I'm having difficultly parsing your sentences, and understanding your point. Why is it that in my scenario all observers agree the flash happens before the bullet hits the vase, but not in yours? The only difference I see is that the bullet causes the light emission. If we just have a randomly emitted light (at the same place where the light emittor was, happening when the bullet would have caused it to happen) isn't that your scenario, or am I missing something from your scenario?

Oh, I think I see the difference. You are assuming that the light flash happens late enough that the bullet reaches the vase before the light-cone of the flash does.

It might be enlightening if you think through what an observer outside the light cone sees and why.

DarJones

[QUOTE=Zeta-Flux;117968]What do you mean by "on the same light cone"?[/QUOTE]

With all due respect, the fact that you asked the above question tells me that while you may be "trying to understand some philosophical implications of relativity", you haven't done the required reading on the basic principles of the subject, the kind anyone with a grasp of basic algebra can and should master. Deeper philosophical implications are something one is only qualified to ponder once one has mastered at least the fundamental principles. [Math-o-phobic Squishy-Liberal-Arts types *hate* to hear this kind of thing, but that doesn't make it less true].

Any freshman or sophomore-level "modern physics" text should have the information you require.

One of the nicest, clearest introductions to this is "Relativity, The Special and the General Theory", a popular exposition by Albert Einstein. It gets pretty hand-wavy when it gets to the General Theory, but at the level of Special Relativity, he really proceeds carefully and makes some nice appeals to intuition. When I took my physics qualifying exam, there was a special relativity question on it, and I couldn't pull the Lorentz transformation equations out of my derriere for the life of me, but I didn't panic - I just thought carefully about what Uncle Al had said and I was able to solve the problem. I think it is available in a Dover reprint now, as is a collection of classic papers by Einstein, Weyl, and Minkowski on Relativity, a little more rigorous but still enjoyable to read.

Not precisely on topic, but from a general viewpoint, highly relevant.

[url]http://www.mathpages.com/rr/rrtoc.htm[/url]

DarJones

ewmayer,

You are correct that I didn't do any pre-reading. I supposed that my questions were simple enough that someone could more easily answer them than for me to take the time to sit down with a physics text-book and study the material. I imagine it took xilman a few minutes to answer the questions I had, whereas if I had read a physics book I would have learned about light cones fairly thoroughly, but not necessarily have had my questions about causality answered.

My question about "on the same light cone" was brought about because xilman's wording and reference to "simultaneity" confused me. As Paul later clarified, this was not meant in the "conventional sense." It wasn't because I didn't understand the concept of a light cone (which I do) that I asked the question.

But, just to make it worth xilman's time in answering my questions, I'll happily take him out to dinner if he ever stops in Iowa City.

Best,
Zeta-Flux

-------------------------------

Fusion-power,

As I understand it, an observer outside the light cone doesn't see anything. :p Okay, dumb joke.

Here is how I understand xilman's setup:

"Let's assume that the bullet is an object with mass, as I think you intended. I.e. the bullet travels slower than light in all frames of reference and your gun is not (for example) a laser. Let's assume the vase is a light year away and your bullet, as you measure it, is travelling at half the speed of light. (You have a very powerful gun and a very good aim.) Of course, as the bullet measures things, it is stationary, you and the gun are receding at c/2 and the vase is approaching at c/2."

So far so good. I understand everything.

"A light year behind you, a flash of light occurs such that it arrives where you are when the bullet is (as you measure things) 90% of the way to the target."

Okay, by "A light year behind you..." I take that to mean that previously I've placed a box which will give off the light pulse, in a position in space, in the opposite direction than the bullet took, the distance of 1 light year. Also, by "as you measure things" I think xilman means that if I pull out my trusty calculator, I figure that the bullet is 90%of the way to the vase when the flash of light from the box also hits my eyes.

"As far as you are concerned, the flash happens before the bullet hits the vase. From the point of a view of an observer sitting in the vase, the flash occurs well after the bullet arrives (assuming the observer survives the collision with the bullet!)."

This I don't follow. A year after I see the flash, the observer in the vase sees the flash. But, knowing where I placed the buoy, he calculates that the flash took place before the bullet hits the vase.

[QUOTE=Zeta-Flux;118076]But, just to make it worth xilman's time in answering my questions, I'll happily take him out to dinner if he ever stops in Iowa City.[/quote]Very generous, thank you. I'll hold you to that next time I'm in the district.
[QUOTE=Zeta-Flux;118076]This I don't follow. A year after I see the flash, the observer in the vase sees the flash. But, knowing where I placed the buoy, he calculates that the flash took place before the bullet hits the vase.[/QUOTE]Nope. It is of no matter at all to the guy in the vase what you saw. What [b]he[/b] sees is the vase shattering and, some time afterwards, a flash of light coming from the same direction as you and your gun.

Now do you see that temporal ordering of events can depend on who is observing the events? You measured the flash to occur before the vase was smashed. The guy in the vase experienced the smashing first and the flash afterwards.

To some extent, I'm crippled by having to explain this stuff without diagrams and at high latency. It is very much easier face to face and with pencil and paper available. Apologies for not being as clear as I could be under more favourable circumstances.

Also: I get the feeling that you are still thinking in terms of Euclidean geometry and of separable space and time. In relativity, space and time are inextricably intermingled and the only thing that everyone can agree on is spacetime. Every individual observer can certainly distinguish between space and time but there is no way in which everyone can all agree on the same separation. The word "Euclidean" also merits expansion. In Special Relativity, spacetime is flat but it is not Euclidean. It is Lorenzian. The distinction is as follows:

In four-dimensional Euclidean spacetime, (the square of) an element of length is given by ds^2= dx^2 + dy^2 + dz^2 + dt^2, where x,y,z,t are the Cartesian axes. That is, essentially, Pythagorus' theorem.

In four-dimensional Lorenzian space time, the formula is ds^2 = dx^2 + dy^2 + dz^2 - dt^2. The minus sign is of critical importance and is responsible for most, if not all, of the initially counter-intuitive features of SR. In particular, it's possible for the length of a vector to be zero even when the spatial cordinates of each end of the vector differ. All that is required is that the separation in time of the ends of the vector have the correct non-zero value. Specifically, if dt^2 = dx^2 + dy^2 +dz^2.

(Note that I'm using the convention that c=1 for simplicity in notation. Replace t by ct in the above formulae if you want to measure (x,y,z) in metres and t in seconds.)

Paul

Paul,

It is clear to me that the order in which one sees the flash and sees the vase smash depends on where one is. But that doesn't have anything to do with the theory of relativity, as such. Rather, with when the light from the initial flash reaches a person. As I use the word "event" there are three events: event 0 is when the initial flash happens, event 1 is person A sees the flash, and event 2 is that person B sees the flash. These are not the same event (using the standard definition of the word--perhaps not using the non-standard definition of simultaneous that you were using previously). But, if we identify all points on a light cone as simultaneous, then (and only then) can I make sense of what you are saying.

[QUOTE]Now do you see that temporal ordering of events can depend on who is observing the events?[/QUOTE]Not really. The person in the vase can quite easily calculate when I (on earth) saw the light, and can tell that I saw it before the vase smashed. So the event of "me seeing the light" preceded the vase smashing event, whereas the event of the "vase-alien seeing the light" happened after the smashing.

[QUOTE=Zeta-Flux;118076]You are correct that I didn't do any pre-reading. I supposed that my questions were simple enough that someone could more easily answer them than for me to take the time to sit down with a physics text-book and study the material.[/QUOTE]

Well, very briefly, since Paul already described the Minkowski metric of special-relativistic spacetime, a light cone is simply a surface in spacetime having constant x^2+y^2+z^2-t^2, where again I've absorbed the speed-of-light factor into the time term.

Note that this only defines a visualizable cone in 3-D, e.g. try it with only the x,y,t dimensions and t playing the role of the 3rd coordinate in a 3-D cartesian picture. In the full 4-D, it's actually a "hypercone", but the math is no more complicated, just the full x,y,z,t coordinates.

As for why there is no concept of absolute simultaneity: well, that's why it's called "relativity."

Rocket in Barn "paradox"
 

[quote=Zeta-Flux;117958]
A rocket can be shooting towards a barn door at nearly the speed of light. From one frame of reference A, the rocket hits the barn door at time t_0, and a person in frame A pushes a button to signify this act. From another frame of reference B, it appears that the person in frame A pushed the button too soon.
....
Am I understanding this correctly?

Thanks,
Zeta-Flux[/quote]

I don't think you have understood the the "paradox",
let alone its resolution.
As you have expressed it, it depends on where the person
in frame A is located.
If he is at the door, all observers agree
that the events "rocket hits door" and "person presses button"
are coincident in spacetime (and simultaneous).
If he is some distance from the door, observers in other frames
may not deem the events simultaneous.

But I think the paradox involves the door on the far side of
the barn opening when the rear of the rocket passes the
front door. The question to be resolved unambiguously by
all observers is "does the rocket crash into the back door
or not".

David