- #1
GRDixon
- 249
- 0
If the fixed stars/galaxies did not exist, would there be a twin paradox?
atyy said:What do you mean by fixed stars?
GRDixon said:All things physical, except for the twins and the rocketship.
atyy said:The twin paradox would not exist without the Minkowski metric.
Why not ? as atyy has said it's inherent in SR.If the fixed stars/galaxies did not exist, would there be a twin paradox?
GRDixon said:If the fixed stars/galaxies did not exist, would there be a twin paradox?
bcrowell said:In GR, there is a twin paradox in an empty universe.
atyy said:Do you think that would be true if we took pure GR with just the metric and matter field equations, and we're not allowed to put twins who don't contribute to spacetime curvature on top of a fixed curved spacetime?
bcrowell said:I'm not quite clear on what you're saying here. When you refer to a fixed curved spacetime, do you mean a prior geometry (which GR assumes does not exist), or a cosmological solution (but one with no matter or radiation in it, as required by the thought experiment)? In standard GR, the twins don't have any significant gravitational effect on one another; they're test particles, to a very good approximation.
atyy said:I meant no prior geometry, which means no test particles.
bcrowell said:Sorry, I still don't follow you. Can you explain more what you had in mind?
atyy said:A universe with test particles has prior geometry, since the test particles propagate on a fixed background.
bcrowell said:I don't think this is right. A test particle just means a particle that has a very small mass-energy, so it has a negligible effect on the spacetime curvature, and follows geodesics that would have been the same if the particle hadn't been there. A prior geometry means one that is set by the theory itself, rather than in a self-consistent way because it just happens to be a solution to the field equations. Newtonian physics has a prior geometry, which is Galilean.
atyy said:But if the mass of the test particle has been neglected, then the geometry was not determined self consistently.
bcrowell said:You could say it's self-consistent in the limit of small mass.
Yes, and the Minkowski metric is a valid solution of the EFE for no mass. Although what you would really want is to solve a GR 3 body problem (home twin, rocket twin, rocket exhaust).atyy said:The twin paradox would not exist without the Minkowski metric.
DaleSpam said:Yes, and the Minkowski metric is a valid solution of the EFE for no mass. Although what you would really want is to solve a GR 3 body problem (home twin, rocket twin, rocket exhaust).
DaleSpam said:Yes, and the Minkowski metric is a valid solution of the EFE for no mass. Although what you would really want is to solve a GR 3 body problem (home twin, rocket twin, rocket exhaust).
bcrowell said:Which are we talking about in the last half-dozen posts, GR or Brans-Dicke?
atyy said:I had GR in mind.
bcrowell said:Hmm...I don't get it. Why would gravity be important for understanding the twin paradox in standard relativity?
The twin paradox is a thought experiment in which one twin stays on Earth while the other travels in a high-speed spaceship and returns to Earth. Due to time dilation, the traveling twin would experience less time than the twin who stayed on Earth, causing them to appear younger.
In general relativity, gravity is not a force but rather a curvature of spacetime. The presence of gravity can cause time to flow at different rates at different points, which can affect the aging process of the twins in the paradox.
Gravity is important in solving the twin paradox because it helps explain the difference in aging between the twins. Without taking gravity into account, the paradox cannot be fully understood.
No, gravity alone cannot solve the twin paradox. Other factors, such as acceleration and velocity, also play a role in the paradox. It is the combination of these factors that leads to the time dilation effect.
Understanding the twin paradox and gravity can help in the development of accurate space travel and navigation systems. It can also aid in the study of the effects of gravity on the aging process and help us better understand the nature of our universe.