{"id":12944,"date":"2016-11-24T10:44:24","date_gmt":"2016-11-24T18:44:24","guid":{"rendered":"http:\/\/www.preposterousuniverse.com\/blog\/?p=12944"},"modified":"2016-11-24T10:44:24","modified_gmt":"2016-11-24T18:44:24","slug":"thanksgiving-11","status":"publish","type":"post","link":"https:\/\/preposterousuniverse.com\/blog\/2016\/11\/24\/thanksgiving-11\/","title":{"rendered":"Thanksgiving"},"content":{"rendered":"

This year we give thanks for a feature of the physical world that many people grumble about rather than celebrating, but is undeniably central to how Nature works at a deep level: the speed of light<\/a>. (We’ve previously given thanks for the Standard Model Lagrangian<\/a>, Hubble’s Law<\/a>, the Spin-Statistics Theorem<\/a>, conservation of momentum<\/a>, effective field theory<\/a>, the error bar<\/a>, gauge symmetry<\/a>, Landauer’s Principle<\/a>, the Fourier Transform<\/a> and Riemannian Geometry<\/a>.)<\/p>\n

The speed of light in vacuum, traditionally denoted by c<\/em>, is 299,792,458 meters per second. It’s exactly that, not just approximately; it turns out to be easier to measure intervals of time to very high precision than it is to measure distances in space, so we measure the length of a second experimentally, then define<\/em> the meter to be “the distance that light travels 299,792,458 of in one second.” Personally I prefer to characterize c<\/em> as “one light-year per year”; that’s equally exact, and it’s easier to remember all the significant figures that way.<\/p>\n

There are a few great things about the speed of light. One is that it’s a fixed, universal constant, as measured by inertial (unaccelerating) observers, in vacuum (empty space). Of course light can slow down if it propagates through a medium, but that’s hardly surprising. The other great thing is that it’s an upper limit; physical particles, as far as we know in the real world, always move at speeds less than or equal to c<\/em>.<\/p>\n

That first fact, the universal constancy of c<\/em>, is the startling feature that set Einstein on the road to figuring out relativity. It’s a crazy claim at first glance: if two people are moving relative to each other (maybe because one is in a moving car and one is standing on the sidewalk) and they measure the speed of a third object (like a plane passing overhead) relative to themselves, of course they will get different answers. But not with light. I can be zipping past you at 99% of c<\/em>, directly at an oncoming light beam, and both you and I will measure it to be moving at the same speed. That’s only sensible if something is wonky about our conventional pre-relativity notions of space and time, which is what Einstein eventually figured out. It was his former teacher Minkowski who realized the real implication is that we should think of the world as a single four-dimensional spacetime<\/a>; Einstein initially scoffed at the idea as typically useless mathematical puffery, but of course it turned out to be central in his eventual development of general relativity (which explains gravity by allowing spacetime to be curved).<\/p>\n

Because the speed of light is universal, when we draw pictures of spacetime we can indicate the possible paths light can take through any point, in a way that will be agreed upon by all observers. Orienting time vertically and space horizontally, the result is the set of light cones — the pictorial way of indicating the universal speed-of-light limit on our motion through the universe. Moving slower than light means moving “upward through your light cones,” and that’s what all massive objects are constrained to do. (When you’ve really internalized the lessons of relativity, deep in your bones, you understand that spacetime diagrams should only indicate light cones, not subjective human constructs like “space” and “time.”)<\/p>\n

\"Light<\/a><\/p>\n

The fact that the speed of light is such an insuperable barrier to the speed of travel is something that really bugs people. On everyday-life scales, c<\/em> is incredibly fast; but once we start contemplating astrophysical distances, suddenly it seems maddeningly slow. It takes just over a second for light to travel from the Earth to the Moon; eight minutes to get to the Sun; over five hours to get to Pluto; four years to get to the nearest star; twenty-six thousand years to get to the galactic center; and two and a half million years to get to the Andromeda galaxy. That’s why almost all good space-opera science fiction takes the easy way out and imagines faster-than-light travel. (In the real world, we won’t ever travel faster than light, but that won’t stop us from reaching the stars; it’s much more feasible to imagine extending human lifespans by many orders of magnitude, or making cryogenic storage feasible. Not easy — but not against the laws of physics, either.)<\/p>\n

It’s understandable, therefore, that we sometimes get excited by breathless news reports about faster-than-light signals<\/a>, though they always eventually disappear. But I think we should do better than just be grumpy about the finite speed of light. Like it or not, it’s an absolutely crucial part of the nature of reality. It didn’t have to be, in the sense of all possible worlds; the Newtonian universe is a relatively sensible set of laws of physics, in which there is no speed-of-light barrier at all.<\/p>\n

That would be a very different world indeed. In Newton’s cosmos, when a planet moves around the Sun, its (admittedly feeble) gravitational field changes instantly<\/em> throughout all of space. In principle, in pre-relativistic laws of physics it would be possible to imagine communication or transportation devices that took you from here to billions of light years away, in as short a time as you can imagine. <\/p>\n

That seems like fun, but think about what you’re giving up. The speed of light enforces what physicists think of as locality<\/a><\/em> — what happens at one point in spacetime influences what happens nearby in spacetime, and those influences gradually spread out. A universe without without the speed of light would be one that allowed for non-local influences; one where different parts of space weren’t safely separated from one another, but were potentially connected in dramatic ways. That would be convenient for some purposes — but so utterly different from the real world that it’s hard to think through all of the consequences consistently. <\/p>\n

As soon as someone figures out that the speed of light is constant, it’s not hard to guess that someone else is going to suggest that maybe it’s secretly variable. Indeed, there has been a decent amount of investigation into what are called “variable speed-of-light”<\/a> theories. Whether the idea is even sensible is somewhat a matter of taste. To many people, it’s best to think of the speed of light as something that simply can’t<\/em> vary, even in principle: it’s always exactly one light-year per year. To even contemplate a varying c<\/em>, you have to tell me that it’s varying with respect to something<\/em> — and there aren’t any other universal speeds to compare it to.<\/p>\n

What you mean by “varying speed of light” is that the number of meters that light travels in a second is different from place to place or time to time. Which means that you need some other objective notion of a “meter” and a “second,” or some alternative ways of separately measuring distance and time. Which is certainly possible — you can choose to measure c<\/em> in units of “the number of Compton wavelengths of an electron that light travels in the time it takes a certain atomic transition to take place,” and that’s a quantity that could conceivably change from place to place in the universe. The problem with that is that you could choose any one of various different such systems of units, and generically the speed of light would change in different ways in each one. The whole game of varying-c<\/em> theories, then, is to find ways that the real dimensionless constants of nature (like the strengths of the fundamental forces, or ratios of particle masses) could change in perfect harmony such as to give you the impression that what’s really changing is c<\/em>. That’s a game that can certainly be played, but it’s not clear why nature would find it a worthwhile pastime.<\/p>\n

What matters is not that light<\/em> travels at a certain speed — it’s that the universe has an ultimate upper speed limit. It just so happens that massless particles, like photons and gravitons, travel at that speed. But even in a world without any massless particles, there would still be a speed limit. We wouldn’t call it the “speed of light” in such a world, but something else, like the “Einstein speed” or some such. We live in a world where it inevitably takes time for signals to travel from one place to another, and I for one am thankful for it.<\/p>\n","protected":false},"excerpt":{"rendered":"

This year we give thanks for a feature of the physical world that many people grumble about rather than celebrating, but is undeniably central to how Nature works at a deep level: the speed of light. (We’ve previously given thanks for the Standard Model Lagrangian, Hubble’s Law, the Spin-Statistics Theorem, conservation of momentum, effective field […]<\/p>\n","protected":false},"author":4,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[28],"tags":[],"class_list":["post-12944","post","type-post","status-publish","format-standard","hentry","category-science"],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/preposterousuniverse.com\/blog\/wp-json\/wp\/v2\/posts\/12944","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/preposterousuniverse.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/preposterousuniverse.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/preposterousuniverse.com\/blog\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/preposterousuniverse.com\/blog\/wp-json\/wp\/v2\/comments?post=12944"}],"version-history":[{"count":4,"href":"https:\/\/preposterousuniverse.com\/blog\/wp-json\/wp\/v2\/posts\/12944\/revisions"}],"predecessor-version":[{"id":12951,"href":"https:\/\/preposterousuniverse.com\/blog\/wp-json\/wp\/v2\/posts\/12944\/revisions\/12951"}],"wp:attachment":[{"href":"https:\/\/preposterousuniverse.com\/blog\/wp-json\/wp\/v2\/media?parent=12944"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/preposterousuniverse.com\/blog\/wp-json\/wp\/v2\/categories?post=12944"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/preposterousuniverse.com\/blog\/wp-json\/wp\/v2\/tags?post=12944"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}