Can velocity be determined in flat space?

[Ibix]

Again, thanks all for the clarifications, especially re terminology. I'm a little curious how time dilation could impact causality (i.e., effect to precede cause) in any frame of reference.

Effect never precedes cause. The Lorentz transforms guarantee this by preserving the sign of the interval between two events.

So it seems that at this extreme through-experimental ~c, where 100 years elapse in Earth's frame of reference, while only one Planck interval in mine, that in my (frame's) next milliseconds, trillions of years might elapse in earth's. And so to both of us the universe would be bigger and darker. Or does my frame's dilated time not impact Hubble's constant expansion? Because, if it did, and if the universe did become a great dark void (as someone here speculated), wouldn't that suggest some universal frame of reference?

No. Hubble's law only applies in the so-called co-moving reference frame where the universe is isotropic. You are not in that frame so your observations would not obey Hubble's Law. You would see a directionally dependent Doppler shift in the microwave background, for one.

There is no preferred reference frame. Please get that through your head. There are frames in which the maths is easier, and the co-moving frame is an example of that for our universe. It doesn't make it "right" or "real" or "absolute"; simply more convenient.

 

[Mister T]

I'm a little curious how time dilation could impact causality (i.e., effect to precede cause) in any frame of reference.

Causality is cause preceding effect. Causality violation would involve effect preceding cause, but as Ibix points out, that never happens.

It's the relativity of simultaneity, not time dilation, that sorts all this out. Two events with spacelike separation can occur in different orders in different reference frames, but those two events cannot be causally connected. That is, neither one can possibly be the cause of the other.

The queen's assumption of duties is an effect caused by the king's death. Thus the queen's assumption of duties cannot precede the king's death. If the two events had a spacelike separation, if for example they were simultaneous in their rest frame, then to some observers the effect would precede the cause.

 

[Chris Miller]

There is no preferred reference frame. Please get that through your [thick] head.

There is no universal frame of reference. Yes, I get that. I can read and trust the education of those who've stressed it for me here.

Hubble's law only applies in the so-called co-moving reference frame where the universe is isotropic. You are not in that frame so your observations would not obey Hubble's Law.

I understand that in my ~c frame the universe appears very different than from Earth's frame of reference. I meant to stop and enter now-trillions-of-years-older Earth's "co-moving" frame to see how H has changed "everyhting." Is the universe not isotropic in my ~c frame? Are you saying H-expansion does or does not operate within some reference frame? Earth's sun will certainly be long dead after a millisecond @~c. In the next second or two, would I also "see" the "end" of the universe? I looked at that MIT video game where c is slowed to a walking pace. Wondered why the sun didn't nova and die... maybe wasn't walking fast enough.Thanks, E=mc2, for clarifiying. I thought you meant the king's death and the queen's assumption of duties occurred in the same inertial frame and location, and couldn't see how they'd be ever observed in different orders.

 

[Nugatory]

I thought you meant the king's death and the queen's assumption of duties occurred in the same inertial frame and location

There are an infinite number of inertial frames and every event happens in every one of them; so the king's death and the queen's assumption of duties did happen in the same inertial frame.

 

[Chris Miller]

There are an infinite number of inertial frames and every event happens in every one of them; so the king's death and the queen's assumption of duties did happen in the same inertial frame.

but not location?

 

[jbriggs444]

but not location?

If you read #34, you will find "London" and "Kenya" mentioned. So yes, not the same location. [At least not the same location in the Earth frame].

 

[Nugatory]

but not location?

For any pair of timelike-separated events there exists an inertial reference frame in which both events happened at the same place, but no inertial reference frame in which both events happened at the same time. One of the two events will happen first, and it will be the same one in all frames.
For any pair of spacelike-separated events, there exists an inertial reference frame in which both events happened at the same time, but no inertial reference frame in which both events happened at the same place. The events will happen in different orders in different frames.

Here we have three relevant events:
1) George VI was found dead and the clock on his bedside table read 0730 GMT.
2) Elizabeth is in Kenya and her wristwatch reads (after allowing for Kenya being in a different time zone) 0730 GMT.
3) Elizabeth is in Kenya and her wristwatch reads (after allowing for Kenya being in a different time zone) 1130 GMT.
There are an infinite number of inertial reference frames, and all three events happen in all of them.

Because #1 and #2 are spacelike-separated, in some of these frames #1 happened before #2 and in others #2 happened before #1. There is one particular reference frame in which they both happened at the same time (exercise: How fast is the Earth moving in that frame?).

Because #1 and #3 are timelike-separated, there is no frame in which #1 did not happen before #3. There is one frame in which they happened at the same place (exercise: How fast is the Earth moving in that frame? You will have to make some reasonable assumption about the distance between the king's bedroom at Sandringham House and Elizabeth's location in Kenya).

#2 and #3 are also timelike-separated, so there is no frame in which #2 did not happen before #3. How fast is the Earth moving in the frame in which both of these events happened at the same place?

 

[Mister T]

There is no universal frame of reference. Yes, I get that. I can read and trust the education of those who've stressed it for me here.

But the statement immediately following seems to indicate you're not incorporating it into your worldview.

I understand that in my ~c frame the universe appears very different than from Earth's frame of reference.

If the two frames are equivalent, and indeed the universe appears different in each frame, ask yourself to describe the differences, and what measurements you could take to confirm those differences. And are those differences symmetrical?

The fact that you call one of them "~c" indicates that perhaps you don't understand that the other one could just as well be called ~c.

Earth's sun will certainly be long dead after a millisecond @~c.

No it won't. The time that elapses in the sun's rest frame between the birth and death of the sun is a proper time. Proper time is a relativistic invariant, meaning it'll be the same in all inertial frames. To an observer in inertail motion relative to it the time that elapses between those same two events will be longer than the proper time, not shorter.

It is this line of reasoning that leads to the often-misunderstood claim that moving clocks run slow. The observer moving relative to the sun would claim the sun's clock is running slow compared to clocks at rest relative to him. But note that in his rest frame the birth and death occur at different locations so the time that elapses between them is not a proper time. It's a dilated time. The observer would need two clocks, one at the location of the birth and one at the entirely different location of the death. And he would need to synchronize those clocks for his measurement of the elapsed time to have any meaning.

 

[m4r35n357]

Speeds like .6 c are usually nicer. That is large enough for all relativistic effects to be apparent, but easier for potential respondents to calculate.

I prefer 0.8. More relativity per decimal point ;)