For the sake of discussion, let's say that Mars is exactly 5 light-minutes away and that Earth and Mars are moving with the exact same velocity so that special relativistic effects are irrelevant. Let's also assume that clocks on Earth and Mars are synchronized so that if a laser is pulsed on Mars towards Earth at 4:00 it is detected on Earth at 4:05. Would a person on Earth at 4:05 say that a laser is pulsing on Mars now, or that it pulsed on Mars 5 minutes ago? When speaking about Mars in the real world it seems that people would say "a laser pulsed on mars five minutes ago." However, it's also clear that if our senses were finely attuned enough to detect things over astronomical distances, it would appear that the laser is pulsing on Mars at 4:05 on Earth, at 4:05 a Earthling would say "a laser is pulsing on mars now." So which interpretation of now is correct?

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    $\begingroup$ There is no fact of the matter about 'now.' Simultaneity is not preserved under Lorentz boost. Things that happen at the same 'now' in one frame, happen at different 'nows' in another. The more precise statement that the Earthling could make is that in a certain reference frame, the state of the electromagnetic field (AKA the laser light) at some point (t,x) is [....] $\endgroup$ – Kevin Driscoll Nov 10 '15 at 7:02
  • $\begingroup$ Let's rephrase this as a Galilean question, then, where the speed of light in the relevant reference frame is c. $\endgroup$ – Dargscisyhp Nov 10 '15 at 7:07
  • $\begingroup$ You could then try and calculate what the state of the field was at point(t', x') some time in the past, say on Mars 5 minutes ago. It can be true both that the state at (t, x) is [....] and the state at (t', x') is [.....]. There is no disagreement about 'now' in this picture. $\endgroup$ – Kevin Driscoll Nov 10 '15 at 7:07

A physicist, me for example, identifies events by choosing a set of coordinates. For example I have a clock that I use to record time and a ruler that I can choose to measure distance. This allows me to set up some coordinates $(t, x, y, z)$ so I can assign every event to some point in my coordinate system.

If I received a laser pulse from Mars at 16:05 then I assign my reception of the laser to the event (4:05, 0, 0, 0). By inference (since I can't measure it) I assign the transmission of the pulse to (4:00, 5 light minutes, 0, 0). This makes the proper time between the two events zero, which is consistent with my knowledge of relativity.

So, assuming I'm a reasonably typical Earthling, an Earthling would not say a laser is pulsing on Mars now at 4:05.

While this is a somewhat facile argument, it does illustrate an important point. Any observer can set up a coordinate system of whatever form they find convenient, then they can use this coordinate system to identify hypersurfaces with constant time (technically this is known as foliation). Events can be identified as simultaneous if they lie on the same hypersurface.

But, and it's a very very important but, this foliation is observer dependant. A different observer using a different coordinate system would not foliate spacetime in the same way and events that are simultaneous in my coordinate system will (in general) not be simultaneous in other coordinate systems. This makes the word now less than useful in relativity. The only way all observers everywhere will agree that two events are simultaneous is if they happen at the same spacetime point i.e. at the same time in the same place.

  • $\begingroup$ Is it philosophically uncontroversial to say things like "that star has probably already gone supernova, but the light hasn't yet reached us". I mean, can we really assert that it already happened, or do things rather unfold when we get informed about them? Is there any sense in saying that "it's already this or that way and the light is on its way, but we don't know what happened yet"? $\endgroup$ – isarandi Nov 11 '15 at 17:24
  • $\begingroup$ @isarandi: yes. The supernova won't unexplode because I didn't detect it. $\endgroup$ – John Rennie Nov 11 '15 at 17:49
  • $\begingroup$ I don't mean it that way of course. I don't mean things changing retroactively. But before having even the theoretical access to the fact whether the supernova exploded or not, can we say it already "happened"? In what sense has it happened if no possible implications (but really absolutely none) of that fact have reached us thus far? $\endgroup$ – isarandi Nov 11 '15 at 19:57

A space train leaves Mars at 14:00pm and arrives on Earth at 19:45. The train moves at 0.001C and has 40Km of length. How long will it take for the whole train to arrive on Earth?
- Disregard re-entry and friction.

Nobody on Earth will say the train is leaving mars now. Same thing with the light, just it moves faster and is smaller than the train above.

We see the laser arriving on Earth at 4:05, but since we know it is 5 light-minutes away, we know it pulsed from mars 5 minutes ago.

An analogous thing would happen if the sun were to go supernova at once (lets say the romulans from 2009's Star Treck arrived just a couple hours ago). We would only see it 8 minutes later, but we know the sun is 8 light minutes away. So our last thought would not be:

The sun is going supernova right now.

  • $\begingroup$ @JohnKugelman It was an assumption. you are right, removed. $\endgroup$ – Mindwin Nov 10 '15 at 20:01

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