Quantum mechanics and the measurement of temperature inside living cells

YOUNGWOOD, Pa. - Nov. 3, 2014 - PRLog -- .
Background
Recently, Physics Today [1] reported N-V defects in NDs allow resolution of temperatures from 300 to 650 K at mK accuracy. N-V stands for nitrogen-vacancy and ND for rnanodiamond. But the experiments [2] were based on bulk mm-scale diamond crystals – not NDs. The N-V spin-levels are shown split by the temperature T dependent ZFS parameter D thought caused by thermally induced lattice strains related to temperature by dD/dT = −2π × 77 kHz K⁻¹. ZFS stands for zero-field splitting.  Hence, N-V spin level thermometry in mm-scale diamond crystals is indeed feasible in temperature measurements at the macroscale, but too large to measure temperatures inside living cells having dimensions of a few 10's of microns. Instead, NDs of 100 nm size are mplanted in living cells [3] to measure cell temperatures.
Problem
Unlike the bulk mm-scale diamond, QM denies the atoms in NDs the heat capacity to allow temperature changes to occur thereby refuting the claim [3] that ND temperature can be measured from thermal strains found [2] in mm-scale diamond samples. QM stands for quantum mechanics. Thermal strains in NDs are therefore not the same as in the mm-scale crystals. Simply put, QM makes the thermal strains in mm-scale crystals for NDs in the thermometry of living cells highly questionable.
Proposal
QED induced EM radiation is proposed as the mechanism by which the local thermal energy of the living cell is conserved in NDs without temperature changes. QED stands for quantum electrodynamics and EM for electromagnetic. QED induced radiation is a consequence of QM that denies the atoms in NDs under TIR confinement to have the heat capacity to allow changes in temperature. TIR stands for total internal reflection. See applications of QED induced EM radiation at http://www.nanoqed.org

Theory and Discussion
Classical heat transfer of NDs shows uniform temperatures throughout that almost spontaneously follow the local cell temperature. QM differs. Since the ND temperatures cannot change by QM, the local thermal energy acquired from the cell may only be conserved by QED creating EM radiation in the ND having Planck energy E = hf, where h and f are Planck’s constant and the TIR frequency of the ND. Since NDs have high surface to volume ratios, almost all of the local thermal cell energy acquired by the ND directly excites its TIR mode. In effect, TIR confines the acquired cell energy to the ND surface having a wavelength given by its circumference, i.e., the TIR frequency f = c / λ, where c is the velocity of light and λ = π d n. Here, n is the refractive index of the ND.

What this means is QM requires the acquired cell energy to be conserved without an increase in ND temperature by the creation of EM radiation at the frequency f of the ND that is then emitted into the cell surroundings.

But if so, how then may the ND infer local temperature in the living cell?

By QM, local cell temperatures are inferred by N-V spin-flips from thermal strains induced in the ND as only the temperature of the surface changes. Atoms in the interior of the ND do not increase in temperature, but the surface atoms having direct contact with the temperature of the living cell do indeed follow the cell temperature. Unlike uniform expansion predicted by classical physics, the ND surface alone undergoes expansion that strains the interior N-V centers as shown in the thumbnail. For cell temperature increase ΔT above ambient To, the ND diameter increases by Δd = α d ΔT, where α is the coefficient of thermal expansion of the ND. Hence, the ND is placed in hydrostatic tension. Diamond noted for sensitivity to strain is therefore correlated by QM to the local cell temperature, the correlation of which cannot be deduced from the uniform ND temperatures predicted by classical physics. .

Conclusions
Classical physics by assuming the atoms in NDs have heat capacity that predicts uniform ND temperatures equal to the local cell temperature cannot induce the thermal strain at interior N-V centers required by QM.

Conversely, QM by negating the heat capacity of the atoms in NDs precludes temperatures within the ND from following local cell temperature. But QM by confining temperature changes to the ND surface induces strain at interior N-V centers to allow correlation of optical transitions with local cell temperature.

The ND measurement of temperatures in living cells based on the spin-flip optical transitions found in mm-scale diamond crystals requires further study.

Although QM allows NDs to measure cell temperatures, the toxicity of the EM radiation at UV frequencies emitted from the NDs to DNA within the cell should be considered in cell temperature measurements.

References
[1] L. Childress, et al., “Atom-like crystal defects,” Physics Today, Oct 2014 38-43.
[2] V. Acosta, et al.,  “Temperature dependence of the nitrogen-vacancy magnetic resonance in diamond,” Phys. Rev. Lett.104, 070801 (2010)
[3] G. Kuczko, et al., “Nanometre-scale thermometry in a living cell,” Nature, 500, 54 (2013)