Smallest Measure in Universe
Date: Fall 2013
What is The smallest piece of something we can measure in the universe?
Here is a web page that summarizes the types of microscopes and their characteristics:
Please note on the far right of the table, the "Transmission Electron Microscope"
This article: http://en.wikipedia.org/wiki/Transmission_electron_microscopy
says "TEMs are capable of imaging at a significantly higher resolution than light microscopes, owing to the small de Broglie wavelength of electrons. This enables the instrument's user to examine fine detail—even as small as a single column of atoms, which is thousands of times smaller than the smallest resolvable object in a light microscope."
and it shows an image at a resolution of 30 nano-meters (30 x 10-9 meters).
But further down in the article, under the section titled "Resolution Limits" it says that a theoretical cutoff value for TEM microscopes might be 42 pico-meters (30 x 10-9 meters) but the most recent advance has only been down to 50 pico-meters.
This is not a measure of the accuracy and resolution of the measurement, but rather a question about the limits of the quantum mechanical behavior of the Universe. You can find it discussed in the citation: http://en.wikipedia.org/wiki/Planck_units . It would seem that the smallest length, given the current state of theoretical physics is the Planck length, which is: 1.616199(97) x 10^-35 meters. The reference above gives the lower limits of other physical parameters. These are based on the best known values of other measurable physical constants. I am not sure what these ?limits? really mean, but they make for interesting reading.
According to our current understanding of the laws of Nature, based on quantum mechanics the smallest length that could, but has not yet been, measured is the Planck length. The Planck length is 1.616 x 10^-35 meters.
Pretty small, but it depends upon what it is you are measuring. For example, we can measure things at an atomic level using electron microscopes, and we can measure the wavelength of light and other electromagnetic radiation using electronic measurement instruments.
The fact seems to be that our ability to measure really small things is determined in large part by the need to do it, and we keep thinking of new ways to measure ever smaller dimensions. There is, however, a theoretical limit to how small a distance it's possible to measure.
An old mental exercise along the same lines asks, if a person standing in front of a wall begins taking steps, each step halving the distance between the person and the wall, does the person ever touch the wall? Reasoning tells you that if it were possible to do this, then no, the person could always halve the distance one more time, and would never reach the wall.
But it turns out that physicists have defined a smallest measurable distance known as the Planck length, and it's defined as 1.616199(97)×10 35 meters. This comes from a formula that includes the speed of light in a vacuum, Planck's constant, and the gravitational constant. It is about 10 20 smaller that the diameter of a proton, so it is extremely small. It is a theoretical value representing what is currently believed to be the shortest measurable length, and no improvement in instruments could ever change that.
To visualize the size, think of making a 0.1mm dot on a piece of paper. (0.1mm is about the smallest distance the human eye can discern.) On a chart with a logarithmic scale, the Planck length on the left side and the size of the universe on the right, your dot would be about in the middle.
Keep in mind that the Planck length is a theoretical value and has yet, as far as I know, to be proven. Its applicability runs throughout physics and is part of the theory of everything. Most of what I have had to say about it came from Wikipedia, where much more on this topic can be found.
To call yours a good question hardly seems to do it justice, since it may indicate an intuitive grasp of the fundamental elements of our existence. We will be looking forward to the possibility of hearing about your work in years to come.
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Update: November 2011