When I think of the speed of light, I imagine something moving really fast. Everyone knows that something moving fast hurts more than something moving slow. So why is something said to have "infinite" mass when traveling at the speed of light if the speed of light is a finite "measurable" speed? Why is this even considered "impossible"? If E = mc(squared) then doesn't it simply make energy proportianal to mass "since the speed of light doesn't change for the equation". Or does the E stand for "potential energy". Does anyone else relate to how I feel about this? Can't you just as justifiably take the speed of a train, write it down, and use that as an absolute? "which would produce a representation of energy that is only practical for use in a relitive sense, and cannot be applied as a number on it's own"
Read up on Special Relativity [tex]E = mc^2[/tex] only applies to the 'rest mass' energy of an object. The total energy is [tex]E = \gamma mc^2[/tex] where [tex]\gamma[/tex] is a function of velocity, and becomes infinite when the velocity approaches the speed of light.
Ahh, thank you very much. I love wikipedia, but anyone I talk to will redicule me if I use it as my source, do you have any favorite books to recommend?
Our feelings about relativity are not relevant. Only nature's "feelings" on the subject are important, and she has spoken quite clearly on the subject for more than a century. The speed of a train is not frame-invariant.
The view of mass increasing as velocity does is, from my recent knowledge, incorrect. The mass of an object is always the same. The momentum or kinetic energy of an object WILL increase, but not the actual mass of an object.
Rest mass is always the same. Momentum/kinetic energy of an object will increase as v increases, but not proportionally to v (or v^2) as in classical mechanics. One perceives objects moving at a great speed relative to oneself to have a great mass than that objects otherwise rest mass. Do the objects really become more massive? In my opinion this question is kind of the same as asking if two things are simultaneous. We have an equation that relates the rest mass to it's measured mass under relative motion. It's just relative to your frame of reference. The idea of mass being something invariant attached as a property of an object really needs to be thrown out. Mass, just like time, length, velocity, and momentum, is simply a relative property based on your frame of reference, were just accustomed to letting that relative velocity be 0, that's why we have rest mass. There's nothing really special about rest mass. It's useless to think of it in terms of an object getting more massive or less massive.
I've read the opposite actually. That the term Relativisitic mass should be thrown out. Does an object traveling at high velocity have more gravitational pull? Not as far as I know. It certainly doesn't in it's rest frame. Its momentum most definitely increases, but not mass. Seems to me that mass is pretty set when talking about matter.
hmmm that is a good point. Does a particle traveling at a high velocity not contribute to the EM/SR Tensor? Energy definitely does, otherwise we wouldn't have gravitational waves, correct? So would a particle traveling at a high velocity not contribute more to the EM Tensor than the same particle at rest? When a particle has an increase in energy we see a corresponding increase in momentum, but not a corresponding increase in speed ( because as energy increases, velocity can only approach c asymptotically) If that energy isn't accounted for as an increase in kinetic energy, there where else can we account for that missing energy?
But, it will contribute to a DIFFERENT components of the tensor, than a particle at rest. In fact, 2 test bodies moving at high speed flying parralel to each other attract slower (in a frame where we see them moving) than when they are at rest. The explanation is simple: if it takes, say, 1s for them to collide in their rest frame, then because time is dilated, it would take LONGER for them to collide if they are moving. There is a special case however, when there are MANY particles or bodies in a bound system with a total momentum of 0. In such case, the movement of particles create pressure, which creates 'more gravity' for an observer who is unaware of the internal structure of a system. Examples: 1. When you heat a body, its gravity slightly increases. 2. Proton. Most of the mass comes from the quarks, moving at relativistic speeds back and forth.
Dmitrey, I've heard of that before as well. However, are we sure that the gravity of a system will increase if you add energy, like in the form of heat to it? And if so, how does that relate to two moving objects moving together slower at relativistic speeds? Would adding energy not cause an increase in the speed of the movement of the particles, which would cause further time dilation?
Because when objects moving in the same direction, there is a rest frame where they are at rest. So you can calculate everything in that rest frame and then just calculate the dilation for the other rest frames. When bodies are moving in DIFFERENT directions, there is no such frame! Compare: 1. Photon gas (photons moving in random directions) self-attract (and attract other bodies) 2. two collinear light beams, going in the same direction, dont gravitate to each other 3. two collinear light beams, going in the opposite directions, attract to each other
As there is no rest frame for a photon, how can you relate to them using the same thing for matter? Also, if I pick a frame of one of the particles, then everything else is moving in relation to it. Wouldn't that mean that everything else is still time dilated in relation to that particle?
Surely you did not mean to say this. If two objects are moving in the same direction, at different speeds, there is not "frame where they are at rest". "Direction" is not important, "velocity" is. As Drakkith says, photons have no "rest frame" so none of this makes any sense.
One photon has no rest frame, but I am sure you are aware that a system of multiple photons going in different directions does have a center of momentum frame, which you can loosely call the system's "rest" frame. That is why a photon gas and antiparallel light beams gravitate while parallel light beams do not.
The convention followed by most physicists nowadays is to denote "rest mass" by m and "relativistic mass" by E/c^{2}. And the terminology used is "mass" and "energy (divided by c^{2})" respectively.