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shivaniits
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if possible could you tag some good video lectures may be feymann or any other good source..thanks...!!
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so can we say this conversion of E=mc^2 doesn't happen at allIn special relativity, time is just another dimension, just like spatial distance. The numerical value of the speed of light is a proportionality factor between time and length units. This identification causes a series of other identifications.
Speed becomes an angle between the time directions between two moving reference frames. This also nicely explains Lorentz transformations and relativistic speed composition.
Mass, momentum and energy are also identified. The proportionality factors between the standard units of these parameters are: momentum is mass times c and energy is mass times c squared. That's all.
Electric and magnetic potentials also undergo an unification into electromagnetic potential.
This is the basic idea of the special relativity. We live in a 4D space. Our common 3D physical properties turn out to be spatial or time-like components of 4-dimensional properties. Time and space are the same, but our standard unit system (say SI system) has different units for them. When we want to convert from time to space, we need to multiply the numerical value of the property by some proportionality factor, which is always some power of c, depending on the dimesionality of our property.
so can we say this conversion of E=mc^2 doesn't happen at all
because it what we perceive from different reference frames due to account of special relativity
and we can't say that
actually a some lump let say of m mass is vanishing(or more precisely should i say converting to energy)... doesn't really happen whatever we measure is due to special relativity effect!!
Prove? This is like asking someone to prove Quantum Mechanics. Mathematically, there are a ridiculous number of consistent theories, so all we can do is fail to disprove it.
You speak about converting rest mass to kinetic energy. This is indeed a physical process.Pair production converts photons to electron-positron pairs. Nuclear fission or nuclear fusion convert mass to energy.
OP was refering to total mass and total energy as I understand. These quantities never change for an isolated system and are always proportional to each other with a factor c^2.
It is, in all known theories. In QM for example, it comes from Noether theorem and the trivial fact that Hamiltonian commutes with itself.It's also not true that total mass is separately conserved.
It is.Mass isn't even additive.
No, they don't. They have zero rest mass, but nonzero total mass. It is a great mistake to confuse those two different quantities.E.g., in Einstein's 1905 paper, the body that emitted the two light rays in opposite direction lost an amount of mass L/c^{2}. Each light ray has zero mass.
You don't need a box for the inertia to be the same. The inertia (total mass) of the system will be equal to the sum of the total masses of each particle.The sum of the masses has been reduced by L/c^{2}. However, if you put the whole system, in its final state, inside a box, its inertia is the same as that of the original system, and unequal to the sum of the three masses.
Total mass is conserved. Total energy is conserved and equal to the total mass with a factor c^2. Rest mass is not conserved. Kinetic energy is not conserved. Potential energy is not conserved. Rest mass (times c^2), kinetic energy and potential energy summed up together give total energy.What's conserved isn't mass or energy separately but mass-energy.
Utter nonsense! Pair production converts photons to electron-positron pairs. Nuclear fission or nuclear fusion convert mass to energy.
I am aware, and that is why I always give the proper adjective here (rest, kinetic, potential, total).haael, it seems you are not aware of the convention used by almost all physicists nowadays that the term "mass" on its own is taken to mean "rest mass". The version of mass you are talking about is nowadays called "energy" (divided by c^{2}).
It's also not true that total mass is separately conserved. Mass isn't even additive.
Rest mass is not conserved. Consider an electron and a position annihilating into two photons. Before the annihilation, the rest mass is two times rest mass of an electron. After the annihilation, the rest mass of the system is zero.Classical inertial mass as defined by p=m·a is additive, the rest mass is not and both are conserved in isolated systems. Conversion of mass into energy or vice versa would violate this conservation as well as the conservation of energy.
Rest mass is not conserved. Consider an electron and a position annihilating into two photons. Before the annihilation, the rest mass is two times rest mass of an electron. After the annihilation, the rest mass of the system is zero.
However, the total mass of the system is conserved and is the same before and after the annihilation.
Roughly speaking: rest mass, plus kinetic mass, plus potential mass. Equivalent definition: rest energy, plus kinetic energy, plus potential energy, divided by c^2.What is your definition for the "total mass"?
Roughly speaking: rest mass, plus kinetic mass, plus potential mass. Equivalent definition: rest energy, plus kinetic energy, plus potential energy, divided by c^2.
Now, what it means to be conserved? Imagine a 4D spacetime with some process happening in it. Suppose we have an inertial frame. Take one moment (a space-like surface). Compute some quantity. Take some other moment. Is the quantity the same?
Rest mass is not conserved.
Actually the real problem here is that there's no universally agreed language for explaining this. "Conservation of (rest) mass" could be interpreted in one of two ways:I am amazed how poorly this topic is understood.
Actually the real problem here is that there's no universally agreed language for explaining this. "Conservation of (rest) mass" could be interpreted in one of two ways:
- Conservation of the sum of the rest masses of the particles of a system. This is not true.
[...]
This is an Youtube video made by a physicist. It is made with simple drawing and it is easily understandable.
Can we say mass of the ball is increased by 2.22x10^{-15} Kg.
In another words, mass of the moving ball is 1+2.22x10^{-15}Kg, and it will act like a ball of mass 1+2.22x10^{-15}Kg.
The classical inertial mass is increased but the rest mass remains unchanged.
Yes to all of the above*. However, there is more than one definition of mass in relativity, and this version ("relativistic mass") is a version most physicists don't like to use any more. They prefer to work in terms of rest mass only (so they usually call rest mass just "mass") and they use equations involving rest mass and not relativistic mass.Here is a dumb thought.
Say, I have a ball in my hand of mass 1 kg.
I throw it with speed 20 m/s.
Its kinetic energy is 200 J. Mass equivalent of this energy is
2.22×10^{-15} kg.
Can we say mass of the ball is increased by 2.22×10^{-15} kg?
In another words, mass of the moving ball is 1+2.22×10^{-15} kg, and it will act like a ball of mass 1+2.22×10^{-15} kg.
Is this the mass increase we see in special relativity caused by speed?
How do you define "classical inertial mass"?
Yes to all of the above*. However, there is more than one definition of mass in relativity, and this version ("relativistic mass") is a version most physicists don't like to use any more. They prefer to work in terms of rest mass only (so they usually call rest mass just "mass") and they use equations involving rest mass and not relativistic mass.
Define "act like"! DrStupid
You just need to argue in terms of energy instead of mass. As I hinted in the tiny footnote to my last post, the correct relativistic formula for kinetic energy isn't [itex]\tfrac{1}{2}mv^2[/itex], it is really[tex]Then we have an interpretation problem with special relativity.
Usually we say, 'one reason speed faster than light is not possible is mass of the
object will become so high it would require all energy of the universe to move'.
This statement then is not correct. The actual mass the energy would work on
is always the rest mass, increased mass is just its energy.
For example, mass of the moon we use for gravitational pull may not be its rest mass, but rest mass + energy from its motion.
No, nuclear fission does not convert mass into energy.
It releases binding energy of a nucleus.
To me so far, E=mc^{2} is a conversion factor.
Conversion of Kg into Joules.