Still confusion in relativity of simultaneity and time dilation .

[ash64449]

Still confusion in relativity of simultaneity and time dilation...

Hello friend,

Still Something in my mind is saying that Relativity of simultaneity is the reason for time dilation even though i had some corrections in my understanding by posting various threads. Well,let me use Einstein's book Theory of Relativity to explain what i mean. I will not use any extra words or extra understandings.. Just i will explain the point by highlighting some important sentences..

Begins with chapter 8: On the Idea Of time In physics

It is clear that this definition can be used to give an exact meaning not only to two events,
but to as many events as we care to choose, and independently of the positions of the scenes
of the events with respect to the body of reference 1) (here the railway embankment). We are
thus led also to a definition of " time " in physics. For this purpose we suppose that clocks
of identical construction are placed at the points A, B and C of the railway line (co-ordinate
system) and that they are set in such a manner that the positions of their pointers are
simultaneously (in the above sense) the same. Under these conditions we understand by the
" time " of an event the reading (position of the hands) of that one of these clocks which is
in the immediate vicinity (in space) of the event. In this manner a time-value is associated
with every event which is essentially capable of observation.

This stipulation contains a further physical hypothesis, the validity of which will hardly
be doubted without empirical evidence to the contrary. It has been assumed that all these
clocks go at the same rate if they are of identical construction. Stated more exactly: When
two clocks arranged at rest in different places of a reference-body are set in such a manner
that a particular position of the pointers of the one clock is simultaneous (in the above
sense) with the same position, of the pointers of the other clock, then identical " settings "
are always simultaneous (in the sense of the above definition).

In this paragraph that i quoted from the book,it gives the idea of time in physics.To explain this he said that clocks were kept at points A,B,C of the railway line and they are set in the manner that their pointers are simultaneously the same. From this condition,we were able to give 'time' of an event which is in immediate vicinity of event.As a result we will be able to record when every event happens. it is from this understandable that time is defined or measured with the help of events.

then by giving this idea he said that in position of their pointers are simultaneous,then these clocks are of identical construction.And again if they are of identical construction,then these clocks go at the same rate. And as the above quote used time as defined as events. so then whatever events that are simultaneous to a tick of a clock will be simultaneous to other clock,if clocks go at that same rate(from the above consideration)

This is an important line and i have got this as conclusion not from my own,i got it from the book.

Then let us go to the next chapter: The Relativity Of simultaneity

Up to now our considerations have been referred to a particular body of reference, which
we have styled a " railway embankment." We suppose a very long train traveling along the
rails with the constant velocity v and in the direction indicated in Fig 1. People traveling in
this train will with a vantage view the train as a rigid reference-body (co-ordinate system);
they regard all events inreference to the train. Then every event which takes place along the line also takes place at
a particular point of the train. Also the definition of simultaneity can be given relative to the
train in exactly the same way as with respect to the embankment. As a natural consequence,
however, the following question arises :
Are two events (e.g. the two strokes of lightning A and B)
which are simultaneous with reference to the railway embankment
also simultaneous relatively to the train? We shall show directly
that the answer must be in the negative.
When we say that the lightning strokes A and B are simultaneous with respect to be
embankment, we mean: the rays of light emitted at the places A and B, where the lightning
occurs, meet each other at the mid-point M of the length A to B of the embankment. But the events A and B also correspond to positions A and B on the train. Let M1
be the midpoint of the distance A to B on the traveling train. Just when the flashes (as judged
from the embankment) of lightning occur, this point M1
naturally coincides with the point
M but it moves towards the right in the diagram with the velocity v of the train. If an
observer sitting in the position M1
in the train did not possesses this velocity, then he would
remain permanently at M, and the light rays emitted by the flashes of lightning A and B
would reach him simultaneously, i.e. they would meet just where he is situated. Now in
reality (considered with reference to the railway embankment) he is hastening towards the
beam of light coming from B, whilst he is riding on ahead of the beam of light coming from
A. Hence the observer will see the beam of light emitted from B earlier than he will see that
emitted from A. Observers who take the railway train as their reference-body must therefore
come to the conclusion that the lightning flash B took place earlier than the lightning flash
A. We thus arrive at the important result:
Events which are simultaneous with reference to the
embankment are not simultaneous with respect to the train, and
vice versa (relativity of simultaneity). Every reference-body (coordinate system) has its own particular time ; unless we are told
the reference-body to which the statement of time refers, there is
no meaning in a statement of the time of an event

Now this paragraph says that clock go at different rates by used Relativity Of Simultaneity. In the example that is given by Einstein, Lightning was simultaneous with respect to embankment but not to train.Then Einstein immediately pointed out that Every Reference body has its own particular time and then said that there is no meaning of 'time' of event. Anyway we can understand that there is no meaning of 'time' of event from the above conclusion. But from the previous chapter we understood that time is defined by events. So the reference frames which sees events defined by same pointers of their clock go at the same rate. But in the case given in example, embankment reference frame needed only one tick of the clock to describe two events,while in train's reference frame needed two ticks of the clock to define those two events. So from the above consideration,These clocks should go at different rates!

But when i said this in other thread,posters said that this directly lead to Relativity Of Simultaneity. Yes,They are right. But it does lead to the clocks going at different rates too.. But i haven't said about the other chapter...

Now through Lorentz transformation,we can understand that Time goes in different rates and it shows something more. Time dilates. Well, i think we cannot get this conclusion from dealing with relativity of simultaneity itself because i don't know what would happen if time beat faster than usual when moves..

This is the reason why i said that Relativity of simultaneity is related to time dilation...
Or relativity Of simultaneity causes Time dilation. Now we know that Lorentz transformation was derived from two postulates. that predicted time dilation. Well, Relativity of simultaneity requires these two postulates.

We can understand this from the chapter on idea of time in physics, The quoted word was written in footnotes of this chapter:

We suppose further, that, when three events A, B and C occur in different places in such a
manner that A is simultaneous with B and B is simultaneous with C (simultaneous in the
sense of the above definition), then the criterion for the simultaneity of the pair of events A,
C is also satisfied. This assumption is a physical hypothesis about the the of propagation of
light: it must certainly be fulfilled if we are to maintain the law of the constancy of the
velocity of light in vacuo.

Well,these words conclusion is that These clocks should go at same rate.But we already described relationship between events and time. So since relativity of simultaneity is derived from these two postulates, time dilation too is and can be derived for these two postulates.

Some General Doubts from the book:

This diminished simplicity would be due to the fact that the carriage K would be in motion
(i.e."really")with respect to K0

In this quote why did he use the word "really"?

We should expect, for instance, that the note emitted by an organpipe placed with its axis parallel to the direction of travel would be different from that
emitted if the axis of the pipe were placed perpendicular to this direction."

What is the meaning of these lines?

Here is the pdf of the book that i used here: http://www.marxists.org/reference/archive/einstein/works/1910s/relative/relativity.pdf

 

[Dale]

can you edit your post using the QUOTE feature so that it is easier to see where Einstein's words end and yours begin?

Just some general advice. It is usually best to learn from more modern presentations rather than from the seminal works.

 

[ash64449]

can you edit your post using the QUOTE feature so that it is easier to see where Einstein's words end and yours begin?

Just some general advice. It is usually best to learn from more modern presentations rather than from the seminal works.

ok. You will have to wait sometime. Remember.i am not trying to invalidate einstein on any account. I just got conclusions like this and i want corrections in my conclusions. That is all

 

[Dale]

Your conclusions have already been corrected. I think that what you want is corrections in your reasoning. Unfortunately, from the above I cannot follow your reasoning. The QUOTE feature would be helpful as would making your point more concisely. If you can organize your thoughts better in the post then I could be more helpful.

 

[ash64449]

Your conclusions have already been corrected. I think that what you want is corrections in your reasoning. Unfortunately, from the above I cannot follow your reasoning. The QUOTE feature would be helpful as would making your point more concisely. If you can organize your thoughts better in the post then I could be more helpful.

ok. i have done the job.. Now Quotes please!

 

[Dale]

That helps, thanks!

 

[Dale]

And again if they are of identical construction,then these clocks go at the same rate.

OK, I looked through the Einstein quotes and found exactly one reference to the word "rate". Specifically:

It has been assumed that all these
clocks go at the same rate if they are of identical construction.

This quote is a reference to the first postulate. Clocks of identical construction at rest wrt each other will tick at the same rate. I think you understand that, so I think I am just confirming what you already know.

So since relativity of simultaneity is derived from these two postulates, time dilation too is and can be derived for these two postulates.

Yes, this is correct. RoS can be derived from the two postulates and TD can also be derived from the two postulates.

I am not sure what you still feel confused about in this regards. It seems that you understand correctly, but are still bothered by something.

 

[ash64449]

Specifically:This quote is a reference to the first postulate. Clocks of identical construction at rest wrt each other will tick at the same rate. I think you understand that, so I think I am just confirming what you already know.

Yes. I know this.. Reference frame which is moving will tick at slower rate.

I am not sure what you still feel confused about in this regards. It seems that you understand correctly, but are still bothered by something.

Why i am in confusion is because i from these conclusion get that Relativity Of simultaneity is the reason for Time Dilation. But if you ask me that isn't the two postulates the reason,i will agree with it too!

 

[ash64449]

OK, I looked through the Einstein quotes and found exactly one reference to the word "rate". Specifically:This quote is a reference to the first postulate. Clocks of identical construction at rest wrt each other will tick at the same rate. I think you understand that, so I think I am just confirming what you already know.

Yes, this is correct. RoS can be derived from the two postulates and TD can also be derived from the two postulates.

I am not sure what you still feel confused about in this regards. It seems that you understand correctly, but are still bothered by something.

I think simultaneous events can be simultaneous in IRF that is moving.. (not always)
ghwellsjr provided an excellent animations to show how MME is in relation with SR. But when i looked at this,i found that in this case,both the reference frame is simultaneous, but the detector of the one who is in IRF(moving) received light cone in slower rate. This is one example in which simultaneous events can be simultaneous in IRF which is moving..

Here is the link to that discussion:
https://www.physicsforums.com/showthread.php?t=626807

 

[ash64449]

DaleSpam,please look into the general doubts that i have asked..

 

[Dale]

Why i am in confusion is because i from these conclusion get that Relativity Of simultaneity is the reason for Time Dilation.

How do you get that? I see no chain of logic in what you presented that indicates this.

 

[Dale]

I think simultaneous events can be simultaneous in IRF that is moving.. (not always)

Indeed, they can. We already discussed the conditions under which they can be simultaneous. Specifically, for relative motion in the x direction, the events must be separated in the y or z directions. If we have two events then the differences between the two events (in units where c=1) are given by:
$$\begin{array}{l} \Delta t' = \gamma \, (\Delta t-\Delta x \, v) \\ \Delta x' = \gamma \, (\Delta x-\Delta t \, v) \\ \Delta y' = \Delta y \\ \Delta z' = \Delta z \\ \end{array}$$

For a pair of events to be simultaneous in both frames means that $\Delta t = \Delta t' = 0$. This can only be true if $\Delta x = 0$ which implies that $\Delta y \ne 0$ or $\Delta z \ne 0$.

 

[1977ub]

Yes. I know this.. Reference frame which is moving will tick at slower rate.

will be *measured* to be ticking slower by someone in a different frame.

Why i am in confusion is because i from these conclusion get that Relativity Of simultaneity is the reason for Time Dilation.

Mathematically the two principles are completely linked. If you initially observe either TD or RofS but not both, things will not add up, and you will soon realize the other is involved.

 

[arildno]

Yes. I know this.. Reference frame which is moving will tick at slower rate.

Do remember that BOTH reference frames will be moving, relative to the other frame.
Thus, from the point of frame A, it is the clocks in B that tick slower, while from the point of frame B, it is the clocks in A that tick slower.