Simultaneity- a physics question
 

I'm trying to understand some philosophical implications of relativity, and I was hoping some of you physics gurus could help me out. As I understand it, the following can happen.

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.

Would this imply the following?: From my point of view, there is a frame of reference occuring *now*, from which it appears I am not born yet? [What I mean is that there is some alien named Charles who, it looks to me, exists right now. However, from his point of view, even taking into account the speed of light, I will only be born years from now.] I'm really trying to get a grasp on what "now" means, and it seems to depend on the frame of reference. Further, it doesn't seem to be a symmetric or transitive relation.

Am I understanding this correctly?

Thanks,
Zeta-Flux

[QUOTE=Zeta-Flux;117958]I'm trying to understand some philosophical implications of relativity, and I was hoping some of you physics gurus could help me out. As I understand it, the following can happen.

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.

Would this imply the following?: From my point of view, there is a frame of reference occuring *now*, from which it appears I am not born yet? [What I mean is that there is some alien named Charles who, it looks to me, exists right now. However, from his point of view, even taking into account the speed of light, I will only be born years from now.] I'm really trying to get a grasp on what "now" means, and it seems to depend on the frame of reference. Further, it doesn't seem to be a symmetric or transitive relation.

Am I understanding this correctly?

Thanks,
Zeta-Flux[/QUOTE]"Before", "after" and "simultaneous" are not particularly useful concepts in relativity. As you state, everything depends on the reference frame.

The concepts that make more sense are "causally connected", "not causally connected" and "on the same light cone".

If two events are "on the same light cone", they are separated in spacetime such that a photon can travel (in either direction) between the events and so that either event could have caused the other. This is probably the closest to a true notion of simultaneity that exists in relativity.

If two events x and y are causally connected (and not on the same ligh ctone) every observer can agree on exactly the same ordering of the two events. Either x could have caused y (and therefore the x could be interpretated as happening "before" y), or the reverse situation holds (and x occurs "after" y); no-one observes the events occurring simultaneously.

In the acausally connected situation, some observers will claim that the event occur in one order, other observers that they occurred in the reverse order and still others that they occurred simultaneously.

I don't know how much this helps, if any.


Paul

[QUOTE=Zeta-Flux;117958]Would this imply the following?: From my point of view, there is a frame of reference occuring *now*, from which it appears I am not born yet? [What I mean is that there is some alien named Charles who, it looks to me, exists right now. However, from his point of view, even taking into account the speed of light, I will only be born years from now.] I'm really trying to get a grasp on what "now" means, and it seems to depend on the frame of reference. Further, it doesn't seem to be a symmetric or transitive relation.

Am I understanding this correctly?[/QUOTE]I 'm not sure whether you are understanding it correctly or not.

Consider this model. Charles lives a hundred light years away from you. On your tenth birthday you saw Charles being born. Ten years later into your life (as you measure time), Charles appears to be ten years old. OK? However, the information that you have been born has reached only 20 light years into space and so Charles can not know of your existence. Your birth and Charles' birth are acausally connected events.

To some observers you were born before Charles. An examples is given by someone who left Charles' home less than ten years before his birth and travelled at very high speed towards you, passing you before photons signalling Charles' birth had caught up with the traveller.

Another observer, on the same trajectory as the first but moving a little bit slower, would see Charles' birth at exactly the same time as he sees your birth.

Others, such as a still slower traveller, sees Charles' birth before yours.

Again, I don't know whether this helps.

Paul

xilman,

[QUOTE]If two events are "on the same light cone", they are separated in spacetime such that a photon can travel (in either direction) between the events and so that either event could have caused the other. This is probably the closest to a true notion of simultaneity that exists in relativity.[/QUOTE]What do you mean by "on the same light cone"? The sun emits a photon, and about 5 minutes later (from my frame of reference) it hits my eye. Is my eye on the "same" light cone as the sun was when it emitted the photon. Or are you speaking of "same" in some other sense (e.g. the identical light cone, from both frames of reference??). I'm simply not following you here. Could you take the time to clarify?

Thanks,
Zeta-Flux

Paul,

I'm not speaking of what they *see* happening first (which clearly depends on when the photons reach them). As I understand it, EVEN accounting for the speed of light, events can happen in different orders, from different frames of reference.

[QUOTE=Zeta-Flux;117968]xilman,

What do you mean by "on the same light cone"? The sun emits a photon, and about 5 minutes later (from my frame of reference) it hits my eye. Is my eye on the "same" light cone as the sun was when it emitted the photon.[/quote]Yes. [b]At the instant that photon hit your eye[/b] your eye and the point of origin of the photon lay on the same light cone. Before the photon hit your eye, your eye was outside the light cone and afterwards it is inside the light cone.
[QUOTE=Zeta-Flux;117968] Or are you speaking of "same" in some other sense (e.g. the identical light cone, from both frames of reference??). I'm simply not following you here. Could you take the time to clarify?

Thanks,
Zeta-Flux[/QUOTE]Also yes. Everyone, no matter where they are or how they are moving with respect to each other, agree that the two events are on the same light cone.

Not sure whether you understand the origin of the phrase "light cone". Forgive me if you don't need the explanation that follows.

In two dimensions, one of which is space and the other time, the path of a photon looks like a straight line and no matter who draws the diagram the line has exactly the same slope. The line is straight because everyone measures that travels at a constant velocity (we're talking about light [i]in vacuo[/i] here). The line has the same slope because everyone measures light travelling at exactly the same velocity [i]c[/i]. Conventionally in relativity we set the measurement scales such that [i]c[/i] = 1, so the line is at an angle of 45 degrees to the axes.

Bringing in two spatial dimensions, the path of a photon now lies on the surface of a cone which has a vertex angle of 45 degrees. This is the "light cone".

In four-dimensional spacetime (such as we apparently live in), the path of a photon is on the surface of a hypercone with vertex angle 45 degrees.

Try to keep in mind that relativity describes events in spacetime and that it's impossible, in general, to separate space from time such that every observer agrees on which is which. Situations arise (called acausally connected events) such that some observers measure events to occur at the same place but at different times, or at the same time but at different places, or at different times and different places.


Paul

[QUOTE=Zeta-Flux;117969]Paul,

I'm not speaking of what they *see* happening first (which clearly depends on when the photons reach them). As I understand it, EVEN accounting for the speed of light, events can happen in different orders, from different frames of reference.[/QUOTE]"See" in this model (and most explanations of the equations of relativity) is shorthand for something like "measure experimentally" and "light" is shorthand for "information carrier". A postulate of relativity is that no information can be transmitted from one place to another faster than a certain speed [i]c[/i] no matter what method is used. It so happens that light travels at [i]c[/i] and, at the time Einstein developed the theory, it was the only phenomenon determined experimentally to do so.

Another postulate of relativity is that [b]every[/b] observer [b]always[/b] measures the speed of light to have exactly the same value of [i]c[/i] no matter how they are moving with respect to othe observers.

It's unfortunate, perhaps, that "see" is ambiguous in this context. Try translating "see" and "light" (or "photon" as appropriate) in my models of you, Charles and the travellers into "measures by experiment" and "information" respectively to see (there's that word again) whether that helps.


Paul

xilman,

I'm following you now. It seems highly counter-intuitive to me to call two events on the same light-cone "simultaneous". Do many people follow this convention? Is this because from some frames of reference, two events on a light cone can "trade-places" so to speak?

At any rate, I think I can now frame the precise question which has puzzled me. I fire a gun and the bullet shatters a vase. From my point of view, there is a flash of light in-between the gun firing and the vase shattering. There is a frame of reference in which the vase shattering is outside the light cone formed by the flash of light, correct? However, in all frames of reference, *after the fact*, they can tell/measure that from my frame of reference, the gun fired first.

How do physicists talk about causality? Clearly the bullet's firing caused the vase to shatter. But, apparently, the *order* of occurances doesn't matter, except in certain frames of reference. What is the method of determining which frame of reference is the 'right' one in which to view causality of events? Or is it possible that there are events which happen, which seem to have no *cause* in any frames we can come up with?

[QUOTE=Zeta-Flux;117979]xilman,

I'm following you now. It seems highly counter-intuitive to me to call two events on the same light-cone "simultaneous". Do many people follow this convention?[/quote]They are not really "simultaneous" in the conventional sense, because the conventional interpretation of that word is nonsensical in relativity. Perhaps I shouldn't have used the sentence "This is probably the closest to a true notion of simultaneity that exists in relativity." earlier because it can be too easily misinterpreted. The sentence must be read in the context of those immediately preceding it.

[QUOTE=Zeta-Flux;117979]Is this because from some frames of reference, two events on a light cone can "trade-places" so to speak?[/quote]Yes, and not only in some frames of reference but in [b]all[/b] frames. That's how I'd intended it to be interpreted.
[QUOTE=Zeta-Flux;117979]At any rate, I think I can now frame the precise question which has puzzled me. I fire a gun and the bullet shatters a vase. From my point of view, there is a flash of light in-between the gun firing and the vase shattering. There is a frame of reference in which the vase shattering is outside the light cone formed by the flash of light, correct?[/quote]First off, every observer everywhere in spacetime agrees on whether a point in space time (an "event") is inside, outside or on any particular light cone and, specifically, that defined by your flash of light.

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 [i]c[/i]/2 and the vase is approaching at [i]c[/i]/2. 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. 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!).

[QUOTE=Zeta-Flux;117979]However, in all frames of reference, *after the fact*, they can tell/measure that from my frame of reference, the gun fired first.
ow do physicists talk about causality? Clearly the bullet's firing caused the vase to shatter. But, apparently, the *order* of occurances doesn't matter, except in certain frames of reference. What is the method of determining which frame of reference is the 'right' one in which to view causality of events? Or is it possible that there are events which happen, which seem to have no *cause* in any frames we can come up with?[/QUOTE]In all frames of reference, the gun fired before the vase was smashed by the bullet. That's what is meant by "causally connected". Because it is possible for information ("light") to be transferred between the point in spacetime where the gun fires and the point where the vase breaks, it is possible for the firing to break the vase. All observers agree on that.

Acausal pairs of events ("event" is a code word for "point in spacetime") are those which, because of their separation in spacetime, information can not be transferred between them. They are, in a real sense, too far apart for light (i.e. information) to travel between them. Depending on who is doing the measurements, either or neither of the pair could occur first.

In the gun and vase model, the emission of the flash of light and the smashing of the vase are acausally connected events.

Paul

xilman,

Thank you for taking the time to explain this. One more question. What makes it so that the light flash and the vase shattering are acausally connected events?

In other words, what if the light flash is caused by the bullet passing a light emittor sitting out in space? The light emittor senses the bullet passing, and sends out a flash of light. Isn't it clear that the flash happens *before* the vase is shattered, in all frames of reference? Or is it that one cannot tell whether the light emittor performed its specified task?

[QUOTE=Zeta-Flux;117988]xilman,

Thank you for taking the time to explain this. One more question. What makes it so that the light flash and the vase shattering are acausally connected events?

In other words, what if the light flash is caused by the bullet passing a light emittor sitting out in space? The light emittor senses the bullet passing, and sends out a flash of light. Isn't it clear that the flash happens *before* the vase is shattered, in all frames of reference? Or is it that one cannot tell whether the light emittor performed its specified task?[/QUOTE]You've just described a situation in which the creation of the flash of light and the shattering of the vase are causally connected and, indeed, all observers agree that the flash occurs before the vase is shattered.

A difference between your scenario and my earlier one is that the creation of the flash of light could (respectively could not) have caused the vase to smash before (whether observed by you, the bullet or the vase) the bullet arrived at the vase. That's what is meant by two events being causally connected --- one event could possibly have caused the other. Two events which are acausally connected are located at points in space time such that neither could have caused the other because they are too far apart (in spacetime remember, not just in space or time separately) for a light signal (meaning information) to travel between them. In this latter case, different observers will observe the two events to occur in either order or at the same time, depending on where they are in space and time.

Paul

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

davieddy,

[QUOTE]But I think the paradox involves the door on the far side of
the barn opening [I]when the rear of the rocket passes the
front door.[/I] The question to be resolved unambiguously by
all observers is "does the rocket crash into the back door
or not". (emphasis added)[/QUOTE]And the event in italics depends on one's frame of reference (since none is specified), and so the question is not well-defined. Yes, I think I understand the paradox. For another version I found:

[url]http://math.ucr.edu/home/baez/physics/Relativity/SR/barn_pole.html[/url]
----------------------------------------

ewmayer,

I understand that if one uses the Minkowski metric in defining distances in space-time, then the "order" of events depends on the observer. Oh, and I think that your statement "that's why it's called "relativity."" is not quite accurate. ;)

[quote=Zeta-Flux;118115]davieddy,

And the event in italics depends on one's frame of reference (since none is specified), and so the question is not well-defined. [/quote]

Since relativity is inherently "consistent", the ambiguity is always
to be found in the posing of the paradox.
But "the rear of the rocket passing the front door" is a clear cut
event identifiable by all observers. What is ambiguius is the frame
in which the back door opens simultaneously.

davieddy,

What exactly is the clear cut observable? The event in question has to be measured and the measurement depends on one's frame. I suppose one could conflate the two events of measurement, but I don't think this is necessary.

So, in other words, what I meant by my statement is that the measurement of the event depends on the frame of reference. And since we only *know* what we can measure, talking about "when the rocket passes the barn door" is not well-defined, unless one posits a specified frame of reference from which to make the measurement.

Anyhow, that is how I understand it.

Best,
Zeta-Flux

[quote=Zeta-Flux;118127]davieddy,

What exactly is the clear cut observable? The event in question has to be measured and the measurement depends on one's frame. I suppose one could conflate the two events of measurement, but I don't think this is necessary.

[/quote]

I think you are confusing relativity with quantum theory.
(Which is not the same thing as amalgamating them!)

If it makes for more of an "event", then say a protrusion
on the rear of the rocket flips a switch at the front of the barn.
One version of the "paradox" says that this switch opens the
back door of the barn.

In relativity, by "observer" we often mean a reference frame
completely populated by observers with synchronized clocks and GPS.
I think lack of this "omniscience" was what Einstein loathed in
quantum mechanics.

David

[QUOTE=davieddy;118161]In relativity, by "observer" we often mean a reference frame completely populated by observers with synchronized clocks and GPS.[/QUOTE]Thank you for posting this clarification.

As with "see", "light", "causal" and a number of other terms, relativity has its own jargon that has grown up over the last century. Newcomers are often misled by common words being used with specialized meanings.

Relativity is not special in this respect (ambiguity intended). Consider the many and varied meanings of the word "field" throughout mathematics and the sciences.

Paul

[quote=xilman;118165]
Consider the many and varied meanings of the word "field" throughout mathematics and the sciences.

Paul[/quote]

I like to think I can distinguish the following:
1) A field of barley
2) A Galois field
3) A magnetic field

I'm sure this list is not complete.

David

[quote=davieddy;118168]I like to think I can distinguish the following:
1) A field of barley
2) A Galois field
3) A magnetic field

I'm sure this list is not complete.

David[/quote]

4) The field of physics (a field of study)

[quote=bsquared;118169]4) The field of physics (a field of study)[/quote]
That was quick:smile:

[QUOTE=bsquared;118169]4) The field of physics (a field of study)[/QUOTE]A set (another jargon term) together with two distinct operations (and another) on its elements (yet another), each forming a group (still another), and with further constraints on its structure (is that a jargon term?).

A Galois field is just a special case of this more general definition.

Paul

[QUOTE=bsquared;118169]4) The field of physics (a field of study)[/QUOTE]So far, only nouns have been considered. To get things started, here are a couple of verbal meanings.

To field (intransitive verb) --- an activity in which a cricketer may be engaged.

To field (transitive verb) a question -- an activity in which a politican may be engaged.

There are more.

Another noun: a quantum field. (I personally consider this to be quite different in nature from a magnetic field.)

Is a vector field something quite different (but related) to a magnetic field?


All this is getting us far away from the original question. :sad:

Paul

[quote=xilman;118175]
Another noun: a quantum field. (I personally consider this to be quite different in nature from a magnetic field.)

Is a vector field something quite different (but related) to a magnetic field?


All this is getting us far away from the original question. :sad:

Paul[/quote]
Answers respectively:

In "quantum field theory" does the adjective(?) quantum refer to
the field or the theory?

I would say that a magnetic field was a special case of a vector field.

Yes but does it merit a new thread?

[quote=xilman;118175]
All this is getting us far away from the original question. :sad:

Paul[/quote]

One could say we're getting farther afield :)

[quote=bsquared;118177]One could say we're getting farther afield :)[/quote]
:lol:And Paul started it anyway.

Here's more than anyone wanted to know about the various meanings of field:

[URL]http://dictionary.reference.com/browse/field[/URL]