Galileo showed that there was no absolute notion of position, but Einsteinian relativity agrees, yes.student34 said:
No. Position and length are well defined. Different frames measure different aspects of a 4d object but both call it length. It's closely analogous to slicing a sausage perpendicular to its length and seeing a circular cross-section and somebody else slicing it diagonally and seeing an elliptical cross section. The sausage is not in a superposition of circular and elliptical - the different people are just making different measurements on it.student34 said:
I am stealing this analogy for future classes.Ibix said:
But wouldn't one of the measurements be of different parts of the sausage than the other?Ibix said:
Yes, because we can’t slice a sausage twice at the same place. That just shows us that the analogy is not exact which isn’t surprising because all analogies are, by definition, not the exact real thing.student34 said:
Yes. Likewise, two length measurements made using different frames' simultaneity conventions are not made at the same time. Each frame will describe the other frame measurement as having a duration, and its own as being instantaneous. So they measure different sections of the 4d object.student34 said:
That is the point. Different measurements of length similarly measure different parts of the 4D object.student34 said:
The same here :-).Orodruin said:I am stealing this analogy for future classes.
Say a measure is at rest in an IFR. The two ends draw two world lines in spacetime. Space distance between the lines so to say space distance between the ends depends on in which IFR the observer is. Observers in different IFRs observe the same lines with different space distance. He or she in the original IFR observes the longest distance.student34 said:
Ok, so for Bob standing next to a meter stick, the particles on the ends of the meter stick are a meter stick apart. For Alice traveling fast, parallel to the meter stick, the meter stick is, say, half the size, and thus the particles are 50 cm from each other.anuttarasammyak said:
They aren't. The frames don't agree on simultaneity so their measurements of where at least one end of the meter stick is aren't taken at the same time, and the meter stick is moving in at least one frame. So according to each frame at least one end of the rod isn't in the same place when measurements are made by the other frame.student34 said:
If you are in a train, looking at your cellphone. To you, your cellphone is stationary. It's not moving and you can operate it easily. To domeone on the platform, your cellphone is moving at 150 km per hour, say.student34 said:
SR as well. We are running out of ways of saying that the two measurements are of different things.student34 said:
Okay, I hope you don't mind if I try to really nail this down here with the following 2 questions. Is the meter stick truly 50 cm for Alice? Is the meter stick truly 100 cm for Bob?Ibix said:
Let's say that the meter stick is on the x coordinate for Bob's frame of reference. Will the meter stick be on the x coordinate for Alice's frame of reference?Nugatory said:
Yes. They are measuring the spatial extent of different 3d slices through a 4d object.student34 said:
Do you mean "on the x axis"?student34 said:
YesIbix said:
Then yes, the rod can lie completely in the ##xt## and ##x't'## plane.student34 said:
So the particles exist in the objective universe as being 50 cm apart and 100cm apart. Is that correct?Ibix said:
50cm along one axis and 100cm along a different axis, yes. That was the point of the sausage analogy - the edges of the sausage are different distances apart if you look along different directions. Similarly, the distance between the particles depends if you measure along Alice's x-axis or Bob's x' axis.student34 said:
Instead of tossing around words like “truly” (what would it mean to say the rod is “not truly”?)we should state the objective facts.student34 said:
This is what happens when you unify space and time into spacetime. It's the spacetime interval between events that is invariant; and not both the space interval and the time interval.student34 said:
Okay thanks a lot. This next part will really answer my question about whether or not there is a superposition of position.Ibix said:
Is the meter stick at rest on the sidewalk that Bob is standing on? Or is it at rest strapped to the rocket that Alice is riding on?student34 said:
No there is not a superposition. Please read that sentence repeatedly until it sinks in. We have all told you this and the posters at scienceforums.net have told you this. I get that you don't understand what is going on, but desperately hoping that it's actually something every subject expert is telling you it's not is not going to help you.student34 said:
The meter stick is at rest on the ground along the x axis. And one end of it is at Bob's feet.jbriggs444 said:
The particles are at rest at each end of the meter stick. The meter stick is lying on the ground with one end of the meter stick at Bob's feet. There is only one meter stick, and it is parallel to the motion of Alice flying by at Bob's feet (this is hard to visualize because Alice is practically touching the ground as she travels parallel to the meter stick which is also on the ground.)Ibix said:
Thanks a lot for this. Why is the meter stick longer in Frame B? Is Frame A traveling fast?jbriggs444 said:
But can't we talk about what the distance between the two particles is in Alice's frame of reference?Ibix said:
Sure, but she needs a meter rule too. Both will see the other's meter rule contracted and therefore cannot agree that the front end of the two meter rules will be at the same place at the same time as the back ends are at the same place. Thus they must measure different distances between the particles.student34 said:
But I am only interested in where the particle is at the meter stick in front of Bob. This will help me understand how there is no superposition of that particle. It is exactly this scenario that is causing me to think that that particle must be in two different locations in space.Ibix said:
It is (edit: at least in some frames), just not at the same time. Thats what jbriggs444's diagram is showing you. Do you understand it? It's really the easiest way to resolve all relativistic weirdness.student34 said:
Yeah, I think that diagram will help me. Is one of the frames in motion?Ibix said:
Yes. In order to get two different simultaneity conventions, the frames need to be in relative motion.student34 said:
Then why do you care what Alice measures? You have already said that both particles are at rest relative to Bob, one at each end of the meter stick. That is a perfectly consistent scenario and there is no "superposition" whatever: each particle has a well-defined unique position relative to Bob and his meter stick.student34 said:
In the example given in the diagram, what is happening with the frames? Why is the meter stick longer in Frame B?jbriggs444 said:
Why would you think that? Each particle is at one end of Bob's meter stick. And that is just as true for Alice as it is for Bob. The particles are moving relative to Alice and Alice's meter stick will measure a different distance between them, but Alice's meter stick will still measure each particle to be co-located with one end of Bob's meter stick. In Alice's frame each particle just moves in sync with its end of Bob's meter stick, instead of being at rest at its end of Bob's meter stick as it is in Bob's frame. The fact of each particle being co-located with one end of Bob's meter stick is an invariant, and is true in all frames.student34 said:
Because, for Alice, the particle seems to be in a different location than for Bob. When Alice is at x with Bob, the particle is only 50 cm from Alice. But as others have responded, we are also using Alice's clock, which is at a different time than Bob's.PeterDonis said:
"When Alice is at x with Bob" is different for Alice than it is for Bob. Alice and Bob have different notions of simultaneity because of their relative motion.student34 said:
It's not just that it's "at a different time". It is running at a different rate. To Alice, Bob's clock is running slow; to Bob, Alice's clock is running slow.student34 said:
And they are never 100cm apart other than in Bob's frame. And in any other frame, they would be a different distance apart, and would be moving at a different speed. And the time dilation and simultaneity would also be different.student34 said:
It would probably be better to reverse the frame nomenclature here. The natural way to interpret this diagram is that what you are calling frame A is Bob's frame (since that's the frame in which both worldlines, representing the two ends of Bob's meter stick, are at rest) and what you are calling frame B is Alice's frame.jbriggs444 said:
Per my post #46 just now, as @jbriggs444 has drawn the diagram, "Frame A" is really what you are calling Bob's frame, and the "Frame A snapshot" is Bob's meter stick at an instant of Bob's time. "Frame B" in the diagram is really what you are calling Alice's frame, and the "Frame B snapshot" is Bob's meter stick at an instant of Alice's time. Because the geometry of the diagram is actually hyperbolic rather than Euclidean, the length of the "Frame B snapshot" is actually shorter than the length of the "Frame A snapshot", corresponding to the fact that Alice sees Bob's meter stick length contracted. And the fact that the "Frame B snapshot" is at an angle to the "Frame A snapshot" corresponds to relativity of simultaneity.student34 said:
If Alice observes one end of Bob's metre stick at her feet at time ##t = 0## and the other end at her feet at a time a fraction of a second later. She might claim that the metre stick has zero length. Why is that wrong?student34 said:
jbriggs444 said:
I am sorry everyone; this is embarrassing. I just realized that this diagram is a description of my thought experiment. I understand now what is going on. Thanks a lot for this diagram.jbriggs444 said:
I don't think this is correct. Only one of them would have the slower clock. It depends which one did the acceleration from when they were at rest with one another. In this case Alice did the acceleration, and so only Alice's clock is slower.PeterDonis said:
