# Found a way around relativity of simultaneity

1. Apr 27, 2012

### vdub

Chapter 9 on the theory of relativity discusses a thought experiment (http://www.bartleby.com/173/9.html) about a passenger on a train that claims that
it is impossible to say in an absolute sense whether two events occur at the same time if those events are separated in space.

I have devised a modification to this thought experiment to disprove this.

Assume you have two long ropes laying side-by-side with the tracks, both going from point A to point B. You have a watchman standing at point A, and a watchman standing at point B. They will pull their rope when they see lightning strike their point. The passenger can see the grooves of the rope shift when it is pulled. If the passenger sees both ropes get pulled simultaneously at the midpoint, he will see them get pulled simultaneously anywhere.
...
This is because all points of the rope get pulled instantaneously. There is no waiting time like with the traveling of light. For example, consider a rope that is one lightyear long. When the rope gets pulled from one endpoint, a person at the other endpoint a lightyear away will see the rope's end move with no delay, due to the laws of matter. Even though no actual material is traveling faster than the speed of light, the knowledge that the rope was pulled is traveling faster than the speed of light.

So if you consider when the rope gets pulled to correspond to when the event of lightning occurs, there seems to be an absolute sense of simultaneity no matter where the train is or how it is moving.

2. Apr 27, 2012

### Staff: Mentor

This is a pretty common suggestion, so we have a FAQ that explains why it doesn't work:

Last edited by a moderator: May 5, 2017
3. Apr 27, 2012

### Matterwave

Basic flaw: all segments of the rope don't react simultaneously.

4. Apr 27, 2012

### vdub

Since relativity of simultaneity ultimately leads to proof that no object can travel faster than light, you can't assume beforehand that no object can travel faster than light.
So shoot something that travels instantaneously to signal that lightning struck the point

5. Apr 27, 2012

### Ryan_m_b

Staff Emeritus
Sorry I have no idea what you are trying to say here.
Huh?
There is nothing that travels instantaneously.

6. Apr 27, 2012

### Staff: Mentor

Like what? Did you even bother to read the FAQ? It explains why there is no such thing.

7. Apr 28, 2012

### mananvpanchal

I know that there is nothing like faster than speed of light. The rope pulling wave has very less speed than light. But, vdub has a fair point.

Suppose, that pulling wave of rope travels at speed of sound. The two lightning events is simultaneous for platform observer and not for train observer. And platform observer also confirms that the two events are not simultaneous for train observer, whereas train observer confirms that the two events are simultaneous for platform observer. Both observer are agree that the two events are simultaneous for platform observer and not for train observer.

Now, if two events occurs simultaneously for platform observer, and he confirms that the two events are not simultaneous for train observer. So, he also confirms that rope pulled by watchmen are simultaneous and the effect of the wave reaches to train observer would also be simultaneous. Because, speed of pulling wave is not related with direction of motion of train. So, what platform observer confirms that is true for train observer, so train observer also see simultaneous pulling wave and unsimultaneous lighting events.

This seems paradox. We have to solve this.

Last edited: Apr 28, 2012
8. Apr 28, 2012

### Staff: Mentor

When you do so you will find that this statement is false:

Last edited: Apr 28, 2012
9. Apr 28, 2012

### Staff: Mentor

Relativity of simultaneity is a *consequence* of the fact that the speed of light is finite and nothing can go faster; it is not a premise used to prove it.

10. Apr 28, 2012

### Staff: Mentor

I'd rather say that relativity of simultaneity and the the presumption that nothing can go faster than light are *both* consequences of the more fundamental premise that the speed of light in vacuum is the same in all reference frames.

In the context of OP's SoWrong(tm) suggestion that "relativity of simultaneity ultimately leads to proof that no object can travel faster than light" this is about a third-order nitpick - I'm offering it up because it might matter to someone else wandering through this thread and trying to understand what is premise and what is conclusion in SR.

11. Apr 28, 2012

### phinds

vdub, when you come up against something that flies so utterly in the face of established science, it is not a good idea to start off reaching different conclusions and stating them as correct but rather to start off with the assumption that you have made a mistake somewhere and try to find out where it is. If you have NOT made a mistake you will find the flaw in the established science, but that is very unlikely to happen. If you start off thinking that you have overturned established science you are likely to just end up embarrassed.

12. Apr 28, 2012

### and9

This is probably the best advice you can possibly find on PF if one desires to become a theoretical physicist.

13. Apr 30, 2012

### mananvpanchal

This is strange statement by me. I was actually trying to say that if the two rope pulled simultaneously in platform frame, then the pulling waves reach to train observer simultaneously in platform frame. Whereas in case of lightning, two stroke occurs simultaneously in platform frame, the beam of the lightning reaches to platform observer simultaneously in platform frame, but the beam of the lightning will not reach to train observer simultaneously in platform frame. So platform observer confirms that the two events wouldn't occur simultaneously in train frame.

Suppose, train running from left to right. Platform observer sees that two events occurs simultaneously at both end of train. Platform observer confirms that information of left event reaches to train observer lately than right event, because speed of light from both direction is same for platform observer. Platform observer confirms that events is simultaneous in platform frame, and if he transforms the timing of events into train frame, he also confirms that the events is not simultaneous in train frame.

Train observer sees both events one by one. Speed of light is same from both direction for train observer. So, train observer confirms that the events is not simultaneous in train frame. But, train observer can calculate that timing of the events in train frame. And if train observer transforms the timings into platform frame, train observer also confirms that the events is simultaneous in platform frame.

Now, platform observer sees that both rope is pulled by watchmen simultaneously in platform frame. The pulling wave speed is faster from left end to middle than right end to middle for platform observer. Platform observer sees that both pulling wave reaches to train observer simultaneously.

The train observer also sees that pulling wave reaches to him simultaneously. But, beam of lightning reached to him unsimultaneously.

Suppose, length of train is 2 ls. Ans speed of train is 0.6c. If the two events occurred in platform frame at $t_{p}=0$, $x_{pl}=-1$ and $x_{pr}=1$. We get $t_{tl}=0.75$ and $t_{tr}=-0.75$ in train frame after lorentz transformation.

Now, suppose that platform observer sees that watchmen pulling rope at $t_{pulling\text{ }rope}=0$, $x_{left\text{ }pulling\text{ }rope}=-1$ and $x_{right\text{ }pulling\text{ }rope}=1$ in platform frame. The rope will reach at middle at some $t_{reaching\text{ }rope}=t$ and $x_{pulling\text{ }rope}=x$ in platform frame. If we transform the $t_{reaching\text{ }rope}=t$ and $x_{pulling\text{ }rope}=x$, we will get some $t'_{reaching\text{ }rope}=t'$ and $x'_{pulling\text{ }rope}=x'$ in train frame. Train observer sees pulling wave reaching to him simultaneously.

The main cause of the paradox is pulling wave and light is not behaving same.

14. Apr 30, 2012

### Staff: Mentor

Are the watchmen and ropes at rest wrt the train or wrt the platform?

15. Apr 30, 2012

### mananvpanchal

Both watchmen are situated on both end of train. They are at rest in train frame and moving in platform frame. The both rope are also at rest in train frame and moving in platform frame.

Last edited: Apr 30, 2012
16. Apr 30, 2012

### Staff: Mentor

This statement ...
and this statement ...
Since the distance is the same and since the mechanical wave speed is the same then if they are pulled non-simultaneously then they will necessarily reach him non-simultaneously also.

17. Apr 30, 2012

### mananvpanchal

I am taking about lightning events which is unsimultaneous in train frame in first statement.
But, rope pulling events is simultaneous in platform frame, so it would reach to train observer simultaneously.

18. Apr 30, 2012

### Staff: Mentor

Each rope pulling event is at the same place and the same time as the corresponding lightning strike event. Therefore, if the lightning events are unsimultaneous in the train frame then the rope pulling events are also unsimultaneous in the train frame.

No. The distances are not the same in the platform frame, nor are the speeds. So this does not follow.

19. May 1, 2012

### mananvpanchal

The distance is same from both watchmen to train observer, and speed is not same for platform observer. That's why pulling wave reaches to train observer simultaneously in platform frame.

Ok, to remove any confusion I demonstrate the scenario with watchmen in both frame.
Now, there are two set of watchmen one are on platform with ropes and other are on train with ropes.

* For lightning Events

- From platform frame

- Two lightning occurs at both end simultaneously in platform frame. The lightning occurred at same distance from platform observer. The lighting beam reaches to platform observer simultaneously. He knows the location and perceiving time of the lighting beam. So, he can calculate that the lightning have occurred simultaneously in platform frame.

- The platform observer knows that train is moving relative to him. So, he concludes that lightning beam from right will reach to train observer before the lightning beam from left. He knows theory of relativity, so he transforms timings of simultaneous events in his frame into train frame. And he can conclude that the events will occur unsimultaneously in train frame.

- From train frame

- The two lightning ccurs at both end unsimultaneously in train frame. The lightning occurred at same distance from train observer. The lighting beam reaches to train observer unsimultaneously. He knows the location and perceiving time of the lighting beam. So, he can calculate that the lightning have occurred unsimultaneously in train frame.

- The train observer knows that platform is moving relative to him. So, he concludes that lightning beam from both direction will reach to platform observer simultaneously. He knows theory of relativity, so he transforms timings of unsimultaneous events in his frame into platform frame. And he can conclude that the events will occur simultaneously in platform frame.

Look nice so far, both observer agrees that lightning occurs in platform frame simultaneously and in train frame unsimultaneously.

* For rope pulling events

- From platform frame

- Two lightning occurs simultaneously in platform frame. Platform observer sees that watchmen on platform pull ropes simultaneously in platform frame. Platform observer sees that pulling wave on platform reaches to him simultaneously in platform frame.

- Platform observer sees that watchmen on train pull ropes simultaneously in platform frame. Platform observer sees that pulling wave on train reaches to train observer simultaneously in platform frame.

- From train frame

- Two lightning occurs unsimultaneously in train frame. Train observer sees that watchmen on train pull ropes unsimultaneously in train frame. Train observer sees that pulling wave on train reaches to him unsimultaneously in train frame.

- Train observer sees that watchmen on platform pull ropes unsimultaneously in train frame. Train observer sees that pulling wave on platform reaches to platform observer unsimultaneously in train frame.

The two bold statement from platform frame contradicts with the two bold statement from train frame. That is why this is a paradox.

20. May 1, 2012

### Staff: Mentor

The apparent paradox will go away if you correctly calculate exactly what each observer sees. Start with the (x,t) coordinate of the following events, as observed by the platform observer:
A) Left-hand bolt of lightning strikes and left-hand watchmen tug their ropes
B) Right-hand bolt of lightning strikes and right-hand watchmen tug their ropes
C) The two flashes meet in the middle
D) The two waves in the platform rope meet somewhere in the platform rope (assume the waves propagate in the rope with speed VR).
E) The two waves in the train rope meet somewhere in the train rope. You will have to use the relativistic law for addition of velocities, so the forward-traveling wave and the backwards-traveling wave will be moving at different speeds as observed by the platform observer, and neither speed will be VR.

Next for events A, B, and C use the Lorentz transforms to calculate the (x',t') coordinates of these events as seen by the train observer.

Then calculate from the speeds of the waves in the two ropes the x' and t' coordinates of the events D' (train observer sees the waves meet in the platform rope) and E' (train observer sees the waves meet in the train rope). Remember to use the relativistic law of addition of velocities to get the speed of the waves in the platform rope as observed by the train observer.

If you get all the calculations right, you will find that D' is what you get when you use the Lorentz transforms on D; and likewise for E' and E. That is, D and D' are the same events, both observers are seeing the same physics, and especially both observers agree about the points in both ropes where the waves meet at the same time.

Last edited: May 1, 2012