Hello everyone. From the elementary courses of science, one of the first things that is always taught are: 1) Two matters containing mass cannot occupy in the same space and time. 2) Matter cannot be created or destroyed. The first statement is quite trivial since we experience it in our everyday life. But about the second statement, I was wondering, who and how was the second it established. I first thought of Einstein with the equation of E = mc^2; but i think his equation intended prove that matter can be converted to energy not about creation or destruction of matter. In addition, i think that the second statement was established before Einstein proved anything about the energy formula. (Although i also heard of mathematical models about creating particles in the quantum world but it is not physically proven yet or at least hopping for the answer with the particle accelerator)
Matter turns out to be a hard to define concept, as you can experience in another recent thread here. If two antiparticles collide (electron + positron for example), their mass is fully converted into energy (photons). Does that destroy matter? If you regard photons as matter than no, it doesn't. But if you don't regard photons as matter than it does. If you actually mean can mass be created/destroyed, you might be referring to the 'conservation of mass'? In that case, conservation of mass I believe is not strictly true (because of E = mc^2). It has been merged with conservation of energy into 'conservation of mass/energy'.
Yes, i was referring to conservation of mass (but i believe this was known before Einstein introduced his formula) No? Edit: I just found a very interesting article in wiki about it http://en.wikipedia.org/wiki/Conservation_of_mass Edit2: Ok... After reading the article i found out the one who established the law. So it was pretty much that in chemical experiments, the lost mass could not be measured it was thought as to be transformed in some other source. Then there is Einstein formula that justifies that besides that, matter is also transformed to energy making it even more difficult to track down where the source went. (but for some reason the article saying that in a open system matter can be lost is more confusing)
For the overwhelming majority of situations that we encounter, Newton's laws work perfectly well, so we use them. It is only in a small number of situations that we realize that they do not work and will have to use a more general description of Special Relativity. The same applies here. In the overwhelming majority of situations, conservation of energy and conservation of mass are perfectly valid. When you work in classical mechanics, they are valid conservation laws separately. However, we have found out that under certain circumstances where mass and energy convert into each other, these conservation laws no longer work and must be replaced by a more general conservation laws of mass and energy together. The separate conservation laws of mass and energy turn out to be a special case for the more general conservation law of mass plus energy together, the same way Newton's laws are a special case of Special Relativity. Zz.
Whenever I think about this, I sidetrack about space exploration. If matter isn't destroyed but turns into some kind of energy instead, doesn't that mean we could have an unlimited amount of fuel if we wanted to go visit some local stars? Physicists should start trying to create a device that turns used feul and the energy given off into reusable fuel.
The conversion isn't easy. Matter-antimatter annihilation is the most obvious choice, but it takes energy to create antimatter. When making realistic devices to do something, we can't just look at what is possible in physics. We have to look at efficiency, reliability, feasibility, etc.. etc. These are consideration external to just the physics. It is why it has been a struggle to use fusion as an energy source. On paper, almost everything looks "easy". Zz.
Matter nor energy can neither be created or destroyed but only redirected or changed, correct? E=MC^2 proposes that matter traveling at the speed of light is converted to energy, no? Matter can not be created or destroyed for the same reason that an object cannot exceed the speed of light.
No, that's not what E=mc^2 means. E=mc^2 means the energy of a particle AT REST is it's mass times c^2. So if you somehow converted all of its mass into energy, that's the amount of energy you would get out. It has nothing to do with the particle "moving at the speed of light". In fact, any particle with mass cannot travel at the speed of light. Practical issues are very hard to overcome in some of these energy schemes. We have had a way of using fusion to get energy since the 50's, yet we have no fusion reactors. Why? Because the only way we know how to get energy out of fusion is by making a fusion bomb which destroys everything in a 50 mile radius. This is a result we don't want when we make energy for regular every-day use. To go that extra step and get controlled fusion while getting more energy out than we put in has pretty much stumped us for the last 50 years. But, we are slowly making progress on that front...
I wasn't suggesting that Einsteins equation directly interpreted to mass moving at the speed of light. I understand what it means, and I know that in practical physics a particle can only travel at a near fraction of the speed of light because space-time itself begins to slow in order to prevent such an occurrence, however, in theory, if a particle could accelerate to the speed of light, according to E=mc^2 it would be converted to energy. Am I wrong?
Yes, you are wrong. Matter IS energy. If you give it a velocity, it simply has more energy in the form of kinetic energy. In fact, [tex]mc^2[/tex] is the MINIMUM energy a free particle will ever have. Accelerating it simply gives more and more energy.
Think about it. Why would a theory try to predict what happens in an event the theory itself predicts cannot happen? Why would Einstein try to predict what would happen to a particle moving at the speed of light if his theory expressly forbids this from ever happening? It's like asking a theory to disprove itself. So yes, that concept is very wrong.
OK, let's go with this last statement and see what we get. Over time we convert mass into an equivalent amount of energy, or the other way around in the center of mass frame. This is a conservation law that looks like this [tex]\frac{d}{dt}(E + mc^2) = constant[/tex] Notice you don't get E=mc^2 out of it.
I think you misunderstood me pengwuino. I simply rendered Matterwave's statement (*) into mathematical form to show that * does not follow from E=mc^2. However * also happens to be false.
Okay, so according to what you are telling me, light would not have mass. While light does not have at rest mass and cannot exhibit a gravitational pull, it does have relative mass meaning that it has energy that can be transformed into mass...... or in other words E=mc^2. If that is true, which by all accounts it is, then theoretically mc^2=E(or mass into energy) should be plausible as well.... Are you just misunderstanding me? I found this forum searching for intelligence....
No, a photon does not have mass. Yes, it does have energy that can be transformed into mass. I don't know what you're doing by switching the order of E = mc^2, though. I'm not sure if you're going this direction, but it is possible for two photons to have a high enough energy that they can create massive particles.
Are you saying that your equation is mathematically more fundamental than e=mc^2? I ask as a philosopher, not as a mathematician.
Take a particle and accelerate it to a velocity v . Newton defined the momentum, p of this particle, so that p behaves in a specific way when the particle is accelerated, or when it is involved in a collision. For this specific behavior to hold, it turns out that p has to be proportional to v. The proportionality constant is called the particle's mass, m, so that p = mv. In special relativity, it turns out that we are still able to define a particle's momentum p so that it acts in well-defined ways that are an extension of the Newtonian case. Although p and v still point in the same direction, it turns out that they are no longer proportional and the best we can do is relate them via the particle's relativistic mass, mrel. Thus p = mrelv . When the particle is at rest, its relativistic mass has a minimum value called the "rest mass" mrest. The rest mass is always the same for the same type of particle. For example, all protons, electrons, and neutrons have the same rest mass; it's something that can be looked up in a table.... As the particle is accelerated to ever higher speeds, its relativistic mass increases without limit. It also turns out that in special relativity, we are able to define the concept of "energy" E, such that E has simple and well-defined properties just like those it has in newtonian mechanics. When a particle has been accelerated so that it has some momentum p (the length of the vector p) and relativistic mass mrel, then its energy E turns out to be given by E = mrelc2 , and also E2 = p2c2 + m2restc4 There are two interesting cases of this last equation: 1 if the particle is at rest, then p = 0, and E = mrestc2. 2 if we set the rest mass equal to zero (regardless of whether or not that's a reasonable thing to do), then E = pc. in classical electromagnetic theory, light turns out to have energy E and momentum p, and these happen to be related by E = pc. Quantum mechanics introduces the idea that light can be viewed as a collection of "particles": photons. Even though these photons cannot be brought to rest, and so the idea of rest mass doesn't really apply to them, we can certainly bring these "particles" of light into the fold of equation 1 by just considering them to have no rest mass. That way, equation 1 gives the correct expression for light, E = pc, and no harm has been done. Equation 1 is now able to be applied to particles of matter and "particles" of light. It can now be used as a fully general equation.....