This is a lively discussion on a fundamental principle in QM.  It reveals a healthy uneasiness of the physics community regarding the foundations of the theory, even though it works remarkably well in the microscopic world!  As I understand it, the point is very much related to the question of measurement.  It is not that a particle does not have a precise position and a precise linear momentum at any instant; but that one cannot measure these 'complementary' quantities simultaneously.  One can measure one of the two quantities with 100% certainty or accuracy, albeit at the expense of the other.  Alternatively, one can strike a 'compromise' between the two, so to speak, according to Heisenberg's well-known statement.  After all, QM is ultimately a theory of measurement; one should not forget that!

Of course, there are other uncertainty 'principles' involving other 'complementary pairs', such as the excitation energy of a particle and its lifetime, and several others.  As you know, there is also an uncertainty principle in wave optics. 

As the theory is constructed, you have to follow the corresponding (boson or fermion) symmetrization rule for the state with which you  compute the quantum average of the relevant quantities that give you the uncertainty principle (the observable its square, and the same for the conjugate observable). The velocity of light is a parameter in relativitic or not relativistic theory, so it is un affected by the computations. If you compute phase or group velocities it can change with the state involved.

The Heisenberg's principle applies to any particle regardless of its statistical character. 

This is a lively discussion on a fundamental principle in QM.  It reveals a healthy uneasiness of the physics community regarding the foundations of the theory, even though it works remarkably well in the microscopic world!  As I understand it, the point is very much related to the question of measurement.  It is not that a particle does not have a precise position and a precise linear momentum at any instant; but that one cannot measure these 'complementary' quantities simultaneously.  One can measure one of the two quantities with 100% certainty or accuracy, albeit at the expense of the other.  Alternatively, one can strike a 'compromise' between the two, so to speak, according to Heisenberg's well-known statement.  After all, QM is ultimately a theory of measurement; one should not forget that!

Of course, there are other uncertainty 'principles' involving other 'complementary pairs', such as the excitation energy of a particle and its lifetime, and several others.  As you know, there is also an uncertainty principle in wave optics. 

Photons are bosons i.e. quantum entities of spin 1 while all fermions, by definition , are all particles of non-integral spin. The main difference resulting from that  is that bosons obey to the Bose-Einstein statistics while fermions to the Fermi-Dirac statistics. This means in practice that one can put  only one fermion in a given quantum state while there is no such restriction for bosons, allowing for formation of the so called Bose-Einstein condensate. From all other quantum aspects, the Uncertainty Principle included, they behave in the same way.  

Dear all

Thank you so much for your nice answers. 

The point I want to reach from the view of EPR paradox is there any differences in the uncertainty of two entangled photons and two entangled fermions? theoretically and experimentally considering the experiment is accomplished in vacuum, so speed of light can be determined well.

Cf. Wightman's paper, ftp://ejde.math.txstate.edu/pub/EJDE/conf-proc/04/w1/wightman.pdf. The short answer is that there aren't any differences, in *non-relativistic* quantum mechanics, between the uncertainty principles for fermions and for bosons. In relativistic quantum mechanics, i.e. quantum field theory, the meaningful generalizations become the relations between correlation functions-and here, of course, the spin-statistics theorem becomes relevant-which Wightman, also, discusses.

``The speed of light in vacuum is well defined, Does this make the uncertainity for photons lesser than electrons because their speeds are not well defined at least in vacuum in comparison with photons?''Not really: the uncertainty relation involves momentum, not velocity. For a photon, momentum is defined as a function of wave vector, and is by no means constant.

The uncertainty principle is simply a mathematical relationship between the distribution of momenta that will be observed if momentum is measured in a given state, and the corresponding distribution for positions, if position is measured. What it says is that, the momentum distribution and the position distribution cannot both be narrow, in the specific sense that the product of their variances is always larger than hbar^2/4.

@Sadeem: ``The point I want to reach from the view of EPR paradox is there any differences in the uncertainty of two entangled photons and two entangled fermions? theoretically and experimentally considering the experiment is accomplished in vacuum, so speed of light can be determined well.''

A good point. However: EPR issues are only marginally related to the uncertainty principle, in that the uncertainty principle is rather straightforward and well understood, whether EPR is not. Further, the degrees of freedom which are usually used in EPR experiments with photons are the polarization degrees of freedom, which have nothing to do either with speed (not related either to EPR or uncertainty) or momentum (which is related to Heisengberg's uncertainty principle). EPR with fermions have also been performed, with similar results.

Dear Sadeem

Heisenberg uncertainty principle is one of the fundamentals of the quantum mechanics like the De Broglie postulate. Both are embedded in the Schroedinger wave equation  which describes the motion of the quantum mechanical particles under the effect of a potential field. It stems from the wave nature of the moving particles, since in the wave motion you can not determine the position and the momentum simultaneously with any required accuracy.

Concerning the motion of electron  freely in vacuum in a boundless medium, the quantum mechanics tell us it can take any arbitrary momentum and  wavelength of its wave. It will extend in a boundless space, and hence its position uncertainty will be infinite and therefore its momentum will be definitive. The momentum value p depends on the kinetic energy E of the electron such that E= P^2/2m. And the wavelength of the motion will be lambda= h/ P where h is the Planck s constant. So, in this case since the velocity v of the electron is P/m, then you can measure also v with high accuracy according to Heienberg principle.

Concerning the motion of light in free space,  it moves as travelling wave in boundless medium, so the position of the photons are not restricted to certain volume in the space, and consequently its momentum can be measured with high accuracy and consequently its speed as in the case of electrons.

I hope i shed some light on the answer

In fact there is a subtle difference in the way one can apply the Heisenberg uncertainty principle to the ordinary (massive) particles and massless photons. The way in which the uncertainty principle can be extended to photons is dicussed in the publication :

Heisenberg uncertainty relations for photons

Iwo Bialynicki-Birula (Warsaw, CFT), Zofia Bialynicka-Birula (Warsaw, Inst. Phys.). 2012. 9 pp.

Published in Phys.Rev. A86 (2012) 022118 

Uncertanity principle Delta p times Delta x = hbar/2 measuring momentum and measuring position of the particle is small or equal  that quantity. This means we can not  measure the positon and momentum of the particle definitely at the same time. There should be an uncertainty. This relation is the basic relation in Quantum Mechanics.

A simple/primitive answer is the following. The uncertainty principle says that we cannot simultaneously know the exact position x and the exact momentum p of a particle. The momentum of a photon equals: p=hv/c, where h is the Planck constant, v is photon frequency, and c is speed of light. So the photon frequency is not defined exactly, though speed of light is constant.

Johan Frans Prins,

for this phrase see, please,

http://ed.ted.com/lessons/what-is-the-heisenberg-uncertainty-principle-chad-orze

Dear J.

no doubt it is so.

https://www.researchgate.net/publication/258835771_Decision_making_under_uncertainty_in_energy_systems_State_of_the_art

Article Decision making under uncertainty in energy systems: State of the art