It seems to me that the answer is yes, first of all because it is impossible in principle to use Einstein's definition of simultaneity in such cases since signals cannot pass from the event to us, and secondly because spatial points or objects at such events are moving away from us at superluminal velocities, and the Lorentz formula gives imaginary number results for the time shift at such velocities. But can anything more be said about this situation?

  • $\begingroup$ how about assigning the time to be the same as proper time passed for particle comoving with average galaxy from big bang to the event? $\endgroup$
    – Umaxo
    Apr 5, 2020 at 19:19
  • $\begingroup$ There is no absolute "when" for distant events, visible or not, since time coordinates are different for different reference frames. But in many cases you can choose a spacetime foliation that assigns meaningful time coordinates even to events outside the visible universe. $\endgroup$
    – Cuspy Code
    Apr 5, 2020 at 19:26
  • $\begingroup$ Just looked at wikipedia on "foliation" hoping for a simplified explanation--no such thing there! Can you give me any hint on how this might work? I know special relativity and the bare bones of general but not much beyond that... $\endgroup$ Apr 5, 2020 at 19:32
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    $\begingroup$ You may find these articles by Davis & Lineweaver helpful: Expanding Confusion: common misconceptions of cosmological horizons and the superluminal expansion of the Universe, and the less technical version originally published in Scientific American. $\endgroup$
    – PM 2Ring
    Apr 6, 2020 at 1:18
  • $\begingroup$ @scottef Yeah, the wikipedia article on foliation is terribly obscure. You can think of a foliation as a way of carving up spacetime into 3-dimensional slices, each of which has a constant $t$ (time coordinate). This can be done in different ways even in flat Minkowski spacetime, since different reference frames synchronize clocks differently. $\endgroup$
    – Cuspy Code
    Apr 6, 2020 at 10:55

1 Answer 1


They are not completely meaningless, but they can be meaningless as is shown in the particular case of quantum entanglement.

I must correct one thing you say. Events are not moving at superluminal, or indeed any other, velocity. An event is, by definition, a point in spacetime $(t,\mathbf x)$. As it has particular time, it cannot be moving.

Strictly speaking, an event outside the light cone is only defined later, when a signal from the event reaches ourselves. However, in so far as physics is deterministic (as is all classical physics) the definition is unique, and in effect, determines the "when" of event (in given coordinates, usually, but not always determined from Einstein's definition of simultaneity). Since the "when" of the event is ultimately uniquely determined (in given coordinates) it may be taken to be always meaningful.

This changes in quantum theory, since it is not deterministic. Hence most of the confusion concerning entanglement. The correlation between Alice and Bob's measurements only becomes meaningful later, when the results of their measurements are brought together. In this case it in genuinely not meaningful to ask which measurement takes place first, and it is not possible to say that one measurement altered the other when the events were outside the light cone.

The above applies in special relativity. In general relativity we do not use Einstein's definition of simultaneity. Instead we use "cosmic time",

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In 1923 Hermann Weyl argued that in order to discuss the distant we should base our ideas, in so far as is possible, on what we can observe in our own neighbourhood. Weyl noted that we define synchronous slices of space in our own neighbourhood of the universe, and assumed that it is possible to extend this definition by defining a synchronous slice in a region centred on a point at the edge of our neighbourhood. An observer can use the radar method to define synchronous surfaces in his neighbourhood with respect to his own proper time, as we do when we define time in the Earth frame (figure 13.3, top left). Earth time may be synchronised to solar time, measured according to the Earth’s orbit and applicable to planetary orbits (figure 13.3, top right). We may further synchronise to galactic time (figure 13.3, bottom left), where the radar method is not viable, but in which the time of an event can be estimated from the distance travelled by light. Cosmic time assumes that it is meaningful to think of a time parameter synchronised across galaxies and groups of galaxies (figure 13.3, bottom right).

Thus Einstein's definition of simultaneity only applies in our immediate neighbourhood. Cosmic time may be considered as the proper time of a galaxy as measured from the initial singularity. This does give a meaningful definition of simultaneity, quite independent of Einstein's definition which applies only in the context of special relativity.

As a final remark, when galaxies are described as "moving at superluminal velocities" this is a very misleading statement. The coordinate velocity may be greater than the speed of light, but coordinate quantities are not real physical quantities. Light moving away from us at the position of the galaxies has an even greater coordinate velocity, and it is quite inaccurate to say that the galaxy has a superluminal velocity. Cosmologists are far more likely to use comoving coordinates, in which the galaxy has zero coordinate velocity! We cannot apply Lorentz transform to coordinates in general relativity.

Consider two ships with equal velocity moving due east at different latitudes. On a Mercator projection one ship will appear to move faster than the other. But this is a property of the map, not a property of the ships. The same is true for recession velocities greater than lightspeed.

  • $\begingroup$ Ah, good point about events; I should instead say that any object at that event is moving away at superluminal speed, and corrected my question to reflect this. But then I'm still a little puzzled by what you say; you say that the "when" can always be uniquely determined and meaningful, but also that "it is only defined later, when a signal from the event reaches us." But since no signal ever reaches us, doesn't that mean its time can never be defined? Help me reconcile these claims here. $\endgroup$ Apr 5, 2020 at 19:29
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    $\begingroup$ I don't think the quantum issue has anything to do with this; A's measurement or B's can come out as first or second as the case may be depending on your reference frame (the weird thing is that it can be either, and so we can't say that one caused the other). The question about events beyond the visible universe is different, since it seems to me we can't even use any reference frame to talk about them, unless "Cuspy Code"'s remark about "foliations" helps us here, but I don't know enough to grasp this concept yet. $\endgroup$ Apr 5, 2020 at 19:37
  • $\begingroup$ Sorry, I have done my trick of answering the text rather than the original question. I will add to my answer. $\endgroup$ Apr 5, 2020 at 19:40
  • $\begingroup$ What book is the added material from? It is very helpful and well-selected, thank you! $\endgroup$ Apr 5, 2020 at 20:28
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    $\begingroup$ @Edouard, cosmic time is not a unique definition of time (any more than Einstein synchroneity is unique), but it is a completely accepted concept, used in standard cosmology, described in numerous established text books, and used in any Friedmann cosmology (including $\Lambda$-CDM). $\endgroup$ Apr 6, 2020 at 5:43

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