Proper time of a 'half-moving object'

[durant]

As I've red, we can measure the proper time of an object with a clock that is at rest with respect to the object. So, how would we measure the proper time of an object that is partially moving and partiall at rest. For instance if I'm moving my head and the rest of my body is at rest, how would this situation be measured? Or how would the rest frame of me in that 'situation' be defined?

 

[PeterDonis]

how would we measure the proper time of an object that is partially moving and partiall at rest.

You wouldn't, because there is no such thing as "the" proper time of such an object. Different parts of the object that are in relative motion will have different proper times.

how would the rest frame of me in that 'situation' be defined?

It wouldn't, because there would be no such thing as a single "rest frame" that is yours. Your head would have one rest frame, and the rest of your body would have another.

 

[durant]

You wouldn't, because there is no such thing as "the" proper time of such an object. Different parts of the object that are in relative motion will have different proper times.



It wouldn't, because there would be no such thing as a single "rest frame" that is yours. Your head would have one rest frame, and the rest of your body would have another.

But shouldn't my body, as a whole, have its unique worldine/worldtube?

 

[Nugatory]

But shouldn't my body, as a whole, have its unique worldine/worldtube?

Worldtube, yes. Worldline, no. Points have worldlines, objects have worldtubes.

The worldtube is the collection of all the worldlines, one for each point of your body. Trace the path of a single point on your body through spacetime, and you'll have a single worldline; put all of these worldlines together like fibers in a bundle and you'll have a world tube.

 

[durant]

Worldtube, yes. Worldline, no. Points have worldlines, objects have worldtubes.

The worldtube is the collection of all the worldlines, one for each point of your body. Trace the path of a single point on your body through spacetime, and you'll have a single worldline; put all of these worldlines together like fibers in a bundle and you'll have a world tube.

Yes, I got that. And thank you for the explanation. What I was referring to is the possible implication of the things DaleSpam mentioned. My opinion is that my body, and any other body that is 'partiall-moving' should have its rest frame because that 'allows' the sequence of timelike-events of that body. It sounds absurd to say that my body as a whole doesn't follow the transition from 'state A' to 'state B', which are timelike events.

 

[Dale]

But shouldn't my body, as a whole, have its unique worldine/worldtube?

As was already mentioned it is an extended object so it has a worldtube, not a worldline. In this case the worldtube would look somewhat like a trumpet. There is no inertial coordinate system where a trumpet-shaped worldtube is entirely parallel to the time axis.

 

[Dale]

My opinion is that my body, and any other body that is 'partiall-moving' should have its rest frame

Your opinion is incorrect.

Draw a trumpet on a piece of paper. Then try to rotate the piece of paper such that each part of the trumpet is vertical.

 

[durant]

Your opinion is incorrect.

Draw a trumpet on a piece of paper. Then try to rotate the piece of paper such that each part of the trumpet is vertical.

And yours is, of course, correct, because you are the omnipotent relativity expert.

Why are you so hard on me, first closing the thread, and then brutally discrimnating what I just wrote. Can you rather explain how is this possible, since all I read is that we define proper time with the events on the worldtube, and we define it as the one measured from the rest frame..

So in one sense you're saying that there exists a worldtube, but no rest frame. How would we know what's happening with the worldtube? And I don't mean any childish 'challenges' to you by this question, cause I'm aware and respect your knowledge, I just want the appropiate answer that makes sense.

 

[PAllen]

And yours is, of course, correct, because you are the omnipotent relativity expert.

Why are you so hard on me, first closing the thread, and then brutally discrimnating what I just wrote. Can you rather explain how is this possible, since all I read is that we define proper time with the events on the worldtube, and we define it as the one measured from the rest frame..

So in one sense you're saying that there exists a worldtube, but no rest frame. How would we know what's happening with the worldtube? And I don't mean any childish 'challenges' to you by this question, cause I'm aware and respect your knowledge, I just want the appropiate answer that makes sense.

To understand physics beyond simple classical physics, you need to expand your sense of what makes sense. Both relativity and quantum theory radically diverge from everyday physical intuition.

Specifics:

For a body, if the constituent parts are in relative motion (turning your head), then there is no rest frame for the object as a whole. Period. There are different frames in which different parts of your body are at rest. Each part of your body will have its own proper time. FYI, your head is older than your feet unless you've spend most of your life sleeping like a bat.

 

[durant]

To understand physics beyond simple classical physics, you need to expand your sense of what makes sense. Both relativity and quantum theory radically diverge from everyday physical intuition.

Specifics:

For a body, if the constituent parts are in relative motion (turning your head), then there is no rest frame for the object as a whole. Period. There are different frames in which different parts of your body are at rest. Each part of your body will have its own proper time. FYI, your head is older than your feet unless you've spend most of your life sleeping like a bat.

On what basis would my head be older than my feet?

 

[Dale]

Why are you so hard on me

Why? Because you ask a question, and get the same perfectly correct answer from multiple sources, and then insist on arguing about it based on nothing other than your preconceptions about how the universe should work. Why bother asking the question if you don't want the answer? It is obnoxious.

The fact is that the universe doesn't conform to your preconceptions. The sooner you recognize that (as we all have had to do) the sooner you can make some actual progress.

 

[Dale]

So in one sense you're saying that there exists a worldtube, but no rest frame.

Yes. In order for there to be a single rest frame there must be a frame where all of the worldlines composing the worldtube are parallel to the time axis. Since the worldlines are not parallel to each other it is not possible for them to all be parallel to another line. This is straightforward geometry.

How would we know what's happening with the worldtube?

We don't need a rest frame to know what is happening with the worldtube. We can calculate anything that we would like to calculate about the worldtube from any frame at all. That is the whole point of the first postulate of relativity.

I just want the appropiate answer that makes sense.

The answers you have received to your questions here on this forum are universally correct and make sense. They may not conform to your preconceptions, but they are correct.

 

[durant]

Why? Because you ask a question, and get the same perfectly correct answer from multiple sources, and then insist on arguing about it based on nothing other than your preconceptions about how the universe should work. Why bother asking the question if you don't want the answer? It is obnoxious.

The fact is that the universe doesn't conform to your preconceptions. The sooner you recognize that (as we all have had to do) the sooner you can make some actual progress.

You're wrong, I'm open to make adjustments on the stuff you guys state, and I respect it. Maybe the problem is my lack of understanding, or mabye the problems is your definition about some things. When you're answering me, you simply state a number of definitions that you probably have in your head without thinking that I'm not in the same knowledge positon as you are. You're attitude is like everybody who's not familiar with relativity is inferior. Secondly, I'm from Croatia, so I put a lot of effort in using english to describe some complicated terms, or to understand some phrases that you guys use when typing on the forum. Again, I'm not some ignorant person who comes here to disrespect your words and knowledge, I want to learn about it, and if you're a polite forum member you will have the patience for me to get through this and understand it.

So, back to the basic question, the object that I described has a worldtube, that's beyond doubt, right? How could we know what's happening inside it? Does the entity that we speak of have stages of its existence which are timelike events? Basically, what I've been searching for is the answers about the properties of that kind of object.

 

[PAllen]

On what basis would my head be older than my feet?

Mostly because it is at higher average elevation than your feet. Thus if there were a particle of uranium lodged in your head, and another in your foot, the one in your head would have emitted more alpha particles over your life (a direct measure of age). This is due to what is called gravitational time dilation. Sticking to special relativity, if you were in deep space and did a lot of activity with your hands, then your hands would be younger than your torso.

 

[durant]

We don't need a rest frame to know what is happening with the worldtube. We can calculate anything that we would like to calculate about the worldtube from any frame at all. That is the whole point of the first postulate of relativity.

So, all observers will agree about the sequence of events and properties of the worldtube?

 

[durant]

Mostly because it is at higher average elevation than your feet. Thus if there were a particle of uranium lodged in your head, and another in your foot, the one in your head would have emitted more alpha particles over your life (a direct measure of age). This is due to what is called gravitational time dilation. Sticking to special relativity, if you were in deep space and did a lot of activity with your hands, then your hands would be younger than your body.

Oh, that's a relief. I thought you meant something else rather than the time dilation. I understand why the effect occurs then.

 

[Nugatory]

my body, and any other body that is 'partially-moving' should have its rest frame because that 'allows' the sequence of timelike-events of that body

If you remember that a rest frame is defined as a frame in which a point is at rest (when you hear someone speaking of "the rest frame of an object" they are using a convenient shortcut for the more precise "a frame in which every point of that object is at rest") it's clear that there is no such thing as "the rest frame of a partially moving object".

However, that doesn't affect the time-like ordering of events in any meaningful way. Let's go back to your extended cat. It catches its tail in a door, a nerve impulse travels from its tail to its brain, and it yowls. Look at the world-line of the tip of the tail and of the point in the brain where the signal arrives; draw a slanting line between those two world lines to track the path of the nerve impulse to its brain. Every observer, regardless of their speed and reference frame or anything else, will agree that the tail-in-door event happened before the signal-reached-brain event. No observer will believe that these two events were simultaneous (that is, no observer will believe that the nerve impulse took no time to travel from tail to brain).

 

[Dale]

So, all observers will agree about the sequence of events and properties of the worldtube?

All observers will agree about the properties of the worldtube because anything that can be termed a property of the worldtube is an invariant.

Things that are not invariant are not properties of the worldtube but rather relationships between the worldtube and the reference frame. The sequence of causally disconnected events is one such thing. The sequence of causally disconnected events is not a property of the worldtube but a relationship between the worldtube and the observer's reference frame. Thus different observers will disagree about that.

 

[durant]

What would happen if the cat was, hypotethically, moving its tail (while the other parts are at relative rest), and changing color as a whole? Would all observers agree on that?

 

[durant]

All observers will agree about the properties of the worldtube because anything that can be termed a property of the worldtube is an invariant.

Things that are not invariant are not properties of the worldtube but rather relationships between the worldtube and the reference frame. The sequence of causally disconnected events is one such thing. The sequence of causally disconnected events is not a property of the worldtube but a relationship between the worldtube and the observer's reference frame. Thus different observers will disagree about that.

Ok, that's one of the things that I've been seekin' clarification for... Good to know that we're on the same page.

 

[Dale]

I'm open to make adjustments on the stuff you guys state, and I respect it.

Then don't do things like waste a half-dozen posts explaining why you think that "events" have parts when you have already been informed that they do not and given explanations about the technical meaning of the term "events" as it is used in relativity.

If you do not understand the meaning of a techincal term then ask for clarification, but arguing against basic definitions is not helpful. When you do that you sound like someone with a philosophical agenda rather than someone interested in learning science, an impression furthered by your post about metaphysics.

 

[durant]

Then don't do things like waste a half-dozen posts explaining why you think that "events" have parts when you have already been informed that they do not and given explanations about the technical meaning of the term "events" as it is used in relativity.

If you do not understand the meaning of a techincal term then ask for clarification, but arguing against basic definitions is not helpful. When you do that you sound like someone with a philosophical agenda rather than someone interested in learning science, an impression furthered by your post about metaphysics.

My opinion is still that the two concepts are related (even more than you think), but I won't insist on it. If you're picture of the world is based solely on measurements and logical positivism, that's okay with me. After all this is a physics forum like you said and all threads should involve a physics judgement of the terms stated. And also, there's a big difference between common sense and metaphysics, so there's no need stating those 'frightening' sentences like 'The relativity destroys your common sense picture' and so on. But as I said, I will adjust, it's my duty as a forum member who seeks opinion from people that are really into this field.

So it's been stated before that the worldtube of the object I described doesn't have a local, or proper time. What if an object was first at rest as a whole, but then changed into a state where it's one part is still at rest, but the other is moving? Does the local time get somehow destroyed, since the object no longer has a specific state of motion as a unity?

 

[Nugatory]

What would happen if the cat was, hypothethically, moving its tail (while the other parts are at relative rest), and changing color as a whole? Would all observers agree on that?

The moving tail would make the shape of the world tube a bit more complicated, but that doesn't change anything in my post.

The color-change question may be more interesting, but it doesn't have a good answer until you have been more precise about exactly what the color-changing process is.

If you imagine a fairy that can wave a magic wand to cast a spell that causes the the cat to instantaneously change its color across its entire body all at once... You will be able to find an observer for whom at least some of the color change happens before the spell is cast, violating causality. All that proves is that such a magic spell is not possible (look into it carefully and you'll see that the spell would have to travel faster than the speed of light).

If you're thinking about some biochemical process (the way chameleons, anoles, flounder, some frogs can change their color), then something will have to start the process and then send some chemical or electrical signal to each point on the skin to make that point change its color. This is very similar to the door-taill-nerveimpluse-brain scenario. All observers will agree that each point on the skin changes color; this effect always comes after the cause.

If you're thinking about going after the cat with a can of spray paint... Draw the slanting worldline of each individual droplet of paint as it leaves the worldline of the spray can nozzle and intersects the worldline of a point on the skin of the cat.

 

[durant]

The moving tail would make the shape of the world tube a bit more complicated, but that doesn't change anything in my post.

The color-change question may be more interesting, but it doesn't have a good answer until you have been more precise about exactly what the color-changing process is.

If you imagine a fairy that can wave a magic wand to cast a spell that causes the the cat to instantaneously change its color across its entire body all at once... You will be able to find an observer for whom at least some of the color change happens before the spell is cast, violating causality. All that proves is that such a magic spell is not possible (look into it carefully and you'll see that the spell would have to travel faster than the speed of light).

If you're thinking about some biochemical process (the way chameleons, anoles, flounder, some frogs can change their color), then something will have to start the process and then send some chemical or electrical signal to each point on the skin to make that point change its color. This is very similar to the door-taill-nerveimpluse-brain scenario. All observers will agree that each point on the skin changes color; this effect always comes after the cause.

If you're thinking about going after the cat with a can of spray paint... Draw the slanting worldline of each individual droplet of paint as it leaves the worldline of the spray can nozzle and intersects the worldline of a point on the skin of the cat.

So to sum-up, despite different parts having different states of motion, all observers must agree on the properties of the worldtube as a whole

 

[Nugatory]

So it's been stated before that the worldtube of the object I described doesn't have a local, or proper time.

Proper time is a property of a path between two points in spacetime - it is the amount of time that an ideal clock would record if it were to move along that path from one point to the other (the points must be time-like separated or no such path exists, of course). There are lots of points in the worldtube, lots of paths between them, but for any given path all observers will agree about the proper time along it. Therefore:

What if an object was first at rest as a whole, but then changed into a state where it's one part is still at rest, but the other is moving? Does the local time get somehow destroyed, since the object no longer has a specific state of motion as a unity?

No. Various parts of the object start moving at different times (in a frame in which all parts of the object are initially at rest - that's what "first at rest as a whole" means!), but we still have a perfectly good world tube and a perfectly good proper time between various points in that worldtube.

 

[pervect]

So it's been stated before that the worldtube of the object I described doesn't have a local, or proper time. What if an object was first at rest as a whole, but then changed into a state where it's one part is still at rest, but the other is moving? Does the local time get somehow destroyed, since the object no longer has a specific state of motion as a unity?

As has been pointed out, this is a physics forum. How would you design a thought-experiment to measure the proper time that you're asking a question about?

I can certainly imagine two clocks, and comparing their proper times. The clocks might be cesium atoms, at their smallest.

Note though that if the clocks aren't at the same point in space, specifying the details of the comparison process is essential - due to the relativity of simultaneity.

What I can't imagine is the significance of the results. It seems to me that if the clocks read the same, or the clocks read differently, that it won't answer your question.

If you've got questions that can't be settled even in principle by experiment, science can't answer them. My impression is that what you're asking is one of those questions - but since I'm not positive I understand what you're trying to ask, I could be wrong.

If I am wrong, then giving the details of the thought experiment that will actually measure this alleged property will hopefully allow us to move forwards - for instance, it might be something we can calculate the predictions of for you (depending on the complexity).

 

[Dale]

If you're picture of the world is based solely on measurements and logical positivism, that's okay with me

My personal "picture of the world" is irrelevant (it also is not even remotely logical positivism). This isn't about promoting my viewpoint; it is about following the rules of the forum. I don't get to talk about my personal philosophy here, and you don't get to talk about yours.

So it's been stated before that the worldtube of the object I described doesn't have a local, or proper time. What if an object was first at rest as a whole, but then changed into a state where it's one part is still at rest, but the other is moving? Does the local time get somehow destroyed, since the object no longer has a specific state of motion as a unity?

Proper time is a characteristic of a worldline. So each of the worldlines in the object's worldtube would have a well-defined proper time, but that would not in general coincide with the proper time of other worldlines in the object.

Geometrically, proper time is the Minkowski "length" of a timelike worldline. Consider an object like a string, with length but no width or depth. Now consider that object rotating about its center with its center at rest. Each point on that object would have a helical worldline. The helixes near the center of rotation would have a different length than the helices near the ends. There is no single "length" that you could give for every worldline, but every worldline has its own well defined length.

 

[durant]

No. Various parts of the object start moving at different times (in a frame in which all parts of the object are initially at rest - that's what "first at rest as a whole" means!), but we still have a perfectly good world tube and a perfectly good proper time between various points in that worldtube.

Except the fact that no observer could determine what's happening in the worldtube at a particular time, since there is no rest frame. So no observer could say 'in the rest frame of his body, the lower part of his body and the movement of his head happened simultaneously? What did you mean when saying that we have a perfectly good worldtube?

A perfectly good worldtube would be the one which allows a rest frame, so the observers could agree on the orderd of events within the worldtube from the perspective/rest frame of the object itself. The worldtube of a partially moving object would not have that property, as I understand. So the order of events within the worldtube, would vary from frame to frame. Please correct me if I'm wrong in my interpretation.

 

[Dale]

Except the fact that no observer could determine what's happening in the worldtube at a particular time, since there is no rest frame.

It is not necessary for there to be a rest frame. Again, the whole point of the principle of relativity is that any inertial frame is as good as any other. Please see my previous comments in post 12.

 

[durant]

My personal "picture of the world" is irrelevant (it also is not even remotely logical positivism). This isn't about promoting my viewpoint; it is about following the rules of the forum. I don't get to talk about my personal philosophy here, and you don't get to talk about yours.

I agree with you, perhaps creating a sub-forum 'metaphysics of physics/science' would be adequate. :P I know that if I could precisely explain to you, Nugatory, or any other experienced forum member what's on my mind regarding this you would answer me instaneously, but the problem is obviously my description. Sorry if you found my post offensive.

 

[durant]

It is not necessary for there to be a rest frame. Again, the whole point of the principle of relativity is that any inertial frame is as good as any other. Please see my previous comments in post 12.

But how would you describe a worldtube without a proper time. I know that all frames are equivalent, I had that in mind while writing. It seems obvious that the worldtube of a partially moving object is a combination of the worldtubes of the part that is moving and a part that is not, and they both have their rest frames. The question is, if a worldtube of a partially moving object doesn't have local time, how can we say anything about it in terms of 'fixed order' of temporal events inside it?

 

[Dale]

The question is, if a worldtube of a partially moving object doesn't have local time, how can we say anything about it in terms of 'fixed order' of temporal events inside it?

The order of causally disconnected events is not fixed.

The order of causally connected events is fixed and can be determined in any reference frame.

 

[Nugatory]

But how would you describe a worldtube without a proper time.

We don't need a rest frame to define proper time. Look carefully at my definition of "proper time" in post 25 - there is no rest frame involved, just a path through spacetime.

And I can completely specify a world tube (and for that matter, any collection of points in space time, whether they form a world tube or not) using just the frame-independent proper time and proper distance.

 

[pervect]

But how would you describe a worldtube without a proper time.

You could define a world tube as a collection (a timelike congruence, to be technical) of worldlines. The nature of a timelike congruence is that one and only one worldline passes through any point of the congruence.

With such a congruence, you can meaningful talk about the proper time of any point in the congruence as being the proper time along the unique worldline passing through that point - at least as long as you define some initial set of points in the congruence that have a proper time of zero.

However, given a worldtube, timelike congruences are not unique - you could specify several different congruences that "cover" some particular worldtube. So there isn't any unique or meaningful way of talking about the proper time in a worldtube without specifying a particular congruence.

 

[durant]

We don't need a rest frame to define proper time. Look carefully at my definition of "proper time" in post 25 - there is no rest frame involved, just a path through spacetime.

And I can completely specify a world tube (and for that matter, any collection of points in space time, whether they form a world tube or not) using just the frame-independent proper time and proper distance.

Nugatory, I apologize, but I still don't understand.

In the first posts on this thread it was written that the worldtube of a partially moving object cannot have its proper time (neither can it have a rest frame), but now you're saying that we can define proper time for any worldtube, even if it's the one I've been mentioning throughout this thread.

I know that you have a valid point, but some posts seem contradictory and I certainly know you're not implying any contradictions, so can you please distinguish the difference? How can this kind of worldtube have a proper time, when it was clearly stated before than only its parts have their own proper time?