Frequency is related to energy (E) as in the Planck's equation E=hv, where v=frequency (Hz) and h=6.626 070 15 x 10-34 J Hz-1 represents relationship between energy and frequency, where 'h' is plank’s constant. And, energy 'E' is equivalent to mass 'm' as in the Einstein's theory of special relativity E=mc².
Therefore, combining these above two equations we get energy-mass (m) is related to frequency of the wave the energy-mass ('f' in Hz or 'v' s–1 in Hz).
frequency 'f' or 'v' of the wave is inversely proportional to the wavelength λ (Lambda), whereas, 'c' and 'h' both are constant in respective equations relevant. --> 'f'∝1/λ or, 'v'∝1/λ
'f' or 'v' of the wave too is inversely proportional to time period 'T' s (second). --> 'f'∝1/T or, 'v'∝1/T
The derived equation from the combination of the above said equations, the frequency (v;f) of mass-energy if somehow gets changed due to the effect of relative gravity or relative speed, then the wavelength (λ) of that mass-energy would also change.
So this would be the main consideration in the following steps.
- The wavelength (λ) of that mass-energy is directly proportional to the time period (T) of the wave. --> λ∝T
In the experiments, it is observed that the time interval for 1° of phase is inversely proportional to the frequency. If the frequency of a wave is given by ‘f’, then the time tdeg (in seconds) corresponding to 1° of phase is
tdeg = 1 / (360f) = T / 360.
Therefore, a 1° phase shift on a 5 MHz wave corresponds to a time shift of 555 picoseconds.
- The maximum frequency of visible light (f)=7.5 x 1014 Hz, its wavelength (λ) = 400 manometer, and its velocity v=c=3 x 1010 cm/s. Einstein's theory of special relativity sets the absolute speed limit at which a wave can travel, which is the speed of light (c) is equal to 3 x 1010 cm/s.
- The maximum frequency of Gamma-rays (f) = 1024 Hz, its wavelength (λ) = <10-12 (i.e., <0.01 nanometres), and its velocity too (v) = 3 x 1010 cm/s.
However, when the frequency (f) of any wave reach infinite (∞), its wavelength must be zero i.e., λ = 0. If wavelength is zero, then as per the scientific understanding, it can't be a wave, as it refers that the wave has no spatial time period or, it is stable at all times.
Similarly, a singularity where gravity approach infinity, space and time cease to exist and current laws of physics cannot be applied. A no-dimensional singularity is considered to be a point form. So a question may arise, "how is it possible that the interaction of no-dimensional singularity occupy anything in three-dimensional space? (E.g. block-hole). Are no-dimensional black holes part of the 3-dimensional Universe?
Moreover, in real sense, a simple mathematical representation of energy (E) would not be possible in that condition, as there is no event or time, absence of light due to absence of stars, even then; energy suddenly can't go vanished but most likely it converted in some other form of energy and behave like vibration - as in the Planck's equation energy (E) is related to frequency.
Whereas, time (t) is indefinite continued progress of existence and events in the past, present, and future, in irreversible progression. It is regarded as an abstract concept, there is increasing evidence that time is conceptualized in the mind in terms of space. That is, instead of thinking about time in a general, abstract way, humans think about time in a spatial way and mentally organize it as such. Using space to think about time allows humans to mentally organize temporal events in a specific way. Therefore, for the time to exist not only existence, either in the form of energy or matter, is necessary, but both existence and events are necessary, as any existence without events, hence without time, would have no real meaning. In absence of time, Planck's equation and the equation of Einstein's theory of special relativity would cease to apply.
Rationally speaking, space too would cease to exist in absence of events, time and also light, moreover, the abstract nature of mathematics very likely to hints us that the energy (E), as in Planck's equation E=hν, likely to prevail as very high vibration frequency, that too without events, time, space and light. A singularity - where gravity approach infinity, space and time cease to exist and current laws of physics cannot be applied.
How energy behaves and what happens to it's frequency in such condition - a mathematical abstraction would probably hints us to conceptualize that frequency of such energy might have achieved infinite value, with the wavelength and it's dimension zero (0), known laws of physics would cease to operate in such condition but we can always conceptualize it though mathematical abstraction.
Note on Time Dilation: What actually happened in the experiment as can be seen in the relationship λ∝T. The experiment actually considered dilated wavelength and not dilated time. If the experiment is considered that it observed dilation of time then it will violate fundamental properties of time. It rather miscalculated T instead of λ, because by appropriately changing either of the value of λ or even the value of T, one will get same result. But the illegality would be considering T as gravity affected factor instead of appropriately considering λ as the gravity affecting factor. A λ can be influence by gravity and change its wavelength but none can change T with the effect of gravity as time is not something changeable by any external influence or interaction unless such changes is in the structure of the events itself, then only time comes into a relative consideration with the changeable events. Time does not participate in any eventual act rather time tracks changes in the events. So a question of changing time is not only absurd but is illegal too as per valid definition and properties of time. Time dilation necessarily needs to be wavelength dilation, when λ∝T comes in to the consideration.
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