Heisenberg photons and particle velocity measurement

[lightparticle]

Hi,
[c=speed of light]
if a particle travels at a velocity x/t and momentum p, such that (c-x/t) < (delta-x)*(delta-p) (ie the Heisenberg limit), how could one tell whether what one was looking at was a photon traveling at speed c or a particle traveling indeterminately CLOSE to c?

also, the speed c itself is that constant in the lorentz transformations which is the same in all intertial frames (by assumption) and at which Ganmma, 1/Sqrt(1-(v^2/c^2) ) approaches infinity.
That is to say c is a limit which the speed v of a mass approaches asymptotically but never reaches because the mass would become infinite as would the energy needed to accelerate it.
That this constant is equal to the speed of light is got from the fact that the speed, V(em), of electromagnetic radiation in the frame of the observer is given by 1/Sqrt(UoEo), where the Uo and Eo constants are the magnetic permeability and electric permitivity of a vacuum respectively, combined with the fact that physical laws are the same in all inertial frames.
BUT
since the experimental measurement of Eo is subject to the same quantum indeterminacy as any other observed measurement with laboratory equipment, there's no way to say that Eo can be measured with infinite precision.

so how can one say that V(em) is EXACTLY c since there is a necessary Heisenberg uncertainty in V(em) ?
or that all 'photons' travel at the same speed?

[notation: f(db) =DeBroglie freguency, f(em)= electromagnetic frequency]

If f(db) is the frequency of a moving particle's De Broglie wave, the total energy of the particle is given by E=(1-1/y)hf(db), (where y is gamma) which for smaller and smaller moving rest-masses each of total energy E (and therefore higher speeds) approaches E=hf(db) as v->c. That is to say the energy is given in terms of the Debroglie frequency (not the usual em frequency)
i.e. f(db)->f(em) as v->c.

Thus various particles, each traveling at speeds indistinguishably (a la Heisenberg uncertainty) close to the theoretical cosmic maximum c, have very different energies and frequencies (since the energies rise asymptotically as v->c) even though they all travel seemingly AT c (but actually immeasurably less than c)!

So how does one distinguish the difference between the two descriptions? or can they be distinguished at all? or that em waves arent just debroglie waves after all. After all Debroglie waves affect the behaviour of electrons as do em waves.
And Finally would a beam of NEUTRONS, of appropriate p and Lambda, passing an antenna ALSO affect the electrons in the antenna by means of their DeBroglie wave. would somebody out there PLEASE do the experiment. :)

 

[eljose79]

Hello,

Thank you for your interesting post and questions. I can provide some insights on how we can determine whether we are looking at a photon traveling at speed c or a particle traveling indeterminately close to c.

First, let's clarify some concepts. The Heisenberg uncertainty principle states that it is impossible to precisely measure both the position and momentum of a particle at the same time. This means that we cannot know with certainty whether a particle is traveling exactly at the speed of light or just very close to it. However, this does not mean that we cannot distinguish between a photon and a particle traveling at a different speed.

One way to determine if we are looking at a photon or a particle is by measuring its energy and momentum. A photon always travels at the speed of light and has a fixed energy and momentum, given by E=hf and p=h/λ respectively, where h is Planck's constant, f is the frequency, and λ is the wavelength. On the other hand, a particle traveling at a different speed would have a different energy and momentum.

Another way to distinguish between a photon and a particle is by looking at its behavior in different mediums. Photons behave differently than particles in terms of scattering, refraction, and other interactions with matter. By studying these behaviors, we can determine if we are dealing with a photon or a particle.

Regarding your question about the speed of light being exactly c, it is true that there is a Heisenberg uncertainty in the measurement of the speed of light, just like any other physical quantity. However, this uncertainty is very small and does not affect our ability to say that the speed of light is indeed c. This is because the uncertainty is much smaller than the difference between c and any other speed.

In terms of distinguishing between De Broglie waves and electromagnetic waves, it is important to note that these are two different concepts. De Broglie waves are associated with particles, while electromagnetic waves are associated with photons. They have different properties and behaviors, and they cannot be considered as the same thing.

Finally, regarding your question about whether a beam of neutrons can affect the electrons in an antenna through their De Broglie waves, this is indeed possible. Neutrons have a wave-like nature, just like electrons, and can interact with matter through their wave properties. This phenomenon is known as neutron diffraction and has been studied extensively in the field of physics.

I hope this helps