Julian Date: 24591120.16
2020-2021: XX
THE DAILY ASTRONOMER
Tuesday, September 29, 2020
Remote Planetarium 98: Special Relativity II - Matter and Energy
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Correction.
My sincerest apologies.
In yesterday's article, I wrote the following sentence:
Accelerate up to 99.9999% light speed and a stationary observer will experience about TWO YEARS for every since you experience.
Yes, a word is missing. The sentence should have read:
"Accelerate up to 99.9999% light speed and a stationary observer will experience about TWO YEARS for every DAY you experience. "
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We begin today by reiterating the fundamental postulate of Special Relativity:
The speed of light is constant in all inertial reference frames.
This single premise revolutionized physics for it became the basis of the Special Theory of Relativity. That theory united space and time which, in Newtonian mechanics, had been regarded as separate aspects of physical reality. Yesterday we focused on Special Relativity's most shocking ramification: time dilation. Time literally dilates within a vessel as it moves. The higher the velocity, the greater the time dilation. The graph below relates a vessel's speed with the corresponding time dilation amount.
[Note: the Time Dilation number is a ratio. For instance, at the value 2.0, a stationary observer experiences twice as much time as the observer within a moving vessel.]
One can see that time dilation is negligible for vessels moving at less than half the speed of light (0.5), but quickly becomes more significant as the vessel accelerates to much higher velocities. The limit is light speed, itself, which is the highest attainable velocity in a vacuum. If a vessel were able to attain light speed, time within it would actually stop.
The problem with vessels moving at such high speeds is mass increase, another effect of Special Relativity. The higher the velocity, the greater the increase in the object's "inertial mass," defined as the object's resistance to changes in its motion. The faster an object moves, the greater its kinetic energy and also its inertial mass. The graph below shows us the relation between the object speed and the mass increase ratio. [Note:A mass of "2" indicates that the relativistic mass has increased to twice the resting mass.]
The faster the vessel, the more massive it becomes. As the craft becomes more massive, more energy is required to accelerate it to higher velocities. If the vessel were able to attain light speed, it would become infinitely massive: an impossibility. Photons can move at light speed because they have no rest mass.
The problem with warp. The USS Enterprise's superluminal velocity capability enables it to traverse vast interstellar distances in brief time periods. Science fiction writers have wisely endowed spacecraft with the ability to exceed light speed so as to move the plots rapidly along. However, Special Relativity forbids any massive object from attaining such speeds due to the effect of mass increase with increasing velocity.
This relation leads us naturally into the final part of today's lesson: the matter-energy equivalence.
The most famous physics equation of them all, except, perhaps F = ma. This equation relates energy (E) to mass (m) and the speed of light (c) squared. (Or c x c.) One should note that c was chosen to represent light because, as we all now know, light speed is constant in all inertial reference frames. This equation tells us that matter and energy are equivalent. Matter is merely crystallized energy. Recall our discussion pertaining to thermonuclear fusion within stellar cores. Some of the matter involved in these processes is converted directly into energy, which powers the stars. Although a minuscule amount of matter (less than one percent) experiences this transmutation, it is sufficient to sustain a star for millions, billions or, in the case of red dwarf stars, trillions of years.
Special Relativity enabled astronomers to finally identify the stellar energy generation method: fusion, or the transmutation of matter into energy.
Tomorrow, we conclude the three part series about Special Relativity with "Light speed and length contraction."
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