# Files Has Mass

Since IBM’s pattern of the first magnetic onerous disk power (RAMAC) in 1956, digital recordsdata storage technologies catch radically transformed our celebrated society. In binary code, digital recordsdata is kept as logical 1s and 0s, identified as bits. Bits of recordsdata shall be kept in any field topic capable of displaying two distinctive and switchable bodily states (magnetic, electrical, optical, and resistive) by allocating a logical 0 or 1 to every bodily state. Digital recordsdata grew to develop into so entrenched in all ingredients of our society that the recent growth in recordsdata manufacturing appears to be like to be unstoppable. Day after day on Earth we generate 500 × 10^{6} tweets, 294 × 10^{9} emails, 4 × 10^{6} gigabytes of Facebook recordsdata, 65 × 10^{9} WhatsApp messages, and 720 000 h of original jabber added day-to-day on YouTube.^{1}1. M. M. Vopson, “The sector’s recordsdata explained: How mighty we’re producing and where it’s all kept,” World Economic Dialogue board, Might 2021, on hand at https://www.weforum.org/agenda/2021/05/world-recordsdata-produced-kept-global-gb-tb-zb/. In 2018, the total quantity of recordsdata created, captured, copied, and consumed in the sector became 33 zettabytes (ZB) or the an identical of 264 × 10^{21} bits,^{2}2. Gape https://www.idc.com/ for estimates of the annual digital recordsdata manufacturing in the sector. where 1 ZB is 8 × 10^{21} bits. This grew to 59 ZB in 2020 and is predicted to reach a 175 ZB by 2025.^{1}1. M. M. Vopson, “The sector’s recordsdata explained: How mighty we’re producing and where it’s all kept,” World Economic Dialogue board, Might 2021, on hand at https://www.weforum.org/agenda/2021/05/world-recordsdata-produced-kept-global-gb-tb-zb/. The remarkable quantity of digital recordsdata being created yearly at planetary scale precipitated a recent explore, wherein it has been estimated that at essentially the most modern digital recordsdata manufacturing growth payment, ∼350 years from now we can fabricate extra digital bits than all atoms on Earth.^{3}3. M. M. Vopson, “The walk wager wretchedness,” AIP Adv. **10**, 085014 (2020). https://doi.org/10.1063/5.0019941 This theoretically predicted phenomenon became termed the walk wager wretchedness.^{3}3. M. M. Vopson, “The walk wager wretchedness,” AIP Adv. **10**, 085014 (2020). https://doi.org/10.1063/5.0019941

A attention-grabbing stutter is then to estimate the conventional limit of digital recordsdata storage as dictated by the bodily realities of our universe and its governing authorized pointers. In other words, restricting the estimate to field topic forms of recordsdata storage, the smallest dimension of a digital bit would must be the smallest bit of topic that’s stable and can exist on its catch. It has been concluded that the smallest theoretical dimension of digital bits would must be the elementary particles, as they’re the smallest identified building blocks of topic in the universe. Obviously, that is a theoretical limit assuming that, at some distant future, recordsdata storage technologies shall be developed to enable write/read of digital recordsdata to/from elementary particles. On the opposite hand, that is terribly instructive as the recent estimate gave an greater limit of ∼6 × 10^{80} bits to the quantity of digital recordsdata that shall be kept in the total universe.^{4}4. M. M. Vopson, “Estimation of the walk wager contained in the considered topic of the universe,” AIP Adv. **11**(10), 105317 (2021). https://doi.org/10.1063/5.0064475 The explore became based totally on Shannon’s recordsdata belief, assuming the most sensible seemingly compression mechanism, which yielded a tag of 1.288 bits of recordsdata kept per electron (e^{−}), proton (p^{+}), and neutron (n^{0}). When quarks were taken into chronicle, the maximum quantity of recordsdata that shall be kept per elementary particle grew to develop into 1.509 bits.^{4}4. M. M. Vopson, “Estimation of the walk wager contained in the considered topic of the universe,” AIP Adv. **11**(10), 105317 (2021). https://doi.org/10.1063/5.0064475 Hence, the estimate of the walk wager jabber of the observable universe shall be interpreted as the maximum quantity of recordsdata that shall be kept digitally if the universe became an unlimited recordsdata storage instrument. Nonetheless, the author of the explore argued that that is no longer only correct a theoretical greater limit of recordsdata storage ability, nonetheless, truly, the elementary particles already retailer recordsdata about themselves. It has been proposed that this recordsdata shall be considered as a particle DNA, or a topic DNA, and it physically represents the distinguishable degrees of freedom of every and every particle or pure quantum states.

In 1961, Landauer first proposed the root that a digital recordsdata bit is bodily and it has a neatly-outlined energy associated with it.^{5,6}5. R. Landauer, “Irreversibility and warmth generation in the computing process,” IBM J. Res. Dev. **5**(3), 183–191 (1961). https://doi.org/10.1147/rd.53.01836. R. Landauer, “The bodily nature of recordsdata,” Phys. Lett. A **217**(4–5), 188–193 (1996). https://doi.org/10.1016/0375-9601(96)00453-7 This is identified as the Landauer notion and it became currently confirmed experimentally.^{7–10}7. J. Hong, B. Lambson, S. Dhuey, and J. Bokor, “Experimental check of Landauer’s notion in single-bit operations on nanomagnetic reminiscence bits,” Sci. Adv. **2**(3), e1501492 (2016). https://doi.org/10.1126/sciadv.15014928. R. Gaudenzi, E. Burzurí, S. Maegawa, H. van der Zant, and F. Luis, “Quantum Landauer erasure with a molecular nanomagnet,” Nat. Phys. **14**, 565–568 (2018). https://doi.org/10.1038/s41567-018-0070-79. A. Bérut, A. Arakelyan, A. Petrosyan, S. Ciliberto, R. Dillenschneider, and E. Lutz, “Experimental verification of Landauer’s notion linking recordsdata and thermodynamics,” Nature **483**, 187–189 (2012). https://doi.org/10.1038/nature1087210. Y. Jun, M. Gavrilov, and J. Bechhoefer, “Excessive-precision check of Landauer’s notion in a feedback entice,” Phys. Rev. Lett. **113**(19), 190601 (2014). https://doi.org/10.1103/physrevlett.113.190601 In a definite explore, the utilization of Shannon’s recordsdata belief and thermodynamic concerns, the Landauer notion has been extended to the Mass–Energy–Files (M/E/I) equivalence notion.^{11}11. M. M. Vopson, “The mass-energy-recordsdata equivalence notion,” AIP Adv. **9**, 095206 (2019). https://doi.org/10.1063/1.5123794 The M/E/I notion states that recordsdata is a influence of topic, it’s a ways bodily, and it must be identified by a particular mass per bit while it stores recordsdata or by an energy dissipation following the irreversible recordsdata erasure operation, as dictated by the Landauer notion.^{5,6}5. R. Landauer, “Irreversibility and warmth generation in the computing process,” IBM J. Res. Dev. **5**(3), 183–191 (1961). https://doi.org/10.1147/rd.53.01836. R. Landauer, “The bodily nature of recordsdata,” Phys. Lett. A **217**(4–5), 188–193 (1996). https://doi.org/10.1016/0375-9601(96)00453-7 The M/E/I notion has been formulated while strictly discussing digital states of recordsdata. Nonetheless, because Shannon’s recordsdata belief is applicable to all forms of recordsdata systems and it’s no longer restricted supreme to digital states, the author extrapolated the applicability of the M/E/I notion to all forms of recordsdata, proposing that recordsdata is the fifth state of topic.^{11,12}11. M. M. Vopson, “The mass-energy-recordsdata equivalence notion,” AIP Adv. **9**, 095206 (2019). https://doi.org/10.1063/1.512379412. M. M. Vopson, The walk wager jabber of the universe and the implications for the missing Darkish Topic, June 2019. These solutions, regarded as as the walk wager conjectures, are truly transformational because, with out violating any authorized pointers of physics, they offer imaginable explanations to a collection of unsolved complications in physics, as neatly as complementing and expanding our thought of all branches of physics and the universe and its governing authorized pointers. Hence, checking out experimentally these recordsdata conjectures is of coarse importance.

The first proposed experiment to envision the M/E/I equivalence notion involved the measurement of the mass trade in 1 Tb recordsdata storage instrument earlier than and after the digital recordsdata is completely erased.^{11}11. M. M. Vopson, “The mass-energy-recordsdata equivalence notion,” AIP Adv. **9**, 095206 (2019). https://doi.org/10.1063/1.5123794 At room temperature, the calculated mass trade for this experiment is in the give an explanation for of ∼10^{−25} kg, making the measurement unachievable with our most modern technologies.

The sizzling prediction of the walk wager mass jabber per elementary particle lets in us to lengthen this experimental belief beyond digital recordsdata storage to a easy field topic physique of mass m. Since the mass of recordsdata is temperature dependent,^{11}11. M. M. Vopson, “The mass-energy-recordsdata equivalence notion,” AIP Adv. **9**, 095206 (2019). https://doi.org/10.1063/1.5123794 on this experiment, one might perchance perchance simply verify the walk wager conjectures by watching the end of the temperature trade on the walk wager mass jabber of elementary particles contained within a bodily physique of a identified mass. Allow us to have confidence in solutions a random mono-atomic stable of mass m made up of an identical atoms of atomic mass weight A, every atom containing *N*_{e−} electrons, *N*_{p+} protons, and *N*_{n0} neutrons. If every elementary particle contains *I* bits of recordsdata, then a mass *m* would devour *N*_{b} bits of recordsdata,

$${N}_{b}=I\cdot \frac{m{N}_{A}}{A}\left({\mathrm{N}}_{{e}^{-}}+\mathrm{3}\left({\mathrm{N}}_{{p}^{+}}+{\mathrm{N}}_{{n}_{0}}\right)\right),$$ | (1) |

where N_{A} is Avogadro’s quantity, N_{A} = 6.022 × 10^{23} mol^{−1}, and the element of three accounts for the fact that every proton and every neutron are made up of three quarks.

In response to the M/E/I notion,^{11}11. M. M. Vopson, “The mass-energy-recordsdata equivalence notion,” AIP Adv. **9**, 095206 (2019). https://doi.org/10.1063/1.5123794 for a temperature trade *ΔT*, the weird and wonderful expression of the walk wager mass trade *Δm*^{inf} of a physique of mass m is

$$\mathrm{\Delta}{m}^{\mathrm{inf}}=I\cdot \frac{m{N}_{A}{\mathrm{okay}}_{b}\mathrm{\Delta}T\mathrm{ln}\left(2\right)}{A{c}^{2}}\left({\mathrm{N}}_{{e}^{-}}+\mathrm{3}\left({\mathrm{N}}_{{p}^{+}}+{\mathrm{N}}_{{n}_{0}}\right)\right),$$ | (2) |

where okay_{b} = 1.380 64 × 10^{−23} J/K is the Boltzmann constant and c is the fling of light.

Relation (2) predicts a temperature dependence of the walk wager mass trade.

Hence, one might perchance perchance safe an experiment to measure the mass trade inflicted by a temperature trade to the physique mass m. For the explanation that bodily mass of the subject topic below check would now not trade with the temperature (assuming stable materials are thermally and chemically stable), the detected mass trade can supreme be linked to the walk wager mass trade, providing an instantaneous confirmation of the proposed recordsdata conjectures.

Allow us to recall a metal physique of *m* = 1 kg copper (Cu), with every Cu atom containing *N*_{e−} = 29 electrons, *N*_{p+} = 29 protons, and *N*_{n0} = 34.5 neutrons. The fractional tag of *N*_{n0} accounts for the existence of the two Cu isotopes containing 34 neutrons (70%) and 36 neutrons (30%), respectively. This proportion of isotopes presents a relative atomic mass quantity *A* = 63.55 g. If every subatomic elementary particle contains *I* = 1.509 bits of recordsdata as predicted beforehand,^{4}4. M. M. Vopson, “Estimation of the walk wager contained in the considered topic of the universe,” AIP Adv. **11**(10), 105317 (2021). https://doi.org/10.1063/5.0064475 then the utilization of (1) we design the total collection of bits of recordsdata kept in a kg of Cu as *N*_{b} = 29.8 × 10^{26} bits.

For a temperature trade ΔT = 100 K of the Cu sample (cooling or heating), the utilization of (2) we design an absolute tag of recordsdata mass trade of *Δm*^{inf} = 3.33 × 10^{−11} kg. This tag a great deal improves the an crucial measurement decision relative to the preliminary proposed experiment (*Δm*^{inf} ∼ 10^{−25} kg), nonetheless an appropriate measurement of ∼10^{−11} kg is soundless extraordinarily engaging.

Therefore, on this paper, we combine the estimates of the walk wager jabber per elementary particle, with the M/E/I equivalence notion, to formulate a brand original experimental protocol just correct to envision the walk wager conjectures.

In give an explanation for to envision experimentally the walk wager conjectures described in the introduction, enable us to first have confidence in solutions an elementary particle. For comfort, we can have confidence in solutions an electron. We also recall that the electron stores

${I}_{{e}^{-}}$bits of recordsdata in itself about itself. In response to M/E/I, the electron’s rest mass is the sum of its bodily mass and the walk wager mass,

Though here we are inspecting an electron, this conjecture applies to any elementary particle that’s stable and has a non-zero rest mass. The mass of a dinky at temperature T is given by^{11,13–16}11. M. M. Vopson, “The mass-energy-recordsdata equivalence notion,” AIP Adv. **9**, 095206 (2019). https://doi.org/10.1063/1.512379413. L. B. Kish, “Gravitational mass of recordsdata?,” Fluctuation Noise Lett. **07**, C51–C68 (2007). https://doi.org/10.1142/s021947750700414814. L. Herrera, “The mass of a dinky of recordsdata and the Brillouin’s notion,” Fluctuation Noise Lett. **13**(01), 1450002 (2014). https://doi.org/10.1142/s021947751450002315. L. B. Kish and C. G. Granqvist, “Does recordsdata catch mass?,” Proc. IEEE **101**(9), 1895–1899 (2013). https://doi.org/10.1109/jproc.2013.227372016. E. Bormashenko, “The Landauer notion: Re–formula of the second thermodynamics law or a step to monumental unification,” Entropy **21**, 918 (2019). https://doi.org/10.3390/e21100918

Hence, the mass of the electron becomes

$${m}_{{e}^{-}}={{m}_{{e}^{-}}}^{phys}+\frac{{I}_{{e}^{-}}{\mathrm{okay}}_{b}T\mathrm{ln}\left(2\right)}{{c}^{2}}.$$ | (5) |

A lickety-split numerical estimate indicates that the walk wager mass of the electron is very dinky so that

$$\frac{{m}_{{e}^{-}}}{{{m}_{{e}^{-}}}^{\mathrm{inf}}}=\frac{9.11\times {10}^{-31}}{{I}_{{e}^{-}}\cdot 3.19\times {10}^{-38}}\approx \frac{2.85}{{I}_{{e}^{-}}}\times 1{0}^{7}.$$ | (6) |

Taking

${I}_{{e}^{-}}=1.288$ bits, it outcomes that the remaining mass of the electron is ∼22 × 10^{6} cases better than its recordsdata mass, indicating that, certainly, the mass of the electron is neatly approximated by its bodily rest mass, while its recordsdata mass is negligible. Again, this makes the experimental checking out no longer doable by strategy of snort mass trade measurements.

Here, we suggest an experiment, which involves the measurement of the walk wager mass no longer straight, by strategy of an recordsdata erasure process. In response to the M/E/I and Landauer solutions, the walk wager mass must be dissipated as energy upon erasure.

A. How can one erase the walk wager contained within an electron?

In give an explanation for to completely erase the walk wager within any elementary particle, one wants to resolve away the particle from existence. This might perchance be done by strategy of a topic–antimatter annihilation reaction. Happily, in the case of an electron, there is a mechanically accessible process identified as electron–positron annihilation, where the positron (e^{+}) is the antiparticle of the electron (e^{−}), and a collision between an electron and a positron can lead to their mutual annihilation. In the annihilation process, the remaining mass energies and the kinetic energies of the electron and positron are converted into radiation.

Depending on the total run of the positron–electron pair, the annihilation process can resolve anguish by strategy of two imaginable pathways for the emitted radiation. When the total run is one, the annihilation produces three gamma photons. When the positron–electron pair has a total run of zero, the annihilation process produces two gamma photons.

This latter process is an ultimate candidate to explore the walk wager jabber of the input particles by inspecting what might perchance perchance also come up from the erasure of the walk wager upon their annihilation. The total energy of the colliding electron–positron pair is

where

${E}_{{e}^{-}}={m}_{{e}^{-}}{c}^{2}$and

${E}_{{e}^{+}}={m}_{{e}^{+}}{c}^{2}$are the remaining mass energies of the electron and positron, respectively.

${K}_{{e}^{-}}={m}_{{e}^{-}}{{v}_{{e}^{-}}}^{2}/2$and

${K}_{{e}^{+}}={m}_{{e}^{+}}{{v}_{{e}^{+}}}^{2}/2$are the kinetic energies of the colliding particles transferring with velocities

${v}_{{e}^{-}}$and

${v}_{{e}^{+}}$, respectively. Since c ≫

${v}_{{e}^{-}}$and

${v}_{{e}^{+}}$, the kinetic energies are negligible. Performing the experiment with a beam of slack positrons and static electrons in the goal can with out downside meet this situation. The electron–positron pair must conserve the total energy, the momentum, and the angular momentum after the annihilation process. The energy conservation ensures that two 511 keV gamma photons are made from the conversion of their rest mass energies. The angular momentum conservation is robotically fulfilled in the two-photon annihilation process, where one run is up and the opposite run is down. The momentum conservation imposes the placement that these two gamma photons trip in the directions 180° to 1 one more. Response (8) and Fig. 1(a) expose the weird and wonderful electron–positron annihilation process that produces two gamma photons,

Nonetheless, relation (7) would now not consist of any recordsdata energy which shall be contained in the particles themselves. Accounting for the walk wager jabber and neglecting the kinetic energies, the total energy is

$${E}_{tot}={m}_{{e}^{-}}{c}^{2}+{m}_{{e}^{+}}{c}^{2}+{I}_{{e}^{-}}{\mathrm{okay}}_{b}T\mathrm{ln}\left(2\right)+{I}_{{e}^{+}}{\mathrm{okay}}_{b}T\mathrm{ln}\left(2\right),$$ | (9) |

where

${T}_{{e}^{-}}={T}_{{e}^{+}}=T$since the positrons will reach thermal equilibrium with the metal sheet containing the goal electrons, so every particle can catch the an identical temperature at the time of collision.

${I}_{{e}^{-}}$and

${I}_{{e}^{+}}$are the quantity of recordsdata bits kept by the electron and the positron, respectively.

The rest a range of the electron and positron as neatly as their recordsdata contents must be equal to 1 one more. The energy conservation ensures again that two gamma photons of about 511 keV are produced. Nonetheless, if particles retailer recordsdata, upon annihilation (i.e., erasure), the walk wager jabber must also be conserved by producing two recordsdata energy photons ν^{+} and ν^{−}.

The momentum conservation imposes the placement that these two extra photons also trip in the reverse course to 1 one more. Response (10) and Fig. 1(b) expose the electron–positron annihilation process that involves the walk wager erasure,

$${m}_{{e}^{-}}{c}^{2}+{m}_{{e}^{+}}{c}^{2}+{I}_{{e}^{-}}{\mathrm{okay}}_{b}T\mathrm{ln}\left(2\right)+{I}_{{e}^{+}}{\mathrm{okay}}_{b}T\mathrm{ln}\left(2\right)=\gamma +\gamma +{\nu}^{+}+{\nu}^{-}.$$ | (10) |

The successful detection of the walk wager energy photons ν^{+} and ν^{−} will verify each and every recordsdata conjectures: (i) the mass–energy–recordsdata equivalence notion and (ii) the bit recordsdata jabber of elementary particles implying the existence of recordsdata as the fifth state of topic.

The walk wager energy photons catch very particular traits that enable their identification with a high diploma of self belief. First, they must emerge simultaneously with the 511 keV gamma photons. This implies that synchronized detection of the gamma and the walk wager energy photons would offer a strong indication of their starting build.

2d, the walk wager energy photons catch very particular wavelengths, which are no longer supreme proportional to the quantity of recordsdata bits kept by the electron and the positron nonetheless also proportional to their temperature.

No longer too long prior to now, the walk wager jabber per elementary particle has been estimated to be 1.509 bits.^{4}4. M. M. Vopson, “Estimation of the walk wager contained in the considered topic of the universe,” AIP Adv. **11**(10), 105317 (2021). https://doi.org/10.1063/5.0064475 Though the estimation accounted just correct for stable elementary particles with the exception of anti-particles, we can recall that the walk wager jabber of the positron is equal to that of the electron, so

bits, and upon erasure, the resulting photons even catch the an identical energies/frequencies ν^{+} = ν^{−} = ν.

In response to the M/E/I equivalence notion, the wavelength of the walk wager energy photons is

where h = 6.62 × 10^{−34} m^{2} kg/s is Planck’s constant. Figure 2 reveals the predicted wavelength of the walk wager energy photons as a characteristic of the temperature, which extends from the mid-infrared (MIR) to a ways-infrared (FIR) spectral areas. For the explanation that recordsdata jabber of 1.509 bits is a theoretical prediction no longer confirmed but, it’s a ways instructive to lengthen the imaginable vary of the bit recordsdata jabber per particle.

Hence, in Fig. 2, we also expose the predicted values for two extra recordsdata contents of 1 and 3 bits per particle, respectively. The recordsdata expose that, for 1.509 bits of recordsdata jabber, the expected recordsdata energy photon wavelength ranges from 3 to 180 *µ*m, counting on the temperature of the experiment. At room temperature, recordsdata energy photons of ∼50 *µ*m wavelength are predicted to emerge. This tag adjustments proportionally to the bit recordsdata jabber, so from 1 to three bits per elementary particle, the wavelength at room temperature ranges broadly from 25 to 75 *µ*m. Incandescent these predicted values is a will have to catch for the experimental safe and the different of IR detectors.

The experiment must be designed to design obvious that no longer supreme the two 511 keV gamma photons are detected nonetheless also the extra two IR photons, ν^{+} and ν^{−}. The detection of the IR photons items some extra challenges because they’re with out downside attenuated all the map by the sample.

For our experiment, we suggest to employ positrons generated by a ^{22}Na radioactive source. Figure 3 reveals the decay design of ^{22}Na. This isotope is terribly helpful as a consequence of its comparatively low-payment, long half-existence of 2.6 years, and high positron yield. Positrons emitted by strategy of nuclear radioactive decay of ^{22}Na sources catch an energy distribution vary from 0 to 545 keV, and 90.4% of the time they decay in step with the following reaction:

$${}_{11}{}^{22}\mathrm{N}\mathrm{a}\to {}_{10}{}^{22}\mathrm{N}\mathrm{e}+{e}^{+}+\nu +\gamma ,$$ | (12) |

where e^{+} is the positron, ν is a neutrino, and γ is a 1274 keV gamma photon.

Unfortunately, the γ-decay reaction of ^{22}Na generates high-energy positrons (also identified as like a flash positrons), and they also’ve a monumental penetration vary into the sample field topic. Therefore, the sample field topic must be thick adequate to soak up the positrons, nonetheless thin adequate to design obvious that it would now not attenuate the 511 keV gamma rays which shall be created in the electron–positron annihilation all the map by the sample. Most importantly, we have to design obvious that the two IR photons ν^{+} and ν^{−} produced at the erasure of the walk wager jabber are also no longer completely attenuated all the map by the sample field topic. In give an explanation for to meet these requirements, one option is to employ a metal thin layer goal field topic bombarded with low energy positrons (also identified as slack positrons). Slack positrons catch a increased chance of electron annihilation, as they diffuse by the goal field topic. When like a flash/high-energy positrons enter a field topic, they lose energy by interacting with the subject topic, slowing all the kind down to thermal energies. This thermalization process takes supreme about a picoseconds, while the positron imply lifetime in metals ranges from 100 to 450 ps.^{17}17. I. K. MacKenzie, *Experimental Solutions of Annihilation Time and Energy Spectrometry, Positron Solid-Explain Physics* (Società Italiana di Fisica, Bologna, Italy, LXXXIII Corso, 1983), pp. 196–264. Immediate-to-slack positron moderation is easy to attain the utilization of a moderation step made of an very just correct field topic that has a detrimental work-characteristic for positrons.^{18,19}18. P. G. Coleman, in *Positron Beams and Their Purposes* (World Scientific, Singapore, 2000), Chap. 2, pp. 11–40.19. D. G. Costello, D. E. Groce, D. F. Herring, and J. Wm. McGowan, “Evidence for the detrimental work characteristic associated with positrons in gold,” Phys. Rev. B **5**(4), 1433–1436 (1972). https://doi.org/10.1103/physrevb.5.1433

Immediate positrons penetrate the moderation step where some will emerge on the opposite facet as like a flash positrons nonetheless with decreased energies, some will annihilate all the map by the moderator, and a few will thermalize and diffuse to reappear at the bottom of the moderation step where they’re spontaneously emitted as mono-filled with life slack positrons of kinetic energy discontinuance to the work characteristic of the moderation field topic (about a eV). The short-to-slack positron conversion effectivity is always ∼10^{−4},^{20}20. A. Vehanen and J. Mäkinen, “Skinny movies for slack positron generation,” Appl. Phys. A **36**, 97–101 (1985). https://doi.org/10.1007/bf00620615 and some of the appropriate moderation materials is the tungsten single-crystal.^{21–24}21. P. J. Schultz and K. G. Lynn, “Interaction of positron beams with surfaces, thin movies, and interfaces,” Rev. Mod. Phys. **60**(3), 701–779 (1988). https://doi.org/10.1103/revmodphys.60.70122. D. M. Chen, K. G. Lynn, R. Pareja, and B. Nielsen, “Dimension of positron reemission from thin single-crystal W(100) movies,” Phys. Rev. B **31**(7), 4123–4130 (1985). https://doi.org/10.1103/physrevb.31.412323. A. Goodyear, A. P. Knights, and P. G. Coleman, “Energy spectroscopy of positrons re-emitted from polycrystalline tungsten,” J. Phys.: Condens. Topic **6**(45), 9601–9611 (1994). https://doi.org/10.1088/0953-8984/6/45/01024. C. Hugenschmidt, B. Straßer, and K. Schreckenbach, “Investigation of positron work characteristic and moderation effectivity of Ni, Ta, Pt and W(100),” Appl. Surf. Sci. **194**(1–4), 283–286 (2002). https://doi.org/10.1016/s0169-4332(02)00135-6

We recommend to duvet the ^{22}Na source with a thin (1–2 *µ*m) single-crystal tungsten foil in (100) orientation,^{22}22. D. M. Chen, K. G. Lynn, R. Pareja, and B. Nielsen, “Dimension of positron reemission from thin single-crystal W(100) movies,” Phys. Rev. B **31**(7), 4123–4130 (1985). https://doi.org/10.1103/physrevb.31.4123 which has a detrimental work-characteristic of around 3 eV.

Alternatively, a polycrystalline thin film tungsten moderator^{23}23. A. Goodyear, A. P. Knights, and P. G. Coleman, “Energy spectroscopy of positrons re-emitted from polycrystalline tungsten,” J. Phys.: Condens. Topic **6**(45), 9601–9611 (1994). https://doi.org/10.1088/0953-8984/6/45/010 shall be lined straight onto the ^{22}Na positron source by strategy of an very just correct thin film deposition process. The low energy positrons leaving the moderator will annihilate in the metal goal field topic. The vary of the positrons in the goal dictates the different of the steel. For example, 545 keV positrons penetrating an Al goal catch a imply lifetime of 166 ps and a range of 0.954 mm, while for an Au goal, the imply lifetime is 118 ps and the vary is 0.194 mm,^{25}25. M. J. Berger, J. S. Coursey, M. A. Zucker, and J. Chang, “Stopping-energy and vary tables for electrons, protons, and helium ions,” NIST Bodily Measurements Laboratory, on hand at www.nist.gov/pml/recordsdata/star/index.cfm. which is quite five cases shorter vary than that of Al. To design obvious a high chance of positron–electron annihilation, we suggest to employ a metal Al thin film as the goal field topic. The thickness of the Al thin film must be in the vary of some nm so the thermalized positrons can endure a ground annihilation in the Al field topic and a monumental part of the resulting photons (gamma and IR) can reach the detectors.

Figure 4 reveals a schematic plan of the proposed experiment (thickness of the layers no longer at scale).

It is extreme that the W moderator and the Al thin film sample completely encapsulate the ^{22}Na source. The experimental safe requires one end of the ^{22}Na source to keep up a correspondence with a temperature controller, while the opposite ground is feeble for the positron beam.

Gamma and IR detectors are placed in the discontinuance proximity of the Al thin film. The temperature controller (cooling and heating) is required since the belief predicts that the IR photons detected at recordsdata erasure expose a linear temperature scaling of their energy. Assuming the successful detection of the IR recordsdata energy photons, the ability to alter the temperature of the sample will act as a double confirmation of the experiment by detecting the wavelength trade in the IR photons with the temperature. This experimental geometry is the most sensible seemingly course to controlling the temperature of the emitter (positrons) and sample (electrons), simultaneously. Nonetheless, if the infrared photons are completely absorbed in the Al sample, then a definite, extra complex experimental geometry shall be designed, wherein the Al film and the W moderator are aloof from the source.

Two recordsdata conjectures had been currently proposed: (a) the mass–energy–recordsdata equivalence notion,^{11}11. M. M. Vopson, “The mass-energy-recordsdata equivalence notion,” AIP Adv. **9**, 095206 (2019). https://doi.org/10.1063/1.5123794 bringing up that recordsdata transcends into mass or energy counting on its bodily state and (b) the existence of an intrinsic recordsdata underpinning the conventional traits of elementary particles in the universe, implying that stable, non-zero rest mass elementary particles retailer a mounted and quantifiable tag of details about themselves.^{4}4. M. M. Vopson, “Estimation of the walk wager contained in the considered topic of the universe,” AIP Adv. **11**(10), 105317 (2021). https://doi.org/10.1063/5.0064475 The two conjectures also imply that the walk wager is a influence of topic, referred to as the fifth state of topic or the fifth element.

These conjectures had been diminutive supreme to theoretical frameworks, nonetheless the acceptance of their validity can supreme approach from a stable experimental confirmation.

In this text, we suggest an experimental protocol designed to substantiate these recordsdata conjectures by validating the existence of the walk wager jabber of elementary particles and by detecting its exact tag. The proposed protocol makes the belief that the walk wager jabber is conserved all by particle–antiparticle annihilation by strategy of the manufacturing of two IR photons. The employ of the predicted tag of 1.509 bits of recordsdata per elementary particle at room temperature, we request a positron–electron annihilation to influence two IR photons of ∼50 *µ*m wavelength resulting from recordsdata erasure, which must be detected simultaneously with the two 511 keV gamma photons emerging resulting from the energy conversion of the remaining a range of the annihilating particles.

The experiment is extremely achievable the utilization of most modern technologies and it presents about a sustain a watch on tools to design obvious that the detection is certainly resulting from recordsdata erasure. The first sustain a watch on instrument is the fact that the wavelength of the walk wager energy IR photons must shift with the temperature of the sample. By performing the experiments at varied temperatures, the detection of the wavelength shift of the IR photons shall be an closing confirmation of this hypothesis.

It is extreme to acknowledge that we design a strong assumption that the switch of the walk wager mass jabber of the annihilating particles takes anguish by strategy of conversion into IR photons. Nonetheless, other mechanisms of conversion are imaginable, at the side of the gamma photons turning into carriers of this excess recordsdata energy. Hence, even when the walk wager conjectures are neatly matched, the proposed experiment is, resulting from this fact, no longer completely assured to be triumphant. Nonetheless, the implications of a successful experiment are so transformational that we hope this text will stimulate learn teams actively working on positron–electron annihilation spectroscopy to are trying this experiment.

#### ACKNOWLEDGMENTS

The author acknowledges the financial make stronger obtained to undertake this learn from the College of Mathematics and Physics, University of Portsmouth.

The recordsdata that make stronger the findings of this explore are on hand all the map by the article.

- 1. M. M. Vopson, “The sector’s recordsdata explained: How mighty we’re producing and where it’s all kept,” World Economic Dialogue board, Might 2021, on hand at https://www.weforum.org/agenda/2021/05/world-recordsdata-produced-kept-global-gb-tb-zb/.
**Google Pupil** - 2. Gape https://www.idc.com/ for estimates of the annual digital recordsdata manufacturing in the sector.
**Google Pupil** - 3. M. M. Vopson, “The walk wager wretchedness,” AIP Adv.
**10**, 085014 (2020). https://doi.org/10.1063/5.0019941,**Google Pupil****Scitation**,**ISI** - 4. M. M. Vopson, “Estimation of the walk wager contained in the considered topic of the universe,” AIP Adv.
**11**(10), 105317 (2021). https://doi.org/10.1063/5.0064475,**Google Pupil****Scitation** - 5. R. Landauer, “Irreversibility and warmth generation in the computing process,” IBM J. Res. Dev.
**5**(3), 183–191 (1961). https://doi.org/10.1147/rd.53.0183,**Google Pupil****Crossref** - 6. R. Landauer, “The bodily nature of recordsdata,” Phys. Lett. A
**217**(4–5), 188–193 (1996). https://doi.org/10.1016/0375-9601(96)00453-7,**Google Pupil****Crossref** - 7. J. Hong, B. Lambson, S. Dhuey, and J. Bokor, “Experimental check of Landauer’s notion in single-bit operations on nanomagnetic reminiscence bits,” Sci. Adv.
**2**(3), e1501492 (2016). https://doi.org/10.1126/sciadv.1501492,**Google Pupil****Crossref** - 8. R. Gaudenzi, E. Burzurí, S. Maegawa, H. van der Zant, and F. Luis, “Quantum Landauer erasure with a molecular nanomagnet,” Nat. Phys.
**14**, 565–568 (2018). https://doi.org/10.1038/s41567-018-0070-7,**Google Pupil****Crossref** - 9. A. Bérut, A. Arakelyan, A. Petrosyan, S. Ciliberto, R. Dillenschneider, and E. Lutz, “Experimental verification of Landauer’s notion linking recordsdata and thermodynamics,” Nature
**483**, 187–189 (2012). https://doi.org/10.1038/nature10872,**Google Pupil****Crossref** - 10. Y. Jun, M. Gavrilov, and J. Bechhoefer, “Excessive-precision check of Landauer’s notion in a feedback entice,” Phys. Rev. Lett.
**113**(19), 190601 (2014). https://doi.org/10.1103/physrevlett.113.190601,**Google Pupil****Crossref** - 11. M. M. Vopson, “The mass-energy-recordsdata equivalence notion,” AIP Adv.
**9**, 095206 (2019). https://doi.org/10.1063/1.5123794,**Google Pupil****Scitation**,**ISI** - 12. M. M. Vopson, The walk wager jabber of the universe and the implications for the missing Darkish Topic, June 2019.
**Google Pupil** - 13. L. B. Kish, “Gravitational mass of recordsdata?,” Fluctuation Noise Lett.
**07**, C51–C68 (2007). https://doi.org/10.1142/s0219477507004148,**Google Pupil****Crossref** - 14. L. Herrera, “The mass of a dinky of recordsdata and the Brillouin’s notion,” Fluctuation Noise Lett.
**13**(01), 1450002 (2014). https://doi.org/10.1142/s0219477514500023,**Google Pupil****Crossref** - 15. L. B. Kish and C. G. Granqvist, “Does recordsdata catch mass?,” Proc. IEEE
**101**(9), 1895–1899 (2013). https://doi.org/10.1109/jproc.2013.2273720,**Google Pupil****Crossref** - 16. E. Bormashenko, “The Landauer notion: Re–formula of the second thermodynamics law or a step to monumental unification,” Entropy
**21**, 918 (2019). https://doi.org/10.3390/e21100918,**Google Pupil****Crossref** - 17. I. K. MacKenzie,
*Experimental Solutions of Annihilation Time and Energy Spectrometry, Positron Solid-Explain Physics*(Società Italiana di Fisica, Bologna, Italy, LXXXIII Corso, 1983), pp. 196–264.**Google Pupil** - 18. P. G. Coleman, in
*Positron Beams and Their Purposes*(World Scientific, Singapore, 2000), Chap. 2, pp. 11–40.**Google Pupil****Crossref** - 19. D. G. Costello, D. E. Groce, D. F. Herring, and J. Wm. McGowan, “Evidence for the detrimental work characteristic associated with positrons in gold,” Phys. Rev. B
**5**(4), 1433–1436 (1972). https://doi.org/10.1103/physrevb.5.1433,**Google Pupil****Crossref** - 20. A. Vehanen and J. Mäkinen, “Skinny movies for slack positron generation,” Appl. Phys. A
**36**, 97–101 (1985). https://doi.org/10.1007/bf00620615,**Google Pupil****Crossref** - 21. P. J. Schultz and K. G. Lynn, “Interaction of positron beams with surfaces, thin movies, and interfaces,” Rev. Mod. Phys.
**60**(3), 701–779 (1988). https://doi.org/10.1103/revmodphys.60.701,**Google Pupil****Crossref** - 22. D. M. Chen, K. G. Lynn, R. Pareja, and B. Nielsen, “Dimension of positron reemission from thin single-crystal W(100) movies,” Phys. Rev. B
**31**(7), 4123–4130 (1985). https://doi.org/10.1103/physrevb.31.4123,**Google Pupil****Crossref** - 23. A. Goodyear, A. P. Knights, and P. G. Coleman, “Energy spectroscopy of positrons re-emitted from polycrystalline tungsten,” J. Phys.: Condens. Topic
**6**(45), 9601–9611 (1994). https://doi.org/10.1088/0953-8984/6/45/010,**Google Pupil****Crossref** - 24. C. Hugenschmidt, B. Straßer, and K. Schreckenbach, “Investigation of positron work characteristic and moderation effectivity of Ni, Ta, Pt and W(100),” Appl. Surf. Sci.
**194**(1–4), 283–286 (2002). https://doi.org/10.1016/s0169-4332(02)00135-6,**Google Pupil****Crossref** - 25. M. J. Berger, J. S. Coursey, M. A. Zucker, and J. Chang, “Stopping-energy and vary tables for electrons, protons, and helium ions,” NIST Bodily Measurements Laboratory, on hand at www.nist.gov/pml/recordsdata/star/index.cfm.
**Google Pupil**

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