The speed of light is a factor in alot of things like atomic energy and physics, but why? how is the speed of light tied into atomic structure?
i know very little about this subject so someone inform me, but why do things like E=MC(squared) exist? how is light tied into matter? it has to be because atomic energy requires calculations that involve the speed of light and because E=MC was the theory that helped invent nuclear weapons.
so is matter made of light somehow? i thought light was massless.
What E = mc[sup]2[/sup] means is that energy (the E) and matter (the m, for mass) are equivelent. Take a certain amount of matter, multiply it by the speed of light squared, and that’s how much energy it is. So matter and energy are two forms of the same thing.
If you could take a photon and somehow hold it still, it would appear to have no mass. But photons are always moving at the speed of light. Indeed, they’re always moving at the speed of light in any inertial reference frame. What this means is, if you drive your car at half the speed of light, and turn your headlights on, the light from the headlights travels away from you at c, not c + .5c. This seems a bit unintuitive since we know that in the everyday world, if you throw something out of a moving car, the object gets to have the velocity of the car plus the velocity of the throw, relative to the ground. But this idea was a crucial assumption in developing Special Relativity and all our modern physics.
So back to those photons. What Special Relativity tells us is that when something is moving relative to us, certain quantities which we can measure about that object will change. These changes always happen, but to be noticable or even measurable, the speeds involved must be quite fast. Quantities like mass, length, and even the passage of time are things that will appear to dilate as things move faster. Because those photons are moving so fast, to we slow mortals, they appear to act as if they do have mass. We can even observe photons reacting to gravity because of things like gravitational lenses.
That’s a very very basic explanatio; I tried to leave out the math and fancy jargon. If you’re interested in learning the details I can reccomend some good books on Relativity and Quantum Mechanics and whatnot, but I reccomend taking undergraduate physics courses instead.
Friedo has explained it pretty well. As a consequence of the speed limit, space-time is curved. Its weird as hell, and if you think thats bad try quantum mechanics.
As for really understanding it, no human can really claim that they do. Understanding advanced physics and mathematics might give you more insight, but it won’t give you a fundamentally better answer than this one - “well, it seems to work”.
I don’t know about that. I’ll grant you that non-newtonian physics is pretty weird stuff, but anyone with basic calculus can understand Special Relativity with some dedicated study and a good teacher. In fact, understanding time and length dilation really only requires basic algebra and geometry.
General Relativity requires some more advanced mathematics, but there are plenty of people who grasp it quite well (not me though.)
I’m not sure we’ve covered the OP, which I understand to be asking why the SoL seems to fundamental to the universe in general and atomic physics in particular.
IANA physicist but my understanding is it’s not, as such; the SoL does not define characteristics of the universe so much as the characteristics of the universe define what the SoL must be.
IOW it’s not that the SoL and subatomic physics are tied together, but both are consequences of the way the universe is and so are indirectly related rather than one being dependent on the other.
So why is C involved in E=MC^2 ? Because it is a way of determining a particular characteristic of the universe which happens to be involved in the matter/energy conversion. The SoL is a fast as it can possibly be in our universe, and so is an indicator of one parameter or characteristic of the universe, which is also involved in the M/E conversion.
The speed of light in general comes into atomic physics only inasmuch as atoms interact with light. Atoms, of course, intearct with light with great enthusiasm. We can express a great many things in electromagnetic theory including why atoms behave the way they do using concepts of electromagnetic field waves (what we call light) to explain the energies of atoms rigorously. It turns out that the speed of electromagnetic waves is the speed of light and since atoms are bound by electromagnetic forces, you better believe that the speed of light is important.
The relativisitic treatment (that is SPECIAL relativity) of matter gives a convenient way to express momentum and rest mass energy as the total energy of the system. This comes from considering the principles of special relativity that the speed of electromagnetic radiation is constant in all reference frames. This naturally leads (after some mathematics) to the concept that the energy associated with the rest mass of an object is equal to the mass times the speed of light squared. I have seen proofs of this that require only a simple knowledge of time dilation and length contraction along with basic physics so it’s a more accessible concept than you might think.
Peculiarly enough, many of the experiments scientists do involving particle physics take place at significant fractions of the speed of light where the kinetic energy of your particles is equivalent to the rest mass energy. That’s where relativity becomes important. And don’t you forget it!
Why does relativity exist? The simplest answer is because Maxwell’s Equations of Electromagnetism give electromagnetic waves whose speed do not depend on the observer. This is different than all other waves in nature (with the possible exception of gravitational waves).
What is so important in physics is this constant of nature, c.
It is the limit that bounds relative speeds between bits of matter. Things that have mass cannot move at a velocity of c or higher relative to one another, and the relativity of motion asymptotically approaches c in a variety of ways.
Information and cause-and-effect also cannot propagate faster than c, though they can propagate at c.
Finally, numerous influences, including electromagnetic radiation in general and light in particular, travel at c. It’s historical accident that visible light was the first thing whose c velocity was understood, but light itself isn’t so particularly fundamental to physics.
Physics was Newtonian and then along came Maxwell and his equations. Turns out that the equations give you a description of a self propagating wave that travels at c. Always. You can’t have a wave that at .999999c it simply can not do that. This led Einstein to his thought experiment where he surfs the light wave. If he’s going at c then the light wave should be traveling at 0 relative to him, but if it does that, it’s no longer a light wave. Einstein said that c must be c in every inertial frame.
This special relativity completely threw down the Newtonian idea of a “god’s eye view” of the universe. The idea that there was some absolute inertial frame. Remember that in Newtonian physics there is no limit to an object’s velocity. Which means its kinetic energy could go to infinitely (KE = 0.5mv2). Well anytime you see infinity in physics it tends to mean that we’re missing something.
So special relativity only works for objects with zero acceleration. Einstien expanded that to General Relativity, where the difference between gravity and acceleration was erased. This led to the idea of a space-time fabric of the universe.
But why is light so important? Basically photons are how particles exchange the electromagnetic force. Of the four forces of nature (the Weak and Strong forces are tied up tight in the nucleus, Gravity is extremely weak) EM is the most “visible” to us. We use it a lot and so it appears more often when we discuss how things work.
a bit of a nitpick here. the “speed of light”, as such, is not a constant. c is the speed of light in a vacuum, and there are things that in certain media can travel faster than light. also, you may recall that photons were stopped toward the end of last year, without removing their energy.
that said, i’ll try to add something substantive here. i agree with the above assessment that the reason c is so fundamental is its constant nature. when it was discovered that c was the same, no matter how fast you were moving relative to the light source, all of classical physics had to be reconsidered. it’s a very counterintuitive concept; how can something be travelling at apparently the same velocity when measured by two things that are moving relative to each other? well, that question is answered in full by special relativity, and i invite you to find more information about that theory. einstein reworked the nature of space and time to fit his special theory of relativity, and that became the general theory of relativity.
so c, in all its glorious constantness, comes into most modern physics as a result of the theories of relativity. the famous mass-energy equation can be derived from the mass dilation equation of special relativity.
Can you clarify this. You say that “the headlights travels away from you at c, not c + .5c”. Do you actually mean that the “the headlights travels away from the static point of reference at c, not c + .5c”?
If you are travelling at 10 mph and throw something at 20 mph it will have a speed relative to the ground of 30 mph but will still only be travelling away from you at 20 mph.
I don’t think there is a difference from the viewpoing of someone in the car, only for someone standing on the road as the car goes past. Is this true?
that’s pretty much what he meant. if you are in a car driving at 0.5c (relative to the road) and someone is driving toward you at 0.5c (relative to the road), your relative speeds would be near c (0.5c + 0.5c doesn’t add up to c for objects that aren’t EM waves), but light from the headlights of the car travelling toward you would be measured by you to be c, and the same for your headlights to them.
The whole point of relativity is that the headlight travels away from the stationary point at c (as the stationary observer measures) and travels away from the moving car at c (as the observer in the car measures).
That’s the key freaky thing about relativity, which makes high (near c ) speeds so different than we’re used to low speeds working.
This is in fact where Einstein started: saying “if you really measure c the same no matter how fast you’re moving, what would happen in this situation…” and reached all the bizarre aspects of relativity like time slowing down for one person, things getting shorter, etc.
and WesleyC – I think AndrewT had the best answer. c is just a fundamental number for the universe. A bunch of things are affected by the value of this number, including how mass and energy translate to each other, and how fast electromagnetic signals travel in a vacuum.
That’s what I thought. I didn’t explain very well but I thought that friedo’s explanation was focusing on the moving observer (when light behaves the same way as anything else) than the stationary observer (where there is a distinct difference). I just wanted to clarify in case anyone else read it the wrong way as well.
That’s not right, and anyway, relativity fails to solve this problem. In SR, the equation for kinetic energy can be derived from the mass dilation formula. It’s given by:
KE = mc[sup]2[/sup]((1-v[sup]2[/sup]/c[sup]2[/sup])[sup]-1/2[/sup] - 1)
It also increases without bound, just like the Newtonian formula The only difference in this regard is that it increases boundlessly as v approaches c, not as v approaches infinity.
Energy is the time component of the energy-momentum four vector, momentum is the space component and mass is the magnitude.
Mass and energy are not the same thing and mass cannot be converted to energy. A vault containing a nuclear weapon will weigh the same both before and after detonation.
Basically, matter and energy are equivalent except for maybe one thing: Matter has intertia. What causes this, nobody really knows. The Standard Model of particle physics is now formulated as if there is a field, called the “Higgs field” (named after Peter Higgs, a Scottish physicist who first proposed the mechanism by which the particles that mediate the weak nuclear force somehow gain their prodigious mass). According to the theory of the “Higgs mechanism”, what we call “matter” can interact with the Higgs field, which kind of drags on it, giving it inertia when you try to change its velocity. Photons (and gluons, the carriers of the color force in nuclei), don’t interact with the Higgs field at all, and so they never “feel” inertia. Photons do change their path around massive objects just like pieces of matter (or large collections of energy), but they don’t experience a “force” per se (they’re not accelerating…they can’t); they simply follow the curvature of space around that object, actually always traveling the shortest distance in space-time between A and B.
One thing that may be worth mentioning, vis c and atoms: The theory of quantum electrodynamics (QED) is known as a “relativistic quantum field theory” partly because it takes into account that electrons are whipping around atoms at a significant fraction of c. When they try to very accurately calculate how these particles behave in atoms, given that this behavior is determined by properties like their mass, charge and magnetic moment (the latter two being related entirely to the the chance they will absorb or emit a photon in a given period of time), and because some of these properties appear to change with relative velocity, the theory has to include special relativity. And special relativity is all about c. (Of course there’s an awful lot more to it than that, but just as an aside).