Quick calculation check please

[maline]

there is no meaning to the question of whether their rest lengths can "change" if they are moving relative to each other. The "length" of each ruler is defined by how many atoms long it is; there is no meaning to the statement "yes, Team B's ruler is the same number of atoms long as Team A's, but it has a different length because it's in a different rest frame"

Peter, why are you bringing in the geometric viewpoint when the OP is still struggling to get the IRF viewpoint straight? Certainly, in team A's IRF, team B's rulers are contracted and shorter. I know that isn't an objectively meaningful measurement (because no one can actually measure it) but it is part of relativity and it's what the OP needs to know right now.

 

[maline]

Wouldn't both team A observers and team B observers agree on the distance in meters between the team A observers?

No, that's what distance being relative means! Read again what I sent before. If you like you can assume the rulers are meter sticks measured out by timing light, or that they're ten- foot poles; it doesn't make any difference.

So yes, in your words, there will not be a disagreement about the amount of rulers laid out on the floor between the Team A observers, because if they're on the floor they're at rest in frame A. But there will be disagreement about the number of rulers on the belt that are between team A members, because each end of each ruler passes each team member at some moment, and the question is at a given moment how many already passed each person, but you get different answers depending on which events you consider simultaneous.

 

[name123]

No, this is the part that doesn't work. If you bring them to rest relative to each other and there is no difference, then there is no meaning to the statement that "they have different lengths while in different rest frames" apart from the ordinary length contraction effects of relative motion. In order to define "length" in a way that allows comparison between different rest frames, you have to define it in some way that can be constructed in different rest frames. Light travel time is one such way. Another way is the one I mentioned before, to define a "meter", for example, by the number of atoms of a particular type that equate to a meter of length if you line them up side by side.

But if, for example, Team A and Team B each have rulers that are $10^{10}$ atoms long, say, and both rulers line up with each other when they are at rest relative to each other, then there is no meaning to the question of whether their rest lengths can "change" if they are moving relative to each other. The "length" of each ruler is defined by how many atoms long it is; there is no meaning to the statement "yes, Team B's ruler is the same number of atoms long as Team A's, but it has a different length because it's in a different rest frame". And if you substitute any other direct observable for "number of atoms long", and define "length" to mean that observable, the same argument goes through.

I wasn't thinking of length being the number of atoms but the distance in space. So if in a hypothetical universe the rulers shrank with motion, the lengths would change, such that end to end they didn't span the same distance as when at rest.

 

[name123]

No, that's what distance being relative means! Read again what I sent before. If you like you can assume the rulers are meter sticks measured out by timing light, or that they're ten- foot poles; it doesn't make any difference.

So with the conveyor belt example let's imagine they are at rest with the same amount of 1m rulers between the A-Team observers and the B-Team observers, (say they are spaced 0.1c apart), and then the conveyor belt starts up and gets to a speed of 0.1c. Could you just show me an example of a point where they would disagree about the number of rulers between either the A-team or B-team observers?

 

[maline]

I wasn't thinking of length being the number of atoms but the distance in space.

You are talking about length as a coordinate difference in some frame, which will be different in other frames. Physicists like Peter prefer to talk about length as an absolute number, the proper length, which is equal to the coordinate length in a frame where the object is at rest.

So with the conveyor belt example let's imagine they are at rest with the same amount of 1m rulers between the A-Team observers and the B-Team observers, (say they are spaced 0.1c apart), and then the conveyor belt starts up and gets to a speed of 0.1c. Could you just show me an example of a point where they would disagree about the number of rulers between either the A-team or B-team observers?

Once the belt is moving, team A will say there are 0.1c*γ=30,130,275.7 B rulers between each team A member, and team B will say 0.1c/γ=29,828,972.94 B rulers, because the team A guys are contracted. As for A rulers between B members, it's the same thing in reverse: A says 29,828,972.94 and B says 30,130,275.7 (you seem to like big numbers so I'm going along with you).
Just remember that these disagreements are not about the distance between the same two spacetime events, because someone is moving and everyone is trying to talk about "some point in time", which in the other frame is not simultaneous.

 

[name123]

You are talking about length as a coordinate difference in some frame, which will be different in other frames. Physicists like Peter prefer to talk about length as an absolute number, the proper length, which is equal to the coordinate length in a frame where the object is at rest.

I'm talking about length from any frame of reference in the sense of there being a barn, and there being a ruler the span of the barn including the barn walls, but if the ruler under motion then fits in the barn, i.e. it spans less space, then regardless of whether given the rest frame it is in, and the clocks in that rest frame, it is considered to be the same amount of metres, or the whether the number of atoms is the same, it has shortened because it now fits in the barn, and therefore spans less space.

Once the belt is moving, team A will say there are 0.1c*γ=30,130,275.7 B rulers between each team A member, and team B will say 0.1c/γ=29,828,972.94 B rulers, because the team A guys are contracted. As for A rulers between B members, it's the same thing in reverse: A says 29,828,972.94 and B says 30,130,275.7 (you seem to like big numbers so I'm going along with you).
Just remember that these disagreements are not about the distance between the same two spacetime events, because someone is moving and everyone is trying to talk about "some point in time", which in the other frame is not simultaneous.

I understood that the B team member is saying that after 1.0050s the A team member that it passed is at t'=0 passed another B team member at x' = 30,130,275.7 whereas the A team members are saying that it happened at x = 29,828.972.94 at t = 1 where both agree that x = x' = 0 where the B-Team member at x' = 0 passed that A team member. But I thought the B team member would be saying that that that A team member passed the next B team member at t' = 1.0050 whereas the A team was thinking it happened at t = 1. The B team members wouldn't be thinking that there is an A team member passing at x = 0 at that time, the next A-Team member to pass at x = 0 would be at t' = 1 I would have thought. Instead I thought they would going by their clocks think it had already passed and was now at presumably 29,828.972.94 * .005 = -151,029.90195091 and so the distance between the two A team members is still 29,828.972.94 in B-Team 1m rulers. Though presumably that would make 30,130,275.7 B team rulers between the B team members. I'm not sure how you got to the amount of A team rulers between the B-team members from the B-team's perspective because I thought that unlike the A team they aren't considering the distance between the A-team observers and the B-team observers to be the same. The A team members though would think that there was 29,828,972.94 1m A-Team rulers between the A team members and 29,828,972.94 1m A-Team rulers between the B team members. The B team would seem to me to be agreeing with one A team measurement but not the other.

So why can't it be correctly stated that both are in agreement that light hasn't traveled the same distance in each frame and that there is a difference in their ruler length: B's being 1/30,130,275.7th of the distance between the B team members, and A's being 1/29,828.972.94th of the B team members, therefore the speed of light isn't invariant?

I'm also not quite clear why before the conveyor belt was started they couldn't have had the A-Team rulers laid out between the B-Team Observers, and when they were up to speed compared the lengths of their B-Team 1m rulers to the A-team rulers in their own rest frame, and conclude that they are a different length, which is especially confusing given that I was told that the rulers would be the same in the same rest frame.

[I think I made a mistake about the time that the B observer at x = 0 thought the second A observer past, I think it might be t' = 1.0050]

 

[maline]

it has shortened because it now fits in the barn, and therefore spans less space.

Nice try, but it won't work. The ruler is moving, so it will crash into the barn wall according to all frames. If you try opening and closing holes in the wall at various times, you're back to the issue of simultaneity.

I'm not sure how you got to the amount of A team rulers between the B-team members from the B-team's perspective because I thought that unlike the A team they aren't considering the distance between the A-team observers and the B-team observers to be the same.

Once again, as long as two frames are in relative motion, they will not agree on any distance anywhere (except if an object is moving at exactly their average speed...). Each one claims that their own rulers are longer and their team members are further apart.

I understood that the B team member is saying that after 1.0050s the A team member that it passed is at passed another B team member at x' = 30,130,275.7 whereas the A team members are saying that it happened at x = 29,828.972.94 where both agree that x = x' = 0 where it passed that A team member. But I thought the B team member would be saying that that was at t' = 1.0050 whereas the A team was thinking it happened at t = 1. The B team members wouldn't be thinking that there is an A team member passing at x = 0 at that time. Instead I thought they would going by their clocks think it had already passed and was now at presumably 29,828.972.94 * .005 = -151,029.90195091 and so the distance between the two A team members is still 29,828.972.94 in B-Team 1m rulers. Though presumably that would make 30,130,275.7 B team rulers between the B team members. I'm not sure how you got to the amount of A team rulers between the B-team members from the B-team's perspective because I thought that unlike the A team they aren't considering the distance between the A-team observers and the B-team observers to be the same. The A team members though would think that there was 29,828,972.94 1m A-Team rulers between the A team members and 29,828,972.94 1m A-Team rulers between the B team members. The B team would seem to me to be agreeing with one A team measurement but not the other.

So why can't it be correctly stated that both are in agreement that light hasn't traveled the same distance in each frame and that there is a difference in their ruler length: B's being 1/30,130,275.7th of the distance between the B team members, and A's being 1/29,828.972.94th of the B team members, therefore the speed of light isn't invariant?

I can't follow this. A couple of suggestions:
0. Be concise.
1. Be more careful with English grammar. It is very important for communication.
2. Use simpler units. I personally imagine these problems using feet and nanoseconds- c is close to one foot per nanosecond. But people will understand better if you use light-seconds for distance.
3. Think about spaceships rather than conveyor belts. If something is attached to the Earth you instinctively start working in the Earth frame.
4. In this example, you can leave out the many "observers" and separate rulers, and just talk about how many markings on A's (one long) ruler correspond to a number of markings on B's ruler.

 

[name123]

Nice try, but it won't work. The ruler is moving, so it will crash into the barn wall according to all frames. If you try opening and closing holes in the wall at various times, you're back to the issue of simultaneity.

Well you can imagine two poles separated in the x direction, and the ruler in motion to have not just an x velocity but also a enough of y velocity to allow it to pass through the two poles if it shrank enough on the x-axis with the x motion.

Once again, as long as two frames are in relative motion, they will not agree on any distance anywhere (except if an object is moving at exactly their average speed...). Each one claims that their own rulers are longer and their team members are further apart.

I can't follow this. A couple of suggestions:
0. Be concise.
1. Be more careful with English grammar. It is very important for communication.
2. Use simpler units. I personally imagine these problems using feet and nanoseconds- c is close to one foot per nanosecond. But people will understand better if you use light-seconds for distance.
3. Think about spaceships rather than conveyor belts. If something is attached to the Earth you instinctively start working in the Earth frame.
4. In this example, you can leave out the many "observers" and separate rulers, and just talk about how many markings on A's (one long) ruler correspond to a number of markings on B's ruler.

I find conveyor belts easier if that's ok, though I appreciate you pointing out the pitfall. So before the conveyor belt starts the A Team and B Team members are in what will, once the conveyor belt starts, be only the A Team's frame of reference. The rulers made in that rest frame, the A-Team 1m rulers are laid out between the B-Team members, and they start the conveyor belt, and it goes up to its 0.1c speed. The B-Team members can count that there are only 29,979,245.8 A-Team 1m rulers laid out between each of them, but when they measure the distance between them with 1m rulers made in their rest frame they find that it takes 30,130,275.702 B-Team 1m rulers. So why shouldn't they conclude:
1) The distance measured by a 1m ruler isn't the same in all frames of reference.
Therefore
2) Light seconds aren't a suitable measurement for distance across all frames of reference

3) The speed of light (the distance light travels within a second isn't the same in all frames of reference)
Therefore
4) The speed of light isn't invariant

Is it that (3) doesn't follow because there could be some scenario where each ruler could have been the same distance when in the frame of reference it was made in but wouldn't be the same distance in another frame of reference?

 

[maline]

Good work on the grammar!

Well you can imagine two poles separated in the x direction, and the ruler in motion to have not just an x velocity but also a enough of y velocity to allow it to pass through the two poles if it shrank enough on the x-axis with the x motion.

In that case, one of the frames will claim the ruler is slanted in the y direction.

The rulers made in that rest frame

Again, it doesn't matter where they were made, as long as their proper length is 1m.

when they measure the distance between them with 1m rulers made in their rest frame they find that it takes 30,130,275.702 B-Team 1m rulers

No, this number is the number of team A's rulers, laid out alongside the belt, that are between team B members according to the B frame. If team B uses any rulers that are with them on the belt, they get 29,979,245.8.

unless rulers shrink in motion:

Rulers do shrink when moving, if you're talking about their coordinate length.

1) The distance measured by a 1m ruler isn't the same in all rest frames.
Therefore
2) The speed of light (the distance light travels within a second isn't the same in all rest frames)

Same old mistake: you are thinking of "in one second" as an absolute. In frames where the ruler is moving, the light's travel time will be more than 1s if the ruler is moving in the same direction as the light, and less than 1s if the directions are opposite.

 

[PeterDonis]

why are you bringing in the geometric viewpoint

Defining "rest length" as "number of atoms laid side by side" has nothing necessarily to do with the geometric viewpoint (meaning spacetime as a 4-dimensional manifold). You can just as easily analyze it using the original Einstein formulation of SR. The point I'm trying to make is that the "rest length" of an object is not some magical property it has independent of all measurements. It has to be defined in terms of some measurement that is made on the object in its own rest frame.

in team A's IRF, team B's rulers are contracted and shorter

Certainly, but the length of Team B's rulers in Team A's IRF is not a rest length. The OP appears to be confused about what "rest length" means, so I'm trying to address that separately from the question of length contraction.

that isn't an objectively meaningful measurement (because no one can actually measure it)

Sure they can. Team A can measure the length contracted length of Team B's rulers in Team A's IRF (and vice versa). It's not a simple as measuring the rest length of an object, but it can be done.

 

[name123]

In that case, one of the frames will claim the ruler is slanted in the y direction.

Supposing the ruler was spherical.

I had written:

"when they measure the distance between them with 1m rulers made in their rest frame they find that it takes 30,130,275.702 B-Team 1m rulers"

and you replied:

No, this number is the number of team A's rulers, laid out alongside the belt, that are between team B members according to the B frame. If team B uses any rulers that are with them on the belt, they get 29,979,245.8.

So the A-Team rulers are laid out on the belt in between the B-Team members. There are 29,979,245.8. Now imagine at t'=0 and A-Team member passes a B-Team member at x = x' = 0, and goes onto pass another B-Team member. How far away from x'=0 does that event happen according the B-Team member at x'=0, in other words, how many B-Team 1m rulers are the B-Team suggesting it would it take to span the gap to the next B-Team member involved in that event the gap that it takes 29,979,245.8 A-Team 1m rulers to span?

 

[PeterDonis]

I wasn't thinking of length being the number of atoms but the distance in space.

And the point I am making is that there is no such thing as "distance in space" independent of any measurement of distance. "Distance in space" is not a magical property that objects have independently of measurements. You have to define "distance in space" (or what I've been calling the "rest length" of an object) in terms of some observable: number of atoms lined up, time it takes light to travel from one end to the other, etc. There is no such thing as a separate "distance in space" that you can compare all these observables to to see whether they're the same. The best you can do is compare one observable with another--for example, you can verify that an object which is a certain number of atoms long always has the same light travel time from one end to the other, when measured in its own rest frame.

if in a hypothetical universe the rulers shrank with motion, the lengths would change, such that end to end they didn't span the same distance as when at rest.

If you're talking about ordinary relativistic length contraction, then this isn't hypothetical, it's real. But if you're talking about some other way that rulers could "change length" with motion, without any change taking place in their rest length, there's no such thing; the concept makes no sense. That is what I have been trying to tell you. If the rest length of a ruler stays the same--meaning, if the observable you are using to define "rest length" stays the same--then the only kind of "length change" that can happen to the ruler based on its motion is ordinary relativistic length contraction.

 

[name123]

And the point I am making is that there is no such thing as "distance in space" independent of any measurement of distance. "Distance in space" is not a magical property that objects have independently of measurements. You have to define "distance in space" (or what I've been calling the "rest length" of an object) in terms of some observable: number of atoms lined up, time it takes light to travel from one end to the other, etc. There is no such thing as a separate "distance in space" that you can compare all these observables to to see whether they're the same. The best you can do is compare one observable with another--for example, you can verify that an object which is a certain number of atoms long always has the same light travel time from one end to the other, when measured in its own rest frame.

The idea that there could be two poles in space, and that there is a spherical ruler with a diameter larger than the gap between the poles in space. But when it speeds up and is given a y momentum as well, it shrinks and passes through the poles. Were you thinking that if it had the same amount of molecules, or it was measured to be a certain amount of metres in diameter in a certain rest frame, that it was inconceivable that there could be another meaning such as spanning a greater distance than the poles when at rest with the poles, but spanning a lesser distance than the poles when in motion. How would you have described the change in diameter of the sphere in motion in that scenario?

 

[PeterDonis]

The idea that there could be two poles in space, and that there is a spherical ruler with a diameter larger than the gap between the poles in space. But when it speeds up and is given a y momentum as well, it shrinks and passes through the poles.

This is ordinary relativistic length contraction. The diameter of the sphere is some fixed number of atoms--say $10^{10}$ atoms. This is what defines its "rest length", because if we take a ruler that is $10^{10}$ atoms long, and bring it to rest relative to the sphere, it will exactly fit into the diameter of the sphere.

Similarly, in the frame in which the two poles are at rest, there will be some fixed number of atoms between the poles--say $5 \times 10^9$. So we can take a ruler that is $5 \times 10^9$ atoms long, bring it to rest relative to the poles, and it will exactly fit between the two poles.

Now we have the sphere moving in the $x$ direction relative to the poles (and the poles are laid along the $x$ direction too). If the sphere's speed is fast enough (faster than 87% of the speed of light, since that's the speed for which the relativistic length contraction factor is 2), it will be length contracted in the $x$ direction in the frame of the poles, so it can fit between them if given a small push in the $y$ direction. But the numbers of atoms don't change; the sphere contains $10^{10}$ atoms in its diameter, and there are $5 \times 10^9$ atoms between the poles. Length contraction has made the $10^{10}$ atoms in the sphere, which are moving in the $x$ direction, fit into the same space, in the $x$ direction, as $5 \times 10^9$ atoms between the poles that are at rest.

 

[name123]

This is ordinary relativistic length contraction. The diameter of the sphere is some fixed number of atoms--say $10^{10}$ atoms. This is what defines its "rest length", because if we take a ruler that is $10^{10}$ atoms long, and bring it to rest relative to the sphere, it will exactly fit into the diameter of the sphere.

Similarly, in the frame in which the two poles are at rest, there will be some fixed number of atoms between the poles--say $5 \times 10^9$. So we can take a ruler that is $5 \times 10^9$ atoms long, bring it to rest relative to the poles, and it will exactly fit between the two poles.

Now we have the sphere moving in the $x$ direction relative to the poles (and the poles are laid along the $x$ direction too). If the sphere's speed is fast enough (faster than 87% of the speed of light, since that's the speed for which the relativistic length contraction factor is 2), it will be length contracted in the $x$ direction in the frame of the poles, so it can fit between them if given a small push in the $y$ direction. But the numbers of atoms don't change; the sphere contains $10^{10}$ atoms in its diameter, and there are $5 \times 10^9$ atoms between the poles. Length contraction has made the $10^{10}$ atoms in the sphere, which are moving in the $x$ direction, fit into the same space, in the $x$ direction, as $5 \times 10^9$ atoms between the poles that are at rest.

I'm not sure why it matters how much the contraction is, as the poles just need to be far apart enough that it is enough. So the conveyor belt scenario could be used I would have thought.
What do you mean the length contracted? You clearly don't mean it changed the number of molecules, so you aren't using the number of molecules to measure the distance, and wouldn't light always be measured to traverse that number of molecules at a set pace if it was invariant or what were you using as distance. So I'm not sure what you do mean.

 

[PeterDonis]

What do you mean the length contracted?

This:

Length contraction has made the $10^{10}$ atoms in the sphere, which are moving in the $x$ direction, fit into the same space, in the $x$ direction, as $5 \times 10^9$ atoms between the poles that are at rest.

The space between the poles fits $5 \times 10^9$ atoms at rest, but twice as many atoms ($10^{10}$) that are moving at 87% of the speed of light. That is an example of relativistic length contraction. When people in SR talk about "length contraction", that is what they are talking about.

 

[name123]

The space between the poles fits $5 \times 10^9$ atoms at rest, but twice as many atoms ($10^{10}$) that are moving at 87% of the speed of light. That is an example of relativistic length contraction. When people in SR talk about "length contraction", that is what they are talking about.

So you are measuring distance by atoms at rest, and the distance is the space between the poles? But if the universe was imagined to be one in which the sphere had shrunk, you'd realize that doing it that way wouldn't always give the right answer. An experimenter on the sphere could come to the conclusion that the poles had parted (that the distance between them had got greater), but why should it be that any more than the sphere had shrunk? Also what were you thinking such a claim would imply, that more atoms could be fitted in it in its rest frame? In a computer model of it for example, you could imagine a difference between whether the sphere shrank or the poles parted.

Would it be considered as likely that when a spaceship applied its thrusters the rest of the universe changed size, as it being that the spaceship did? There would be some change in distance somewhere presumably.

 

[PeterDonis]

So you are measuring distance by atoms at rest.

In this example, yes. There are other possible observables you could use.

if the universe was imagined to be one in which the sphere had shrunk

And what observable would tell you that "the sphere had shrunk"? You keep on talking as if there is some way to tell that "shrinking" has occurred even if there is no physical observable that has changed. One more time: that makes no sense. If "shrinking" has occurred in the rest frame of the object, some observable must change. So unless you can tell me what observable changed in the sphere's rest frame, imagining that it has "shrunk" is imagining something that makes no sense. I have repeatedly said this and you have repeatedly ignored it.

An experimenter on the sphere could come to the conclusion that the poles had parted

No, he wouldn't. He would observe the distance between the poles to be length contracted in the $x$ direction. But he would also observe them to be offset in the $y$ direction, so the sphere can slip between them. (Relativity of simultaneity is involved here, and you have to include it to understand what is going on; maline has been trying to describe this to you in his posts.)

why should it be that any more than the sphere had shrunk?

Because the experimenter, at rest on the sphere, measures all the same observables for the sphere. The only observable changes he measures involve the poles, not the sphere.

 

[name123]

And what observable would tell you that "the sphere had shrunk"? You keep on talking as if there is some way to tell that "shrinking" has occurred even if there is no physical observable that has changed. One more time: that makes no sense. If "shrinking" has occurred in the rest frame of the object, some observable must change. So unless you can tell me what observable changed in the sphere's rest frame, imagining that it has "shrunk" is imagining something that makes no sense. I have repeatedly said this and you have repeatedly ignored it.

I'm not saying that shrinking has occurred even if no physical observable has changed, the sphere managed to get through the poles which it couldn't before. Nor am I saying that there is a way to tell if shrinking had occurred, and I'm not saying that anything in an observers rest frame will be observed to shrink relative to anything else in the same reference frame. What I am saying is that if you were to make a computer model and used some arbitrary coordinates for the spatial locations of the objects, you could imagine doing a 3d rendition of the situation (using some 3d modelling tool) and either making the poles wider apart, or making the sphere diameter smaller with motion, or some combination of the two. You could also have some cartoon characters watching the simulation, and reasoning that if they couldn't tell which way the author had done it, it meant that the truth is that it wasn't either way, but I think that reasoning is flawed.

 

[PeterDonis]

What I am saying is that if you were to make a computer model and used some arbitrary coordinates for the spatial locations of the objects, you could imagine doing a 3d rendition of the situation (using some 3d modelling tool) and either making the poles wider apart, or making the sphere diameter smaller with motion, or some combination of the two.

So what? The numbers in the computer don't mean anything by themselves; they only have meaning when they are linked to observable quantities. "Making the poles wider apart" vs. "making the sphere diameter smaller with motion" doesn't change any observable quantities; all it changes is the mathematical relationship between observable quantities and the numbers in the computer. That mathematical relationship has no physical meaning; it's just an artifact of the computer model.

You could also have some cartoon characters watching the simulation, and reasoning that if they couldn't tell which way the author had done it, it meant that the truth is that it wasn't either way, but I think that reasoning is flawed.

Of course it is. The cartoon characters are ignoring the actual observable quantities. If they looked at those, it would be obvious "which way the author had done it", because the two different ways he could have done it correspond to two different mathematical relationships between the numbers in the computer and the observable quantities.

 

[name123]

So what? The numbers in the computer don't mean anything by themselves; they only have meaning when they are linked to observable quantities. "Making the poles wider apart" vs. "making the sphere diameter smaller with motion" doesn't change any observable quantities; all it changes is the mathematical relationship between observable quantities and the numbers in the computer. That mathematical relationship has no physical meaning; it's just an artifact of the computer model.

Why couldn't it have a physical meaning, why couldn't it be that when the spaceship applies its thrusters its size changes and not the size of the universe (cause and effect for starters I would have thought) for some physical reason.

Of course it is. The cartoon characters are ignoring the actual observable quantities. If they looked at those, it would be obvious "which way the author had done it", because the two different ways he could have done it correspond to two different mathematical relationships between the numbers in the computer and the observable quantities.

The cartoon characters could use a whole library of cartoons on the same simulation, with switching camera angles or whatever, in slow motion or however, showing experimenters doing whatever tests from the various reference frames they like. What are you saying the cartoon characters would be ignoring that you wouldn't be?

 

[PeterDonis]

Why couldn't it have a physical meaning

Um, because it's a computer model, not the real thing?

why couldn't it be that when the spaceship applies its thrusters its size changes and not the size of the universe (cause and effect for starters I would have thought) for some physical reason.

Here you're not talking about a computer model, you're talking about a real spaceship. The reason its size doesn't change when its thrusters are turned on is that its size doesn't change: a person in the spaceship making measurements of its size will get the same results as they did before the thrusters were turned on. That's what "its size doesn't change" means. It is simply meaningless to talk about its "size changing" in its own rest frame when all the measurement results in its own rest frame are the same.

The cartoon characters could use a whole library of cartoons on the same simulation, with switching camera angles or whatever, in slow motion or however, showing experimenters doing whatever tests from the various reference frames they like.

And what results do the experimenters get?

What are you saying the cartoon characters would be ignoring that you wouldn't be?

I was saying that, in order for them to not be able to tell whether the moving sphere was shrinking, or the stationary poles were getting farther apart, they would have to be ignoring the measurement results obtained by the experimenters. If they take those results into account, they will see that the experimenters at rest relative to the poles have unchanged measurement results for the distance between the poles, but different measurement results for the diameter of the sphere (compared to when the sphere was at rest relative to them and the poles). And that makes it clear that the sphere shrank; that is what "the sphere shrank but the poles stayed the same" means. If the numbers in the computer representing the sphere stayed the same while the numbers representing the poles changed, that just means the relationship between those numbers and the measurement results had to change. That's fine, because the numbers in the computers have no physical meaning by themselves; the only things with physical meaning are the measurement results.

 

[name123]

Um, because it's a computer model, not the real thing?

You had seemed to be saying that shrinking or expanding had no physical meaning and only had a meaning in the computer model. So I was asking you why shrinking couldn't have a physical meaning, why couldn't it be that when the spaceship applies its thrusters its size changes and not the size of the universe (cause and effect for starters I would have thought) for some physical reason?

Here you're not talking about a computer model, you're talking about a real spaceship. The reason its size doesn't change when its thrusters are turned on is that its size doesn't change: a person in the spaceship making measurements of its size will get the same results as they did before the thrusters were turned on. That's what "its size doesn't change" means. It is simply meaningless to talk about its "size changing" in its own rest frame when all the measurement results in its own rest frame are the same.

So what happens to its size from the perspective of an observer not in its rest frame?

Regarding the cartoon characters you asked:

And what results do the experimenters get?

I was saying that, in order for them to not be able to tell whether the moving sphere was shrinking, or the stationary poles were getting farther apart, they would have to be ignoring the measurement results obtained by the experimenters. If they take those results into account, they will see that the experimenters at rest relative to the poles have unchanged measurement results for the distance between the poles, but different measurement results for the diameter of the sphere (compared to when the sphere was at rest relative to them and the poles). And that makes it clear that the sphere shrank; that is what "the sphere shrank but the poles stayed the same" means. If the numbers in the computer representing the sphere stayed the same while the numbers representing the poles changed, that just means the relationship between those numbers and the measurement results had to change. That's fine, because the numbers in the computers have no physical meaning by themselves; the only things with physical meaning are the measurement results.

Why would they be ignoring them, they can have the experimenter results from any rest frame they like. And imagine they look at all the simulation perspectives that you think they'd need to look at. And they get the results you would expect from the equations. Also in reality it wouldn't be correct to say that only the measurement results were important. For example, consider the "now" that you experience. At any point in the "now" that you experience, it seems reasonable to assume that others are also experiencing the "now", and that there was only one experience they were having associated with your now, so you can conclude that if you were an A team observer passing a B team observer, if you disagree about what the now is for the A team member further down, you can be sure that you're not both right and still keeping the same meaning of now, because it won't be having an experience of two different times simultaneously. Just because no clock can be shown to be in synch with the now, it doesn't mean that there isn't one. Presumably it would have to be one of them. We can understand "now" from the experience. Could a robot have such an experience, could you measure it, could it ever be meaningless? If the answer to the last one is no, as what you know is that you're not experiencing nothing, then any reasoning that leads you contradict reality, i.e. claim it would be meaningless would be flawed (I think).

 

[PeterDonis]

You had seemed to be saying that shrinking or expanding had no physical meaning

No, I said that the numbers in the computer model, by themselves, have no physical meaning. I have repeatedly explained what the physical meaning of "shrinking" is: it means the result you get when you measure the object's length, using the observable that defines "length", changes.

So what happens to its size from the perspective of an observer not in its rest frame?

We've been over this. See post #49. The spaceship acts just like the sphere in that post; if the spaceship is, say, $10^{10}$ atoms long, then those $10^{10}$ atoms, when the spaceship is moving, will fit in the same space as some smaller number of atoms at rest ($5 \times 10^9$ atoms in the example in post #49).

 

[PeterDonis]

Why would they be ignoring them

Why are you asking me? You're the one that made up the computer scenario. I merely pointed out a logical consequence of your original description of the scenario. Your original description said the cartoon characters couldn't tell whether the spaceship had shrunk or the poles had gotten farther apart. I pointed out that, if the characters looked at the experimenters' measurement results, they would be able to tell; so your statement that they couldn't tell implies that they must not be looking at the experimenters' measurement results.

For example, consider the "now" that you experience.

I really think you need to get clear on what "length" means before you start speculating about "now".

At any point in the "now" that you experience, it seems reasonable to assume that others are also experiencing the "now"

I'm not sure what this (and the rest of your post that expands on it) means, but if you are trying to say that "now" must have some absolute meaning, that's not correct. In relativity, "now" has no absolute meaning; it is frame-dependent.

We can understand "now" from the experience.

Relativity is not a theory of consciousness. The word "observer" is used, but an "observer" in the sense of relativity does not have to be conscious. Anything that can record permanent records of experimental results is an "observer" in the sense of relativity. We don't need to bring in consciousness (which is good, since consciousness is off topic for this forum anyway).

 

[name123]

Why are you asking me? You're the one that made up the computer scenario. I merely pointed out a logical consequence of your original description of the scenario. Your original description said the cartoon characters couldn't tell whether the spaceship had shrunk or the poles had gotten farther apart. I pointed out that, if the characters looked at the experimenters' measurement results, they would be able to tell; so your statement that they couldn't tell implies that they must not be looking at the experimenters' measurement results.

And I've said you can imagine that they that they have a video library of what happened. In slow motion, from different rest frame perspectives, different experimenter results. Now from your other post you seem to have acknowledged that in the computer model how it is done whether the sphere shrank or the poles grew further apart can have a meaning, and when I asked about why shrinking and expanding couldn't have a physical meaning (so that the computer simulation one is analogous to an imagined physical one) that when the spaceship applies its thrusters its size changes and not the size of the universe (cause and effect for starters I would have thought) for some physical reason, you seem to be saying that you are ok with shrinking and expanding having a physical meaning, and that you were just saying that the computer model itself wouldn't have that literal physical meaning. You can imagine you are the cartoon character you can look at any of the videos you like, and get any experimenter results you like, and you can conclude if you like that because you can't tell whether the author had it that the sphere shrank or the poles got further apart, that it is safe to conclude that it wasn't done either way, or that it is a meaningless question (even though if the cartoon avatar of the author came on it could understand the question, and give the right answer). As I said, I think there is a flaw in that reasoning. But what would you deduce from the videos as the cartoon character (the experiment results are as expected given the equations)?

I'm not sure what this (and the rest of your post that expands on it) means, but if you are trying to say that "now" must have some absolute meaning, that's not correct. In relativity, "now" has no absolute meaning; it is frame-dependent.

Now does have an absolute meaning for you personally though doesn't it? And would have for the next team A observer down. So can you see how it could true that simultaneously to you experiencing, a team A member was experiencing simultaneously to the team B member opposite to it who was experiencing simultaneously with another team B member experiencing who was simultaneously experiencing with you in the future?

 

[PeterDonis]

And I've said you can imagine that they that they have a video library of what happened. In slow motion, from different rest frame perspectives, different experimenter results.

In which case the cartoon characters can tell, from the experimental results, whether the sphere shrank or the poles got farther apart. Which you said they couldn't do, when you originally described the computer model setup. Make up your mind what you are trying to describe.

you seem to be saying that you are ok with shrinking and expanding having a physical meaning

Sure; it means somebody's experimental results changed.

you were just saying that the computer model itself wouldn't have that literal physical meaning

Not by itself, no, because the computer model is just a computer model. For it to have physical meaning, you have to know the relationship between the numbers in the computer model and experimental results. If the numbers in the computer model change but the experimental results stay the same, then nothing physical has changed.

You can imagine you are the cartoon character you can look at any of the videos you like, and get any experimenter results you like

How? Isn't this computer model supposed to be a model of what actually happens in the actual experiments in the real world? If whatever is labeled "experimental results" in the computer model doesn't match up with any experimental results in the real world, what's the point? And if whatever is labeled "experimental results" in the computer does have to match up with experimental results in the real world, then the cartoon characters cannot just "get any experimenter results" that they like. They can only get the actual experimental results that happen in the actual world. Otherwise the computer model is broken and needs to be fixed.

You seem to think you can make a computer model, label some numbers in it "experimental results", have those numbers be different from actual experimental results in the real world, and still conclude something about the real world from the computer model. That does not seem like a fruitful strategy to me.

what would you deduce from the videos as the cartoon character (the experiment results are as expected given the equations)?

If the cartoon characters can only get the experimental results that are obtained in the real world, they they can tell whether the sphere shrank or the poles got further apart. They just look at the appropriate experimental results. I've been over this repeatedly; I'm not going to go through the details again.

 

[PeterDonis]

Now does have an absolute meaning for you personally though doesn't it?

If by "now" you mean "what is happening to me at a given reading on my clock", then yes, of course. But I don't see what that has to do with the rest of what you said.

 

[name123]

In which case the cartoon characters can tell, from the experimental results, whether the sphere shrank or the poles got farther apart. Which you said they couldn't do, when you originally described the computer model setup. Make up your mind what you are trying to describe.

Well you know the scenario, and they can have videos from the pole's rest frame, the sphere's rest frame whatever. So imagine you are the cartoon character. You can imagine the experiment, point out what the result would be in which ever frame you might choose to look at a video from. So what would the results tell you about whether the author shrank the sphere, or made the poles wider or did something else? In other words explain how the videos will tell them which way it happened.

 

[PeterDonis]

what would the results tell you about whether the author shrank the sphere, or made the poles wider or did something else?

Look at whichever results changed when the sphere is moving relative to the poles, compared to when the sphere is at rest relative to the poles. I've already explained this. And I've already pointed you again at that explanation. I'm not going to keep repeating myself.

 

[name123]

Look at whichever results changed when the sphere is moving relative to the poles, compared to when the sphere is at rest relative to the poles. I've already explained this. And I've already pointed you again at that explanation. I'm not going to keep repeating myself.

You may have think you've explained it but I can't remember reading an explanation. As far as I have read, you'd be saying that from the perspective of the poles the sphere contracted and the poles didn't change size. From the perspective of the sphere it looks as though the distance between the poles expands. So there would be some experimental results that I'd assume imply something has changed the distance it spans. But I also understand you to be stating that if you go around asking in any given frame of reference nothing has changed distance and had seemed to conclude that it therefore was meaningless to ask whether that something was now spanning a larger or smaller distance. But seemed to accept that it could have a meaning in the computer model, and that analogous to that it might be possible to imagine a physical reality in which there were physical reasons why it was the spaceship getting smaller, and not the universe getting bigger. I haven't heard you state how any of this would enable the cartoon characters to tell if the computer program running had shrunk the sphere or expanded the distance between the poles, or whether you would conclude neither, or both, or that the question was meaningless. So could you please just explain clearly how you could tell if you were the cartoon character in a video library of with whatever videos of the event you think you'd need. So what videos you'd need and what conclusion you thought you could draw from them would be useful, because I don't see how you can do it. (The author could have made any rest frame absolute rest, and you could't tell which. The equations allow any frame of reference to be considered absolute rest).

 

[PeterDonis]

As far as I have read, you'd be saying that from the perspective of the poles the sphere contracted and the poles didn't change size.

More precisely: from the perspective of the poles, the sphere, which is $10^{10}$ atoms long (note that that number is an invariant, it's the same in all frames), can fit between the poles, which are separated by only $5 \times 10^9$ atoms, when the sphere is moving relative to the poles at 87% of the speed of light.

From the perspective of the sphere it looks as though the distance between the poles expands.

No, it doesn't. I talked about this in a previous post, and maline was trying to explain it to you too. From the perspective of the sphere, the distance between the poles in the $x$ direction contracts. Length contraction is symmetric: the sphere looks shorter in the frame of the poles, and the pole separation looks shorter in the frame of the spheres.

However, from the perspective of the sphere, the poles also move in the $y$ direction (just as, from the perspective of the poles, the sphere moves in the $y$ direction in order to slip between the poles), and they start moving in that direction at different times. (This is where relativity of simultaneity comes into it.) One pole moves before the other, so the sphere can slip in between the poles even though the distance between the poles in the $x$ direction is shortened.

In terms of the "length in atoms" that I have been using as the definition of length, in the sphere's frame, there are $5 \times 10^9$ atoms between the poles in the $x$ direction, but they are moving at 87% of the speed of light in the $x$ direction, so they fit in the $x$ direction alongside only $2.5 \times 10^9$ atoms of the sphere's diameter--i.e., 1/4 of that diameter. The motion of the poles in the $y$ direction is what let's the sphere slip between them.

 

[PeterDonis]

I also understand you to be stating that if you go around asking in any given frame of reference nothing has changed distance.

That's not quite what I said. What I said is that the length of each object in its own rest frame doesn't change. That's because the number of atoms that make up its length doesn't change. The sphere's length is $10^{10}$ atoms, and the pole separation is $5 \times 10^9$ atoms, and those numbers never change, and are the same in all frames. And since the number of atoms is the same, the rest length is the same--any measurement of length that is done at rest relative to the object will always get the same answer. The length contraction only comes in when there is relative motion between the object and whatever is measuring its length.

could you please just explain clearly how you could tell if you were the cartoon character

In each video, count the number of atoms separating the two poles, and the number of atoms in the sphere along its diameter. They are always the same. That indicates that none of the rest lengths (lengths measured by a device at rest relative to the object) change. So any change in length of objects that are moving (the sphere appearing shorter in the frame of the poles, or the pole separation appearing shorter in the frame of the sphere) can only be due to the relative motion; it can't be due to any "intrinsic" change in the objects, since that would have shown up as a change in the number of atoms making up the length of the object.

 

[name123]

In each video, count the number of atoms separating the two poles, and the number of atoms in the sphere along its diameter. They are always the same. That indicates that none of the rest lengths (lengths measured by a device at rest relative to the object) change. So any change in length of objects that are moving (the sphere appearing shorter in the frame of the poles, or the pole separation appearing shorter in the frame of the sphere) can only be due to the relative motion; it can't be due to any "intrinsic" change in the objects, since that would have shown up as a change in the number of atoms making up the length of the object.

Why couldn't it be a greater density, rather than a greater amount? From the poles frame of reference the atom density is greater in sphere and so it can claim that the sphere has undergone length contraction as you defined it. So there is a claim there that the sphere has shrunk, and from the sphere's perspective less atoms fit between the poles, and presumably this is the same for the change of distance in y between the two poles if there had of been one to start with (it would have got smaller). So they both note that a change in span has occurred. So they're pretty sure something has changed span but neither of them can notice anything changing in their rest frame, so you think it might be ok to conclude that the change occurred in neither (you mention that they won't detect any change in the rest frame), or both, or one maybe, I'm not clear, but you seem to be stating that you thought it was logical to assume that neither could have been the the rest frame in the program, even though you knew the equations allowed any frame of reference to be considered the rest frame?

 

[PeterDonis]

Why couldn't it be a greater density, rather than a greater amount?

In other words, why couldn't the distance between the atoms that are lined up change? We can verify that that doesn't change too, by measurements. In addition to counting the atoms, we also use strain gauges to measure the inter-atomic forces, and verify that they don't change either--all of the strain gauges mounted on the sphere read the same when it is moving at 87% of the speed of light relative to the poles, as when it is at rest relative to the poles. (Or think up any other measure of density you like; the measurement, if made by apparatus at rest relative to the sphere, will be the same regardless of the sphere's speed relative to the poles.)

To cut things short: think up any measurement you like that can be made on the sphere. As long as it is made by measuring devices at rest relative to the sphere, it will give the same results regardless of the sphere's speed relative to the poles. That is why the length contraction of the sphere, as measured from the perspective of the poles, cannot be due to any intrinsic change in the sphere.

there is a claim there that the sphere has shrunk, and from the sphere's perspective less atoms fit between the poles

Just to be clear, these are two different claims. The claim that "the sphere is shrunk" is from the perspective of the poles: the moving sphere, with $10^{10}$ atoms lined up, can fit between the two poles at rest, with only $5 \times 10^9$ atoms between them.

The claim that "from the sphere's perspective less atoms fit between the poles" is, as it says right there, from the sphere's perspective, not the poles' perspective. In the $x$ direction, the two poles take up only $2.5 \times 10^9$ atoms along the sphere, even though there are $5 \times 10^9$ atoms between the poles.

presumably this is the same for the change of distance in y between the two poles

No. The length contraction is only in the $x$ direction. The relative motion in the $y$ direction between the sphere and the poles is too slow to have any significant length contraction effect.

they both note that a change in span has occurred.

They each measure the other to be length contracted in the $x$ direction. But these are two different measurements.

they're pretty sure something has changed span in neither of them can notice anything changing in their rest frame.

This sentence is a bit garbled, but I assume you mean "they're pretty sure something has changed even though neither of them can notice anything changing in their rest frame".

As you state it, this is false; each of them, in their own rest frame, measures the other to be length contracted, whereas if they were both at rest relative to each other they would not. So their relative motion does cause an observable change. The point is simply that there is no observable change in measurements that each one makes in their own rest frame of themselves--no measurement of the sphere in the sphere's rest frame changes, and no measurement of the poles in the poles' rest frame changes. But that doesn't mean there is no observable change anywhere.