The Concept of Time | |
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Summary: The concept of time and its correlation to entropy is discussed. We discuss time as a variable specific to the observer and his capability to make a PE1 measurement. What is time? Can we understand it or should we just assume that it exists like everything else? What if nothing ever existed, would time still have a meaning? And what if nothing ever moved and we existed but never grew old, what would time mean then? In first scenario of no existence, it is an indeterminate state as we do not have enough data. An event may or may not exist but the observers can not measure it. In second case the time will exist since the measurements exist, but it will be considered frozen. We have introduced two different types of space, i-space and j-space. What will be the definition of time in i-space? We can not say. But we know a little about j-space and therefore let us try to develop a description of time from the information we have from the measurements. Earlier when we described the progress of information in discrete measurement space, we introduced the concept of the <t=0 _{j}> state. The <t=0_{j}> state represented the instant at
which the measurements began in j-space. Consequently as more and more states were created with the progress of time the entropy increased. Thus
an important assumption is made when the increment in time as measured
by the observer in discrete space is considered equivalent to the
increment in entropy. The observers have their own time-axis based on
their capabilities. Therefore time is a part of the description from
measurements. Then how do we correlate it to the universe as we know
it?
We can consider the universe itself as
a PE1 measurement (in a Qbox if we may) which is yet to be completed.
_{j}'s which we may call PE1_{j1}, PE1_{j2}...............PE1_{jN}
measurements where N is a very large number. The various time-axes for
the lower capability observers may be independent of each other but they are correlated to the time-axis
of the universe as the observer making the PE1_{j}
measurement of the universe has lot more information than the
low-capability observers. If we recall we set the initial conditions in j-space based on Obs_{i} criterion or in other words the observer with maximum information controls the clock in j-space. For Obs_{j} whose status is no different than
the bug making
measurements of the circle, the time may be an infinite entity but for
the observer Obs_{i} whose capability is infinite the time-axis does not exist
as it does not have to apply any measurement force to make a
determination.Thus we can simplify our description of time in terms of the applied measurement force in j-space. If the observer, for example Obs _{i},
does not need to apply a measurement
force, the time-axis does not start. The time in the discrete
measurement space
signifies the presence of an information source of much higher
capability than that of the observer making the measurements. The time
is taken as the characteristics of the discrete nature of the
measurement space. The time has significance for Obs_{j}-pair and Obs_{M} both, however the space-time or (t, x, y, z) description, is specific to the macroscopic observer Obs_{M} only.Before we close out this section we would like to discuss a rather interesting comment made by Kerson Huang and we quote, "The connection between quantum field theory and statistical mechanics rests on the apparent accident that the operator of time translation in quantum mechanics, exp (-itH/ħ ), where H is the Hamiltonian, maps into the density operator of the canonical ensemble exp (-βH), where β is the inverse temperature, if one makes the substitution t → iħβ. That is, time corresponds to a pure-imaginary inverse temperature. The reason for this coincidence remains unknown. This mystery, and the deeper meaning of renormalization, are left for the reader's contemplation." Let us consider a situation in the discrete measurement space or j-space, where only a single PE1 state is created in the beginning, which is the initial <t = 0 _{j}> state represented by the q = 1 value. All the information from the δ_{i}
(source for discrete space) is contained within this state. The
temperature of such state will be measured by the discrete j-space
observer as infinite. As the time progresses, more states are created
and more and more information will be lost due to increasing entropy.
As a consequence the measured temperature will go down. Therefore the
time and
measured temperature will have an inverse
relationship in the description provide by the finite-capability
observers in discrete j-space. We note the for the observer Obs _{i}, there is only one shallow-well state referred to as <S_{i}>
state and hence entropy is zero and the time-axis will not exist. We
can also say that once a PE1 measurement is completed the time-axis is
terminated. Let us take a look at the Obs _{i} criterion. The numbers with indices such as 0_{j}, 1_{j},.......,
etc. represent the "measured" numbers in the discrete measurement space
or j-space. We consider a field being measured in the j-space. Assume the it is characterized by its divergence and curl as,div F = 0 and curl F = 0. (i)
Per Obs
_{i} criterion we replace the zeros on the R.H.S. of the equation by measured numbers 0_{j} as, div F = 0
_{j} and curl F = 0_{j}. (ii)
Therefore the field being measured as source-free and irrotational by Obs _{M} in j-space, will always have a source and a boundary per Obs_{i} who measures 0_{j}
as finite. These two important characteristics, i.e. the source and the
boundary, are not necessarily with in the measurement resolution of the
finite-capability observers of the discrete j-space. As a result what
is being measured by Obs_{M} as zero is actually indeterminate. The field F will be measured as with "content" by Obs_{i}. But Obs_{M}
with its poor resolution may characterize it as non-existent whereas it
is indeterminate at best. Thus if we had a situation expressed
as,
∂b
∂x_{μ}/(iii)_{μ} = 0,
we can apply the Obs
∂b
∂x_{μ}/(iv)_{μ} = 0_{j}, and
it can not be source-free and it will have material characteristics
which may not be visible in the low-energy measurement domain. If b can not be measured by Obs
The limits of an infinite integral i.e. the interval [0, ∞] measured as an infinite interval by the discrete space observer, will be measured as a finite interval [0 Similarly the infinitesimal period used for differentiation in j-space may contain multiple PE1 events measured by Obs Time in the discrete measurement space is either a temporary measure per Obs Added on 30
^{th} April 2014.
Information on
www.ijspace.org is licensed under a Creative Commons
Attribution 4.0 International License.
| What were the "boundary conditions" at the beginning of time? - Stephen Hawking, A Brief History of Time, Bantam Books. "The quantum mechanics does not, strictly speaking "know" the concept of the (discontinuous) "process" since all the temporal changes of the state take place continuously." - W. Pauli, General Principles of Quantum Mechanics, Springer-Verlag. Kerson Huang, Quantum Field Theory From Operators to Path Integrals, WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim,2010. "Sensible mathematics involves neglecting a quantity when it is small - not neglecting it just because it is infinitely great and you do not want it!" - Dirac as quoted in Wikipedia. |