Looking to understand time dilation

[Dale]

And that time shown by that clock will be proper time?

Yes. All ideal clocks measure proper time along their worldline.

Which leads me to the conclusion that Proper time and Proper lengths are the units of an inertial FoR's coordinates? Of any inertial FoR?

I don't know what you mean by "units of an inertial FoR's coordinates". You could certainly use a clock that gives units of seconds in a FoR using years, as long as you convert properly. Do you somehow think that proper time and coordinate time are measured in different units?

 

[Dale]

Then if two events have the same time coordinate, in one FoR, they must be simultaneous? For that is what having the same time coordinate means? Surely.

They must be simultaneous in that FoR. They will not be simultaneous in most other FoR's.

Coordinate time depends on the observer's perspective, but what of proper-time, i.e. the time of space-time itself? Every observer can translate their coordinate time into proper time but is that into a common 'proper-time' that all agree upon or does it still vary according to the observer's perspective?

There is not a common proper time, per se. Proper time is defined along a particular path in spacetime (i.e. along a worldline). It is geometrically equivalent to the arc length along that path, and just like arc length is invariant under rotations, so also the proper time is invariant under Lorentz transforms.

Consider two hikers that are looking at a map and determining how far they have to hike to reach their campsite. One hiker uses a GPS system so he uses celestial north and determines that he needs to hike 4 miles north and 3 miles east. The other hiker uses a compass so he uses magnetic north and determines that he needs to hike 3 miles north and 4 miles east. But both hikers agree that the distance they will hike is 5 miles. The GPS hiker will determine that the compass hiker's "north-meter" is "going slow", but that doesn't mean that they are using different units, just that they are talking about different directions when they each say "north".

 

[Grimble]

Most of the statements you made are pretty much as you have said, but I will elaborate on these.

Just to be clear, if two events occur simultaneously according to a frame, then they happen at the same time according to that frame's coordinate system, yes, but simultaneity issues in general actually refer to differences in simultaneity, where events that occur simultaneously according to the coordinate system of one frame do not necessarily occur simultaneously according to the coordinate system of another frame, depending upon the simultaneity convention that is set for each frame.

I must admit to being a little puzzled, perhaps just by the way you have expressed this but what do you mean by a 'simultaneity convention'?
To me, a set of coordinates are a means of relating points to different axes.
If we have a time axis then simultaneity relates to points having the same time coordinate.
It depends on where they are not how they are labelled.

For instance, if we have two observers in a frame that are separated by some distance, and they both then instantly and simultaneously accelerate to the same speed in the same direction and they leave their clocks alone, then if the original frame measures events simultaneously, the two observers in their new frame will still measure them as simultaneous also, but the two observers will also measure the speed of light anisotropically. But if the two observers re-synchronize their clocks to measure the same speed of light in every direction in accordance with the Einstein simultaneity convention, then they will no longer measure the events as simultaneous as the original frame does, because in order to synchronize in this way to measure an isotropic speed of light, the front observer's clock must be set back somewhat or the rear observer's clock set forward..

I'm sorry but can you expand upon this?
.

Yes. We start by placing clocks at all points within a frame, all stationary to each other within the frame. Now let's say we want to re-synchronize the clocks along the x axis.

Why? what can that achieve?
Synchronising one's clocks, as per Einstein to a common time, is a requirement for reading the coordinates of different points.
Synchronising to any scheme is only going to confuse things.

We can begin at the origin and add, say, one second on the clocks per meter along the positive x direction, so add one second at one meter, two seconds at two meters, and so on, and subtract one second per meter in the negative x direction. Observers within the frame will consider the clocks to be synchronized regardless of how they are set since the readings upon clocks for events can only be measured directly by clocks that coincide in the same place, just as long as the synchronization method is linear along any direction so that objects that travel inertially will still be measured as such.

You have lost me here as to what you are trying to elucidate.

Only one observer in a particular frame can measure the proper time between two events, since that observer's clock must coincide with both events to measure the time of the events directly. In other words, the proper time can only be measured directly by a single clock. However, since all of the observer's clocks in the same frame as that observer, no matter how they have actually been synchronized, are considered by observers within that frame to be in perfect synch with each other, then all observers within the frame with the observer that measures the proper time of the two events will agree upon the time of both events also, each occurring in the same place as that particular observer, so with zero spatial difference as measured by that frame. All other frames, however, moving at some relative speed to the frame in which the proper time is measured, will measure some distance between the events due to the relative speed. They will also measure a different difference in time between the events, depending upon how their clocks are synchronized. If both frame's clocks have been synchronized according to the Einstein simultaneity convention, then the difference in times and distances measured by each frame will be related by the Minkowski metric.

It seems to me after further thought that time must be isotropic and homogeneous.
I can imagine this like seeing the images from a CTI scan but being able to see them not as images of a single time but as moving images where one could scan backwards and forwards in time.

 

[grav-universe]

I must admit to being a little puzzled, perhaps just by the way you have expressed this but what do you mean by a 'simultaneity convention'?
To me, a set of coordinates are a means of relating points to different axes.
If we have a time axis then simultaneity relates to points having the same time coordinate.
It depends on where they are not how they are labelled.

I'm sorry but can you expand upon this?
.
Why? what can that achieve?

It doesn't achieve anything one way or the way, only depending upon what we decide is the best way to synchronize clocks. That is all a simultaneity convention is after all, a method by which to synchronize clocks, or a way to determine what a frame's clock settings will be in relation to each other.

Synchronising one's clocks, as per Einstein to a common time, is a requirement for reading the coordinates of different points.
Synchronising to any scheme is only going to confuse things.

You have lost me here as to what you are trying to elucidate.


It seems to me after further thought that time must be isotropic and homogeneous.
I can imagine this like seeing the images from a CTI scan but being able to see them not as images of a single time but as moving images where one could scan backwards and forwards in time.

There is no absolute way that clocks must be synchronized, that is the point. For instance, repeating the earlier scenario in a slightly different way, let's say that clocks in frame A are synchronized according to the Einstein simultaneity convention, so that observers in that frame measure light to travel at c in all directions. Now let's say that two observers with some distance between them simultaneously accelerate to a speed v relative to frame A. If the two observers leave their clocks alone, they will no longer measure the speed of light to be the same in each direction between themselves, but since they have both accelerated simultaneously in the same way to the same speed v, their clocks will read the same according to observers in frame A, and any events that frame A says occur simultaneously, the two observers in their new frame will say the events occur simultaneously as well.

But now let's re-synchronize the clocks of the two observers in their new frame by applying the Einstein simultaneity convention, meaning they will synchronize their clocks so that light will now be measured at the same speed between themselves. In order to do that, the front observer must set her clock back by d v / c^2 or the back observer must set his clock forward by d v / c^2. Now the two observers will measure the same speed of light in either direction, but since one of the observers has changed the setting on their clock, frame A says that the back observer's clock is now set ahead of the front observer's clock by d v / c^2, so events that occur simultaneously according to frame A cannot occur simultaneously to the two observers anymore since their clocks read differently.

 

[Grimble]

Yes. All ideal clocks measure proper time along their worldline.

I don't know what you mean by "units of an inertial FoR's coordinates". You could certainly use a clock that gives units of seconds in a FoR using years, as long as you convert properly. Do you somehow think that proper time and coordinate time are measured in different units?

Well they are, aren't they?

In post #346 you explained (with my highlighting):

In the formula
ds² = -c²dt² + dx² + dy² + dz²

the dt, dx, dy, and dz are all coordinate times and distances in some inertial frame while the ds is the frame-invariant spacetime interval. If ds² > 0 then the interval is called "spacelike" and ds is the proper distance. If ds² < 0 then the interval is called "timelike" and dτ = sqrt(-ds²/c²) is the proper time. If ds² = 0 then the interval is called "lightlike" or "null" and represents the path of a pulse of light.

The value of this formula is that all reference frames can use their own coordinate values and come up with the same value for ds². This formula also let's you easily see where the formula you posted comes from:

dτ² = -ds²/c² = dt² - dx²/c² - dy²/c² - dz²/c²
dτ²/dt² = 1 - (dx²/dt² - dy²/dt² - dz²/dt²)/c²
dτ²/dt² = 1 - v²/c²
dτ/dt = 1/γ

Where dτ/dt = (by your definitions above) proper time/coordinate time = 1/γ
i.e. dτ = dt/γ which is surely a conversion between different unit sizes? As in feet = yards/3?

They must be simultaneous in that FoR. They will not be simultaneous in most other FoR's.

I agree

There is not a common proper time, per se. Proper time is defined along a particular path in spacetime (i.e. along a worldline). It is geometrically equivalent to the arc length along that path, and just like arc length is invariant under rotations, so also the proper time is invariant under Lorentz transforms.

Yet if we examine ANY inertial FoR , we agreed that the ideal clock, at rest at the origin of that FoR has a worldline that defines the time axis of that FoR's coordinate system viz:

Now it seems to me that within our 4 dimensional coordinate system any inertial frame of reference may be considered to have a clocks at rest with respect to it. Those clocks will have straight worldlines that are parallel one to the other. The world line of the one at the origin of that frame of reference will describe the time coordinate of our 4D set of coordinates.

Yes, exactly. That clock defines the time axis of the coordinate system, (ct,0,0,0).

Therefore I conclude that ANY inertial FoR has a time axis that is defined by an ideal clock's worldline and that the time shown by that clock, the time of the time axis, is proper time; and according to Einstein's first postulate viz:

“The Principle of Relativity – The laws by which the states of physical systems undergo change are not affected, whether these changes of state be referred to the one or the other of two systems in uniform translatory motion relative to each other.”

that proper-time will be the same for ANY IFoR.

Consider two hikers that are looking at a map and determining how far they have to hike to reach their campsite. One hiker uses a GPS system so he uses celestial north and determines that he needs to hike 4 miles north and 3 miles east. The other hiker uses a compass so he uses magnetic north and determines that he needs to hike 3 miles north and 4 miles east. But both hikers agree that the distance they will hike is 5 miles. The GPS hiker will determine that the compass hiker's "north-meter" is "going slow", but that doesn't mean that they are using different units, just that they are talking about different directions when they each say "north".

But is that not the equivalent of having two IFoR's at rest with one another but with their space coordinates just having a different alignment? Each will measure the same unit size, it is only when the observer is moving with respect to the observed that measurements are transformed according to the LT equations. transformed between different unit sizes.

 

[Dale]

Where dτ/dt = (by your definitions above) proper time/coordinate time = 1/γ
i.e. dτ = dt/γ which is surely a conversion between different unit sizes? As in feet = yards/3?

In the trigonometric expression r = x/cos(θ) would you say that it is a conversion between different unit sizes? The expressions are of the same form. What about the diameter and the circumference of a circle, or the length and width of a rectangle, are those conversions between different unit sizes? They also have the same form.

If you would agree with me that they are not conversions between different unit sizes, then can you identify what is the distinction between this class of expressions and unit conversions? After all, as you pointed out, they do have the same mathematical form, so what distinguishes them?

But is that not the equivalent of having two IFoR's at rest with one another but with their space coordinates just having a different alignment?

Yes, exactly, it is just the time axes having a different alignment instead of the space axes. A boost is geometrically equivalent to a rotation, rotations preserve the Euclidean distance and boosts preserve the Minkowski interval.

 

[Grimble]

In the trigonometric expression r = x/cos(θ) would you say that it is a conversion between different unit sizes? The expressions are of the same form. What about the diameter and the circumference of a circle, or the length and width of a rectangle, are those conversions between different unit sizes? They also have the same form.

If you would agree with me that they are not conversions between different unit sizes, then can you identify what is the distinction between this class of expressions and unit conversions? After all, as you pointed out, they do have the same mathematical form, so what distinguishes them?

The fact that they refer to quantities of the same kind: lengths, times etc.

The fact that they may be written as ratios e.g. τ : t

indeed I understand it may be described as *a dimensionless*quotient*of the two terms.

Yes, exactly, it is just the time axes having a different alignment instead of the space axes. A boost is geometrically equivalent to a rotation, rotations preserve the Euclidean distance and boosts preserve the Minkowski interval.

But how can the time axes have alignment?

As I said in post #353 viz:

“It seems to me after further thought that time must be isotropic and homogeneous.”

And if it is then how can it have any alignment? Does it not just exist at every point in space?

 

[Dale]

The fact that they refer to quantities of the same kind: lengths, times etc.

The fact that they may be written as ratios e.g. τ : t

indeed I understand it may be described as *a dimensionless*quotient*of the two terms.

That is not what distinguishes the above examples from a unit conversion. In both cases you can write it as a dimensionless quotient:
yard/foot = 3
circumference/diameter = 3.1416...
adjacent/hypotenuse = cos

All of the above are dimensionless quotients of the two terms. The difference is that in the case of the unit conversion you are measuring the same thing using two different units (yard or foot), but in the geometric ratios you are measuring different things (circumference or diameter) using the same unit.

When you are talking about time dilation you need to realize that clocks measure proper time, and proper time is the length of the worldline of the clock. So, if the clocks are not traveling along the same worldline then they are measuring different things. Thus the time dilation factor is a geometric factor (like cos), rather than a unit conversion factor.

But how can the time axes have alignment?

Draw a spacetime diagram showing two sets of coordinates. The answer should be clear.

 

[Grimble]

That is not what distinguishes the above examples from a unit conversion. In both cases you can write it as a dimensionless quotient:
yard/foot = 3
circumference/diameter = 3.1416...
adjacent/hypotenuse = cos

All of the above are dimensionless quotients of the two terms. The difference is that in the case of the unit conversion you are measuring the same thing using two different units (yard or foot), but in the geometric ratios you are measuring different things (circumference or diameter) using the same unit.

But those are not quantities of the same kind as I specified.

if you had said circumference/circumference or hypotenuse/hypotenuse you would be comparing like with like!

When you are talking about time dilation you need to realize that clocks measure proper time, and proper time is the length of the worldline of the clock. So, if the clocks are not traveling along the same worldline then they are measuring different things. Thus the time dilation factor is a geometric factor (like cos), rather than a unit conversion factor.

Draw a spacetime diagram showing two sets of coordinates. The answer should be clear.

I'm sorry I can't comment on that unless you specify which clocks you are referring to.

Proper time is the scale of time that is measured by an observer adjacent to an ideal clock.
Coordinate time is the scale of time measured by an observer remote from the same clock.
The remote observer uses the time measured by the adjacent observer (proper time) and, using the LT equations, transforms that proper time into coordinate time. (transforming between two different scales of measurement)

The only other way of taking the measurement remotely would be for the observer to use her rulers and clocks to measure a moving object - which would be very difficult.

 

[Dale]

if you had said circumference/circumference or hypotenuse/hypotenuse you would be comparing like with like!

Yes, exactly. And since you are measuring the same thing the ratio will be 1 (dimensionless). Similarly, if two clocks measure the same worldline the ratio will be 1.

I'm sorry I can't comment on that unless you specify which clocks you are referring to.

You have had plenty of time to do the spacetime diagram I suggested earlier. How is that coming. Have you finished it yet?

 

[Grimble]

Yes, exactly. And since you are measuring the same thing the ratio will be 1 (dimensionless). Similarly, if two clocks measure the same worldline the ratio will be 1.

No, of course I don't mean the SAME circumference, I mean if one were to compare two different circumferences, then one has a ratio; but to compare an entity like a circumference to a diameter, a different entity, then one has the relationship between the two entities, which is not a ratio.

You have had plenty of time to do the spacetime diagram I suggested earlier. How is that coming. Have you finished it yet?

We have one clock that is measuring proper-time along its world-line but how do you define your second clock? Is it the one held by the remote observer? If it is how does it measure the time of a moving body? Or is it just the Lorentz Transformation of the 1st clock's times?

As for the clocks measuring different things; that is the whole point, they are not, they are measuring the same thing (a duration) but in different ways, from different perspectives, which is what relativity is all about! And the ratio between those two measurements is the key to relativity for that is surely how the apparent incompatibility of Einstein's two postulates is resolved. (viz: http://www.bartleby.com/173/7.html" )

 

[Grimble]

It doesn't achieve anything one way or the way, only depending upon what we decide is the best way to synchronize clocks. That is all a simultaneity convention is after all, a method by which to synchronize clocks, or a way to determine what a frame's clock settings will be in relation to each other.

I'm afraid I still don't see why anyone would want to synchronise clocks to other than the same time? That is what synchronising clocks means, isn't it, to set them to the same time?

There is no absolute way that clocks must be synchronized, that is the point. For instance, repeating the earlier scenario in a slightly different way, let's say that clocks in frame A are synchronized according to the Einstein simultaneity convention, so that observers in that frame measure light to travel at c in all directions. Now let's say that two observers with some distance between them simultaneously accelerate to a speed v relative to frame A. If the two observers leave their clocks alone, they will no longer measure the speed of light to be the same in each direction between themselves,

?So we have the two observers now in a new FoR, traveling at the same speed with synchronised clocks (showing the same time) at some distance apart, how does this alter their calculation of the speed of light?

but since they have both accelerated simultaneously in the same way to the same speed v, their clocks will read the same according to observers in frame A, and any events that frame A says occur simultaneously, the two observers in their new frame will say the events occur simultaneously as well.

But now let's re-synchronize the clocks of the two observers in their new frame by applying the Einstein simultaneity convention,

But why? They are already sychronised to read the same time and the result of using the Einstein simultaneity convention will be to synchronise them to the same time, how can synchronising them set them to different times?

 

[Dale]

No, of course I don't mean the SAME circumference, I mean if one were to compare two different circumferences, then one has a ratio; but to compare an entity like a circumference to a diameter, a different entity, then one has the relationship between the two entities, which is not a ratio.

Sure it is a ratio. For rectangles it is even called a ratio: the aspect ratio. For circles the ratio is fixed and it is one of the most famous ratios: pi. For right triangles the various ratios are a function of the angle and the ratios are the subject of the trigonometric functions: sin, cos, etc.

Just like all of the above examples, the ratio of two different circumferences is also a dimensionless number. It represents a geometric difference between the two different things being measured, not a conversion between units. Similarly with clocks, they are dilated because geometrically they are measuring the proper time along different world lines.

We have one clock that is measuring proper-time along its world-line but how do you define your second clock? Is it the one held by the remote observer? If it is how does it measure the time of a moving body? Or is it just the Lorentz Transformation of the 1st clock's times?

Don't worry about putting specific clocks on your spacetime diagram. Just draw the coordinate lines t'=0,1,2 and x'=0,1,2 on top of the unprimed frame's coordinate lines t=0,1,2 and x=0,1,2. Use v=0.6c for simplicity

 

[Grimble]

Sure it is a ratio. For rectangles it is even called a ratio: the aspect ratio. For circles the ratio is fixed and it is one of the most famous ratios: pi. For right triangles the various ratios are a function of the angle and the ratios are the subject of the trigonometric functions: sin, cos, etc.

If I were to say that an elephant has four legs, that is not the same as saying that everything with four legs is an elephant, is it?
What we are discussing is two measurements of the same distance or the same time.
Those two measurements are different; i.e. contracted or dilated depending upon the perspective of the observers who are performing the measuring.
If two measurements of the same quantity give different values due to the different perspectives of the observers, or due to different ways of measuring then, are they not measuring on different scales?

Anyway we are not here to discuss semantics. We are concerned with relativity, Special Relativity
Now in respect of the apparent incompatability ofthis two postulates, Einstein said http://www.bartleby.com/173/7.html"

At this juncture the theory of relativity entered the arena. As a result of an analysis of the physical conceptions of time and space, it became evident that*in reality there is not the least incompatibility between the principle of relativity and the law of propagation of light,*and that by systematically holding fast to both these laws a logically rigid theory could be arrived at.*

So can you explain HOW he does that, using the moving light clock thought experiment?
For it seems to me that only changing the scale of a measurement achieves this. Maybe that is where I am becoming confused.

 

[JesseM]

I'm afraid I still don't see why anyone would want to synchronise clocks to other than the same time? That is what synchronising clocks means, isn't it, to set them to the same time?

How are you going to define "same time"? Each observer synchronizes their own clocks using the assumption that light signals travel at the same speed in all directions relative to themselves, and the result is that according to each observer's definition of simultaneity, the clocks of the other observer are out-of-sync. If I think my clocks are synchronized and I use my clocks to determine that your clocks are out-of-sync, but you think your clocks are synchronized and you use your clocks to determine that my clocks are out-of-sync, how do you propose to settle the matter? Remember that if we construct our own coordinate systems using clocks synchronized this way, the laws of physics will obey exactly the same equations in both coordinate systems, which means any experiment I do with an apparatus at rest in my frame will give the same result if you do the same experiment with the same apparatus at rest in your frame.

Relativity doesn't rule out the notion that there is some metaphysical truth about simultaneity, so that only one observer's clocks are "really" synchronized. But only God could no that truth--according to relativity, there is no experimental way to show that the laws of physics "prefer" one frame, they are all exactly equivalent as far as empirical experiments go so there can be no experimental basis for judging one frame's definition of simultaneity to be "correct" and another's to be "incorrect".

 

[Dale]

What we are discussing is two measurements of the same distance or the same time.

No, we are not. I have explained this several times already. Please finish the spacetime diagram I suggested. Then you can see geometrically what I am saying.

For it seems to me that only changing the scale of a measurement achieves this. Maybe that is where I am becoming confused.

I think that the problem is more that you have not made any substantial effort to understand the many good explanations you have been given already. Your confusion is therefore likely to remain.

 

[Grimble]

How are you going to define "same time"? Each observer synchronizes their own clocks using the assumption that light signals travel at the same speed in all directions relative to themselves, and the result is that according to each observer's definition of simultaneity, the clocks of the other observer are out-of-sync. If I think my clocks are synchronized and I use my clocks to determine that your clocks are out-of-sync, but you think your clocks are synchronized and you use your clocks to determine that my clocks are out-of-sync, how do you propose to settle the matter? Remember that if we construct our own coordinate systems using clocks synchronized this way, the laws of physics will obey exactly the same equations in both coordinate systems, which means any experiment I do with an apparatus at rest in my frame will give the same result if you do the same experiment with the same apparatus at rest in your frame.

Relativity doesn't rule out the notion that there is some metaphysical truth about simultaneity, so that only one observer's clocks are "really" synchronized. But only God could no that truth--according to relativity, there is no experimental way to show that the laws of physics "prefer" one frame, they are all exactly equivalent as far as empirical experiments go so there can be no experimental basis for judging one frame's definition of simultaneity to be "correct" and another's to be "incorrect".

Then you deny Einstein's notion of simultaneity, two events occurring 'at the same time' as set out http://www.bartleby.com/173/8.html" ?

 

[Dale]

Then you deny Einstein's notion of simultaneity, two events occurring 'at the same time' as set out http://www.bartleby.com/173/8.html" ?

Don't be silly, comments like this to someone of JesseM's knowledge are not productive at all. JesseM understands the Einstein synchronization convention quite well. You are admittedly confused on the matter, but seem to be unwilling to learn despite the large amount of good information provided.

 

[JesseM]

Then you deny Einstein's notion of simultaneity, two events occurring 'at the same time' as set out http://www.bartleby.com/173/8.html" ?

This part of my comment was clearly assuming Einstein's definition: "Each observer synchronizes their own clocks using the assumption that light signals travel at the same speed in all directions relative to themselves, and the result is that according to each observer's definition of simultaneity, the clocks of the other observer are out-of-sync."

Do you not understand that Einstein's definition is based on the assumption that each frame defines "simultaneity" using light signals, making the assumption that all light signals travel at the same speed relative to that frame? He says this in the section you quote:

After thinking the matter over for some time you then offer the following suggestion with which to test simultaneity. By measuring along the rails, the connecting line AB should be measured up and an observer placed at the mid-point M of the distance AB. This observer should be supplied with an arrangement (e.g. two mirrors inclined at 90°) which allows him visually to observe both places A and B at the same time. If the observer perceives the two flashes of lightning at the same time, then they are simultaneous.

Obviously if we assumed the light from A did not travel at the same speed as the light from B in the observer's frame, then the fact that the light reached him at the same time would not mean the flashes were simultaneous.

But the in the very next section Einstein makes clear that if observers in different frames all assume light travels at a constant speed relative to themselves, then they will disagree about whether a given pair of events (like the lightning strikes in his example) are simultaneous, which is equivalent to my comment that if each frame synchronizes their own clocks using light-signals, each frame will say the other frame's clocks are out-of-sync. Did you read this part of Einstein's text?

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 (co-ordinate 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.

Do you understand that Einstein's definition of "same time" is frame-dependent, i.e. a pair of events that occur at the "same time" in one frame occurred at "different times" in other frames?

If you have trouble following Einstein's example, you might also consider this one. According to Einstein's definition, two clocks in my frame are "synchronized" in my frame (i.e. they always show a given reading, say 3:00, simultaneously) if, whenever I set off a flash of light at the exact midpoint between the two clocks, both clocks are showing the same reading at the moment the light from the flash reaches them. But now suppose I am on a rocket (with the clocks at the front and back of the rocket) being observed by someone in a different frame who defines simultaneity by assuming light travels at the same speed in all directions relative to himself. If he sees the rocket traveling forward, then after the flash is set off at the middle of the rocket he will see the clock at the back moving towards the position (in his frame) where the flash was set off, while the clock at the front is moving away from that position, so if he assumes the light travels at the same speed in both directions, he must conclude the light reaches the back clock before it reaches the front clock. But I have set my clocks to both show the same reading (say, 3:00) at the instant the light from the flash hits them, so in the observer's frame the clock at the back shows a reading of 3:00 before the clock at the front shows a reading of 3:00, and thus in his frame my two clocks are out-of-sync. Of course as I said, the effect is totally symmetrical, since if he synchronizes his own clocks under the assumption that light travels at a constant speed relative to himself, then in my frame (using my definition of simultaneity) his clocks will be out-of-sync.

So do you understand that according to Einstein's definition, each frame has their own definition of simultaneity and clock synchronization which different frames disagree about, and there is no physical basis to judge one frame's opinion as more "correct" than any other's? If so please read my comment again more carefully and tell me if you disagree with any specific part of it:

How are you going to define "same time"? Each observer synchronizes their own clocks using the assumption that light signals travel at the same speed in all directions relative to themselves, and the result is that according to each observer's definition of simultaneity, the clocks of the other observer are out-of-sync. If I think my clocks are synchronized and I use my clocks to determine that your clocks are out-of-sync, but you think your clocks are synchronized and you use your clocks to determine that my clocks are out-of-sync, how do you propose to settle the matter? Remember that if we construct our own coordinate systems using clocks synchronized this way, the laws of physics will obey exactly the same equations in both coordinate systems, which means any experiment I do with an apparatus at rest in my frame will give the same result if you do the same experiment with the same apparatus at rest in your frame.

Relativity doesn't rule out the notion that there is some metaphysical truth about simultaneity, so that only one observer's clocks are "really" synchronized. But only God could no that truth--according to relativity, there is no experimental way to show that the laws of physics "prefer" one frame, they are all exactly equivalent as far as empirical experiments go so there can be no experimental basis for judging one frame's definition of simultaneity to be "correct" and another's to be "incorrect".

 

[Grimble]

Don't be silly, comments like this to someone of JesseM's knowledge are not productive at all. JesseM understands the Einstein synchronization convention quite well. You are admittedly confused on the matter, but seem to be unwilling to learn despite the large amount of good information provided.

I apologise, that comment was not helpful.

I will draw some diagrams.

It may take me a day or two but I will be back. Thank you.

 

[Grimble]

Relativity doesn't rule out the notion that there is some metaphysical truth about simultaneity, so that only one observer's clocks are "really" synchronized. But only God could no that truth--according to relativity, there is no experimental way to show that the laws of physics "prefer" one frame, they are all exactly equivalent as far as empirical experiments go so there can be no experimental basis for judging one frame's definition of simultaneity to be "correct" and another's to be "incorrect".

Thank you Jesse I have never seen it explained better. I do see where I was getting confused by still thinking there was some specific reality.
Would I be right in saying that it isn't so much that light always travels at the same speed in vacuo where ever it travels, but that it is seen to travel at the same speed, in vacuo from whichever frame (perspective) it is viewed from.?

PS will show my diagrams soon.

 

[harrylin]

Thank you Jesse I have never seen it explained better. I do see where I was getting confused by still thinking there was some specific reality.
Would I be right in saying that it isn't so much that light always travels at the same speed in vacuo where ever it travels, but that it is seen to travel at the same speed, in vacuo from whichever frame (perspective) it is viewed from.?

PS will show my diagrams soon.

Quite. The first statement ("it isn't so much..") may be a statement about invisible physical reality, while SRT only makes statements about observables. Your second statement ("but..") corresponds to SRT's light principle, if with "whichever frame" you mean whichever standard "frame". In that context Einstein's formulation of 1907 may also be useful here:

"We [...] assume that the clocks can be adjusted in such a way that
the propagation velocity of every light ray in vacuum - measured by
means of these clocks - becomes everywhere equal to a universal
constant c, provided that the coordinate system is not accelerated."

Note that in GRT that isn't exactly valid anymore.

 

[invain2]

Hi, I am learning SR and I need help to get the idea of relativity with two clocks.

Yet I can understand that two different frames of reference can each one claim to be at rest, since this is just a logical argument.
But I am not getting the point how they can each claim the other ones clock is the one who slows down, after all this is physical question and it is like two people arguing whether the Earth is flat or round in which case only one can be right.

To show an example of what bothers me, let's say that I and another person have synchronized clocks.
Now when it is 12:00 on both of our clocks this person takes off in a linear motion [STRIKE]and will never return[/STRIKE].
so when my clock will show 5:00, then if the other person is the one who moves then his clock will show 4:00, and if I am the one who moves then the other person's clock will show 6:00.
So the person's clock can be either 4:00 or 6:00 but not both, yet we don't know what it is, but this is like if we don't know if the Earth is flat or not and it is a physical question, and can have only one answer, even if we don't know what the answer is.

It is clear to me that I am missing something, so what is it?

I believe that, assuming he keeps moving at the speed of light, it will stay 12:00 for him according to Einstein's theory.

 

[JesseM]

I believe that, assuming he keeps moving at the speed of light, it will stay 12:00 for him according to Einstein's theory.

hprog didn't say anything about the clock "moving at the speed of light", it would just be impossible for an object with mass like a clock to do so in relativity.