Relativity - problem of simultaneity

[conradcook]

Relativity -- problem of simultaneity

I wrote a basic outline of relativity on my blog. I think I got it right, as far as it goes:

wp.me/p2ukOd-D

--As I understand it, relativity says there is no *preferred* sequencing of events. Two events can be considered to be simultaneous, or one can be considered to happen before the other, or vice versa, depending on your frame of reference.

The more I thought about this, the more I wondered:

Can't the time distance between the event and the beginning of the Universe be measured objectively? Does that not make room for a notionally objective observational frame of reference, albeit one no human observer could occupy?

Or have I just misunderstood the implications of the theory of relativity?


Conrad.

 

[PeterDonis]

As I understand it, relativity says there is no *preferred* sequencing of events. Two events can be considered to be simultaneous, or one can be considered to happen before the other, or vice versa, depending on your frame of reference.

This is only true for events that are spacelike separated--in other words, there is some frame of reference in which they are simultaneous. For events that are timelike or null separated, the order of occurrence is invariant; it's the same for all observers. A pair of events is timelike separated if there is some observer who experiences both events, i.e., they both lie on a single observer's worldline. A pair of events is null separated if there is some light ray that passes through both.

Can't the time distance between the event and the beginning of the Universe be measured objectively?

There is a way to assign a "time distance" between, say, the Earth at this instant and the Big Bang; the usual term is "proper time". But those two events are timelike separated--they have to be, because they both lie on the same worldline (that of the Earth--we are idealizing the "Earth" here as existing back to the Big Bang, actually we would have to pick some particular point within the Earth and keep track of it all the way back). So their time ordering is frame invariant.

 

[conradcook]

Peter,

I grew up reading books on relativity -- popular books -- and have never heard of spacelike or timelike separation.

I'm googling around.

Can you draw out the difference between timelike and null separation? It seems to me the cosmic background radiation means that, at least notionally, there could be a light ray passing between the Big Bang and Earth-2012.

-----

The larger question I'm having is, if we can assign a proper time to Earth-6/5/2012 and to Andromeda-[the same temporal distance from the Big Bang], does that not establish an objective frame of reference in which correct sequencing of events is unambiguous?

Conrad.

 

[PeterDonis]

I grew up reading books on relativity -- popular books -- and have never heard of spacelike or timelike separation.

Wow. Even popular books should be at least acquainting you with those terms, since they're very basic in relativity. I guess this is another illustration of why it's never a good idea to start with popular books if you really want to learn about a scientific theory. I would recommend a good textbook: my favorite is Taylor-Wheeler's Spacetime Physics to start with.

For a quick way to visualize timelike, null, and spacelike separation, take a sheet of graph paper and draw two axes: a horizontal axis for space, x, and a vertical axis for time, t. The x-axis is an example of a spacelike line; the t axis is an example of a timelike line. A line moving up and to the right at 45 degrees is an example of a null line: a possible path for a light ray. (We are using units in which the speed of light is 1, so x and t have the same units: for example, years and light-years, or meters and "light-meters", the time it takes light to travel 1 meter.)

In fact, once you've drawn the 45 degree lines, you should be able to convince yourself that they separate spacetime, the thing you are drawing the graph of, into three sections: the "past", which is the portion below the origin and between the 45 degree lines that go down to the left and right; the "future", which is the portion above the origin and between the 45 degree lines that go up to the left and right; and "elsewhere", the region to the left and right of the origin and between the 45 degree lines. The origin is timelike separated from every event (a point on the graph is an "event") in the past and future, spacelike separated from every event in "elsewhere". and null separated from every event on the 45 degree lines themselves.

I should emphasize that this graph is not meant to represent the universe: it's just a small piece of spacetime around a chosen event (such as Earth right now), in a particular frame in which a chosen object (like the Earth) is at rest, so its worldline is the t-axis.

Can you draw out the difference between timelike and null separation? It seems to me the cosmic background radiation means that, at least notionally, there could be a light ray passing between the Big Bang and Earth-2012.

The CMBR doesn't come from the Big Bang. It comes from a few hundred thousand years after the Big Bang. The Big Bang itself is timelike separated from every event after it.

The larger question I'm having is, if we can assign a proper time to Earth-6/5/2012 and to Andromeda-[the same temporal distance from the Big Bang], does that not establish an objective frame of reference in which correct sequencing of events is unambiguous?

It establishes a frame of reference which can be used to assign an unambiguous time ordering to any pair of events, with one proviso: events which lie on the same "surface of constant time" (which will be any pair of events, such as Earth and Andromeda, that have experienced the same proper time since the Big Bang) will have the same time assigned to them, so they will not be "ordered".

However, to say that this sequencing of events is "correct" is too strong: there are other frames of reference which are equally valid, and in which the ordering of some pairs of spacelike separated events would be different.

In fact, strictly speaking, we on Earth, ourselves, are in one of those other frames. Strictly speaking, the frame I described above, which is called the "comoving" frame, is a frame in which observers at rest see the universe as homogeneous and isotropic; it looks the same in all directions, and it looks the same from every point in space. We on Earth do not see that; we see a large dipole anisotropy in the CMBR, for example, which indicates that we are not at rest in the "comoving" frame. So the time ordering we would assign to some pairs of spacelike separated events would be different than the ordering a "comoving" observer passing Earth right now would assign. Also, the proper time the Earth (the idealized Earth, in the sense I described in my previous post) has experienced since the Big Bang is slightly different than the proper time experienced since the Big Bang by a "comoving" observer passing Earth right now.

 

[stevendaryl]

Can't the time distance between the event and the beginning of the Universe be measured objectively? Does that not make room for a notionally objective observational frame of reference, albeit one no human observer could occupy?

Or have I just misunderstood the implications of the theory of relativity?

Relativity doesn't say that there is no way to pick a preferred frame, it just says that the (local) laws of physics are frame-independent. The Big Bang produced a bunch of radiation going in all directions. In one frame of reference, this radiation is isotropic (the same in all directions). In another frame of reference it is anisotropic, the radiation looks more intense in one direction than another. You can use this background radiation to single out a reference frame. That doesn't violate relativity, because you can use any frame of reference to compute how the radiation propagates; the laws of physics governing the radiation are the same for every frame.

This has to do with the way that "laws of physics" work. You have some initial state of the universe. You apply the laws of physics to get the state at a later time. The laws themselves don't make a distinction between reference frames. But the initial state may very well look different in different frames.

 

[harrylin]

[..] --As I understand it, relativity says there is no *preferred* sequencing of events. Two events can be considered to be simultaneous, or one can be considered to happen before the other, or vice versa, depending on your frame of reference[..]

As Peter tried to clarify, the sequence of events is only "relative" or depending on the chosen reference system if the time that separates the events is small enough and the distance large enough. If, as established from one reference system, a light signal can travel from the one place to the other in the time between the events, then this will be so according to all systems. Causality demands that this is so (imagine that the signal sets off a bomb blast!). The sequence is then "absolute" (also: "outside of the light cone" - https://en.wikipedia.org/wiki/Light_cone).

Possibly the first paper in which this was explained was the following (starting from p.42):
https://en.wikisource.org/wiki/The_Evolution_of_Space_and_Time

PS: The first comment on your page cannot be disproved. Your last claim is disputed, both implicitly in the above-mentioned paper and explicitly in recent times by some interpretations of quantum mechanics. We can only say that as we think that nothing substantial will be able to go faster than (or even as fast as) light, we have no reason to believe that warp drive will be possible one day.

 

[conradcook]

Ah, I know about light cones; I guess that's a diagrammatic form of space/time/lightlike separation.

Very interesting discussion. I'm following it diligently. Thanks to all.Conrad.