# B Order of events and cause and effect

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1. Dec 27, 2017

### joneall

I'm reading "Bang!", by Brian May, Patrick Moore and Chris Lintott. On page 40, they say:

"So one [observer] may believe A preceded B by a minute, and another that A and B were simultaneous, it is impossible for any observer to see B preceding A. Hence cause and effect are preserved..."

But in the standard "paradox" of the pole and the barn (or the stretch limo and the VW-beetle garage), the runner sees the pole's forward end leave the garage before the back end enters, whereas the person standing next to the garage sees those two events in the opposite order.

Have I misunderstood something? Granted, I'm not sure what this has to do with cause and effect. Could that make the difference?

2. Dec 27, 2017

### Orodruin

Staff Emeritus
It actually has nothing to do with cause and effect, it only has something to do with simultaneity.

A cause would be if there was no back door in the garage and the pole instead hit the back. You might think that this would stop the pole from entering the garage in the runner's rest frame, but in order to do so a signal would have to travel through the pole from the front to the back with a speed greater than c, which cannot happen. (In reality, the signal of the pole hitting the back of the garage will travel along the pole at the speed of sound in the pole.) Since the events "front of pole exiting the garage" and "end of pole entering the garage" have spacelike separation, what happens at one of those events cannot affect the other.

3. Dec 27, 2017

### Ibix

Nothing travels faster than light. So if A caused B and A happened a minute before B, it can't have been more than a light minute away. Otherwise not even light could have made it from A to B so A can't have had anything to do with B.

This means that there are three groups of events.
1. Ones that were too far away to have been caused by A or to have caused it.
2. Ones that were close enough to it and happened before it (which could have caused A).
3. Ones that were close enough to it and happened after it (which could have been caused by A).
Everyone will agree that group two events happened before A. Everyone agrees that group three events happened after A. But not everyone will agree which events in group one happened before, after, or at the same time as A. But that doesn't matter because they can't affect each other - so this can never lead to a cause preceding an effect.

In the ladder/barn paradox the events "front exits barn" and "rear enters barn" happen at the same time in one frame - so are clearly too far apart to affect each other. So the order doesn't matter and frames may disagree over it.

However, you quote the book as saying
...which sounds wrong to me. If A could be simultaneous with B for anyone, it must be too far away to affect B. So the order doesn't matter and may be anything. On the other hand, if B can't be before A then that implies that there could be a causal connection. Someone could see A being a millisecond before B (and length contraction would ensure that they were less than a light millisecond apart), but not simultaneous.

So basically I think the book is wrong. Unless there's some major context you left out.

4. Dec 27, 2017

### joneall

So in any case, there is no caused effect here and what the authors of "Bang!" say is ... not wrong. And the order of the two events differs between the two observers.

5. Dec 27, 2017

### Orodruin

Staff Emeritus
See Ibix's post. I read it a bit fast. If there is a frame where A and B are simultaneous, there will also be frames where A is before B and frames where B is before A. The formulation of the text is unfortunate. What they really want to convey is that if the time ordering of two evens depends on the frame, then there can be no causal link between them.

6. Dec 27, 2017

### DrStupid

This is not possible if A is the cause of B or vice versa.

Is this really what the really want to convey or just what you think what the really want to convey? I'm afraid we would need to ask the authors to answer this question.

7. Dec 27, 2017

### Orodruin

Staff Emeritus
So? If the events are simultaneous (and different events), they cannot have a causal connection. If they have a causal connection, they cannot be simultaneous. I do not understand your objection as your assertion that A is the cause of B violates my qualifying clause that A and B are simultaneous.

8. Dec 27, 2017

### DrStupid

The citation of the OP is about cause and effect and such causual connected events cannot be simultaneous. You are simply off-topic.

9. Dec 27, 2017

### vanhees71

10. Dec 27, 2017

### joneall

This sounds right, intuitively. It's the case of the pole jumper, for instance. But I can't quite see it mathematically (or on a light-cone diagram).

11. Dec 27, 2017

### Orodruin

Staff Emeritus
I am sorry, but you are simply wrong here. This is the quote of the OP:
It clearly talks about simultaneity in relation to causality and an event that is perceived as simultaneous in some frame. The main point in this regard is that events with space-like separation cannot be causally connected, leading to causality not being violated as a result of the time ordering of A and B differing between frames. For events with non-space-like separation, the situation described in the quote simply does not occur - there is no frame where causally separated events are simultaneous.

To claim that I am off-topic is inflammatory, wrong, and just bound to confuse the OP further.

12. Dec 27, 2017

### Orodruin

Staff Emeritus
Consider the following Minkowski diagram with the light cone for the event E

Here the events A and B are time-like separated from E (A is in the future light cone and B is in the past light cone, the light cone here is the grey area). The events that are simultaneous with E in the given coordinate system are all on the x-axis. For all other inertial frames, the events simultaneous with E will be on a line that goes through E and has a slope smaller than 1 but bigger than -1. Regardless of which event on the x-axis you consider, it is always possible to find such a line which is above the event (and in the same way, it is possible to find such a line that is below the event), corresponding to the simultaneity of E in a frame where the event occurs before (after) E.

With regards to the events A and B in this diagram, there is no surface of simultaneity with E for any frame such that B is above it or A is below it. Hence, time ordering of causally connected events is preserved between frames.

Edit: Mathematically, you can see it through the Lorentz transformations. Consider two events A and B that are simultaneous in some frame S. We can always arrange our coordinate system such that A is at the origin and B then has coordinates $t = 0$ and $x = x_0 > 0$. Making a Lorentz transformation with velocity $v$ results in A still being at the origin and the coordinates of B being given by
$$t' = -\gamma vx_0/c^2,\quad x' = \gamma x_0.$$
Depending on the sign of $v$, B might therefore occur either earlier ($v > 0$) or later ($v < 0$) than A in the new frame.

13. Dec 27, 2017

### Staff: Mentor

I agree with @Ibix. This quote is wrong. If A and B are simultaneous in any inertial frame then there do exist frames where B precedes A and frames where A precedes B. Cause and effect are preserved because neither A nor B can cause the other.

14. Dec 27, 2017

### vanhees71

Indeed the contradiction is in the OP not in @Orodruin's answer. The problem is again that everybody shys back from making clear mathematical statements. Two events by definition cannot be causally connected, if they are spacelike separated. Of course two space-like separated events can have any coordinate-time ordering depending on the reference frame you want. It's easy to show that there's always a reference frame, where the events take place simultaneously. It's also clear that two events that are simultaneous in one reference frame are spacelike separated.

If you have time (or light) like separated events, these have a fixed time ordering, i.e., their time ordering is independent of the reference frame from which it is observed. Such events can (but do not need necessarily have to) be causally connected.

15. Dec 27, 2017

### Staff: Mentor

I do not have this book, but this can't possibly be right as it's stated. If there is any frame in which A and B are simultaneous, then A and B cannot be causally connected, and there must be some other frame in which B happens before A. So either you are leaving out some crucial context or the book is simply wrong.

16. Dec 27, 2017

### Staff: Mentor

In which case, as several of us have already pointed out, the quotation given from the book cannot be right as it's given, since it says there is a frame in which A and B are simultaneous, and they therefore cannot be causally connected.

No, he isn't, but you're getting close to it.

17. Dec 28, 2017

### joneall

For those of you who are (quite logically) worrying I have misquoted the book, here is the whole paragraph. It follows an example of time dilation, which terminates and then goes on as follows:

"... In other words, while I may observe ten seconds elapsing, you, who are accelerating away from me, may observe only six.

"The temptation is first of all to ask who is right, and then to look for some subterfuge that may have altered the clocks. Yet relativity tells us firmly that both are right and there is no trick -- different observers really do experience time flowing at different rates. Some rules of common sense are preserved; two observers will always agree on the order of events, for example. So although one may believe A preceded B by a minute, and another that A and B were simultaneous, it is impossible for any observer to see B preceding A. Hence cause and effect are preserved, but many other common-sense ideas that seem second nature to us must be abandoned."

18. Dec 28, 2017

### Ibix

Unless the section is specifically referring to causally connected events this is wrong, as you pointed out with your rod/barn example.
And this is still problematic even with your added context. If A and B can be simultaneous for one observer then they could be in either order for another observer.

Actually, the quote above is problematic on merely logical grounds. If A and B are simultaneous for one observer, how can that observer determine which one is "allowed" to be first? The only get-out I can think of is if they are discussing non-standard simultaneity conventions which imply spatial anisotropy. But forty pages into a pop-sci text I'd regard that as trolling their readers.

Either way, I'd sugest taking this book with a pinch of salt. Or not taking it at all - get a proper text book.

19. Dec 28, 2017

### PeroK

@joneall what is true is that a sequence of timeline separated events occur in the same order for all observers.

But, if two events are simultaneous in one reference frame then, by definition, they are spacelike separated. In which case their order is frame dependent.

20. Dec 28, 2017

### joneall

Sure. I've read textbooks. Just reading this to see how they explain it simply to laymen. Simply does not necessarily equal correctly.

Also, they talk a lot about galaxy formation, about which I know very little. It appears all those (again) simple explanations of just gravity pulling dust particles together are not adequate and there were more steps involved. Any references on that? Sorry, I guess I'm changing the subject.