# Have scientists ever experimentally proved the Andromeda paradox-like events? [closed]

We all know that a light year is of the order of 1016 metres and all the objects in the space are beyond a light year.

So the Andromeda paradox should give considerable difference in time while observing an event happening even for a shorter distance like Alpha Centauri observed by a stationary observer and an observer moving (10-15 m/s) in the direction that points to the place of the event (Alpha Centauri in this case).

That being the case this paradox can be easily verified and can be used for helping people realize the effects of the non intuitive relativity.

But I haven't heard of this paradox until I dug up more deeper to know about relativity. So I was wondering if there is any problem in my thinking

Edit: From what you guys say this is what I understand. Both the observers record the event (happening at say alpha centauri) at the same time. And the time difference between the observers is not much because they are close together and the relative velocity between them is also very small compared to speed of light. While recording the event, if the moving observer understands relativity, he knows that w.r.t him the event is happening at a time frame that is earlier to his time frame. So when he adjusts this time so that it coincides with the time frame that the stationary observer recorded the event, he will find the distance of the event to be contracted. Have I understood it right?

## closed as unclear what you're asking by WillO, Diracology, Cosmas Zachos, CuriousOne, Peter Shor Jul 14 '16 at 20:42

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• Comments are not for extended discussion; this conversation has been moved to chat. – David Z Jul 16 '16 at 10:58

No, this is not a thing that can be directly observed -- for several reasons.

First, in order to observe a difference, some concrete event would have to happen out at Alpha Centauri, which can be observed here with sufficient accuracy that the two observers can even form concrete impressions about when it happened. That's not a commonplace occurrence over astronomical distances.

If we have two observers with a relative speed of 100 km/h, whose time coordinates agree on Earth, their time coordinates at Alpha Centauri will differ by less than a microsecond. A comparison event in the Andromeda Galaxy (roughly a million times farther away) will still need to be pinpointable to better than about a second in order to get any clear difference. Even supernova collapses are not that quick -- neutrinos observed from the SN1987A collapse were spread out over more than ten times that.

(Hmm, there are pulsars in the Magellanic Clouds whose beeps may qualify. But if we're doing the experiment in order convince a skeptic, then we'd need to argue that the sending of a beep is an "event", which can get murky because the event is defined by the output ray from the pulsar pointing towards earth. Does that even mean the same in different coordinate systems? (Answer: Yes it does, but we'd need to provide a skeptic with an argument that makes this more certain than the common-sense conviction that simultaneity is absolute.))

Second, relativity predicts that the two observers agree that they both observed the event at the same time -- just like good old common sense says. Their only difference in opinion is that they disagree about how far away Alpha Centauri was when the event happened, and therefore compute that the event must have happened different amounts of time ago.

This means that their disagreement is not really about direct observations, but about the result of computations they make under the assumptions that relativity already works, more or less.

If we want a direct contradiction between our observers we would have to do something like radar measurements -- each observer sends a light pulse off towards Alpha Centauri; by some freak accident the two pulses arrive there at the same event and bounce back towards earth; the two observers see their pulses arrive just as they pass each other. But in order for them to draw any direct conclusions from that, they would need to have had their small mutual velocity continuously for all the eight years it took for the pulses to bounce back. Which means that both of them are flying around in spaceships rather than following Earth -- which means that this is science fiction rather than an experiment that can actually be done on these scales.

• A supernova can be timed quite nicely. Or see nasa.gov/mission_pages/hubble/science/star-v1.html for a variable star that played a crucial role in the history of astronomy. – CuriousOne Jul 14 '16 at 19:35
• Relativity is in fact all about the coordinates that different observers assign to different events. If we observe the computations, we are observing those assignments, and thus directly observing the predictions of relativity. – WillO Jul 14 '16 at 23:20
• I am not trying to question relativity, my question is that if I am about to conduct an experiment with two sensors instead of two physical human observers in the setup I have mentioned in the question that is sensing a cosmological event happening far away, Will I get a considerable difference in the time of the event recorded by the sensors or am I missing something? – Shravan Muralidharan M Jul 15 '16 at 5:18
• @ShravanMuralidharanM: The point I'm trying to make is that there's no such thing as a "sensor" that directly detects simultaneity of events far away. Your sensors can at best record light signals from the far-away event, and those light signals will (eventually) reach the two sensors simultaneously. The observers merely differ in how they interpret their more-or-less identical (up to doppler shifts, which is a local effect anyway) observations. – Henning Makholm Jul 15 '16 at 8:31
• @ShravanMuralidharanM: Yes, you should take Henning's last comment seriously. This is exactly the point. In this instance, relativity makes a prediction not about what the detectors will show, but about how people will interpret them. One way to test that prediction is to observe the calculations people make, but you rejected that when I suggested it earlier. So what sort of test do you propose? – WillO Jul 15 '16 at 12:43

• @WillO: However, that much of a difference corresponds to a $\gamma$ of about $1.2$, which says your two sensors have a mutual speed of $>0.5c$. The "Andromeda Paradox" is usually presented in popular sources as being about observers that move at about walking speed. If one actually does the calculations for that situation, the difference in the distances to Andromeda ends up being on the order of one light-second ... – Henning Makholm Jul 15 '16 at 13:41