Why does gravity enjoy a privileged status in determining how the space should curve? I will try to develop my line of though as I go along, so please bear with me. It could be said that space curves according to fields present in it. But why only the gravitational fields? Let's consider three examples. Let's have two objects A and B initially stationary with regards to each other. If a gravitational field centered on point G exists in a given space and objects A and B which have mass find themselves in this space where A is nearer to G than B, then A will be accelerating towards G faster than B. So even though the objects A and B are moving relative to each other, they are not moving relative to their respective intristic gravitational fields, so both in a sense are at rest. To rephrase it. If B did not exist in this system, then as far as A was concerned its accelerating motion towards G could be considered as a stationary/rest motion since there would be no other reference point in the system. The object A would not feel any acceleration taking place, and as far as it was concerned to all intents and purposes it was stationary. So one could argue that gravity defines the space curvature according to the magnitude of the field's strength acting in a given space. If B is present then this complicates matters a bit since B having a mass just like A would tend to alter somewhat the gravitational field G. Overall however, for each object A and B some state of motion exists which could be called a natural/stationary/rest state consisting of the cumulative gravitational fields acting on the specific region of space which A and B occupy. But now let's have B WITH MASS and an electric charge and A WITHOUT ANY MASS but with an electric charge. And let's have an electric field with a center E removed some distance away from the center of the earlier said gravitational field G. And let's now have A and B initially occupy the exact same region of space. So how can you describe relativity in this system? What will be a natural/stationary motion for A and B? How will the same space occupied initially by A and B be curving now? Will it curve only towards G, only towards E or will its curvature be influenced by both fields? Here the object A's natural state of motion will be to accelerate towards E, while that of the object B will be to accelerate towards both E and G. One can argue that object B will only 'feel' itself accelerating relative to E but not G. But in the case of object A which cannot 'feel' the gravity, what if its inner ear sensory organs evolved to pick up motion relative to the electric field it's in rather than the gravitational field?
I think you may be shifting concepts a bit. (But I'm admittedly not an expert.) 1. Acceleration doesn't require gravity. Acceleration can be relative to a point in space, such as the point that the object was at when it started accelerating. Feeling acceleration isn't a requirement. (Actually, the way we feel or even detect acceleration is usually by detecting the difference in acceleration between two things, such as a human's semicircular canals and the fluid inside of them.) Interestingly enough, steady linear acceleration "feels" just like gravity and is virtually indistinguishable. Regardless, gravity isn't required to "feel" acceleration. 2. One of the best current theories of gravity is that it is nothing more than a description of the curvature of space-time. It isn't that gravity is curving space-time, but that when we observe objects encountering curved space-time, we describe the way that curvature affects those objects as being gravity. It is similar to the effect that we call "centrifugal force" - which is not actually a force, but is a description of the effect that occurs when inertia of a moving object interacts with a centripetal force. I'll reread your post and give it further consideration, but I wanted to offer those two points for you to think on.
But how would the curvature of space affect the behaviour/motion of objects with no mass? Any object should affect the curvature of space around it. Objects which have no mass but which exhibit say electric properties should alter the space curvature with their electric fields.
Why? Perhaps mass affects the curvature of space, but EM fields don't. Or perhaps the effect of an EM field on space is so negligible as to be undetectable. Consider the way EM fields affect various materials. Ferrous metals are strongly affected by EM fields. Many materials are virtually unaffected by EM fields. There is no reason to assume that every known basic factor will affect every other factor. Mass may affect space time, but the strong, weak and EM forces may not.
Well, let's talk about electromagnetic fields, anything with charged particle constituents, anything that can exchange photons. By the virtue of generating a field, any kind of field not necessarily gravitational, you affect the motion of other particles in the vicinity which can interact with such a field. If you affect the motion of other particles using fields, then you are causing the space to curve.
Consider E=MC^2. That's a buttload of energy jammed into mass. Perhaps if an EM field was packing that kind of energy, it could affect spacetime like mass does. That's the idea behind Star Trek's warp drive, anyway.
Sandtrap; Nobody has done it with magnets, but Gravity has been shown to bend light. (1) Gravitational lens were predicted by Einstein. Theoretically, a Magnet may do the same thing, but the principle is that a magnet interacts with a particle, while gravity is acting in some sort of intermediary between particles(i.e space). Another point is that, I think its called the electrostatic force, but lets just say magnetism, is many magnitudes stronger than gravity. A magnet overcomes the whole gravity (field) OF EARTH when it lifts a paper clip. I think its something like 17 magnitudes higher(x10^17) Theoretically, this should make space curve tests from EM ultra easy, but it may also automatically negate them, because we haven't seen it thus-far. Keep up questioning though, I have suspicions of my own that are pretty similar A point to make is that photons are incredibly tricky to do proper wave collapse, or doppler effect. Its relevant, but I don't want to really speculate too much on light physics. Anyways, gravity overcomes many problems assumable by creating paths of least resistance where light and its entropy have no other choice but to go and causethe bend. 1(http://en.wikipedia.org/wiki/Gravitational_lens
No. That would mean that if there is ferrous metal present near an EM field, then the space is curved, but if no EM reactive metal is there, then it's not curved (by the EM field). I REALLY doubt that it works like that.
There is one fundamental difference between gravity and the other three known forces (electromagnetic, strong, and weak). It affects everything we know the same way. Let me put this in simple maths. The gravitational force can be written like this (accurate for most of the stuff happening on earth). (Inertial mass) * (Acceleration) = (Gravitational mass) * (Intensity of the gravitational field) For an electric field, the corresponding equation looks like this. (Inertial mass) * (Acceleration) = (Electric charge) * (Intensity of the electric field) The equations look very similar. Essentially, the gravitational mass gets exchanged with the electric charge. What makes gravity special is the additional equation (Inertial mass) = (Gravitational mass) There is no known exception to this equation and it's not an equation that can be derived*. It's just the nature of gravity. Unlike every other force, you don't need to know an additional property that varies in between kinds of particles like electric charge, color charge, or weak isospin to determine how a particle behaves in a gravitational field. Using a curvature of space-time to describe gravity makes sense because every body is affected the same way by gravity. When no forces other than gravity are at work, you can replace any sample particle with any other kind of particle and it follows the same path through space-time (if the disturbance of its surroundings due to a difference in mass is negligible). It would be a bad idea to describe electromagnetism using a curvature of space-time though. A positively and a negatively charged body experience completely different forces and therefore travel on different trajectories. Unless they live in a different space-time, that's a contradiction. They would 'experience' the same space-time completely differently. * Until, maybe, someone comes up with a working Theory of Everything.
According to the General Theory of Relativity, the space will curve where ever a presence of a field, here a gravitational field will induce an acceleration on an object. But let's see how complications may arise if we were dealing with massless objects. Picture yourself in a gravitational interaction with the Sun's field and finding yourself in a freefall towards the Sun (mind you, you're free-falling towards the Sun even when you're in orbit around it). If you're free-falling towards something, you don't feel any g's or acceleration. Call this an intristic motion. Now, let's say the Sun orbits the galactic center once every second, but then let's say the galactic center has no gravitational field and interacts with the Sun using an electromagnetic field. You carry no ability to interact with electromagnatic fields, but only with gravitational fields. The Sun does both. Would you then feel any g's as a result of orbiting the galactic center together with the Sun? No you would not, because your perception of acceleration due to your limited senses is locked in only, exclusively with the gravitational fields. Does this mean no centripetal acceleration around the galactic center (and no curvature of space) occurrs at all just because you cannot sense it? No. On the other hand it could mean that acceleration is relative, depending which type fields you wish to consider. Or let's have an opposite scenario. The Sun orbiting in the galactic center's gravitational field, and you free-falling towards the Sun. But you consist of atom-like entities which are all massless and charged and also so you won't get ripped to shreds all have the same charge to mass ratio (or I guess charge to something else ratio since in this instance you don't have a mass), and you can only interact with the Sun's electric field, and let's assume in this universe the Sun possessed one that was quite extensive. Your senses which detect acceleration are locked in with the electric fields. By free-falling, you don't feel any g's with respect to the electric field. Should you then feel any g's as a result of orbiting around the galactic center? You won't, since your senses are locked in only with the electric field of the Sun. Yet it doesn't mean you're not accelerating and that space doesn't curve as a result of gravity.
In any case, I'm not talking math here, but only in lose, general concepts. So let me try again. The reason why you presumably have only the gravity stamping out how the space should curve is because gravity is neat on macroscales while electric and magnetic forces are not. Gravity exerts a uniform force on all parts/atoms comprising a large, composite, multi-atomic object. Moreover, all atoms are electrically neutral, so all charges cancel out. If they were not, you would get ripped to shreds since electric forces would overwhelm anything else. But now if you had an object consisting of charged atoms, but these atoms would all exhibit identical charge to mass ratio, such an object would behave in an electric field in a similar manner to how anything with mass behaves in gravitational fields. The odds of finding such an object even if charged atoms were common would be next to nil since different atoms would exhibit different charge to mass ratios. But on subatomic scales, isolated charged particles abound, so on such scales electric and magnetic fields could determine space curvature just as readily as gravitational fields would. (a problem here concerns the fact that fields themselves consist of subatomic particles - photons or electrons, so if you reduce an object down to a subatomic scale, it may become a constituent part of the field, provided you end up with a right type of a particle). Let's approach this problem differently. Let's say the only gravitational field you experience is the Earth's gravitational field. Then you can bounce the Earth around like a ping-pong ball and all the time you would not feel any acceleration aside from the one g which renders you tendency to accelerate towards the Earth's center. That's because your sensory organs which evolved to perceive acceleration are locked in with the gravitational field i.e. they have evolved to measure any acceleration or force against this "control" gravitational field, henceforth if this gravitational field itself moves or vibrates within some higher dimension, your sense organs would not detect this sort of oscillating acceleration, because they are locked-in with the Earth's gravitational field. But now let's say you consisted of atoms where gravity and anti-gravity cancelled out but where charges did not cancel out, and your acceleration-measuring senses were locked in with an electric field. Of course in the real macroscale world you would not normally find such objects with reversed properties unless you moved down to subatomic scales, where you have particle objects with single charges, so you can talk in concepts of charge to mass ratios, where perception of acceleration may be locked in either with a gravitational or electric fields since either force will exert itself uniformly on all parts constituting these particle objects. And then you can push the concept further and do away with gravity all together if you hypothetically assume entities can exist with their gravity and hypothetical anti-gravity cancelling out.
You keep using the phrase "locked-in with a kind of field", but I don't know what that means. Could you explain that? Hypothetical scenarios aside, our acceleration-measuring sense is comparing the acceleration of the head to the acceleration of liquids inside small tubes. It's mostly an electromagnetic process, since electromagnetism holds our body and all the chemical compounds together. The sensing and signaling to our brain is also electromagnetic. Since the gravitational field is almost constant within our head, we cannot sense gravity directly. What we sense is the fluids trying to fall due to gravity while we're standing on the ground (due to the em force), which prevents the head around the fluids from falling freely.
I would think you are right, the earth does rotate around the sun and nobody can really feel which quadrant of the orbit we are on. We may or may not even feel the rotation of the earth to be honest. I imagine if it were to change we definitely would. Why the talk of perception? I mean, realistically, atoms do curve space. The remaining forces that govern subatomic scales are so astronomically high that anything which exhibits a physical reaction will undoubtedly be more controlled by the close-knit effect that the (overarching) gravity. Assuming, that ⌂g does not mean a change in physical laws. Let me see if I can word this out: A: Gravity bends space H: If atoms demonstrate the same characteristics or effects of gravity, then they are also bending space. (http://www.astro.virginia.edu) Looking near the sun in a clear sky, around noon, we can see just how powerful its light is. Pure White and very difficult to look at. When we look at the surrounding sky, we see the scattered "blue", it is very soft and easy to look at. At sunset, the blues become rich reds and oranges near the sun, and even purples. 1. Sun produces light. 2. The light changes colors at different times of the day. (Ruling out several assumptions, things like weird fields in space) 3. Certain spectrum of light refract off ambient air. 4. Light changes angles based on its interaction with molecules OR 5. Light is completely absorbed by molecule and a resulting wave balances the system. What is the criteria for bending space curvature? If it was just solely a predictable lens-like result, then it happens everywhere naturally in atoms. I think you have a point with gravity being "overrated". It is an enigma, but it is maybe a hair more mysterious than quantum mechanics.
Then again, going back to fundamentals, you cannot have acceleration without mass. F=ma a=F/m. Oh, well, no fireworks here.
I would prefer to say that this equation is just inadequate when it comes to describing massless particles. Sure, a hundred years or more ago, I might have answered that there are no massless particles because Newtonian mechanics breaks down without mass. As it turns out, nature doesn't work that way. We observe that massless particles always travel at the speed of light in vacuum. Therefore, massless particles can only accelerate perpendicular to their direction of motion. Force can be defined without using mass though, if you describe it as a change in momentum: F=dp/dt. In relativity, the connection between energy, momentum, and mass is given by: E^2=m^2*c^4 + p^2*c^2. For a massless particle this reduces to E=|p|c (p is a vector, |p| is its absolute value, this is the positive energy solution only). From that, you can build a kinda-Newtonian, witch doctor math approach to describe the motion of light when it's affected by an external force. Consider two cases: 1. F is perpendicular to p p changes its direction, but its absolute value remains the same and E remains the same. 2. F is parallel to p p keeps its direction, but its absolute value changes and so does E. Since the energy of a photon is given by E=hf according to quantum mechanics, a force in the direction of p increases frequency (blue shift) and a force in the opposite direction reduces frequency (red shift). The speed, however, remains c. Those results agree with nature at least qualitatively. Of course, you would need to have an expression for the gravitational force on a massless particle for this to work properly. Hmmm....
