# Force law in material media, hidden momentum and quantum phases

## Abstract

We address to the force law in classical electrodynamics of material media, paying attention on the force term due to time variation of hidden momentum of magnetic dipoles. We highlight that the emergence of this force component is required by the general theorem, deriving zero total momentum for any static configuration of charges/currents. At the same time, we disclose the impossibility to add this force term covariantly to the Lorentz force law in material media. We further show that the adoption of the Einstein–Laub force law does not resolve the issue, because for a small electric/magnetic dipole, the density of Einstein–Laub force integrates exactly to the same equation, like the Lorentz force with the inclusion of hidden momentum contribution. Thus, none of the available expressions for the force on a moving dipole is compatible with the relativistic transformation of force, and we support this statement with a number of particular examples. In this respect, we suggest applying the Lagrangian approach to the derivation of the force law in a magnetized/polarized medium. In the framework of this approach we obtain the novel expression for the force on a small electric/magnetic dipole, with the novel expression for its generalized momentum. The lattermore »

- Authors:

- Belarusian State University, Minsk (Belarus)
- Institute for Nuclear Problems, Belarusian State University, Minsk (Belarus)
- Okan University, Akfirat, Istanbul (Turkey)
- (Turkey)

- Publication Date:

- OSTI Identifier:
- 22560327

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Annals of Physics; Journal Volume: 369; Journal Issue: Complete; Other Information: Copyright (c) 2016 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ELECTRIC DIPOLES; ELECTRIC FIELDS; ELECTRODYNAMICS; LAGRANGIAN FUNCTION; LORENTZ FORCE; MAGNETIC DIPOLES; MAGNETIC FIELDS; QUANTUM MECHANICS; RELATIVISTIC RANGE; TRANSFORMATIONS; VARIATIONS

### Citation Formats

```
Kholmetskii, Alexander L., E-mail: alkholmetskii@gmail.com, Missevitch, Oleg V., Yarman, T., and Savronik, Eskisehir.
```*Force law in material media, hidden momentum and quantum phases*. United States: N. p., 2016.
Web. doi:10.1016/J.AOP.2016.03.004.

```
Kholmetskii, Alexander L., E-mail: alkholmetskii@gmail.com, Missevitch, Oleg V., Yarman, T., & Savronik, Eskisehir.
```*Force law in material media, hidden momentum and quantum phases*. United States. doi:10.1016/J.AOP.2016.03.004.

```
Kholmetskii, Alexander L., E-mail: alkholmetskii@gmail.com, Missevitch, Oleg V., Yarman, T., and Savronik, Eskisehir. Wed .
"Force law in material media, hidden momentum and quantum phases". United States.
doi:10.1016/J.AOP.2016.03.004.
```

```
@article{osti_22560327,
```

title = {Force law in material media, hidden momentum and quantum phases},

author = {Kholmetskii, Alexander L., E-mail: alkholmetskii@gmail.com and Missevitch, Oleg V. and Yarman, T. and Savronik, Eskisehir},

abstractNote = {We address to the force law in classical electrodynamics of material media, paying attention on the force term due to time variation of hidden momentum of magnetic dipoles. We highlight that the emergence of this force component is required by the general theorem, deriving zero total momentum for any static configuration of charges/currents. At the same time, we disclose the impossibility to add this force term covariantly to the Lorentz force law in material media. We further show that the adoption of the Einstein–Laub force law does not resolve the issue, because for a small electric/magnetic dipole, the density of Einstein–Laub force integrates exactly to the same equation, like the Lorentz force with the inclusion of hidden momentum contribution. Thus, none of the available expressions for the force on a moving dipole is compatible with the relativistic transformation of force, and we support this statement with a number of particular examples. In this respect, we suggest applying the Lagrangian approach to the derivation of the force law in a magnetized/polarized medium. In the framework of this approach we obtain the novel expression for the force on a small electric/magnetic dipole, with the novel expression for its generalized momentum. The latter expression implies two novel quantum effects with non-topological phases, when an electric dipole is moving in an electric field, and when a magnetic dipole is moving in a magnetic field. These phases, in general, are not related to dynamical effects, because they are not equal to zero, when the classical force on a dipole is vanishing. The implications of the obtained results are discussed.},

doi = {10.1016/J.AOP.2016.03.004},

journal = {Annals of Physics},

number = Complete,

volume = 369,

place = {United States},

year = {Wed Jun 15 00:00:00 EDT 2016},

month = {Wed Jun 15 00:00:00 EDT 2016}

}