by Michio » Sat Feb 01, 2014 12:31 am
Because its rest mass is zero It's not really true that an object "gains mass". In fact, its "mass" turns out not to be an intrinsic property of the object at all. You can only measure it relative to its speed. It's similar to the way you can't ask how far "left" an object is; it's only meaningful relative to your position. That, an object moving very fast relative to you has more mass than an object that's at rest, i.e. right where you are. That "right where you are" mass is called the "rest mass", and that IS an intrinsic property of the object. If you know the rest mass of an object, and you know how fast it's moving, you can determine its mass relative(its "relative mass") to you by this formula:where "m" is the rest mass, "v" is the speed, and "c" is the speed of light. We humans move slowly, and nothing we see without a telescope is moving anywhere near c. So v^2/c^2 is very close to 0, and(we call that part of the equation "gamma", or ?) is very close to 1, and mrel is equal to m. A photon, however, has v = c, and m = 0. So v^2/c^2=1, and the formula reduces to 0/0. That's not infinity. It's actually undefined; it can be anything. We have to use the more general formulas. While a photon has zero rest mass, it turns out it DOES have energy and momentum. We have another formula for those:You've probably heard of it. In it, m is the relativistic mass, not the rest mass. We know c, and we can compute the energy of a photon by this formula:E = hc/?where ? is the wavelength, and h is called Planck's constant. We can rearrange the formula to get:m = h/c?Since h and c are constants, it falls out that the mass is inversely proportional to the wavelength. Long wavelengths(like red light) have little mass; short wavelengths(like blue light, x rays, and gamma waves) have more. The "problem" you refer to is that we want to go faster than the speed of light, but we can't because we have mass. Even if we could reduce our mass to zero, we could only travel exactly at the speed of light. There are a few "solutions" to the problem. The most practical is just to redefine what we're looking for. Consider that ? term earlier. In a lot of ways, ? acts like infinity. As v gets closer to c, ? goes to infinity. You can be frustrated that v can't be greater than c, but if you think of it in terms of ? rather than v, you CAN go arbitrarily fast. Not infinitely, but it means that you can always go faster. There's no finite limit to run up against. In fact, since ? applies to both length and time as well, it's not just a wave of the hand to say that we're going infinitely fast. The ? term applies to both length and time:t' = ?td' = d/?where t is the time and d is the distance. The t' and d' are the relativistic length and time; t and d are the "rest" length and time. So... when ? gets large(i.e. you're going very, very fast), the distance you have to go actually gets shorter!(I don't usually use bold italics, but this is really, really big). In other words, you really do seem to be going as fast as you want, and the distance just gets shorter. If you want to go to a far-off star, you can get there in as little time as you want, shipboard time. It takes a LOT of energy to accelerate like that, but you've got time. It's not so good if you're trying to get there by a particular time, however. If you have friends on that planet, they'll be dead by the time you get there. Time passes more quickly for them. It gets a bit more complicated than that, because if you actually want to slow down to hang out them, you're no longer in an inertial reference frame and everything gets more complicated than we can answer in this question. We can use other, more speculative routes to get faster-than-light travel. There are theoretical particles called tachyons that move at IMAGINARY velocity, so that v^2 is a negative number and ? can actually be less than 1, or even imaginary itself. But nobody knows what this means yet, and nobody knows what it means to "convert" yourself into tachyons. So this is really science fiction more than science. There are also wormholes, and other quantum-mechanical ways of distorting space so that you're not really going all that far. This is slightly more science than sci-fi, but only slightly. PamPerdue 69 months ago Please sign in to give a compliment. Please verify your account to give a compliment. Please sign in to send a message. Please verify your account to send a message.