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arXiv:physics/0111186

Space-Time Encoding

Mitra, Arindam

Published Nov 26, 2001• 0 citations
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Abstract

It is widely believed that one signal can carry maximum one bit of information, and minimum KTlog2 energy is required to transmit or to erase a bit. Here it is shown four bits of information can be transmitted by one signal in four dimensional space-time. It implies space-time cannot be ignored to determine the minimal energy cost of information processing.

DOI
10.48550/arxiv.physics/0111186

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It is widely believed that one signal can carry maximum one bit of information, and minimum KTlog2 energy is required to transmit or to erase a bit. Here it is shown four bits of information can be transmitted by one signal in four dimensional space-time. It implies space-time cannot be ignored to determine the minimal energy cost of information processing.
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The literature describing the energy needs for a communications channel has been dominated by analyses of linear electromagnetic transmission, often without awareness that this is a special case. This case leads to the conclusion that an amount of energy equal to kTln 2, where kT is the thermal noise per unit bandwidth, is needed to transmit a bit, and more if quantized channels are used with photon energies hnu > kT. Alternative communication methods are proposed to show that there is no unavoidable minimal energy requirement per transmitted bit. These methods are invoked as part of an analysis of ultimate limits and not as practical procedures.
The minimum energy expenditure required in performing basic observations and measurements is analyzed. The energy cost, in ergs per binary unit (bit) of information, is found for three fundamental cases using idealized experimental procedures: 1) the determination of the presence (or absence) of an input signal on an indicating instrument, 2) the measurement of a time interval and 3) the measurement of a distance. The variation of energy cost with the reliability and accuracy of the experiment is determined; it is found that with a suitable procedure the minimum value ofkT \ln2ergs per bit predicted by the Second Law (interpreted so as to include informational entropy) can be approached arbitrarily closely under conditions of small reliability and high accuracy. The present results are compared with those derivable from C. E. Shannon's equation for the capacity of a communication channel.