Journal of Modern Physics, 2012, 3, 955-956
http://dx.doi.org/10.4236/jmp.2012.39125 Published Online September 2012 (http://www.SciRP.org/journal/jmp)
Dark Experiments: From Black Holes to Cosmic Rays
Allen D. Allen
Physics Section, New Terra Enterprises, Glorieta, USA
Received July 3, 2012; revised August 16, 2012; accepted August 23, 2012
ABSTRACT
Some nagging questions in modern physics can be resolved rigorously using a basic mathematical formalism, albeit
with the need to admit that non-isomorphic realities arise to various degrees in a given universe. Let

,Umm


 be
an unordered pair of distinct massive objects in different reference frames. A dark experiment is an ordering ,mm


of the elements of U, either ,mm

or, exclusively, ,mm


, where the left-hand member of the ordered pair is
called the observer, and where there exists a 1-to-1 mapping



:, evfmm



tsen, such that both elements of an
ordered pair in a dark experiment agree on the events that unfold in the experiment. However, since ,,mm
 
mm ,
it follows that

,,mmf mm
 

f
. This describes non-isomorphic realities wherein both elements of each or-
dered pair mapping two distinct sets of unfolding events will agree on their respective events. Consequently, there is an
inherent limitation on what can be determined directly from experimentation. Examples arise in the context of the
Hawking information paradox, relativistic time travel, and cosmic ray experiments.
Keywords: Experimental Physics; Physical Reality; Hawking Information Paradox; Cosmic Rays; Relativistic Time
Travel; Lorentz Contraction; Cosmology
Although its roots extend far back in history to philoso-
phical, psychological, and relativistic debates, the con-
cept of what is here referred to as a dark experiment was
brought into focus by a recent thought experiment in-
volving a weatherman who jumps out of a spacecraft that
is accelerating in the vicinity of a black hole [1]. For the
weatherman, this change to a free falling frame negates
the existence of the hot stretc hed h orizon due to Hawking
radiation. But the hot stretched horizon continues to exist
in the accelerating frame, a key to Susskind’s resolution
of the Hawking information paradox [2]. This leads to
the question of what the weatherman reports about the
local temperature, and what he himself experiences, in
each frame. Indeed, the weatherman will be vaporized
when he encounters the stretched horizon in the acceler-
ated frame of the spacecraft. But in his free-falling frame
he falls through the event horizon unscathed. The dark
experiment places an inherent limitation on the scope of
what can be determined directly by experimentation.
Clearly, the field should be aware of this limitation. Fur-
thermore, a failure to admit to dark experiments has re-
sulted in apparent paradoxes appearing in a diversity of
contexts. In light of this, the purpose of the present paper
is to formally and explicitly introduce the dark experi-
ment.


,Umm

Let   be an unordered pair of distinct
massive objects in different reference frames. A dark
experiment is an ordering ,mm


of the elements of
U, either ,mm

 or, exclusively, ,mm  , where the
left-hand member of the ordered pair is called the ob-
server, and where



1to1: ,eventsfmm

  (1)
such that both elements of an ordered pair in a dark ex-
periment agree on the events that unfold in the experi-
ment.
Note that,
,,mm mm

   (2)
such that


,,.fmm fmm

 
 (3)
In other words, reality

,fmm
 m
for

as the
observer in the experiment ,mm

is not the same as
the reality


,
f
mm

 m
when is being observed in
the experiment ,mm


m. Consequently, the observer

cannot determine directly from the experiment
,mm

 how the experiment ,mm  unfolds, that is,
C
opyright © 2012 SciRes. JMP

A. D. ALLEN
956
without invoking some theory such as a conservation law
or transformation algorithm. Of course, as the observer in
the experiment ,mm
 m

, 
m
directly observes how
that experiment unfolds. But he cannot communicate this
to the observer because in the experiment ,mm


m m,
agrees with as to the events


,,
f
mm
f mm 
that unfold in the experiment
,,mm
 
mm
 .
Now while
 

,,
m
m



,,fmm fm
fmm fm
 



 (4)
is mathematically inherent in a dark experiment, no in-
consistency arises if we choose to assume
 
,.mm
 
m

,fmm f

 (5)
In the thought experiment involving a weatherman
who jumps out of a spacecraft that is accelerating in the
vicinity of a black hole, inequality (5) reflects the fact
that the weatherman’s radio signal is always lost when he
falls through the event horizon, either because he and his
equipment are vaporized by the stretched horizon or be-
cause the signal is trapped inside the black hole. In order
to see what else this does and does not mean, let

be
a particle detector at rest on the surface of the Earth and
let be an exotic, sh ort-lived particle in a cosmic ray
shower. In the dark experiment
m
,mm




m , the fact that the particle is detected by m means that in the
frame of the Earth the particle must have survived longer
than its proper survival time would allow. This provides
direct evidence for relativistic time dilation. But it tells
us nothing directly about Lorentz contraction in the other
frame, that is, in the experiment ,mm
 . If we accept
Lorentz contraction for purposes of inequality (5), then
the difference between

,fmm
 and

,
f
mm

 is
only that the particle ages faster in its own frame but
spends proportionally less time traveling due to the
shorter path. As a result, it is the same age when detected
in each frame.
There is a conceptual reason to consider a more lim-
ited view that lends some credence to the famous twin
paradox of special relativity. If space and time are truly
unified in the 4-tuple we call spacetime, then speed v
through space should be monotone increasing as dimen-
sionless, nonlinear speed through time,
1
22 2
1.vc 





(6)
Under this interpretation of (6) it is not enough to say
that moving clocks run slow but the effect cancels out
because in the frame of the clock the duration of an ex-
periment is shortened proportionally. It prevents asym-
metric aging based on relativistic speed. Of course, this is
precisely what modern cosmology assumes: that the
cosmos and everything in it has aged for a fixed number of
giga-years since the Big Bang. Putting aside speculations
about General Relativity, this would have an unfortunate
consequence for futurists. No matter how powerful our
propulsion methods might be we could not travel into the
future by cruising through space at a relativistic speed,
something Carl Sagan [3] among others believed in. When
we returned to our home world we would find that it had
not aged any more than we had. This is because in our
own reference frame the journey through space did not last
all that long and was shortened just enough to cancel out
the effect of our faster running clocks.
On the other hand if we accept Equation (6) as speed
through time and allow asymmetric aging, then we must
limit Lorentz contraction in the cosmic ray experiment.
This is easily done by staying in the frame of the Earth so
that Lorentz contraction simply alters the shape of the
particle and not the duration of the experiment. For,
suppose in the experiment ,mm

†
m
†
mm
there is a third
identical but colder particle generated in the labo-
ratory. Then will decay at its proper rate while


will be younger and last longer akin to the twin paradox.
As of this writing there is a certain reason that it would
be convenient to constrain Lorentz contraction. If Equa-
tion (6) is speed through time, then a particle moving at
the speed of light would be moving infinitely fast
through time. What better way to convince those who
need to know that nothing could move faster? This would
also allow us to define a rest mass as a particle that has a
finite speed through time, perhaps because of the Higgs
field if there is one. Since it would take an infinite
amount of time to accelerate a rest mass to an infinite
speed through time, dynamic mass indicates that inertia
for space is also inertia for time. The annihilation of an
electron and a positron could then be deemed to jump
rest mass instantaneously to an infinite speed through
time. Recent results from Ogonowski [4] suggest all this
could also have implications fo r gravity.
REFERENCES
[1] A. D. Allen, “The Weatherman Who Fell down a Black
Hole: What He Can Teach us about Reality,” Physics Es-
says, Vol. 25, No. 1, 2012, pp. 76-83.
doi:10.4006/0836-1398-25.1.76
[2] L. Susskind, “The Black Hole War: My Battle With
Stephen Hawking to Make The World Safe for Quantum
Mechanics,” Little Brown and Company, New York,
2008.
[3] C. Sagan, “Contact,” Simon and Schuster, New York,
1985.
[4] P. Ogonowski, “Time Dilation as Field,” Journal of Mo-
dern Physics, Vol. 3, No. 2, 2012, pp. 200-207.
doi:10.4236/jmp.2012.32027