| MadSci Network: Physics |
Greetings, Keith:In a way, you have asked a trick question. The problem is that energy is not a force, and therefore energy alone is not responsible for forcing anything to happen. On the other hand, energy is always involved whenever an actual force causes something to happen, so there is no doubt that the two concepts are connected. Sorting the situation out is as tricky as your question.
In terms of definitions, "force" is a more primitive concept than "energy", so we'll examine that subject first. Mathematically, "force" equals "mass" multiplied by "acceleration" -- and already we have two other concepts deal with. Not to mention that "acceleration" is itself a concept derived from dividing "velocity" by "time duration" -- and "velocity" can also be further broken down, into "speed" and "direction", with "speed' being "spatial distance" divided by "time duration".
Fortunately, the fundamental concepts here are only "mass", "space" and "time". Every particle possesses mass (or an equivalent), exists in space, and experiences time. Of the three, "time" is the least understood; we measure it and talk about it, but that's about all. There is one notion that may be worth quoting here: "Time is what keeps everything from happening all at once." -- but that, too, is only a description, not a fundamental point of understanding of the "essence of time". Nevertheless, we are all familiar with the idea of "waiting", and since this is a key aspect to the thing labeled above as "time duration", I see no reason to say anything more about it, except this: Time duration is a MEASURED AMOUNT of waiting.
Next, "spatial distance" may possibly be described as "what keeps everything from existing in the same spot". Believe it or not, what might be referred to as the "essence of space" is actually only understood by mathematicians. They are comfortable with the fact that the difference between a mathematical point and a line is not merely infinite, but instead is "transfinite". The relationship between transfinity and ordinary infinity is similar to the relationship between ordinary infinity and ordinary counting. Furthermore, for obscure mathematical reasons, there are the same number of mathematical points in all of three-dimensional space as in any two-dimensional plane or in any one-dimensional line segment. This is why it takes a mathematician to truly understand "spatial distance". Nevertheless, since we have all personally experienced "spatial distance", I can be confident that you will agree that there is no reason to say more about its essence here...except, of course, that in the realm of Physics we must concern ourselves with MEASURED AMOUNTS of the stuff.
When one examines the various objects that make up the Universe, one will notice that everything is moving. The term "speed" may be used to describe a particular quantity of motion, for any one object. As already mentioned, we obtain "speed" by dividing a "spatial distance" by a "time duration". Depending on the measuring units chosen, this could be "inches per decade", "kilometers per second", or something else. (We typically use whatever seems convenient for the particular object being described.) Yet that is not a complete enough explanation, because a SECOND thing is also required; it is known as a "point of reference". This point must be ARBITRARILY ASSIGNED a speed (and it is most convenient to choose Zero); the speed of any other thing is always described in terms of its relationship to that point of reference.
For millenia people thought that the speed of the surface of the Earth was zero, and all speed measurements were based on that reference point. Eventually it was proven that the Earth rotates on an axis, and also revolves around the Sun -- and the Sun is is orbit around the center of the Milky Way Galaxy, which in turn is moving among a small cluster of galaxies known as the Local Group, the whole of which is heading towards a giant cluster in the constellation of Virgo.... As mentioned, everything in the Universe is moving. That is why we are now forced to select an arbitrary point, and declare that we will pretend it is stationary, before we can talk about the phenomenon known as "speed" with any sense of accuracy.
Regarding "velocity", most people seem to think it is a synonym for "speed", but physicists have a more precise definition: To become a true "velocity", a mere "speed" must have a "direction of motion" associated with it. That is, "speed" is a general-purpose word handy whenever we do not care about the direction that something is moving (obviously it must be moving in SOME direction), while "velocity" includes the requirement that we know as much about an object's "direction" as we know about its "speed". This is simply part of the precision of Physics, where everything is measured. Yet it has its uses, also. A gasoline truck moving at 60 kilometers per hour towards your left may have the same "speed" as a bus full of smokers moving at 60 kilometers per hour towards your right, but they most certainly possess different "velocities". This information can be important, if you wish to be far away from the scene of a possible collision.... Anyway, it is usually convenient to establish a "default direction", similar to establishing an arbitary "point of reference". With respect to that default, other "directions" may be labeled either "positive" (the SAME "direction") or "negative" (the opposite "direction", of course).
Next, "acceleration" is deceptively simple, existing whenever there is ANY CHANGE in a "velocity". It is because "change" is always measured in units of "time duration" that the mathematical description of "acceleration" is "velocity" divided by "time duration". Note, though, that a "velocity" can be changed in either of two different ways: If its "speed" aspect OR if its "spatial direction" aspect changes, then an "acceleration" is occurring. Most people know about how "acceleration" is associated with a change in "speed"; they are often surprised to learn that a simple change in the "spatial direction" of a moving object also constitutes an "acceleration". (Details of this aspect may be found in another Answer, regarding balloons in a car.) Also, because "direction" is an important aspect of "acceleration", there can exist "positive" and "negative" varieties of "acceleration", relative to a "default direction". Usually the default is chosen such that when an "acceleration" increases the "speed" of an object, we call the accelration "positive", and when it decreases the "speed", we call it "negative acceleration".
Moving on to "mass", we approach another rather misunderstood subject. It is a fundamental and unique property of every physical object known, and yet finding an equivalently unique way to describe it is a daunting task. Possibly the easiest way to think about a "mass" is to consider Isaac Newton's First Law of Motion: "The motion of any object will remain constant, unless and until some force comes along to affect it." Even if its motion appears to be zero, ANYTHING that obeys this Law can be said to possess "mass" (or some equivalent thereof). The only problem I have with this description is that it brings up the concept of "force" before the proper time to discuss it (at least as far as this Answer is concerned). Possibly a better definition uses Einstein's famous equation describing how "mass" is simply a compact FORM of "energy" -- and yet this also brings up a concept that properly should be discussed later in this Answer. Finally, what of this definition? "Mass" (and/or mass-equivalent) is the source of all Gravitation in the Universe. There are TWO problems with that:
(A) Gravitation is generally regarded as a "force".
(B) There is no widely accepted proof that "gravitational mass" is identical to the "inertial mass" described by Newton's First Law of Motion! Sometimes mere English just isn't adequate (which is why physicists use lots of math).Fortunately, the proper time to discuss "force" is now. As mentioned earlier, "force" is defined as "mass" multiplied by "acceleration". If one takes a moment to recall that "acceleration" is any change in "velocity", and "velocity" is always a description of an object's motion, then one may quickly discover the horns of a dilemma: Newton's First Law of Motion was just used to describe "mass" in terms of constant motion, while "force" is being described as something which can change that motion! Are we not indulging in definitions that are a wee bit circular, each needing the other? Perhaps. I tend to think, however, that a way out may be found by strictly associating "mass" with "constancy", and "force" with "change". Perhaps you will agree, as this Answer progresses (a slightly more complete pair of associations will be offered shortly).
At first glance, it may appear that the thing called "force" exhibits a wide variety of types. It actual fact (and with respect to the physical Universe only), there are fewer than four types, and quite possibly only one type of "force". All those apparent other types would merely be variations on a theme. Physicists have been working for most of a century to gather evidence and to work out the details of how only one truly fundamental type of "force" can manifest in so many different ways. We need not concern ourselves with those details here, but there ARE a couple of general things about the concept of "force" that need to be mentioned.
Most importantly, "force" in Physics usually only counts when it is an ACTIVE thing. Consider a plain rock laying on the surface of the Earth: Neither is moving with respect to the other, yet the Earth exhibits Gravitation, a known "force". Why doesn't the "mass" of the rock "accelerate"? That is, after all, the DEFINITION of "force"!
One correct way to answer that question is to say, "The rock already did." If we had gently placed it upon the ground, it DID "accelerate" immediately and momentarily. This acceleration caused the ground underneath it to compress slightly, perhaps unnoticeably, and AS that compression occurred, a counterforce became noticeable. The rock ceased compressing the ground the moment the counterforce equalled and balanced the Earth's Gravitation. However, we now have the problem of understanding why we CALL them "force" and "counterforce" when no "mass" is "accelerating"! I would tend to say that whoever created those labels (or stole them from elsewhere, such as military terminology) didn't properly pay attention to the precision required of physicists, when "force" is discussed. If we truly have a "force" worthy of close examination, then a "mass" MUST be "accelerating"....
Because of the preceding, I now offer the notion that a "mass" embodies the "potential to stay unchanged", while an "unbalanced force" is present whenever an "actual change happens". With respect to a rock on the ground, there was indeed an "unbalanced force" present while the ground underneath it experienced some slight compression. This does count as being of interest to physicists, but as soon as the imbalance disappears, so does the interest of most physicists. (Some few may concern themselves with considering ways in which an imbalance might again occur, but we must move on.)
Experimentation by physicists has revealed that on the microscopic scale every "force" has one (and on the macroscopic scale, frequently very many) of what we may call a "point of origin". It should be noted that also on the macroscopic scale, is is frequently possible to mathematically combine a lot of individual "forces" together, and to describe an "overall force" that behaves as if it had a SINGLE "point of origin". (Isaac Newton invented calculus just so he could do that one mathematical trick -- although, of course, plenty of other uses for it were since found by him and others.) For this reason we shall herein take advantage of the ability to ignore all but one or two "points of origin of force".
One more critical concept associated with "force" is something often referred to as a "field gradient". CAUTION: More imperfect terminology ahead! In this particular concept, we are attempting to describe the fundamental thing BEHIND every "force": the actual "environment" necessary before any "force" can exist. The "field gradient" is the thing that surrounds a "point of origin of force", and the overall region of "space", encompassing the entire "field", is the "environment" in which a "force" might be observed to do its thing. For the sake of convenience, let us refer to any location away from the "point of origin" as a "point of potential force". (No actual "force" has any chance of existing until a "mass" occupies that location.) Next, because we are dealing with a "field gradient", we must note that the closer that location is to "point of origin", the greater the "intensity" of the "potential force", while the farther from the "origin", the lesser the "intensity". The essence of the "environment" is the complete set of all the "points of potential force", and their individual "intensities" within the "field gradient".
We may now envision a "mass" existing somewhere in the "field gradient" of a "force". This should be easy, because EVERY "MASS" IN THE UNIVERSE exists in at least one, and often several, such "field gradients". (NOTE: very often, most of the "points of origin" of many of those "field gradients" are far enough away from the location of the mass, that the "forces" associated with those "points of origin" are negligably insignificant. If you ever see a phrase such as "a force came into existence during a collision", well, that doesn't mean the "force" was never previously there; it merely means that the "force" finally became significant and noticeable.) Every "mass" which appears to be moving at some constant "speed" (as if it was not experiencing a "force") is in reality experiencing a balance between some "force" and another "counterforce". I am deliberatly focussing on "speed" as the thing to watch, when one wishes to detect an unbalanced "force". Consider an object in a perfectly circular orbit around the Earth: Its "direction of motion" changes constantly (since it is moving in a circle), and therefore its "velocity" changes constantly...and therefore it is continually "accelerating". But its "speed" changes not at all! An object in orbit is experiencing a balance between the Gravitational "force" and its tendency to obey the First Law of Motion (which describes "inertia" via the STRAIGHTFORWARD movement of anything). This balance is as stable as a rock laying on the ground, even though we are dealing with "constant change". The CONSTANCY is more important here than the "change", because a perfect orbit is boringly repetitive. We will return to the subject of a "mass" in a "field gradient" later.
At last we reach the topic of "energy". This stuff comes in a large variety of forms, "mass" included, but the first of these needing description here is usually known as "work". Mathematically, "work" equals "force" multiplied by "spatial distance". Since "force" is linked to an "acceleration" of "mass", one obvious consequence is that WHILE the "force" is doing its thing, the "mass" is traversing "spatial distance". THIS is the particular "spatial distance" that is plugged into the equation for "work". (While it is also obvious that a "mass" might be traversing plenty of "spatial distance" even in the absence of a "force", we say that "work is accomplished" only during the application of "force", AND as the traverse occurs.) Note, however, that a change in "speed" is a vital part of this description, even if it is not normally mentioned in Physics textbooks. The object in a circular orbit is, after all, continuously experiencing Gravitational "force" while traversing a great deal of "spatial distance". Yet NO "work" is accomplished while that happens, and this is entirely due to the fact that its "speed" remains constant.
The next relevant topic is known as "kinetic energy". This is essentially a simple description of ALL the "work" associated with "forcing" a "mass" to "accelerate" to any ordinary "velocity". The equation is: "kinetic energy" equals one-half of ["mass" multiplied by "velocity", and multiplied again by "velocity"]. It happens that the direction of motion is not a critical aspect of "kinetic energy", so perhaps the term "speed" should be used in the equation, instead of "velocity". (But even physicists can be conservatively overzealous at times; I'm not planning on trying to talk them into making that change.) Anyway, "speed" IS relevant here, because of the way "work" is associated with any change in it. For example -- NO! SOME UNITS OF MEASURE ARE NEEDED, FIRST.
Because I'm using a simple text editor that doesn't do subscripts, superscripts, and other fancy stuff, I will use the following labels/definitions:
1 kilogram = 1mu ("mass" unit)
1 meter = 1du ("distance" unit)
1 second = 1tu ("time" unit)
1 meter per second = 1su OR 1vu ("speed" unit OR "velocity" unit, AS APPROPRIATE)
1 v-unit per second = 1au ("acceleration" unit)
1 m-unit times 1 a-unit = 1fu ("force" unit)
1 f-unit times 1 d-unit = 1wu ("work" unit)
1 "kinetic-energy" unit = 1ku, in terms of prior units. Because its equation has that "one-half" in it, amounts of ku will often not be whole numbers.NOW suppose we take 1mu and initially pretend it is stationary relative to us, who we assume are stationary observers (recall what was mentioned earlier about needing an arbitrary "point of reference"). If 1fu causes the 1mu to experience 1au for 1tu, you can bet I was just itching to write that! But please notice the discrepancy just presented: Why did I put 1tu in the description, instead of 1du??? The answer is, "partly habit, and partly pragmatism". If YOU were in remote-control of 1fu that needed to be applied to 1mu for 1000du, and the 1mu is already moving at 1000vu, would you enjoy racing it from the beginning to the end of the "distance", just so you can precisely tell when the position of the 1mu is such that the 1fu should be turned on, and then off? Or would you rather just use a clock? Physicists generally chose clocks centuries ago, so by now the habit is ingrained. However, this means that things like "velocity" and "distance" must be calculated. DURING an acceleration, the "velocity" equals "acceleration" multiplied by "time duration", and the "spatial distance" traversed equals one-half of ["acceleration" multiplied by "time duration", multiplied again by "time duration"]. Note the similarity of this second equation to the equation for "kinetic energy"; it is not a coincidence.
Using the "spatial distance" equation, how many du are traversed when 1fu causes an initially stationary 1mu to experience 1au for 1tu? One-half. How much "work" is accomplished? Recall the equation for "work" and compute: 1/2wu. What final "velocity" will the 1mu be moving at, and how much "kinetic energy" will it have acquired? 1vu and 1/2ku, respectively. Using the equations herein, you could easily specify any ordinary initial amounts of "mass" and "velocity", and then compute its "kinetic energy". Even though it would be traversing "spatial distance" at some steady rate, you could compute the ADDITIONAL "distance" that the "mass" would move if a "force" was applied for some "time duration", and an "acceleration" changed its "speed". You could compute the "work" done during that "additional distance", and the amount of "kinetic energy" acquired. You could also compute the final "velocity", after the "acceleration" was finished, and then compute the total "kinetic energy' based on that. The final "kinetic energy" will ALWAYS equal the sum of the original and acquired "kinetic energies". As previously mentioned, "kinetic energy" is a description of ALL the "work" associated with "forcing" a "mass" to reach a given "velocity", relative to a stationary "point of reference". You now have the tools to prove it to yourself.
Let's take a moment recall something stated very near the start of this Answer: "...energy is always involved whenever an actual force causes something to happen, so there is no doubt that the two concepts are connected." By now it should be clear that the "something to happen" refers to a change in an object's "speed", while the equations of "work" and "kinetic energy" show exactly how "energy is always involved". But this Answer is not yet complete! We have yet to address the aspect of where the "kinetic energy" came from, that a "mass" acquires during its "acceleration".
In one sense the wording of the original trick Question that we are dealing with is partly correct: if "generic energy" is available, molecules can indeed move faster and farther apart, as they acquire it in the form of "kinetic energy". But that is not the same thing as saying (or implying) that the "generic energy" CAUSES the molecules to move more. There is, for example, a quite Natural tendency for ANY concentration of "energy" to "flow" towards places where it is less concentrated, very much similar to water flowing downhill. With respect to some moving molecules, what FORM does that concentrated "generic energy" take? Suppose we have a container of gas, and its temperature is 100 degrees Celsius. Further suppose we also have an ice cube, and its temperature is -10 degrees Celsius. It can be mathematically proven that the ice cube contains a significant amount of POSITIVE "energy", yet if we ADD that "energy" to the container of gas, the gas molecules will move SLOWER and CLOSER together. Their "energy" is the greater-concentrated, and thus it will "flow" from the gas towards the ice. The mechanism of that "flow" is pretty simple: gas molecules collide with ice molecules; "forces" appear during the collisions; and those "forces" cause the gas molecules to "accelerate" to lesser "speeds", while simultaneously causing the ice molecules to "accelerate" to greater "speeds". In very direct fashion, "kinetic energy" simply transfers from one type of molecule to the other. We hardly need mention that if we had added a white-hot iron nail to the container of gas, instead of an ice cube, then "kinetic energy" will "flow" from the iron to the gas, during collisions between molecules, because the greater concentration of "energy" is in the nail in this case.
Of the many forms that "energy" can take, one of the most important is known as "potential energy". This is most simply explained in terms of the "field gradient" described earlier. Since that thing consists of a plethora of "points of potential force", it should be reasonably obvious that as soon as a "mass" is placed at any one point, that "mass" WILL immediately be subjected to a real "force". However, what OTHER things are ALREADY located in that "field gradient"? Perhaps the newly added "mass" will no more accelerate than a rock placed upon the ground.... Remember that every "mass" often exists in more than one "field gradient". In the case of the rock, one such is the Gravitation of the Earth, and MANY others are the electrostatic repulsions between electrons of atoms at the surface of the rock, and electrons of atoms at the surface of the ground.
On the other hand, if the "field gradient" into which we place a "mass" is otherwise unoccupied, the "mass" will begin to "accelerate" under the influence of a no-longer-potential "force". The direction the "mass" takes depends on whether the "force" is attractive or repulsive; in general, the mass will "accelerate" either directly towards, or directly away from, the "point of origin" of the "force". Since this "force" is unbalanced, and the "acceleration" will change the "speed" of the "mass", AND since this will change the "kinetic energy" of the "mass", the crucial question is, "What form of "energy" is becoming that "kinetic energy"?"
The original answer to that question was provided by Isaac Newton, who was mostly concerned with "potential energy" in the Earth's Gravitational "field gradient". He worked out equations showing how "spatial distance" from the "point of origin" can be correlated exactly with the "kinetic energy" of the "mass". If you throw a baseball upwards, your arm will have exerted significant "force", and imparted some initial "velocity" and "kinetic energy" to that "mass". In accordance with the First Law of Motion, the ball might have a chance of hitting the Moon. However, the Earth's Gravitational "force" acts to change the ball's "velocity"; a "negative acceleration" occurs, and the "speed" of the ball eventually reaches zero. WHILE that "negative acceleration" occurred, the ball was reaching greater and greater height, albeit more and more slowly. Now let us suppose that there just happens to be a ledge that the ball just happens to reach, and roll onto, JUST as its upward "speed" shrinks to exactly zero. ON the ledge, the situation of the ball is pretty much the same as the situation of a rock on the ground. The main difference is that the ball has the POTENTIAL to roll off the ledge, and to fall back down to where you might catch it. In Newton's explanation, the upwards "spatial distance" reached by the ball is correlated with the amount of "kinetic energy" that disappeared as the ball rose towards the ledge. If the ball rolled off the ledge, it would re-acquire exactly the same amount of "kinetic energy" that it originally possessed when you threw it upwards. (Note that while originally the ball's "kinetic energy" was associated with the upwards "direction", upon falling the ball's "kinetic energy" is associated with the downwards "direction". Since the two "kinetic energies" ARE the same, this is why "direction" in general is not important here, and why I mentioned that perhaps "speed" and not "velocity" should be specified in the equation for "kinetic energy".) So, according to Newton, "potential energy" is associated with "spatial distance" from the "point of origin" of a "force". As the location of an object changes in the "field gradient", so also changes BOTH its "potential energy" and its "kinetic energy"; the TOTAL is always a constant value.
The concept of "potential energy" underwent a radical change when Albert Einstein showed that "mass" is actually a form of "energy". Nuclear reactions in particular are capable of changing measurable amounts of "mass" into "energy". For this reason, "mass" is also considered to be a kind of "potential energy". It is the interaction between a "mass" and a "field gradient" that causes some "mass" to disappear, and some "kinetic energy" to appear -- but it only happens when it is possible for the "mass" to change its location in the "field gradient". Personally, I think we should throw out Newton's explanation altogether, and consider ALL "mass" to be pure "potential energy". Certainly this is known to be absolutely true, with respect to matter/anti-matter reactions. I see absolutely no reason why we can't imagine the baseball on the ledge as having VERY SLIGHTLY more mass than when the baseball is in your glove; the difference is the amount of "kinetic energy" that disappears or reappears in the Earth's Gravitational "field gradient". Keep in mind that Einstein's version of "potential energy" is KNOWN TO BE TRUE, while Newton's version is MERELY KNOWN TO WORK. (And Ptolemaic astronomy is known to work, too...astrologers use it to this day!) If you desire more information on this aspect of Mad Science, send me e-mail; my address is: vnemitz@pinn.net
By now you might have figured out that with every "mass" in the Universe located in at least one and often several "field gradients", with "unbalanced forces" moving things every which way, with "energy" relentlessly "flowing" from high to low concentrations, and changing from "potential" to "kinetic" and to yet other forms, there is enough going on to keep physicists interested for many years to come. One of those other forms of "energy" may be more relevent to your Question than the others described so far. This is "radiant energy", and it usually occurs in the form of particles known as "photons". These particles possess NO true "mass", but they do possess real "energy" -- and according to Einstein's famous equation, "energy" is EQUIVALENT to "mass". One physical property possessed both by photons and by ordinary "mass-possessing" particles is known as "momentum", which equals the magnitude of a "mass" (or equivalent) multiplied by its "velocity". While a photon possesses very little "mass-equivalent", it does move at the very enormous speed of light, and therefore possesses an amount of "momentum" that is not insignificant. When a photon bumps into a "mass-possessing" subatomic particle, such as an electron, that particle WILL be "bumped". A "force" will come into existence during the collision, just as "forces" do when two "mass-possessing" particles collide. This particular "force" is electromagnetic in nature: the electron possesses a static-electric charge and a magnetic field, while a photon consists of two oscillating fields, one electrical and one magnetic. Almost certainly BOTH fields are involved, causing two independent pieces of an overall "force" to come into existence, during the collision process. Afterwards, the two particles will rebound in new "directions", but their "energies" are likely to remain the same. In this case, therefore, any atom or molecule "owning" the electron may also move off into a new "direction", even though it will not move any faster or slower than before.
Finally, if the conditions of the collision are right for it, the electron may entirely ABSORB the "energy" of the photon. If this happens, then it will acquire all the photon's "kinetic energy" and "momentum". Since this is a true change in the total "energy" of the atom or molecule that "owns" the electron, that particle will likely move at a faster speed than before. And that, I think, completes this Answer.
Try the links in the MadSci Library for more information on Physics.