"The Alternate View" columns of John G. Cramer

Published in the January-February-2022 issue of

This column was written and submitted 09/07/2021 and is copyrighted ©2021 by John G. Cramer.

All rights reserved. No part may be reproduced in any form without

The new
development that we will discuss in this column is that European theorists
Blazquez-Salenco, Knoll, and Radu (B-SKR) have reconsidered the physics of
wormholes, but using the assumption they are made with *fermion
*particles. They employ Einstein-Dirac-Maxwell
(EDM) theory, a semiclassical way of uniting aspects of quantum mechanics and
general relativity. Their
calculation uses Planck units that set G = c = ħ
= 1, so their results are in units of the Planck length, mass, and time,
and the Planck unit charge, which is about 3.3 electron charges.
Their calculations assume that the matter components of the wormhole are
two Dirac fermions with half-integer spins arranged to have opposite spin
orientations. The resulting wormhole
has mass **M** and is threaded by lines
of electric flux that enter one wormhole mouth (giving the appearance of a
negative charge **-Q _{e}**)
and emerge from the other wormhole mouth (giving the appearance of a positive
charge

The EDM formalism allows the fermionic matter to be described by quantum wave functions rather than by quantum fields. (We note that the EDM approach avoids the ugly self-energy infinities and absurdly large cosmological constant that are major problems for standard quantum field theory and contribute to its incompatibility with general relativity.) The EDM semi-classical approach leads to a more tractable model. If there was no electric flux through the wormhole throat, a discontinuity at the throat would require a layer of matter. However, the inclusion of the wormhole-threading electric field tends to smooth the wormhole geometry, eliminating the discontinuity and the need for matter, exotic or otherwise, at the wormhole throat.

The result of
the B-SKR calculation is a stationary spherically-symmetric wormhole that
requires no exotic matter for stability. They
model this system analytically and numerically and show the behavior over a
range of parameters. Using their
graphs, I conclude that a fermionic wormhole with an electric charge **Q _{e}**
of about 330 electron charges will have a mass

B-SKR point out that although the configuration they analyze only includes two fermions, their approach can be extended to include states with an arbitrarily large number of fermions. Adding fermions would presumably increase the size, mass, and quantum effects. Increasing the throat-threading electric field would linearly increase the throat area. Therefore, perhaps by making a wormhole with a very large number of fermions and increasing the size of the threading electric field, one could arrive at a throat aperture that might be large enough for light-wave communication or even for the passage of matter.

Thus, the
B-SKR calculation raises the possibility of stable particle-like wormholes that
are very small but have a mass and electric charge that are manageable in the
laboratory. In my AV column
"Shooting Wormholes to the Stars" (AV-162,
May-2012 ** Analog**),
I described how one mouth of a hypothetical stable electrically charged wormhole
with the charge-to-mass ratio around that of a proton could be accelerated to
very close to the speed of light in an existing accelerator (e.g. the CERN LHC)
and aimed at a distant star.

Because of the
wonders of relativistic time dilation, the arrival time at the star is greatly
reduced, as viewed through the wormhole's aperture.
The arrival time as viewed in the external world is **T=L/c**,
where **L** is the distance to the star
and **c** is the speed of light.
For example, the sun-like star Tau Ceti is 11.9 light years from Earth,
so as viewed from Earth the arrival time of a near-lightspeed wormhole end would
be about **T**=11.9 years.

The arrival
time as viewed through a wormhole is **T****'****
= T/g**, where **g**
is the Lorentz factor [**g=
(1-v/c) ^{-½}**] and

The fermionic
wormholes described by B-SKR are almost a fit for this concept.
They are stable, particle-like, and have an electric charge that can be
used for acceleration. However, the
estimated wormhole mass is much too large (100 Planck masses is about 10^{21}
proton masses) to be accelerated in a synchrotron like the LHC.
A linear accelerator could perhaps perform the needed acceleration, but
it would need to be a huge specially-constructed linear accelerator that could
handle the tiny charge-to-mass ratio of the accelerated wormhole mouth and give
the accelerated wormhole end a near-lightspeed relativistic velocity.

Perhaps producing a fermionic wormhole built from a very large number of fermions and a large threading field would save the day. It would grow in mass, size, and charge. If the aperture could be made large enough to pass electrons, one could direct a beam of accelerated electrons through the negatively-charged wormhole mouth and boost the effective charge by threading more electric lines of force through it. This might result in a wormhole with a large enough charge-to-mass to be accelerated in a synchrotron and with a large enough aperture for viewing, steering, and fast interstellar exploration. In other words, the B-SKR theory needs to be extended to cover more fermions and larger threading electric fields.

One interesting implication of the B-SKR calculation is the possibility that, because of their simplicity and stability, fermionic wormholes might have been produced naturally in the super-hot era just after the Big Bang. If that happened, primordial fermionic wormholes should still be around, and it might be sensible to search for them.

They might be a super-heavy component of cosmic rays. One might search among the particles arriving from space for those that have a charge of many electron charges, but with a very large mass, so that they produce an electric pulse as they go by but with a trajectory that does not bend in a magnetic field

Alternatively, they might be trapped in rocks and minerals, awaiting discovery. In a mass spectrograph, they could be in principle be pulled out of a vaporized sample by the electric potential, but would be so heavy that they would move in an essentially undeflected straight line in the magnetic field. Or they might be so heavy that they would have been pulled by gravity to the center of the Earth as it formed. Even in that case, such wormhole ends might still be found in meteorites that formed in a gravity free environment.

We should go
out and look for them.**
**

John
G. Cramer's 2016 nonfiction book (Amazon gives it 5 stars) describing his transactional interpretation of
quantum mechanics, ** The
Quantum Handshake - Entanglement, Nonlocality, and Transactions,**
(Springer, January-2016) is available online as a hardcover or eBook at:
http://www.springer.com/gp/book/9783319246406
or https://www.amazon.com/dp/3319246402.

**SF
Novels by John Cramer:**
Printed editions of
John's hard SF novels ** Twistor**
and

**Alternate
View Columns Online**: Electronic reprints of 216 or more "The Alternate
View" columns by John G. Cramer published in ** Analog**
between 1984 and the present are currently available online at:

**References:
**

**Fermionic Wormholes:
**

Jose
Luis Blázquez-Salcedo,
Christian Knoll, and Eugen Radu, "Transversable wormholes in Einstein-Dirac-Maxwell
theory", Physical Review Letters **126**, 101102 (2021); ArXiv:
2010.07317v2 [gr-qc].

**Bosonic
Wormholes:
**

Michael
S. Morris, Kip **61**, 1446 (1988).

Matt
Visser, "Traversable wormholes: Some simple examples", Phys. Rev. D** 39**,
3182 (1989).