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I have been studying causality (specifically why there is no such thing as a simultaneous instant of time across all observers) recently and I keep hearing references to the Andromeda paradox. Can anyone tell me what it is and how it is resolved?

I've tried reading what Wikipedia says about it, but I could really use someone's explanation.

Edit
Ok, after reading the related question, now I'd like to know does this imply there is some sort of privileged reference frame, in which there exists absolute velocity and absolute time? I ask because the answer for the other question seemed to indicate that the actions seem to be at different points of simultaneity but that in fact the person not moving is getting it right. But this seems strange to me because if we accelerated our galaxy to a different speed, we would still perceive our stationary observer as being right even though they'd see something different than before the acceleration.

So who is right? In what frame can we be sure that our present is Andromeda's present?

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Hi Dan. Welcome to Physics.SE. Please provide some reference on your study (just for some clarification) ;-) –  Waffle's Crazy Peanut May 2 '13 at 14:46
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Related question physics.stackexchange.com/questions/21975/… –  twistor59 May 2 '13 at 15:17
    
@Val and Dan this is not the place for arguments. Val, if you don't want to answer the question then don't, if someone else does, let them. You should know that no good can come of calling people stupid. Dan, sometime people are unfair, leave it alone so it doesn't escalate. No more fighting in the comments, please. –  Jim May 2 '13 at 16:12
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A number of comments deleted. Indicating, clearly what you do and do not already know is part of asking a good question not only on Stack Exchange or the whole internet, but in all of life. Providing links for the aid of possible answers who may know related fields is also a good practice. –  dmckee May 2 '13 at 17:04
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Oh dear this paradox again. It's only confusing because it assumes planes of simultaneity are important, whereas in fact they are (both physically and philosophically) artificial constructs that don't mean anything. There is no such thing as "the present" in relativity. There is "past," "future," and "spacelike separated." –  Chris White May 2 '13 at 22:50

2 Answers 2

up vote 6 down vote accepted

There can be at least two different flavors of paradoxes. In one, a result such as 2+2=5 is proved, and the problem must be either incorrect reasoning or a set of assumptions that was invalid. In the other type, exemplified by the EPR paradox, the correct result of an argument is so surprising that it seems like it must be a mistake.

Based on the description in the quote by Penrose, the Andromeda paradox is of the latter type. It is simply a dramatized example of the relativity of simultaneity, which is contrary to our intuition based on everyday life. In Penrose's presentation, the dramatization includes a summary of an imaginary dialog between the two observers, who seem to be confused because they don't understand relativity and expect simultaneity to be absolute. Penrose also comments that logical consistency is retained because events in Andromeda can only be learned about on Earth much later.

The paradox is both trivial and nontrivial. It's trivial because it's simply a description of how the relativity of simultaneity works, and therefore it doesn't require any complicated arguments to resolve. It's nontrivial because the relativity of simultaneity is a surprising and difficult concept when you encounter it for the first time.

It may help if we note that this would be the 2+2=5 type of paradox if it were possible to transmit signals instantaneously in relativity. Then the two observers would be disagreeing about something that they could easily check by faster-than-light communication. One of them would find out that he was wrong, and his frame of reference would have been found to be invalid -- which contradicts the basic assumptions of relativity.

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As Wikipedia authros put in Minkowski_diagram: 'Due to the principle of relativity the question of "who is right" has no answer and does not make sense.' –  Val May 5 '13 at 19:29
    
I very much like how you've written this answer, but it seems to imply at the end that there exists a privileged reference frame whose time and velocity are absolute (right) over the rest of them. Is that solely in the existence of instantaneous communication? –  Dan II May 6 '13 at 15:45
    
@Dan: Yes, it's solely if you assume instantaneous communication. If you assume instantaneous communication, the whole structure of SR breaks down. –  Ben Crowell May 6 '13 at 22:03

I put my negative comment in the from of the answer. Here are the very basics of the simultaneity implications (or causes) of relativity:

According to the special theory of relativity, it is impossible to say in an absolute sense whether two distinct events occur at the same time if those events are separated in space, such as a car crash in London and another in New York. The question of whether the events are simultaneous is relative: in some reference frames the two accidents may happen at the same time, in other frames (in a different state of motion relative to the events) the crash in London may occur first, and in still other frames the New York crash may occur first. However, if the two events are causally connected ("event A causes event B"), the causal order is preserved (i.e. "event A precedes event B") in all frames of reference.

enter image description here

Events A, B, and C occur in different order depending on the motion of the observer. The white line represents a plane of simultaneity being moved from the past to the future.

If we imagine one reference frame assigns precisely the same time to two events that are at different points in space, a reference frame that is moving relative to the first will generally assign different times to the two events. This is illustrated in the ladder paradox, a thought experiment which uses the example of a ladder moving at high speed through a garage.

I see that this paradox is a basis of Einstein's theory. It is used to explain rather than to confuse. Once you understand that your daily experience of simultaneity is wrong, that there is no simultaneity between the spatially-separated places, then you should wonder: "where is paradox?". But, I guess the internet-banned people are already asking another question: "what is the ladder paradox?". Why do you ask for Andromeda paradox but not for explanation of velocity-related simultaneity? What is the question?

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+1 for the amazing graphic. –  Dan II May 7 '13 at 14:22

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