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Sep
10
awarded  Teacher
Sep
10
answered If gravitation causes constant acceleration why moon does not fall into earth?
Sep
9
comment Should I abandon my thought experiment about time?
@brightmagus - " the light coming from the clock must travel a longer distance to reach my eye as it moves away. This would make time appear to slow down? If, on the other hand, the clock is moving towards me, the distance the light must travel to reach my eye becomes shorter and shorter, thus time would appear to speed up?" The OP seemed to be concentrating on the distance being the cause, not the relative velocity. But we'll never know unless the OP comes back to comment.
Sep
9
comment Should I abandon my thought experiment about time?
@brightmagus - According to your own example, the clock ticks are observed at 2s, 4s, 6s, etc. So the time interval between each observed tick is a constant 2 seconds, no matter how far away the clock moves. Everyone agrees that the clock appears to be ticking slower than 1 tick per second. What I was saying is that it doesn't slow down more and more as the distance increases - the time between ticks is constant when the velocity is constant.
Sep
9
comment Should I abandon my thought experiment about time?
@brightmagus - Assuming 1 tick per second (in clock's reference frame), between each click the clock moves v * 1 second further away than where it was at the last click. So, the time difference between the two clicks is (1 second + v/c), which is constant.
Sep
9
comment Should I abandon my thought experiment about time?
Your intuition is about the doppler shifting of the clock ticks is incorrect. I believe that you think the perceived interval between ticks will increase as the clock moves further away, but it won't. The interval will increase as the velocity increases, but once the final velocity is reached, the interval will remain constant.
Aug
13
awarded  Critic
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?