How Does Spacetime Manipulation Affect the Flow of Time?

[Yuripe]

Time is integral part of spacetime.

If so, how would you explain the persistent unidirectional and significant flow of time and such a small dilation when time is influenced by spacetime manipulation?
Does time flow have to do with overall spacetime expansion?

 

[Eynstone]

Time is not a 'part' of spacetime - the dichotomy between space & time is out of place in relativity.
Please explain what you mean by the 'flow' of time (in physicsl terms).

 

[Phrak]

Welcome to Physics formum, Yuripe.

And I don't know why you you are in disagreement, Eynstone. Time-like R¹ submanifolds of spacetime (world lines) are submanifolds of spacetime, aren't they?

Can you rephrase your question, Yuripe?

 

[Yuripe]

My assumption that time is a part of spacetime is rather simple.
Mainly because it's space-time and because time is influenced along with space when spacetime is bend by gravity.

By flow of time I meant that there is an order of succession of things, there is an irreversible entropy and you can measure seconds "flowing" in your local spacetime. This rate of "flow" should be common across spacetime and is substantial compared to what gravity (bend of spacetme) needs to be to make some change to that rate of "flow".
Seconds success quite fast without any visible influence, but you need to make quite a big bend of spacetime if you want to make a very small change to that "flow".

Time won't stop in any location of an empty volume of spacetime, no matter how folded it is inside.
If you view it like this, then you could expect that there is some other cause of this "flow" then folded spacetime.

So I asked this question, if this "flow" of time could be the effect of the expansion of the whole spacetime in the universe. Because if so, this I think would nicely fit together "flow" of time with its part in spacetime.

 

[Phrak]

You seem to have a cosmology question; are the rates of clocks dependent upon the expansion of the universe?

You might request to have one of the mentors move this thread to the Cosmology folder.

 

[Dale]

By flow of time I meant that there is an order of succession of things

That is simply due to the fact that there is only one timelike dimension. If there were two or more timelike dimensions then you could have closed timelike curves in flat spacetime.

 

[Yuripe]

That is simply due to the fact that there is only one timelike dimension. If there were two or more timelike dimensions then you could have closed timelike curves in flat spacetime.

How do you define timelike dimension?
What is different about it in accordance to plain dimension and how do you know there is only one?

 

[Yuripe]

You seem to have a cosmology question; are the rates of clocks dependent upon the expansion of the universe?

You might request to have one of the mentors move this thread to the Cosmology folder.

You are probably right, but its kind of mixed topic.
I'm trying to determine if that what we perceive as passing time can in reality be the effect of expanding spacetime and in accordance to that, if a gravity is just the local effect of mass on the rate of this expansion.

 

[Dale]

How do you define timelike dimension?
What is different about it in accordance to plain dimension and how do you know there is only one?

By the minus sign in the metric:
ds^2=-dt^2+dx^2+dy^2+dz^2

 

[Yuripe]

By the minus sign in the metric:
ds^2=-dt^2+dx^2+dy^2+dz^2

Nice , but is this a definition of timelike dimension?
It looks to me as a description of spacetime and it doesn't say anything about why there is a minus sign before time component.

 

[my_wan]

It can also be written:
ds^2=dt^2-dx^2-dy^2-dz^2
It really makes no physical difference.

I don't really get the problem with unidirectional time. You have processes that are more likely that others, making a reversal absurdly unlikely. But the physical progression states that we call a time flow are just as physical (classically) as a pool balls that, after bouncing around, end up back in the initial triangle pattern. It's a progression, not a direction.

The other issue is varying time rates, as in relativity. But if everything is defined by a classical state which evolves, how can it be presumed that time, which measures the changes, not vary under some circumstances, even at the most fundamental level?

Suppose time did stop for the next hour? But wait, how was it an hour if time was stopped? The mistake is to presume that time exist separately from the changes of states in the things we measure. If it's simply a change of state, then direction is simply an illusion of probabilities.

So my question to you is how is a change of state defined by a spacetime expansion fundamentally any different from a change of state defined by a glass breaking as it hits the floor? Are you implying that if the Universe was contracting, rather than expanding, that the glass would bounce up off the floor and unbreak? I think not. But if it was you wouldn't know it, because you'd simply be unreading my post and forgetting what yesterday will bring. And still wondering what the spacetime expansion that is unexpanding has to do with it, at least until you get too young and forget what you learned about expansion.

 

[Naty1]

Does time flow have to do with overall spacetime expansion

The expansion of the universe has varied since initial inflation ceased...expansion was rapid and gradually slowed but did not stop and it seems to be accelerating right now...

Has the flow of time changed?? It doesn't appear to me that the expansion of the universe affects our local time to vary here in the Milky Way.

On the other hand as the universe expands, density decreases and hence gravity as well; so a distant observer could see our time apparently slower than at some time in the denser past.

 

[Dale]

It looks to me as a description of spacetime and it doesn't say anything about why there is a minus sign before time component.

When you get to a fundamental level you always find that all science is "a description" and never says "anything about why". If you want a "why" answer to a fundamental question then you need to see a philosopher or a priest, not a scientist. And such answers are not appropriate on this forum.

 

[Rasalhague]

It might help to distingush between (1) the fact of spacetime having one timelike dimension and (2) the existence of a thermodynamic "arrow of time" (connected to the idea of entropy) which, at certain scales, gives a natural causal orientation to spacetime, a way to tell past from future.

http://xxx.lanl.gov/abs/gr-qc/0403121

 

[my_wan]

It might help to distingush between (1) the fact of spacetime having one timelike dimension and (2) the existence of a thermodynamic "arrow of time" (connected to the idea of entropy) which, at certain scales, gives a natural causal orientation to spacetime, a way to tell past from future.

http://xxx.lanl.gov/abs/gr-qc/0403121

Very good point. The timelike dimension is a mere coordinate choice and is no more physical, or have any more unique physical significance, than any coordinate choice.

 

[Rasalhague]

When you get to a fundamental level you always find that all science is "a description" and never says "anything about why". If you want a "why" answer to a fundamental question then you need to see a philosopher or a priest, not a scientist. And such answers are not appropriate on this forum.

At the risk of posting something inappropriate (albeit funny), here's one such answer in the 14th century English mystical treatse The Cloud of Unknowing [ http://www.lib.rochester.edu/camelot/teams/cloufrm.htm ] (lines 351-360). Why are events ordered one after another in time?

So that man schal have none excusacion agens God in the Dome and at the gevyng of acompte of dispendyng of tyme, seiing: "Thou gevest two tymes at ones, and I have bot o steryng at ones."

(So that man shall have no grounds for accusation against God at the Last Judgment when he must give account of how he has spent his time, saying, "You gave two times at once, and I have only one impulse at once.")

 

[petm1]

Nice , but is this a definition of timelike dimension?
It looks to me as a description of spacetime and it doesn't say anything about why there is a minus sign before time component.

I like thinking about this as a change in direction, space to time. Like the focal point within my eye where photons emitted at different times all come together in a pseudo-emission that I see as my now.

 

[matheinste]

It can also be written:
ds^2=dt^2-dx^2-dy^2-dz^2
It really makes no physical difference.

There is no differernce. It is just the fact that the sign of the time dimension is opposite to that of the spatial dimension that defines the metric, makes the interval not positive definite and so the spacetime geometry follows.

I don't think anyone would suggest that the sign of the time dimension in the expression for the interval gives time its direction. But of course it must the opposite sign to the spatial dimensions.

Matheinste.

 

[karkas]

At the risk of also posting something a bit irrelevant to the subject, I will point out that the idea of a second dimension of time has already been studied by Izthak Bars of USCalifornia. I shall give a link or two for you to check it out:

http://physics1.usc.edu/~bars/

and

http://www.slac.stanford.edu/spires/find/hep/www?rawcmd=FIND+T+DUALITY+OR+S+TH%23+OR+TWO%23+OR+TIME%23+OR+MULTI%23+OR+TWELVE%23+OR+2T%23+OR+TWISTOR%23+OR+EMERGENT%23+NOT+U+DUAL%23+AND+A+BARS%2CI+AND+D%3E1993&FORMAT=www&SEQUENCE=

This is called 2T-Physics, if I remember correctly deals slightly with String Theory (or M-Theory) cosmology and might as well be too advanced to be posted in this section. I'll break the rule, nevertheless, considering the case it might be helpful.

 

[Yuripe]

According to SR time "flows" at different rates according to the speed of the object.
So time is relative to the speed, and speed is also relative to the observer.
If I start to move at certain speed and also take a role of the observer (of myself) than for me time will be passing at normal rate, same as I would be stationary.
If we now change to the perspective of the external observer who is slower than me or stationary, he would see that I'm living in "slow motion" in other words in time that runs slower.

I might suspect from the above, that there is a connection between the speed at which spacetime of the universe expands and perception of the rate at which time flows.

According to GR, local value of gravity has the same effect on time as speed in SR.
So higher gravity means slower time flow.

Let's say for now we are in point A in spacetime (A' in space) and I have two synchronized clocks.
I take one of them for a near light speed spin around the galaxy or into a high gravity location for a certain period of time.
Then I come back to compare readings on these clocks at point B in spacetime (same A' in space). What I see is that the clock I took is delayed to the clock I left.
I started this experiment at point A and ended in point B of my spacetime, what is different between these clocks is the spacetime distance between points A-B they traveled.

So how come the distance in spacetime from point A to B be different?
The time must've been flowing at different rates, and if the rates are different shouldn't there be a rate at which normally time flows when observer is stationary?

 

[Naty1]

If you want a "why" answer to a fundamental question then you need to see a philosopher or a priest, not a scientist.

not at all...I see that stated here from time to time and disagree completely...

Ask most any qualified physicsts if they seek both "how" and "why" and I'd hope they answer "of course"...That's one reason we have physical interpretation discussions here...not only "what is the math" but also "what does it mean?"

It's true, for example, no one really knows why fundamental particles differ from one another, but you can be sure most physicsts would like to know why. We just haven't figured that out yet.

Once we figure the origin of anything... energy,time, mass, or particles, for example, ...we should get important insights into everything...

 

[Dale]

It's true, for example, no one really knows why fundamental particles differ from one another, but you can be sure most physicsts would like to know why. We just haven't figured that out yet.

This is actually a perfect example to make my point. In current theory there is no answer to that question. The only way to answer that question would be in terms of a new theory. That new theory would then be the fundamental theory and again, you could not get a "why" answer to a fundamental question about this new theory.

Admittedly, my argument is somewhat tautological. You cannot get a scientific answer to a fundamental question and fundamental questions are the ones that current theories cannot answer. But the point is that there are such questions, they have no answer other than "it fits the data".

 

[Academic]

I agree DaleSpam, science cannot and should never be expected to answer a fundamental 'why'. We can reduce the number of our unknowns by relating them to each other, but there is no experiment or model that can provide an answer to the last, fundamental 'why'.

 

[Dale]

According to SR time "flows" at different rates according to the speed of the object.

The use of the word "flows" is rather confusing and obscures your meaning.

Everything that SR says is encapsulated in the expression I posted above which is called the (Minkowski) metric. The ds term is the time measured by a clock and the other terms are the time and distance measured in an inertial coordinate system.

From the metric you can see that in SR time is more similar to distance (Pythagorean theorem or arc length formula) than it is to anything to do with flow. A geometric analogy is much more appropriate than a material analogy.

 

[Rasalhague]

In some of their uses, "why" and "how" overlap. In fact, the OP actually used the expression "how would you explain". If someone asks "Why does the amount of time between two events depend on the speed of the spacetime coordinate system you chart them in?" they might mean exactly the same as someone who asks "How does...?" (They may be looking for an explanation of the way this happens, how such an unintuitive notion can be self-consistent, what the theory actually says, what the jargon means, what it predicts, what makes physicists are convinced this makes a good model for the universe we live in.) All perfectly reasonable questions.

When a distinction is made between why and how, why can connote: "I want more insight." Someone may feel they understand a method; they can plug numbers into a formula and get the right answer on a test, but they aren't satisfied with this level of understanding; they want to know more: where does this formula come from, how can it be derived, what structures of knowledge does it relate to, is it a special case of something, are there equivalent ways of getting the same result, does this algebra have a geometric interpretation, is this case analogous to other aspects of nature. Again, good questions.

Or the why may come from someone who knows as much as anyone does about the theory, in which case they may be looking for a further insight that they feel is missing from current models. Not necessarily a bad question, depending on who's asking!

Or it can be the why that DaleSpam refers us to philosophers and priests for, the teleological why that Richard Dawkins warns against, the kind that asks for an answer such as that medieval author gave: "why do events succeed each other in time?" meaning "for what purpose?", "to what end?", where the only satisfying answer can be one that personifies nature or its governing preinciples as something with a rational purpose.

 

[Rasalhague]

The use of the word "flows" is rather confusing and obscures your meaning.

The idea of a flow, a natural way of orienting timelike vectors, seems more to do with thermodynamics. I suggest, Yuripe, that you tackle seperately the questions of (1) what time means geometrically in relativity, thinking of "coordinate time" as a dimension like the dimensions of space (except that flat spacetime has this slightly different version of Pythagoras's theorem), and "proper time" as arc length along a timelike curve in spacetime, and (2) what thermodynamics has to say about the "arrow of time" (an emergent property of large systems, like temperature?), and--probably related to this--what psychology has to say about our perception of time. (Timelike is a technical term in relativity.)

One way of thinking about relativity is to picturef 4-d spacetime as a "block universe" with events as fixed points in spacetime. Some discussion of this and other views in Ch. 4 of Friedel Weinert's The Scientist as Philosopher [ http://books.google.co.uk/books?id=8eN9zoprUT4C&pg=PA175#v=onepage&q&f=false ].

You might find some interesting leads and overviews of subject areas in the online Stanford Encyclopedia of Philosophy [ http://plato.stanford.edu/ ].

 

[Yuripe]

Very well. Let's focus now on coordinate view of spacetime.
Can there be a stationary object in expanding spacetime?
Distance between every body in spacetime increases with time without any apparent force and independent of their respective speeds and there seem to be even acceleration of this increase.
How do you accord to that when calculating distance in spacetime between bodies where you have relative speed between them and distance increase due to expansion of spacetime?
If bodies A and B pass each other at certain relative speed then from the point of view of body A time passes slower to the body B, but from the point of view of body B time passes slower to the body A. So time passes differently to every point of view depending on speeds relative to this point. If speed between bodies is zero, time will still pass.
This means everything is moving in time dimension but each point goes at different rate.
It's like looking at stars, and what you see is a composite image where each point is from different time but we can see them all now, at this point in time.

 

[Chronos]

Show the pictures of your grandfather aging in reverse and being born, or stars decompressing and expanding into gas clouds. You offer no observational evidence supporting this failed hypothesis. The arrow of time points to the future. Liking it is optional.

 

[Rasalhague]

Yuripe, you mention three different phenomena: (1) the expanding universe, (2) how time intervals are affected by a kind of coordinate transformation called a "(Lorentz) boost" or hyperbolic rotation", (3) the delay between emission and reception of light given that light has a finite speed.

Number (3) is easiest to understand. I think you have the right idea, except that it might be worth adding that, according to special relativity, there's no one coordinate-independent "point in time" when the light you see now left stars at a given distance from you. In a coordinate system where you're not moving, the events you're seeing on two stars in different places, each 10 light years away from you, happened simultaneously 10 years ago. But in a coordinate system moving relative to you, the event you're seeing now on one of those stars could have happened before or after the event you're seeing now on the other star. (Whether before or after depends on the direction of movement. By how much depends on the speed.) So simultaneity of events in different places depends on which coordinate system you choose.

(2) is a key element of special relativity which should be covered by any basic introduction to the subject. I like the explanation in chapter 7 of Benjamin Crowell's online textbook Simple Nature [ http://www.lightandmatter.com/html_books/0sn/ ]. Another highly-regarded book is Spacetime Physics by Tayor and Wheeler. Not to do down PF, which is great, but a few hours study of a good textbook can get you further than, well, a long time of guessing the right question to ask on internet forums and sifting for the useful replies! You say (2) is "like" (3), but it's important to know the difference; special relativistic effects such as "time dilation" are the weirdness that's left after you've taken into account that delay.

(1) Hmm, these numbers are going backwards... Anyway, the expanding universe: can an object be stationary in it. I think the answer should be yes because you could just define a coordinate system in which that object is stationary, then the galaxies will, mostly, be moving away from that object. But I don't know much about cosmology, so I'd better leave that to the experts.

 

[Dale]

Or it can be the why that DaleSpam refers us to philosophers and priests for, the teleological why that Richard Dawkins warns against, the kind that asks for an answer such as that medieval author gave: "why do events succeed each other in time?" meaning "for what purpose?", "to what end?", where the only satisfying answer can be one that personifies nature or its governing preinciples as something with a rational purpose.

You are correct, there are many different "flavors" of "why" and I try not to use my "philosopher or priest" rant spuriously. The reason that I answered as I did in this case is that I believe that this kind of "why" that you described here was exactly what the OP wanted.

Remember, he specifically rejected any explanation that was just "a description of spacetime". At a fundamental level, that is all science ever is! We invent a theory and describing nature in terms of that theory leads to accurate predictions of experimental results. Why nature should be accurately described by the theory is always unknown, all that is known is that the description is good.

So, if you are specifically not looking for a descriptive answer then it is my belief that you are asking a non-scientific flavor of "why".

 

[Dale]

Can there be a stationary object in expanding spacetime?

Certainly. You can always develop a coordinate system where the spatial coordinates of any single object are not a function of the time coordinate.

Distance between every body in spacetime increases with time without any apparent force and independent of their respective speeds and there seem to be even acceleration of this increase.
How do you accord to that when calculating distance in spacetime between bodies where you have relative speed between them and distance increase due to expansion of spacetime?

The distance between two bodies depends on the coordinate system, even in flat spacetime. This is because the concept of distance depends on simultaneity, which is a frame-dependent quantity.

 

[Rasalhague]

You are correct, there are many different "flavors" of "why" and I try not to use my "philosopher or priest" rant spuriously. The reason that I answered as I did in this case is that I believe that this kind of "why" that you described here was exactly what the OP wanted.

Remember, he specifically rejected any explanation that was just "a description of spacetime". At a fundamental level, that is all science ever is! We invent a theory and describing nature in terms of that theory leads to accurate predictions of experimental results. Why nature should be accurately described by the theory is always unknown, all that is known is that the description is good.

So, if you are specifically not looking for a descriptive answer then it is my belief that you are asking a non-scientific flavor of "why".

Indeed, but giving Yuripe the benefit of the doubt, I wonder if it was just an unfortunately worded request for some more context for the metric equation or explanation of its meaning or elaboration on its consequences:

"Nice , but is this a definition of timelike dimension? It looks to me as a description of spacetime and it doesn't say anything about why there is a minus sign before time component."

 

[Passionflower]

The distance between two bodies depends on the coordinate system, even in flat spacetime. This is because the concept of distance depends on simultaneity, which is a frame-dependent quantity.

Coordinate free measurements of distance exist, for instance radar distance and ruler distance.

 

[Yuripe]

We are describing time as the one dimension of spacetime but you can see that it's a little different from the other dimensions. We're not free to stop in time or change direction of our movement in it as we can do in spatial dimensions.
The metric quoted earlier by DaleSpam works regardless of the direction of movement in time dimension and that's fine, but we don't observe such freedom in real world.

I'm also not clear how you would translate expansion of the universe to changes to the coordinate system chosen for not expanding spacetime. Is 1 second/meter in point A in spacetime equal to 1 second/meter in point B? Does spacetime gets added throughout all its volume or does it get stretched?

Going back to my original question, I wanted to know if you can see any relationship between moving though time and expansion of the universe/spacetime.

 

[Dale]

Coordinate free measurements of distance exist, for instance radar distance and ruler distance.

Good point, I should have said "coordinate distance" to be explicit. Radar distance is coordinate free, but ruler distance is the same as coordinate distance AFAIK. After all, that is conceptually how you make an inertial frame, as a system of rulers and clocks. In any case, I was indeed lax.

 

[Dale]

We are describing time as the one dimension of spacetime but you can see that it's a little different from the other dimensions. We're not free to stop in time or change direction of our movement in it as we can do in spatial dimensions.
The metric quoted earlier by DaleSpam works regardless of the direction of movement in time dimension and that's fine, but we don't observe such freedom in real world.

The English gets a little difficult here, but in the geometric view of spacetime we are not "moving" through time nor are we "moving" through space. We have some worldline which is fixed and unchanging in spacetime. That worldline may have different tangent vectors at different points along it, but there is not a red dot labeled "you are here" which slides along the worldline.

Sorry if that is confusing, it is a weird concept and the words are rather imprecise. In the geometric view we cannot have dt=0 along our worldline because our worldline is timelike. If it were spacelike then we could not have dx=0. Timelike and spacelike are frame invariant concepts.

 

[Rasalhague]

Coordinate free measurements of distance exist, for instance radar distance and ruler distance.

I don't understand, unless by distance you mean spectime interval (in flat spacetime), or spacetime arc length (more generally), rather than spatial distance. The derivations of the length contraction formula that I've seen in elementary textbooks typically use a radar style measurement, although they may call it a pulse of light. The equations for a Lorentz boost, which show how distance measurements change with one kind of change of coordinates, don't specify "except for distances measured by the following devices". Don't they purport to be true whatever kind of equipment is used, in so far as that equipment is accurate?

 

[Rasalhague]

We are describing time as the one dimension of spacetime but you can see that it's a little different from the other dimensions. We're not free to stop in time or change direction of our movement in it as we can do in spatial dimensions.
The metric quoted earlier by DaleSpam works regardless of the direction of movement in time dimension and that's fine, but we don't observe such freedom in real world.

You're right, the metric doesn't single out a preferred orientation of past and future, and at the level of very simple systems of just a few particles, I gather, there is no preferred orientation. Even at a macroscopic scale, if you look at a simplified model of planets moving under the influence of gravity, "playing the film backwards" doesn't look fundamentally different, except that they'd be moving in the opposite spatial direction. The difference we observe between past and future that makes it possible for us to agree on which is which seems to be something statistical that emerges from complex systems. I find all this mysterious and fascinating, and certainly don't claim to understand it. I keep mentioning thermodynamics because I think some of the answers to your questions may lie there; but haven't got very far with my studies of this, so I can't say much useful about it.

But although the metric doesn't tell you which is the best way to call the future, the fact that this metric isn't changed by circular or hyperbolic rotations of coordinates makes it impossible to reverse time orientation by such means. No combinations of turns or changes of velocity will turn your past into your future and vice-versa, whatever that would mean physically.

Changing direction. We can change direction in space because there's more than one dimension of space. I can take a step north, then a step east. I don't have to stick to the north south line all the time. When an object changes its speed, even if it doesn't change its direction of movement through space, there is something analogous to a change of direction that happens in spacetime: that hyperbolic rotation I mentioned. This is covered in any good introduction to special relativity. It's an interchange of time and space coordinates, analogous to the way a circular rotation interchanges different space coordinates. As there is only one dimension of time in this model, there's never a circular rotation-like interchange of two time coordinates, and that's something that makes time different from space.

The speed of light being a cosmic speed limit, and the related geometric properties of flat spacetime (non-curved spacetime, spacetime without gravity), make it impossible to have a "closed timelike curve" in flat spacetime: a traversible path that forms a loop. As far as I know, it's an open question whether such a thing could exist in curved spacetime. If it did, the article I linked to argues, there would be no natural way of specifying which direction was the future for the whole closed curve. The local future at one point on the curve would inevitably be pointing towards the past from the perspective of another point on the curve. What this would mean in practice, I don't know!

 

[Dale]

Radar distance works as follows: a clock is attached to a radar transciever, a radar pulse is emitted at te and the reflection is received at tr. The proper time tr-te is a frame invariant quantity and the radar distance is c/2 times that proper time. Other observers will not agree that this procedure correctly measures distance, but they will agree on what value the measurement produces.

EDIT: see below, I made a mistake

 

[Dale]

But although the metric doesn't tell you which is the best way to call the future, the fact that this metric isn't changed by circular or hyperbolic rotations of coordinates makes it impossible to reverse time orientation by such means. No combinations of turns or changes of velocity will turn your past into your future and vice-versa, whatever that would mean physically.

That is a really good point that I hadn't seen expressed like that. Thinking geometrically, a surface of constant spacetime interval forms a 4D hyperboloid. Spacelike intervals make hyperboloids of one sheet but timelike intervals make hyperboloids of two sheets. That is the geometric reason that you cannot smoothly transform a future directed timelike interval into a past directed timelike interval.

 

[Passionflower]

But although the metric doesn't tell you which is the best way to call the future, the fact that this metric isn't changed by circular or hyperbolic rotations of coordinates makes it impossible to reverse time orientation by such means. No combinations of turns or changes of velocity will turn your past into your future and vice-versa, whatever that would mean physically.

General relativity does not exclude the possibility of closed timelike curves (CTCs). The theory cannot determine however if such scenarios are physically possible.

 

[Rasalhague]

General relativity does not exclude the possibility of closed timelike curves (CTCs). The theory cannot determine however if such scenarios are physically possible.

Good point, I rearranged my post as I wrote it, and forgot this paragraph now comes before the final one with the proviso about it being only forbidden in flat spacetime, and the possibility of a CTS in curved spacetime.

Radar distance works as follows: a clock is attached to a radar transciever, a radar pulse is emitted at te and the reflection is received at tr. The proper time tr-te is a frame invariant quantity and the radar distance is c/2 times that proper time. Other observers will not agree that this procedure correctly measures distance, but they will agree on what value the measurement produces.

If "other observers" is synonymous with "other coordinate systems", doesn't this make it a coordinate dependent measurement of distance like any other? Well, maybe it's just a matter of words, but if we can adopt a special definition of distance in this instance, why not in any instance, and just define a particular distance measured in a particular way as "invariant". But I suppose that would undermine the distinction between "coordinate dependent" and "invariant", causing us to have to find new words for those concepts, which would be a nuisence...

 

[Phrak]

General relativity does not exclude the possibility of closed timelike curves (CTCs). The theory cannot determine however if such scenarios are physically possible.

Awfully good point. Neither does special relativity. All you have to do is draw a closed curve and there you have it. So Dale and Rasalhague are talking about the continuous Lorentz transformation of a vector attached to a single point on a world line. (These are transformations within the Lorentz subgroup (SO+(3,1).) If the vector is postive-timelike to start with, it is always positive-timelike. Classically, over the world line of a particle, no matter how the energy of the particle is changed, from point to point, in a continuous manner, the displacement vector will remain positive-timelike.

I hadn't thought to consider what sort of discontinuous changes in energy or mass a particle would need to undergo to jump to the other sheet of the hyperboloid. These transformations are improper Lorentz transforms of positive determinant.

 

[Dale]

General relativity does not exclude the possibility of closed timelike curves (CTCs).

However, even in a closed timelike curve you can never have a future directed timelike worldline turn into a past directed timelike worldline.

 

[Dale]

If "other observers" is synonymous with "other coordinate systems", doesn't this make it a coordinate dependent measurement of distance like any other? Well, maybe it's just a matter of words, but if we can adopt a special definition of distance in this instance, why not in any instance, and just define a particular distance measured in a particular way as "invariant". But I suppose that would undermine the distinction between "coordinate dependent" and "invariant", causing us to have to find new words for those concepts, which would be a nuisence...

Oops I may have acquiesed to Passionflower's criticism too early.

In the sense that I mentioned the quantitative results of ALL physical experiments are frame invariant. The question is whether or not the experimental result is distance in a given frame. Although the numerical result of a radar-time experiment is agreed upon by all reference frames, equating that result to distance is only correct in the frame where the clock is at rest.

 

[Dale]

Awfully good point. Neither does special relativity. All you have to do is draw a closed curve and there you have it.

This is not correct. Such a curve is indeed closed, but it is not timelike. Closed timelike curves (CTC) are NOT possible in SR.

 

[Phrak]

This is not correct. Such a curve is indeed closed, but it is not timelike. Closed timelike curves (CTC) are NOT possible in SR.

Perhaps not, but I confused definitions in any case. Feel free to replace references to CTC in my past, above, with just 'loop'.

 

[Max™]

Don't think of time as a process, or a flow. Time is an axis against which you can measure differences in spatial components, be they extended objects, or spatial dimensions themselves.

 

[Yuripe]

Don't think of time as a process, or a flow. Time is an axis against which you can measure differences in spatial components, be they extended objects, or spatial dimensions themselves.

Time would be then one dimension of spacetime, where theoretically you can "move" forward of backward by dt as a vector.
Direction of this vector distinguishes if it's forward or backward and it's length describes the rate of this "movement".
This is as viewed from a perspective of the observer confined to this one time dimension.
In reality we see only dt>0 so it would seem time is unidirectional.

Another thing is a use of terms dependent of time to describe time, like moving, speed, etc. It's hard to talk about time or spacetime and use terms that are independent of them.
Sometimes we even do it by looking at time or spacetime from a perspective of extra added dimension(s).
If you look at spacetime, there is no movement in it, everything in it is placed and stationary.

Another interesting thing that comes to my mind as I read along is an idea of worldline for a tunneling particle.
Experiments with light show that while it's tunneling through space, the light travels at speeds at least a few times grater that normal speed of light.
I think the same goes in other types of tunneling for example when atom absorbs light, electron changes it's orbital and this change occurs by tunneling.
Do these particles cross wordline or just temporarily "detach" from spacetime?

 

[Max™]

Charge seems to effect your motion through time, and any motion through space, be it possessing mass, being near a gravity well, or accelerating, affects your motion through time.

If you look at spacetime, there is no movement in it, everything in it is placed and stationary.

Yup, your awareness is a process which updates itself to note the last time it updated itself, giving you the persistent illusion that now is the only moment that has ever existed.

You felt that way a second ago, you'll feel that way after you finish reading this sentence.

Those moments still exist, over there *points towards the past*, or are waiting for you to see them over there *waves a hand in the direction of the future*.