These twins are hurting my head!

[popeye85]

Having just watched cosmos and about half way through 'a brief history of time', one topic which pops up now and then is the theory of time dilation and the so called 'twin paradox' and I am really struggling to get my head around it! Can someone please explain it to me in lay man's terms as it absolutely fascinates me and I'm desperate to know how it comes about. 

Cheers 

Popeye.

P.s-I'm a bit of a dummie so simple terms would be appreciated!!

 

 

[Knight of Clear Skies]

Hopefully these Minute Physics video will help.

https://youtu.be/Bg9MVRQYmBQ

https://youtu.be/0iJZ_QGMLD0

(For bonus credit, someone could calculate how fast an observer would have to be travelling for these videos (2:49 and 3:33) to appear to be a minute long....)

[SilverAstro]

40 minutes ago, popeye85 said:

 theory of time dilation and the so called 'twin paradox' / and I'm desperate to know how it comes about. 

For the speed of light to remain constant for all observers no matter how and where they are moving relative to each other then something else must change. If you change the time that they each experience then the speed of light will be measured the same by each twin no matter how fast they go. (up to a limit - the speed of light)

So, the fast twin experiences slow time and thus ages slowly. The slow twin that stays home experiences faster time and ages more quickly. Young twin comes home and is surprised that his sibling has a long white beard ( especially if it was his sister )  QED.

[popeye85]

OK but how can time change in a biological sense? How can slowing the breakdown of our body's be allowed?

[Knight of Clear Skies]

25 minutes ago, popeye85 said:

OK but how can time change in a biological sense? How can slowing the breakdown of our body's be allowed?

From the perspective of the travelling twin, time doesn't slow down. It's only in comparison to their twin's clock that less time has elapsed. Another way of putting it is that the twin has travelled into the future.

[vlaiv]

12 minutes ago, popeye85 said:

OK but how can time change in a biological sense? How can slowing the breakdown of our body's be allowed?

Each persons "biological" clock runs at the same speed in their reference system (this is a bit weird to say, since we define speed via time so we enter a loop trying to define speed of time - concept depending on time it self). So you don't feel slowed down, or sped up. It is only when you look / measure other person that you see the their processes / time run slower / faster.

Also don't think in terms what is allowed, think in terms - nature is behaving this way - you can't tell nature or allow it to behave in certain way rather then other.

Or let me try to explain this way: if you were suddenly slowed down - everything around you is slowed down, all processes, all the physics and biology - how would you know? Your mind will slow down also, only thing that will remain the same is ratios between "times" of how long things "take" to complete - happen, and that is everything you have in order to determine time - ratios between time periods - this is how we measure things (ratios between physical values). Special relativity tells us that between two frames of reference these ratios change, but not inside single frame of reference.

[JOC]

There is a brilliant demo of this on one of the series of Royal Institute Christmas lectures.  They get two atomic clocks and synchronise them.  Then they fly one around the world by aeroplane and when it comes back they are out of synch by fractions of a second.  I can't explain how it works, but that demo to me was proof that is did - its no doubt on YouTube somewhere.

[David Levi]

@Knight of Clear Skies and @vlaiv explain it correctly. You won't experience any difference in the passing of time as it goes by.

The best explanation of why it happens was given, for me, by Brian Greene in his brilliant book The Elegant Universe. To sum it up, consider when you move in a north direction, 100% of your motion is towards north. When you move in a west direction, 100% of your motion is towards west. If however you move in a north west direction, 50% of your speed is now in the north direction and 50% in the west direction. This is the mathematical concept of vectors if you want to get technical. Now, time can be considered as another dimension just like up/down, left/right and backwards/forwards. When you are standing still you are travelling through time at 100% speed. If you move in any direction some of that speed through time is transferred to your speed through space just like in the north/west direction analogy. The faster you travel the less speed you have through time and the more speed you have through space.

[JOC]

Further thoughts, as a thought experiment I wonder if you had placed a rapidly evolving bacterial colony of the flight with the clock and kept its identical partner in the lab (and removing biological variation from this) whether both colonies would evolve the same number of generations by the time they were back together?

[David Levi]

@JOC I saw that Christmas Lecture at the time and very impressive the demonstration was. It has stuck with me without ever having seen it again and that must be a fair few years ago now.

[SilverAstro]

52 minutes ago, popeye85 said:

OK but how can time change in a biological sense? How can slowing the breakdown of our body's be allowed?

Haha, you wanted the simple explanation ! now stand back and be amazed

I said "you change the time that they each experience" that includes what their bodies experiece, what their cells and their bacteria experience, what the clock on their bedside table experiences (is subjected to, if you dont like inanimates experiencing things ) : the stone tossed into the pool in their space ship will cause a splash which will take the same slow time to subside. Exerything in their local environment (aka  their frame of reference ) experiences the slowed time. It is their space-time that determines it.

,,, then we come to Lorentz and Fitzgerald muhhwahhhhaaa

[ollypenrice]

Thee are two forms of the twins paradox. The one you usually read goes like this:

When one twin stays at home and the other races off in a spacecraft their clocks begin to run at different rates. The fast-moving twin's clock, as seen by the stationary twin, is running very slowly. The fast-moving twin's clock looks normal to him but when he looks back at the stationary twin's clock he sees it running very fast. (They can't really see each others' clocks but this is a 'thought experiment.') So when the fast moving twin comes home he has aged less because his time, like his clock, has been running slowly. They are no longer the same age.

However, in my optinion this is not the Twins Paradox.

For me the real paradox arises from thinking about the story. We get from Special Relativity the idea that observers with clocks moving fast relative to each other tick at different rates. So, fine, the story is explained, right? No, wrong. Because unfortunately Special Relativity does not allow us to consider that there is any such thing as being stationary. Movement can only be defined as being relative, so the twins are moving relative to each other  but we cannot define either of them as being 'stationary.' Stationary relative to what? Space has no fixed co-ordinates. So the real twins paradox  arises from the fact that Special Relativity tells us that their clocks are moving at different speeds so they are not keeping time with each other, but since we can't say that either twin was fixed or stationary, which one should be older?

This, the real paradox, is resolved by General Relativity. In General Relativity we can distinguish between the stationary and the fast moving twin because the fast moving twin has been subject to acceleration, has been in an accelerated environment. The blast off, the U turn and the deceleration all count as acceleration in physics. In GR accelerated environments and gravitational ones are equivalent. So the space travel twin's time was slowed down by acceleration.

The twin paradox arises from Special Relativity and is resolved by General Relativity.

Olly

[SilverAstro]

If we start talking about 'stationary' - we should say relatively stationary

and the simple explanation then gets tangled into explaining why the effect does not reverse on the deceleration , , ,

spanners

[SilverAstro]

@popeye85 dont despair, non of us fully understands it either, we are just pretending Even Einstein himself was not immune from tossing toys out of his pram and introducing things into his equations on a whim. He never did come up with a GUT either

[vlaiv]

I agree with Olly - real paradox is just that - I see my twin moving away from me - his clock must be slower then mine. My twin also sees me moving away he concludes my clock is slower than his. So which one is slower?

But there is problem with this reasoning. In asking a question which clock is slower - we are assuming either - there is universal clock to compare these two clocks against - no there is no universal clock, or we are mentally adopting one frame of reference, and without proper transformations trying to apply logic to other frame of reference. Also not valid. For example, we conclude that twin will also conclude the same about us. But there are differences, let me give you specific example, without acceleration. Just clocks at fixed speed.

So lets have following setup: 3 clocks, one is in our frame of reference, standing still, other is going "left", and at the time it passes us by we synchronize clocks. Clock that is traveling to the left viewed from our point of reference continues travel for certain amount of time - reaches some point - a star and there it meets another clock going right - they sync so that clock going "right" now carries time and when it reaches us we do time sync and compare times. This is somewhat similar setup to twins but broken down into steps and avoids acceleration.

First thing to note is: in our frame of reference we see left and right clock meeting at the star, or at certain distance away from us at a certain local time. But they will not actually meet there looking in their frame of reference. Why is this? Because length gets contracted, so what is one ly away in our reference frame, will be shorter in "left" clock reference frame. So we have moved away from "left" clock less then 1Ly as seen in its reference frame. Similarly we can see that right clock will also see us move less than we see it move. This is why it is said there is no simultaneity in special relativity - we see clock pass each other at the same time they pass star, but they see them selves pass each other before, or after passing the star. We see them move certain distance in certain time, they "see" us moving different distance in opposite direction in different time.

Instinctively one might ask so what really happened? And the answer to that question is there is no single universal timeline, and what happened depends on where were you - it happened to you, or rather in your frame of reference. There is however single truth - things did happen and by knowing what happened in your frame of reference you can tell what happened in other frames of reference, so truth is not "what happened", but rather different things happened in different frames of reference and there is well defined set of rules / transformations that link these happenings, by knowing one you can deduce other.

 

[vlaiv]

I just thought of one more "paradox", that is probably easier to imagine and understand.

Let's take a train of certain length and a tunnel of exactly the same length when in same frame of reference / "at rest".

Next we stand next to the tunnel and observe approaching train - it is moving relative to us, it's length is contracted - it is shorter then tunnel. At the point in time that whole train is in a tunnel, and it can fit whole with room to spare because it is shorter than tunnel - because it's moving - we decide to flip a switch - which engages ultra fast gates at ends of tunnel that shut and open at incredible speed (we are imagining this now, but to make story more dramatic ) - if gates are fast enough in our frame of reference nothing special happens - gates close and open while train is in tunnel and trains exits out ok at the other side.

But what happens in train's frame of reference? Well tunnel is moving relative to it so it is shorter in it's frame of reference - so whole train can't fit inside that tunnel, and there are those diabolical gates to worry about - no way they can close and open without slicing into the train!

So what really happened? (there is that question again). We know what happened in our frame of reference - train was shorter it managed to fit inside tunnel - gates closed and opened while train was in the tunnel and everything is ok. And what happened in train's frame of reference? Following did: train started entering the tunnel, while it was half way in with its tail sticking out at the back, gate in front of the train, the one on the back of the tunnel closed, and then opened. Train then appeared on the other side, while its end still not reaching tunnels entrance. Ok, first bullet dodged :D. So train continues motion, it's end finally enters the tunnel and after that gate at front of the tunnel closes and opens.

And all of this show how "paradox" is resolved really nicely when you don't assume simultaneity of events - something that happens in one frame of reference "at the same time" - gates closing and opening at the same time, does not happen at the same time in other frame of reference.

[ollypenrice]

59 minutes ago, SilverAstro said:

 

and the simple explanation then gets tangled into explaining why the effect does not reverse on the deceleration , , ,

 

The effect doesn't reverse because acceleration and deceleration both subject the environment to 'G.'

It's worth adding that these effects are real and have been measured by subjecting previously synchronized atomic clocks both to acceleration and to different gravitational fields on the earth. They lose synchronization in accurate accordance with theory.

Olly

[ollypenrice]

19 minutes ago, vlaiv said:

I just thought of one more "paradox", that is probably easier to imagine and understand.

Let's take a train of certain length and a tunnel of exactly the same length when in same frame of reference / "at rest".

Next we stand next to the tunnel and observe approaching train - it is moving relative to us, it's length is contracted - it is shorter then tunnel. At the point in time that whole train is in a tunnel, and it can fit whole with room to spare because it is shorter than tunnel - because it's moving - we decide to flip a switch - which engages ultra fast gates at ends of tunnel that shut and open at incredible speed (we are imagining this now, but to make story more dramatic ) - if gates are fast enough in our frame of reference nothing special happens - gates close and open while train is in tunnel and trains exits out ok at the other side.

But what happens in train's frame of reference? Well tunnel is moving relative to it so it is shorter in it's frame of reference - so whole train can't fit inside that tunnel, and there are those diabolical gates to worry about - no way they can close and open without slicing into the train!

So what really happened? (there is that question again). We know what happened in our frame of reference - train was shorter it managed to fit inside tunnel - gates closed and opened while train was in the tunnel and everything is ok. And what happened in train's frame of reference? Following did: train started entering the tunnel, while it was half way in with its tail sticking out at the back, gate in front of the train, the one on the back of the tunnel closed, and then opened. Train then appeared on the other side, while its end still not reaching tunnels entrance. Ok, first bullet dodged :D. So train continues motion, it's end finally enters the tunnel and after that gate at front of the tunnel closes and opens.

And all of this show how "paradox" is resolved really nicely when you don't assume simultaneity of events - something that happens in one frame of reference "at the same time" - gates closing and opening at the same time, does not happen at the same time in other frame of reference.

Schrodinger's train! It's trapped and it's not trapped....

[SilverAstro]

38 minutes ago, ollypenrice said:

The effect doesn't reverse because acceleration and deceleration both subject the environment to 'G.'

Yes, we know that but OP wanted a simple explanation ! In truth there is not a simple explanation and frames of reference are for the OU course

 

[Knight of Clear Skies]

38 minutes ago, vlaiv said:

At the point in time that whole train is in a tunnel, and it can fit whole with room to spare because it is shorter than tunnel - because it's moving - we decide to flip a switch - which engages ultra fast gates at ends of tunnel that shut and open at incredible speed (we are imagining this now, but to make story more dramatic ) - if gates are fast enough in our frame of reference nothing special happens - gates close and open while train is in tunnel and trains exits out ok at the other side.

If Maxwell's Demon worked for British Rail...

[ollypenrice]

8 minutes ago, SilverAstro said:

Yes, we know that but OP wanted a simple explanation ! In truth there is not a simple explanation and frames of reference are for the OU course

 

I don't agree. I think frames of reference make it easier.

For a simple explanation I'd go for this: G forces (like their close relation gravity) slow time down. (Take one atomic clock up a skyscraper and the other down a mine. The one down the mine is in a slightly stronger gravitational field being nearer the Earth's centre of gravity and it runs slow. Or put it in a fast jet, speed it up, slow it down, corner with it, so gving it lots of G loadings - and it will also run slow.)

The earth twin doesn't live in an environment with big G forces operating. The travel twin does. These G forces slow the travel twin's time down so he is younger when he gets back.

(The general relativity model is actually simpler than the special relativity model because the GR model works properly and is paradox-free!)

Olly

[SilverAstro]

29 minutes ago, Knight of Clear Skies said:

If Maxwell's Demon worked for British Rail...

Nah, he gave up on BR, last I heard he was on a ship, ,

More like a Hilch Vortex and London Underground  - now and again a fast one escapes the Circle and whizzes off to Heathrow.

[cloudsweeper]

53 minutes ago, ollypenrice said:

I don't agree. I think frames of reference make it easier.

For a simple explanation I'd go for this: G forces (like their close relation gravity) slow time down. (Take one atomic clock up a skyscraper and the other down a mine. The one down the mine is in a slightly stronger gravitational field being nearer the Earth's centre of gravity and it runs slow. Or put it in a fast jet, speed it up, slow it down, corner with it, so gving it lots of G loadings - and it will also run slow.)

The earth twin doesn't live in an environment with big G forces operating. The travel twin does. These G forces slow the travel twin's time down so he is younger when he gets back.

(The general relativity model is actually simpler than the special relativity model because the GR model works properly and is paradox-free!)

Olly

Hi Olly - gravitational field strength decreases below the surface of the Earth, as well above it.  Think of it like this - as you go below ground, the mass above attracts you in the opposite direction.  Eventually, at the centre, there is zero gravitational field because grav. attractions in opposite directions cancel each other out.

Doug.

[ollypenrice]

1 hour ago, cloudsweeper said:

Hi Olly - gravitational field strength decreases below the surface of the Earth, as well above it.  Think of it like this - as you go below ground, the mass above attracts you in the opposite direction.  Eventually, at the centre, there is zero gravitational field because grav. attractions in opposite directions cancel each other out.

Doug.

OK, sorry, we shouldn't go below the surface. But this covers the point I was trying to make: https://www.nist.gov/news-events/news/2010/09/nist-pair-aluminum-atomic-clocks-reveal-einsteins-relativity-personal-scale

Olly

[saac]

I'm not so convinced that simply stating that "gravitational fields or acceleration affects time" equates to "easier to understand" than time dilation via special relativity.  The dilation of time is a glaringly clear consequence of Einstein's assumptions which frame  SR, chiefly that the speed of light holds the same value to all observers. The mathematics to show this consequence is easily within the grasp of a second year geometry class in secondary school and the public at large.  While special relativity appears in High School Physics curricula (Higher, A level, I Bac) with expectation of derivation and handling of Lorentz factor.  General relativity by contrast is approached only in a qualitative approach.  I'd be delighted to hear from anyone who can explain without reference to the curvature of space time why gravitational fields affect time

Popeye, regarding your question concerning the effect of time dilation on a biological system. What mechanism is at play that allows the biological entity to sense/experience the dilation in time?  That is a really good question and can't be answered satisfactorily until we understand that the dilation of time is not felt or experienced by the observer within their own frame of reference! That sounds like a cope out, because it is   But in truth the difference in the passage of time is only seen between the two observers in different frames of reference ( one of earth and one on the spaceship).  The effect is absolutely counter intuitive so don't give yourself too hard a time trying to get your head around it.  The twins paradox is not really meant to explain what is happening rather it is more a bit of entertainment founded on an aspect of Special Relativity (there are so many holes in the paradox that undermine it as a true paradox). However, there are some hard examples of evidence which support the effect of time dilation due to special relativity.  Here you may want to search for time dilation and muon half life and the time signal correction required of gps satellites. Good luck with it, it really is an interesting subject and actually not that difficult to follow if not understand fully.

 

Jim