|MadSci Network: Physics|
‘Sorry if it’s dumb’? No, there are no dumb questions. Just dumb answers. And I fear I’m about to give you some! Q: “So,how much time has passed for a photon emitted let's say 1000 years ago, earth time?” A: None. Zero seconds. A photon emitted 1000 years ago is just as ‘old’ as a photon emitted at the birth of the universe. That, at least, is the standard story. See: http: //www.madsci.org/posts/archives/nov98/911849900.As.r.html http: //www.madsci.org/posts/archives/oct98/909146207.Ph.r.html http: //www.madsci.org/posts/archives/mar97/859296621.Ph.r.html htt p://www.madsci.org/posts/archives/oct2000/972950826.Ph.r.html but I admit I find that answer very unsatisfactory. I’ll give my interpretation of the answer, based on the following postulate for the behavior of light: the speed of light measured in any frame of reference is always the same – the speed of light. In other words, a photon will travel at the speed of light in no matter what reference frame you view it. Think about that. It means that there is no reference frame in which light isn’t traveling at the speed of light, and therefore no reference frame in which one could look at how a photon ‘at rest’ experiences time. You can imagine and calculate for inertial frames passing by at speeds very close to the speed of light, but none AT the speed of light. This means that the question of how old a photon is in its ‘rest-frame’ is meaningless: there is no such frame. The stock answer of ‘zero’ comes from looking at the limiting behavior of particles traveling at speeds that approach that of light. The time experienced by these particles when traveling over a fixed distance becomes shorter and shorter until, if their speed is EXTRAPOLATED to c, it becomes zero. The postulate I quoted serves as a foundation of special relativity. See: http://ww w2.corepower.com:8080/~relfaq/speed_of_light.html This is part of a more comprehensive relativity FAQ: http://www2.c orepower.com:8080/~relfaq/relativity.html If you want a very good written introduction to the subject, I highly recommend “Spacetime Physics,” written by Edwin F. Taylor and John Archibald Wheeler, published by W. H. Freeman and Company, ISBN 0-7167- 0336-X. It has much of the math, but far more importantly it has clear explanations. Q: “Or, just to put it another way, if I somehow manage to travel at 99.999999% of the speed of light, would I be able to reach the edge of the universe during my lifetime?” A: Not quite, but you’ve got the idea – if the universe were static and bounded. This is the path you take to explore reference frames that approach the speed of light. Check out: http://www.astronomycaf e.net/qadir/q917.html They define a ‘warp factor’ such that ‘warp 2’ would be traveling 99% of the speed of light, ‘warp 3’ traveling at 99.9% of the speed of light, etc. Your example is at warp 8. At this speed you could travel a distance of 7071 light years, as viewed by the earth, in just 1 year of your time. The center of our galaxy (according to the site) is 26,000 light years away, so you could get there in under four years. The ‘edge’ of what we can see is supposed to be ~15 billion light years out, so traveling at warp 8 isn’t going to get you there any time soon. You can get there in 67 years of your time if you travel at ‘warp 17’, while it will take only 2.4 days at ‘warp 25’. More problematically, however, the universe isn’t static, nor necessarily bounded. The principles of special relativity hold only in the limit of “inertial reference frames.” When considering the universe, that condition is violated. I’m not an expert, so I’ll just mention a couple of the issues that are relevant. It’s an open question as to whether the universe will always be expanding or whether it will start to contract, but if it’s always expanding then some portions of space will always be just a little ahead of you. Furthermore, a hazy memory of Hawking’s book “A Brief History of Time” tells me that if you really were able to travel straight through the universe you’d wind up right back where you started, so there isn’t really an ‘edge’ of the universe to travel to. Questions along these lines should go to a cosmologist, and I certainly don’t claim to be one. Q: “A friend (physics graduate) says something about the fact that even objects standing still in the 3D space are actually traveling at the speed of light on the time axis in a complex 4D space and then some other stuff...” A: Your friend may be referring to the fact that an object sitting still in space nonetheless has a trajectory in time. It does. That does not mean, however, that it is traveling at the speed of light! The proper manner in which to describe the trajectory of an object, within the confines of special relativity, is to include four values at each point: three values for position (X,Y,Z) and a value for the time (T). Trajectories are found by determining the path of these variables for a single object moving through spacetime. All the fun stuff in special relativity comes from the fact that distances along these trajectories are measured in a far different way than what you’d expect. For more details, see the earlier reference for special relativity: http://www2.c orepower.com:8080/~relfaq/relativity.html Your friend may also have been trying to communicate some of the cosmology issues I alluded to earlier: the universe isn’t sitting still, so even light might not be able to travel fully throughout its extent.
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