Your mathematical representation of mass m0 in the equation {m = m0/√(1 − v2/c2)}, when v = c, is an incorrect approach in mathematics and also in special relativity.
The reason is that the equation, which you mentioned in your paper, does not apply when you consider a speed v = c.
Also, at a speed (c), m0 is no longer mass.
When the momentum of such a massless photon needs to be evaluated by the equation
- p = h/λ,
where λ is the photon wavelength, p (roh) is the photon momentum and h is Planck's constant.
Such a massless photon would have energy
- E = hf,
- since, f = c/λ; E = hc/λ, p = h/λ
- Therefore, E = pc
The equation you chose to calculate the mass m0 at speed v = c is an incorrect application.
Please note, the time dilation equation (due to motion) is also an incorrect application, because the speed v and c used in the time dilation equation, should not modify the proper time (t), unless intentionally inviting error in the calculation.
The part of the equation √(1 - v²/c²) in {t' = t/√(1 − v2/c2)} should not modify the proper time (t), to get the dilated time (t'), because the proper time t should not be interfered by some external effect, such as speed (v), unless one invites intentional error in calculations.
Regarding the last comment above, this paper is noteworthy
Preprint Relativistic effects on phaseshift in frequencies invalidate...
Relative mass is the mass assigned to a body in motion:
Relativistic mass is also invariant mass, just as the relativistic energy of a single particle is equal to its rest energy as seen from its rest frame.
Relative velocity is the motion of an object relative to an observer, as described by the theory of relativity. Basically, special relativity explains the relationship between space, time, mass and energy in speed or velocity but does not include gravity. Therefore, relative speed or velocity is relevant in special relativity.
Relative speed:
Refers to the speed at which relativistic effects become significant for the desired accuracy of measurement of the observed phenomenon. Time dilation, in special relativity, is the difference in elapsed time measured by two clocks due to a relative velocity between them.
Note that Time distortion occurs only in clocks with mass under relativistic effects, not in electromagnetic waves, where electromagnetic waves move at the speed (c). Therefore, at the speed (c) there will be no clock to measure the time for massless photon. Refer here -
Chapter Time distortion occurs only in clocks with mass under relativistic ...
Necessarily such relative velocities, in special relativity, are less than the speed of light (c). However, at the speed of light (c), there will be no time dilation, because electromagnetic waves traveling at the speed of (c) do not have time dilation, but there is a propagation delay in (c).
Also, in (c) motion there will be no clock to measure relative time.
From the relativistic mass equation, it can be seen that as the object accelerates faster and faster, its mass becomes larger and larger. However, consider that such mass must be between and less than the speed of light (c), because at speed (c) there would be no clock to measure relative time. But (c) has propagation delay.
Therefore, your mathematical representation of the mass m0 in the equation {m = m0/√(1 − v2/c2)}, when v = c, is an incorrect approach in mathematics and also in special relativity.
The reason is that the equation, which you mentioned in your paper, does not apply when you consider a speed v = c.
Also, at a speed (c), m0 is no longer mass, but energy.
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