## Miscellaneous Science Questions

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yurell
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### Re: RELATIVITY QUESTIONS! (and other common queries)

+PK+ wrote:Why, now that the track/earth is moving near lightspeed, does the observer on the train see that his clock is moving slower than the man at the station?

He shouldn't — an observer on the train should see the station's clock move slower, while an observer on the station should see the train's clock move slower.

Edit: I somehow missed the fact the train was moving in a circle, thought it was a straight line >.>
Last edited by yurell on Thu Jul 10, 2014 11:39 pm UTC, edited 1 time in total.
cemper93 wrote:Dude, I just presented an elaborate multiple fraction in Comic Sans. Who are you to question me?

Hypnosifl
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### Re: RELATIVITY QUESTIONS! (and other common queries)

+PK+ wrote:This is a little off topic now that you guys have moved on, but I've been trying to wrap my head around SR for the past couple days. I think I get reference frames now. So in the train's POV it is at rest and the track/earth combo is moving close to the speed of light thus distorting the track to a shorter distance allowing the train to traverse it's length without breaking the speed of light. That raises another question to me though. Why, now that the track/earth is moving near lightspeed, does the observer on the train see that his clock is moving slower than the man at the station?

If the train is moving inertially (which requires the track to be straight), then in the train's rest frame, the clock of the man at the station is ticking slower. If the track is circular, keep in mind that there is no unique "correct" way to define a non-inertial coordinate system for a non-inertial observer, unlike with inertial frames for inertial observers...and how the clock of the man at the station behaves will be different in different non-inertial coordinate systems (the time dilation equation relating a clock's velocity to the rate it ticks only works in inertial frames). There is a frame-independent answer to what the train-observer sees visually using light signals, though--note that when physicists talk about moving clocks running slow in inertial frames, they usually aren't talking about what inertial observers see visually but rather what time-coordinates they assign to different ticks of a moving clock, with the time-coordinates assigned in such a way as to factor out effects of light travel time delays. The delay between when a signal is emitted and when it reaches your eyes is responsible for the Doppler effect, for example, and due to the Doppler effect a clock moving towards you will actually appear visually to tick faster than your own, not slower, even if you are moving inertially. And if we're talking about what's seen visually as opposed to coordinates assigned in some frame, if an observer in a train moving on a circular track looks at a clock that's sitting at the center of the circular track, visually he'll see that clock running faster than his own.

+PK+
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### Re: RELATIVITY QUESTIONS! (and other common queries)

Hypnosifl wrote:If the train is moving inertially (which requires the track to be straight), then in the train's rest frame, the clock of the man at the station is ticking slower. If the track is circular, keep in mind that there is no unique "correct" way to define a non-inertial coordinate system for a non-inertial observer, unlike with inertial frames for inertial observers...and how the clock of the man at the station behaves will be different in different non-inertial coordinate systems (the time dilation equation relating a clock's velocity to the rate it ticks only works in inertial frames). There is a frame-independent answer to what the train-observer sees visually using light signals, though--note that when physicists talk about moving clocks running slow in inertial frames, they usually aren't talking about what inertial observers see visually but rather what time-coordinates they assign to different ticks of a moving clock, with the time-coordinates assigned in such a way as to factor out effects of light travel time delays. The delay between when a signal is emitted and when it reaches your eyes is responsible for the Doppler effect, for example, and due to the Doppler effect a clock moving towards you will actually appear visually to tick faster than your own, not slower, even if you are moving inertially. And if we're talking about what's seen visually as opposed to coordinates assigned in some frame, if an observer in a train moving on a circular track looks at a clock that's sitting at the center of the circular track, visually he'll see that clock running faster than his own.

Okay so the problem is that the track is a circle. I'm just trying to wrap my head around how the man at the station's clock says the train was gone for 2.4 minutes but the man in the train sees the station clock move slower than his own which says the train was gone only 1 minute. Is it because the train is moving at a constant speed relative to the track but not relative to the station?

Hypnosifl
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### Re: RELATIVITY QUESTIONS! (and other common queries)

+PK+ wrote:Okay so the problem is that the track is a circle. I'm just trying to wrap my head around how the man at the station's clock says the train was gone for 2.4 minutes but the man in the train sees the station clock move slower than his

He doesn't, I said "if an observer in a train moving on a circular track looks at a clock that's sitting at the center of the circular track, visually he'll see that clock running faster than his own." If the station clock wasn't at the center of the circular track, but was still at rest relative to the track, then the person on the train might see it change its visual speed depending on his direction of motion relative to it (the Doppler shift), but on average over one complete circular journey, he'll still see the station clock was ticking at a faster rate than his own.

Basically, time dilation is symmetrical for a pair of inertial observers (each assigns the same slowed-down rate of ticking to the other one's clock in their own rest frame), but you can't assume it still is for non-inertial observers--that's the key to understanding why the twin paradox is not really paradoxical, for example.

Eebster the Great
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### Re: RELATIVITY QUESTIONS! (and other common queries)

It's a bit confusing, but both observers see the other clock as moving slow relative to their own clock.

+PK+
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### Re: RELATIVITY QUESTIONS! (and other common queries)

Hypnosifl wrote:
+PK+ wrote:Okay so the problem is that the track is a circle. I'm just trying to wrap my head around how the man at the station's clock says the train was gone for 2.4 minutes but the man in the train sees the station clock move slower than his

He doesn't, I said "if an observer in a train moving on a circular track looks at a clock that's sitting at the center of the circular track, visually he'll see that clock running faster than his own." If the station clock wasn't at the center of the circular track, but was still at rest relative to the track, then the person on the train might see it change its visual speed depending on his direction of motion relative to it (the Doppler shift), but on average over one complete circular journey, he'll still see the station clock was ticking at a faster rate than his own.

My mistake, I was thinking about what the earlier poster said about the station clock moving slower. The station can't be at the center of the track, but that's beside the point. So because the track's a circle the station clock moves slower as the train moves away and then moves faster as it moves towards the station so in total the train sees over two minutes having gone by at the station at various speeds due to Doppler shift. The man at the station sees a similar effect on the train's clock due to Doppler shit but only one minute passes. Why does the man on the station see the train's clock go slower overall and the train see the station clock go faster overall if both the train and the station are moving at the same speed in each other's reference frames?

+PK+
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### Re: RELATIVITY QUESTIONS! (and other common queries)

Eebster the Great wrote:It's a bit confusing, but both observers see the other clock as moving slow relative to their own clock.

If this is true how can the man on the train comprehend seeing a clock moving slower than his own yet the clock reading a time twice as long as his own upon completion?

yurell
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### Re: RELATIVITY QUESTIONS! (and other common queries)

To compare clocks properly, you need to be in the same inertial frame. This means the symmetry of the situation is broken by acceleration.
cemper93 wrote:Dude, I just presented an elaborate multiple fraction in Comic Sans. Who are you to question me?

Hypnosifl
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### Re: RELATIVITY QUESTIONS! (and other common queries)

+PK+ wrote:My mistake, I was thinking about what the earlier poster said about the station clock moving slower. The station can't be at the center of the track, but that's beside the point. So because the track's a circle the station clock moves slower as the train moves away and then moves faster as it moves towards the station so in total the train sees over two minutes having gone by at the station at various speeds due to Doppler shift. The man at the station sees a similar effect on the train's clock due to Doppler shit but only one minute passes. Why does the man on the station see the train's clock go slower overall and the train see the station clock go faster overall if both the train and the station are moving at the same speed in each other's reference frames?

The man on the train doesn't have a single inertial rest frame, his comoving inertial frame is constantly changing. You can design all sorts of different non-inertial reference frames in which he is at rest throughout the journey (and which will have different judgments about the station's clock coordinate velocity as a function of coordinate time, and its rate of ticking as a function of coordinate time), but the familiar time dilation equation relating the velocity of a clock to its rate of ticking only works in inertial frames. I don't know if you saw the extra paragraph I added to my last post in an edit, but like I said there, this is key to understanding the resolution of the twin paradox.

+PK+
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### Re: RELATIVITY QUESTIONS! (and other common queries)

yurell wrote:To compare clocks properly, you need to be in the same inertial frame. This means the symmetry of the situation is broken by acceleration.

Okay so from the point of view of the train, as it decelerates the station clock accelerates to show 2.4 minutes, and from the station's point of view as the train decelerates the train's clock remains as it was to show 1 minute?

+PK+
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### Re: RELATIVITY QUESTIONS! (and other common queries)

+PK+ wrote:
yurell wrote:To compare clocks properly, you need to be in the same inertial frame. This means the symmetry of the situation is broken by acceleration.

Okay so from the point of view of the train, as it decelerates the station clock accelerates to show 2.4 minutes, and from the station's point of view as the train decelerates the train's clock remains as it was to show 1 minute?

Nvm, Inertial rest frames don't work for accelerating objects you can't really think of it like that. I was just wondering what the train would see if they looked out the window. Would everyone appear in slow motion or would they look like they were in fast forward? Still not sure what that answer is but I'm not sure if anyone is.

Hypnosifl
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### Re: RELATIVITY QUESTIONS! (and other common queries)

+PK+ wrote:
+PK+ wrote:
yurell wrote:To compare clocks properly, you need to be in the same inertial frame. This means the symmetry of the situation is broken by acceleration.

Okay so from the point of view of the train, as it decelerates the station clock accelerates to show 2.4 minutes, and from the station's point of view as the train decelerates the train's clock remains as it was to show 1 minute?

Nvm, Inertial rest frames don't work for accelerating objects you can't really think of it like that. I was just wondering what the train would see if they looked out the window. Would everyone appear in slow motion or would they look like they were in fast forward? Still not sure what that answer is but I'm not sure if anyone is.

It would depend on the position of each person being looked at and how the train was moving at that instant, but you could calculate it using the relativistic Doppler shift equation.

+PK+
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### Re: RELATIVITY QUESTIONS! (and other common queries)

Hypnosifl wrote:
+PK+ wrote:
+PK+ wrote:
yurell wrote:To compare clocks properly, you need to be in the same inertial frame. This means the symmetry of the situation is broken by acceleration.

Okay so from the point of view of the train, as it decelerates the station clock accelerates to show 2.4 minutes, and from the station's point of view as the train decelerates the train's clock remains as it was to show 1 minute?

Nvm, Inertial rest frames don't work for accelerating objects you can't really think of it like that. I was just wondering what the train would see if they looked out the window. Would everyone appear in slow motion or would they look like they were in fast forward? Still not sure what that answer is but I'm not sure if anyone is.

It would depend on the position of each person being looked at and how the train was moving at that instant, but you could calculate it using the relativistic Doppler shift equation.

Thanks for that twin paradox link. It helped a lot. It's still very difficult to comprehend though. Once the train starts heading towards the station at light speed the clock still is seen to tick at the right speed to the man at the station, but because the train is moving almost as fast as the light coming from it all instances of the clock appear almost simultaneously to the observer. So even though inertial reference frames are useful, the break in symmetry comes from the fact that in reality only one is actually moving and undergoing doppler shift. Still trying to completely get it though.

Goemon
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### Re: RELATIVITY QUESTIONS! (and other common queries)

+PK+ wrote:I was just wondering what the train would see if they looked out the window.

From the point of view of someone standing at the station, the clock on the train is always ticking at a constant rate, but slower than his own. When the train gets back to the station, the clock carried by the train shows less elapsed time.

A train passenger would calculate * that a person standing at the track immediately outside the train window would have a clock ticking much slower than his own. But a clock carried by a person standing beside the track on the opposite side of the circle would be ticking much faster than his own. Loiterers 90 degrees away would be somewhere in between.

Therefore, the clock on the station wall, as computed by the train passenger, runs slower than his own as the train passes through the station, speeds up to a very high rate as the train rounds the opposite side of the circle, and then slows down again as the train approaches the station.

* However, as Hypnosifl was describing, the actual time that the passenger SEES also depends on how far he is from the clock, since there can be a longer or shorter lag as the light travels from the clock to his eyes. So as he's pulling away from the station, the clock is ticking slowly and it's taking longer and longer for the light pulses to reach him, so it appears to be running even more slowly. As he rounds the far side and starts to approach, it's ticking really fast and he's starting to approach, so it appears to be changing REALLY fast. Then it's slowing down, but he's getting closer and closer (shorter and shorter delays), so it might even appear to be running at "normal" speed briefly before slowing down again as he enters the station.

The net result of slow, REALLY fast, normal, slow is that the total time elapsed on the station clock is 2.4 minutes compared to the 1 minute it took him to make the trip.
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+PK+
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### Re: RELATIVITY QUESTIONS! (and other common queries)

Goemon wrote:
+PK+ wrote:I was just wondering what the train would see if they looked out the window.

From the point of view of someone standing at the station, the clock on the train is always ticking at a constant rate, but slower than his own. When the train gets back to the station, the clock carried by the train shows less elapsed time.

A train passenger would calculate * that a person standing at the track immediately outside the train window would have a clock ticking much slower than his own. But a clock carried by a person standing beside the track on the opposite side of the circle would be ticking much faster than his own. Loiterers 90 degrees away would be somewhere in between.

Therefore, the clock on the station wall, as computed by the train passenger, runs slower than his own as the train passes through the station, speeds up to a very high rate as the train rounds the opposite side of the circle, and then slows down again as the train approaches the station.

* However, as Hypnosifl was describing, the actual time that the passenger SEES also depends on how far he is from the clock, since there can be a longer or shorter lag as the light travels from the clock to his eyes. So as he's pulling away from the station, the clock is ticking slowly and it's taking longer and longer for the light pulses to reach him, so it appears to be running even more slowly. As he rounds the far side and starts to approach, it's ticking really fast and he's starting to approach, so it appears to be changing REALLY fast. Then it's slowing down, but he's getting closer and closer (shorter and shorter delays), so it might even appear to be running at "normal" speed briefly before slowing down again as he enters the station.

The net result of slow, REALLY fast, normal, slow is that the total time elapsed on the station clock is 2.4 minutes compared to the 1 minute it took him to make the trip.

I guess my biggest cognitive dissonance is the break in symmetry. In relative frames the station and train move at identical velocities, but the train experiences time shortening from the station's point of view, and the station experiences time lengthening from the train's point of view. Still though they see the other's clock dilating the exact same amount during transit.

EDIT: My opinion, based on no facts whatsoever, is that space is unique at all points and that an object moving faster through it with mass is just inherently different than an object at rest. So it warps space like gravity does. Observers on the train would see things moving more quickly on the station no matter which direction the train went. Of course with Doppler shift the clock at the staion would appear to move at varying speeds, but on average the motion on the platform would appear faster than normal to the train. There's no need to break symmetry because none exists. I'm sure there's a reason that's wrong though. It just feels so much more right.
Last edited by +PK+ on Fri Jul 11, 2014 3:09 am UTC, edited 1 time in total.

ConMan
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### Re: RELATIVITY QUESTIONS! (and other common queries)

+PK+ wrote:EDIT: My opinion, based on no facts whatsoever, is that space is unique at all points and that an object moving faster through it with mass is just inherently different than an object at rest. So it warps space like gravity does. Observers on the train would see things moving more quickly on the station no matter which direction the train went. There's no need to break symmetry because none exists. I'm sure there's a reason that's wrong though. It just feels so much more right.

That perspective fails because an observer at rest at a given point will observe the space around him to behave the same whether or not another observer travels through the same point. So it can't be that space is distorting otherwise the passage of the second observer would warp space for both of them. What happens is that *measurements* of space and time are distorted relative to each other, and this all comes out of the postulate that the one thing that *all* observers will *always* agree on is the speed of light in a vacuum.
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### Re: RELATIVITY QUESTIONS! (and other common queries)

ConMan wrote:
+PK+ wrote:EDIT: My opinion, based on no facts whatsoever, is that space is unique at all points and that an object moving faster through it with mass is just inherently different than an object at rest. So it warps space like gravity does. Observers on the train would see things moving more quickly on the station no matter which direction the train went. There's no need to break symmetry because none exists. I'm sure there's a reason that's wrong though. It just feels so much more right.

That perspective fails because an observer at rest at a given point will observe the space around him to behave the same whether or not another observer travels through the same point. So it can't be that space is distorting otherwise the passage of the second observer would warp space for both of them. What happens is that *measurements* of space and time are distorted relative to each other, and this all comes out of the postulate that the one thing that *all* observers will *always* agree on is the speed of light in a vacuum.

Yeah that makes sense except nothing can exist in two places at once so an observer could never occupy the same space as the train. If he did space would definitely not be behaving normally. If the train was a ghost then light(edit:shone by an outside observer occupying the same space as the train) would appear to be going slower to an observer outside that space, but a person within the dilated space could report the actual amount of time going by in that space to the observer and light would actually be going the right speed. It's like when light passes through a denser medium and appears to be going slower.

Edit: Yeah none of that works. Just go on about your business and I won't trouble you nice folks anymore.

Eebster the Great
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### Re: RELATIVITY QUESTIONS! (and other common queries)

Two things can occupy the same space, just not at the same time. But if simultaneity is relative, you can get strange effects. See the ladder paradox for instance.

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### Re: RELATIVITY QUESTIONS! (and other common queries)

+PK+ wrote:I was just wondering what the train would see if they looked out the window. Would everyone appear in slow motion or would they look like they were in fast forward? Still not sure what that answer is but I'm not sure if anyone is.

Everything appears in slow motion. Plus the normal doppler effect, which is: everything ahead appears fast and everything behind appears slow.

Ok so somehow we kind of know that the clock at the middle of the track loop should be looking like running fast .... So therefore we know that that clock always seems to be in the front direction as seen from the train.

Hypnosifl
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### Re: RELATIVITY QUESTIONS! (and other common queries)

+PK+ wrote:I guess my biggest cognitive dissonance is the break in symmetry. In relative frames the station and train move at identical velocities

What "relative frames" do you mean? Are you talking about a non-inertial coordinate system where the train is at rest throughout the loop? Keep in mind that unlike with inertial frames, which have a specific physical recipe for how you should define them (involving a network of rulers and clocks moving inertially and at rest relative to one another and the inertial observer), there is no unique "correct" way to define a non-inertial coordinate system for a non-inertial observer. The observer on the train could assign coordinates such that the event of his clock reading 0 minutes is assigned the same time-coordinate as (=is simultaneous with) the station clock reading 0 minutes, and the event of his clock reading 1 minute is simultaneous with the event of the station clock reading 2.4 minutes, but he could equally well choose a different non-inertial coordinate system where both clocks still read 0 minutes simultaneously but the event of his clock reading 1 minute is assigned the same time-coordinate as the station clock reading 0.001 minutes, or 10^15 minutes. Non-inertial coordinate systems are just arbitrary ways of labeling physical events with time-coordinates and position-coordinates, similar to the different possible spatial coordinate systems used for the same arrangement of blocks in the following animated gif from this article:

So, intuitively there's really no reason at all to think that if you just make up some arbitrary labeling scheme for the train observer and call it "his" frame, that there should be any symmetry between his frame and the inertial frame of the station observer. Light doesn't even need to have a constant speed in non-inertial frames! Of course, all frames always agree on the truth about localized events like what the train observer's clock reads when he passes right next to a particular marking on the track, or what his clock reads at the moment that light from a given reading on the station clock is reaching his eyes. But you can't define things like the "velocity" of the station observer relative to the train observer without using some sort of coordinate system.

You might learn more from a different scenario where the train moves on a straight track, so that both the train and the station observer can have inertial rest frames. Say the train is moving at 0.8c between markers on the track 20 light-seconds apart in the rest frame of the track, so in the track frame it takes the train 20/0.8 = 25 seconds to get from one marker to the other, but in this frame the train's clock is slowed down by a factor of 0.6 so it only ticks forward by 25*0.6 = 15 seconds going from one marker to the other. How can it make sense that the train saw a clock at rest in the track frame next to the first marker reading 0 seconds as it departed from that position, and also saw another clock at rest in the track frame next to the second marker reading 25 seconds as it arrived at that position, if in the train frame those track clocks should be slowed down relative to its own clock, and its own clock only showed the 15 seconds passing between those events? If you figure out (or learn) the answer to that, it may give you a better idea of how time dilation can really be symmetrical between different inertial frames.

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### Re: RELATIVITY QUESTIONS! (and other common queries)

Hypnosifl wrote:If you figure out (or learn) the answer to that, it may give you a better idea of how time dilation can really be symmetrical between different inertial frames.

Hey! I'm trying to create a new theory of space-time here. Let's not let facts get in the way.

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### Re: RELATIVITY QUESTIONS! (and other common queries)

+PK+ wrote:
Hypnosifl wrote:If you figure out (or learn) the answer to that, it may give you a better idea of how time dilation can really be symmetrical between different inertial frames.

Hey! I'm trying to create a new theory of space-time here. Let's not let facts get in the way.

This is the correct approach to crackpottery.

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### Re: RELATIVITY QUESTIONS! (and other common queries)

+PK+ wrote:Yeah that makes sense except nothing can exist in two places at once so an observer could never occupy the same space as the train. If he did space would definitely not be behaving normally. If the train was a ghost then light(edit:shone by an outside observer occupying the same space as the train) would appear to be going slower to an observer outside that space, but a person within the dilated space could report the actual amount of time going by in that space to the observer and light would actually be going the right speed. It's like when light passes through a denser medium and appears to be going slower.

Generally when we talk about observers we don't give them actual physical presence for a number of reasons, not least because the actual presence of a physical object would change the system too much without much effort at all. If you really wanted to be pedantic you could make the observers miss each other by an arbitrary distance, and then you just have to do the maths to show that everything falls into place when you take the limit of that distance approaching zero.
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### Re: RELATIVITY QUESTIONS! (and other common queries)

I've been studying it a bit and I think I get it, but I'm still not very satisfied with the explanation of the twin paradox. I understand that length and time are contracted for the traveling twin, but the SR explanation is kinda weak. The doppler shift explains why they see each other's clocks moving at various speeds but it doesn't explain the time dilation. Even though the traveling twin see's the earth twin's clock moving more slowly the traveller would notice the time dilation as soon as he slows down. Which would appear to him as if light is catching up to him. Do you guys see where I'm getting confused? If inertial reference frames are all we can use for SR I don't think it properly explains the time dilation. I mean if you had to travel ten light-years to deliver a message, and you were moving so close to the speed of light it only seemed like five light-years to you, it doesn't mean you traveled five light-years. The people on the new planet will say that the radio broadcast of you leaving earth arrived just moments ago, but that both planets had agreed, through a very long series of communications of course, that you would leave ten years ago. Yet you saw earth's clock moving slower than your own the whole time while traveling. So at some point light is going to appear to you to have gone faster than it should, as you're view of earth's clock while you sere traveling catches up to the earth clock you now see at rest.

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### Re: RELATIVITY QUESTIONS! (and other common queries)

The big way SR resolves the Twin Paradox is with relativity of simultaneity, not doppler shift. When ship A is moving away from B, its surface of simultaneity intersects B's worldline in (from B's perspective) the past. When ship A is moving back towards B, this shifts and now intersect's B's worldline in the future. In terms of how they calculate the universe (ignoring direct observation for the moment), from A's perspective B simply skips over all the intervening time by which her age will exceed A's when they're reunited.
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### Re: RELATIVITY QUESTIONS! (and other common queries)

You can do the calculation the doppler shift way though, it's quite revealing.
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### Re: RELATIVITY QUESTIONS! (and other common queries)

+PK+ wrote:I've been studying it a bit and I think I get it, but I'm still not very satisfied with the explanation of the twin paradox. I understand that length and time are contracted for the traveling twin,

"length and time are contracted for the traveling twin" isn't a very clear explanation--it's not as if you are required to analyze the problem in the inertial rest frame of the Earth twin, in relativity you're always free to use whatever frame you like to analyze a problem. For example, you could choose to analyze things from the perspective of an inertial frame where the Earth twin is moving at a constant velocity, whereas the traveling twin is at rest for the first phase of the journey, then after the turnaround is traveling towards the Earth twin at an even faster velocity so he can catch up. In this frame the Earth twin's clock is running slower during the first phase, but then in the second phase the traveling twin's clock is running even slower than that since his velocity is higher.
+PK+ wrote:but the SR explanation is kinda weak. The doppler shift explains why they see each other's clocks moving at various speeds but it doesn't explain the time dilation. Even though the traveling twin see's the earth twin's clock moving more slowly the traveller would notice the time dilation as soon as he slows down. Which would appear to him as if light is catching up to him.

If by "catching up" you mean he'd see the Earth twin's clock suddenly jumping forward that's not correct. If the traveling twin travels away from Earth at 0.8c, then while he's traveling he sees the Earth clock visually slowed by a factor of 3 due to the Doppler effect, so if he travels for 25 years in the Earth frame = 15 years according to his own clock (using the time dilation equation), he'll visually only see the Earth clock showing that 15/3 = 5 years have passed. Then if he "slows down" relative to Earth (there is no non-relative notion of 'slowing down' in relativity), and comes to rest relative to Earth at a distance of 0.8c*25 = 20 light-years away, from then on he'll see the Earth clock ticking at the same rate as his own since he's at rest relative to it, but visually it'll always be 10 years behind his own, just like it was when he first came to rest relative to Earth and saw his clock reading 15 years and the Earth clock reading 5 (so if he stays at that position for another 40 years, then when his own clock shows 55 years have passed since his original departure, he'll see the Earth clock reading only 45 years).
+PK+ wrote:Do you guys see where I'm getting confused? If inertial reference frames are all we can use for SR I don't think it properly explains the time dilation. I mean if you had to travel ten light-years to deliver a message, and you were moving so close to the speed of light it only seemed like five light-years to you, it doesn't mean you traveled five light-years. The people on the new planet will say that the radio broadcast of you leaving earth arrived just moments ago, but that both planets had agreed, through a very long series of communications of course, that you would leave ten years ago. Yet you saw earth's clock moving slower than your own the whole time while traveling. So at some point light is going to appear to you to have gone faster than it should, as you're view of earth's clock while you sere traveling catches up to the earth clock you now see at rest.

No, the key to a problem like this (and many others, like the one I hinted you should think about with the train on the straight track) is the relativity of simultaneity, which says different inertial frames disagree about whether two events happened at the "same time", which means they also disagree about whether a pair of clocks at rest relative to one another are "synchronized" or not. If two clocks are at rest relative to each other and a distance d apart in their own inertial rest frame, and they are synchronized in that frame, then in a different inertial frame where the two clocks are both moving at speed v along a straight line, at any given moment in this new frame the rear clock's time is ahead of the front clock's time by an amount vd/c^2.

So if this other planet is at rest relative to the Earth, and in their mutual rest frame their clocks are synchronized (and the distance d between them is 10 light-years in this frame), then in the inertial rest frame of a traveler moving relative to them at 0.99999c, they are out-of-sync by 9.9999 years. Thus if the Earth clock shows a reading of 0 years when this traveler is leaving it, in the traveler's frame the other planet's clock already reads 9.9999 years "simultaneously" with the event of the traveler leaving Earth. So there is nothing inconsistent from the traveler's point of view about the fact that the other planet's clock reads just over 10 years when he reaches that planet, in spite of the fact that the other planet's clock was ticking very slowly in his frame, since it already had a "head start" of just under 10 years.

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### Re: RELATIVITY QUESTIONS! (and other common queries)

Yeah I totally get what you're saying. In my example I was assuming something totally false. The traveller will see the earth almost as he left it because the light is just reaching the new planet. I don't know why I thought he would see earth's time farther ahead. I even said that the radio broadcast had just arrived so of course the light from earth should say the clock was still around 0 just as it almost stopped while he was traveling. So he measured 5 years to make the journey, earth measured 20, and the new planet measured almost none. Although after the traveler calculates time dilation due to his speed, and both planets calculate the doppler shift, they all agree on the distance he traveled, and that none of them measured light to be moving at any speed other than c. My numbers don't add up quite right because I arbitrarily said that he measured 5 years and that light had just arrived at the new planet without mathing it but whatever. Overall I think I viewed the doppler effect as light moving towards the traveller slower. Which is true, but I was being too ambiguous with my thoughts by taking slower to mean traveling slower but in this case it means it takes more time because the distance increases. This kinda makes it seem like light is changing speeds as it strikes the traveller, but the time dilation allows the light to strike the traveller at the same speed that it left the earth. And earth sees the light striking the traveller at the right speed because of doppler shift. So basically I was still trying to view a photon with a rest frame because it seems like everything should have one, but the whole point is that it can't. Now I just need to understand why the pieces wouldn't click and maybe I'll become a faster learner. I think it's because I'm having to unlearn the fact that everything's speed is relative to something else. Light is the exception to that rule and it makes things seem odd, but the fact that it has a constant speed fixes any problems that it having a constant speed creates. I mean really it's not even an exception to that rule, just that relative to everything else light is moving at the same speed. The idea of things moving relative to light though is impossible because it's always light that is moving, never the object. Thanks for taking the time to explain everything to me.

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### Re: RELATIVITY QUESTIONS! (and other common queries)

The classic rubber-sheet for visualising gravitational curvature implies that there is 'more' space in the region of a mass than in the same bounded region without a mass (since the sides of the dip in the sheet will have a larger surface area than a flat region). Is this just me over-thinking the rubber sheet thing, or is the inference correct? Does mass create space?
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### Re: RELATIVITY QUESTIONS! (and other common queries)

Naive response here, but from simply geometrical arguments, I'd say yes. The circumference of a circle gets longer when its radius increases. The area of the sheet is larger when it's distended. That part of the analogy doesn't go away when you add dimensions and remove the higher dimensional space that is embedded into.

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### Re: RELATIVITY QUESTIONS! (and other common queries)

tomandlu wrote:The classic rubber-sheet for visualising gravitational curvature implies that there is 'more' space in the region of a mass than in the same bounded region without a mass (since the sides of the dip in the sheet will have a larger surface area than a flat region). Is this just me over-thinking the rubber sheet thing, or is the inference correct? Does mass create space?
The basic inference is correct, but the rubber sheet potential well analogy wouldn't give you the right numbers for how much space is involved.
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### Re: RELATIVITY QUESTIONS! (and other common queries)

gmalivuk wrote:The basic inference is correct, but the rubber sheet potential well analogy wouldn't give you the right numbers for how much space is involved.

Thanks. Is there any practical result from this? I think this is a stupid question, but I'm assuming that if you increased the mass of a sphere without changing its shape, you wouldn't suddenly have more real estate? (If for no other reason than such a change would affect your measuring tape as well)
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### Re: RELATIVITY QUESTIONS! (and other common queries)

My understanding is that it increases the radial space without increasing circumference, so no, you wouldn't get any more surface area out of a more massive sphere.
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### Re: RELATIVITY QUESTIONS! (and other common queries)

In another thread, I seem to remember someone saying that gravitational waves are produced by changing quadrupole moments but I'm having a hard time gelling this with the fact that orbiting bodies emit gravitational radiation.

A body in an elliptical orbit can be decomposed into two oscillating dipoles π/2 out of phase with a constant mass at the centre. For two bodies orbiting their barycentre, each body's motion can be decomposed like this.

Because the two body's orbits must be in antiphase (to maintain the right centre of mass), I'm having a hard time seeing where any quadrupole comes from.
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### Re: RELATIVITY QUESTIONS! (and other common queries)

If I'm holding a dumbbell or baton whose (massive) ends are also the ends of a powerful magnet, and you're standing some distance away with a magnetic compass and an accelerometer, what happens when I spin the dumbbell?

Assuming your instruments are in the plane of the dumbbell's rotation, then your compass will execute a complete rotation with each rotation of the dumbbell. The "north" end of your compass points first toward the dumbbell, then away from it. The magnetic field has a dipole component. Your accelerometer shows that the gravitational field coming from the dumbbell does NOT rotate - the g vector always points toward the dumbbell, never away; the gravitational field does not have a dipole component.

However, the gravitational field you measure from the dumbbell isn't constant either. For instance, when the dumbbell is pointed directly at you, the weight on the end nearest you is generating a gravitational field g1 = m/(R-r)^2, where R is the distance from you to the center of mass and r half the length of the dumbbell. The far mass has a field g2 = m/(R+r)^2. The sum of these two fields is actually slightly greater than 2m/R^2. When the dumbbell is perpendicular to you, the distance from you to each mass is slightly greater than R, and a small portion of the two fields cancel out as each end of the dumbbell is trying to pull you in a slightly different direction, for a net field that's less than 2m/R^2.

So the total gravitational field you measure IS varying sinusoidally as the dumbbell rotates, but it's a second order effect rather than first order: a quadropole moment. And of course change in gravitational field = gravitational wave.
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### Re: RELATIVITY QUESTIONS! (and other common queries)

I think I see.

The only examples of quadrupoles I'd actually seen worked through explicitly were 'square' quadrupoles whilst this is a 'linear' quadrupole (not sure if there's a standard terminology I should be using) so I was having trouble reconciling the two pictures because I'd forgotten that that was only a subset of archetypical quadrupoles.
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### Re: RELATIVITY QUESTIONS! (and other common queries)

I've always been confused by gravity waves. When an electron moves, there are two kinds of waves possible:
• The "information wave" as the new location of the charge spreads (which I guess is a "real" wave if there's a nearby dielectric to re-orient), but this does no work
• Occasionally, a photon, which does work

Are there gravity waves analogous to both? I have these contradictory understandings: that a body in freefall does no work, and that orbiting bodies gradually radiate energy away via gravity waves. I are confuzed.
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### Re: RELATIVITY QUESTIONS! (and other common queries)

We only call the kind that carries energy away a gravitational wave. And even then, gravitational waves are just the linear perturbation of a metric. GR is full of awesome nonlinear things.
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### Re: RELATIVITY QUESTIONS! (and other common queries)

doogly wrote:We only call the kind that carries energy away a gravitational wave. And even then, gravitational waves are just the linear perturbation of a metric. GR is full of awesome nonlinear things.

Thanks for the explanation! So there's nothing particle-like about the energy-carrying one? (Gravitons are the virtual ones IIRC, or are they?)

Now I'm curious about said "awesome nonlinear things"!
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### Re: RELATIVITY QUESTIONS! (and other common queries)

Nonlinear effects in GR? Event horizons are a favorite, for sure.

Nothing in GR is particle like though, it's a classical theory and it's all fields / geometry. If you do a perturbative quantization (which may or may not converge, so ehhhhhhh) and get an effective field theory for gravity, you call the quantized bits gravitons. But we can't quantize the full theory of gravity.
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