Pis’ma v ZhETF, vol. 115, iss. 10, pp. 610 - 610

May 25

On Lorentz invariance and the minimum length¹⁾

M. D. Pollock²⁾

V. A. Steklov Mathematical Institute, Russian Academy of Sciences, 119991 Moscow, Russia

Submitted 22 March 2022

Resubmitted 17 April 2022

Accepted 17 April 2022

DOI: 10.31857/S1234567822100020, EDN: dyhtsn

It was shown by Kirzhnits and Chechen [1], following

energy ∼ 250 MeV, however, would be ruled out, since

an earlier paper by Mead [2], that the minimum length

then l ∼ 10^-13 cm. We emphasize that these results all

scale l is constrained by the Mössbauer effect [3], which

presuppose a de Sitter momentum space, for the alter-

leads to the result l ≲ 10^-20 cm, assuming the Snyder

native anti-de Sitter momentum space implies no mini-

discrete space-time [4] and conventional nuclides. Here,

mum length scale, and therefore seems unphysical.

we note, firstly, that some recently discussed nuclides,

This is an excerpt of the article

“On Lorentz

for example¹⁸⁹⁷⁶Os, have much narrower natural line

invariance and the minimum length”. Full text of

widths, which, if excited by synchrotron radiation, could

the paper is published in JETP Letters journal.

potentially decrease the limiting value to l ≲ 10^-24 cm

DOI: 10.1134/S0021364022600616

in future experiments. The Snyder space-time and the

superstring theory are both locally Lorentz invariant,

and give rise to the same form of generalized indeter-

√

1. D. A. Kirzhnits and V. A. Chechen, Yad. Fiz. 7, 431

minacy principle, if we set l ≈ 2

πα^′, where α^′ is the

(1968) [Sov. J. Nucl. Phys. 7, 295 (1968)].

Regge slope parameter, which is thus also constrained

2. C. A. Mead, Phys. Rev. 143, 990 (1966).

by the Mössbauer effect. For the heterotic superstring,

√

3. R. L. Mössbauer, Z. Phys. 151, 124 (1958).

in particular,

α^′ = 4√2πGN ≈ 10-32 cm, apparently

beyond experimental reach. A hadron string theory at

4. H. S. Snyder, Phys. Rev. 71, 38 (1947).

¹⁾Supplementary materials are available for this article at

DOI: 10.1134/S0021364022600616 and are accessible for autho-

rized users.

²⁾e-mail: mdp30@cam.ac.uk

610

Письма в ЖЭТФ том 115 вып. 9 - 10

2022