Thanks for the response about the triangle. But I wonder, is it really a useful experiment? Allow me to explain:
First, let me describe how this experiment might be done.
You get three guys, and give each a really bright light (that shines in all directions) and a protractor. They go to three different locations. Each one looks at the lights of the other two, and measures the angle between them. The three guys meet later, and add up their measurements. In a “flat” (part of the) universe, these numbers should add up to 180. (or pi, as my old math teacher would insist).
Now, let’s suppose you repeat this experiment in a heavy gravitational field (maybe near a black hole). You’ll get a number that’s bigger than 180, I suppose. But why? Certainly, one explanation is that space-time is curved in that area. Another explanation is that gravity bends the rays of light and distorts the measurements.
I suspect that these two “explanations” are more interpretations than explanations. Why do I think so? Well, describe an experiment that would distinguish between the two explanations.
Near a strong gravitational field, the curvature of space is negative. So your triangle would have less than 180 degrees (or pi radians).
You are correct that the two explanations are both valid. Distance, time, straight lines, and simultaneity are all matters of coordinate definition.
A universal force is a force that affects everything equally. Heat causes (most) materials to expand. Heat is not a universal force because it affects different materials differently. If you want your space to be flat, you may do so by allowing universal forces. In this way space does not curve, but matter is distorted by universal forces. One of the problems with universal forces is detecting them; all of your instruments are affected equally. It is more usually more useful to define your coordinate system so that universal forces are zero by definition. If you do this, you will end up with curved space. If someone says light is bent by a gravitational field, they are probably trying to impose a flat coordinate system on space.
It is not meaningful to ask which is correct or true. Rather the question should be whether a system useful. As long as both systems make accurate predictions about observations, both are “correct”.
“Everything, be it matter or light, traces out geodesics in space-time if under the influence of no force other than gravity.”
Thus, if I drop a bullet, and shoot a laser-gun at the same time . . .
Anyway, I would just like to pursue the 180 degrees issue. Let’s suppose that we do our experiment on the surface of the Earth, with one person standing at the North Pole; one person standing in Portland, Oregon; and one person standing in Montreal, Quebec. Let’s further assume that there’s a black hole or something at the center of the earth, and gravity is really really strong. (But somehow doesn’t kill us all :)) Gravity is so strong in fact, that light basically travels along the surface of the earth. So each of our guys sees the others’ lights right on the horizon.
In this scenario, our friend in Portland measures an angle of about 90 degrees, since the North Pole is due north, and Montreal is (basically) due East. Similarly, our man in Quebec measures an angle of 90 degrees. Finally, Santa Claus (or whoever) measures an angle of 45 degrees, since Quebec is 45 degrees of longitude east of Portland. The total? 225 degrees. Thus, I believe that in a strong gravitational field, you would measure a triangle with greater than 180 degrees.
>>For instance, since gravitational effects propagate at the speed of light, the graviton must be massless, and because it’s a tensor field, not a vector field like EM, the graviton must have a spin of 2, unlike most fundamental particles with a spin of 1/2 or 1.<<
ok, so maybe I am an idiot.
But…
What is a tensor field and a vector field?
What is a spin?
First, stop criticizing gabbyhayes and each other. Second, I notice one of the repliers put in that it isn’t objects that are expanding in the universe but the space that hasn’t got much in it “between celestial objects.” AHA!!! Here’s the problem. First a person reads that the universe is expanding. Then upon closer examination it turns out that this doesn’t mean like our solar system is getting farther from other ones. It means our entire galaxy is getting farther from other ones. No, wait when you read further, it is groups of galaxies like our whol e Local Group that is moving farther from others. But then it says the Local Group is on the edge of a cluster a big cluster and ultimately part of the Virgo cluster I think. And one soon runs out of anything left to expand. The expansion of the universe turns out to be one of those laymens explanations that upon close inspection falls apart. Third, where can I get a sheet of rubber? Ever since I discovered topology back in high school I have wanted a sheet of rubber, but nobody ever says where to send away for them. Also, where can I get mathematical models like I used to see in the math department glass cases back in college.The University of Illinois had these beautiful plaster shapes of hyperbolic paraboloids and so on and functions in glass cases in this dark hall in a Gothic or I mean a Romanesque building calledAltgeld Hall. KNowing how big institutions are run, I assume they threw away the models and junked the building and replaced it with a box. But anyway, isn’t there some place that makes models I could send away for, as if I were buying them for a class?
Let me give a try until someone better comes along …
A field is a mathematical quantity that is defined as a function of position in space. Scalar fields are those in which just one number (the “value” of the field) is associated with each spatial point. In vector and tensor fields, more than one number is associated with each spatial point. Newtonian gravity is a vector field, in which three numbers (that specify the magnitude and direction of the number) are associated with each point in space.
Tensors are very similar to vectors; vectors are actually “first order tensors”. Tensors are quantities for which the rules for transforming between differerent coordinate systems take a particular form. The order of the tensor is the number of cosine functions that appear in each term of the transformation. As a mechanical engineer, the tensor with which I am most familiar is the stress tensor, a second order symmetric tensor described by six numbers (three normal stresses and three shear stresses). A general second order Cartesian tensor is described by nine numbers.
A property of subatomic “particles” that is somewhat analogous to, but not the same as, a spinning top. All “matter particles” have spin 1/2 (the units are h/(2*pi), where “h” is Planck’s constant) and all “force mediation particles” detected to date have spin 1. You can think of spin somewhat like angular momentum; it is conserved like angular momentum.
Nah. It remains a fact that cosmologically-distant galaxies appear to be receeding from us due to the expansion of space. (I say “appear” because, from the viewpoint of that distant galaxy, our galaxy appears to be receeding.) The overall point was that the expansion of space takes place on huge scales (megaparsecs) and the effect can be canceled out on closer scales due to gravity, etc.
