Open Access
Review
 Issue EPJ Applied Metamaterials Volume 1, 2014 9 2 https://doi.org/10.1051/epjam/2015003 23 June 2015

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It is appropriate to recall that the relation (3) relates to the mass transported only with portable energy, not affecting the linear momentum of transferred mass. To clarify this fact we, following [3], consider this process from a different point of view, based primarily on the laws of conservation of energy and momentum.

First let’s inert body (called the “radiator”) with a rest mass M0, rest energy E0 = M0c2, and linear momentum P0 = 0 emits (“radiates”, “throws”, “shoots”) a particle (body, photon, wave packet) with energy E1 ≪ E0, speed v1 ≪ c and linear momentum P1. Let us not discuss at the beginning the relationships between E1, P1 and v1.

After the emission of a particle, emitter with the mass M0 begins to move with speed:(5)in the direction opposite to the direction of linear momentum of emitted particle.

Let us now assume that at the distance L from the emitter is another body, called as receiver, and after some time t the particle emitted by the emitter reaches the receiver and blends (absorbed) with him, changing its mass.

Obviously, time t will be equal:(6)

During this time the emitter will move at a distance Δx equal to:(7)

This equation could be represented as:(8)

Taking in the account stable position of center of mass of the entire system “emitter-emitted particles-receiver”, it is obvious that the equation (8) should be understood that during the time t emitter with the mass M0 will move in one direction at a distance Δx, and the emitted particle will move in the opposite direction on distance L and changes mass of the receiver on the value P1/v1.

Now, let us refine the specific nature of the emitted particles. First, let us consider the usual material particles, the energy and linear momentum which could are the subject of Lorentz transformations. Then, we write the relation of the particle energy and its linear momentum in the form:(9)and substitution of this expression in equation (8) gives:(10)

From this relation follows at once well-known fact that the change in the rest energy of the body on the value of E1 leads to a change in its resting mass on the value . Now consider the case when the emitter emits a wave (wave packet, the light pulse, the photon) with energy E1. The linear momentum of the emitted wave is equal:(11)

A substitution of equation (11) into (8) gives:(12)

If we assume that the wave velocity v1 in this ratio is really the group velocity vgr, then we immediately obtain from equation (4).

From equation (4) follows that in media with negative refraction, radiation transfers the mass not from the transmitter to receiver, but rather from the receiver to the transmitter.

In addition, from the above conclusion follows, that the mass transferred from the transmitter to the receiver is determined not only by transferred energy, but also by transferred linear momentum, which may be associated with energy in different ways, such as is seen from the relation (9) or (11). Thus, the well-known relation (3) is only special case of equation (4).

## References

1. V.G. Veselago, Sov. Phys. Usp. 10 (1968) 509. [CrossRef] (In the text)
2. V.G. Veselago, Phys. Usp. 52 (2009) 649. [CrossRef] (In the text)
3. A. Einstein, Ann. Phys. 20 (1906) 627. [CrossRef] (In the text)

Cite this article as: Veselago VG: Negative refraction, light pressure and attraction, equation E = mc2 and wave-particle dualism. EPJ Appl. Metamat. 2015, 1, 9.

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