Relativistic Quantum Mechanics

A particle that defies classical mechanics !

A photon has no mass but energy and it has speed and it has momentum although it does not have mass. Thats impossible in Classical Mechanics. Because Classical Mechanics associates with every mass; momentum and kinetic and potential energy. All those would be zero if mass were to be zero.

Also the speed of the photon is constant while its energy and momentum are changing. This is unimaginable in classical mechanics. In CM first momentum can’t be defined from mass and speed if mass is zero, then while speed is not changing how is momentum changing? So both variables speed and mass fail to define a momentum for the photon, and not just the failure to have a mass. How then momentum is defined for this particle? Its not defined as long as photon is just a particle. Thats impossible.

Nature of photons.

Also (without any direct theoretical connection, but correlation through reality of nature)
3. Photons are classical only in the sense that we perceive light only when photons are produced in large numbers. So large that the laws of the small do not incur large errors because they are in large numbers. Statistically the errors are well understood and eliminated. But when they are produced in very small numbers we can not deduce their laws a priori. [which is why Quantum Mechanics was discovered only in 1920s and not in Galileo’s time, In his time the macroscopic behavior were understood and microscopic laws can never be produced from the understanding of macro scope just like a particular individuals attribute can’t be found from a large number of individual’s group attribute]

Uncertainty Principle Again.

2. The object can be a large object, eg say something whose picture you are taking. But as explained above its not the energy of the object (or momentum) which is directly coming into the problem. That would be an added degree of concern if the object is moving with certain velocity, a reason why pictures are blurred. Because motion of objects introduces additional energy-time-momentum-position variables and their corresponding uncertainties. For the argument of the above problem one can imagine the large sized object, lets say a bird, is standing still on a tree while its picture is being taken. In that case if the wavelength of the light [few 100 nano meters = 1/10th of a micrometer] is used (eg in a digital-camera) the corresponding accuracy of the light will be less than micrometers. You can take a very sharp picture of the bird, which is lets say 6 inch long. But when you zoom in to a large degree, the inaccuracies will show up. [in this case how to see a micrometer level image? Is a computer sufficient to show us the uncertain edges of the pixels?] If the wavelength (here visible light) is so small, evidently by de-Broglie relationship, momentum or energy of such light is very large. But its not as large to disturb the feelings of the bird. The bird doesn’t have a problem with visible light, and such energy does not disturb its position or energy or any thing so to say. So while Quantum Mechanics is valid, we are accustomed to say this is a classical mechanics situation. To say QM is invalid is incorrect. To say QM is understood to be valid is a knowledgeable position.

What are Gauge Potential, Whats a “Theory” in Physics?

Potential was, as said above, is, energy per unit mass or charge. So, we see that, in defining the higher quantity energy or potential (higher therefore closer to action, hence more fundamental or unified) we have to INTEGRATE the lower variable, here, Force, Field or (Any ) 3-vector. This entails therefore arbitrariness into the Physical solution when we solve for these quantities. These physical problems, as they involve differentials or integration, leads to a differential equation. Under further suitable physical conditions called eg laws of nature or physics, become whats called a wave-equation or for particles, equation of motion. We can say equation of motion for particles or equation of motion for waves if they are separate.

Now that we understand what are potential, field, vector and gradient and integral in relation to each other, comes requirements called as symmetry or laws of nature or laws of physics or in simple, boundary conditions to these differential equations known as, wave equation or equation of motion of particles OR waves. ( — which are separate so far )

These equations constrained by the conditions or restrictions which are attributes of physical observation, must therefore unite these variables (potential, field) into one entity which would satisfy the wave or particle equations of motion, the differential equations of motion in PARTICULAR ways only, known as Laws of Nature or Physics. So they become, from their 3-vector or scalar attributes, 4-vectors (or still higher, Tensors).

Still some gravity !!

So talking about gravity fondly I have made a remark “Its not gravity that makes you fall”. You would be shocked as if you fell down but its not due to gravity but something else is at work, Am I a Physicist propounding a phantom theory? The actual statement I made is “Its not gravity that makes you fall, it only makes you fall FASTER”. That was known to Galileo, which we often very conveniently forget and make an erroneous statement that things fall because of Gravity. So it caters to the law of inertia also. So satellites would still fall irrespective of the absence or presence of Gravity. (although the inertia would mean they would be at absolute rest if we do not take into account enough of its past when something had hit it harder to slow it down or sped it up, in any case when enough history has been allowed to see that no forces or extra actions were disturbing its inertia, IT MUST BE MOVING AT UNIFORM MOTION without any debt to a force-bank called Gravity. If Gravity isn’t there the inertia is still the same and it would continue to be moving at the same speed, which as a specific possibility be ZERO)

So apart from the fact that Gravity only causes us to fall faster its also an erroneous fact to say: Gravity is caused by Masses. Or its innocuous looking twin-statement masses attract masses and thats called Gravity. It has two basic history why its often thought or said so. 1. History of how theory of Gravity developed. 2. History of how Gravity was taught.