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It is often said that "everything is in a state of constant vibration". What led to this statement? And can I get any source of this statement that I can cite?

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    $\begingroup$ I can't tell you the historical answer (which does not belong onto this site, to begin with), but the logical argument from basic physics would probably start with the third law of thermodynamics, which states that no physical system can attain a temperature of $T=0K$, which means that some vibrational degrees of freedom are always excited thermally. $\endgroup$ – CuriousOne May 15 '16 at 21:36
  • $\begingroup$ It just occurred to me that I should have been a little more careful with the phrase "always". If we have small pieces of matter then the modes of the phonon spectrum (i.e. the quantized lattice vibrations) will be spaced fairly widely. I am nearly certain that ultra-low temperature experiments can "freeze" at least nano-particles to the point where even the lowest phonon mode is essentially unpopulated, i.e. for all practical purposes the vibration would have stopped. $\endgroup$ – CuriousOne May 15 '16 at 21:51
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    $\begingroup$ It is an ancient idea, the music of the spheres en.wikipedia.org/wiki/Musica_universalis . Maybe, if strings do become the theory of everything, it will be a future one. $\endgroup$ – anna v May 16 '16 at 5:09
  • $\begingroup$ @CuriousOne. It's a pity you did not make these comments of yours an answer, because it would have been a very good one. $\endgroup$ – Stéphane Rollandin May 16 '16 at 9:17
  • $\begingroup$ @StéphaneRollandin: I can't answer the question "What led to this statement?", which I believe is more historic in nature than physical. Even so, I up-voted the question and I hope we can get an answer. I would like to know, too. $\endgroup$ – CuriousOne May 16 '16 at 9:20
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Billy Jean's answer pretty much covers the most likely answer, but I'll answer the less likely one. Everything above Absolute 0, -273.15 degrees Celcius, 0 degrees Kelvin, and -459.67 degrees Fahrenheit, has molecules that are moving around. In fact, temperature is nothing but the average kinetic energy of the molecules. The molecules bounce around faster with hotter objects. This is how conduction heating works: as faster moving molecules bump into slower moving molecules, they make them have higher kinetic energy, heating up the object. Because of temperature, you can say everything above Absolute Zero is vibrating, though "vibrating" is usually used on a much larger scale(usually visible with the naked eye).

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The following would be a very basic look at things being described by string theory. A theory of vibrations.

If you are to zoom with a microscope smaller and smaller, you eventually hit a size that is "too small". This is known as Plank Length, approximately~ 1.616199(97)×10−35 meters. After this size, things smaller, dont really make sense. At this size, it says that there must be strings, that make up the "fabric" of space/time (consider it one entity [ie. x,y,z,w]). It is these strings that are infinitely vibrating, oscillating energy throughout our unobservable universe. These strings, in theory, when vibrating infinitely, create "pockets" during periods of excited energy or from colliding strings. We, our current perception of time, is theorized to be one of these pockets.

Like a rock colliding in water, it ripples. Like that ripple, we are said to be experiencing the ripple of time. And like anything that ripples, it echoes. We are the "echoes" of vibrating strings.

Scientists have in essence been measuring these "ripples" aka vibrations, inversely, from the time of the ancient Sumerians. We have begun from the macroscopic measurement of the universe, arguably mapped by ancient astrology. To Galileo and Newton, measuring the ripples of space, by mapping the solar system and figuring out our rules governing the laws of gravity.

With current particle accelerators and the rate of exponential technological growth and computational processing, we don't have very much longer (in my opinion), before we have a strong grasp and understanding of our quantum critical world. Once we reach this point, I believe we will begin experimenting with larger "quantum" experiments that will give us a better understanding of our origins.

There are hundreds of scholarly articles correlating vibrations to the function of pretty much everything. We can describe almost anything as wave if we break it down. Here is a generic set of results from google scholar correlating wave functions to (X). Feel free to tinker with the keywords and see what things you would like to find correlating to vibrations.

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