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Most examples of HS assume infinite measurements, which is what you are talking about. But this extremely changes the statistics of states, and has nothing to do with a real quantum-experiment-discription (which needs a discrete topology). Otherwise tell me, how shall I ever measure an action of PI*h, without infinite measurements. With continouus space this would be possible, but in our world (and it's corresponding HS) its not. what do you mean with "open balls"? p.s: thanks for your reply, it made me think

Hi! Studiing pysics somehow makes me understand what you want to ask. And to give an answer to your question: The space is defined over a property it has at each point: The scalar product. Now, in physics, Hilbertspace is representing the possible states of a physical system. The actual state is represented by a coordinate in hilbertspace, and the probability of measuring this state is the scalar product between this coordinate in hilbertspace and the same coordinate in a dual-hilbertspace (which is almost exactly the same space). So Hilbertspace just indicates the posibillities of a system. SOmetimes the axes of Hilbertspace are continously (like the angle of a pendulum would make a cont. axis in HS) and sometimes the axis can be discrete (like the energyvalues of the hydrogen atom) building an axis of HS. Between the points of a discrete axis NO Measurement is possible. (because one hydrogen atom will never pop up in energystate 1.5. only in state 1 or in state 2) For such discrete axis your question is relevant. Answer: No, between every two neighbouring "objects" (="coordinates") in a discrete Hilbertspace no measurement can be made inbetween. this all is just in case that you are making a single measurement on a discrete system. as soon as you talk of mean values, and do a lot of measurements, also values between the discrete values can be resulting. Energystate of a hydrogen cloud can be 1.5, if one half is state1 and the others are state2... As you see, Hilberspace really is just a mathematical tool, to categorize your system. though it has it's well defined role in physics, it remains a tool, not a space that is somehow existing in our world... hope that helped

So this is just in case, you send a second photon while the first still is on it's way... so trying to measure a rotation with more photons just leads from "rotation uncertainty" to "photon uncertainty" as shown above... still the uncertainty on rotation builds a whole set of energystates all leading to the same measurement. anybody heard about this before?

exactly, same result on measurement with or without revolution. thats the point. if pointlike quantized photons are used for the signal, you are somehow restricted to just use one photon at a time (cycle). an uncertainty would appear, if a second photon is used, before the first one is absorbed, the observer couldn't destinct the correlation of emitted and absorbed signals definitely. case1=(e1-a1)+(e2-a2) or case2(e1-a2)+(e2-a1) are two different equally possible/probable cases leading to four different "distance-measurement"-results...

An accellerating frame means an "already made" measurement, to submit a frame (coordinate system). But I'm talking about the local process of building a frame. where local means at the place of the observer For example, you wont find a difference if the observer makes (or doesn't make) a whole revolution, while the signal (h) emitts, reflects at the starship, and get absorbed by the observer again. or two revolutions, or three... he will always get the photon from the same angle, at the same time, hence can't differ...and will build the same coordinatespace, to react on. so the rotation of the observer has different phenomena as they rotation of a frame... isn't it?

"independence of clocks and rods from their past" is the fact that it doens't matter how the clocks and rods came to their place. imagine a rectangular field of clocks covering a big area in space. so we know how fast time is running at the place of each clock (and relatively faster/slower in respect to other clocks). Independence means, it doesn't matter how the clocks came there. So we may synchronize the clocks on one place, and slowly move them to their points. slowly enough, to ignore relativistic effects of their movement. the same for the rods...

Hi! I'm studying physics for quite some time, and some time ago a thought popped up in my head....: In classical distance measurement (Einstein, 1905) a lightsignal is emitted, and the time delay "T" is measured, it takes to reflect at a distance "X". Einstein said the observer has orientation with the starfield surrounding him. I'd like to ignore this assumption. So let's say it's dark and cloudy within a cosmic nebular. And an observer flying there wants to measure the distance to the (dark) spaceship next to him. He send a lightsignal, and gets it back, after T. All fine. But what if he recieves it from a different angle, than he emitted the lightsignal? Is a rotation of the observer the only cause that leads to an open angle between emission and absorption? Remember, that in a moving frame, a double mirror reflecting light between the mirrors, also an angle (>0) appears... So can the observer be certain, that a simple Rotation of the observer took place? (I'm talking about pointlike (quantum acting) lightsignals. nothing continouus... so the observer can't just differnetiate the signals...) any suggestions? I know that's actually not a yes/no question, but did you ever hear of such thoughts? Are there papers on that subject ("relativity without starfield"), to learn more in that subject?