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A physics meme is circulating on the Interwebs, suggesting that any length shorter than the so-called Planck length makes “no physical sense”.<\/p>\nA physics meme is circulating on the Interwebs, suggesting that any length shorter than the so-called Planck length makes “no physical sense”.<\/p>\n
Which, of course, is pure nonsense.<\/p>\n
The Planck length is formed using the three most fundamental constants in physics: the speed of light, \\(c = 3\\times 10^8~{\\rm m}\/{\\rm s}\\); the gravitational constant, \\(G = 6.67\\times 10^{-11}~{\\rm m}^3\/{\\rm kg}\\cdot{\\rm s}^2\\); and the reduced Planck constant, \\(\\hbar = h\/2\\pi = 1.05\\times 10^{-34}~{\\rm m}^2{\\rm kg}\/{\\rm s}\\).<\/p>\n
Of these, the speed of light just relates two human-defined units: the unit of length and the unit of time. Nothing prevents us from using units in which \\(c = 1\\); for instance, we could use the second as our unit of time, and the light-second (\\(= 300,000~{\\rm km}\\)) as our unit of length. In other words, the expression \\(c = 300,000,000~{\\rm m}\/{\\rm s}\\) is just an instruction to replace every occurrence of the symbol \\({\\rm s}\\) with the quantity \\(300,000,000~{\\rm m}\\).<\/p>\n
If we did this in the definition of \\(G\\), we get a new value: \\(G’ = G\/c^2 = 7.41\\times 10^{-28}~{\\rm m}\/{\\rm kg}\\).<\/p>\n
Splendid, because this reveals that the gravitational constant is also just a relationship between human-defined units: the unit of length vs. the unit of mass. It allows us to replace every occurrence of the symbol \\({\\rm kg}\\) with the quantity \\(7.41\\times 10^{-28}~{\\rm m}\\).<\/p>\n
So let’s do this to the reduced Planck constant: \\(\\hbar’ = \\hbar G\/c^3 = 2.61\\times 10^{-70}~{\\rm m}^2\\). This is not a relationship between two human-defined units. This is a unit of area. Arguably, a natural unit of area. Taking its square root, we get what is called the Planck length: \\(l_P = 1.61\\times 10^{-35}~{\\rm m}\\).<\/p>\n
The meme suggests that a distance less than \\(l_P\\) has no physical meaning.<\/p>\n
But then, take two gamma rays, with almost identical energies, differing in wavelength by one Planck length, or about \\(10^{-35}~{\\rm m}\\).<\/p>\n
Suppose these gamma rays originate from a spacecraft one astronomical unit (AU), or about \\(1.5\\times 10^{11}~{\\rm m}\\) from the Earth.<\/p>\n
The wavelength of a modest, \\(1~{\\rm MeV}\\) gamma ray is about \\(1.2\\times 10^{-12}~{\\rm m}\\).<\/p>\n
The number of full waves that fit in a distance of \\(1.5\\times 10^{11}~{\\rm m}\\) is, therefore, is about \\(1.25\\times 10^{23}\\) waves.<\/p>\n
A difference of \\(10^{-35}~{\\rm m}\\), or one Planck length, in wavelength adds up to a difference of \\(1.25\\times 10^{-12}~{\\rm m}\\) over the \\(1~{\\rm AU}\\) distance, or more than one full wavelength of our gamma ray.<\/p>\n
In other words, a difference of less than one Planck length in wavelength between two gamma rays is quite easily measurable in principle.<\/p>\n
In practice, of course we’d need stable gamma ray lasers placed on interplanetary spacecraft and a sufficiently sensitive gamma ray interferometer, but nothing in principle prevents us from carrying out such a measurement, and all the energy, distance, and time scales involved are well within accessible limits at present day technology.<\/p>\n
And if we used much stronger gamma rays, say at the energy level of the LHC (which is several million times more powerful), a distance of only a few thousand kilometers would be sufficient to detect the interference.<\/p>\n
So please don’t tell me that a distance less than one Planck length has no physical meaning.<\/p>\n A physics meme is circulating on the Interwebs, suggesting that any length shorter than the so-called Planck length makes “no physical sense”. Which, of course, is pure nonsense. The Planck length is formed using the three most fundamental constants in physics: the speed of light, \\(c = 3\\times 10^8~{\\rm m}\/{\\rm s}\\); the gravitational constant, \\(G […]<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"class_list":["post-5872","post","type-post","status-publish","format-standard","hentry","category-physics","category-3-id","post-seq-1","post-parity-odd","meta-position-corners","fix"],"_links":{"self":[{"href":"https:\/\/spinor.info\/weblog\/index.php?rest_route=\/wp\/v2\/posts\/5872","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/spinor.info\/weblog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/spinor.info\/weblog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/spinor.info\/weblog\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/spinor.info\/weblog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=5872"}],"version-history":[{"count":16,"href":"https:\/\/spinor.info\/weblog\/index.php?rest_route=\/wp\/v2\/posts\/5872\/revisions"}],"predecessor-version":[{"id":5889,"href":"https:\/\/spinor.info\/weblog\/index.php?rest_route=\/wp\/v2\/posts\/5872\/revisions\/5889"}],"wp:attachment":[{"href":"https:\/\/spinor.info\/weblog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=5872"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/spinor.info\/weblog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=5872"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/spinor.info\/weblog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=5872"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}