How can Relativity talk about simultaneity planes when the events are actually quantum in nature so they are indetermined ? How can you say that if you walk on the street with 1m/s you are simultaneous with a certain event A in Andromeda, and if you start running with 2m/s you become simultaneous with an event B many years in the future of A (that is an effect of A) in Andromeda, when there is no causality in the first place at the most fundamental level ? So isn't this concept of simultaneity a little suspicious ?
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$\begingroup$ Curiously, the most precise clocks, especially the ones that were used to test relativity to the highest precision, are all based on quantum mechanics... $\endgroup$– CuriousOneMay 7, 2015 at 2:51
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3 Answers
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How can you say that if you walk on the street with 1m/s you are simultaneous with a certain event A in Andromeda, and if you start running with 2m/s you become simultaneous with an event B many years in the future of A (that is an effect of A) in Andromeda, when there is no causality in the first place at the most fundamental level ? So isn't this concept of simultaneity a little suspicious ?
This is solved in Einstein's 1905 paper using the idea of an Einstein synchronization procedure. This allows us to define a coordinate system in a frame of reference with a plane of simultaneity, in special relativity. Basically, you start at some time a long time in the past, send out a bunch of clocks and keep them synchronized, and that's one coordinate system. If you do this for many coordinate systems and then bring the clocks all back to the same point some time later to analyze the data, you'll find that, indeed, in the frame where you were walking at 2m/s you were simultaneous with events many years in the future of Andromeda, compared with the frame where you were walking at 0m/s.
This synchronization spells out exactly what is physical and what is not in the situation you describe. No quantum necessary.
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$\begingroup$ I'm a bit of an Einstein fan, but I have to say that Einstein clock synchronization contains a flaw wherein the travel time to the mirror is deemed to be the same as the travel time back. There's [google.co.uk/#q=einstein+clock+synchronization+flaw](various articles) about this. $\endgroup$ May 6, 2015 at 16:43
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$\begingroup$ @Abc2000ro Exactly - because the notion of simultaneity of two spacelike separated events has no inherent physical meaning. The physical meaning comes about when you establish real, physical clocks, and then collect the data at some point. $\endgroup$– user12029May 6, 2015 at 18:36
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$\begingroup$ @JohnDuffield All the articles I get are about the constancy of the speed of light? Yes, if you don't assume the length of a meter (SI convention) is constant, you run into all sorts of problems. $\endgroup$– user12029May 6, 2015 at 18:40
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$\begingroup$ I think Poincare should get some of the credit. $\endgroup$ May 6, 2015 at 20:35
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When you discuss simultaneity in special relativity you are talking about classical events (locations and times together) that are simultaneous in a frame. A frame extends outwards in space and time. When you change your speed you find out there is a totally different frame at which you are now at rest.
Your old frame (which extended throughout space and time) considered old you and Andromeda event A to happen at the same time.
Your new frame (which also extends throughout space and time) considers new you and Andromeda event B to happen at the same time.
Each of these frames always had totally different opinions about which events in Andromeda were considered simultaneous with events on Earth. All that happened is you switched from one frame to another. It's like having a new favorite sports team and realizing you need to learn new songs or deal with a different game schedule. Those songs and game schedules were there all along, it's you that switched to a different system.
There are other ways to assign ideas of simultaneity such as radar time. Radar time looks at the average of 1) your own clock reading when you send a signal to the event and 2) your own clock reading when you receive a signal to the event. It reduces to the regular special relativity simultaneity convention if you move inertially during that whole interval (i.e. you don't change frames). If you do move a tiny bit for a small time and then go back to normal, it only changes the times assigned to events a little bit. So it might be a generalization you like.
It has nothing to do with quantum mechanics. That said, sometimes people refer to phrases such as "at the same time" in quantum mechanics when the "time" in question is actually a pure hypothetical time back when you choose which experimental setup to realize, this happens when people discuss the uncertainty principle for example.
If you are studying Special Relativity, it's best just to consider an event to be a region of spacetime where you can assign both a location and a time to the best precision you can. You can't assign locations or times perfectly, so a whole region will get the same label in any actual practice. But the idealization would include mathematical points in a 4D space. And the niceness of that is that everyone can use the same idealization even if in practice one person does assign more precise numbers than someone else. So the idealization can be a nice thing to study.
It might also help if you recall that Special Relativity is basically older than quantum mechanics, no one knew about the uncertainty principle or the Schrödinger equation in 1905.
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$\begingroup$ I'm not interested in Special Relativity. I'm interested in how the Universe is. What can this conflict between simultaneity and quantum indeterminism tell us about how the universe actually is ? For example, does General Relativity get rid of this problematic concept ? $\endgroup$ May 6, 2015 at 17:47
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1$\begingroup$ @Abc2000ro I see no conflict. Different theories define the word "simultaneous" differently. If you want to use words to communicate with people you have to be clear what definitions you use. When people discuss quantum indeterminism they use the words "at the same time" to refer to a hypothetical time e.g. when they went shopping for equipment or applied for a grant or set up new equipment on the lab table. When someone refers to simultaneity in the theory of special relativity they are usually referring to an entire frame. The frame (by definition) won't change the speed it walks at. $\endgroup$– TimaeusMay 6, 2015 at 17:55
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$\begingroup$ @Abc2000ro As for General Relativity, it is called General exactly because it gets rid of global frames. Because they aren't necessary, not because they are problematic with quantum mechanics. In fact we know how to do quantum mechanics with special relativity just fine but no one knows how to do quantum theory fully in general relativity. I'd suggest learning special relativity if you want to understand quantum theory. $\endgroup$– TimaeusMay 6, 2015 at 17:59
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$\begingroup$ I'm a little surprised that simultaneity in SR is frame dependent; are you asserting that it matters which frame I use when two different events occur at the same place and at the same time? Surely frame dependence of simultaneity is dependent on the classical (Newtonian) background of absolute space and absolute time? $\endgroup$ May 6, 2015 at 20:29
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1$\begingroup$ Hi @MoziburUllah, in the terminology anyone is using if they say "relativity of simultaneity", events are defined to be simultaneous if events $(t_1,x_1,y_1,z_1)$ and $(t_2,x_2,y_2,z_2)$ have $t_1=t_2$, which is of course not a lorentz-invariant concept, hence "relativity of simultaneity". $\endgroup$– user12029May 7, 2015 at 1:21
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Simultaneity of two events relies on the two events occurring at the same time and at the same place; it is in fact the bare minimum that a notion of simultaneity has to satisfy and is derived from the classical motion; moreover in this picture the older classical notion of simultaneity no longer even makes sense; ie it's frame dependent.
The classical situation relied on a background picture of absolute time and space; so it was meaningful in this picture to talk about two events that occurred at the same time but in two different places; it turned out this picture had to be altered.
answered May 6, 2015 at 16:36
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$\begingroup$ If you have the same time and the same place, that is called an identity of events. The word event in special relativity is simply a fancy name for specifying all four coordinates $(t,x,y,z)$. It's a generalization of location or of time to the four dimensional spacetime. We needed a name for that, we called the "points" in 4D spacetime "events". Every frame agrees when two events are identical, but two frames do not agree that event A and event B are simultaneous when they are not identical. $\endgroup$– TimaeusMay 7, 2015 at 1:31
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$\begingroup$ It's only possible in Newtonian space and time for two events to be simultaneous at the same time but at different spatial distances. $\endgroup$ May 7, 2015 at 12:55
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$\begingroup$ In SR that spatial seperation has to be put to zero. $\endgroup$ May 7, 2015 at 12:57
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$\begingroup$ Every textbook I've seen in the last 20 years defines the words the way I do. They usually have a whole section on the "relativity of simultaneity" where they say simultaneity is frame dependant in SR. There are usually pictures too. Showing you what the different t axis and x axis look like in different frames. For instance they make equal angles with the line x=ct and if you boost in the x direction the positive x axis rotates towards the line x=ct and the positive t axis also rotates towards the line x=ct and that's what a rotation in the xt plane in Minkowski space looks like. $\endgroup$– TimaeusMay 7, 2015 at 13:06
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$\begingroup$ Regarding spatial separation being zero, we already have the idea of identity or equality of events, making another word that means the same thing is pointless. And in a textbook you do want to teach people about the differences between Galilean relativity and Special relativity so you to tell them that "having the same time coordinate" is now frame dependant. And the word used for "having the same time coordinate" is simultaneous, as usual. We are arguing about definitions and semantics here. But I can't imagine any reason anyone would even want to use your alleged definitions. $\endgroup$– TimaeusMay 7, 2015 at 13:12