B Which Watch Will Have Slower Time: Object 1 or Object 2?

[PeroK]

Edwin Hubble said universe is expanding at the speed faster than light. Galaxy at 14 billion light years are going far away from Earth at speed of light. Some galaxies farther than 14 billion light years cannot be seen by human as light will not reach to earth.

Why it will happen if you all say its only "C" my above question?

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References:
https://www.space.com/33306-how-does-the-universe-expand-faster-than-light.html

https://www.loc.gov/rr/scitech/mysteries/universe.html

https://phys.org/news/2015-02-fast-universe.html

Is this thread about time dilation or the expanding universe?

One thing at a time, please!

 

[Dale]

Why it will happen if you all say its only "C" my above question?

The second postulate states that the speed of light in vacuum is c in any inertial frame. There is no inertial frame that contains both the Earth and a galaxy 14 billion ly away.

The equivalent statement in GR is that light always travels on null geodesics. In inertial frames this statement reduces to the usual second postulate, but in non inertial frames it remains valid.

I strongly recommend that you stick with SR for now

 

[Ibix]

Why it will happen if you all say its only "C" my above question?

Because the concept of velocity of a distant object is a rather ambiguous one in curved spacetime. Invariably, you will find that the velocity of light as measured by a local observer is c. Distant observers can measure more or less any value, but it has no physical significance.

You are currently struggling with special relativity. You need to get that understood before you try seriously grappling with general relativity.

 

[phinds]

Edwin Hubble said universe is expanding at the speed faster than light.

To add to what others have already pointed out, you are confusing recession velocity, which is unlimited because nothing is "moving" in the sense you think it is, with actual proper motion which is where the limit of c applies. I agree w/ Dale. Let's drop consideration of the expanding universe (GR) since you apparently haven't studied it yet, and stick with special relativity.

EDIT: I see ibix beat me to it.

 

[nitsuj]

time dilatation happen, which watch will have slowed down time. Please help me understand the practical result if we have such case.

The practical result is called differential aging. To be specific, it's not really correct to say "slowed down", it's accurate to say one clock measured more time than the other. Some conceptualize this as a path; a distance measured.

 

[nitsuj]

Edwin Hubble said universe is expanding at the speed faster than light. Galaxy at 14 billion light years are going far away from Earth at speed of light. Some galaxies farther than 14 billion light years cannot be seen by human as light will not reach to earth.

Why it will happen if you all say its only "C" my above question?

The universe is allowed too! That is spacetime "itself" that, cumulatively over vast distances sum to recession velocities greater than c.

The stuff "within" obeys c.

imo it's a fair point the op raised regarding recession velocity, and seems a common consideration when learning about c. The distinction is vast & easily understood and "important".

 

[Ibix]

The practical result is called differential aging.

No - differential aging is what you get in a frame-invariant experiment like the twin paradox, where two clocks meet up, part, and meet up again. Time dilation is an effect between two inertial frames where clocks can only meet at most once.

While you can view it in terms of the same "interval" based analysis as is often used for the twin paradox, you need more than just distance. The two worldlines are at an angle to each other and their own planes of "now" are orthogonal to the lines. Thus they differ over what counts as "the same time" except when they meet and the distance from the meeting point "now" differs.

 

[nitsuj]

No - differential aging is what you get in a frame-invariant experiment like the twin paradox, where two clocks meet up, part, and meet up again. Time dilation is an effect between two inertial frames where clocks can only meet at most once.

Was presuming the OP was meaning the clocks are compared (at rest to each other) after time dilation, worded as "practical result".

Why must the clocks meet up at the start? I appreciate they need to be synchronized, but don't follow why they must "meet up" at the start for it to be called differential aging.

Err..never mind, I see it now. You said it in the first sentence, frame invariant scenario.