Why does Einstein say that a clock slows when it is moving?

[Al68]

A valid clock in SR runs at the same rate as a non-mechanical light clock it is at rest with.

Yes we all agree. In a frame clocks work as expected.

The confusion is between frames. The other guys clock always looks/appears/seems slow relative to the clock in my frame.

I was referring to two clocks at rest with each other, not at rest in my frame. Both are in motion relative to me.

So, I'll rephrase: If a clock, at the same velocity relative to me as a non-mechanical light clock, runs at a different rate than that light clock, relative to my rest frame, it's not a valid clock in SR.

 

[Grimble]

Hello again Matheinste

Time is not a law of physics.

We measure time with things we call clocks which are mechanisms or systems which have a cyclic nature and whose workings are governed by the laws of physics. At the end of every cycle the mechanism returns to exactly the same state it was in at the end of the previous cycle. As the mechanisms of these clocks, whatever they may be, are governed by the laws of physics and as the first postulate says that these laws are the same in all inertial systems, the behaviour of clocks must be the same in all inertial systems.

Yes, that is precisely how I understand it!

Therefore, if two identical clocks, moving inertially relative to each other, record different elapsed times

but do they? Surely, given what you have just said, their local (proper) times will be identical?

it is because the elapsed times ARE different,

but are they? is it not that it is the observed time that is different? If the clock is as you describe and it had a clock face, then the time that clock face displays must still be that it displays in proper time, it is the observer's clock that measures a different time, is it not?

whatever time thay are measuring, even if your reasoning or intuition says that these times should be the same. It is not because the clocks are behaving differently.

Think of a clock as some device that generatres ticks. The interval between these ticks is the unit of time. All identical clocks, by definition, whatever there inertial motion, generate the same unit interval between ticks. The observers role is to count these ticks, or by means of some sort of readout to read the number of ticks. The counted number of ticks is a measure of the time elapsed. It is a measure of the total number of EQUAL unit time intervals. If the count of ticks of the clocks is different it is because they have measured different numbers of equal unit time intervals.

So are you saying that the said clock is keeping, and displaying, two separate times, its proper local time and its coordinate time, the time measured by the remote observer?

That the conditions under which the observation is made causes the difference seems much more plausible to me.

Grimble

 

[Grimble]

I have been working on producing a diagram that pulls the multiplicity of elements constituting time dilation and length contraction together to see if I can find a visual representation that enables me to get a feel for just what is happening and this is what I have arrived at so far:

http://img41.imageshack.us/img41/287/specialrelativitydiagrar.jpg

A Special Relativity diagram to demonstrate the relationship between two Inertial Frames of Reference moving with a constant relative velocity.
A and B represent a single axis (time or length) of Minkowski spacetime for each of the two IFoRs. They are drawn against a common background representing Proper Units - see Note 1
An observer at rest within each IFoR will be experiencing proper units (length and time) within that system; as shewn by the horizontal lines, labelled A and B.
But from each IFoR, the other frame's axis -- rotated according to their relative velocity -- will be reckoned in co-ordinate units, as shewn by the perpendicular projections from the coloured diagonals onto the observer's own axis.
The diagram is drawn to scale to represent two IFoRs with a constant relative velocity = 0.6c, giving γ = 1.25 and 1/γ = 0.8

From this we can see exactly what Einstein was saying in http://www.bartleby.com/173/12.html" , when he writes:


For the metre rod moving with the velocity 0.6c relative to B would be represented in the diagram by the number 1 on the red diagonal and we can see the projection onto B's x-axis (as it would be in this scenario) where it would be the green 1 co-ordinate unit.
And this agrees with x' = x/γ
i.e. x' = 0.8x

Similarly, in the second part of that same chapter, Einstein writes:


And again we can see just how this works, for this time he is converting the time from the observer's frame, t (proper time units) into the observed time t' (co-ordinate time units) which would be to take the blue, 1 proper unit and project it upwards onto the red diagonal line or, indeed, one could read it off the green co-ordinate scale on B's axis.

Not surprisingly this agrees with Einstein's own equation:

or t = γt' = 1.25 co-ordinate units

I am fairly certain that this diagram meets all the conditions, references and relationships between the elements that compose SR as far as I have understood it.

For instance, the co-ordinate units are greater in number but reduced in size.

The principal problem that is brought to light here is that there are far more elements than at first appear.
Consider if you will:
1) We start with a solitary IFoR where the measurements are all, by definition, in proper units.
2) We add a 2nd IFoR moving at a constant velocity with respect to the first: both are measured in proper units and their times are identical and synchronous.
3) They then observe one another and upon doing so we find that the observed frames are rotated with respect to their observers, as shewn, but their units are still proper units.
4) When observing the rotated frames, their proper units are projected vertically onto the observer's frame of reference, being there-by transformed into co-ordinate units.
5) So we have the axis of each IFoR and its rotation, both measured in Proper units and its projection onto the other's axis measured in co-ordinate units.
6) And as all this is matched reciprocally by the other IFoR we have this duplicated giving 4 measures in proper units and two in co-ordinate units.

Is it any wonder that we become confused when trying to deal with this using only primed and unprimed symbols?
And this is with it all reduced to two dimensions...

This exercise has certainly helped me to see how it can all fit together.:)


Note 1 Proper time is that experienced within an Inertial Frame of Reference.
It has to be the same in any IFoR for the following reasons:
i.If two IFoRs are at rest with one another they are both effectively in the same IFoR and share the same proper time.
ii.If they are moving relative to one another, i.e. have a relative velocity, each can still be considered to be at rest and must, therefore, still measure the same proper time.
iii.Every IFoR obeys the same simple physical laws, therefore identical, synchronised, clocks situated in such frames must keep identical time.
iv.If the proper time in IFoRs COULD be anything other that identical, then the differences could negate the need for Special Relativity! As any conflicts between Einstein's first and second postulates would, possibly, be explained by the differences in the different measurements of time.
v.The proper times of two IFoRs can be calculated from a third IFoR by means of the Lorentz Transformation equations; and, if that third IFoR was permanently positioned at the midpoint between the two IFoRs in question, those calculated proper times would have to be identical. Otherwise we would be contravening the Special Principal of Relativity, Einstein's 1st Postulate, - The laws of physics are the same in all inertial frames of reference, in other words, there are no privileged inertial frames of reference.
vi.If two IFoRs are moving with a constant relative velocity with respect to one another, then the movement of one, being a combination of time and distance relative to the second, must be the reciprocal of the movement of that second one with respect to the first. Therefore they must be using the same proper units.

I don't know whether this will be considered to be ATM or not, but no doubt some will claim so, but to me it is drawing what Einstein described.

Grimble