 (see our Fig.1, as well as Fig.22 in
the rst one of refs.1). This led them to claim: (i) that a bradyon B is not expected to
\emit" CER(B) in any Super-luminal media, due to the fact that the apparent refraction
index n in this case is smaller than 1, thus giving rise to an apparent light speed v in
the medium larger than c: a speed that B will never exceed [actually, in Fig.1 we can see
that Super-luminal media possess a refraction index n which is smaller than 1 and aims
asymptotically at 1=n]; and, because of the Duality Principle:1 (ii) that analogously a
tachyon T will not be able to \emit" CER(T) in any sub-luminal media.
But, of course, media also exist possessing a proper refraction index n0 smaller than
1; in this case, eq.(1) yields the behaviour depicted in our Fig.2. And from Fig.2 one
can infere that in fact a tachyon T can \emit" CER(T) in a sub-luminal medium with
n < 1, provided that its speed w obeys the constraint c < w < v, where v = c=n > 1.
3
Analogously, because of the Duality Principle, a bradyon B will be able to \emit" CER(B)
in a Super-luminal medium such that n0 < 1 (as can be derived from Fig.2).
4. Experimental considerations. { The fact that tachyons T are now expected
to emit CER(T) also in suitable sub-luminal media (for speeds ranging between c and
c=n) has of course some experimental consequences. In fact, we do not know of any
Super-luminal media; on the contrary, sub-luminal media with n0 < 1 are available, e.g.,
in the form of plasmas. We shall therefore consider the possible signature of CER(T) in
a plasma.
Let us rst assume the following: Any particle in a medium will nd its way to
loose quickly energy (e.g., by inducing emissions from the medium), when it happens to
be outside its \allowed speed{region"; namely, in the case of a tachyon, when its speed
w is between c and the apparent light speed v. This Assumption seems to be supported
also by the observation that |in the case of bradyons| the function−dE=dx vs. speed
presents for most particles an enhancement when crossing the v = c=n line (the so-called
\relativistic rise"). Such an enhancement, incidentally, is observed in several energy{
deposit channels, and not solely in the EM channel (which constitutes just a portion of
the energy loss).
A tachyonic CER(T) in a plasma is expected to be non-coherent, i.e., non-conic; and
therefore weak. In fact, the interested tachyon has to move slower than the apparent light
speed, so that the standard Cherenkov geometry is not realysed. This does constitute a
real diculty for any experimental search dedicated to CER(T) in plasmas, and it might
seem preferable to look for conic IER(T) in the speed range above c=n, if it weren’t for
our Assumption above. Actually, tachyon interactions with electromagnetic elds and
with ordinary matter are not yet completely known [dierent eects, such as that a point
charge when Super-luminal is expected to be spread over a double cone,1;8 have not yet
been fully dealt with]; and in particular we do not know how and how much IER would
be emitted by a tachyon. In any case, those tachyon interactions can be predicted to be
weak, on the basis of the fact that a Super-luminal electric charge is predicted to behave
as a magnetic pole1;9 [in the sense, roughly speaking, that the intensities of the electric
and magnetic elds generated by a charge get interchanged between themselves when
passing from the speed w to the \dual" speed W = c2=w].10 Therefore, in force of our
Assumption, we are entitled to consider as theoretically reasonable a search for CER(T),
in the speed range c to c=n.
We might then suggest the use of an array of detectors, situated parallel to the
tachyonic flight path, in order to try to observe the advance of the Super-luminal source.
Another suggestion would be to conne the plasma within a n > 1 substance (the border
between the two substances being parallel to the expected tachyonic track and close to
it), in which a part of the radiation circles emitted by the plasma will form a coherent
4
Cherenkov front with angles larger than those permitted for bradyon sources.
5. Conclusions and discussion { After having mentioned some recent experimen-
tal results, that might indicate the existence of Superluminal objects, we revised and
corrected in this note the theoretical reasons why it seemed till now that direct detec-
tion of Cherenkov radiation, induced by tachyons in ordinary (subluminal) media, was
impossible.
Then, we presented arguments favouring |on the contrary| the possibility of search-
ing for Cherenkov emission induced by tachyons in (subluminal) plasmas.
We wish to conclude with the following discussion.
First of all, one should not forget that, as mentioned above, while the electric inter-
action constitutes the major interaction betwen a charged bradyon and matter, on the
contrary the magnetic interaction will possibly be the dominant one for a charged tachyon
interacting with ordinary matter.1;9;10 So that, generally speaking, one ought to try to
detect Super-luminal sources via the magnetic eld they are supposed to generate. More
in general, it would be quite useful to solve |before all| the Maxwell equations suitably
generalized for Superluminal charges, in order to nd out the electric and magnetic eld
that a charged tachyon is expected to create in space-time; since such a study (preliminary
performed in ref.11, at an elementary level) will indicate how a Superluminal charge is
expected to interact with ordinary matter. Let us recall that two dierent generalizations
for Maxwell equations have been proposed: cf. refs.1;10 and refs.12, respectively.
Second, the question of wherefrom (i.e., from what sources) tachyons are expected
to come is still an open problem; even if dierent sources (including cosmic showers13)
have been suggested.1;14
At last, let us remark that another interesting search could be the one devoted
to detect the (conic) OER(T) emitted by tachyons |in vacuum, for instance| when
accelerating because of bremsstrahlung{type processes.
Acknowledgements: This brief note is dedicated to the memory of the late Professor
W. Yourgrau and the many discussions we had with him (and T.K. Shah) on similar
subjects at Trieste about fteen years ago. One of us (R.F.) would like to thank M.T.
Teli for enlightening discussions; while the second author (E.R.) acknowledges the kind
collaboration of A. Bugini, R. Garattini, L. Lo Monaco, R. Monaco, E.C. de Oliveiras,
M. Pignanelli, G.M. Prosperi, W.A. Rodrigues, S. Sambataro, P. Saurgnani, M.T. Vas-
conselos and particularly F. Raciti and G. Salesi.
5
Figure Captions
Fig.1 { The \drag eect" behaviour considered by Recami and Mignani,1 on the basis of
equation (1). It refers to the case in which the proper refraction index of the considered
medium is n0 > 1.
Fig.2 { The \drag eect" complementary behaviour [still derived from eq.(1)] for the case
in which the proper refraction index of the considered medium is n0 < 1. This case had
been overlooked in ref.1. For the possible consequences, see the text.
6
References
[1] See, e.g., E. Recami and R. Mignani: Rivista Nuovo Cim. 4 (1974) 209-290, E398;
E. Recami: Rivista Nuovo Cim. 9 (1986), issue no.6, pp.1-178, and refs. therein.
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[8] For some experimental data, and their discussion, see refs.1 and refs. therein.
[9] Cf., e.g., A.O. Barut, G.D.Maccarrone and E. Recami: Nuovo Cimento A71 (1982)
509; Lett. Nuovo Cim. 37 (1983) 345.
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367; Nuovo Cimento A30 (1975) 533.
[11] See, e.g., M.M. Ferreira: (in preparation).
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703; in Tachyons, monopoles, and related topics, ed. by E. Recami (North-Holland;
Amsterdam, 1978), p.31.
7
[13] Cf., e.g., R.W. Clay and P.C. Crouch: Nature 248 (1974) 28.
[14] Cf., e.g., T. Alvager and M.N. Kreisler: Phys. Rev. 171 (1968) 1357; C. Baltay et
al.: Phys. Rev. D1 (1970) 759; J.S. Danburg et al.: Phys. Rev. D4 (1971) 53.
8


On the Phenomenology of Tachyon Radiation

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