Teeming millions help me!! Who among you is conversant in astrophysics??
If I am travelling in my car toward another oncoming car, and we both have our headlights on, then, according to the cosmological constant of the speed of light, observers in each car will measure the speed of light at the same rate as if we were standing still. Does this not mean that space is bending between our cars? Does this not imply that space bends around us all the time to accommodate us??
Also, just how much mass does it take to bend spacetime and attract other bodies?? Does my body have enough mass to attract particles, or is this attraction electrical instead of gravitational? If I ate enough chili dogs, could I effect my own gravitational field??
Astrophysics?
OK, but, the cosmological constant is something else.
I don’t think that it implies that.
Any amount, if you’re thinking about gravity as distorting spacetime.
Mostly not gravitational.
I knew you were being silly.
andy: Don’t feel bad, Einstein invented Special Relativity when he asked himself this question. What happens is that time and space both distort as you approach the speed of light. Time passes more slowly as measured by an outside observer, and your car contracts along the axis of motion.
Space and time are constantly being warped by our motion and mass, but it’s all very tiny and irrelevant. As RM M noted, this has nothing to do with astrophysics or the cosmological constant.
As RM Mentock mentions, the “cosmological constant”[sup]1[/sup] is not the term you’re looking for here. You’re talking about Special Relativity. Special Relativity assumes a constant speed of light in a vacuum.
The “space bending” analogy is usually used with General Relativity (aka Einsteinian Gravity). Special Relativity really has to do with how measurements occur under constant (i.e. unaccelerated) motion. According to SR, space and time do not have independent existence. Rather, space is what we measure with a ruler, and time is what we measure with a clock.
Suppose your friend is in his spaceship at rest relative to you. He has an odd “clock” aboard that emits a pulse once every second. You point your telescope at him and measure the time between successive pulses. Unsurprisingly, you measure exactly one second between each pair of pulses.
Now suppose he starts travelling towards you and eventually reaches half the speed of light (relative to you, of course) and starts coasting (if he’s still accelerating, we can’t use special relativity). Again, you turn your trusty telescope towards him and start measuring the time between pulses. Obviously each pulse of light starts off considerably closer to you than the previous pulse. Since light always travels at a constant rate and each pulse has less distance to travel, you will see each pulse arrive much less than a second after the previous pulse. Since time is what you measure with a clock, you correctly conclude that time is elapsing on the ship at a faster rate than your own time.
Similarly, you have a similar pulse-emitting clock, and he has a telescope pointed towards you. When he receives a pulse he is much closer to you than he was when he received the previous pulse, thus it will arrive sooner, and he will see your time as elapsing faster than his. A curious seeming paradox, which gets resolved with General Relativity. Such an outcome has to occur: there should be no physics experiment that would distinguish the cases of him moving and you at rest, you moving and him at rest, or you both moving.
Note: I’ve probably made some horrendous errors. I really should wait until Chronos gets here, but why should he get all the fun?
Now we get to General Relativity. GR talks about how measurements come out during accellerated motion or in a gravitational field. An important side issue is that GR actually shows that acceleration and gravity are really the same thing, as are mass and energy (thus we call it mass-energy). Also, space and time are just two components of space-time; space (ruler measurements) and time (clock measurements) may vary according to how fast you’re moving/accelerating relative to what you’re measuring, but space-time is always the same (a feature of the GR that Minkowski noted even before Einstein).
Note that “bending” space-time (as noted in other threads) is only a good analogy if you don’t examine it too carefully. The only way to really understand GR is to learn the math. But some of the effects of GR do come out pretty close if you think about space bending (contrawise, you can think of it as shrinking rulers and speeding up clocks directly, the math ends up the same).
According to GR, any amount of mass-energy “bends” space-time and displays a gravitational field. It just does it, though, because it does, not to “accomodate” us.
Your body does indeed have enough mass to “bend” space and does show a gravitational field. Remember, though, gravity is very very very … very weak. It takes the entire mass of you plus the Earth just to keep you sitting in your chair with (typically) 150 lbs of force. The gravitational force your body exerts on a thimble is to small to measure with even the most sensitive instruments.
Since your body is usually elecrically neutral (it has an equal amount of positive and negative charged particles), it’s net electrical attraction is zero (unless you have a particularly magnetic personality! :D)
Yes! By concentrating more mass in the same amount of space, you would indeed increase the nearby gravitation field (the field outside the original location of you and the chili dogs would be unchanged). However, since gravity is a very weak force (did I mention that it’s really really weak?), the difference wouldn’t be detectable.
Relativity is a very complicated subject. You might try some books about it. I did a quick Amazon search for “General Relativity” and came up with some interesting hits, including (no offense intended) The Complete Idiot’s Guide to Understanding Einstein which garnered some good reviews.
[sup]1[/sup]The original “cosmological constant” was a negative gravitational force Einstein made up to try to make the GR equations predict a static (neither expanding or contracting) universe. However, in according to Quantum Mechanics, even the vacuum may have actual energy; if so, that energy would show a negative gravitational force, similar in nature to Einstein’s cosmological constant.
Joe Malik
Your explaination was pretty good, but you are incorrect about the time dialation. A moving clock measures time more slowly that a stationary clock. This effect is not caused by the time between light-images of the clock, and the time dialation occurs whether the moving clock is moving towards you or away from you. The effect you describe happens even without relativity. Relativity predicts a difference when this effect is accounted for.
Also, I wouldn’t call it a paradox that each observer sees the other’s clock as moving more slowly. This is only a paradox if you cling to the idea that there is some absolute time.