A macroscopic object equipped with synchronized clocks is examined. General physical relations are directly derived from Lorentz transformations for the case of one-dimensional motion (along the X axis) – the uncertainty relation of the object's x coordinate and the projection of its impulse along the X axis, px, and the uncertainty relation of the object's observation time, t, and its energy, E. The relations take the form: \(\Delta\)px\(\Delta\)x \(\ge\) H and \(\Delta\)E\(\Delta\)t \(\ge\) H. The H value in the relation has action dimensions and is dependent upon the precision of the rod's clocks and its mass. It is shown that if the macroscopic object in and of itself performs the function of an ideal physical clock, the relations derived in the limiting case then take the form of \(\Delta\)px\(\Delta\)x \(\ge\) h and \(\Delta\)E\(\Delta\)t \(\ge\) h, where h is the Planck constant.
A macroscopic object equipped with synchronized clocks is examined. General physical relations are directly derived from Lorentz transformations for the case of one-dimensional motion (along the X axis) – the uncertainty relation of the object's x coordinate and the projection of its impulse along the X axis, px, and the uncertainty relation of the object's observation time, t, and its energy, E. The relations take the form: (\Delta)px(\Delta)x (\ge) H and (\Delta)E(\Delta)t (\ge) H. The H value in the relation has action dimensions and is dependent upon the precision of the rod's clocks and its mass. It is shown that if the macroscopic object in and of itself performs the function of an ideal physical clock, the relations derived in the limiting case then take the form of (\Delta)px(\Delta)x (\ge) h and (\Delta)E(\Delta)t (\ge) h, where h is the Planck constant.
It is believed that the uncertainty relation of momentum and coordinates, as well as the uncertainty relation of energy and time in practice are not observed in the macrocosm. The objective of the work at hand was to demonstrate the existence of general physical uncertainty relations that extend to macrobodies. A macroscopic object consisting of a rod equipped with a pair of synchronized clocks and a macroscopic object in and of itself performing the function of an ideal physical clock are examined. General physical relations are directly derived from Lorentz transformations for the case of the object's one-dimensional motion (along the X axis) – the uncertainty relation of the object's x coordinate and the projection of its impulse along the X axis, px, and the uncertainty relation of the object's observation time, t, and its energy, E. The relations take the form: ΔpxΔx ≥ H and ΔEΔt ≥ H. The H value in the relation has action dimensions and is dependent upon the precision of the object's clocks and/or upon the properties of the physical clock. Despite the interpretation of the concept of uncertainty being different from that in quantum mechanics, the relations derived in the limiting case with ideal physical clock take the form of ΔpxΔx ≥ h and ΔEΔt ≥ h, where h is the Planck constant.
In previous notes (1) we discussed how (p=0, E=mocc,) (x=0, to) transforms to p’, E’, x’,t’ such that x’/t’=v. We noted that (x=0, to) is a special (x,t) vector linked to a stationary frame. We noted that a general vector (x,t) = (0,t) + (x,0) and that (x,0) Lorentz transforms such that the Lorentz invariantt -Et+px =0. We also noted that E scales t and p scales x and argued that this was the basis for the frequency and wavelength for a quantum free particle. In this note we investigate this idea further. In particular we argue that given -Et+px, it is not only the case that (x,0) transforms into (x1,t1) such that -E’x1+p’t1=0, but that 1/E=t and 1/p=x also yields -E 1/E + p/p=0. In other words there is freedom in both t and x proportional to 1/E and 1/p even though the special vector (0,to) defines the velocity i.e. x’/t’=v. This freedom may be associated with uncertainty in position and time even though there is a well defined x’/t’=v. This uncertainty has important consequences if interactions occur i.e. interference effects.These are usually associated with a wave which has the dispersion relationship E=pv, but we argue that they also hold for a particle with rest mass i.e p=E(v) v because it is the uncertainty in t and x which keeps -Et+px=0 which is the source. This also happens to hold for a photon which is a wave in the sense that it has no rest mass.The uncertainty itself yields the velocity i.e. x/t = 1/p / (1/E) = E/p = c. Given the periodic nature of -E 1/E + p 1/p=0 i.e. -E n/E + p/p = 0 where n=1,2,3… we argue that a periodic function be sought such that it describes a kind of probability due to uncertainty in x,t, but this uncertainty disappears when t=n/E and x=n/p.
1. Amend the two postulates of the special relativity. 2. Set “the measurement is founded to change the object by destroying the original quantum coherence between the object and its environment” as the third postulate. 3. From the third postulate (new added postulate) educe: the concept of the reference system’s referenced weight and perhaps the reference system’s space is something nearby the referenced weight; time coordinate should be something as space coordinate there is not the problem to have to synchronize the clocks of the two reference systems before simultaneous time measurement; the essence of Heisenberg Uncertainty Principle; the “actual length” of the same measurement unit in different case is different; it is the reference system’s taking measurement instead of the ether or the object’s motion that changes the being measured object; two reference systems (e.g. Σ and Σa and their relative motion may be uniform or not) taking simultaneously measure of the same quantity of the same object their measurement will disturb each other and “the numerical values before Σ’s unit” ≠ “the numerical values before Σa’s unit” (only when the relative motion speed v≡0 or uniform relative speed v=0 can the sign ≠ just turn into =); even in uniform relative motion Σ and Σa still are different for the relative motion and they may have different referenced weight, in taking simultaneously measure of the same speed of relative motion the speed numerical values of Σa is v while of Σ is va11/a44. 4. From the three postulates express the relation between the numerical values of the two reference systems taking simultaneous measurement of the same speed by matrix and the same small moving particle’s mass by the element of the matrix; determine the speed of the photon which come from “in motion” light source by the photon’s speed when light source “in stationary” and the reference systems’ coordinate relation; determine two reference systems’ coordinates relation when reduced the case educe generally there is not the invariant interval and then there is not the proper time, re-reduced the case and re-re-reduced the case then educe the essence of “in motion” time dilate or contract meanwhile space contract or dilate in all directions, moving micro-particle’s time to dilate and space to contract in all directions, superluminal photonic tunneling experiment, quasar’s super-luminal expansion and fine structure constant’s lessening, took Michelson-Morley experiment with the light from the sun or quasars or high-speed (close to C) moving micro-particle all obtained zero result.
The quantum-mechanical framework in which observables are associated with Hermitian operators is too narrow to discuss measurements of such important physical quantities as elapsed time or harmonic-oscillator phase. We introduce a broader framework that allows us to derive quantum-mechanical limits on the precision to which a parameter---e.g., elapsed time---may be determined via arbitrary data analysis of arbitrary measurements on N identically prepared quantum systems. The limits are expressed as generalized Mandelstam-Tamm uncertainty relations, which involve the operator that generates displacements of the parameter---e.g., the Hamiltonian operator in the case of elapsed time. This approach avoids entirely the problem of associating a Hermitian operator with the parameter. We illustrate the general formalism, first, with nonrelativistic uncertainty relations for spatial displacement and momentum, harmonic-oscillator phase and number of quanta, and time and energy and, second, with Lorentz-invariant uncertainty relations involving the displacement and Lorentz-rotation parameters of the Poincar\\'e group.
We argue that correct account of the quantum properties of macroscopic objects which form reference frames (RF) demand the change of the standard space-time picture accepted in Quantum Mechanics. Galilean or Lorentz space-time transformations are shown to become incorrect in this case and for the description of transformations between different RF the special quantum space-time transformations are introduced. Consequently it results in the generalised Schrodinger equation which depends on the observer mass. The experiments with macroscopic coherent states are proposed in which this effects can be tested.
In classical physics, velocity follows from exact measurements of space and time intervals (i.e perfect resolution of both). Inertial mass follows from a resistance of an object to a force (push or pull). Momentum, however, which nonrelativistically is mv and should be associated with ideas of inertial mass, and space time resolution may be instead linked to the physical idea of an impulse. An impulse seems to be like a hit and does not appear to be linked directly to space time physically, although its consequences are i.e. a particle receiving the impulse moves in space and time. In classical mechanics, x(t) and so one considers either equally spaced dt intervals and corresponding dx(t) or vice versa (constant dx) if an integral only involves space dependent values. In quantum mechanics, one has two uncertainty principles, one related to E and t and the other to p and x. We argue that p is linked to the notion of an impulse which does not on the surface involve space or time. Given that p, even in nonrelativistic quantum mechanics, is mv there should at least be some built in notion of dx and dt. From the uncertainty principles one sees that dx (i.e. the wavelength) is linked to hbar/p and dt to hbar/E. Thus neither dt nor dx are constants, but depend on the motion. In the high energy quantum limit dt —> W(x)W(x) dx →1/v(x) dx where v(x) is classical velocity and W(x) the bound state wavefunction. The bound state wavefunction, however, applies to the envelope of WW (not the actual crests and troughs) and so the dx-dt scheme which emerges is a smoothed over one and not the actual dx -dp of quantum mechanics. We try to examine some of these ideas in this note.