DHowell.ES@Xerox.ARPA (07/10/85)
Here's a question I've had in my mind that I haven't resolved yet. In physics I was taught that energy is not a substance and does not have a definite location. However relativity says that energy is/has mass. Mass does have a definite location. If energy is mass, how can it be and not be in a definite location? If energy has mass, where is the gravitational field caused by that mass if it has no definite location? Dan
tan@ihlpg.UUCP (Bill Tanenbaum - AT&T Bell Labs - Naperville IL) (07/12/85)
> Here's a question I've had in my mind that I haven't resolved yet. > > In physics I was taught that energy is not a substance and does not have > a definite location. > > However relativity says that energy is/has mass. Mass does have a > definite location. > > If energy is mass, how can it be and not be in a definite location? If > energy has mass, where is the gravitational field caused by that mass if > it has no definite location? > > Dan An excellent question. The answer is simply that energy DOES have a definite location (at least if we ignore quantum effects). In elementary physics, concepts such as potential energy prove useful. The potential energy is viewed as a property of the entire configuration of the system, rather than as a local quantity. In a more sophisticated formulation, we see that the potential energy can be explained as the energy stored in the gravitational or electromagnetic field. The energy density of the electromagnetic or gravitational field is well defined at every point, i.e. has a definite location. -- Bill Tanenbaum - AT&T Bell Labs - Naperville IL ihnp4!ihlpg!tan
gwyn@brl-tgr.ARPA (Doug Gwyn <gwyn>) (07/14/85)
> In physics I was taught that energy is not a substance and does not have > a definite location. > > However relativity says that energy is/has mass. Mass does have a > definite location. > > If energy is mass, how can it be and not be in a definite location? If > energy has mass, where is the gravitational field caused by that mass if > it has no definite location? The main problem here is that you are trying to take too literally statements made (perhaps by more than one source) that: (1) are qualitative, not quantitative (2) oversimplify in order to convey a general feeling for an idea (3) use terms loosely (4) use terms in different ways "Energy" is a concept that is almost defined by being conserved. A certain amount of energy is in prinicple capable of doing a certain well-defined amount of "work". Work is measured as the path integral of opposing "force". Force is supposed to relate fairly directly to one's common experience of muscular reaction. There is nothing in this general idea of energy that requires it to be associated with a material substance or to be in a well- localized packet. Indeed, a propagating plane electromagnetic wave violates both but does carry energy as given by its Poynting vector. Special relativity shows that there is no essential difference between mass and energy in that they are interconvertible (E = m c^2), but certainly mass is characterized by being rather localized. If you look at the modern theories involving the "elementary particles", the distinction between mass (particles) and various forms of energy transport becomes blurred, since these theories consider all interaction to be merely the exchange of particles. In particular, the electromagnetic field is just a cloud of "photons", which are particles, and subsidiary particles. Another view, less popular at present, is that "field" is the fundamental entity and masses are either singularities in the field or concentrations of the field. (Just what field this is, is a long story.) To answer the last question, it is probable that any form of energy contributes to producing the "gravitational field". But most forms of energy outside that which we normally call "matter" are too unconcentrated to have much effect. (It is even more probable that a generalization of gravitation is fundamental and energy is a derived notion, but that is part of the "long story".)
cpf@lasspvax.UUCP (Courtenay Footman) (07/14/85)
>> >> In physics I was taught that energy is not a substance and does not have >> a definite location. >> >> However relativity says that energy is/has mass. Mass does have a >> definite location. >> >> If energy is mass, how can it be and not be in a definite location? If >> energy has mass, where is the gravitational field caused by that mass if >> it has no definite location? >> >> Dan > >An excellent question. The answer is simply that energy DOES have a >definite location (at least if we ignore quantum effects). In >elementary physics, concepts such as potential energy prove useful. >The potential energy is viewed as a property of the entire configuration >of the system, rather than as a local quantity. In a more sophisticated >formulation, we see that the potential energy can be explained as the >energy stored in the gravitational or electromagnetic field. The energy >density of the electromagnetic or gravitational field is well defined >at every point, i.e. has a definite location. >-- >Bill Tanenbaum - AT&T Bell Labs - Naperville IL ihnp4!ihlpg!tan Unfortunately, this is not totally correct. Most energy can be located someplace; for example, electromagnetic energy has a well defined location (E**2/(8*pi) + B**2/(8*pi). Since EM energy has a well defined location, that means that most forms of energy have a well defined location, since EM accounts for most everyday phenomena (in particular, chemistry). Kinetic energy is also not a problem, and so heat is O.K. also. The problem is gravitation. All other forms of energy have (at least) one thing in common: in general relativity, they are source terms on the right hand side of Einstein's field equation, G = 8piT. That is, they curve space, and cause a relative geodesic deviation of nearby world lines that pass through that region of space. No such thing is true of any definable "local gravitational energy" because of the equivalence principal. The equivalence principal implies that for every neighborhood in space-time there is a coordinate frame in which all local gravitational fields disappear. (I.e., all Christoffel symbols vanish.) Thus any attempt to define a local gravitational energy (or, more precisely, an energy momentum tensor) will fail. Note, however, that gravitation does contribute to the energy; the energy of the solar system is less than the energy that the system would have if its parts were at infinite separation. That is undeniable. What is deniable is the localizability of gravitational energy. Gravitational energy is a global effect, caused by global curvature. This difficulty is why it took seventy years after the discovery of GR to prove that the total energy in a region surrounded by asymptotically flat space is positive, because, by choosing an appropriate coordinate system, you can make the energy at any point whatever you want. Most of this argument was take from Misner, Thorne, and Wheeler, "Gravitation", p466ff. -- Courtenay Footman arpa: cpf@lnsvax Newman Lab. of Nuclear Studies usenet: cornell!lnsvax!cpf Cornell University
ethan@utastro.UUCP (Ethan Vishniac) (07/17/85)
> The problem is gravitation. All other forms of energy have (at least) > one thing in common: in general relativity, they are source terms on > the right hand side of Einstein's field equation, G = 8piT. That is, they > curve space, and cause a relative geodesic deviation of nearby world lines > that pass through that region of space. No such thing is true of any > definable "local gravitational energy" because of the equivalence principal. > The equivalence principal implies that for every neighborhood in space-time > there is a coordinate frame in which all local gravitational fields > disappear. (I.e., all Christoffel symbols vanish.) Thus any attempt > to define a local gravitational energy (or, more precisely, an energy > momentum tensor) will fail. > Note, however, that gravitation does contribute to the energy; > the energy of the solar system is less than the energy that the system > would have if its parts were at infinite separation. That is undeniable. > What is deniable is the localizability of gravitational energy. > Gravitational energy is a global effect, caused by global curvature. > This difficulty is why it took seventy years after the discovery of > GR to prove that the total energy in a region surrounded by asymptotically > flat space is positive, because, by choosing an appropriate coordinate > system, you can make the energy at any point whatever you want. > > Most of this argument was take from Misner, Thorne, and Wheeler, > "Gravitation", p466ff. There is, however, at least one *nonlocal* rigorous definition of energy due to Penrose which allows us to calculate the energy contained inside any volume on an arbitrarily chosen hyperspatial plane. The definition is analogous to Gauss's law for electromagnetism in that it uses only the value of the metric (and various derivatives) on the surface of the volume. The main drawback to this method is that "calculable" is a theoretical not a practical, description of the definition. In practice only a few simple situations give calculable answers. -- "Don't argue with a fool. Ethan Vishniac Borrow his money." {charm,ut-sally,ut-ngp,noao}!utastro!ethan Department of Astronomy University of Texas
js2j@mhuxt.UUCP (sonntag) (07/18/85)
> Indeed, a propagating plane electromagnetic > wave violates both but does carry energy as given by its Poynting > vector. A propagating electromatic wave -- an electric field and a magnetic field chasing each other through free space -- a 'photon', right? > In particular, the electromagnetic field is just a > cloud of "photons", which are particles, and subsidiary particles. What about the electromagnetic field which makes up a photon? How can this be 'just a cloud of photons'? -- Jeff Sonntag ihnp4!mhuxt!js2j "Well I've been burned before, and I know the score, so you won't hear me complain. Are you willing to risk it all, or is your love in vain?"-Dylan
gwyn@brl-tgr.ARPA (Doug Gwyn <gwyn>) (07/21/85)
> > Indeed, a propagating plane electromagnetic > > wave violates both but does carry energy as given by its Poynting > > vector. > A propagating electromatic wave -- an electric field and a > magnetic field chasing each other through free space -- a 'photon', right? No. I was taking about something much "bigger" than a photon. > > In particular, the electromagnetic field is just a > > cloud of "photons", which are particles, and subsidiary particles. > What about the electromagnetic field which makes up a photon? How > can this be 'just a cloud of photons'? Every elementary particle can be thought of as "made" of an infinite number of others (subject to definite rules!). Again, I was talking about a macroscopic E-M field, though.
pmk@prometheus.UUCP (Paul M Koloc) (07/29/85)
> A propagating electromatic wave -- an electric field and a > magnetic field chasing each other through free space -- a 'photon', right? > > > In particular, the electromagnetic field is just a > > cloud of "photons", which are particles, and subsidiary particles. > > What about the electromagnetic field which makes up a photon? How > can this be 'just a cloud of photons'? > -- > Jeff Sonntag I thought about that. Instead of viewing the resultant electromagnetic fields, it is interesting to view the "information flow (vector A)" field. The photon seems to be repeating a "search" path routine. The vector A field flows in a manner which seems to repeatingly trace out the path of two adjacent bed springs. Starting at the top of the first it follows a helical path to the bottom of the first and then "transfers" to an adjacent spring in the row but follows it upward and spiraling in the opposite direction. At the top it then "transfers" to the next spring over. It then repeats forming an line of spring like "vorticies until it is absorbed. If the springs "touch" tangentially at the top and bottom the path at the transfer point isn't "discontinuous". Now looking at the flow from the top, the curl (rotation) is obvious. But also from the top a pair of adjacent springs generate a net flow transverse to the axis of the springs in one direction between the pair, and in the opposite transverse direction between the next adjacent springs on either side. The resultant EM fields are then transverse to each other, because the E field is parallel to the transverse A field which alternates direction between each set of adjacent springs. The magnetic field is perpendicular to the "curl" or rotation path traced out by following the helical spring path and that direction of rotation changes in adjacent springs so the magnetic field first points up along the helical axis and then down along the helical axis of the adjacent field. Such flow patterns are also seen in turbulence of fluids perturbed by translating solids. If this is confusing try the Sealy Corporation. (Unfortunately they insulate each coil) :-) vector "A" is real boss! INFORMATION in action. Photon torpedoes away! Until the ARPA domains are functioning prometheus.UUCP collides with PROMETHEUS.MIT.ARPA at umcp-cs. However, seismo!prometheus!pmk.UUCP works. +-------------------------------------------------------+--------+ | Paul M. Koloc, President: (301) 445-1075; | FUSION | | Prometheus II Ltd., College Park, MD 20740-0222 | this | | pmk@prometheus.UUCP: ..seismo!prometheus!pmk.UUCP | decade | +-------------------------------------------------------+--------+
gwyn@brl-tgr.ARPA (Doug Gwyn <gwyn>) (07/30/85)
> fields, it is interesting to view the "information flow (vector A)" field. If you're talking about the "vector potential" traditionally denoted by "A", then you must be using the word "information" in a nonstandard way. If not, then what ARE you talking about? > The photon seems to be repeating a "search" path routine. The vector > A field flows in a manner which seems to repeatingly trace out the path of > two adjacent bed springs. Starting at the top of the first it follows a > helical path to the bottom of the first and then "transfers" to an adjacent > spring in the row but follows it upward and spiraling in the opposite > direction. At the top it then "transfers" to the next spring over. It then > repeats forming an line of spring like "vorticies until it is absorbed. If > the springs "touch" tangentially at the top and bottom the path at the > transfer point isn't "discontinuous". What is the evidence for this picture? It seems rather complicated. I don't think a photon in transit can be considered localized anyhow..