# Cause and effect

kini.Amith
Prove that cause precedes effect in all inertial reference frames.

## Answers and Replies

Are you just asking for a proof that all inertial frames agree on the order of two causally related events--i.e. if A and B are causally related, and one frame says A happened before B, then all frames agree that A happened before B? This is not too hard to prove. On the other hand, if you're saying that even if we know A happened before B in all frames, we still need to prove that this implies B is the "effect" of A rather than the "cause" of A, I don't think such a proof would really be possible without precise definitions of "cause" and "effect", which aren't technical terms in physics (and it's hard to see how we could even make sense of the notion given the Time-symmetry of most laws of physics).

Mentor
2021 Award
Prove that cause precedes effect in all inertial reference frames.
The interval from cause to effect is a future-directed timelike interval in some frame therefore it is a future-directed timelike interval in all frames.

kini.Amith
i want to prove that if the temporal separation dt between 2 events is positive in 1 inertial frame then it is positive in all inertial frames

Mentor
i want to prove that if the temporal separation dt between 2 events is positive in 1 inertial frame then it is positive in all inertial frames
That's not true in general. Just because two events are in a particular temporal order in one frame does not mean that they are causally related.

i want to prove that if the temporal separation dt between 2 events is positive in 1 inertial frame then it is positive in all inertial frames
As Doc Al was hinting at, this is only true if the events have either a time-like or light-like separation (meaning they could be causally related), but it's not true if the events have a space-like separation (meaning they couldn't be causally related, at least not unless there exist particles which travel faster than light, which would make a mess of causality anyway). If you're not familiar with the meaning of these different types of spacetime separations, see here.

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Mueiz
Prove that cause precedes effect in all inertial reference frames.

cause and effect are also relativistic.
If you see in your frame the cause ( the cause accoding to another frame)of an event happen after
the effect (the effect according to the other frame) then your cause is the effect of the other frame .
This is a result from the first postulate of SR of the laws of physics.
If you talk of event and cause that means you apply a law of physics which must hold in all inertial frames.
That is because the fact that if the sequence of events is changed then the events also will be changed in such a way that it keep both casusality principle and relativity of time
You can prove this using any example of cause-effect event.

Soumya_M
In this context I would like to point out that the "delayed choice" double-slit experiment seem to suggest that a measurement done, in the present, is able to change the past (history) of a particle. So, evidently a cause arising in the future can change the past.

In our common sense view of causality, we make two assumptions. These are: -
1. Cause precedes the effect in time.
2. Effect is dependent on the cause.

These assumptions agree perfectly with our everyday observations. We always see things of the past having an effect on the present and not the other way. So, causality seems to follow the so called arrow of time perfectly. But the delayed choice experiment suggests that our first assumption about causality may well be wrong.

But the question then is how can the past be changed if it is pre-determined? I think the answer is that there is not a single past as we think, but indeed there are many pasts. The observer chooses the past by our observing the present. In the words of Stephen Hawking "We create history by our observations, rather than History creating us."

However, I think the second assumption still holds good. That is, irrespective of the point of time at which events take place, they may be causally related simply by interdependence, i.e. the effect always depends on the cause and not the other way (unless we resort to some sort of destiny or "divine purpose").

kini.Amith
This is a question from the book 'problems in physics' by i e irodov. so i'm sure the question
wont be wrong

kini.Amith
Are you just asking for a proof that all inertial frames agree on the order of two causally related events--i.e. if A and B are causally related, and one frame says A happened before B, then all frames agree that A happened before B? This is not too hard to prove.
that's exactly what i want. how can you prove it.

Mentor
2021 Award
that's exactly what i want. how can you prove it.
I already proved it above:
The interval from cause to effect is a future-directed timelike interval in some frame therefore it is a future-directed timelike interval in all frames.

kini.Amith
i mean using the lorentz transformation equations. would it be possible to do it mathematically.

Mentor
2021 Award
Yes, start with the formula for the spacetime interval and then prove that it is invariant under the Lorentz transform.

Yes, start with the formula for the spacetime interval and then prove that it is invariant under the Lorentz transform.
For this question one also needs to prove that the order of two timelike-separated events can't change under the Lorentz transformation, not just that all frames agree the separation is timelike (and likewise for lightlike separated events).

Dmitry67
You can't prove it, because GR has solutions with closed time curves. But even in flat spacetime, "cause" and "effect" are just DEFINITIONS. So cause precedes the effect BY DEFINITION.