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

,,

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

,

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

Copyright © 2012 SciRes. JMP