Mass (m) becomes Energy (E) as E = mc^2. But if the speed of light depends on the density of vacuum space (dvs), it would impact the speed like this: 'the speed of photons' / 'the density of space' = 'c^2' / '(dvs)^2'. If we can find the mass density in space like this: 'Mass of space in a Planck volume' / Planck volume, then we can apply the mass density in space ((Mass in Planck space)/ℓp^3) into the E = mc^2 equation to show the connection between the speed of light with the density of space as well. If we write the mass in a Planck volume like this Mps/ℓp^3, we can find the energy like this: E = m(c^2/(Mps/ℓp^3)^2). There are Kg^-1 m^8 s^-2 units in that energy equation. Perhaps the Energy per Kilogram (Kg^-1) unit with m^8 s^-2 units represents the fundamental (quantum) units in energy better than Kg m^2 s^-2 units. c = 299792458 ms^-1, ℓp^3 = 4.2217×10^-105 m^3 E = m(c^2/(Mps/ℓp^3)^2) == mc^2
E = m ((c^2 / (Mps / 4.2217×10^-105)^2) == mc^2
E = m x (c^2 x 4.2217×10^-105)^2) / Mps^2 == mc^2
Mps^2 = (4.2217×10^-105)^2
The current mass of vacuum space in a Planck volume: Mps = 4.2217×10^-105 kg Based on the accelerating expansion of the universe, the calculated mass density of the vacuum is about 6.5±0.5 ×10^-27 kg/m^3. So that vacuum mass/energy of space in a Planck volume == (6.5±0.5 ×10^-27)/(4.2217×10^-105) == 1.54±1 ×10^-132 kg. It is not equal to the above Mps value of 4.2217×10^-105 kg. Perhaps, calculating the mass density of the vacuum space based on the accelerating expansion of the universe doesn't show its real value. Based on that energy equation, the minimum Planck mass in spacetime is the mass density in Planck space. The Planck energy in space: Eps = m ((c^2 / (Mps / 4.2217×10^-105)^2)
Eps = 4.2217×10^-105 x ((89875517873681760 / (4.2217×10^-105 / 4.2217×10^-105)^2)
Eps = 4.2217×10^-105 x 89875517873681760
Eps = 3.794274738×10^-88 Kg^-1 m^8 s^-2
Does the E=mc^2 equation represent all the dimensions in actual quantum energy? Isn't these Kg^-1 m^8 s^-2 units are representing energy better than these Kg m^2 s^-2 units?
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No. It would be a good idea to learn classical electrodynamics and quantum field theory to understand how relativistic quantum systems can and are described in a mathematically consistent way.
It doesn't matter.
If the theory is invariant under Lorentz transformations, the mass of any particle can receive corrections from quantum effects, that describe the interaction of the particle of that mass with other particles, beyond the effects of the classical equations of motion. At any given approximation in which these corrections are calculated, mc^2 is invariant under Lorentz transformations. Quantum effects remain consistent with global Lorentz invariance. The mass of any particle is as Lorentz invariant as the speed of light in vacuum.
For particles, whose mass is constrained by certain symmetries, such as the photon and the gluons, their mass, which is zero at the classical level, due to gauge invariance, remains zero due to the property that invariance under gauge transformations can be imposed in a way that's consistent with how quantum effects are taken into account; so quantum effects don't give rise to a mass for the photon or the gluons.
Stam Nicolis, Vector Space is not the real space. The energy/mass density in space is the bottom layer of quantum nature. This equation E = m(c^2/(Mps/ℓp^3)^2) contains the dimensions/units in the real space too. If there are kg^-1 m^8 s^-2 units in a unit of energy, then there are 11 dimensions (kg^-1 m^8 s^-2: 1+8+2 = 11) in a quantum unit of energy.
The energy/mass in elementary particles/waves is related to their frequency. Perhaps, the mass represents a complex quantum process in frequency. The wave function in the Schrödinger equation is a complex (unexplained) function. And quantum field theory uses complex/imaginary numbers (Eg: √2) to get real solutions. So possibly the most fundamental (super quantum) nature of frequency/energy is based on sets of linear dimensions (linear kg, m, s units).
Classical spacetime defines the speed of light, by the property of global invariance under Lorentz transformations as symmetries of the equations of motion. Quantum spacetime defines the speed of light by the property of global invariance under Lorentz transformations of the correlation functions, that define the measure on the space of configurations of the physical system, that takes into account the quantum fluctuations. Such configurations aren't solutions of the equations of motion. So the space of configurations in this case is much bigger. It turns out that the speed of light defined in both ways is the same, which is another way of saying that quantum effects are compatible with global Lorentz invariance.
Dimensions don't have anything to do with units. It's possible to measure mass in any units (whether in kilograms or Planck units doesn't matter); the mass is an invariant quantity under global Lorentz trasformations. We're talking about spacetime, where particles move and fields evolve.
That energy, under certain circumstances, can only take discrete, not continuous, values is a totally different matter. If one has a finite number of particles, labeled by their rest mass, then mc2 takes a finite number of values. However when these particles move in spacetime, their energy is given by the expression E2=|p|2c2+(mc2)2 and the momentum and, thus, the energy, can take continuous values-indeed if it can't then Lorentz invariance isn't globally defined, since energy and momentum depend on the reference frame and Lorentz transformations are continuous transformations.
Energy-and frequency-isn't a Lorentz invariant quantity. The relation E = mc2 holds in a very particular reference frame. In any other frame, E2-|p|2c2 is the Lorentz invariant quantity, that defines the mass of the particle in any inertial frame-and if this combination vanishes, the particle is massless.
These statements hold whether quantum effects are taken into account, or not.
In the presence of external effects-such as potentials or boundary conditions-it can occur that quantum effects can change the allowed values for the energy and momentum. The most striking example is that of the hydrogen atom, where, classically, the electron can't remain bound to the proton due to electromagnetic radiation that, when quantum effects are taken into account, isn't present. The reason was found by W. Pauli in 1926 and fully explained by V. A. Fock in 1935.
Stam Nicolis, I'm not talking about modern quantum physics. Spacetime is not vectors. There is a mass density (quantum form) in vacuum space. Energy is not only based on the fake space called Vector/Hilbert Space. E^2=|p|^2c^2+(mc^2)^2 equation doesn't work with mass. It only works with massless particles like photons as E=|p|c. So it is not a good equation too. Making another error to fix an error is not a good/intelligent thing. Changing the reference frame and equation is not a good way to justify the problems in those equations. E=mc^2 is not completely wrong, but it is not completely correct too. The unit called Kilogram (Kg) is not a single thing/dimension like distance (m) and time (s). So, If we want to make it a quantum unit, we need an equation to make it a single (linear) dimension. Everything interacts on dimensions of moments (directional moments), whether you accept it or not. I guess you can't understand it using popular quantum mechanics.
I have explained fundamental/original quantum mechanics in my research book: Preprint Verifying The Origin Of Everything
No, vacuum is zero energy density (since particles can be massless and can carry energy, it's energy density, not mass density that's relevant), therefore, no particles-this is unique, when invariance under Lorentz transformations can be globally defined and isn't when they can't, i.e. in curved spacetime (in which case the vacuum isn't uniquely defined and therefore can be observer dependent). Energy doesn't have anything to do, as such, with Hilbert space, which is the space of states of a quantum system. Energy describes the property of physical systems to be invariant under time translations-i.e. in spacetime.
The equation E2=|p|2c2+(mc2)2 contains a parameter, m. It ``works'' whatever the value of m, precisely because it can be proved that the combination E2-|p|2c2 is invariant under global Lorentz transformations and this invariance is relevant for our world. It is this property that allows the definition of mass as a quantity independent of the reference frame and implies that a massless particle in one inertial frame is massless in any other inertial frame.
In the particular frame where p=0, E=mc2 and this frame exists only for massive particles.
All this is the material of physics courses, all over the world, isn't new and, since it doesn't involve Planck's constant, doesn't have anything to do with quantum mechanics. What is interesting is that when quantum effects become relevant, it is possible to describe relativistic effects and quantum effects in a compatible way.
Quantum effects are those where Planck's constant appears and it's not possible to ``make it'' from other constants-it's a new constant, that describes our world. Classical physics corresponds to the limiting case in which angular momenta, or the product of energy and time or the product of momenta and position and so on, that all have the dimensions of Planck's constant, take values much greater than Planck's constant. When combinations that have the dimensions of Planck's constant take values comparable to Planck's constant, quantum effects can't be neglected and classical effects don't make sense. Since Planck's constant is dimensionful, it's possible to choose units such that it takes the value equal to 2π (i.e. hbar=h/(2π)=1). This simplifies many expressions.
This isn't new, either.
Stam Nicolis, E=pc can be applied to particles that DON'T have a rest mass. The standard equation for Kinetic Energy is 'K. E = 1/2 m v^2'. It's NOT E=pc. The Mass disappears in E=pc. The Momentum (p) is related to the Mass. Changing Mass (m) into Momentum (p) shouldn't cause to disappear Mass if the way those equations use Kilogram (Kg) is fundamental. So, the Kg unit in the units of energy (Kg m^2 s^-2) doesn't represent the fundamentally related units of energy. If we count the mass/energy density in the vacuum space, these units Kg^-1 m^8 s^-2 for energy (E) are more fundamental than that.
Thanks for your replies. I don't like to repeat the same arguments. And I'm currently busy with some personal work, and I can't spend more time explaining more about it in detail, like trying to explain something to a baby. So, bye for now.
Hadi Jabbar Alagealy, I'm studying quantum field theory. But I have a better theory. Mathematical Science and Buddhism: Preprint Verifying The Origin Of Everything
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