How is the concept of simultaneity affected by relativity?

[IntuitioN]

I think I asked this a while back but I don't think I worded my question properly... so here it is:

Imagine if you're in space traveling at a speed in which the time dilation is 1:4 (ie from Earth's frame of ref, 1 hour pass in spaceship for every 4 hours pass on earth).

Suppose that we have a clock on Earth and a clock in the spaceship. Both says 12pm.

The two parties agreed to look at each other at 1pm in accordance to the Earth time.

So at 1pm on Earth time the person on Earth looks at the spaceship but on the spaceship the clock says 12:15pm

For the person in the spaceship to look at the Earth at 1pm Earth time, he must look at the Earth at 4pm spaceship time.

How is this possible? I have googled it but it didn't come up with anything useful.

 

[ramollari]

Implicitly you are saying this: to the Earth observer the spaceship clocks are running slower, but by symmetry to the spaceship observer the Earth clocks are also running slower.
The truth is that the spaceship clocks are running slower than the Earth clocks. This means that to the spaceship passenger the Earth clocks are running faster, so that when it is 12.15 on the spaceship, on the Earth it will be 1.00 (faster clock on Earth).

 

[Tamsco]

Well, relativity says it is possible for different observers to observe things in reverse order as long as they are spacelike sperated, which means no information traveleing at the speed of light from one could affect the other. Also keep in mind when you say one observer looks at another's clock, you have to take into account how long it will take for the light to travel.

Look up the twin paradox.

 

[Doc Al]

Imagine if you're in space traveling at a speed in which the time dilation is 1:4 (ie from Earth's frame of ref, 1 hour pass in spaceship for every 4 hours pass on earth).

So far, so good. Realize that time dilation is symmetric: from the spaceship frame, 1 hour passes on Earth for every 4 hours that pass on the ship.

Suppose that we have a clock on Earth and a clock in the spaceship. Both says 12pm.

This is ambiguous. Both say 12pm... but when? Realize if one frame observes both clocks to read 12pm at the same time, the other frame will disagree.

For simplicity, let's assume that the spaceship passes close to the Earth at the exact moment that both clocks read 12pm. This is OK, since the clocks will be at the same place at the same time.

The two parties agreed to look at each other at 1pm in accordance to the Earth time.

Again, the clocks are not synchronized so this is ambiguous.

So at 1pm on Earth time the person on Earth looks at the spaceship but on the spaceship the clock says 12:15pm

Right. From the Earth frame when the Earth clock reads 1pm the Earth observer will say that the spaceship clock will read 12:15pm. The spaceship observer will disagree.

For the person in the spaceship to look at the Earth at 1pm Earth time, he must look at the Earth at 4pm spaceship time.

Right. From the spaceship frame, when the Earth clock reads 1pm the spaceship clock will read 4pm. The Earth observers will disagree.

How is this possible? I have googled it but it didn't come up with anything useful.

It's possible because different frames will disagree about how clocks are synchronized. To understand relativistic effects, you must consider all the relativistic effects together, not just time dilation. We've had this discussion before: https://www.physicsforums.com/showpost.php?p=502102&postcount=4

 

[Doc Al]

Implicitly you are saying this: to the Earth observer the spaceship clocks are running slower, but by symmetry to the spaceship observer the Earth clocks are also running slower.

This is true; time dilation is symmetric.

The truth is that the spaceship clocks are running slower than the Earth clocks.

This is not true. What's so special about the spaceship clocks that time dilation applies to them but not Earth clocks?

This means that to the spaceship passenger the Earth clocks are running faster, so that when it is 12.15 on the spaceship, on the Earth it will be 1.00 (faster clock on Earth).

Incorrect. To the spaceship passenger, the Earth clocks run slow!

 

[Hurkyl]

How is this possible?

It's a demonstration of relativity of simultaneity. Different frames generally disagree on statements like "These two events happened at the same time".

Earth's frame says "Earth's clock reading 1 PM happened at the same time as the spaceship's clock reading 12:15 PM".

The spaceship's frame disagrees. It says "Earth's clock reading 1 PM happened at the same time as the spaceship'sc lock reading 4 PM".

Other statements by the spaceship's frame that may be of interest are:

"Earth's clock reading 12:15 PM happened at the same time as the spaceship's clock reading 1 PM".
"Earth's clock reading 12:03:45 PM happened at the same time as the spaceship's clock reading 12:15 PM".