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I have been reading a bit on Einstein’s special theory of relativity. It seems clear to me from the theory that two observers do not necessarily agree on what events occur simultaneously. However I have difficulty understanding how that relates with the concept of now.

Let’s consider that in my reference frame I am holding my phone typing this question. Suppose that in my reference frame there is someone approaching me from a far distance at a speed close to that of light. Then that person would find my future self to be simultaneous with his/her now (let’s say it’s a future self that is asleep because it’s night time).

I do not know how to interpret this. I am not yet in that state. It seems that I will eventually become that future self but that is not what I am yet. Should I interpret this as simply saying that experiments carried out by that person will reveal my future self to be simultaneous with the person BUT NOT to mean that the future self exists yet (experiments such as obtaining the distance between him/herself and my future self and dividing it by the speed of light)? In other words should I interpret this as saying that the laws of physics only give you what is simultaneous IN your reference frame but not necessarily what is happening in the moment (in the way that it is the case that I am typing on my phone at this moment and not sleeping). And if I bite that bullet it seems I’m forced to consider that the person I say is approaching me might only be doing that in my reference frame and not in his.

The question itself is a bit confusing as well because according to relativity the moment depends on the observer. I guess the question might be a bit more philosophical than scientific but if there is any light you can shed on the problem it would be very appreciated.

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It seems clear to me from the theory that two observers do not necessarily agree on what events occur simultaneously. However I have difficulty understanding how that relates with the concept of now.

The concept of “now” is not a physical concept, it is a philosophical concept typically associated with the metaphysical ontology known as presentism. From a physics perspective the concept of now is neither theoretically necessary nor experimentally measurable.

If you have some particular affinity for the concept then you are free to use it. You can identify any spacelike surface you choose and call it “now” without fear that some experiment could disagree. You could choose a surface of simultaneity for some specific observer, but it is not mandatory.

It is also possible to say that “now” is a purely local concept so that “now” has meaning for some observer but there is no sense in which a given observer’s “now” coordinates with other locations.

Because it is a philosophical concept you will find a lot of disagreement on it, and none of it is important for physics. If it bothers you, then discard it, or if you like it then keep it. Just recognize that it is not physical.

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  • $\begingroup$ From a physical perspective "now" is only well defined when it is also "here". That may be a philosophical concept, but we use this "here-now" as the foundation of most of our theories. $\endgroup$ Commented Oct 7, 2022 at 21:48
  • $\begingroup$ @FlatterMann we use events in our theories, but there is no need to identify any particular event as “here-now”. There is no harm in doing so, but it certainly is not any sort of foundation of our theories $\endgroup$
    – Dale
    Commented Oct 8, 2022 at 0:18
  • $\begingroup$ Here-now is the coordinate origin of the local observer. It is, whether we like it or not, the most important point in the universe. It's the only place where we can ever be. This is what we mean when we say "all physics is local". I do agree that it is a limiting perspective, but we are, for better or for worse, the prisoners of the here and the now. $\endgroup$ Commented Oct 8, 2022 at 0:27
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    $\begingroup$ @FlatterMann every event in the manifold can be the focal point of a light cone. steemitimages.com/0x0/http://212.201.48.1/course/fall02/c210101/… Please just stop. This is tiresome $\endgroup$
    – Dale
    Commented Oct 8, 2022 at 11:15
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    $\begingroup$ @FlatterMann I am not deliberately misunderstanding. I am pointing out your mistake. You falsely claim that the “here-now” is “the foundation of most of our theories”. There is nothing in our theories that makes an event on my worldline any more foundational than an event on a planet eighty million light years away. I can choose to distinguish an event on my worldline as “here-now”, but it is not required by any current theory, nor is any current theory founded on doing so. The concept of events is foundational, not one specific event called here-now $\endgroup$
    – Dale
    Commented Oct 8, 2022 at 12:36
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There is something you don't mention explicitly in your question, but your unease may be connected with it: a question whether relativity of simultaneity challenges our notion of causality.

The interesting thing is: it does not. If an event B is triggered by an event A then there is no transformation that would lead to a presentation where that happens out of order.


For instance, let's say there is a setup where a light source B will emit a pulse of light at the point in time that a photosensitive cell strapped to B registers a pulse of light coming from source A.

You can transform to a coordinate system such that the distance between the sources A and B is length contracted in terms of that coordinate system, so that the time for the light to traverse the distance is correspondingly shorter, but there is a limit to that. There are only transformations that make that duration shorter, no transformation is available that would reverse the order.

Relativity of simultaneity presents a degree of freedom that leaves causality unaffected.



Here is another comparison.

The following is not a complete description of relativity of simultaneity (something essential is left out), but it may help to open a window.

Let's say that you are in the 18th century, exchanging letters with someone on another continent. For the sake of the thought demonstration: the ships on which the letters make the journey do not report how many days it takes them to travel from west to east, and from east to west.

It could be the same amount of days, but maybe there are predominent east-to-west blowing winds which would result in the east-to-west journey taking less days than the west-to-east journey.

Let's say the arrival time of the letters is the only information you have to try and synchronize calenders with the person you are exchanging letters with.

The simplest approach is that you take the round trip time, and you divide that by 2. If the round trip time is 60 days the a single journey could be just half that, 30, and on that assumption you could decide on calender synchronization.

But: you don't know.

It could be that the actual distribution of the round trip time is 20-40. The interesting thing is: the fact that you don't know does not present an obstacle. As long as everybody doing business with each other is using the same convention no discrepancy will be encountered.


Relativity of simultaneity in terms of special relativity goes a step further than the above. In the story above there is the detail: "the ships on which the letters make the journey do not report how many days it takes them"

In the special relativity flavor of relativity of simultaneity there is intrinsically no way of measuring how the round trip time breaks down.

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  • $\begingroup$ I don’t quite get the second example sorry. When you say all I have to work with is the arrival time do you mean the time that the letters sent by the other person arrives? Or the time that the letter I send arrives. If it’s the former, how does that let me synchronize my calendar with that of the other person? Also, my problem with the relativity of simultaneity isn’t causality, it’s the idea of how my past, present and future states are more than just theoretical things but rather are just as real as I am. $\endgroup$ Commented Oct 7, 2022 at 21:03
  • $\begingroup$ @DavidOkogbenin I don't know what you mean by "theoretical". On some level you sound like somebody who is still trying to push past solipsism. Physics is no help with that. Physics takes absolutely everything that can influence us and that can be influenced by us as "real" in the most naive sense of the word. We start with absolute trust in the reality of the universe. That is the reason why physics is so successful. It doesn't gaze at its own navel all the time. $\endgroup$ Commented Oct 8, 2022 at 23:24
  • $\begingroup$ @FlatterMann I made a mistake in my comment. I included my present state in the comment. I should not have. I meant to say “ it’s the idea of how my past and future states are more than just theoretical things but rather are just as real as I am.“ I definitely believe that things other than myself exist so I am not a solipsist. My problem is seeing how multiple states (past, present, future) of things can all be equally real. Having said that, your comment is making some things start to make sense to me so thank you for that. $\endgroup$ Commented Oct 9, 2022 at 13:57
  • $\begingroup$ @DavidOkogbenin My point was entirely that naive reasoning about "what is real" does not work in physics. There is a real physical question here, of course. "What is physical reality?" does not have a simple answer, neither in special and general relativity or in quantum mechanics. I would suggest that we have to make peace with there being no such thing as "one physical reality", or that if there is, it's incredibly narrow. Different observers can and will see the universe from different angles, some of which are incompatible from a classical physics perspective. Classical physics is wrong... $\endgroup$ Commented Oct 9, 2022 at 21:14
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What it means is that our common sense notion of simultaneity is rather meaningless when we consider events that are spacelike separated.

For you, your local 'now' is a particular point in spacetime at which you exist, and its time coordinate is continually increasing at a fixed rate in your frame- if you like, you can think of it as a series of successive events at the spatial location you occupy.

If someone elsewhere is travelling towards you, they will also have a local 'now' which is a point in spacetime travelling forward through time at a fixed rate in their frame.

Each of you has a plane of simultaneity, but that simply means a slice through spacetime with common t coordinate. In the frame of a person moving relative to you, your horizontal slice through spacetime is a sloping one, with a t' coordinate that varies all along your direction of travel.

As a consequence, you and the traveller will label distant events with different time coordinates, but each event has only one location in spacetime- it is just that you and the traveller use different coordinates to label it.

To make that more concrete, imagine you are standing still and you have two friends, one walking away from you to the right and one walking towards you from the right. At a suitably great distance, the time corresponding to 'now' for each of you might vary by a year, so you might consider it to be October 2022 at that distance point, while one friend will consider it to be October 2023 and the other October 2021.

Now suppose there is a planet at that distant point, on which there are three people, one stationary relative to you, one walking towards you and one walking away, so the three people on the distant planet share the same relative movements, and hence the same three frames as you and the two people here on Earth. All three of the distant people share the same 'now'. What they disagree about is the date of 'now'. If the person who is stationary relative to you considers the date 'now' to be October 2022 (ie simultaneous with your current 'now') because their time is synched with yours, then the other two people will consult their calendars, and one will say it is October 2021 while the other will say it is October 2023.

You will see some philosophers argue that presentism (which is the idea that things only exist in the present) cannot be true, owing to the relativity of simultaneity, but that is a specious argument. The three people on the distant planet can all exist at a common 'now'- they just label it differently.

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  • $\begingroup$ You wouldn’t believe I asked this question hoping you’d be one of the people to answer. Alright, you’re right that my local ‘now’ is where I exist. But while someone on the planet can check the time on their calendar and find that the time where I’m at is 2023, that isn’t the time where I’m actually at. I am at 2022. 2023 is the time I will be at eventually. But it doesn’t exist yet (not to me at least). How do I make sense of this? The three people people exist now in my reference frame. But they disagree on what my now is. $\endgroup$ Commented Oct 7, 2022 at 20:33
  • $\begingroup$ @DavidOkogbenin They don't disagree on what your "now" is. They only disagree on how the "nows" of different people are being ordered, or, to be more precise, there is no such ordering in relativity while in the Galilean world there is. $\endgroup$ Commented Oct 7, 2022 at 21:51
  • $\begingroup$ @FlatterMann I suppose so. But they disagree on the what distance events are simultaneous with their now, is it not? $\endgroup$ Commented Oct 7, 2022 at 23:31
  • $\begingroup$ @DavidOkogbenin Yes, there is a loose order that defines causality, but whatever is not causally related (and the way I understand it, most events in the universe are not), can not be viewed consistently by different observers. The hard part, for me, is to view event order that is not causal as "unimportant", rather than "inconsistent". $\endgroup$ Commented Oct 8, 2022 at 0:32
  • $\begingroup$ @Flatterman I see. I also have difficulty understanding why it seems that time is changing. As though we are moving from one space time event to the other. At the very least it seems to make our now spacetime event more special than our past and future space time events (because the past has already happened and the future is yet to happen, as such it seems like there is a special “happening” event that keeps changing). $\endgroup$ Commented Oct 8, 2022 at 17:29

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