# Thread: Can anyone figure this out?

1. ## Can anyone figure this out?

There are two rulers with identical lengths, when they are at rest relative to one another.

Call one of them the unprimed ruler AB, and call the other ruler the primed ruler A`B`.

Thus, the rulers can be made to coincide as illustrated below:

A____________________B
A`___________________B`

Now, suppose that both rulers are in relative motion, at a constant speed v, and that neither ruler is being subjected to an external force.

Now, consider things from the rest frame of the unprimed ruler.

Assume SR is correct, in all its postulates, as well as any statements which follow from those postulates. Thus, in the rest frame of ruler AB, the primed ruler is length contracted.

Now lets not worry about the exact value of v, but lets say that the relative speed v is so great that the primed ruler is now less than half the length of AB (in AB's rest frame), and view the motion as the primed ruler moves from right to left as illustrated below:

Moment in time X
A____________________B
..................................A`____B`

Moment in time Y
A____________________B
........................A`____B`

Moment in time Z
A____________________B
A`____B`

As you can see, B` coincided with B, before A` coincided with A.

Now, view the same event from the rest frame of the primed ruler.

By the postulate of SR which states that the laws of physics are the same in all inertial reference frames, it must be the case that the unprimed ruler is length contracted.

In the rest frame of ruler A`B` we have:

Moment in time R
A_____B
..........A`___________________B`

Moment in time S

..........A_____B
..........A`___________________B`

Moment in time T

..................................A_____B
..........A`___________________B`

As you can see, in this inertial frame, A` coincides with A before B` coincides with B.

But the ends of each ruler can coincide only once during the entire event, regardless of which of the two frames is regarded as being at rest.

From the six diagrams above, you can infer the following:

X=R
Y=T
Z=S

Y before Z AND Z before Y

How is that possible?

2. If an observer at rest with the unprimed ruler observes the primed ruler moving right-to-left, then surely an observer at rest with the primed ruler will see the unprimed ruler moving left-to-right.

That's a pretty stupid mistake for a truly advanced intelligence, eh?

- Warren

3. Originally Posted by Johnny5
There are two rulers with identical lengths, when they are at rest relative to one another.

Call one of them the unprimed ruler AB, and call the other ruler the primed ruler A`B`.

Thus, the rulers can be made to coincide as illustrated below:

A____________________B
A`___________________B`

Now, suppose that both rulers are in relative motion, at a constant speed v, and that neither ruler is being subjected to an external force.

Now, consider things from the rest frame of the unprimed ruler.

Assume SR is correct, in all its postulates, as well as any statements which follow from those postulates. Thus, in the rest frame of ruler AB, the primed ruler is length contracted.

Now lets not worry about the exact value of v, but lets say that the relative speed v is so great that the primed ruler is now less than half the length of AB (in AB's rest frame), and view the motion as the primed ruler moves from right to left as illustrated below:

Moment in time X
A____________________B
..................................A`____B`

Moment in time Y
A____________________B
........................A`____B`

Moment in time Z
A____________________B
A`____B`

As you can see, B` coincided with B, before A` coincided with A.

Now, view the same event from the rest frame of the primed ruler.

By the postulate of SR which states that the laws of physics are the same in all inertial reference frames, it must be the case that the unprimed ruler is length contracted.

In the rest frame of ruler A`B` we have:

Moment in time R
A_____B
..........A`___________________B`

Moment in time S

..........A_____B
..........A`___________________B`

Moment in time T

..................................A_____B
..........A`___________________B`

As you can see, in this inertial frame, A` coincides with A before B` coincides with B.

But the ends of each ruler can coincide only once during the entire event, regardless of which of the two frames is regarded as being at rest.

From the six diagrams above, you can infer the following:

X=R
Y=T
Z=S

Y before Z AND Z before Y

How is that possible?
Are you familiar with the barn and pole paradox? Is something similar to your "paradox". In SR, the order of events can be different for different observers

4. The ends do coincide only once. But since Simultaneity is also relative, according to the rules of Relativity, the two frames just don't agree as to what order they coincide.
This is no problem because you can only measure the events from one frame(the frame you happen to be measuring from). There is no "uber-frame" from which events can be measured as if from both frames.

5. Originally Posted by chroot
If an observer at rest with the unprimed ruler observes the primed ruler moving right-to-left, then surely an observer at rest with the primed ruler will see the unprimed ruler moving left-to-right.

That's a pretty stupid mistake for a truly advanced intelligence, eh?

- Warren
You read the post wrong einstein.

The word 'left' appears but once in the entire thread, when i say...

Moving from right to left.

You do not see that phrase appear again.

6. Originally Posted by Lucas
Are you familiar with the barn and pole paradox? Is something similar to your "paradox".
I sure am. If you have a million mile long pole, and a ten foot barn, and you run along the surface of the earth really really fast, the pole fits inside of the barn with both doors closed... at least according to special relativity theory.

And, i may add, with the correct acceleration, the million mile pole can remain inside of the ten foot barn forever... according to SR theory that is.

Reality is a different story.

Originally Posted by Lucas
In SR, the order of events can be different for different observers
And in reality, the order of events must be the same for all observers. My statement was formulated using General Order Spatiotemporal logic...

Yours wasnt.

Figure out which one has meaning.

7. Originally Posted by Janus58
The ends do coincide only once. But since Simultaneity is also relative, according to the rules of Relativity, the two frames just don't agree as to what order they coincide.
This is no problem because you can only measure the events from one frame(the frame you happen to be measuring from). There is no "uber-frame" from which events can be measured as if from both frames.
The ends do coincide, and they do so simultaneously (because neither ruler undergoes relativistic contraction), and the ends coincide simultaneously only once, at a single moment in time, and simultaneity is absolute, and simultaneity is absolute in all reference frames, inertial AND/OR otherwise.

That you cannot see why this is true, is because you do not know how to use General Order Spatiotemporal modal logic.

8. Originally Posted by Johnny5
I sure am. If you have a million mile long pole, and a ten foot barn, and you run along the surface of the earth, the pole fits inside of the barn with both doors closed... at least according to special relativity theory.

And, i may add, with the correct acceleration, the million mile pole can remain inside of the ten foot barn forever... according to SR theory that is.

Reality is a different story.

And in reality, the order of events must be the same for all observers. My statement was formulated using General Order Spatiotemporal logic...

Yours wasnt.

Figure out which one has meaning.
if you are familiar with the pole-barn paradox, why are you confused with the problem? In the barn-pole paradox according to the frame of the pole, the tip of the pole leave the rear door before the rear of the pole enters the front door. in the frame of the barn, the posterior part of the pole enters the front door before the tip of the pole leave the rear door. So, the order of events is changed, like in the problem you presented. But, this is a consequence of the Lorentz transformations. Drawing a space time diagram can help a lot

9. So.... simply saying that simultaneity is absolute makes simultaneity absolute, eh? Such investigative powers!

- Warren

10. Originally Posted by Lucas
if you are familiar with the pole-barn paradox, why are you confused with the problem? In the barn-pole paradox according to the frame of the pole, the tip of the pole leave the rear door before the rear of the pole enters the front door. in the frame of the barn, the posterior part of the pole enters the front door before the tip of the pole leave the rear door. So, the order of events is changed, like in the problem you presented. But, this is a consequence of the Lorentz transformations. Drawing a space time diagram can help a lot
Sadly, there is no need to. All you have to do to become as intelligent as I am, is understand the meaning of the word AND, which is the simultaneity operator of binary logic.

If you cannot understand the meaning of AND, then no amount of intelligence possessed by me can help you.

The Lorentz transformations contain the same contradiction found here.

11. General Order Spatiotemporal modal logic.

- Warren

12. Originally Posted by chroot

- Warren
AND?

13. Originally Posted by Johnny5
The Lorentz transformations contain the same contradiction found here.
Please demonstrate the contradiction mathematically. It should be easy for such an advanced intelligence!

- Warren

14. Originally Posted by chroot
So.... simply saying that simultaneity is absolute makes simultaneity absolute, eh? Such investigative powers!

- Warren
No, if you want I can prove so using quaternions, but that would be beyond the scope of your current knowledge.

15. Originally Posted by chroot
Please demonstrate the contradiction mathematically. It should be easy for such an advanced intelligence!

- Warren
Consider two overlapping inertial frames, at moment in time Z.

Call one the S inertial frame, and call the other the S` inertial frame.

Let them coincide perfectly, at moment in time Z, and let moment in time Z denote the first moment of time.

Thus, at the first moment in time, the following four relations give the spatiotemporal coordinate transformations from S to S`:

x=x`
y=y`
z=z`
t=t`

Where (x,y,z,t) denotes a spacetime point in frame S, and (x,y,z,t`) denotes a spacetime point in frame S`.

16. Originally Posted by Johnny5
No, if you want I can prove so using quaternions, but that would be beyond the scope of your current knowledge.
I know quaternions quite well, in fact. Lay it on me.

- Warren

17. Originally Posted by Johnny5
Let them coincide perfectly, at moment in time Z, and let moment in time Z denote the first moment of time.
As measured by whose clock?

- Warren

18. Originally Posted by chroot
I know quaternions quite well, in fact. Lay it on me.

- Warren

Well for starters, what is the geometrical interpretation of a quaternion?

19. Originally Posted by Johnny5
x=x`
y=y`
z=z`
t=t`
These transformations are not valid generally, unless the two frames are identical for all times. You've said they only coincide at one instant, so these coordinate transforms are incorrect for all other instants.

- Warren

20. Originally Posted by chroot
As measured by whose clock?

- Warren
A moment in time is a point, you cannot measure it using a clock, clocks only measure amounts of time.

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