which says that a state
which has an accurate energy (time) has an inaccurate time (energy).
UNCERTAINTY PRINCIPLE AND THE GAMMA RAY LIMIT
James
Constant
grav@coolissues.com
The Large Scale Uncertainty Principle Prevents a Gravitational Theory From Making Absolute Statements of Its Predictions at or Near Its Singularities
Until the statement of the uncertainty principle by Heisenberg in 1927, modern physics held to that idea of a classical determinism, and the rejection of such determinism became a cause for descent between Einstein (as a believer in a classical determinism) and Bohr and the other supporters of the quantum revolution. On the scale of atoms and elementary particles the effect of the uncertainty principle is very important. Because of the uncertainties existing at this level, a picture of the sub-microscopic world emerges as one of statistical probabilities rather than measurable certainties. On the large scale it is still possible to speak of causality in a framework described in terms of space and time; on the atomic scale this is not possible. Such a description would require exact measurements of such quantities as position, momentum, energy, and time, and these quantities cannot be measured exactly because of the uncertainty principle. It does not limit the accuracy of single measurements, of non-simultaneous measurements, or of simultaneous measurements of pairs of quantities other than those specifically restricted by the principle. Even so, its restrictions are sufficient to prevent scientists from being able to make absolute predictions about future states of the system being studied.1
in the uncertainty relation is the time during which the system exists
unperturbed, not the time during which the experimental equipment is
turned on.2
Large Scale Uncertainty Principle
The uncertainty principle is concerned
with measurements of position r, momentum p,
energy E and time t of objects
and their corresponding uncertainties 
.
Generally, all quantities are available within the scope of classical
and quantum mechanics. At extremely long galactic distances
measurements become less deterministic and more uncertain giving rise
to a large scale uncertainty principle.
At any scale, an uncertainty principle is obtained from the universal properties of all waves
in which 
=time uncertainty, 
=frequency
uncertainty, 
=position uncertainty, and 
=momentum
uncertainty.3
Equations (1) represent the uncertainty principle of waves, such as
light from a galaxy, traveling through an instrument. The small scale
uncertainty principle is obtained by combining equations (1) with the
Einstein de-Broglie relations 
and 
to obtain the Heisenberg relations of quantum
mechanics
Unfortunately,
because of a lack of galactic Einstein de-Broglie relations, a large
scale uncertainty principle while easy to conceptualize is difficult to
express as a predictive theory like quantum mechanics. Basically, we
receive light from a galaxy and measure frequency v
with uncertainty
and deduce doppler speed v from the formula4
in which v=received frequency, vo=source frequency, v=speed, c=velocity of light and, we measure flux F with uncertaintyDF and deduce distance r from the formula5
in which F=flux (watts/cm2), L=luminosity (watts), r=ct=distance.
In classical mechanics, the main uncertainties are instrument
uncertainties but in large scale galactic measurements, the main
uncertainties are source uncertainties. In practice, the measurement of
equations (3) and (4) assume that vo=source
frequency and L=luminosity are known constants.
However, vo=source frequency
must change as atomic energy levels change with speed and, as distance
increases L=luminosity becomes more uncertain and
dependent on the logical chain whereby numerical distances are measured.6
With these assumptions, the large scale uncertainty principle is
expressed by equation (1) which states that the simultaneous
measurement of time and frequency and thus of doppler speed and
distance cannot determine the exact values of time t
and frequency v. Instead, the precision of
measurement is inherently limited by equation (1). In practice,
measurements of time t and frequency v
are made non simultaneously which reduces the product 
and makes it more likely to violate the uncertainty principle equation
(1).
In practice, to reduce uncertainties, measurements are made non simultaneously. The measurement of frequency uncertainty at time 1 and distance uncertainty at time 2 are obtained directly from the first of equations (1)
which may, or may not satisfy the
uncertainty principle 
but
certainly must still satisfy
Non simultaneous
measurements, therefore, violate the uncertainty principle especially
when 
and also because speed
and distance change in time. For the best possible accuracy,
simultaneous measurements of frequency and time are
required.
Gamma Ray and Optical Measurement Limits
The highest frequencies and shortest wavelengths known in nature and
practically available for measurements are gamma rays. Typical values
for gamma rays are v=1021/s
and 
=3x10-11cm.
This is the gamma ray measurement limit. In practice measurement
instruments are most easily realized at (and below) optical frequencies
with typical values for optical frequencies v=1015/s
and 
=3x10-5cm.
This is the optical measurement limit. The
gamma ray measurement limit is a theoretical limit and the optical
limit is a practical limit of our means and ability to measure the
frequency and wavelength of galaxies at all distances. That gamma rays
are the highest observed frequencies and shortest observed wavelengths
suggest that their measurement is also a limit on theory confirmation.
At
ultimate distances cosmology theories fall apart because beyond some
distance, roughly at the high end of Hubble's linear law, they violate
the gamma ray and optical measurement limits and the uncertainty
principle. Measurements, required for capturing signals of galaxy
frequency and distance, make predictions increasingly uncertain if not
impossible as distance increases. Since the Planck length is
substantially short of the optical limit 
,
theories of quantum gravity based on the Planck length are in violation
of the optical measurement limit because measurements are impossible.
Even assuming arguendo that the gamma ray limit is not the ultimate measurement limit for a confirmable theory, a theory which fails the uncertainty principle is baseless theory. For sure, a theory cannot make absolute statements from its predictions near its singularities. The Big Bang, Black Hole, Newton's law singularities (infinitely small distance infinite energy), and the Steady State Universe (infinite distance infinite energy) cannot be found consistent with that principle in any meaningful way.
Singularities
are at odds with everything else in physics, quantum mechanics and
cosmology. Consider a theory which has a singularity with infinitely
short 
and infinitely long 
. In
the limit 
and 
which
makes the product 
indeterminate. The theory violates the uncertainty principle at and
near its singularity. As example, from classical theory, the formula
for gravitational frequency shift is
GM/c2>>r M=Mo/(1-(v/c)2)1/2 (9)
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Copyright © 2008 by James Constant
By the same author http://www.coolissues.com/gravitation/sameauthor.htm
(2)
(3)
(4)
(5)
is
reduced by increasing time uncertainty 
, and distance uncertainty
is
reduced by increasing frequency uncertainty 
. The result is
(6)
(7)
(8)
is
dictated by the fact that gamma rays are the highest known frequencies
from space on Earth. If 
, as the case might be as 
,
equation (8) becomes 
,
and
.
However, the measurement of equation (9) on receding
galaxies, where 
is assumed likely,
must satisfy the uncertainty principle
.
In other words, we cannot assume that 
physically
exists, as a singularity in mathematical equation (8), because as 
the 
measurement becomes infinitely small and, to
satisfy equation (10), the 
measurement becomes infinitely large, an impossibility since means and
ability of measurement become impossible. Uncertainty principle
equation (10), therefore, limits what we can say about gravitational
frequency shift equation (8) at or near its singularity. Note that on
Earth, 
r Earth's radius so that the
limit is physical not the uncertainty principle. In galaxies, physical
limits disappear as mass M converts to energy.
becomes
infinitely small and 
becomes infinitely great so that, since 
is a fixed number, at some point
(11)
(12)
at
such small distances are impossible. The theory of equation (8) is
confirmable on Earth and is credible on receding galaxies but, absent a
physical limit, fails at its mathematical singularity as 
.
is
satisfied near the singularity. Accordingly, a credible theory deduced
from measurements on Earth, cannot make absolute statements from its
predictions at or near its singularities.