Length Contraction causes Time Dilation?

[harrylin]

>.<

I checked in on them, and noticed one of them saying this:

"Of course it's only 2 light years, because we measure light taking 2 years to get here from there, if it wasn't a shorter distance, we'd have to be moving FTL"...

...or you could be moving slower through time.

Then they tried to justify it by saying "Euclidean distances are the ones we have to use in normal life, so we have to use them to explain relativity too"... wut?

Uh, no, Relativity is defined as a non-euclidean geometry, you can convert results from that to a euclidean one... but you don't have to do that, last I checked, given the way hyperbolic rotations work in non-euclidean spacetime, I don't see why you would try to force it back into a totally flat geometry, am I missing some amazing benefit from doing that?

The space-coordinates of any standard reference system of special relativity (as well as of the GR-based GPS system) are Euclidean or "flat", and there is an obvious practical benefit of describing events in the units with which they are measured.

Now, it may be preferable to choose a reference system in which the visible universe as a whole is approximately in rest, and it seems that that is what you take for granted.
However, as I pointed out earlier, for special relativity (which seems to be what you are discussing here) there is no observable preference for doing so; there is no observational basis for claiming that it's "them" who are moving, and not you, or both you and them. From their perspective - if they choose a reference system that is co-moving with them - the distance between the planets is only 2 light years and it's you who suffers relativistic effects. SR thus explains how both points of view are on equal footing and it sounds as if both you and them don't fully understand that.

Note that so far nothing discussed in this thread is directly related to "explaining relativity" in the sense of "what causes it"; and that would go beyond our knowledge, as it's a matter of opinions.

Harald

PS: see also the parallel thread with similar contents:
https://www.physicsforums.com/showthread.php?t=484798

 

[Max™]

Yeah, I don't have a problem with it being 2 light years in that reference system, and yes I do tend to take for granted that such frames are not as... interesting as ones where the "background stars" are at rest.

My problem is, I know when he measures the time it takes a beam of light to cross a given distance in his frame, he's experiencing significant time dilation, so he's measuring 2 years in his frame for a beam of light to cross 640 light years in the Earth/Betelgeuse/Background frame.

It just seems... inelegant to me to ignore the understanding which can be gained from dealing with the causes of the effect he's describing, rather than simply stating them as brute realities.


More to the point, it feels like to a lie to describe a scenario purely in terms of SR, neglecting the changes which accelerated frames introduce to situations like that.

The whole thing just set off all kinds of alarm buzzers when I read over it, and the worst part was how he was presenting it to the general board crowd. When I pointed out the problems with describing it that way, to an audience which includes people with no real grasp of the subject, they began informing me I must not know what I'm talking about if I was disagreeing with him.

 

[Dale]

More to the point, it feels like to a lie to describe a scenario purely in terms of SR, neglecting the changes which accelerated frames introduce to situations like that.

Note that there is a difference between a frame and an object. In introductory relativity we like to attach frames to every object and associate every frame with some object. That often leaves students with a mistaken impression that frames must always follow some object, which is not correct. In many realistic applications the most convenient reference frame is actually the center of momentum frame, which is an inertial reference in which everything is moving, and often accelerating.

In this case it is not a lie to describe this scenario purely in terms of SR. There is no need to consider an accelerated frame at all. As long as you are neglecting gravity SR may be used regardless of whether or not one or more objects are accelerating.

 

[Max™]

Well, I said feels like, it just doesn't appeal to my sense of aesthetics I guess, how could you not love hyperbolic rotations, right?

I do understand that a frame can be attached to anything, that is generally how I look at it anyways, assigning an arbitrary godseye observer to "peek" into the frame, but I guess that tendency would make one less eager to simply go along with statements like "it's valid in my frame" without asking "but what about other frames of interest??" huh?

My biggest issue with how he phrased it was the declaration that "since I can make the distance shorter by going faster, it takes less time to get there", with the implication that there is no distortion to his motion through time, and that it is simply a matter of warping the universe into a more convenient form to get from here to Betelgeuse by 2013.

THAT is what sent me off in a tizzy, the way he was implying that moving really fast makes distances shorter, and crossing those shorter distances takes less time... which stabs at my brain trying to figure out why he would claim that without clarifying things better.

 

[Passionflower]

"since I can make the distance shorter by going faster, it takes less time to get there",

Max™ that statement is absolutely true.

Frankly I am still not convinced you fully accepted the implications of special relativity.

 

[Rap]

Naturally it isn't incorrect to say you measure/observe the universe contracting while you remain unchanged if you assume you're in an inertial frame. How can you make the assumption that you are actually in an inertial frame if you know you accelerated/will need to decelerate at the end of the journey?

An inertial frame is one that is moving at a constant velocity. It does not depend on what happened in the past, nor what is expected to happen in the future.

When you say "the universe contracting" what you are saying that certain objects in the universe are moving with respect to you and the distances between them are Lorentz contracted - according to you. Remember that according to one of those objects, you are the one who is moving and is Lorentz contracted. Similarly, the clocks on those objects appear to be ticking more slowly to you. But to them, your clock is ticking more slowly than theirs. The situation is symmetric, neither one is "right".

 

[Max™]

Max™ that statement is absolutely true.

Frankly I am still not convinced you fully accepted the implications of special relativity.

No, the distance being contracted doesn't mean you only have to cross 2 light years which would take just over 2 years at your velocity, either that statement is not true, or I am quite mistaken about special relativity.

If you crossed 640 light years fast enough that it was contracted down to 2 light years in your frame, while avoiding any time dilation strangely, and you then crossed THAT distance fast enough that you took just a little over 2 years to do so, wouldn't you then experience time dilation on THAT duration, and observe quite a bit less than 2 years during your trip?



If the 2 light years in your frame was 640 light years for a signal laser you fired on the same trajectory when you left, then your trip would take more than the 640 years required for a detector at your destination to receive the signal.


Yes, in your frame, you'd only experience/age/observe 2~ years, and claim your laser beam only crossed 2 light years.



If you then turned around and fired a reply laser while going fast enough that you again measure the beam traveling for only 2 years as it crossed 2 light years, you would return 1280+ years after you left, roughly 4 years older.


If the contraction observed from your frame meant you only took 2 years to cross that distance without any effects from time dilation, you'd arrive at Betelgeuse 638~ years before the signal laser, and you'd make it home a thousand years or so before you even left!

 

[Rap]

No, the distance being contracted doesn't mean you only have to cross 2 light years which would take just over 2 years at your velocity, either that statement is not true, or I am quite mistaken about special relativity.

It is true.

If you crossed 640 light years fast enough that it was contracted down to 2 light years in your frame, while avoiding any time dilation strangely, and you then crossed THAT distance fast enough that you took just a little over 2 years to do so, wouldn't you then experience time dilation on THAT duration, and observe quite a bit less than 2 years during your trip?

Sorry, I don't understand. Anyway, let's not suspend time dilation while keeping Lorentz contraction, it totally confuses everything.

If the 2 light years in your frame was 640 light years for a signal laser you fired on the same trajectory when you left, then your trip would take more than the 640 years required for a detector at your destination to receive the signal.

Betelguese is 640 light years away according to Earth. It takes 640 years for the light beam to travel there *according to Earth*, not according to the light beam. According to the spaceship, it is 2 light years away, and the light takes 2 years to make the trip.

If you then turned around and fired a reply laser while going fast enough that you again measure the beam traveling for only 2 years as it crossed 2 light years, you would return 1280+ years after you left, roughly 4 years older.

Right - this is the twin "paradox".

If the contraction observed from your frame meant you only took 2 years to cross that distance without any effects from time dilation, you'd arrive at Betelgeuse 638~ years before the signal laser, and you'd make it home a thousand years or so before you even left!

This is what the Earth experiences - you and a light beam leave Earth simultaneously, the light beam gets to Betelguese in 640 years, you get there in 640+ years. This is what you experience - you and a light beam leave Earth simultaneously, the light beam gets to Betelguese in 2 years, you get there in 2+ years. If you turn around and head back, along with a light beam, Earth will say that second light beam took 640 years to make the trip, got to Earth 1280+ years after you left. Earth will say you arrived back at Earth 1280++ years after you left. You will say that second light beam took 2 years to reach Earth, and you took 2+ years to get back to Earth, arriving 4++ years after you left. (Here I am using + to mean x+>x and ++ to mean x++ > x+).

The fact that you have only aged 4++ years while those on Earth have aged 1280++ years is called the twin "paradox".

 

[harrylin]

In addition:

[..]
Yes, in your frame, you'd only experience/age/observe 2~ years, and claim your laser beam only crossed 2 light years.

Again: not in "your frame" but in the inertial frame in which you happen to be in rest at that time. That may sound picky but it becomes essential in a continuation of discussion, as now happened:

If you then turned around and fired a reply laser while going fast enough that you again measure the beam traveling for only 2 years as it crossed 2 light years, you would return 1280+ years after you left, roughly 4 years older. [..]

From the experience of the traveler, indeed this will be the case, and he may have difficulty in explaining - based on that experience - why the stay-at home aged so much. You may next want to argue that this proves that the inertial frame of the Earth is something like a True Rest frame - but that's wrong. In relativity all inertial frames are equally valid in the sense that no such frame can be identified from observations.
Here you switched from using one inertial frame to another for one observer. For a reality-like description that is not allowed; in that sense, the class of inertial frames is preferred in special relativity.

For "twin-paradox" scenarios in which one observer switches inertial frames (or in which he uses a non-inertial frame), only* the description of the other observer who does not switch frames provides a consistent and realistic explanation in SR (loosely said: "frame-hopping" leads to inconsistent or unreal descriptions).

Cheers,
Harald

*Einstein tried to get rid of that with GR, but most people nowadays don't appreciate the reality of "induced gravitational fields".

 

[Max™]

It is true.



Sorry, I don't understand. Anyway, let's not suspend time dilation while keeping Lorentz contraction, it totally confuses everything.

This is why that statement wasn't true, the thread was started in response to someone insisting that you don't just suspend time dilation, but that it was caused by the shorter Lortenz contracted distance.

Betelguese is 640 light years away according to Earth. It takes 640 years for the light beam to travel there *according to Earth*, not according to the light beam. According to the spaceship, it is 2 light years away, and the light takes 2 years to make the trip.

A lightlike path connecting Earth and Betelgeuse is 640 light years long and takes 640 years to travel.



There are two events at the start of the thought experiment, we'll just assume the ship was flying past the Earth to confirm that it is not simply a confusion on my part due to an admitted preference for background star reference frames, and to take acceleration out of the equation entirely.


The ship flies past the Earth at the spacetime event: (x+y+z=0, t=2011 CE), and fired a signal laser towards Betelgeuse, the ship synchronized their clocks as they passed by, so they're now tallying up information which they can perform a measurement with. A bored astronomer decides to tally up measurement as well, he records the ship hauling off along the x-axis (for simplicity), with the laser inching further and further ahead of it.


In the ships frame the Earth whizzed past at nearly the speed of light, and continued receding along the x axis, while the laser the ship fired races away at the speed of light towards Betelgeuse.


There is another event of note here, Betelgeuse, located at (x=+640 light years from the Earth/Ship rendezvous point, t=3/30/2011 CE) along a spacelike trajectory oriented along the ships flight path.


In the Earth frame it is just sitting there, 640 years away at the speed of light, picking it's red supergiant nose.

In the ship frame it is hurtling towards the point where the Earth was when the ship passed it at nearly the speed of light.



In 2 years, Earth frame, the astronomer notes that the beam of light has traveled 2 light years, the ship has traveled 1.9999999~ whatever light years, and that Betelgeuse flicked a massive coronal booger roughly in the direction of Rigel... but otherwise did nothing of interest.


At the spacetime event (x=+2 light years from the Earth/Ship rendezvous point, t=3/30/2013 CE), the passenger on the ship checks his instruments and determines that he is at (x=+.011~ or so light years from the E/SrP, t=4/3/2011), a mere 3 days have passed since the Earth flew past him... for some reason, probably a sale at the interstellar mall... and he notes that since his signal laser can't be more than 3 light days ahead of him at this point, he inputs that measurement into his super parallax measuring doohickie and it tells him Betelgeuse is a bit more than 200 times as far away from him as his signal laser, so it must be just under 2 light years away!



Is he correct?

Well yeah, I guess, in a sense, as he has no reason to think he's actually in a frame experiencing major relativistic effects. He did measure the correct distances/duration as far as his frame is concerned.



The question here is, is there any manner in which his completely real and accurate measurements can be reconciled with any frame besides his (besides the arbitrary selection of suitably chosen frames which someone would point out exist if I didn't mention them)?


Is he doomed to watch the squished up universe hurtle past him, Unable to consider that perhaps he was in a boosted frame, and that just maybe his measurements were distorted by it?

Right - this is the twin "paradox".

Uh... no, it's just an aspect of relativity, make no mistake, my issue has nothing to do with a false paradox.


If there was no way for the guy in the ship to determine that he had been in motion, that would give the appearance of a paradox, and this often confuses people upon first hearing it.


If you can't tell by now, my problem is being all too aware of how that "paradox" is resolved. The only way the passenger on the ship can claim the universe is contracted around him is if he can't break the symmetry between his frame and another observers frame.


Setting aside the issue that he would remember accelerating, and putting him in the above described flyby scenario, then yes, he could claim that his frame was inertial and undistorted.

It's a rather scary place, his choice of coordinates, what with stars and planets hurtling past at nearly the speed of light... I mean, yes, we're whirling around along several different axes at anything from a few hundred, to a several thousands, all the way up to a million or so miles an hour depending on which motion you want to consider... but that's pretty far from sitting there with gigantic balls of nuclear fire hurtling towards you at 670 million mph.

This is what the Earth experiences - you and a light beam leave Earth simultaneously, the light beam gets to Betelguese in 640 years, you get there in 640+ years. This is what you experience - you and a light beam leave Earth simultaneously, the light beam gets to Betelguese in 2 years, you get there in 2+ years. If you turn around and head back, along with a light beam, Earth will say that second light beam took 640 years to make the trip, got to Earth 1280+ years after you left. Earth will say you arrived back at Earth 1280++ years after you left. You will say that second light beam took 2 years to reach Earth, and you took 2+ years to get back to Earth, arriving 4++ years after you left. (Here I am using + to mean x+>x and ++ to mean x++ > x+).

The fact that you have only aged 4++ years while those on Earth have aged 1280++ years is called the twin "paradox".

...

/sigh

Again, my issue is in no way related to an inability to understand an example I put forth in an effort to be understood, though the irony is rich enough that it could smother the heart of a massive star and cause it to supernova.



Technically, the twin paradox ONLY arises if you neglect acceleration completely, ANY change in direction breaks the symmetry between the frames, resolving the apparent paradox to be nothing but a quirky result of the way spacetime rotations work.

 

[harrylin]

[...]
If there was no way for the guy in the ship to determine that he had been in motion, that would give the appearance of a paradox, and this often confuses people upon first hearing it.
If you can't tell by now, my problem is being all too aware of how that "paradox" is resolved. The only way the passenger on the ship can claim the universe is contracted around him is if he can't break the symmetry between his frame and another observers frame.

That's the heart of relativity - the PoR or symmetry of inertial frames! No need to start talking about twin paradoxes, this is more straightforward. According to relativity there is no way for the guy in the ship to determine that he is "truly" in motion at a certain time, other than a mere assumption about the likely state of "true" motion of the stars. Do you find the Lorentz transformation paradoxical? Did you understand Tiny-tim's explanation in the parallel thread that I linked to (his post #3)?

 

[Passionflower]

No, the distance being contracted doesn't mean you only have to cross 2 light years which would take just over 2 years at your velocity, either that statement is not true, or I am quite mistaken about special relativity.

Well the statement is true. It takes the traveler a little over 2 years to reach the destination which is 2 lights years away.

 

[Max™]

I know all about that, but there is a way for him to determine his frame is not symmetrical with all others, he accelerated.

The "true" motion of the stars doesn't require a mere assumption if you notice they all have a significant vector and velocity relative to you. At rest or not, it pushes the limits of realistic explanations, plus he would notice the blue shift/red shift and aberration of the CMBR... but those are all far above the level of this conversation.

For the record, I first learned about relativity back in the mid 80's, and am well versed in not just the stripped down explanations of the theory as usually provided to laymen, but also the mathematical underpinnings, as well as the rich scientific principles upon which the whole theoretical structure was built almost a hundred years ago.

Now, I was a little datasponge of a 6 year old Aspie, between the bookshelf full of various out of date encyclopedias (I still pull up random factoids from the old white cover 1963 Britannica at the strangest times, my favorites were the A's, M's, P's, and the S's!), and my precious books on Relativity (Black Holes and Warped Spacetime, and Einstein: the Life and Times)... so while it may sound a little improbable for someone to say they've been studying something like Relativity since they were a little kid... it isn't that odd if you've ever met a 6 year old with Asperger's Syndrome. If it wasn't the rock collection, dinosaur trivia, or Legos... I was talking your ear off about how awesome Wheeler and Kerr metrics were.

 

[Passionflower]

I know all about that, but there is a way for him to determine his frame is not symmetrical with all others, he accelerated.

Ok, how does that invalidate anything?

The "true" motion of the stars doesn't require a mere assumption if you notice they all have a significant vector and velocity relative to you. At rest or not, it pushes the limits of realistic explanations, plus he would notice the blue shift/red shift and aberration of the CMBR... but those are all far above the level of this conversation.

If your point is absolute motion then it is really back to square one. Motion is relative.

You wrote:

No, the distance being contracted doesn't mean you only have to cross 2 light years which would take just over 2 years at your velocity, either that statement is not true, or I am quite mistaken about special relativity.

And here is another statement that is true but one that you consider is false:

"since I can make the distance shorter by going faster, it takes less time to get there",

You keep putting wagers out that some statement is false or you don't understand relativity. Then when people say the statement is actually true, you just come up with other statements and the process repeats.

 

[Max™]

Well the statement is true. It takes the traveler a little over 2 years to reach the destination which is 2 lights years away.

Except they don't take 2 years because the distance is contracted, they are in a significantly dilated frame of reference performing distance measurements which are skewed by their reduced motion through time.


You observe a beam of light moving away from you at the speed of light, even if you're going .99999999999999999999~ c, it still races off at full speed, rather than gradually creeping ahead due to you ALMOST being at light speed yourself.


If you're in a Ferrari 458 doing 198 mph side by side with a McLaren MP4-12c doing 200 mph, he's going to ever so slightly nudge out in front and continue crawling further and further ahead.


If you're racing along at almost the speed of light, to an observer as you rush past, you're going to lag bit by bit behind a beam of light. Yet you see the beam zoom off like you were standing still... why?


When you're moving faster through space, you're moving slower through time. What you register as being a second in which the beam of light gains nearly 300,000 kilometers on you is a much longer time for an observer who isn't scooting along quite so quickly as you are.


Note that they don't have to be at rest, if you're doing .99999999999999999999995 c and I'm doing .99995 c, we'll each observe the other appearing to slow down, the clocks we're conveniently holding both seem to tick slower for the other guy, as we've all established repeatedly.


Once we come to a stop though, my clock will have ticked more than yours, I'll have aged a bit quicker than you did, though we both hardly aged compared to someone waiting for us back at Earth.



This is why you can't say "the distances contract, so you take less time to cross them", it's completely backwards. You experience less time because of your velocity, which causes you to claim everything else is contracted.

http://www.phys.unsw.edu.au/einsteinlight/jw/module4_time_dilation.htm#true

So Jasper observes Zoe's clock to tick more slowly by a factor γ, which is always greater than or equal to one. This factor γ occurs regularly in special relativity, so we have plotted it at right. (The dashed line plots 1/γ.) We notice that, unless v is a substantial fraction of c, γ is approximately 1. This of course is why we don't notice time dilation at ordinary speeds. For an airplane traveling near the speed of sound, γ = 1.0000000000005.

Note that 1/γ(v/c) is the equation of a circle, although we have stretched the horizontal axis so that the dashed line looks like an elipse. So γ (the solid line) is conveniently remembered as the reciprocal of a circle.

In the animations, Zoe's car travels at 0.8c, so γ = 1.67, so Jasper measures Zoe's clock to have ticks that are 60% of the time that Zoe measures.

Length contraction
You have probably noticed that, in Jasper's version of events, Zoe's car has shrunk. And vice versa. We haven't proved that yet, but it's logically simple. Suppose that Zoe and Jasper choose to measure lengths in lightyears, lightseconds, lightnanoseconds* etc: ie they measure distance by how long light takes to cover the distance. If they agree on the speed of light, but disagree on measurements of time, they must inevitably disagree on length as well. If you observe someone's clocks run slowly by a factor γ, you will also observe her rulers to be short by a factor of γ: that's the only way that she can measure the speed of light to have the same value you get.

* The lightnanosecond is a convenient unit. c is about 3 x10^8 metres per second, and a nanosecond is 10^-9 seconds, so a lightnanosecond is 0.3 metres. (Americans, who use British imperial units, can therefore remember that the speed of light is about one foot per nanosecond. The rest of us can remember it as 30 centimetres per nanosecond.)

Zoe, who is a graffiti artist in her spare time, will demonstrate this: she decides to tag the two ends of the verandah. (The paint can is green, and it sprays purple paint.) For Jasper, the distance between the tags will be his proper length, ie the length measured in his frame, because they are stationary with respect to him. Zoe can measure the time between the two tags, and thus get her measurement of the length of the verandah.

 

[Passionflower]

Except they don't take 2 years because the distance is contracted,

Well then it seems we can agree to disagree. The travelers clock is still going at one second per second. No changes for him at all.

distance measurements which are skewed by their reduced motion through time.

Their distance measurements are as real as can be.

you're going .99999999999999999999~ c,

There is no such thing as absolute speed. You can measure the speed of something that has mass only wrt something else that has mass.

 

[Max™]

I never said he would notice any changes, his clock ticks off one second every time he expects it should, like... clockwork.


Another observer watching his clock tick from a slower moving frame would see it tick slower (and vice versa), but if the faster moving traveler came to rest beside the slower moving observer it would be obvious that the traveler's clock had ticked less.


I actually was using velocity, and never said anything about absolute speed.

If we were both at rest together in an inertial frame and pulled out two completely identical stopwatches, started them at exactly the same moment, then we both accelerated up to particular fraction of the speed of light, except you got much closer to c than I did, when we came to a stop afterwards your watch would read a shorter duration for your trip than mine would.


Where is the confusion here?

 

[Dale]

A lightlike path connecting Earth and Betelgeuse is 640 light years long and takes 640 years to travel.

This is an example of some sloppy writing which I think is betraying some sloppy thinking that may be the source of your confusion. The quoted sentence is MEANINGLESS as written because the reference frame for the distance and the time measurement are not specified. In order for this statement to be meaningful it would have to be amended as follows:

A lightlike path connecting Earth and Betelgeuse is 640 light years long in the Earth frame and takes 640 years to travel in the Earth frame.

Distance and time are relative quantities, and like all relative quantities, you must identify the reference frame to which they refer. The following statements are also correct for your scenario.

There exists some frame in which a lightlike path connecting Earth and Betelgeuse is 2 light years long and takes 2 years to travel.

In a frame moving 0.999995 c wrt Earth in the direction from Earth to Betelgeuse the distance between Earth and Betelgeuse is 2 light years. In this frame it takes light 1.000002 years to go from Earth to Betelgeuse or 409599 years to go from Betelgeuse to Earth. In this frame it takes 2.00001 years from the time that Earth passes the origin for Betelgeuse to pass the origin.

Notice how relative quantities are always referenced to some specific frame. You make other comments like "they are in a significantly dilated frame of reference" and "he's actually in a frame experiencing major relativistic effects" which lead me to believe that the omission I point out above is not simply a gaffe, but is a basic misunderstanding.

 

[Max™]

See, here's the problem, you're saying the effects are real in that they do happen, I'm saying that as well, but that the cause is due to measurement from a particular frame, not the universe actually smushing up around you.

Time dilation and length contraction are not just optical illusions, but neither do they represent a physical contraction. These effects are the result of a measurement from a given inertial frame that is performed on body moving with respect to that frame. We assume that the measurements always take into account the finite travel time of light. Consider two observers moving relative to one another. You have no difficulty with the idea of their velocities being relative - each thinks the other is "really moving." In SR, time intervals and space intervals are also relative. You don't shrink or see your own clock run slow. The other observer sees your clocks slow and meter sticks contracted from his frame. Similarly you will observe his clocks slow and meters sticks short from your frame. The time dilation and length contraction are inherent properties of the way measurements must be performed in spacetime.

http://www.astro.virginia.edu/~jh8h/Foundations/Foundations_1/quest7.html


I do admit that I'm a bit overly insistent about the broken symmetry, but the length required to treat someone flying from here to another star as an intertial frame leaves a bad taste in my mouth.

I know his frame is accelerated, he knows his frame is accelerated, thinking about the hypothetical inertial frame is one thing, but it is another to claim the particular details of measurement within said hypothetical inertial frame are the cause of the effects you experience in an accelerated frame.

At that point it isn't just a matter of "earth and betelgeuse went flying past me", unless you're pretending GR doesn't exist, and topping it off by pretending that you can't handle acceleration at all in SR (you can, it just doesn't do it very easily).

 

[Passionflower]

At that point it isn't just a matter of "earth and betelgeuse went flying past me", unless you're pretending GR doesn't exist, and topping it off by pretending that you can't handle acceleration at all in SR (you can, it just doesn't do it very easily).

What has GR to do with this?

 

[Dale]

thinking about the hypothetical inertial frame is one thing

There is nothing hypothetical about the inertial reference frame.

thinking about the hypothetical inertial frame is one thing, but it is another to claim the particular details of measurement within said hypothetical inertial frame are the cause of the effects you experience in an accelerated frame.

Nobody claimed that. The explanations would be different in a non-inertial frame, but equally valid.

 

[Max™]

What has GR to do with this?

Well, working with just SR is kinda like me telling you calculate integrals and differentials, but not letting you use the fundamental theorem of calculus to flesh the structure out properly.

SR is great because the mathematical form doesn't require you to keep track of multi-dimensional tensor systems, but it's just not the same as the richer understanding you gain when you include GR into the structure.



As for the inertial frame, if you were flying from here to Betelgeuse you would need to accelerate until the halfway point and then decelerate the rest of the way in order to reach relativistic speeds such as we're discussing, presumably some sort of nuke-pusher drive or maybe an anti-matter pulse engine.


In such a scenario, yes, the inertial frame is a hypothetical, there wouldn't be a period where you would be able to claim you were at rest, much less that your frame hadn't been boosted compared to your origin frame.

 

[Passionflower]

Well, working with just SR is kinda like me telling you calculate integrals and differentials, but not letting you use the fundamental theorem of calculus to flesh the structure out properly.

SR is great because the mathematical form doesn't require you to keep track of multi-dimensional tensor systems, but it's just not the same as the richer understanding you gain when you include GR into the structure.



As for the inertial frame, if you were flying from here to Betelgeuse you would need to accelerate until the halfway point and then decelerate the rest of the way in order to reach relativistic speeds such as we're discussing, presumably some sort of nuke-pusher drive or maybe an anti-matter pulse engine.


In such a scenario, yes, the inertial frame is a hypothetical, there wouldn't be a period where you would be able to claim you were at rest, much less that your frame hadn't been boosted compared to your origin frame.

Sorry Max I lost you completely here.

 

[Dale]

In such a scenario, yes, the inertial frame is a hypothetical, there wouldn't be a period where you would be able to claim you were at rest, much less that your frame hadn't been boosted compared to your origin frame.

No, the inertial frame is not hypothetical in any way regardless of whether or not the ship is ever at rest in it.

In addition to the sloppy language I pointed out above you seem to have this mistaken notion that there is a requirement for some object to be at rest in order for a reference frame to be valid. That is simply not the case. We need not restrict our analysis to frames where some object is at rest and we need not restrict our analysis to objects which are at rest in our chosen frame.

 

[Max™]

Again, why would you think that is what I was saying?

I said an observer who is undergoing constant acceleration can't claim they are in an inertial frame, is this wrong now?

 

[Dale]

I said an observer who is undergoing constant acceleration can't claim they are in an inertial frame, is this wrong now?

Yes, this is wrong as written. It is not possible for something to be "in a frame" or "out of a frame". A frame is a coordinate system, it has infinite spatial extent. An object may be "at rest in a frame" or "moving in a frame", but it exists in every possible frame at all times regardless of its motion.

An observer who is undergoing constant proper acceleration can't claim that they are at rest in an inertial frame. But they may certainly use any arbitrary inertial frame to do physics calculations in anyway.

If you really understand this then why would you repeatedly use the word "hypothetical" to describe the inertial frame where the Earth-Betelgeuse distance is 2 ly?

 

[Max™]

I said they can't claim they are in an inertial frame, by which I would have assumed at this point in the discussion it would be implied that I meant "can't claim they are at rest in one", so it is a hypothetical scenario to argue that said observer would be unable to distinguish changes due to a boosted frame of reference from changes due to the universe being smushed up around them.


Yes, from a suitably chosen frame the distance is measured as 2 ly, and if you were at rest in such a frame you would not claim this distortion was due to time dilation.

The observer being described in this scenario can not make such a claim, and accordingly would conclude that the distortion of their measurements was due to time dilation/them experiencing lorentz contraction with their measuring rods.



Similarly, it is hard to ignore the variations in gravity between the Earth and Betelgeuse, though they may be exceptionally slight, nonetheless they break symmetry between all frames, any gravity is an acceleration, even if you were "coasting at rest" (free fall), a sufficiently accurate clock/ruler would display the effects compared to what you would expect when you compared a clock/ruler you know to be in a well at Earth or Betelgeuse to a hypothetical situation where you're coasting between them in perfectly flat spacetime at infinite distance from a gravity well such as those described in SR.

You can define a local frame in GR as an inertial one (assuming you're not spinning, ideally), and if you can get your acceleration components to vanish you could claim your hypothetical ideal observer in that frame is at rest in their locally flat spacetime (i.e. is following a path congruent to a geodesic in that spacetime), and that is about as close as GR gets to the ideal Lorentz frames from SR.

 

[Dale]

Yes, from a suitably chosen frame the distance is measured as 2 ly, and if you were at rest in such a frame you would not claim this distortion was due to time dilation.

The observer being described in this scenario can not make such a claim, and accordingly would conclude that the distortion of their measurements was due to time dilation/them experiencing lorentz contraction with their measuring rods.

Even if you are not at rest in such a frame you may still use it, and if you used that frame then your time dilation would only be due to your velocity in that frame and other frames (including the Earth frame) would be time dilated.

You seem to think that it is essential for an accelerating observer to refer their observations (including their acceleration) back to the Earth inertial frame and that any other view (either a non-inertial frame or a different inertial frame) represents a "distortion". That misses the point of relativity entirely. Any inertial frame is equally valid and is not considered distorted or invalid in any way. From the 2-ly frame it is the Earth rods and clocks that are so contracted and dilated that they measure 640 ly.

So why insist on referring the ship observations back to the Earth frame rather than some other perfectly valid frame?

 

[Max™]

Even if you are not at rest in such a frame you may still use it, and if you used that frame then your time dilation would only be due to your velocity in that frame and other frames (including the Earth frame) would be time dilated.

Yes, I am aware that this is the case in SR, this is what I was saying, SR is an idealized hypothetical case of GR where acceleration is less important, and where spacetime is a flat Minkowski spacetime.

You seem to think that it is essential for an accelerating observer to refer their observations (including their acceleration) back to the Earth inertial frame and that any other view (either a non-inertial frame or a different inertial frame) represents a "distortion". That misses the point of relativity entirely. Any inertial frame is equally valid and is not considered distorted or invalid in any way. From the 2-ly frame it is the Earth rods and clocks that are so contracted and dilated that they measure 640 ly.

No, I am pointing out that the only important things in General Relativity are paths and their lengths, and as such it is important to treat your choice of frames in a manner which best suits the state in your local region or the local region of another hypothetical observer.

Similarly, an arbitrary choice of Lorentz frames can only be inserted into GR as an approximation of the local spacetime for a particular ideal observer. GR is all about ideal observers, they're everydamnwhere, and it is convenient to assume ideal test particles following true geodesic paths.

In such a situation, those geodesics between two events define minimum possible lengths in time for timelike paths, or space for spacelike paths.


Any inertial frame is equally valid in SR, but not GR, at most they are locally valid.

So why insist on referring the ship observations back to the Earth frame rather than some other perfectly valid frame?

I am actually comparing the observations to an idealized geodesic path between Earth and Betelgeuse, perhaps I shouldn't assume everyone else will take GR into consideration, but there is no reason to NOT use GR to better explain some of the less intuitive aspects of SR, is there?

 

[Dale]

Yes, I am aware that this is the case in SR, this is what I was saying, SR is an idealized hypothetical case of GR where acceleration is less important, and where spacetime is a flat Minkowski spacetime. ...

perhaps I shouldn't assume everyone else will take GR into consideration, but there is no reason to NOT use GR to better explain some of the less intuitive aspects of SR, is there?

Sure, but at these scales both the FLRW metric and the Schwarzschild metric are essentially flat. So GR doesn't add anything significant here.

No, I am pointing out that the only important things in General Relativity are paths and their lengths, and as such it is important to treat your choice of frames in a manner which best suits the state in your local region or the local region of another hypothetical observer. ...

In such a situation, those geodesics between two events define minimum possible lengths in time for timelike paths, or space for spacelike paths. ...

I am actually comparing the observations to an idealized geodesic path between Earth and Betelgeuse

And in this case the length of the geodesic in question is ~2 ly, not 640 ly. So in terms of paths and lengths the 2 ly frame is the one which best suits the problem, not the Earth frame.