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However the total energy of the particle E and its relativistic momentum p are frame-dependent; relative motion between two frames causes the observers in those frames to measure different values of the particle's energy and momentum; one frame measures E and p, while the other frame measures E ′ and p ′, where E ′ ≠ E and p ′ ≠ p ...
There exists an equivalent formulation of the relativistic Lagrangian, which has two advantages: it allows for a generalization to massless particles and tachyons; it is based on an energy functional instead of a length functional, such that it does not contain a square root. In this alternative formulation, the Lagrangian is given by
The thermodynamic limit is essentially a consequence of the central limit theorem of probability theory. The internal energy of a gas of N molecules is the sum of order N contributions, each of which is approximately independent, and so the central limit theorem predicts that the ratio of the size of the fluctuations to the mean is of order 1/N 1/2.
The Greisen–Zatsepin–Kuzmin limit (GZK limit or GZK cutoff) is a theoretical upper limit on the energy of cosmic ray protons traveling from other galaxies through the intergalactic medium to our galaxy. The limit is 5 × 10 19 eV (50 EeV), or about 8 joules (the energy of a proton travelling at ≈ 99.999 999 999 999 999 999 98 % the
The property of spin relates to another basic property concerning systems of N identical particles: the Pauli exclusion principle, which is a consequence of the following permutation behaviour of an N-particle wave function; again in the position representation one must postulate that for the transposition of any two of the N particles one ...
In quantum mechanics and quantum field theory, a Schrödinger field, named after Erwin Schrödinger, is a quantum field which obeys the Schrödinger equation. [1] While any situation described by a Schrödinger field can also be described by a many-body Schrödinger equation for identical particles, the field theory is more suitable for situations where the particle number changes.
The quantum potential or quantum potentiality is a central concept of the de Broglie–Bohm formulation of quantum mechanics, introduced by David Bohm in 1952.. Initially presented under the name quantum-mechanical potential, subsequently quantum potential, it was later elaborated upon by Bohm and Basil Hiley in its interpretation as an information potential which acts on a quantum particle.
Based on how non-local the box (, |,) happens to be, Alice and Bob estimate how much knowledge an external quantum adversary Eve (the eavesdropper) could possess on the value of Alice and Bob's outputs. This estimation allows them to devise a reconciliation protocol at the end of which Alice and Bob share a perfectly correlated one-time pad of ...