# The Naked Scientists Forum

#### EEK

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« on: 10/04/2015 19:43:30 »
Imagine two circular light clocks LC and LC’ of radius of one light second one above each other such that their centres lie on the origin of time axis and spatial x-axis. Let LC’ starts moving with say 0.5c while the other remains stationary. The time bubble of both circles starts expanding on spatial axis (surface of the circle /cone) which also moves at “c” in time “t” on times axis.

Now we know about the second postulate of relativity that the speed of light in free space has the same value c in all inertial frames of reference therefore after one second

Stationary light clock: A light cone of radius “c” is formed but since it is not moving therefore the centre of the circle/ cone will remain at its original place.

Moving light clock:  A light cone of radius “c” is also formed but since it moves relative to the stationary clock on spatial x-axis (surface of the cone) which also moves at “c” on times axis therefore according to moving observer a pulse has already reached at the circle in his stationary frame of reference while for stationary observer a pulse has yet to arrive at the boundary of circle of a moving circular clock.

This means each clock moves into the space like curve of the other but still remains on the spatial x-axis and same world line upon the separation of two circles/ light cones. This means non of them has gone into the past or future cone of the other.

Now how come a moving clock slow down when itself moves through the same time and space in which a stationary clock lies?

Does this mean space-times are lagging or elsewhere in space like curve relative to each other if yes then how come they see each other?

Can aforementioned clocks tick at different rate present in the same space and TIME?

If they both tick at same rate on the same world line in same space-time then there is something wrong with the postulates.

Only interested replies.

Thanks

#### David Cooper

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« Reply #1 on: 13/04/2015 18:01:47 »
Only interested replies.

Replies can't be interested, so the above accidentally serves as an instruction not to reply to this thread. For this reason, I held a conversation with EEK in PMs instead. I'll now transfer some of the content of that conversation here (missing anything out that might have been intended to remain private) so that it can continue in the open instead as it should - there may be a lot for people to gain by discussing this.

http://visualrelativity.com/LIGHTCONE/LightClock/default.html

2/3 of the way down that page is a section with “Circular Light Clocks  (Visualizing Proper Time)” written on a yellow banner. There are links to videos on the right on a cyan background and the first of these appears to be the one that's most relevant to this discussion.

I commented on clocks running at different speeds relative to each other, but I'll say more about that later. EEK then replied with this (which might help you work out what his question is, though I find it just as confusing as the original version):-

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My question is more related to the geometry of the problem not clocks which may or may not tick at the same rate.

Reasons: Since the exact speed of the light is measured on the surface of light-cone not its true distance of apothem therefore concentrate on the surfaces of cone while playing the animation of the circular clocks in the following link.

http://visualrelativity.com/LIGHTCONE/LightClock/default.html

1-   Events start at t0 upon the explosion of time bubbles of both clocks
2-   Apex of the past light cones of both events is at t0 / on spatial x-axis
3-   Radius of the time bubble of stationary clock is expanding with c
4-   The pulse of stationary clock is also moves with c but on the circle in (3) till it reflected back by the mirror
5-   Relative to stationary clock : The distance of the pulse of moving clock from the origin on the surface of cone is always greater than the (r=c) on spatial axis because of its velocity  (v)
6-   Thus according to first postulate: Stationary observer wouldn’t be able to see the pulse until it reflected back in in the region of “r”. (This mean space-time of moving frame is disappeared) .
7-   However according to second postulate: Stationary observer always sees pulse (may be just an image) of moving clock moving at “c” at the same rate of its time bubble on the surface of cone until it reflected back
8-   Possibility of two pulses: As per (7); stationary observer always sees a pulse while as per (6); since a pulse moves back  and forth in between the mirrors therefore it can also be found in the region of time bubble of stationary clock. So there are chances of seeing two pulses within the moving clock.

I replied to that as follows:-

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I can't work out which of the videos I should be watching there, and I'm not sure what you're trying to ask either. However, I've just watched a video there in which two light clocks send out pulses of light in all directions and they use circular mirrors (or I suppose they could be spherical ones, but we're only seeing two space dimensions in the diagrams) to reflect the light back to the centre, and every time the light returns to the centre it counts as the tick of a clock. One of the clocks is moving and that makes the light paths longer, so it ticks more slowly than the stationary one. What we're seeing in these diagrams is a calculation of what is going on from a frame of reference in which one of the clocks is stationary, but that doesn't actually show what events would look like if you were standing there watching the action play out. If we imagine that the mirrors are made of unsilvered glass so that we can see through them, they will still reflect enough light to work as mirrors because some of the light will be reflected, so this will let us see inside them as they function. If we also roughen some parts of the glass, light will be scattered in all directions when it hits those rough patches, and this will allow us to see both clocks in action as we stand at the centre of one of them - the glass will now light up whenever a pulse of light hits it and we will have a clear view of all the events.

When we run through the events now, we will see light leave the emitter at the centre, but we won't see anything happen with our stationary clock until the light has bounced off the glass and come all the way back to the centre - we will see the whole mirror light up and we will see the pulse arrive back at the centre simultaneously. The light will actually have reached the mirror/glass in half that time, but we don't see it light up at the moment when it lights up because we have to wait for that light to reach our eyes before we can see it. The video is quite different from this - we see all the events at the actual moments when they happen without having to wait for the light to travel to our eyes, so the video provides a view of events which is impossible to see in real life.

When we look at the moving clock instead, we will see light being emitted from right beside us as the clock starts moving away. We will then see part of the moving mirror light up as that part races towards us, and then we'll see that bit go dark while other parts of the mirror to either side light up, and the two bright patches will race round the mirror until they meet up at the opposite side. At that moment when they meet, we will see the moving clock's emitter light up too as all the light arrives back at it, but we're actually watching a past event because it has taken time for the light we're seeing to travel from where the emitter was (when the light hit it) to where we are standing, so the tick of that clock has already happened before we saw it complete. Almost at the same moment as we see this first pulse hit the emitter and light it up, we will see a new pulse of light emerge from the emitter.

If we now repeat events while moving alongside the emitter of the moving clock, we will see exactly the same events play out, but the clock that we are moving with will now complete its ticks first and the stationary clock will look just like the moving one did the previous time, so it will look as if we aren't moving and as if the stationary clock is the one that's moving.

So, that's what events would actually look like if you were there watching them. The videos are different - they show the same events but with no delays between things happening and you seeing them, so instead of something being lit up by light and you having to wait for that light to reach you before you see the event happen, it's as if you can see the events exactly when they happen without having to wait for the light to reach your eyes. If you keep that in mind as you watch the videos and also as you imagine things as they would actually be seen by a real observer, hopefully you will be able to find the answers to your questions there. If not, feel free to try asking again and hopefully I'll be able to work out what it is you want to know.

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Since its hard to express or imagine such situation therefore the link was just mentioned for simplicity in order to get a better understanding of the idea. You can choose any one however I have seen the first one under the topic  “Circular Light Clocks  (Visualizing Proper Time)”

Reasons :

Since everything is happening on the spatial surface and the said surface is moving upward in time direction at the same rate therefore by my reckoning all clocks either stationary or moving  should tick at the same rate as they are also moving upward on time axis at the same rate as that of spatial surface. I don’t see anything below the spatial surface therefore nothing is lagging behind.

The information of ticking which we receive late doesn’t mean that the other clock lies in our past cone.

Since clocks are originally lie in the elsewhere position (unreachable) on one or the same slice of spatial surface relative to each other therefore ticking information can be received upon expanding of their respective time bubbles otherwise no information would be received if they were located in the past cone w.r.t each other..

For example:

Let the time bubble of both clocks (one stationary and the other moving relative to other) separated by conspicuous distance on the spatial surface start expanding at time t0 as soon as they start ticking at the same time (by chance).

Spatial surface which carrying both clocks is also moving upward at the same rate on time axis and therefore expansion of both circles can always be seen moving upward on spatial surface .

The apex of the cones (past and future) of both circles formed at t0 separated by the same conspicuous distance on the same slice of the spatial surface where the explosion of time bubbles occured.

So any thing below the apex of above mentioned slice of spatial surface are either in elsewhere position or past cone of aforesaid bubbles.

Anything above the apex of above-mentioned slice of spatial surface are either in elsewhere position or future cone of aforementioned time bubbles.

Now the boundaries of these two circles (cone surfaces) which carrying information of their respective event of ticking, are expanding and expanding on spatial surface which moves in upward direction on time axis and therefore eventually will meet at some movement of time on the same spatial surface.

My second Question is about the Einstein postulates

its just my opinion that it should work out like above however an opinion can be wrong too.

Again I find the wording confusing to the point that I still can't work out what the question is, but I'm sure we'll get there eventually. For now, I'll pick out this bit and comment on it:-

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Since everything is happening on the spatial surface and the said surface is moving upward in time direction at the same rate therefore by my reckoning all clocks either stationary or moving  should tick at the same rate as they are also moving upward on time axis at the same rate as that of spatial surface. I don’t see anything below the spatial surface therefore nothing is lagging behind.

The horizontal slices through the diagrams represent time, but this is coordinate time tied to a specific frame of reference. All the events that take place on the same horizontal slice can be thought of as being simultaneous with respect to that frame of reference, but they will not be simultaneous if you draw events out working from other frames of reference. The ticks that the clocks register is "proper time", the word "proper" meaning "own" (as in the clock's own time - it's an unusual usage of the word "proper" which feels more natural in other languages: propre temps; propio tiempo). Proper time is only the same as coordinate time when a clock is at rest in the frame of reference that you're using. The clock which is moving through the frame of reference that you're using will tick more slowly than the coordinate time used for that frame. The coordinate time is considered to be artificial and not part of reality, while the proper time is the only real time. If you use a different frame of reference to analyse events from and you choose the one in which the moving clock is stationary, your new coordinate time will then match the proper time of that clock while the other clock is found to tick more slowly (its proper time) than the new coordinate time that you're now using.

According to Special Relativity, Spacetime is non-Euclidean, and this is why the coordinate time is considered to be an artifice - the moving clock is taking a shorter path through time into the future than the stationary clock, and that means it isn't really ticking more slowly than the stationary clock.

#### David Cooper

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• Posts: 1505
« Reply #2 on: 14/04/2015 01:46:35 »
And here's a new chunk from the PM conversation:-

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I realized later on that my first reply was confusing as I mentioned circular clocks but expounded the other type. Sorry about the confusion.

Here is correct one which may help.

Since the exact speed of the light is measured on the surface of light-cone not its true distance of apothem therefore concentrate only on the surface of spatial axis while imagining the two clocks AB and CD of length say 1 light second one above each other. A of AB and C of CD are at origin of time axis and spatial x-axis while B and D are on the right side of spatial axis. Let CD moves with 0.8c while AB remains stationary. This means CD moves towards right on spatial axis as well as time axis while AB remains on time axis but also moves (not with 0.8c) at the same rate as CD on time axis.

1.   Events start at t0 when CD starts moving and hence explosion of time bubbles of both clocks occur. Pulses in the clocks are also start moving from A to B and C to D upon the start of events.
2.   Apex of the light cones (past and future) of both events formed at t0 on the slice of spatial x-axis
3.   Radius of the time bubbles (information circles) of AB and CD starts expanding (on spatial axis which moves on time axis) with c at t0. Both informatory circles starts separating upon the explosion of time bubbles due the velocity of CD.
4.   The center of the AB circle remains on time axis while the center of the CD moves towards right from origin on spatial axis in time “t”. Both circles are always seen on spatial axis which also moves in time “t” on time axis.
5.   The pulse of AB is moves with “c” and is on its circle till it is reflected back by the mirror B
6.   The pulse of CD also moves with “c” as soon as C depart from origin but within the radius of CD circle
7.   Relative to stationary clock : The distance of the pulse of CD from the origin on the spatial surface is always greater than the radius of AB circle on spatial axis because of the velocity of CD
8.   Thus according to first postulate: Stationary observer wouldn’t be able to see the pulse as it is outside the information circle of AB until it reflected back by mirror D in the region of AB circle.
9.   However according to second postulate: Stationary observer always sees pulse (may be just an image) of CD within the radius of its time bubble
10.   Possibility of two pulses: As per (9); stationary observer always sees a pulse while as per (8); since a pulse moves back and forth in between the mirrors therefore its appearance in the region of time bubble of AB is on and off. So there are chances of seeing two pulses within the moving clock.

I still can't follow what's being asked (the way it's written just makes my mind go blank), but I'll just comment on the alignment of the linear light clocks that are now being used - it sounds as if the moving one is aligned with the direction of travel, so it should be length-contracted to 60% of its normal length.

#### PmbPhy

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« Reply #3 on: 14/04/2015 16:24:19 »
Quote from: EEK
Imagine two circular light clocks LC and LC’ of radius of one light second one above each other such that their centres lie on the origin of time axis and spatial x-axis.
I don't understand this. What is a "circular clock"? A clock in relativity must be defined ideally to be localized to a point in space. It can have no spatial dimensions which means that it can't have a radius of 1 light second. It can't even have a radius of 1 mm either.

Quote from: EEK
Now how come a moving clock slow down when itself moves through the same time and space in which a stationary clock lies?
Because you used an poorly constructed clock.

Quote from: EEK
Can aforementioned clocks tick at different rate present in the same space and TIME?
No.

Quote from: EEK
If they both tick at same rate on the same world line in same space-time then there is something wrong with the postulates.
That is incorrect. The only thing wrong is your notion of a clock.

#### David Cooper

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« Reply #4 on: 14/04/2015 16:42:59 »
The idea of the circular light clock (which I had never heard of before either) has been taken from the page he linked to - it's a circular mirror with an emitter at the centre, so the light goes out in all directions, bounces off the mirror and returns back in to the centre where a "tick" is completed and the next pulse of light is sent out.

#### yor_on

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« Reply #5 on: 15/04/2015 20:55:10 »
Is it like a reflecting dyson sphere surrounding a light source (center)? And then a assumption of it all being one 'system' that then should have a 'defined (same)  time' for the whole contraption, to make sense? when it comes to a local clock and ruler one sometimes see a reference to ones wrist watch, as presenting you your 'proper time'. But it is a idealization, you just need to consider NIST and their experiments at centimeter on gravitational time dilations to see that.

I presume that the assumption is that we have some sort of observers, either relative the whole 'system'/contraption being 'outside it', or that the question is about observers resting inside, on the dyson sphere that reflects the light back to the source, measuring a clock at the 'center' relative their local clock and ruler? And it's about uniform motion, not acceleration? First of all, the 'system' as a whole is comoving, including observers, if so.
=

Or better expressed, all ingredients in this 'system' are 'at rest' with each other, equivalent to what we find here on earth. Also, a uniform motion can only be defined relative something else, and depending on what you pick you will get different answers. The equivalence to a uniform motion should be not moving at all, because that is the idealized definition from a 'black box' scenario. You inside it being unable to prove any motion.

Now, if what I assume to be the the idea is correct? We then can translate it to this black box, imagining it to have a light source 'floating' inside it, being situated in the middle of the box. If your assumption would be correct we now find that we can use that lightbulb to prove a 'gold standard' of motion, depending on from where you measure inside that box, relative your own 'clock and ruler'. Is that how you think?
« Last Edit: 15/04/2015 21:09:30 by yor_on »

#### yor_on

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« Reply #6 on: 15/04/2015 21:52:16 »
There's your experiment EEK :), and one you should be able to do on earth too. It would turn relativity on its head if that was correct. And light would not be a constant but would differ slightly depending on Earths 'real' motion. With a risk of sounding slightly inane I will propose that motion isn't what it seems to be. We have two (generally speaking) types, one that is called uniform motion, equivalent to being 'still', the other is accelerations. In a accelerating frame (rocket) you still won't be able to set a 'gold standard' of your speed, except relative something else, be it a suns light, the CBR, or Earth. But you will be able to use blue respective red shift to define a direction of 'motion'.
=

the reason I question 'motion' is that I keep to a local definition. Then, using that 'black box', only a acceleration will be provable, and when it comes to a constantly uniformly accelerating frame also becoming inseparable from a gravity.

Thinking some more about it. That's one of the really big obstacles I have with this idea of Higgs particles (field). It goes out from a bulk universe, doesn't it? What I call a 'container definition', in where we have a bulk called SpaceTime in where those particles then 'exist', able to prove inertia, and in its extension 'mass', all of it without considering it locally. Uniformly moving 'c' will be 'c', no matter how you define your speed relative something else, but this 'Higgs field' becomes a sort of 'gold standard', doesn't it? As well as it presumes a lot, defining a container without defining how it exist.
« Last Edit: 15/04/2015 22:25:20 by yor_on »