Confused about some aspects of GR

[John Stanly]

Hey all,

GR has just been explained to me in a lecture and I'm a little confused about a few things. I've been running through a few scenarios in my head and I don't see how they can occur without a paradox.

One scenario is if you have two spaceships traveling parallel to each other at relativistic speeds in opposite directions a large distance away from one another, both with light clocks visible to the other. From my understanding, if one spaceship views the other spaceship's light clock it will see fewer ticks than on their own light clock. But if the other spaceship was doing the same thing they too would notice the other spaceship going slower.

For arguments sake, let's say that both spaceships believe that for every 10 ticks of the other spaceship's clock, their clock ticks 20 times. To me, this fits all of the constraints of GR, but it doesn't make sense to me then how both spaceships could be going slower than the other.

Could someone just clarify this for me?

Thanks,
John

 

[ModusPwnd]

It doesn't make sense to most people. At least, not at first. But that is how we observe nature to operate. In the end nature is under no mandate to make sense to us, as disturbing as that may be.

 

[John Stanly]

Is there an aspect of GR, such as relativity of simultaneity etc., that explains these observations well?

 

[Vorde]

Not really, except the first (second?) postulate of relativity: all inertial frames are equally valid. If you try to understand the mathematics (which really only needs high school algebra but won't feel complete without a thorough treatment with calculus/basic linear algebra) you'll see a proof that this happens.

The problem is that even though relativity makes complete sense, it goes against the (incorrect) laws by which our common sense perceives to be true, the only real way to truly feel comfortable with GR/SR is to either change your common sense completely (if that is possible) or understand the mathematics and be comfortable with your knowledge that mathematical truth is truth.

EDIT: It's worth mentioning that the math always works out so that if the two spaceships ever meet, either the same amount of time will have passed between the two or both will agree that one ship experienced more time than the other. It's only in these cases when you are observing two objects that are separated in space (what card-carrying physicists call a space-like separation) that seeming paradoxes can occur.

 

[harrylin]

Hey all,

GR has just been explained to me in a lecture and I'm a little confused about a few things. [..]
One scenario is if you have two spaceships traveling parallel to each other at relativistic speeds in opposite directions a large distance away from one another, both with light clocks visible to the other. From my understanding, if one spaceship views the other spaceship's light clock it will see fewer ticks than on their own light clock. But if the other spaceship was doing the same thing they too would notice the other spaceship going slower.

For arguments sake, let's say that both spaceships believe that for every 10 ticks of the other spaceship's clock, their clock ticks 20 times. To me, this fits all of the constraints of GR, but it doesn't make sense to me then how both spaceships could be going slower than the other.

Could someone just clarify this for me?

Thanks,
John

Hi John,
Welcome to physicsforums!

First of all, you don't need GR for that; SR suffices - that simplifies matters a lot.

Second, the basic thing to understand is the very first item that is discussed in Einstein's first main paper on this topic: the spaceships interpret distant time differently and even set distant clocks differently.

[EDIT: I now see that you set up your particular example such that at first sight this doesn't matter - thus I expand on my last remark, see further after the small print].

You can read it here:

http://www.fourmilab.ch/etexts/einstein/specrel/www/

The introduction is useful, especially section I.1: Definition of Simultaneity.
As a consequence, different "frames" disagree about distant simultaneity, and this definition affects their time dilation calculations. See also:
http://www.bartleby.com/173/9.html

It would be a self contradiction if "both spaceship [clocks] could be going slower than the other" (I suppose that you didn't mean both spaceships! ).

Better: "The clocks of the other spaceship appear to go slower than your own clocks".

For most people that clarifies matters, but in a parallel thread it is remarked that also that shorthand description can lead to misunderstanding. So here also a much longer, hopefully fully correct phrasing (due to its length possibly difficult to grasp and impractical for normal discussions):

"If you set up a standard inertial reference system in which your spaceship is at rest, then according to that system the clocks that are in rest in the other spaceship tick slower than the clocks that are at rest in your spaceship".

Now, in your example the Doppler effect and directionality play a main role.
Your "if you have two spaceships traveling parallel to each" is likely much more ambiguous than you thought. For if you assume that you are in rest, then the light that you receive at a straight angle from the other ship is supposed to have propagated at a straight angle. However, if you assume that you are moving (the other ship's perspective), then those same light rays are supposed to have propagated under an angle (aberration), and thus you should add a Doppler effect to your reconstruction of what happened according to that perspective.

 

[harrylin]

[..]
The problem is that even though relativity makes complete sense, it goes against the (incorrect) laws by which our common sense perceives to be true, the only real way to truly feel comfortable with GR/SR is to either change your common sense completely (if that is possible) or understand the mathematics and be comfortable with your knowledge that mathematical truth is truth.[..]

Not in my experience. At least for SR (and the little that I know of GR), a good way to feel truly comfortable with SR/GR for me was to adapt my common sense to the mathematics (but regretfully, this has not been possible with QM...).

 

[Fredrik]

GR has just been explained to me in a lecture and I'm a little confused about a few things. I've been running through a few scenarios in my head and I don't see how they can occur without a paradox.

One scenario is if you have two spaceships traveling parallel to each other at relativistic speeds in opposite directions a large distance away from one another, both with light clocks visible to the other. From my understanding, if one spaceship views the other spaceship's light clock it will see fewer ticks than on their own light clock. But if the other spaceship was doing the same thing they too would notice the other spaceship going slower.

For arguments sake, let's say that both spaceships believe that for every 10 ticks of the other spaceship's clock, their clock ticks 20 times. To me, this fits all of the constraints of GR, but it doesn't make sense to me then how both spaceships could be going slower than the other.

When we say that A "views" B's clock as slow, what we really mean is that the coordinate system that we (by convention) associate with A's motion, assigns time coordinates to events on B's world line that increase faster than the numbers displayed by B's clock.

Similarly, when we say that B "views" A's clock as slow, we mean that the coordinate system that we (by the same convention) associate with B's motion, assigns time coordinates to events on A's world line that increase faster than the numbers displayed by A's clock.

This is why the two statements can't be immediately dismissed as a contradiction. They are statements about assignments made by two different coordinate systems.

By the way, GR is mainly about the relationship between the metric of spacetime and the matter content of spacetime. The issue you're asking about is as much an issue in Minkowski spacetime (the spacetime of SR) as in any other, so there's no reason to consider any other spacetime here. This is a typical SR problem.