If you want some understanding of general relativity, I’d suggest A book by Kip Thorne, titled something like “Spacetime, Time Warps and Black Holes.”
I’m currently reading Brian Greenes “The Elegant Universe,” which someone here already mentioned. This one gets into 10 dimensonal string theory, including why 10.
If you really want some understanding of this, I’d strongly suggest reading these books, at least as a start.
The source for gravitation IS energy, not simply mass. This isn’t the only source. In electromagnetics, charge AND current are sources of electric and magnetc fields, so you have a 4-vector source term (charge, and three components of current. Analogously, in GR, the source term is a 4x4 tensor, where energy is one term, momentum are three more terms, and angular momentum are the other 6.
Since gravitational fields carry energy, they are sources for themselves, which makes solving the equations difficult without approximation. Contrast this with the electromagnetic field, whch doesn’t carry charge, and so isn’t its own source.
You’re putting words in my mouth. I never said interchangable - I said transmutable. Bodies at rest have an inherent potential energy as given by Einstein’s most famous equation. We can use a process called fission to split these atoms, resulting in heat energy, photons, and subatomic particles with kinetic energy. Variants of this equation show that when energy is applied to a body in order to increase it’s velocity, a certain amount of that energy will add to the mass of that body. The contribution of this additional mass increases exponentially as the velocity approaches the speed of light.
I certainly see the point you are trying to make, however I have to admit that my knowledge of the physics of matter - antimatter reactions is weak. As I understand it, the result of this reaction is pure photon energy and classically we assume that photons have no mass. Does this mean that the total mass within the box decreases? I don’t know… Therefore I don’t have a decent response to your query. I do have a counter-query, though.
Let’s say that we have billions of huge, high powered spotlights all focused around a single point in the vacuum of space such that at any given instant we have a lot of photons arriving at this point simultaneously. Let’s say that we arrange it such that this cumulative photon energy is exactly the same as would be released by your particle - antiparticle annihilation event in the box. Would you argue that this focused photon energy would have the same gravity as the particle - anitparticle pair?
JoeyBlades, photons will contribute to gravitation as much as an equivalent mass will. If you put enough photons in a small enough volume, you can create a black hole, even without any rest mass.
Photons are massless. That’s why they can travel at the speed of light.
Interesting that both you and DrMatrix seem to have been exposed to the concept of a high density of photons being able to create a black hole. I’d be interested if either of you could point out the exact reference.
“Gravitation and Cosmology,” by Steven Weinberg is the text we used when I took GR in college. The author discusses gravitational radiation as being a source for gravitational fields, but not photons directly. Both photons and gravitons are massless, so if gravitons are a source, so are photons.
I’ll see if Kip Thorne’s “Black holes and time warps” has anything on it. Worth reading if you’re interested in this sort of stuff.
You can also derive it by considering gravitational deflection of a photon by a charge-neutral mass. When the photon deflects, it changes its momentum. Since momemtum of the system is conserved, the mass must have changed momemtum also, so it must have been attracted to the photon, due to the gravitational field of the photon.
Well, most of the recent texts I’ve read have put it this way. Electromagnetic radiation always follows the shortest geodesic in Minkowski space-time. Light bends near large gravitational fields because space-time geodesics are distorted by gravitational fields.
I’ve seen the conservation of momentum argument downplayed in recent years because it relies on a concept known as “relativistic mass”. Check out the “mass” section of the Relativity FAQ: http://math.ucr.edu/home/baez/physics/mass.html
I said Stephen Hawking said it but I could not find the reference. (Since I can’t find it I am not positive that he actually said it.) I found the following in “Introducing Black Holes” by John A. Wheeler and Remo Ruffini appearing in Physics Today, Vol. 24 No. 1, pp. 30-41(1971)
I said Both photons and gravitons are massless, so if gravitons are a source, so are photons.
To which you replied
I don’t see that this follows, necessarily…
Well, that was poorly phrased. What I should have said was that if gravitons, being massless, can be a source of the gravitational field, then photons aren’t necessarily excluded because they are massless. Which is certainly a much weaker statement than what I said.
About the rest, I don’t think any current theories fail to exactly conserve momemtum. And the argument with the photon being deflected byt the mass doesn’t use any “relativistic mass” argument.
Wait. I know these are only speculations, but I’m not sure that I understand the logic here. If you’re going on the assumption that energy also produces gravity, why would you expect a net change when the energy is converted to mass?
People have been looking for gravitational waves, though.
JoeyBlades Thanks for the link. It looks like some of my terminology can use some updating. In particular, using mass and relativistic mass where I usually use rest mass and mass.
BIGMatt I haven’t forgotten your earlier question “What is gravity?”. The following is my interpretations of GR and QM that relate to the question: (This ought to generate some lively discussion ;))
GR and QM give different answers to the question “What is gravity?”. In both the effects of gravity travels at light speed.
GR explains gravity as a distortion of space-time caused by mass-energy. The image of marbles in a rubber sheet illustrates the distortion of space. (Though not the distortion of time.) If a mass is moved the distortions of the sheet move at light speed. (I am not sure how to justify the speed being light speed.) So gravity can be said to travel at light speed.
QM explains forces by the exchange of virtual particles. The lifetime of virtual particles is limited by the uncertainty principle. The product of the lifetime and the mass (well actually the energy) must be less than Plank’s constant. The graviton is the particle that mediates gravity. Since it has zero invariant mass, its range is unlimited. Also massless particles move at light speed. I should point out that the logic of the above is reversed. The mass must be zero because we know the range is infinite. That is, we start out knowing the range and deduce the mass, not the other way around.
RM Mentock - the reason that I said ‘gravity shock wave’ is that although if energy creates gravity, then the energy released from the sudden conversion of the massive quantities of matter to energy will dissipate into space at a relatively rapid rate, and so it’s gravitational effects will drop rapidly also.
I know it sems like quite an ill-thought-out idea, but that’s because it is. It was just a thought that occurred to me and so I put it on here for those wiser than myself to think about.
DrMatrix - thanks for that. Although I am a bit confused about why a gravitons mass would be zero. I f the range is infinite then wouldn’t the mass be infinitely small, but not actually zero? (I could be totally wrong about this).
Also, do you have any idea about why in GR the effects of gravity across the ‘rubber sheet’ should be restricted to the speed of light? Is it just because when the laws were written up it was automatically assumed that nothing could travel faster than light? Is there any way to prove/disprove this either way?
“Now be quiet before I rather clumsily knight you with this meat cleaver” - Edmund Blackadder
There is a branch of mathematics that uses infinitesimals called nonstandard analysis. However, from what I have seen of it, it is used only to justify the original formulation of calculus and as far as I have seen there are no physical quantities that are infinitely small and still nonzero. If gravitons have any mass their range would be limited by the uncertainty principle.
The assumption that no signal can travel faster is fundamental to relativity. If any signal travels faster than light, this would lead to causality contradictions. Specifically, if a signal goes from A to B faster than light then there exists a coordinate system in which the event B precedes the event A. As to how this could be proven/disproven… Hmm. I’ll have to get back after some checking.
What I still don’t understand is how modern physics explains ‘fields’. I can’t seem to find an explanation that is universally excepted. Is there one? Was there ever one?
Michael Faraday introduced the concept of a field in his study of electro-magnetism.
A field is a function that assigns to every point in space(-time) a value. This value can be a scalar or a vector. A gravitational field is an example of a vector field; the field assigns to each point the magnatude and strength of gravity. A temperature field is a scalar field; each point has a value but no direction.
I’m not sure I agree with this statement. It certainly means that mass has energy and it also means that as you increas the energy of a particle accelerating it near the speed of light, some of the energy goes into increasing the mass. However, neither of these things means that energy necessarily is mass - just that the two are transmutable.
IMHO, according to current interpretations, and so on:
Formally it is incorrect to call E = mc^2 an equation! It is, instead, an identity. An equation asserts that the thing on one side of the equals sign is equivalent to the thing on the other side of the equals sign in the relevant ways. An identity asserts that the thing on one side of the equals sign (which some write as a triple of horizontal bars to distinguish it from the equation equals sign) is the same thing as, and indistinguishable from, the thing on the other side of the equals sign. The fact that we seem to see a difference between energy and mass is an artifact of our inadequate senses.
I’ve heard it said that one way of looking at the differences between Einstinian gravitation and Newtonian gravitation in cases such as the precesssion of Mercury’s orbit is to consider that in Einstinian gravitation the Sun’s gravitiaononal field, being energy, is mass, which in turn has its own gravitational field, which is mass, which in turn … leads to an infinite series that (lucky for us!) has a finite sum. It’s a hell of a cute statement, but I confess that I don’t know if it’s rigorously correct.
If this is so, shouldn’t everything in the proximity of, say a supernova (where very very dense matter is converted into energy in the form of light, heat etc.) be hit not only by an energy shock wave, but also a gravitational ‘shock wave’, especially if the core of the ex-star then compresses into a black hole where energy starts ‘dissappearing’ from the measureable Universe?"
I don’t think so, but the following is definitely not an oracular pronouncement.
Energy is mass is energy. A supernova event does not change the amount of mass-energy, it merely redistributes it in a spectacular manner. A body in the immediate proximity of a supernova would “see” a decrease in gravitational force from that supernova as debris and other forms of energy leave the immediate vicinity (from the well-known calculation that the gravitational attraction of a spherical shell on anything inside that shell is zero), but the decrease would start when the first debris reached the body and be continuous from then on. I don’t think there would be any discontinuity (shock wave) in the gravitational force.
As I understand it, the result of this reaction is pure photon energy and classically we assume that photons have no mass
Photons are thought to have no rest mass; if we could somehow measure teh mass of one in a frame of reference in which it was not moving, wee think we would measure zero.
However, when they are moving, they have mass because they have energy. Yeah, the universe is weirder than a snake’s suspenders. Fun, isn’t it?