Let me try to restate to see if I get what you’re saying (in which case you’re flatly wrong).

Observer O on a planet, observers A and B in ships traveling in opposide directions from the planet with velocities v[sub]A[/sub] and v[sub]B[/sub], respectively, as measured by O. A says B is moving away at a speed given by the Einsteinian sum of v[sub]A[/sub] and v[sub]B[/sub], and B says the same for A. However, you contend that O says A and B are moving apart at the Galilean sum of v[sub]A[/sub] and v[sub]B[/sub]?

Getting back to the OP, because I am sitting in a chair at my desk, the earth is currently stationary (other than a slight rocking). If I get hungry later, I suspect the earth will move in precisely the right way as to bring my kitchen to me. The earth is generally quite cooperative about such things.

To give a slightly more serious answer, Newton believed that space had an absolute position. (This is a philosophical idea called “substantivalism”.) Leibniz, Newton’s rival, believed that it is only meaningful to talk about the relative positions of objects, not positions relative to some fixed position of space. (This is the “relationist” view). Even though Newton is a few centuries out of date, and most modern day scientists probably assume relationism, it isn’t really so simple to prove Newton wrong. You can’t show that space doesn’t have a position, only that the position of space has no observable consequences. Of course, some would say it’s absurd to ascribe properties to the universe that have no obervational consequences, and in fact this was one of Leibniz’s arguments against substantivalism. Newton’s response was that there are at least consequences of an object being accelerated relative to the universe, namely that it won’t be in an inertial reference frame. (In Whack-A-Mole’s two person universe, if person A and person B move relative to each other at a constant velocity, then there’s no way to distinguish whether person A or person B is moving. However, if one accelerates, then it is possible to distinguish in a meaningful way which one is accelerating.) So in Newton’s view we can at least conclude that all objects in inertial reference frames are moving at constant velocities relative to the position of space. The standard relationist answer is that all we can really conclude is that there are some objects that have the property that they are in an inertial frame, and that all of these objects must move with constant velocities relative to each other.

This is true in SR, however in GR we can’t tell if A is stationary while B accelerates or if B is stationary while A is in a gravitational field. Once you throw GR into the mix, Lorentz invariance (which states the equivalence of the laws of physics in all frames inertial with respect to each other) gets promoted to “general covariance”.

In case you didn’t follow Mathochist’s answer… no.

Even though they’re each moving away from you at just under c, and they’re going in opposite directions, the difference between their speeds is just under c, not just under 2c.

When dealing with relativity, you can’t simply add and subtract velocity vectors near the speed of light. It’s more complex than that.

Nah, I figured out my mistake this morning.
If the near lightspeed traveller shoots a laser beam in front of him, the light beam is no longer in his timespace frame of reference because it has higher velocity. In effect, the light beam is a new observer to the system.

If one takes a wormhole, or whatever shortcut proves feasible, they’ll arrive at their destination before their observable self leaves the take-off point. Nobody will be able to see this, but they’ll know it.
Say you go to Alpha Centauri. Say it only takes one year. You could stand on the pad and wave, then 2 1/2 years after you arrive you could look back and see that wave.
Anyway, your “effective” speed (for want of a better term) would be way faster than light. Does science forsee any penalty for that?

What if both Persons had a device that fires a soccer ball at a fixed speed (assuming no effective gravity in this nearly empty universe) with pinpoint accuracy. They both fire a soccer ball at each other. When the two balls collide, whichever is going faster will bounce the other one backward, won’t it? I’m thinking of velocities way below c.

Let’s say both Person A & B measure each other’s velocity as 100 km/h coming directly at each other. The soccer ball guns fire balls at 100 km/hr. So the possible range is Soccer Ball A going 200 km/h and B is going 100 km/hr, both going 150 km/hr, or somewhere in between.

Couldn’t you just measure the resultant collision and determine pretty accurately which Person was moving faster, and by how much?

That’s only true if you actually travel alongside light, but at a speed faster than light. A wormhole is supposed to give you a much shorter traveling distance, which can be traversed at conventional speeds, resulting in reaching a destination that can arbitrarily exceed the light cone.

So if you entered a wormhole that went to another galaxy, but which appeared about a mile long, and then turned around and came back through it, you wouldn’t necessarily be traveling through time. Although I confess that I find it highly unlikely that a wormhole burrowing a shortcut through space would leave time untouched.

We have that whole observer/point of view issue here, too. If you don’t have some fixed point of reference, the only thing that matters is the difference between their velocities (delta-v). If you’re moving along with ball A, it will look like a stationary ball A being hit by ball B at 100mph. If your velocity is exactly between theirs, then it will look like a collision between two balls moving at 50mph each. If you’re moving along with B, it will look like A is moving at 100mph and hitting a stationary B.

that we are moving at a substantial fraction of the speed of light? That would mean that we are experiencing time dilation (with respect to the rest of the univers). This copuld also explain the red shifts we see observing distant stars. Also, t would mean that we are measuring the age of the universe totally wrong-while our measurements find the universe to be 5-7 billion years old, we may in fact be in substantial error.

Redshifts are how we measure the speeds of distant objects. There’s no need to explain them in terms of some vast unexpected velocity.
The latest measurements of the age of the universe give a figure of 13.7 billion years.

But the rest of the universe isn’t “stationary”. We are moving at different velocities (and in different directions) relative to different parts of the universe.

Except that we observe the red shift from stars in completely opposite points in the sky, which, if it were caused solely by our motion relative to a “stationary” universe, would require us to be moving in two directions at once.

But if both balls are moving at roughly the same speed, after the collision they will bounce away from each other. If one is stationary, they will both end up moving in the same direction, continuing the path of the ball that was moving. In your example of moving along with Ball A, let’s say three cases: ball A is stationary, moving at 50 km/h, and 100 km/h with Ball B being stationary.

Okay, in all 3 cases, it appears to you, moving along with Ball A, that Ball A is stationary. In the first case, where the ball really is stationary, your observation is that after the collision, both balls travel backward away from you. In the second case, where both velocities are equal, after the collision Ball A will bounce backward away from you, while Ball B will travel in your same direction at about half your speed. In the third example, with Ball B stationary, after the collision Ball B will now be traveling along with you, appearing to stay stationary, while Ball A will follow you at about half your speed.

All three scenarios apppear (to me) to produce measurably different results. I know I’m missing something. What is it?

Actually, any method for getting from point A to point B before light could get there travelling in a vacuum can be used as a method of time travel. It doesn’t matter whether your travelling method is a wormhole, or a warp drve, or a tesseract, or a magic carpet, so long as it’s consistent with Special Relativity (that is to say, that it has no preferred reference frame).

OK, take that example where they both move in the same direction. Unless they end up stuck together, one will be moving faster than the other. Now suppose you move alongside the balls, at a speed in between the speeds of the two balls. What will you see, in that reference frame? You’ll see the two balls moving away from each other, one forward, the other back, just as in the case where they started off moving at the same speed.

And here’s the key: In the situation where you throw the balls such that one is “moving” and the other is “stationary” (relative to some particular reference frame), that’s because you are, in fact, in that frame moving at the average speed of the balls. So either way, in your reference frame, you see the two balls hit and them reverse direction, moving away from each other.

Chronos, I’m surprised at you. A wormhole doesn’t allow you to get from point A to point B faster than light could get there. Say I’ve got a wormhole in my closet (I very well might: I haven’t seen the back in a long, long time). Say it leads to the closet of a very messy mathematician living on a planet orbiting Alpha Centauri and takes about a minute to get through. Yes, I can get to Alpha Centauri in about a minute, which is far less than it takes light to get there normally, but light can go through the wormhole, getting there in less than the minute it would take me to get there.

I won’t claim to speak for Mathochist but I think I know what he’s on about. I also seem to remember a conversation like this one a long time ago with Chronos and brought up the same issue but I do not recall an answer to it.

The idea here is you have two paths a beam of light can take. One the long way through normal space and one through the wormhole. Long way is a 4.4 light year trip while the wormhole is, say, 1,000 miles long.

If you travel through the wormhole you get there before light taking the long route but any light travelling with you down the wormhole beats you to the other side. You are not actually travelling faster than the speed of light…you are merely taking a shortcut through space.

As an example say I point a laser at a reflector on the moon and point another laser across my room to a detector 1 foot away. I shoot a photon at the moon and step the 1 foot to the detector beating the photon that went to the moon. However, the photon shot the 1 foot across the room handily beats me to the detector.

Another way to think of it would be to build a tunnel through the earth. Light going around the earth takes longer to arrive than light going down the tunnel but no one would say time travel is happening merely because you have a shorter route.

I do not see how a wormhole would violate any causality. Certainly you could get some weirdness like if I went to Alpha Centauri and looked back at earth with my super-duper telescope I could watch myself walking about some 4+ years in the past. However, I cannot go back to earth having “time travelled” via the wormhole and go talk to myself (or in any way communicate with my past self to violate causality).