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Natural Science Forum / Physics / Relativity / July 2005Light & very small distances - paradox??
Hi, This is my first post to this group. I've always been intrested in phsyics but tonight in particular I just can't sleep because I have a thought that keeps running throught me head. I just read a post about how the speed of time is the same as the speed of light. That seems obvious -- the smallest unit of time would be the time it takes for a photon to travel the shortest possible distance in the universe. But then I thought "how big is the smallest distance in the universe?" I would assume it would be infinitely small, right? It would have to be because if it came in chunks, light would have to travel between the chunks instantly. Well the question becomes "how long does it take a photon to travel an infinetesimally small distance?" It can't be instantly right?? That would be impossible but on the other hand, how can it take any more than zero seconds to travel an infinitely small distance? So if you extend this out to infinity, light jumps between points instantly meaning it will go an infinite distance in zero time??? Tell me what I'm missing - I doubt I'm smart enough to find something every other physisyist in history overlooked. I need some sleep! Thanks, RC > Hi, > This is my first post to this group. Welcome. > I've always been intrested in > phsyics but tonight in particular I just can't sleep because I have a > thought that keeps running throught me head. That is why some are drawn to physics. > I just read a post about how the speed of time is the same as the speed > of light. Hmmmmm. I am not sure what you mean by speed of time. If you can explain it to me then perhaps we determine if it is the same a the speed of light. Could in be you mean the 4 velocity of a stationary particle is the speed of light? > That seems obvious -- the smallest unit of time would be the > time it takes for a photon to travel the shortest possible distance in > the universe. That is what is known as time in plank units http://www.planck.com/ > But then I thought "how big is the smallest distance in > the universe?" I would assume it would be infinitely small, right? It > would have to be because if it came in chunks, light would have to > travel between the chunks instantly. The smallest distances and times are set by natural units - see the link above. > Well the question becomes "how long does it take a photon to travel an > infinetesimally small distance?" It can't be instantly right?? That [quoted text clipped - 5 lines] > Tell me what I'm missing - I doubt I'm smart enough to find something > every other physisyist in history overlooked. I need some sleep! Have a read of the link, think a bit then repost. Have fun. Thanks Bill > Thanks, > RC Dear Rjcflyer: ... > the universe. But then I thought "how big is the smallest > distance in the universe?" Heisenberg's uncertainty principle will not allow this distance to be measured. We can detect/determine the size of composite particles, namely protons and neutrons. Non-composite paticles (electrons, photons, and the like) are point particles, and ever finer attempts to measure their size result in values within the "bin" containing zero. > I would assume it would be infinitely small, right? No. Distance is an illusion that us large beings perceive. The quantum world has neither time nor space, but supports the illusion of the macroscopic world. Think of "population mean" as applied to a single individual. > Well the question becomes "how long does it take a > photon to travel an infinetesimally small distance?" > It can't be instantly right?? Actually, it very well could be. There are "quarter wave effects" (or "quarter wavelength effects") in which the photon is: * detected before it is emitted * detected in much less time than distance / c I know this won't help you sleep. David A. Smith >how long does it take a photon to travel an >infinetesimally small distance?" Perhaps you can view your problem mathematically. v=s/t. If the distance is infinitely small, then the time is infinitely small : t=s/v. If s tends to zero, then t tends to zero. Or, if s is infinitely small, t is 300000000 smaller. >So if you extend this out to infinity, light jumps between points >instantly meaning it will go an infinite distance in zero time??? No, You have t infinitly small being done and infinite number of times. thus t*infinite is not necesarely zero, nor finite nor infinite. It depends on the order of magnitude of the variables. Here all is proportional (or inversely...). This is just a variant of zeno's paradox. Your words are confusing you with the mathematical concepts. "infinitly small" and "instantly" do not mean the same thing. "instantly" means "zero time". Infinitly small" (time interval) means TENDS to zero. Moreover, "infinity" is not a number. You can not apply usual math operations on it. ---- If you want to be sure, then always doubt. }:-) > >how long does it take a photon to travel an > >infinetesimally small distance?" [quoted text clipped - 25 lines] > If you want to be sure, then always doubt. > }:-) Basically when you deal with infinitely small distances Heisenberg's uncertainty principle comes into effect. We cannot only guess what happens in these regions.  SignatureSongs in the 50s were often carefree and happy now the songs on the radio tend to be gloomy and troubled. Observations of Bernard - No 81 > Well the question becomes "how long does it take a photon to travel an > infinetesimally small distance?" You should study calculus. :-) It's all about answering questions like this in a rigorous way. The basic idea is that you start by assuming that there actually is a "finitesimal" (i.e. bigger than infinitesimal) minimum distance and time, and you look at how the predictions of the theory vary as you change what that distance is. If your theory is well designed, you can prove mathematically that whatever precision (epsilon) you need in your predictions, you can get it from the theory by assuming *any* minimum distance smaller than a certain amount (delta). In other words, you can use the theory to make predictions without knowing what the real minimum distance is, as long as you're predicting on a large enough scale compared to the real minimum distance. When a theory has this property, it's common to think of the real minimum distance as infinitesimal, and say that it's a continuum theory. But you could also think of the distance as very very small, and say that it's an "effective large-scale theory". The real strength of a theory like this is that it doesn't depend on what's going on at small scales. -- Ben rotchm, instantly has nothing to do with no time; it is the least time, whatever that is. David, there are no illusions; everything looks like how it's supposed to. There are only delusions. Bill, that Planck site is too scatterbrained to explain how to derive the various Planck units. Try my heap of linked expressions at http://www.advancedphysics.org/viewthread.php?tid=1585&page=1#pid7925. My notation even distinguishes between linear and rectangular exponentiation, which no one carelessly does. The smallest distance is defined as the equivalence of light's wavelength to the gravital separation between the mass-energy of that light. As gravity is the weakest force, and light is the commodity of endless interaction, the lower limit for light propagation is quite short. I don't know why Baez is on with that useless "Planck area". Is he getting another unique vector from it? -Aut |
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