# Proper time of a 'half-moving object'

1. Jun 3, 2013

### 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?

2. Jun 3, 2013

### Staff: Mentor

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.

3. Jun 3, 2013

### durant

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

4. Jun 3, 2013

### Staff: Mentor

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.

5. Jun 3, 2013

### durant

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.

6. Jun 3, 2013

### Staff: Mentor

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.

7. Jun 3, 2013

### Staff: Mentor

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.

8. Jun 3, 2013

### durant

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.

9. Jun 3, 2013

### PAllen

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.

10. Jun 3, 2013

### durant

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

11. Jun 3, 2013

### Staff: Mentor

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.

12. Jun 3, 2013

### Staff: Mentor

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.

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.

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.

13. Jun 3, 2013

### durant

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.

14. Jun 3, 2013

### PAllen

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.

15. Jun 3, 2013

### durant

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

16. Jun 3, 2013

### durant

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

17. Jun 3, 2013

### Staff: Mentor

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).

Last edited: Jun 3, 2013
18. Jun 3, 2013

### Staff: Mentor

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.

19. Jun 3, 2013

### 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?

20. Jun 3, 2013

### durant

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

21. Jun 3, 2013

### Staff: Mentor

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.

22. Jun 3, 2013

### durant

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?

23. Jun 3, 2013

### Staff: Mentor

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.

24. Jun 3, 2013

### durant

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

25. Jun 3, 2013

### Staff: Mentor

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:

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.