Special Relativity – How Does Causality Align with the Order of Events?

special-relativity

I have been trying to study special relativity. However, I do not have the mathematical knowledge to understand any technical explanations. I started reading A Brief History in Time and I thought I should have some background knowledge on this special relativity Stephen Hawking was describing. So I went online and did a bit of research and I found out about the following:

If there are two observers, Observer A and Observer B, they will agree on the following:

  • Space time interval between two events
  • Causality

While they do disagree on these:

  • Time of an event
  • Space of an event
  • Order of events

However, disagreeing on these factors does not mean they are wrong, both are right.

That means that if I have three events: Event A, Event B, Event C. They can take place in this order: A, B, C. However, it was explained that they can also take place in the order: C, B, A.

My confusion lies in two questions:

  1. How can the order of events be C, B, A if we assume that event B was caused by event A, and event C was caused by event B, then wouldn't the order of event be forced to be the same every time due to causality?

  2. How can observers disagree on the order of events and we don't notice? I am having problems visualizing how this could apply to the real world? Is it just at a microscopic scale so we can't really notice the change of events?

I am a beginner in the topic of special relativity so I apologize for any lack of understanding on the subject.

Best Answer

I am a beginner in the topic of special relativity so I apologize for any lack of understanding on the subject.

I can't improve on Samuel's comment except to expand a little bit, in light of your comment above, on what special relativity describes. It is a more sophisticated method (and accurate description) of physical phenomenona in 4 D spacetime. But, although for example, this site is packed with apparent paradox after apparent paradox based on this new, better explanation, such as the one you brought up about the ordering of events, they all turn out to have explanations that do not contravene any existing physical laws that we previously accepted, other than the mixing of space and time that SR allows for.

SR did permit the discovery and explanation of lots of new ideas and observation, but they fit in with what we previously established, again once we accept the SR postulates.

enter image description here

In the diagram the interval AB is 'time-like'; i.e., there is a frame of reference in which events A and B occur at the same location in space, separated only by occurring at different times. If A precedes B in that frame, then A precedes B in all frames. It is hypothetically possible for matter (or information) to travel from A to B, so there can be a causal relationship (with A the cause and B the effect).

The interval AC in the diagram is 'space-like'; i.e., there is a frame of reference in which events A and C occur simultaneously, separated only in space. There are also frames in which A precedes C (as shown) and frames in which C precedes A. If it were possible for a cause-and-effect relationship to exist between events A and C, then paradoxes of causality would result. For example, if A was the cause, and C the effect, then there would be frames of reference in which the effect preceded the cause. Although this in itself won't give rise to a paradox, one can show that faster than light signals can be sent back into one's own past. A causal paradox can then be constructed by sending the signal if and only if no signal was received previously.

Image Source and Extract: Causality and SR Wikipedia

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