# Relativity of simultaneity implies a universe for each reference frame?

1. Apr 4, 2010

### jaketodd

The fact that the relativity of simultaneity causes events to not happen at the same time, dependent on reference frame, seems to imply a separate universe or world for each and every thing in the universe. Different events at different times due to the relativity of simultaneity would lead to different futures. Is this true?

Thanks,

Jake

2. Apr 4, 2010

### Staff: Mentor

No. Different frames are just different ways of describing the same world.

3. Apr 4, 2010

### jaketodd

But different futures playing out... isn't that "many worlds"? How can one claim that there is one cohesive universe when within it, there are different versions of it playing out? I suppose you could say that the fact that things with different futures interact with each other implies a common place where they do that, but I don't see how all reference frames could coexist in one universe when each one has a different version of the universe. Perhaps the best description is "many worlds interacting"?

4. Apr 4, 2010

### Staff: Mentor

If you're referring to the "Many Worlds" interpretation of quantum mechanics, that is not implied by the relativity of simultaneity. Special relativity describes the structure of space-time and how observations made in different reference frames can be related--all within the same world.

5. Apr 4, 2010

### matheinste

All events occur in all reference frames. A reference frame is really only an overlay of a coordinate system on the whole universe. Two obsevers moving relative to each other assign different coordinate systems to the universe. Although what happens for one happens for all, and everyone agrees on the order in which things happen, they disagree about the where and when and to that extent you could say that the futures are in some way different.

Matheinste.

6. Apr 4, 2010

### jaketodd

Does the relativity of simultaneity apply to relative speed exclusively or are angles of trajectories also taken into account?

Also, can local variables of an object be effected by relativity such as acceleration?

Thanks again,

Jake

7. Apr 4, 2010

### matheinste

The relative speed used in special relativity calculations is the relative speed of objects or observers along the line joining them, so you need to know their relative velocities ( speed and direction ) to arrive at this value.

I am not sure what you mean by local variables.

Matheinste.

8. Apr 4, 2010

### jaketodd

And if everyone agrees on the order of things happening, then let us consider the following scenario: Two objects are moving with each other. They are separated but each movement made by one is made by the other. So they are in inertial reference frames related to each other. For another observer, they are moving. So for the third party, the two objects are moving but for the two objects, they are at rest. You said "everyone agrees on the order in which things happen." But for the two objects in inertial reference frames related to each other, there was never any movement event that happened. So, how can that quote be true? Those are events that never happened for the two objects in inertial reference frames related to each other.

9. Apr 4, 2010

### jaketodd

Well is acceleration of an object effected by relativity to other reference frames? In other words, is acceleration relative?

10. Apr 4, 2010

### Staff: Mentor

If A is the cause of B then A preceeds B in all reference frames. It is only when A and B cannot be causally related that their order is ambiguous, and if neither could be the cause of the other then their order does not matter.

11. Apr 4, 2010

### matheinste

Don't forget we are talking about relative movement. All observers agree that both frames in your scenario are moving relative to each other.

Matheinste.

12. Apr 4, 2010

### matheinste

Yes, an important clarification. My reply only took into account timelike separated events.

Matheinste.

13. Apr 4, 2010

### Staff: Mentor

That's only true for events that could be causally related, as in "event A" could have caused "event B". (Another way of saying this is that the two events are separated by a 'time-like' interval.) An example: Bob fires a torpedo (event A) that hits and blows up an asteroid (event B). Every frame agrees that the torpedo was fired before the asteroid blew up.

Events that occur far enough away from each other such that no signal could possibly connect them can be seen to occur in different order in different frames.

14. Apr 4, 2010

### jaketodd

What if two objects are 5 meters away from each other and one undergoes an acceleration due to nothing. I know that sounds weird, but I'm curious. Since there is no causal connection between those two objects (or any object) and the acceleration, then would the relativity of simultaneity not apply?

Thanks for bearing with me, guys.

Jake

15. Apr 4, 2010

### yuiop

The relativity of simultaneity still applies. The sequence of causally connected events can not be reversed by a change of reference frame and that still applies even if one event was not actually caused by the other. By causally connected we mean that the two events are connected by a timelike vector and are sufficiently close to each other that there is enough time for one event to be caused by the other, even if in practice they were not.

16. Apr 6, 2010

### jaketodd

Does relativity allow something to be in more than one place at the same time because of multiple reference frames viewing the object?

Thanks,

Jake

17. Apr 6, 2010

### Staff: Mentor

No, it doesn't.

18. Apr 6, 2010

### Staff: Mentor

To expand on this, no it doesn't, but it does allow something to have multiple coordinate labels for where it is in the different reference frames. In other words, an object is in one place at one time, but Alice may assign the place the coordinate x=6 and Bob may assign the place the coordinate x'=10. It is the same place, just different labels.

19. Apr 6, 2010

### yuiop

To expand on this even further, in relativity we do not consider spatial and time coordinates in isolation from each other. We always consider the "location" of something in terms of time AND space. In ordinary Euclidean geometry it is OK to say the coordinates of an object is (x,y,z) but in relativity the coordinates are (t,x,y,z). Now Alice might say the coordinates are (t,6,0,0) and Bob might say the coordinates of the same object are (t',10,0,0) but t does not equal t' and it turns out that $t^2-6^2-0-0 = t '^2-10^2-0-0[/tex]. In Euclidean geometry the distance between two points is [tex]\sqrt{(\Delta x^2 + \Delta y^2 + \Delta z^2)}$ using good old Pythagoras. In relativity the distance between two points is [tex]\sqrt{\Delta t^2 - (\Delta x^2 + \Delta y^2 + \Delta z^2)}[/itex]. This is called the spacetime interval and all observers obtain the same value for this quantity, no matter what their state of relative motion is.

Last edited: Apr 6, 2010
20. Apr 6, 2010

### jaketodd

Cool, thanks guys.

Jake