Unraveling the Implications of Simultaneity in Special Relativity

[durant]

Hi, this question may sound similar to the one I asked about a month ago, but I will give my shot to explain what's been bothering me. In almost all interpretations of the special relativity, it is stated that two events that are simultaneous in one reference frame are not in another. And that's okay, it's understandable. The question that's been triggering me is the further implications when implying this to everyday objects.

Basically, special relativity say that both persons will agree what happened, they will both have the one and the same event, with its properties in their present reference. What differes is that different observers will have different events in their present frame, but nonetheless as far as the definition of an event goes, they will all have 'that what happened' sooner or later in their present reference frame. The part which gets tricky is applying this to the parts of events or objects. While we may agree on the identity of the event or the state of the object involved, it implies that that event or state is made of something, it has parts, and if the identity of the event or state of thing in question is invariant then it must have parts that are simultaneous (if it's a state) or that occur in a fixed time order (events). The parts of an object at some time may be spacelike separated, so how do we define their simultaneity?

If an event/stage of an object has a fixed identity regardless of the frame it happens in, what does this imply for the parts of the events? How is it possible that all observers won't agree on the composition, but they will on the very identity of the thing? It sounds contradictory and I hope some with an understanding could help me.

 

[mfb]

If parts are space-like separated, the time-order is arbitrary, and does not matter.
If parts are time-like or light-like separated, they can influence each other, and their time-order is the same in all reference frames.

 

[pervect]

In general, extended objects can't be assigned properties - even simple ones like energy and momentum - unless they are isolated and non-interacting, in which case the time slice issue can perhaps be sidestepped.

In the context of defining the energy and momentum of the object, for instance, if it's isolated, the object has a well defined energy and momentum regardless of the time slice used to describe it. But if it's NOT isolated, it won't have these properties.

This is mentioned in, for instance, http://arxiv.org/abs/physics/0505004 in the context of relativistic thermodynamics.

It is known that the volume of an object viewed from distinct inertial frames
are different physical entities that are not connected each other by a Lorentz
transformation. Consequently total energy-momentum of an object in one
frame is not connected to that in another frame, i.e., energy-momentum of
an object with a finite volume is not a covariant entity.

The cure for this is not to consider extended objects. Rather than talking about an extended object and giving it some mass, we talk about the density of an object.

The density, which is not an extended object, and being defined only at or around some point, IS covariant. The density of energy and momentum turns out to be a rank two tensor, the stress energy tensor.

This is usually glossed over in introductory SR textbooks, which talk about the momentum and energy of objects, though they'll usually mention that the object must be an isolated system - without, however, going into the details of why

Rindler's textbook, "Relativity: Special, General, and Cosmological" is one of the few that I can think of that goes into this in detail (with regards to the stress-energy tensor, and the old puzzle about a stressed rod having more mass than an unstressed one).

 

[Dale]

The part which gets tricky is applying this to the parts of events or objects.

Objects have parts, but events do not. Events are "points" in spacetime. They cannot be subdivided and they have no spatial nor temporal extent.

While we may agree on the identity of the event or the state of the object involved, it implies that that event or state is made of something, it has parts, and if the identity of the event or state of thing in question is invariant then it must have parts that are simultaneous (if it's a state) or that occur in a fixed time order (events).

Again, events do not have parts.

The parts of an object at some time may be spacelike separated, so how do we define their simultaneity?

Different frames may disagree about the simultaneity of different parts of an object. A typical example is Einstein's train. The train has a front part and a back part which are struck by lightning simultaneously in some frame, in that frame there is never a time where only one part of the train was struck. In a different frame the front part is struck first and so there exists a time where only one part of the train was struck. They disagree on the simultaneity.

If an event/stage of an object has a fixed identity regardless of the frame it happens in, what does this imply for the parts of the events?

EVENTS DO NOT HAVE PARTS!

How is it possible that all observers won't agree on the composition, but they will on the very identity of the thing? It sounds contradictory and I hope some with an understanding could help me.

What is "very identity"? It isn't a physics term. It sounds like a philosophical term. I have never seen a scientific manuscript discussing "very identity". If it is a philosophical term then you shouldn't be surprised in contradictions.

"Identity" and "object" and "composition" are not physically important. What is important is cause and effect. If an event on one part of an object can cause some other event to happen in another part then the cause will always preceed the effect in any frame. If different frames disagree about the order of two events on different parts of the object then neither event can cause the other and the order doesn't matter physically.

 

[durant]

How do events don't have parts? For instance, me taking a cup consists in sub-events, me stretching my hand than putting it on the cup and finally grabbing it. This is trivial and common-sensical.

Anyway, all observers will agree what is happening in the rest frame of the object, so they will have their version of the object which is determined by the coordinates and the version of the object in its 'proper time', by this I mean one stage along its worldline in the rest frame. Please correct me if I'm wrong.

 

[durant]

What confuses me is that a worldine of an object is desribed as invariant, but it seems that it is observer dependent is some sense. One observer will see the train which front and back parts are hit simultaneously and another will see a train which front part is hit first and the back part second. So what happens in the objects worldine? Only the stuff from the rest frame's plane of simultaneity?

 

[PAllen]

How do events don't have parts? For instance, me taking a cup consists in sub-events, me stretching my hand than putting it on the cup and finally grabbing it. This is trivial and common-sensical.

Well that's the problem with every day English meanings versus mathematical or physical terms. In physics, event is defined as a specific point in space and time. Then, what you are calling an event is large collection of events. From the point of view of physics, what you call 'trivial and common-sensical' is just simply wrong.

Anyway, all observers will agree what is happening in the rest frame of the object, so they will have their version of the object which is determined by the coordinates and the version of the object in its 'proper time', by this I mean one stage along its worldline in the rest frame. Please correct me if I'm wrong.

Objects of nonzero size have world tubes, rather than world lines. One important point is that any spacelike slice through a world tube represents a collection of causally disconnected events. For example, if there is a micro-explosion at an event in an object's world tube, matter elsewhere on a simultaneity slice through object will behave exactly as if the explosion didn't happen, until each bit of matter's world line enters the future light cone of the explosion.

 

[Dale]

How do events don't have parts?

By definition an event is a specific location at a specific time which can be identified by 4 coordinates. For example, the event $(t,x,y,z)=(1,6,5,-2)$ in some specified coordinate system. It is a point in a 4 dimensional spacetime manifold, points don't have parts by definition.

For instance, me taking a cup consists in sub-events, me stretching my hand than putting it on the cup and finally grabbing it. This is trivial and common-sensical.

You taking a cup is not an event, precisely because it has parts. It is an infinite number of events, one corresponding to each instant and location involved. You might call taking a cup a process, or even a sequence of events, but not an event.

The common-sensical definition is irrelevant. The term "event" is precisely defined in relativity and has a specific technical meaning. EVENTS DO NOT HAVE PARTS.

 

[PAllen]

What confuses me is that a worldine of an object is desribed as invariant, but it seems that it is observer dependent is some sense. One observer will see the train which front and back parts are hit simultaneously and another will see a train which front part is hit first and the back part second. So what happens in the objects worldine? Only the stuff from the rest frame's plane of simultaneity?

Train's don't have world lines. They have world tubes, or better, separate world lines for every 'bit' of matter. (Let's assume we stick to scenarios where we approximate using classical particles). You cannot treat a collection of world lines as if it were one world line.

Though it might be hard for you, I suggest you put effort into studying Pervect's description, then asking specific questions about parts you don't understand.

 

[phinds]

durant, your apparent dislike of using precise scientific terminology rather than sloppy, often useless or misleading, English language terminology is not going to stand you in good stead if you plan on learning science.

 

[Dale]

What confuses me is that a worldine of an object is desribed as invariant, but it seems that it is observer dependent is some sense.

The worldline is a geometrical object. Like a curve on an otherwise blank piece of paper.

If you have a curve on an otherwise blank piece of paper there are many things that you can say about that curve. You can give its length, you can tell if it is straight or bent, if it is bent you can give it a radius of curvature at each point, you can measure angles between different parts of the line, etc. These are all geometrical properties of the curve.

Now, you can take that blank piece of paper and draw coordinates on it. Once you have done that you can say additional things about the curve. You can give it a beginning location and an ending location, you can write it as a function of some parameter, you can give its slope, you can give its total extent in each coordinate direction. Furthermore, you can use the coordinates to help calculate the geometrical properties.

Now, you can draw a second set of coordinates on it. You can calculate all of those things about the curve in this coordinate system, the geometrical properties will all be the same and so they are called "invariant", while the other calculations will be different so they are called "variant". The invariant quantities describe the geometrical object itself, whereas the variant quantities describe the relationship between the geometrical object and the coordinate system.

Similarly with a worldline. It is a geometrical object, independent of any coordinate system or reference frame. You can calculate many invariants about it, and additionally you can define coordinates and calculate frame-variant quantities.

One observer will see the train which front and back parts are hit simultaneously and another will see a train which front part is hit first and the back part second. So what happens in the objects worldine? Only the stuff from the rest frame's plane of simultaneity?

The order of the lightning strikes is a frame variant quantity. I.e. it is NOT a property of the train's worldtube itself, it is a relationship between the worldtube and a specific coordinate system. Nothing physical about the train can possibly depend on the order.

Stated simplistically, nature doesn't care about simultaneity, it only cares about causality.

 

[ghwellsjr]

Hi, this question may sound similar to the one I asked about a month ago, but I will give my shot to explain what's been bothering me.

Yes, you did ask all these same questions in at least two threads that you started. Just go back and study the answers you were given instead of continuing to ask exactly the same questions in a new thread.

Why do you think you will get any different answers? Remember, you asked about a car exploding? Remember, you asked about your cat? These are everyday objects and even though I and others responded to your questions about them on your other thread and asked questions to clarify what you meant and to see if you understood, you never responded. Please go back and read and study your other threads.

You need to learn about the Lorentz Transformation process. It's not hard. You need to specify your scenarios in terms of one Inertial Reference Frame (IRF). Got that? One. Not two. Not three. Not four. Not any more. You need to assign coordinates to each event. Remember, at the start of your scenario your cat has one event for the tip of his tail, one event for the tip of his big toe on his front right foot, one event for the end of the longest whisker on the left side of his face, etc. Then you can transform the coordinates of all these events to another IRF. Until you are willing to learn this process you are forever going to remain confused and there will be no end of the threads you're going to want to start.

 

[durant]

Well that's the problem with every day English meanings versus mathematical or physical terms. In physics, event is defined as a specific point in space and time. Then, what you are calling an event is large collection of events. From the point of view of physics, what you call 'trivial and common-sensical' is just simply wrong.


Objects of nonzero size have world tubes, rather than world lines. One important point is that any spacelike slice through a world tube represents a collection of causally disconnected events. For example, if there is a micro-explosion at an event in an object's world tube, matter elsewhere on a simultaneity slice through object will behave exactly as if the explosion didn't happen, until each bit of matter's world line enters the future light cone of the explosion.

Okay, so we may separate the metaphysical meaning of the event and the relativistic meaning of the event, no problem. What I consider as an event is of metaphysical value and certainly stands in causal processes. Why I ask so many questions about this is because I can't make sense of some things. I've learned something about Lorentz transformations and sure it makes stuff more easier, but I believe that this kind of physics is impossible without implying metaphysics. So it's not irrelevant to speak of the kind of stuff that I speak about and not simply using maths, because in the end stuff and things exist out there, not numbers. By this I don't mean to be discrespectful to anybody but seeing some members attacking me because of a question that is fundamental to this theory really makes me feel like a fool for no reason, because if anybody answered me (which is of course not you obligation) in a proper way, which can be related to concrete examples, and not simply by throwing out equations that may be complicated for a 21 year old (obviously most of you have an attidute that is discrespectful to members who are new to this field). Anyway, some people are ignorant about this stuff because it doesn't fit their intuitions, I'm not, I want to learn and have some level of understanding without discriminating anyone's opinion.

This question is fundamental because, in my head, on the one side you have events and objects with a frame invariant collection of properties. And on the other hand you have the 'same' events and objects in different frames with different properties. Now, I guess the thing that's connecting these two things is the rest frame of the object that we speak of. All observers agree what's the state of the object in its rest frame (without it being privileged). So we may speak of an identity of the object that is frame invariant (in its rest frame), and the identity relative to some particular frame of reference. All these combined give us 'the object', or the entity. I guess it should be like that. I hope that in the next posts there won't be another set of opinion discreditings. All I'm asking is an explanation, and I'm not using rival theories here or eliminating anyone's knowledge about my question. Thanks for the answers in advance.

 

[Dale]

I believe that this kind of physics is impossible without implying metaphysics

Not only is it possible, it is required on this forum.

Thread closed. I recommend that you spend some time reading and thinking about the many excellent answers that you have already received on all of your threads.