Can velocity be determined in flat space?

[Chris Miller]

The problem is that you and Earth disagree about what "at the same time as i arrive at the star, on Earth" means. So what happens on Earth is that you pass Earth at time zero, then what your frame calls the same time as you arriving at the star happens some tiny fraction of a second later, then what Earth's frame calls the same time as you arriving at the star happens a hundred years later. So what you mean by "while I was travelling" isn't the same period as what Earth would call it.
That seems excessive. One Planck length is $10^{-35}$m and 100ly is $10^{18}$m. That means you need a gamma factor of about $10^{53}$ for the length contraction you specified. That makes the energy requirement on the order of $10^{70}$J per kilogram of spaceship, or about $10^{54}$ megatons per kilogram. Which is still absurd, but rather smaller than the $10^{400\text{-odd}}$ that you have.

Edit: ...unless you've done a full relativistic rocket calculation, carrying your fuel. In which case your answer might be plausible. I can't do that on the back of an envelope.

This v is, as others have commented, annoying. In trying to find a "narrative" for SR that I can conceive of, I've taken parameters to the extreme.

Using the equation,

1/sqrt(1-(v²/c²))= p
so
v = sqrt( c² * (1 - (1/p²)
where
p=$9E0A634641C0A69F1EB8293A18CEAB7A000000000000 // Planck lengths in 100 lightyears
and
c= $11DE784A M/sec
I get
v=$11DE7849.FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE88E9659DAA M/sec

or p=
.FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEB024F2C521FD454EB07E8C818A955B70B8F3A73EC210DC98C8956DCA9705617ED752C7C
(as a percentage of c)

Then I plug this percent (and 1 gram) into the equation
L = 1/sqrt(1 - p²)
then
KE = (L - 1)mc^{^2}

I used huge integer arithmetic for max accuracy and got all balled up in the hex decimal places (especially in square roots of small fractions) so that (ironically) my super-accurate result is garbage that's hundreds of exponential powers out. Doh. Thanks for your much simpler, and explanatory, approach. The whole no universal "now" or "while" or any other temporal conjunctions is barely sinking in. "Like Chris washes the dishes while Hennie does the laundry" makes no sense in SR? Like "What are you wearing now?" is a meaningless question in SR sexting?

I want to alter my thought experiment to:

It's 2001 on Earth when my craft passes some 100 lightyear distant (from earth) star heading toward Earth at this ridiculous v. So Earth is, to me, 1 Planck length away, and I am there in 1 Planck interval of my time. What year is it on Earth when I pass it?

Also, what year is it on Earth after I've circumnavigated the universe back to it? (assume no H)

but suspect my "when" and "after" again miss some point?

The idea that I exist in my own personal now at the center of my own universe aggravates my solipsistic bent.

 

[Dale]

The whole no universal "now" or "while" or any other temporal conjunctions is barely sinking in. "Like Chris washes the dishes while Hennie does the laundry" makes no sense in SR? Like "What are you wearing now?" is a meaningless question in SR sexting?

Those questions are incomplete. You need to specify the reference frame used. "What are you wearing now in the Earth centered inertial frame?" would be complete.

 

[PeterDonis]

"Like Chris washes the dishes while Hennie does the laundry" makes no sense in SR? Like "What are you wearing now?" is a meaningless question in SR sexting?

No. But "now" in ordinary language does not have the precise meaning that "now" in SR discussions of this point has. When you ask someone what they are wearing "now", are you really insisting on asking "what are you wearing at the exact event on your worldline that is simultaneous with mine in a particular inertial frame"? Of course not. By "now" you really mean, in more precise SR language, "at the event on your worldline when you receive this text from me". You don't care what the coordinates of that event are in any inertial frame; you just care that the person gives you an answer based on their state when they get your text. The event when they get your text will actually be timelike separated (in the extreme it could be null separated, if you were communicating directly by light signals, but texting doesn't quite work that way) from the event when you sent the text, which means that it will not be "now" in the sense of simultaneity relative to the event when you send the text in any frame whatever. But so what? That makes no difference at all in ordinary experience.

but suspect my "when" and "after" again miss some point?

Only that your use of those terms makes your specification of the scenario incomplete. "When", in reference to spatially separated events (like it being 2001 on Earth "when" you pass the star), always needs to come with a specification of a frame: in this case, what you probably meant was something like "the event at which I pass the star is simultaneous, in the Earth's rest frame, to the event of the clock striking noon, Greenwich Mean Time, in London on January 1, 2001". But you need to specify all that to make "when" meaningful. Similarly, you need to specify distances in some particular frame--for example, "at the event when I pass it, the star is 100 light years from Earth in the Earth's rest frame".

Given the specifications as I have fixed them above, the answer to your question is that the event of you reaching Earth will be at noon GMT in London on January 1, 2101, by Earth clocks, plus some very small amount of time which I haven't done the exact math to calculate.

what year is it on Earth after I've circumnavigated the universe back to it?

It depends on the circumference of the universe. Heuristically, it will be the time it takes in the Earth's rest frame for a light ray to travel the circumference of the universe, plus some small additional time which I haven't done the exact math to calculate.

The idea that I exist in my own personal now at the center of my own universe

Is not at all what we have been trying to explain. The fact that you can, in principle, adopt coordinates in which you are always at rest at the spatial origin does not mean that your choice of coordinates affects anything else. It doesn't. It certainly doesn't affect the physics of the universe or anything in it.

 

[Herman Trivilino]

The whole no universal "now" or "while" or any other temporal conjunctions is barely sinking in. "Like Chris washes the dishes while Hennie does the laundry" makes no sense in SR?

Sure it does, it's just that the frame of reference needs to be known for it to make sense.

Like "What are you wearing now?" is a meaningless question in SR sexting?

The two events (the sending and the receiving of the text message) can never occur at the same time in any frame of reference, so as long as everyone understands that, the question does make sense. Note that this has nothing to do with specifying a reference frame, so it's different from the previous example.

Consider this historical claim:

On February 6, 1952, King George VI died, and Elizabeth assumed the responsibilities of the ruling monarch.

On the morning of February 6 King George was indeed found dead in his bed in London. Had the servant who discovered him declared "The king is dead now" that would indeed have been a meaningful statement, because it was made at the same location as the discovery. It is also said that four hours later Elizabeth, vacationing in Kenya, received news of her father's death. So the question is, when did she assume duties as queen?

You might say right away, or you might say fours later, because during that four-hour period she had no way of knowing she had become queen.

So that is a dispute based solely on the delay due to the travel time of the signal.

An entirely different issue arises from the relativity of simultaneity. Since the two events (death of father, daughter becoming queen) occurred in the same rest frame, we might argue that to everyone else who is at rest in that frame of reference, the two events were simultaneous. That is, the daughter assumed the duties of queen at the instant of her father's death. The problem with that claim, however, is that to some observers in motion relative to them, she would have assumed duties before her father died! Now, we can get around that by saying that the fastest the news could have traveled is at the speed of light, so she assumed duties as queen the instant a light signal sent from the king's death bed would have arrived in Kenya. In that case all observers will agree that she assumed duties as queen after her father died.

 

[Chris Miller]

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.

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?

 

[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.

 

[Herman Trivilino]

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?

 

[Herman Trivilino]

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 ;)