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Author Topic: spacetime question ! more time or less time ?  (Read 3792 times)

franck

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spacetime question ! more time or less time ?
« on: 18/05/2011 16:59:59 »
Hi,

I'm new to this community so maybe my question is not in the good forum but here it is anyways.

I'm reading a very interesting book titled "Why does E=mc^2" by Brian Cox and Jeff Forshaw. So in the first chapters they explain how time is not absolute and how time slows down for moving bodies relative to bodies that are at rest. That part I understand. Then they introduce spacetime and how distances are calculated in spacetime. Basically they explain how distances in space and time can separately be different for different observers (whether they are moving or not) but everyone must agree on the same distance in spacetime which is independant of the observer (the distance between 2 events). They give the formula as being: s^2 = (ct)^2 - x^2. They then give an exemple of a guy who gets to bed at 10hPM and gets back up at 8hAM the next day. So for him the distance in spacetime only takes into account the ' time ' part since he didn't move. Let's say that at the same time another guy flies by at a great speed. Since the second guy is moving we must take into account the ' time ' and the ' space ' part. Since the distance between these 2 events (going to bed and getting up the next day) must be the same, the (ct)^2 part of the formula must be greater. They finish by saying that for the guy moving MORE time has passed for him (more than 10 hours).

So the question being, why MORE time has passed for the guy moving ? Isn't time flow for moving bodies supposed to slow down relative to bodies at rest ? If so, I would have thought that LESS time would have passed since the time flow slowed down. I can't quite understand this. Well I understand the 2 concepts, but one says that time slows down and the other one is saying that more time has passed...

Why am I missing ?

granpa

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spacetime question ! more time or less time ?
« Reply #1 on: 18/05/2011 21:40:16 »
you are missing the 'relative' part of relativity.

speed is relative.

From the moving mans point of view it is the other guy that is moving.
« Last Edit: 19/05/2011 15:01:47 by granpa »

yor_on

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spacetime question ! more time or less time ?
« Reply #2 on: 18/05/2011 22:23:37 »
that should be a typo I think?

As I agree with you, the guy moving will be the 'younger' one, relatively speaking. To make it real simple you can consider SpaceTime as a whole figure, in a same 'frame of reference', loosely speaking, giving the exact same experience of motion and time (Earth).

But I said Space Time right? So we will need both the space as well as the time for defining each one of those 'frames of reference'. If you have two persons on earth, and one of them gets into a rocket, speeding away near light he will change his 'SpaceTime' relative Earth. The guy speeding away will change his 'room time' by motion, not his 'local time' as such, as that one always will be the same when measured inside that 'frame'. Instead the whole geometry of his 'SpaceTime' gets deformed by his motion giving him some strange effects as the Lorentz contraction, whereas from Earths side we will find that his not 'aging' as fast as us.

But what did it is time, always the same for him, suddenly staring to cover a lot of more distance. So in a way you could define it as SpaceTime getting a 'higher' value, which I presume is what they did there, as it is the distance covered in this case that brings forth the time dilation from Earths point of view.

And the rest is wrong. If it was true what the book seem to state then there would be no way to define a twin experiment, as you then could define 'aging' arbitrarily to any frame of reference, which is not possible, as proved by the 'muon experiments' and a lot of other examples.

The original question that granpa lifts up can, as I see it, be defined to the one of 'uniformly moving' (coasting) primarily. Where, according to the Equivalence principle, you arbitrarily can refer the relative 'motion' to any of the two parts 'A' or 'B' (spacecrafts), depending on your choice. That as all uniform motion, you measuring it being inside a 'black box', will become inseparable, allowing you the exact same outcome of all experiments, not caring a iota about what uniform 'speed' you believe yourself to have relative some origin like Earth.

And that one has been tested in the blue shift of light. When accelerating your spacecraft will act with a 'gravity' blue shifting that light, the same as light propagating in Earths gravity. But as soon as you stop accelerating that blue shift must disappear in Einsteins universe, and it does. That is to me the ultimate example the universe can give us that all 'uniform motion' is the same. And it is also there it will be hardest to define who is aging relative who as it suddenly seems that all uniform motion is interchangeable between the 'parts' in your 'system'. But the Lorentz contraction should still only belong to the ship moving uniformly, close to light speed, not to Earth (loosely speaking again) so we know that the universe has a way of knowing who is moving relative who as I see it. The other way to do it is to use fix stars, such stars that seems 'unmovable' relative us looking at them for defining a uniform speed. And that approach has been used too.
==

Hmm, as always I make, my very own, typos :)

And to get back to the question, 'more time'(?) Is not a relevant expression. When it comes to any clock measured first handedly the time you measure will have the exact same durations no matter where you are, at a black hole or on Earth. The time-dilation will only exist in the comparison of frames, and can only be seen when using the same definitions as in the 'twin experiment' where you have a same origin, introduce speeding for one twin, then take him back to his original frame (Earth), then measuring his biological 'age', relative his twin sister :)

Only in such situations will it show itself clearly, or if staying at a black hole then getting back to Earth after some sightseeing there. Then the Earth will have 'aged' relative you. But if you had stayed at that black hole, and we assume that we all have a hundred millions heartbeats per life, then you would have got no more heartbeats out of just staying there, if you see what I mean? Your life's measure do not change, its only relations relative other 'frames of reference' that does, creating that 'time-dilation'.

And expressed yet another way, as this is what seems to confuse a lot of thinkers. You will get no more done under a lifetime by staying at that black hole. So although the universe may die as you wait there, your own life does not 'slow down' allowing you to do all that one could expect to be done in a universes lifetime. That one is crucial to the understanding of a 'time-dilation' as I see it, as lot of people seems to assume that a 'time-dilation' somehow magically expresses itself 'locally'. It does not, only the Lorentz contraction will be there, and Doppler shift.
« Last Edit: 18/05/2011 23:10:09 by yor_on »

Soul Surfer

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spacetime question ! more time or less time ?
« Reply #3 on: 18/05/2011 22:45:03 »
The critical thing that everyone tends to forget is that time ALWAYS moves at the normal rate for you and anyone else travelling with you.  It only appears to move slower for observers from the outside who see you moving quickly.

Firstly this means that the net effect is that when you get back from a fast journey more time has past there than you expect.  Also assuming that you accelerate say at a rate of 1G you always continue to go faster from your point of view even though you are limited by the velocity of light from the point of view of the outside observer.  The slowing down of time from the outside observers point of view allows you to get further as you continue to accelerate closer to the speed of light even though you never actually reach it however long you accelerate for.

This has the effect that it is in theory possible by accelerating continually at 1g to reach the farthest limits of the universe during your lifetime from your point of view assuming that you started reasonably young.  however it would still take you 13 billion years to achieve this journey from the point of view of an outside observer.

yor_on

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spacetime question ! more time or less time ?
« Reply #4 on: 18/05/2011 22:57:09 »
Yeah SoulSurfer, we seem to have noticed the exact same phenomena there. To think that time 'locally' is changing will make time dilation a very fuzzy definition as you won't get more done just by earth stating that you have a 'slower clock'. It's the whole room time geometry you deform with gravity and motion, but in that invisible 'box', created 'momentarily' by motion for example, your life's measure always stay the same.

franck

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spacetime question ! more time or less time ?
« Reply #5 on: 19/05/2011 14:28:00 »

I undertand the fact that you don't actually ' extend ' you life when traveling faster. to make sure I correctly explain the question, I'm going to type the paragraph that i can't understand and you can then tell me it it's a typo or not :) here it goes:

"By now we are familiar with the statement that the distances in time and space bwtween events are measures differently by observers moving at different speeds relative to each other, but they must change in such a way that the spacetime distance always remains the same. Because of the strange Minkowski geometry, this means that the tip of the vector can move around on a hyperbola that lies in the future lightcone. To be absolutely concretem if the two events are "going to bed at 10PM" and "waking up at 8AM", then an observer in the bed concludes that the spacetime distance vector points up his time axis, as illustrated in Figure 9 (an arrow pointing up) and its lenght is simply the time elapsed on his watch (10 hours) multiplied by c. Someone fying past at high speed would be free to interpret the person in bed as doing the moving. She would then have to add in a bit of space movement as well when she viewed the person in bed, and that moves the tip of the vector off her time axix. Because the arrow's lenght cannot change, it must stay on the hyperbola. The second, tilted arrow in Figure 9 (an arrow that points north-east) illustrates the point. As you can see, the amount of the vector pointing in the time direction has increase and this means that the fast moving observer concludes that more time passes between the two events (more than 10 hours elapsed on her watch)."

Forgive me for the mistakes, I've typed this in a hurry :D. Maybe you've answered the question but I can't quite get why more than 10 hours has passed for the person moving between the two events. Correct me if I'm wrong, but from the point of view of the person sleeping on Earth, the moving person ages ' less fast '. So for the point of view of the moving person, the people on Earth age ' faster '. If so, why is the person moving feels that more time has elapsed between the two events than the person on Earth ? I know it's a complicated concept, but try to keep it simple for me alright ?! ;)

Thx,
Franck

Phractality

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spacetime question ! more time or less time ?
« Reply #6 on: 19/05/2011 17:27:26 »
Frank,

In SR (special relativity, where there is no gravity or acceleration), each observer sees the other guy's clock running slower than his own. You can't say one observer is moving and the other one is stationary; each is stationary in his own reference frame, and the other guy is moving.

The twins paradox is a result of applying SR to a round trip problem; you can't make a round trip without accelerating, so you can't use special relativity. If you do apply SR, you will conclude that each twin thinks the other twin is younger than he is; that is the paradox.

A twin making a round trip must accelerate, while the stay-at-home twin does not. In general relativity, less time passes for the accelerated twin, so he is younger than the stay-at-home twin when he returns. Both twins see that the traveling twin is younger, so there is no paradox.

The distance formula in space-time is s² = Δr² -c²Δt², which is the same as Δx² +Δy² +Δy² +Δz² -c²Δt². Notice the minus before the time factor; dimension that subtract from distance like that are called time-like dimensions; dimensions that add to distance are space-like dimensions.

yor_on

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spacetime question ! more time or less time ?
« Reply #7 on: 20/05/2011 03:19:05 »
It's a pleasure reading you Phractality :) you're perfectly correct and it nicely express how it's the lights constant speed in a vacuum combined with motion changing your 'room time geometry' that creates a 'time dilation'. What I think myself that we can state in your situation is that this 'light clock' measured between the two frames of reference won't define what the 'real time' is for any of them. Even though you always can define your 'speed' relative your place of origin (Earth) that will not tell you your 'real speed' as I think of it now. And so, as you compare that other clock (spacecrafts light signals/transmission) to your own, you will only have a arbitrarily defined time that describes a relation.

Someone might wonder about why we can't use the blueshift as a way to define a 'speed'? We find the blue shift both in the case of a acceleration and in the case of matters 'gravity', don't we? Yep, we do, but as soon as you start to move uniformly (coasting away in space) that blueshift will disappear, leaving you with no information of a speed, although you still will have one defined relative your origin and the universe (stars) at large.

So inside that black box there will be no way for you to tell a 'speed' using the blueshift, measuring the light from a light bulb (situated at the front of your spacecrafts motion, for example). What does that tells us?

And what is it you do when 'uniformly moving'? Well, according to Einstein you are following a 'geodesic', so how can I define that 'geodesic'? There is one simple thing you can use for defining it, all geodesics will leave you weightless. That means, if falling of that ladder as you paint your house, you're actually uniformly moving (gravitationally 'accelerating' as it also is called) for that short bit, being at absolute rest with gravity, weightless (tidal forces ignored here).

Weird, ain't it :)

JP

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spacetime question ! more time or less time ?
« Reply #8 on: 20/05/2011 06:26:40 »
Yor_on, the Doppler shift is a blue shift/red shift for things moving with constant velocity.

yor_on

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spacetime question ! more time or less time ?
« Reply #9 on: 21/05/2011 00:03:03 »
You lost me there JP?

As far as I know we have both?
=

At around 0.4-0.5 'c' the relativistic Lorentz will start to make itself noticed though.
Or did you mean that I should have wrote both out?
« Last Edit: 21/05/2011 00:06:00 by yor_on »

JP

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« Reply #10 on: 21/05/2011 02:40:20 »
Someone might wonder about why we can't use the blueshift as a way to define a 'speed'? We find the blue shift both in the case of a acceleration and in the case of matters 'gravity', don't we? Yep, we do, but as soon as you start to move uniformly (coasting away in space) that blueshift will disappear, leaving you with no information of a speed, although you still will have one defined relative your origin and the universe (stars) at large.

I was replying to this quote.  If you're moving uniformly with respect to a source, it's still blueshifted or redshifted due to the Doppler effect.

yor_on

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« Reply #11 on: 21/05/2011 05:00:08 »
Ah, okay. That was a miss.

I was thinking of my black box there. I should have made that explicit of course, sometimes you think you covered it, forgetting the simplest definitions needed. Blue/redshift, as when measuring it on a source moving relative you, will always exist, it will not give you that ships, or yours, 'absolute' speed relative SpaceTime though. But it will deliver a true measure of the energy of the light transmitted between you, making you into a 'system' of sorts.

But, inside a black box, the only time I expect you to see a blueshift is relative you accelerating, where you're sitting at the ships tail measuring photons/waves coming from a lightbulb situated at its front. And that's why there's a difference and why you can't use it to measure any 'absolute' speed.

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spacetime question ! more time or less time ?
« Reply #11 on: 21/05/2011 05:00:08 »