Posted on 10/01/2005 8:10:18 PM PDT by GummyIII
Correction Appended
DURING the summer of 1905, while fulfilling his duties in the patent office in Bern, Switzerland, Albert Einstein was fiddling with a tantalizing outcome of the special theory of relativity he'd published in June. His new insight, at once simple and startling, led him to wonder whether "the Lord might be laughing ... and leading me around by the nose."
But by September, confident in the result, Einstein wrote a three-page supplement to the June paper, publishing perhaps the most profound afterthought in the history of science. A hundred years ago this month, the final equation of his short article gave the world E = mc².
In the century since, E = mc² has become the most recognized icon of the modern scientific era. Yet for all its symbolic worth, the equation's intimate presence in everyday life goes largely unnoticed. There is nothing you can do, not a move you can make, not a thought you can have, that doesn't tap directly into E = mc². Einstein's equation is constantly at work, providing an unseen hand that shapes the world into its familiar form. It's an equation that tells of matter, energy and a remarkable bridge between them.
(Excerpt) Read more at nytimes.com ...
When you burn gasoline, matter is not destroyed but chemical bonds are altered.
Hmm...
I tried to side step this a little, hoping to keep the picture simpler.
In the case of a helium atom, the binding energy is negative. That is one way of saying that energy is released during the process of binding. That is why one can use "fusion" as a source of energy. That energy has to be added back in order to "un-fuse" the atom, so the separated particles end up having more mass than the original helium atom.
Fission of uranium exhibits the opposite case. It takes just a little energy to cause the uranium atom to separate into smaller particles. As the separation occurs, much stored energy is released. The mass of all the particles at the end is less than the mass of the original atom.
The fission example is like a compressed spring with a string tied to keep the spring compressed. If a little energy is added to break the string, the spring can release its stored energy.
Yes, even chemical or kinetic energy can be be related to mass change. I believe the term used is "mass defect" and for ordinary chemical reactions and speeds we experience the mass defect is extremely small.
Here are some links that may clarify :
http://www.einstein-online.info/en/spotlights/binding_energy/
http://www.newton.dep.anl.gov/askasci/chem03/chem03534.htm
Tell her it's the hair.
And I'm not reading this right before bed, either.... As I recall, I needed Martin Gardner to explain the whole thing to me in the first place. Couldn't follow Einstein's paper a'tall. 'Course that was years back - maybe I should give it another shot.
The force responsible for fission or fusion is the "strong nuclear force". I don't have the numbers readily at hand, but the strong nuclear force exceeds what we normally encounter in the physical world by many, many orders of magnitude. This causes the very small mass converted into enormous energy in the case of a nuclear bomb to be readily measurable. But any of the physical forces operate similarly.
Let's try another thought experiment.
Imagine a proton at rest relative to you, the observer. If you apply a slight force to the proton, it will accelerate. Newton's Second Law dictates that the aceleration will follow F=ma. That is, for a given mass, a slight force causes a slight aceleration.
If not for Einstein's discovery, Newton's Second Law would dictate that the aceleration could continue at the same rate as long as the force remained constant. If we push on the proton long enough, it should exceed the speed of light eventually.
Einstein's discovery of E=mc2 modifies the situation so that the speed of light can never be exceeded. Instead, what is observed is an increase in mass as the velocity increases. F=ma still applies, but the observed mass becomes greater than the "rest mass".
The observed increase in mass is exactly what is required to account for the energy stored in the moving proton. Energy added to the moving proton can be calculated by multiplying the force applied times the distance through which the force acts. This works out to mv2/2. This is called the kinetic energy of the particle, where m is the observed mass and v is the velocity.
At low velocities, energy added to the proton causes an increase in velocity and the observed mass is near the rest mass. As velocities are reached which are near the speed of light, additional energy added appears as an increase in observed mass and the velocity changes only slightly. The observed mass grows sufficiently large as the speed of light is approached that the force cannot cause the velocity of that large mass to exceed the speed of light.
But it does.
Fission and Fusion are special cases.
No they're not.
The only thing different between the two is that the vast amounts of energy involved in fission/fusion result in a net change of mass that's large enough to be "noticeable", whereas the amount of energy involved in chemical reactions (or kinetic energy, etc.) are small enough that the net change of mass is so tiny that it can be disregarded for most practical purposes (and indeed, next to impossible to actually measure much less notice).
But in all cases, the "books must balance" relative to E=mc2.
Now you've lost me, though your prolly didn't know you ever had me. lol
What would produce (release) energy from this atom at the time it breaks up? I mean, the way your describe it makes it look like a basic chemical reaction, such as combustion would be an energy user, not energy producer. Aren't chemical reactions mostly conversion of one kind of energy into another kind, so there's not actually much, if any involvement of conversion of mass into energy involved? I thought combustion converts potential energy (stored kinetic energy?) into heat & light, no? (Am I dating myself & my education by saying this? lol) Maybe things have changed, but I didn't think there was much change, if any on the atomic level & it happens on the molecular level in chemical reactions. I know E=mc^2 still applies to chemical reactions, but I thought it mostly explained why mass & energy remain constant.
Ask her opinion about who is/was the most famous lawyer in history & after she names one, ask her why she picked that one. When she's finished, just say, "Einstein, same thing only he did it in physics."
Yep. I corrected my typo in a later post. It's amazing how one can type the word "electron" but be thinking "neutron".
If I understand your question, the answer is "yes". That is, mass and energy remain constant because not very much mass is "converted". The accounting of energy typically includes "potential" energy. This is a way of treating the energy as if it had not been converted into mass. Since the amount of energy is low, the mass change is extremely tiny and can be ignored. The potential energy term keeps the energy calculation in balance.
In most cases, "binding" energy is negative. That means that energy was given off during the binding and is missing from the bound particle. The potential energy of the bound particle is then negative. The bound particle will, I believe, have a mass which exactly accounts for this missing energy.
How about when plants grow? Light energy (Sun) gets transformed into mass (plant). Cool.
This explains why there is more sound energy in heavy metal rock.
When a particle is created from energy, an anti-matter particle of equal mass is created. The mass of both of them convert into energy if they come in contact with each other, so I'd have to think that there has to be some potential energy in at least one of the particles (either matter or anti-matter)... When you say a bound (matter) particle has negative potential energy, I begin to wonder how any matter has potential energy.
I thought all matter *was* potential energy, where matter & energy have the ability to convert from one to the other, depending on externals. A particle with negative potential energy that you're talking about is making no kind of sense to me. What am I missing?
I mis-spoke a little. Let me try to re-phrase before going further.
I previously wrote: "The potential energy of the bound particle is then negative. The bound particle will, I believe, have a mass which exactly accounts for this missing energy."
I should have written: "The potential energy of the bound particle is then negative. The bound system of particles will, I believe, have a mass which exactly accounts for this missing energy."
It is the entire system which will reveal the change in mass, not necessarily the "bound particle".
Let's talk a little about potential energy. One of the simplifications in physics involves treating particle interactions using the concept of a "field".
The laws of electromagnetics tell us that a proton and an electron will attract each other. There is a force law which describes how the amount of force changes with distance.
A simplification of the interaction of these two particles consists of ignoring the proton, for example, treating it as if it is at a fixed point in space. (Because the proton is so much heavier than the electron, it can often be treated as if it is stationary.) Then one imagines that there exists a "field" in space and the electron exists in this field. The value of the force in that field at any point can be calculated using the known electromagnetic force law.
Knowing the force which is acting on the electron at any position, one can then calculate the amount of energy needed to move the electron from any one position to another position. The net change in energy represents how much work must be done to move the electron from the first position to the second. If the amount of energy required is positive, then the "potential energy" of the second point is said to be greater than at the first point.
If the amount of net energy needed to move from the first point to the second point is negative, then the second point has a lesser potential energy than the first point.
Finally, there is a singularity at the location of the proton. That is, the force between a proton and an electron becomes infinite, according to the force law, if the distance from proton to electron is zero. For this reason, the reference position used for zero potential energy is at an infinite distance from the proton, rather than at zero distance.
Calculus allows one to calculate the energy required to move the electron from an infinite distance to any given finite distance. Since the force is attractive, this energy is always negative. That is, the electron accelerates as it moves from infinity to any given finite distance.
The potential energy at infinity is being converted into kinetic energy at some finite distance from the proton by virtue of the force acting on the electron.
At some finite distance from the proton, the positive kinetic energy observed is equal to the change in potential energy. That means that all finite positions have negative potential energy and that the potential energy gets more negative as the electron approaches the proton. At the same time, the kinetic energy increases. Total energy is conserved.
There isn't any absolute potential energy quantity. It can be defined any way we want, but we choose the way that is most convenient. Once a reference is chosen, then we are only interested in changes in potential energy.
For example, if we start with an electron at rest one meter from the proton and then allow that electron to "fall" toward the proton until it is one-half meter away, then we know by the conservation of energy that the kinetic energy of the electron must be equal to the difference between the potential energy at which it ended and the potential energy at which it started.
We only end up interested in the potential energy change. Where we chose the reference becomes irrelevant. The "potential energy" at any given position is simply a number which tells us how the electron will behave in moving to some other position. The difference in potential energy tells us whether we have to expend "work" to move the electron or whether the electron can do "work" in moving to the new position.
In summary, then, when we say some particle has a negative potential energy, we are describing the fact that we must expend energy to move it to the zero reference position. The magnitude of the negative potential energy is the amount of energy to move the electron to the zero potential energy position.
The explanations I gave in my previous post explain how "potential energy" can be negative. It is simply relative to a pre-defined reference. The conservation calculations will involve changes in potential energy.
In the case of a particle-anti-particle interaction, the mass of both particles represents the potential energy. All of the mass may be converted such that no particles with finite rest mass are created. Note that such interactions not only require conservation of mass-energy, using E=mc2, but other conservation laws come into play.
If the interaction is an electron-anti-electon event resulting in particle anihilation, then the total number of electrons before the interaction must equal the total number of electrons after the anihilation. This accounting is done with an anti-electron counting as -1 electrons.
My background is not sufficient to suggest how the energy to create a particle-anti-particle is converted into mass. I don't know what the present understanding of the mechanism is. Some of these phenomenon only have mathematical descriptions of what happens, but without an understanding of the specific forces in play. By that I mean that there may not be an analogy from classical physics which helps to explain the mechanism and from which one might infer other properties.
It is SO cool to read this scientific nerdy stuff and actually see people responding and discussing it. I think I am in heaven...
However, I am more a mathematics nerd. Can't wait for that thread to come along.
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*sigh* How so much has changed in the world (Einstein, Madame Curie, Tesla, the Wrights..etc. :) in such a small (just 50 years) span of time. ...Good and Bad (Lenin, Stalin, Mao, Hitler...etc.).
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