Comparing Event Occurrence Across PORs

[GeorgeDishman]

Can anyone please read only the opening message of the thread: "synchronized clocks with respect to rest frame" and answer me this:

Answer #2 in that thread is correct but also note that #3 is an important qualifier.

When the train returns, we can see that somthing happened, e.g. we have time dilation on the clock, and we agree that at least part of that time dilation was produced by constant speed (CS). There is evidence of say "nature 1" that somthing happened there.

There is a cumulative time difference between the clocks that went on the journey and an identical clock that remained on the station. That is the essence of the Twins scenario.

Now regarding the clocks that are not synchronized, although they are both on the same train (but apart from each other):

While moving, they are not synchronised as determined by observer "O" but they are synchronised as determined by observer "R". It is important to specify the observer since simultaneity is frame-dependent.

is there an experiment that can be done, which will show us this difference of de-synchroniztion between them, after the clocks will return to the station (nature 1),

Off-hand, I'm not sure if there is one that addresses synchronisation specifically but the cumulative difference between the train clocks and the station clock was famously tested by Hafele and Keating, while the effect on moving "clocks" was first tested by Ives and Stilwell.

http://en.wikipedia.org/wiki/Hafele–Keating_experiment

http://en.wikipedia.org/wiki/Ives–Stilwell_experiment

It is important if you want to understand this stuff to note that this is not indicative of flaws in the clocks, in the thought experiments they are assumed to be working perfectly at all times and in real experiments, the accuracy of the instruments is adequate to demonstrate the results. What you are supposed to understand from them is that the measurement we call "time" is path-dependent, like the mileage reading from odometers in cars taking different paths between two locations.

 

[whosapopstar?]

Please see attached diagram:
Here is an apparatus aboard a train. It is activated once when the train is at bay and once when it is moving at constant speed. Results are the same at both cases.

What would be the reason that while time dilation is influencing clock C, still when the train is on the move, clock A shows X+C (clock C increment) and not X+D (a different clock C increment).

i cannot find the reason to be anyone of the following:
1. Light speed - can't be, always stays the same, either if the apparatus is at station or moving.
2. Clock A and B de-synchronization - can't be, they are aligned at the same vertical line.
3. Length contraction - can't be, the apparatus is symmetric.

 

[ghwellsjr]

If you are saying that clock C introduces a delay of C, then why should moving at any speed have any effect on the result? Remember, time dilation is what another observer moving with respect to the train would see happening to the clocks on board the train.

 

[GeorgeDishman]

What would be the reason that while time dilation is influencing clock C, still when the train is on the move, clock A shows X+C (clock C increment) and not X+D (a different clock C increment).

It doesn't matter where on the train you put the delay so put it at the end, the light pulses then arrive simultaneously and then the delay runs.

The delay will have duration C as measured by some on the train next to it but a longer time as measured by someone on the platform (the clock seems to run too slowly).

 

[whosapopstar?]

If we still don't have the technology to build a Planck clock (a clock which fundamental unit is 1 Planck unit), how can we ever validate the existence of time dilation?

 

[GeorgeDishman]

If we still don't have the technology to build a Planck clock (a clock which fundamental unit is 1 Planck unit), ..

Just multiply the scale of any good clock by the number of Planck units in a second.

how can we ever validate the existence of time dilation?

First done in 1938:

http://en.wikipedia.org/wiki/Ives–Stilwell_experiment

 

[whosapopstar?]

Yes but how can we know that this clock that you take its results and divide them by the Planck unit, gives you always, say, 1 NPU (Not Planck Unit) per 10 Planck units and not, say, once, 1 NPU per 10 Planck units and again, when measuring against a Planck clock, but at different constant velocity conditions, say 1.8 NPU units per 10 Planck units?

 

[GeorgeDishman]

Yes but how can we know that this clock that you take its results and divide them by the Planck unit, gives you always, say, 1 NPU (Not Planck Unit) per 10 Planck units and not, say, once, 1 NPU per 10 Planck units and again, when measuring against a Planck clock, but at different constant velocity conditions, say 1.8 NPU units per 10 Planck units?

Velocity relative to what?

 

[whosapopstar?]

Velocity relative to the station. One pair of NPU clock + Planck clock on the station and another pair of that sort, on the train, moving at constant speed. Should the Planck clock on the train be able to discover that the NPU clock is experiencing time dilation? or only when they retun to station? how come? there is no length contration at a Planck scale. On the other hand, relativity principle has to preserve itself...

 

[GeorgeDishman]

Velocity relative to the station. One pair of NPU clock + Planck clock on the station and another pair of that sort, on the train, moving at constant speed. Should the Planck clock on the train be able to discover that the NPU clock is experiencing time dilation? or only when they retun to station?

Yes, they will behave exactly the same as modern atomic clocks.

how come?

Because the effects of relativity are caused by geometry.

Draw a vertical line on a sheet of paper. Draw another line nearly vertical but crosssing the first near the bottom. Put marks every 1cm starting at the crossing point along each line. Now draw horizontal lines from the marks on the sloping line to the vertical. Those projections will not cross on the 1cm marks on the vertical line.

It doesn't matter whether the scale is 1cm=1 Planck time or 1cm = 1 second, the geometry always produces the same effect. The same is true for distances in space whether the ticks are 1 Planck length or 1 light second of distance.

there is no length contration at a Planck scale.

Geometry applies at all scales.

Perhaps you should learn how SR works before trying to find faults in it, you'll save yourself a lot of wasted time.

 

[whosapopstar?]

Nope. this does not answer my question. If i want to draw on that paper marks, at closer and closer distance, then i need a thinner and thinner pencil, right? Doesn't the Planck scale say that at certain point i will not be able anymore to draw the marks closer, no matter what kind of pencil i use?

 

[GeorgeDishman]

Nope. this does not answer my question.

Maybe you need to give it more thought, it's not difficult. The analogy isn't perfect but if you spot the flaw, I'll explain how to fix it, it doesn't alter the basic understanding.

If i want to draw on that paper marks, at closer and closer distance, then i need a thinner and thinner pencil, right?

No, the ticks represent instants of time so have no width. You also need to remember that GR is a classical theory, not quantum. It is the difference between the spacing of ticks drawn along one line to the projection of those on the other which is called "time dilation".

Doesn't the Planck scale say that at certain point i will not be able anymore to draw the marks closer, no matter what kind of pencil i use?

IMHO it says that at some small distance, the uncertainty principle means nothing can be located well enough to distinguish between being in the same place and being separated but regardless of its interpretation, since there is no preferred frame, the scale must be the same for the clock on the train and that on the station. The operation would be identical to that of standard atomic clocks.

 

[whosapopstar?]

Is there any free and simple geometry animation software where i can build all kinds of scenarios with light beams and moving spaceships and trains and clocks etc...and see with my own eyes that things work in a certain way and not another?

 

[GeorgeDishman]

Is there any free and simple geometry animation software where i can build all kinds of scenarios with light beams and moving spaceships and trains and clocks etc...and see with my own eyes that things work in a certain way and not another?

This page has an applet at the top that implements the Lorentz Transforms and is very simple to use though you have to be a little careful as the cursor doesn't snap to the grid. There are other geometries farther down the page for comparison:

http://www.reagenix.com/personal/sci/space_time/test.html

It shows a standard spacetime diagram so an item at rest is a vertical line. A surface joining simultaneous events is a horizontal line. The speed of light is 45 degrees.

The slider at the top allows you to view the whole thing from the point of view of different observers.

To investigate the train and station, draw two vertical lines representing the ends of the platform. Then move the slider a little (so that you view the platform from the point of view of someone on the train) and draw two more vertical lines representing the ends of the train. Now you can add lines at 45 degrees representing the light signals and see how everything transforms.

You can add small dots on any line to represent the ticks of a clock, for example put them on the horizontal gridlines but make sure each line is vertical when adding them to get the same tick frequency for all clocks.

 

[whosapopstar?]

This is not what i meant. i need an animation software where i can draw objects and let them move between two or more points that i draw, and then put clocks and light sources inside and outside these objects, and while the objects are moving, send light beams from within these objects and outside of them to points i draw outside and inside the objects, and then let the whole thing run as animation by itself, while the constancy of speed of light and time dilation and length contraction are kept as rules in that animation, relating to a FoR of one of these objects that i mark in advance. What I need is that sort of educational and flexible tool.

 

[GeorgeDishman]

What I need is that sort of educational and flexible tool.

The applet is precisely what you need. What you asked for would not explain how SR works, it would be nothing more than a toy for making pretty pictures. If you only use a tool that incorporates what you already know, you won't learn anything new.

Try drawing out the train and station, or the twins paradox and see how it works.

 

[whosapopstar?]

No it would not be just a toy. And because such a thing does not exist, now i have to look for some kind of flash animation or graphic expert, only in order to be able to bring to life, some really not too complicated scenarios i have in question.

 

[GeorgeDishman]

No it would not be just a toy. And because such a thing does not exist, now i have to look for some kind of flash animation or graphic expert, only in order to be able to bring to life, some really not too complicated scenarios i have in question.

Here's a suggestion then. Draw your scenario in the applet as I suggest. Then move the slider to select a particular observer frame. The horizontal lines represent observer times so for each horizontal line, note the location of each body and then draw a picture representing that. Now make a movie from the sequence of pictures (there are free applications to create animated gifs). That gives you one observer's view.

Move the slider to a different position and repeat the process for any other observers you want.

If you intend to get someone to do the graphics for you, that is what they would need to do as well.

However, what I expect will happen is that once you draw your scenario in the applet and move the slider, you will immediately see not only what happens but why the various effects occur. That explanation will not be visible in your flash version.

It's your choice of course, but if you want to learn SR, the applet will be of more more use.

 

[whosapopstar?]

If existing educational tools for SR teaching where more flexible, i would draw three points that represent the clocks in the diagram, presented here before, and attach visible time counters to each of them. Then i would change the rate of the common time rate of the clocks, while keeping the two animated advancing lines that represent the light beams, at their former speeds. Then i would play with the common constant speeds of light beams and common rates of clocks (each time changing twice the clocks per one change of light speed), to see that no matter what changes i make with these parameters, both light beams would arrive together at the two clocks, although there is an apparent non-symmetry, in the form of one light beam going through the third clock 'barrier', while the other light beam has no barriers on the way. i would also attach flickering effect of dots to the clocks, so maybe when changing the parameters to extreme values, i would be able to feel the scenario better, only by looking at the flickering rate of dots and light beams 'sprint' to the finish line (extreme enough to make the difference of positions on the screen itself negligible - i hope no one is going to claim a problem of this sort!). Then maybe i would be able at last after many years, to overcome the notorious, counter-intuitive and even frustrating on purpose, in some people hands, thing with SR. The sliders applet would never do the job, since they will not let me the feeling that i built the scenario, according the way my imagination works (of course, as long as physical rules are kept in form, in such a hypothetical 'SR flash animation' tool).

 

[yuiop]

Is there any free and simple geometry animation software where i can build all kinds of scenarios with light beams and moving spaceships and trains and clocks etc...and see with my own eyes that things work in a certain way and not another?

Is this more like the sort of thing you are looking for? http://www.its.caltech.edu/~phys1/java/phys1/Einstein/Einstein.html

You usually have to enter the relative velocity of the other frame before pressing start and then use the switch frames button. It shows motion in space as an animation along with the same motion depicted on a spacetime diagram alongside. It creates animations but I think there only preset scenarios.

 

[whosapopstar?]

Ok, let's go back to static images!
Attached is this diagram, please observe details.

d is a very small distance, especially when comparing with the path that ligth beams take between clocks, even very small comparing to the horizontal difference of position between clock A and clock B.

Clock A will indicate which light beam came first: the one from clock C or the one from clock B.

We know that time dilation exists at constant speed and that when we calibrated the apparatus at a slower constant speed, the C clock hindrance of the light beam was exactly in the order to compensate the horizontal difference between clocks A and B and thus, we had the exact same time indications on these clocks (A and B), and hence, clock B indicated that the light beam from clock C arrived first. As well, the mirror reflection time is very small, comparing to anything else described here.

Now we are at a different and faster constant speed, we do not change the apparatus calibration, but still- we know that according to the principle of relativity, time indication of both beams arriving at the clocks, clock A and B, will be an equal time and also as before, clock A will indicate that light arrived first from clock C and not from clock B.

How come? What is the reason? What effect counteracts time dilation, that we know that takes place at a higher constant speed?

 

[GeorgeDishman]

Your description lacks some details but if I understand you correctly, the first of the attached files shows how you would draw it in the applet. The light is emitted at F, triggers clock C as it passes then reflects from the mirror at B before stopping the clock at A. Clock C sends the delayed pulse at D and if I follow your description, the delay is such that the light arrives at A to start the clock (which I show as event E).

The second file shows what the events look like from another frame, i.e. an observer moving right to left hence the clocks are moving left to right. All I did for that was to move the slider. You should be able to see that the diagram shows length contraction, time dilation and the relativity of simultaneity as you move the slider.

p.s. The short horizontal lines on C-D and E-A are the ticks of the clocks.