Events in Relativity: Can Simultaneous Occurrences Exist?

[Salman2]

I have a question about the concept of an 'event' in relativity theory.

Can an 'event' occur simultaneously at two spatial locations, A & B where (A=x1,y1,z1, B=x2,y2,z2), AT THE SAME MOMENT IN TIME ? For example, suppose two observers at locations A and B not far separated. Can they both experience the same 'event' at the same moment in time ?

 

[PeterDonis]

Can an 'event' occur simultaneously at two spatial locations, A & B where (A=x1,y1,z1, B=x2,y2,z2), AT THE SAME MOMENT IN TIME ?

No. The definition of an event is a single point in spacetime--that means a single spatial location at a single instant of time.

 

[WannabeNewton]

Note that simultaneity is frame dependent, it has no absolute meaning. So to continue, we must pick some frame $O$ and talk about simultaneous events with respect to $O$. Given that, certainly two events can have different spatial locations but the same time as represented in $O$ - for example the observer associated with $O$ might see two bombs go off at the same time but at two different locations in space. However, it makes no sense to say a single event can have two different spatial locations as represented in $O$ because the event gets a unique coordinate representation in $O$.

 

[Salman2]

.. it makes no sense to say a single event can have two different spatial locations as represented in $O$

Thanks for the comment, but, does not a quantum of energy as a wave enter the two different spatial locations of the two slits in the double-slit experiment as a single event ?

Edit: Suppose we assume the two slits are in the frame of reference O of the quantum wave, and not from the frame of the structure into which the slits are cut from.

 

[Salman2]

No. The definition of an event is a single point in spacetime--that means a single spatial location at a single instant of time.

OK thanks.

But, just asking...how would relativity theory be modified if an event was defined as: an event is defined as a phenomenon that occurs simultaneously at two spatial locations, A & B where (A=x1,y1,z1, B=x2,y2,z2), AT THE SAME MOMENT IN TIME ?

 

[Mentz114]

OK thanks.

But, just asking...how would relativity theory be modified if an event was defined as: an event is defined as a phenomenon that occurs simultaneously at two spatial locations, A & B where (A=x1,y1,z1, B=x2,y2,z2), AT THE SAME MOMENT IN TIME ?

Add another time dimension. There was a theory proposed once that had 3 timelike and 3 spacelike dimensions and it explains the double-slit very well. But it is otherwise intolerably weird.

 

[WannabeNewton]

Thanks for the comment, but, does not a quantum of energy as a wave enter the two different spatial locations of the two slits in the double-slit experiment as a single event ?

I am not sure about how events work in quantum theory but the notion of an event, as represented in an observer's frame, only makes sense when the observer actually makes a measurement of the position and time of the event. For the double-slit experiment, a measurement of position would cause the state vector to take on a definite eigenstate of the position operator although I don't know if this has the same meaning as making a measurement in special relativity so don't take my word for it.

 

[PeterDonis]

does not a quantum of energy as a wave enter the two different spatial locations of the two slits in the double-slit experiment as a single event ?

No. There are two separate events, each of which has an amplitude associated with it. (At least, that's true if "event" is defined in the standard way. See my next post for a comment about that.)

 

[PeterDonis]

how would relativity theory be modified if an event was defined as: an event is defined as a phenomenon that occurs simultaneously at two spatial locations, A & B where (A=x1,y1,z1, B=x2,y2,z2), AT THE SAME MOMENT IN TIME ?

I don't see how this modifies the theory of relativity; it just modifies the definition of an English word, "event". Relativity as a theory is not done in English; it is done in math. Redefining the word "event" doesn't change the math at all. In the math, you still have two spatial locations at some instant of time.

 

[Nugatory]

OK thanks.

But, just asking...how would relativity theory be modified if an event was defined as: an event is defined as a phenomenon that occurs simultaneously at two spatial locations, A & B where (A=x1,y1,z1, B=x2,y2,z2), AT THE SAME MOMENT IN TIME ?

Google around for Einstein's thought experiment involving the train and the relativity of simultaneity (hereis one reasonable-looking link high in Google's page rank).

If you think through that example you'll see that there's no way of defining an event, or anything else for that matter, in terms of things that happen at the same moment in time but at different spatial locations. There cannot be any generally agreed-upon definition of "at the same moment of time".

 

[Salman2]

Add another time dimension. There was a theory proposed once that had 3 timelike and 3 spacelike dimensions and it explains the double-slit very well. But it is otherwise intolerably weird.

Thanks. Do you have a reference for a publication on this theory ?