21 grams to 70 kg

  • 21 grams is the total mass of electrons that make up a 70kg body
  • This e mass comes from Higgs Mechanism ie as the electrons are moving in space time (as localized variation in electron field), they interact with the Higgs Field, which slows them down from travelling at speed of light and hence gives them mass
  • So Most of the mass of body doesn’t come from Higgs Field. It comes from Protons and Neutrons.
  • Protons and Neutrons are made of Quarks and though the quarks too interact with the Higgs field, that gives them only 1% of their mass. The rest comes from the Potential Energy of these quarks which they derive from their interactions in the Gluon Field using the Strong Nuclear Force. Remember m = E / c2

History of Quantum Mechanics

 

  • Started in 1920s with Schrodinger’s Equation that explained why electrons have only certain/discrete/QUANTIZED energies and positions when the circle the atom
  • Mass Charge Position and Energy were proved to be Quantized ie have discrete values only
  • Schrodinger’s Equation did not take into account:
    • Relativity
    • Discrete Electrical field of atom. (instead it used classical smooth/continuous representation of electric field)
  • These above shortcomings were completed by Paul Dirac
    • He merged Special Relativity with QM
    • He also found Quantum formulation of electric field
  • This is called “Second Quantization revolution”
  • Over the yrs, all other forces like strong and weak nuclear force, electromagnetism are merged with QM
  • The QM of all these fields/forces is together known as Quantum Field Theory
  • In Modern QFT Physics:
    • all subatomic particles can be seen as localized vibrations in the field and that all fields are all pervasive ie everywhere
    • So the movement of an electron is simply the wave of vibration in the electron
    • If this electron emits a photon, some of the energy of the electron field sets up a localized vibration of a photon field which then moves away

Space Time

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  • Time (sequence of events) and space (distance) are different for observers in different frames
  • A good starting point for objective reality is Causality ie space-time interval (SI) between events. This will be the same for all observers in all frames of reference observing the same event. SI = (Square of Distance b/w events) – square of(speed of light times the time b/w events)
    • +ve SI means event A has influenced/caused B
  •  Space-Time is a 4D Non Euclidean Mathematical Space that’s just there and points in which correspond to events, instead of the previous belief that Universe is 3D space growing with time
  • Events that have geometric relations in this 4D space-time (ST) are the only objectively real events.
  • So your life from birth to death is a line segment on the FLAT 4D ST. So your future is not only predetermined, it already exists
  • A future event is simply “The next Causally connected point of ST”
  • Mass of an atom is more than just the sum of masses of it’s constituent atoms. For instance, the mass of a working clock is more than that of a stopped one. Why? Running clock has more:
    • Kinetic and Potential Energy
    • Heat Energy (due to friction b/w moving parts)
  • This extra mass of the running clock = Total Energy (from above) / square of c
  • The mass of Sun drops 4 billion kg/sec coz it shines ie gives off energy
  • Hot tea has more mass than cold tea
  • Also, all atoms in the periodic table weigh less than the sum of their parts (constituents). This is coz their potential energy is negative (potential energy of 2 electrons at infinite distance is 0, so for electrons in atom, PE is always -ve) and though they have +ve KE by virtue of the spin, the net is -ve. Hence for all atoms, Mextra =  Additional Mass dut to Energy of substance = E/c2 < 0
  • Same is true for Molecules as the energy of bond is -ve
  • But, the mass of Protons and Electrons, that are made of Quarks is 2k to 3k times the mass of constituent quarks. This is due to Quark Potential Energy that it derives from Interaction with the :
    • 1% mass from Higgs Field
    • 99% mass from Gluon Field (that they themselves produce, like electron produces electric field)
  • Mass is basically not fundamental. It’s just a property that energy exhibits.
  • Mass is just an indicator of the amount of energy
  • Read:
  • In Inertial FOR (Frame Of Ref), F = ma
  • But in Accelerating FOR, that’s not true. In Fact for a person inside acc FOR like accelerating train, there appears to be an acc of outside things outside the train. This can be thought of as artificial gravity in the opposite direction. THis is also explained here.
  • So basically Gravity and Accelerated FOR is the same thing.
  • There is no way to distinguish b/w a free fall and lack of gravity. This is called the Equivalence Principle. So falling frames are inertial. So the gravity that we feel can be seen as a consequence of being in an accelerated FOR

 

  • Einstein preoved that Gravity is not a Force, but a consequence of SpaceTime curvature
  • In General Relativity (GR) objects that seem to fall (apple to ground) or Orbit (Earth orbiting sun) aren’t being pulled by any Force. They’re simply following strainght line constant speed path in curved straight line
  • What is Straight Line: A curve is straight when tangent vectors stay tangent, when parallel transported to along the curve
  • Curvature is similarly defined as the change in vector when it is parallel transported from A to B. If vector direction remains same, curve is flat else its Not.