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kini.Amith
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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 said:Prove that cause precedes effect in all inertial reference 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.kini.Amith said: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.kini.Amith said: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
kini.Amith said:Prove that cause precedes effect in all inertial reference frames.
that's exactly what i want. how can you prove it.JesseM said: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.
I already proved it above:kini.Amith said:that's exactly what i want. how can you prove it.
DaleSpam said: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.
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).DaleSpam said:Yes, start with the formula for the spacetime interval and then prove that it is invariant under the Lorentz transform.
I think the question was specifically about SR.Dmitry67 said:You can't prove it, because GR has solutions with closed time curves.
I think the point of the question was that for two causally-related events, all frames would agree which event came earlier and was therefore the "cause", and which event came later and was therefore the "effect". This is not true by definition, and it would be violated in SR if events with a spacelike separation could be causally related.Dmitry67 said:But even in flat spacetime, "cause" and "effect" are just DEFINITIONS. So cause precedes the effect BY DEFINITION.
JesseM said:I think the point of the question was that for two causally-related events, all frames would agree which event came earlier and was therefore the "cause", and which event came later and was therefore the "effect". This is not true by definition, and it would be violated in SR if events with a spacelike separation could be causally related.
An inertial reference frame is a frame of reference in which Newton's laws of motion hold true. This means that an object at rest will remain at rest, and an object in motion will continue in a straight line at a constant speed unless acted upon by an outside force.
Proving that cause precedes effect in inertial reference frames is important because it confirms the validity of Newton's laws of motion. By showing that the cause of an object's motion is always present before the effect, we can trust that these laws accurately describe the behavior of objects in our physical world.
One way to experimentally demonstrate this concept is to use a pendulum. By releasing the pendulum at different heights and measuring the time it takes to swing back and forth, we can confirm that the length of the pendulum (the cause) affects its period (the effect). This supports the idea that the cause (length) precedes the effect (period).
No, the principle of cause preceding effect only applies to inertial reference frames. In non-inertial reference frames, such as those experiencing acceleration, the concept of causality becomes more complex and may not hold true.
The concept of cause preceding effect is closely related to determinism, which is the idea that all events have a cause and that the future is determined by the present. In inertial reference frames, this idea is supported by the fact that the cause of an object's motion is always present before the effect. However, in non-inertial reference frames, the concept of determinism may not hold true due to the influence of outside forces.