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Jun
13
awarded  Scholar
Jun
13
accepted Uncertainty principle - momentum so precise that uncertainty of position is outside light-cone?
Jun
13
comment Uncertainty principle - momentum so precise that uncertainty of position is outside light-cone?
Thanks! That explains my "locality" confusion - the amount of time necessary to make the measurement works out to be exactly the amount of time necessary for information to travel from the furthest reaches of the Δx. What about when spacetime itself is smaller than Δx (for example, accurately measuring momentum of a photon in the early moments after the Big Bang). Is it like @doetoe suggests, that the boundary conditions would place a limit on how accurately the momentum can be measured, so that Δx does not exceed the size of the universe?
Jun
13
comment Uncertainty principle - momentum so precise that uncertainty of position is outside light-cone?
Interesting. Thanks!
Jun
13
comment Uncertainty principle - momentum so precise that uncertainty of position is outside light-cone?
Do you have a citation handy for the first equation? A quick google search didn't yield any information on the concept of "characteristic size" with respect to the uncertainty principle.
Jun
13
awarded  Nice Question
Jun
13
awarded  Commentator
Jun
13
comment Uncertainty principle - momentum so precise that uncertainty of position is outside light-cone?
"Finally in this case there is no contradiction: no information has to travel" - can you explain what you mean by that? Let's say I just made a very precise measurement of a particle's momentum, such that it has a non-zero probability of being very far away at the time of that measurement. I did gain information (about the momentum). If the particle was indeed very far away, how is it that no information had to travel?
Jun
13
comment Uncertainty principle - momentum so precise that uncertainty of position is outside light-cone?
How is the uncertainty principle different for a closed universe?
Jun
13
comment Uncertainty principle - momentum so precise that uncertainty of position is outside light-cone?
Unless the time is also uncertain - maybe we're measuring the momentum of a particle one light-year away as it was one year ago?
Jun
13
comment Uncertainty principle - momentum so precise that uncertainty of position is outside light-cone?
"First of all, it is certainly possible to interact with a particle that has a non-zero probability of being measured at arbitrarily large distances". Even though we don't have a quantum theory of relativity, I still think you can't make a claim in quantum mechanics that contradicts a claim in relativity, without admitting that one of them must be wrong. Since information can't travel arbitrarily large distances in a short amount of time, I don't see how you can get information about the momentum of a particle that is a very large distance away.
Jun
13
comment Uncertainty principle - momentum so precise that uncertainty of position is outside light-cone?
I don't believe a universe of finite size is the same as confinement in a box. Consider a one dimensional example. Confinement in a box means that there is a potential to your left and to your right, preventing you from going further in either direction. A finite sized (closed) universe means that your one dimension is a loop. There is no potential confining your space - it's just that space is closed, so if you go far enough, you end up back where you started.
Jun
12
comment Uncertainty principle and multiple observers
Do we know what mechanism would cause the experiment to fail? For example, if the two measuring devices were tested separately and verified to work to a certain precision, what would go wrong and cause the precision to be reduced for each device when they try to measure simultaneously? Is there some inherent property of the particle itself that could resist precise measurement?
Jun
12
awarded  Student
Jun
12
asked Uncertainty principle - momentum so precise that uncertainty of position is outside light-cone?
Mar
18
comment Is the flow of time regular?
People are asking how you define "flow of time". Let me know if you agree with the following reformulation of your question: "Is it possible to observe a location in space-time, wait a couple minutes in your reference frame, then observe the same space-time location?" In other words, you look at the same spatial location a little later, and note that the time coordinate has not changed. I don't think this is possible.
Feb
20
comment Can Flow of time become still?
@Cruncher - But it is only a non-inertial frame while it is accelerating. Once it reaches its "cruising speed", it is now in an inertial frame. At that point, do all observers agree that the spaceship clock is currently ticking slower than the Earth clock? From what JohnRennie just said, it seems like the answer is no.
Feb
20
comment Can Flow of time become still?
Thanks for the clarification. I've never been 100% clear on the twin paradox. The way it was explained to me is that it is not a paradox, because all observers will agree that the spaceship clock is moving slower, since it is the reference frame that accelerated from the Earth reference frame. But I never could accept that explanation, because it seems to imply an absolute rest frame.
Feb
20
comment Can Flow of time become still?
"...it is just running slowly relative to a clock on Earth as observed by the observer on Earth." Does that mean observers from other reference frames might disagree about whether the Earth clock is running slower than the spaceship clock or vice versa?
May
23
comment Why does sound move faster in solids?
Here's a way to think of it. If I shove my open palm towards you, will you feel it more quickly if: a) there is water between us, and a wave ripples towards you and eventually splashes you, or b) if there is a solid rod between us, and it smacks into you?